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In the figure posted below (source: doi.org/10.1021/ie00077a027), the third virial coefficient of water shows some interesting features: it crosses the origin around 590K and exhibits a peak at approximately 670K.
Questions:
Physical Interpretation: What is the physical significance of both the peak and the zero-cros... | Okay, so I need to understand the physical significance of the peak and the zero-crossing in the third virial coefficient (C(T)) of water. Also, how changing the dipole moment or molecular size affects these features. Let me start by recalling what virial coefficients are.
The virial equation of state expands the pres... | ### Physical Interpretation of the Third Virial Coefficient Features
1. **Zero-Crossing Point (~590K):**
The temperature at which the third virial coefficient \( C(T) \) crosses zero signifies a balance between three-body attractive and repulsive interactions. At lower temperatures, three-body attractions (e.g., ... | 25,729 | stackexchange-physics | <think>
Okay, so I need to understand the physical significance of the peak and the zero-crossing in the third virial coefficient (C(T)) of water. Also, how changing the dipole moment or molecular size affects these features. Let me start by recalling what virial coefficients are.
The virial equation of state expands ... | [
{
"from": "human",
"value": "In the figure posted below (source: doi.org/10.1021/ie00077a027), the third virial coefficient of water shows some interesting features: it crosses the origin around 590K and exhibits a peak at approximately 670K.\n\nQuestions:\n\nPhysical Interpretation: What is the physical si... |
For a curved interface between two adjacent poorly conducting materials with different electrical properties, when applying a DC voltage difference between the two materials, as in a capacitor, the free charges will accumulate at the interface. The distribution of the charges is interesting. In general, more charges ac... | Okay, so I need to explain why free charges accumulate more at regions of higher curvature on a curved interface between two poorly conducting materials when a DC voltage is applied. Also, the charge density along the interface has two "cups," which I assume means two peaks or dips. Hmm. Let me start by recalling some ... | The accumulation of free charges at regions of higher curvature on a curved interface between two poorly conducting materials under a DC voltage can be explained through the following key principles of electrostatics and current continuity:
1. **Surface Charge and Boundary Conditions**:
At the interface, the norm... | 33,753 | stackexchange-physics | <think>
Okay, so I need to explain why free charges accumulate more at regions of higher curvature on a curved interface between two poorly conducting materials when a DC voltage is applied. Also, the charge density along the interface has two "cups," which I assume means two peaks or dips. Hmm. Let me start by recalli... | [
{
"from": "human",
"value": "For a curved interface between two adjacent poorly conducting materials with different electrical properties, when applying a DC voltage difference between the two materials, as in a capacitor, the free charges will accumulate at the interface. The distribution of the charges is... |
When an EM wave travels inside a conductor , we find that there is a phase difference between the Electric and magnetic fields within the conductor. The magnetic field lags behind the E field and this lag is roughly equal to 45 degrees within a good conductor (all from Griffiths chp 9.4). What is the cause of this pha... | Okay, so I need to figure out why there's a 45-degree phase difference between the electric and magnetic fields in a conductor when an EM wave travels through it. In a dielectric, they stay in phase, but in a conductor, the magnetic field lags behind the electric field by about 45 degrees. Also, how does this relate to... | The phase difference of approximately 45 degrees between the electric field (E) and magnetic field (B) in a good conductor arises due to the complex nature of the wave number \( k \) inside the conductor. This complexity stems from the interplay between conduction currents (σE, in phase with E) and displacement current... | 21,032 | stackexchange-physics | <think>
Okay, so I need to figure out why there's a 45-degree phase difference between the electric and magnetic fields in a conductor when an EM wave travels through it. In a dielectric, they stay in phase, but in a conductor, the magnetic field lags behind the electric field by about 45 degrees. Also, how does this r... | [
{
"from": "human",
"value": "When an EM wave travels inside a conductor , we find that there is a phase difference between the Electric and magnetic fields within the conductor. The magnetic field lags behind the E field and this lag is roughly equal to 45 degrees within a good conductor (all from Griffith... |
I'm studying fluid mechanics and I have the following doubt: on the book, the author first deduces the differential form of the equation of balance of momentum. First he argues that if the fluid is ideal and is contained in a region $D\subset \mathbb{R}^3$ and if the pressure is $p : D\times \mathbb{R}\to \mathbb{R}$ t... | Okay, so I need to figure out why when deriving the integral form of the momentum balance from the differential form, we use a fixed region, but when starting from basic principles, we consider a moving region that follows the fluid. The user also mentions a possible connection to the Lagrangian and Eulerian viewpoints... | The difference in considering fixed versus moving regions when deriving the integral form of the momentum balance law is indeed connected to the Eulerian and Lagrangian viewpoints in fluid mechanics.
1. **Eulerian Perspective (Fixed Region):**
- When deriving the integral form from the differential equation, we con... | 12,271 | stackexchange-physics | <think>
Okay, so I need to figure out why when deriving the integral form of the momentum balance from the differential form, we use a fixed region, but when starting from basic principles, we consider a moving region that follows the fluid. The user also mentions a possible connection to the Lagrangian and Eulerian vi... | [
{
"from": "human",
"value": "I'm studying fluid mechanics and I have the following doubt: on the book, the author first deduces the differential form of the equation of balance of momentum. First he argues that if the fluid is ideal and is contained in a region $D\\subset \\mathbb{R}^3$ and if the pressure ... |
There are similar questions answered already but the answers disagree. I understand that simultaneity/time is local in GR and that in a given region of space, an event horizon and singularity can form in finite proper time for a local observer. For a distant observer, will the event horizon form in a finite amount of t... | Okay, so I need to figure out whether, from the perspective of a distant observer, an event horizon forms in a finite amount of their proper time. Also, if it doesn't, can an observer move between frames where the horizon has formed and where it hasn't. Let me start by recalling what I know about black hole formation a... | For a distant observer, the event horizon of a collapsing object does **not** form in a finite amount of their proper time. In the idealized framework of general relativity (using Schwarzschild coordinates), the distant observer sees the collapse slow asymptotically as the object approaches the event horizon, with the ... | 19,669 | stackexchange-physics | <think>
Okay, so I need to figure out whether, from the perspective of a distant observer, an event horizon forms in a finite amount of their proper time. Also, if it doesn't, can an observer move between frames where the horizon has formed and where it hasn't. Let me start by recalling what I know about black hole for... | [
{
"from": "human",
"value": "There are similar questions answered already but the answers disagree. I understand that simultaneity/time is local in GR and that in a given region of space, an event horizon and singularity can form in finite proper time for a local observer. For a distant observer, will the e... |
I am trying to change the integral in this equation for the energy shift due to quasiparticle energy renormalization from being over the momentum space, $d\boldsymbol{k}'$ to being over $d\epsilon$.
Equation 1 (for the energy shift):
$$
\epsilon_{\boldsymbol{k}} - \mu = \epsilon_{\boldsymbol{k}}^0 - \mu - \int{\frac{d\... | Okay, so I need to convert the integral in the energy shift equation from momentum space to an integral over energy ε. The original integral is over dk', and they want me to change variables to dε'. The hints are to neglect the momentum dependence of the coupling constant g and replace the phonon frequency with ω_D, wh... | To convert the momentum integral to an energy integral, follow these steps:
1. **Simplify the Coupling Constant and Phonon Frequency**:
- Neglect the momentum dependence of \( g \), so \( |g_{\boldsymbol{k} - \boldsymbol{k}'}|^2 \to g^2 \).
- Replace the phonon frequency \( \omega(\boldsymbol{k} - \boldsymbo... | 1,256 | stackexchange-physics | <think>
Okay, so I need to convert the integral in the energy shift equation from momentum space to an integral over energy ε. The original integral is over dk', and they want me to change variables to dε'. The hints are to neglect the momentum dependence of the coupling constant g and replace the phonon frequency with... | [
{
"from": "human",
"value": "I am trying to change the integral in this equation for the energy shift due to quasiparticle energy renormalization from being over the momentum space, $d\\boldsymbol{k}'$ to being over $d\\epsilon$.\nEquation 1 (for the energy shift):\n$$\n\\epsilon_{\\boldsymbol{k}} - \\mu = ... |
While reading some papers about the nonlinear schrodinger equation (NLS) I noticed that the authors sometimes use (for the linear case)
$$\partial_zE=\frac{i}{2k_0}\nabla^2E$$
and sometimes
$$\partial_tE=\frac{i}{2k_0}\nabla^2E$$
I assume it is possible to rewrite the first equation as
$$\partial_zE=\frac{\partial t}{... | Okay, let's try to figure this out. So, the user is asking about converting between two different forms of the linear Schrödinger equation, one with a spatial derivative ∂z and the other with a time derivative ∂t. They noticed that in some papers, the equation is written using a spatial derivative, and in others, a tim... | To address the conversion between the spatial (∂ₐE) and temporal (∂ₜE) forms of the linear Schrödinger equation, we use the relationship between propagation distance **z** and time **t** via the group velocity **v_g = c/n**, where **n** is the refractive index. Here's the breakdown:
1. **Chain Rule Application**:
-... | 14,707 | stackexchange-physics | <think>
Okay, let's try to figure this out. So, the user is asking about converting between two different forms of the linear Schrödinger equation, one with a spatial derivative ∂z and the other with a time derivative ∂t. They noticed that in some papers, the equation is written using a spatial derivative, and in other... | [
{
"from": "human",
"value": "While reading some papers about the nonlinear schrodinger equation (NLS) I noticed that the authors sometimes use (for the linear case)\n$$\\partial_zE=\\frac{i}{2k_0}\\nabla^2E$$\nand sometimes \n$$\\partial_tE=\\frac{i}{2k_0}\\nabla^2E$$\nI assume it is possible to rewrite the... |
I'm looking for a good reference that defines the Bondi mass aspect and his relations to Bondi and ADM mass.
Googling a bit I've not founded any satisfactory exposition of the subject.
A short explanation of the concept is welcome.
| Okay, so the user is asking about the Bondi mass aspect and its relation to Bondi mass and ADM mass. They mentioned they couldn't find a satisfactory explanation through Google, so they want a good reference and a short explanation. Let me start by recalling what I know about these concepts.
First, I remember that in ... | The **Bondi mass aspect** and its relation to Bondi and ADM masses are key concepts in general relativity for describing the mass-energy of isolated systems in asymptotically flat spacetimes. Here's a concise explanation and recommended references:
---
### **Short Explanation**
1. **Bondi Mass Aspect**
- A funct... | 15,691 | stackexchange-physics | <think>
Okay, so the user is asking about the Bondi mass aspect and its relation to Bondi mass and ADM mass. They mentioned they couldn't find a satisfactory explanation through Google, so they want a good reference and a short explanation. Let me start by recalling what I know about these concepts.
First, I remember ... | [
{
"from": "human",
"value": "I'm looking for a good reference that defines the Bondi mass aspect and his relations to Bondi and ADM mass.\nGoogling a bit I've not founded any satisfactory exposition of the subject.\nA short explanation of the concept is welcome. \n"
},
{
"from": "gpt",
"value": ... |
I can understand why the $x=ct$ line is needed as follows:
If $c \Delta t \geq \Delta x$ then the event can be causally related to your current position, so the event could not appear in reverse order for any observer; therefore that event must be in the absolute future.
Similarly, if $c \Delta t < \Delta x$ then the e... | Okay, so I'm trying to understand why the line x = -ct is important in special relativity alongside the x = ct line. I know that x = ct represents the maximum speed at which information can travel, which is the speed of light. Events inside the future light cone (where cΔt ≥ Δx) can be causally related to the current e... | The $x = -ct$ line plays a crucial role in delineating the boundaries of the **absolute future** in special relativity, complementing the $x = ct$ line. Here's why both lines are necessary:
1. **Causal Structure and Light Cones**:
- The **future light cone** (for $t > 0$) is defined by the lines $x = ct$ and $x =... | 23,652 | stackexchange-physics | <think>
Okay, so I'm trying to understand why the line x = -ct is important in special relativity alongside the x = ct line. I know that x = ct represents the maximum speed at which information can travel, which is the speed of light. Events inside the future light cone (where cΔt ≥ Δx) can be causally related to the c... | [
{
"from": "human",
"value": "I can understand why the $x=ct$ line is needed as follows:\nIf $c \\Delta t \\geq \\Delta x$ then the event can be causally related to your current position, so the event could not appear in reverse order for any observer; therefore that event must be in the absolute future.\nSi... |
There are many questions about gyroscopes, and this one: (Confusion about what happens when the rotating axis of a gyroscope is rotated) remind me of an odd behaviour of a toy gyroscope that I had.
It is made in a way that besides the rotor, also the case spins when placed on the ground. So, I think it is not same sit... | Okay, so I'm trying to figure out why my toy gyroscope sometimes switches from precessing to standing vertically before it falls. Let me start by recalling what I know about gyroscopes. Normally, when a gyroscope is spinning and you tilt it, it starts precessing around the vertical axis. The precession is due to the to... | The unusual behavior of your toy gyroscope transitioning from precession to a vertical spin can be explained by the interplay between two rotating components (rotor and case), energy dissipation, and angular momentum dynamics. Here's a structured breakdown:
### Key Factors:
1. **Dual Rotating Components**:
- The **... | 15,810 | stackexchange-physics | <think>
Okay, so I'm trying to figure out why my toy gyroscope sometimes switches from precessing to standing vertically before it falls. Let me start by recalling what I know about gyroscopes. Normally, when a gyroscope is spinning and you tilt it, it starts precessing around the vertical axis. The precession is due t... | [
{
"from": "human",
"value": "There are many questions about gyroscopes, and this one: (Confusion about what happens when the rotating axis of a gyroscope is rotated) remind me of an odd behaviour of a toy gyroscope that I had. \nIt is made in a way that besides the rotor, also the case spins when placed on ... |
I read somewhere that
If the expansion rate of the universe were larger or the density of the universe were less , no galaxies would form.
If the expansion rate of the universe were smaller or the density of the universe were more, the universe would rapidly collapse.
Is it true that if the expansion rate or the dens... | Okay, so I need to figure out if it's true that slight changes in the expansion rate or density of the universe would prevent it from existing as we see it. The user mentioned that if the expansion rate were higher or density lower, no galaxies would form. Conversely, if expansion were slower or density higher, the uni... | The statement you encountered aligns with current cosmological understanding, highlighting the delicate balance required for the universe to evolve as observed. Here's a breakdown of the key concepts:
1. **Expansion Rate and Density Balance**:
- The universe's evolution is governed by the interplay between its expa... | 29,041 | stackexchange-physics | <think>
Okay, so I need to figure out if it's true that slight changes in the expansion rate or density of the universe would prevent it from existing as we see it. The user mentioned that if the expansion rate were higher or density lower, no galaxies would form. Conversely, if expansion were slower or density higher,... | [
{
"from": "human",
"value": "I read somewhere that\n\nIf the expansion rate of the universe were larger or the density of the universe were less , no galaxies would form.\nIf the expansion rate of the universe were smaller or the density of the universe were more, the universe would rapidly collapse.\n\nIs ... |
In many portions of physics (like Maxwell's velocity distribution law) we assume statements like-
Number of molecules having velocity between $c$ to $c+dc$ is $dn$.
But number of molecules $n$ is always an integer and thus $dn$ i.e. differential coefficient of $n$ can't be determined due to infinite discontinuity be... | Alright, so I came across this question about why we use dn, like a differential element for the number of molecules in physics, even though the number of molecules has to be an integer. Hmm, that's an interesting point. Let me think this through step by step.
First, the user mentions Maxwell's velocity distribution l... | The use of differential quantities like \( dn \) in physics, such as in Maxwell's velocity distribution, is justified through several key considerations rooted in the nature of large systems and probabilistic reasoning:
1. **Large Number Approximation**:
In macroscopic systems (e.g., gases with ~10²³ molecules), ... | 10,581 | stackexchange-physics | <think>
Alright, so I came across this question about why we use dn, like a differential element for the number of molecules in physics, even though the number of molecules has to be an integer. Hmm, that's an interesting point. Let me think this through step by step.
First, the user mentions Maxwell's velocity distri... | [
{
"from": "human",
"value": "In many portions of physics (like Maxwell's velocity distribution law) we assume statements like- \n\nNumber of molecules having velocity between $c$ to $c+dc$ is $dn$.\n\nBut number of molecules $n$ is always an integer and thus $dn$ i.e. differential coefficient of $n$ can't b... |
I have been given the following:
$$y''(x)+\omega^2y(x)=s(x),$$
$$s(x)= \delta(x)-\delta\left(x-\frac{1}{2}\right)$$ for $-\frac{1}{4}<x<\frac{3}{4}$.
(Periodically repeating for $x$ outside this interval.)
Question:
Find the Fourier series solution y(x) of the above differential equation.
I understand how to comput... | Okay, so I need to find the Fourier series solution y(x) for the differential equation y''(x) + ω²y(x) = s(x), where s(x) is a periodic function made up of delta functions at x=0 and x=1/2, repeating every 1 unit interval. The domain given is -1/4 < x < 3/4, and it's periodically extended outside this interval.
First... | To find the Fourier series solution \( y(x) \) of the differential equation \( y''(x) + \omega^2 y(x) = s(x) \), where \( s(x) = \delta(x) - \delta(x - \frac{1}{2}) \) for \( -\frac{1}{4} < x < \frac{3}{4} \) and periodically repeating, we follow these steps:
1. **Fourier Series of \( s(x) \)**:
- The function \( s... | 35,679 | stackexchange-physics | <think>
Okay, so I need to find the Fourier series solution y(x) for the differential equation y''(x) + ω²y(x) = s(x), where s(x) is a periodic function made up of delta functions at x=0 and x=1/2, repeating every 1 unit interval. The domain given is -1/4 < x < 3/4, and it's periodically extended outside this interval.... | [
{
"from": "human",
"value": "I have been given the following:\n$$y''(x)+\\omega^2y(x)=s(x),$$\n$$s(x)= \\delta(x)-\\delta\\left(x-\\frac{1}{2}\\right)$$ for $-\\frac{1}{4}<x<\\frac{3}{4}$. \n (Periodically repeating for $x$ outside this interval.)\nQuestion:\nFind the Fourier series solution y(x) of the a... |
Hello fellow physics experts,
In reference to a recent electrodynamics course a question about electric potential difference was asked. This question states why the dangling parachutist in de picture below is not electrocuted by the power lines. A possible explanation could be that the parachutist is the unintented 'co... | Okay, so there's this question about why a parachutist dangling from power lines isn't getting electrocuted. The initial thought is that maybe the two cables they're touching have a potential difference of 0V, so there's no electric field, hence no current. Hmm. Let me break this down.
First, power lines are usually h... | The parachutist isn't electrocuted because they are bridging two points **at the same electric potential** (e.g., two conductors of the same phase in a power line). Here's the breakdown:
1. **No Voltage Difference, No Current**:
- Power lines often operate at very high voltages (thousands of volts), but the criti... | 21,589 | stackexchange-physics | <think>
Okay, so there's this question about why a parachutist dangling from power lines isn't getting electrocuted. The initial thought is that maybe the two cables they're touching have a potential difference of 0V, so there's no electric field, hence no current. Hmm. Let me break this down.
First, power lines are u... | [
{
"from": "human",
"value": "Hello fellow physics experts,\nIn reference to a recent electrodynamics course a question about electric potential difference was asked. This question states why the dangling parachutist in de picture below is not electrocuted by the power lines. A possible explanation could be ... |
Einstein's theory of general relativity put forward the concept of the space manifold theory. According to this ,all masses create depressions in the manifold which causes matter to attract each other. But when anti matter(not yet discovered)
and matter are thought to repel each other.Then, will anti matter form hills?... | Okay, let me try to wrap my head around this question about antimatter and general relativity. So, the user is asking if antimatter would create "hills" in the spacetime manifold instead of the "depressions" that regular matter creates, given that matter and antimatter might repel each other. Hmm.
First, I need to rec... | In Einstein's theory of general relativity (GR), the curvature of spacetime is determined by the stress-energy tensor, which depends on mass, energy, and momentum. Here's a breakdown of how antimatter fits into this framework:
### 1. **General Relativity and Antimatter: The Standard View**
- **Matter and Spacetime ... | 31,296 | stackexchange-physics | <think>
Okay, let me try to wrap my head around this question about antimatter and general relativity. So, the user is asking if antimatter would create "hills" in the spacetime manifold instead of the "depressions" that regular matter creates, given that matter and antimatter might repel each other. Hmm.
First, I nee... | [
{
"from": "human",
"value": "Einstein's theory of general relativity put forward the concept of the space manifold theory. According to this ,all masses create depressions in the manifold which causes matter to attract each other. But when anti matter(not yet discovered)\nand matter are thought to repel eac... |
My textbook states that:
TISE is a generic eigenvalue problem and the superposition state is not a solution to the TISE.
Another part of textbook (in context of infinite square well):
The most general solutions will be linear combination of these energy eigenstates with their associated time-dependence:
We have de... | Okay, so I'm trying to understand why the textbook says that the Time-Independent Schrödinger Equation (TISE) is a generic eigenvalue problem and that superposition states aren't solutions to the TISE. Then, in another part, it talks about the most general solutions being linear combinations of these energy eigenstates... | The Time-Independent Schrödinger Equation (TISE), \( \hat{H} u_n(x) = E_n u_n(x) \), is an eigenvalue problem where the solutions \( u_n(x) \) are energy eigenstates with definite energies \( E_n \). These eigenstates are stationary and do not evolve in time except for a phase factor.
**Why superpositions are not sol... | 14,345 | stackexchange-physics | <think>
Okay, so I'm trying to understand why the textbook says that the Time-Independent Schrödinger Equation (TISE) is a generic eigenvalue problem and that superposition states aren't solutions to the TISE. Then, in another part, it talks about the most general solutions being linear combinations of these energy eig... | [
{
"from": "human",
"value": "My textbook states that:\n\nTISE is a generic eigenvalue problem and the superposition state is not a solution to the TISE.\n\nAnother part of textbook (in context of infinite square well):\n\nThe most general solutions will be linear combination of these energy eigenstates with... |
I'm trying to see why we get this energy config here
As far as I understood, up/down or down/up contributes +, and same direction, ie up up or down down negative. So it should be all negative on the first picture. However there is a "random" plus to the right hand side. Can someone tell me why that is?
Thanks in advan... | Okay, let me try to figure this out. So the user is confused about why there's a plus sign on the right-hand side of the energy configuration in their problem. They thought that when spins are opposite (up/down or down/up), the interaction energy is positive, and when they're the same (up/up or down/down), it's negativ... | The unexpected positive energy contribution on the right-hand side of your configuration likely arises from a pair of neighboring spins that are anti-aligned (one up, one down). Here's the breakdown:
1. **Energy Rules**: In the Ising model (ferromagnetic case), neighboring spins contribute:
- **Negative energy (−J)... | 3,036 | stackexchange-physics | <think>
Okay, let me try to figure this out. So the user is confused about why there's a plus sign on the right-hand side of the energy configuration in their problem. They thought that when spins are opposite (up/down or down/up), the interaction energy is positive, and when they're the same (up/up or down/down), it's... | [
{
"from": "human",
"value": "I'm trying to see why we get this energy config here \nAs far as I understood, up/down or down/up contributes +, and same direction, ie up up or down down negative. So it should be all negative on the first picture. However there is a \"random\" plus to the right hand side. Can ... |
Eisberg's 'Fundamentals of Modern Physics' derives the space contraction formula from a mirror experiment in which A reflects a light beam in a direction perpendicular to the motion of B, both observers measure the time and position of the beam's return to the path of motion. He needs this result to derive the LT; it u... | Alright, so the user is asking whether it's possible to derive the Lorentz transformations (LT) without using more than one spatial dimension, right? They mentioned Eisberg's approach with the mirror experiment involving two spatial dimensions (perpendicular to the direction of motion) to get the gamma factor via the P... | Yes, it is indeed possible to derive the Lorentz transformations (LT) using only **1+1 dimensions** (one spatial and one temporal dimension) without invoking a second spatial dimension. Here's how:
---
### **Key Steps in the Derivation**:
1. **Linear Transformations**: Assume linear relations between coordinates in t... | 37,606 | stackexchange-physics | <think>
Alright, so the user is asking whether it's possible to derive the Lorentz transformations (LT) without using more than one spatial dimension, right? They mentioned Eisberg's approach with the mirror experiment involving two spatial dimensions (perpendicular to the direction of motion) to get the gamma factor v... | [
{
"from": "human",
"value": "Eisberg's 'Fundamentals of Modern Physics' derives the space contraction formula from a mirror experiment in which A reflects a light beam in a direction perpendicular to the motion of B, both observers measure the time and position of the beam's return to the path of motion. He... |
Has there ever been any high carbon stainless steel made with iridium as one of the alloy components? Is there any research in this direction?
There is a paper from 2016 comparing various iridium structures to more well known/studied structures, with the finding that iridium dinitrogen exhibits the highest bulk modul... | Okay, so the user is asking about whether high carbon stainless steel has ever been made with iridium as an alloy component and if there's any research in that direction. They also mentioned some specific papers from 2016 and 2011 about iridium compounds and want to know if there's more recent work, especially towards ... | The integration of iridium into high-carbon stainless steel alloys remains largely unexplored in both academic research and industrial applications. Here's a synthesis of the current state of knowledge and related research directions:
### 1. **Iridium in Steel Alloys: Feasibility and Challenges**
- **Cost and Scarc... | 17,790 | stackexchange-physics | <think>
Okay, so the user is asking about whether high carbon stainless steel has ever been made with iridium as an alloy component and if there's any research in that direction. They also mentioned some specific papers from 2016 and 2011 about iridium compounds and want to know if there's more recent work, especially ... | [
{
"from": "human",
"value": "\nHas there ever been any high carbon stainless steel made with iridium as one of the alloy components? Is there any research in this direction?\n\nThere is a paper from 2016 comparing various iridium structures to more well known/studied structures, with the finding that iridiu... |
Picture source:
This is the spark in a spark gap transmitter, a transmitter in the early of radio is discovered, or maybe including the Hertz's experiment itself. This is also we may see in a spark plug of our car. The similar thing we see with lightning in nature. The interesting thing for me, and it is my question, ... | Okay, so the user is asking why sparks, like those in a spark gap transmitter or a car's spark plug, don't jump in a straight line and instead take a random, zigzag path. They mentioned ionization of air as a possible factor and want to know more about what's in the air that causes this.
First, I need to recall what I... | The erratic, branching paths of sparks, such as those in a spark gap transmitter, car spark plugs, or lightning, arise due to the interplay of several factors related to air's composition and the stochastic nature of ionization. Here's a breakdown:
### 1. **Non-Uniform Air Composition**
Air is a mixture of gases ... | 6,815 | stackexchange-physics | <think>
Okay, so the user is asking why sparks, like those in a spark gap transmitter or a car's spark plug, don't jump in a straight line and instead take a random, zigzag path. They mentioned ionization of air as a possible factor and want to know more about what's in the air that causes this.
First, I need to recal... | [
{
"from": "human",
"value": "\nPicture source:\nThis is the spark in a spark gap transmitter, a transmitter in the early of radio is discovered, or maybe including the Hertz's experiment itself. This is also we may see in a spark plug of our car. The similar thing we see with lightning in nature. The intere... |
I'm trying to understand how to describe the quantum state after weak measurement using these two toy examples. Hopefully, these simple examples and your answer will help others who want to learn about weak measurement.
Suppose photons are prepared in a superposition of horizontal and vertical polarization: $ \frac{1}... | Alright, let me try to work through these questions step by step. I'm a bit new to weak measurements, so I need to take it slowly.
Starting with the first example: photons in a superposition (1/√2)(|H> + |V>). The weak measurement setup uses Brewster angle glass plates. From what I remember, at Brewster's angle, horiz... | For the first example, the transmitted photons' state is indeed modified due to the partial reflection of the vertical component. However, the correct normalized state is obtained by considering the attenuation of the vertical polarization and renormalizing:
**Transmitted State (First Example):**
The transmitted pho... | 29,900 | stackexchange-physics | <think>
Alright, let me try to work through these questions step by step. I'm a bit new to weak measurements, so I need to take it slowly.
Starting with the first example: photons in a superposition (1/√2)(|H> + |V>). The weak measurement setup uses Brewster angle glass plates. From what I remember, at Brewster's angl... | [
{
"from": "human",
"value": "I'm trying to understand how to describe the quantum state after weak measurement using these two toy examples. Hopefully, these simple examples and your answer will help others who want to learn about weak measurement.\n\nSuppose photons are prepared in a superposition of horiz... |
Let $A$ and $B$ be two subsystems of the system AB which is in a pure or isolated bipartite state and $$|\psi_{AB}\rangle=\sum_{i}\sqrt{p_i}|\psi^{i}_{AB}\rangle$$, then by definition
\begin{equation}
\tag{1}
\rho_{AB}=\sum_{i}p_i|\psi^{i}_{AB}\rangle\langle \psi^i_{AB}|
\label{eqn:Definition}
\end{equation}
Here... | Okay, let me try to figure out where I'm getting confused here. So, the problem is about the density matrix of a composite system AB when it's in a pure state. The user mentions that they have a state |ψ_AB⟩ written as a sum over i of sqrt(p_i) times |ψ_AB^i⟩, where each |ψ_AB^i⟩ is a tensor product of states from A an... | The confusion arises from a misunderstanding of density matrices for pure versus mixed states and the role of orthogonality in the decomposition of states. Here's the step-by-step explanation:
1. **Pure State Density Matrix**: If the composite system AB is in a pure state \( |\psi_{AB}\rangle \), its density matrix is... | 36,259 | stackexchange-physics | <think>
Okay, let me try to figure out where I'm getting confused here. So, the problem is about the density matrix of a composite system AB when it's in a pure state. The user mentions that they have a state |ψ_AB⟩ written as a sum over i of sqrt(p_i) times |ψ_AB^i⟩, where each |ψ_AB^i⟩ is a tensor product of states f... | [
{
"from": "human",
"value": "Let $A$ and $B$ be two subsystems of the system AB which is in a pure or isolated bipartite state and $$|\\psi_{AB}\\rangle=\\sum_{i}\\sqrt{p_i}|\\psi^{i}_{AB}\\rangle$$, then by definition\n\\begin{equation}\n \\tag{1}\n \\rho_{AB}=\\sum_{i}p_i|\\psi^{i}_{AB}\\rangle\\langle ... |
Does the power weakening of an electromagnetic transmission over distance depends on the beam's width?
If I emit an omnidirectional electromagnetic transmission, its power weakens in the ratio of $1/R^2$, if I remember correctly.
My question is if I transmit a very narrow beam (say, 0.001 degrees, and "collect" the who... | Okay, so the user is asking whether the power weakening of an electromagnetic transmission over distance depends on the beam's width. They know that for an omnidirectional source, the power decreases with the inverse square law, which is 1/R². But they're wondering if using a very narrow beam, like 0.001 degrees, and c... | The power weakening (intensity) of an electromagnetic transmission over distance **does depend on the beam's width**, but the relationship is nuanced:
1. **Omnidirectional Source**:
For an isotropic (omnidirectional) emitter, intensity decreases as \( \frac{1}{R^2} \) due to spherical spreading. This is the class... | 37,113 | stackexchange-physics | <think>
Okay, so the user is asking whether the power weakening of an electromagnetic transmission over distance depends on the beam's width. They know that for an omnidirectional source, the power decreases with the inverse square law, which is 1/R². But they're wondering if using a very narrow beam, like 0.001 degree... | [
{
"from": "human",
"value": "Does the power weakening of an electromagnetic transmission over distance depends on the beam's width?\nIf I emit an omnidirectional electromagnetic transmission, its power weakens in the ratio of $1/R^2$, if I remember correctly.\nMy question is if I transmit a very narrow beam... |
I came to watch two videos related to fighter jets, one in which the pilot pours red bull in a glass and another in which pilot pours water from a bottle to cup while doing rolls and while being upside down and not a drop of water got spilt. Here is the link of both the videos: https://www.youtube.com/watch?v=zG9Xsb0YP... | Okay, so I saw these two videos where fighter jet pilots are pouring drinks—Red Bull and water—while doing rolls and flying upside down, and not a single drop spills. That's really cool, but how does that even work? Let me try to figure this out.
First, I know that when planes do maneuvers like rolls or loops, the pil... | The phenomenon observed in the videos where pilots pour liquids without spilling during aerobatic maneuvers can be explained through the physics of **G-forces** and **controlled acceleration**. Here's a breakdown:
### Key Concepts:
1. **G-Forces and Acceleration**:
- When a fighter jet maneuvers, the pilot experien... | 36,820 | stackexchange-physics | <think>
Okay, so I saw these two videos where fighter jet pilots are pouring drinks—Red Bull and water—while doing rolls and flying upside down, and not a single drop spills. That's really cool, but how does that even work? Let me try to figure this out.
First, I know that when planes do maneuvers like rolls or loops,... | [
{
"from": "human",
"value": "I came to watch two videos related to fighter jets, one in which the pilot pours red bull in a glass and another in which pilot pours water from a bottle to cup while doing rolls and while being upside down and not a drop of water got spilt. Here is the link of both the videos: ... |
It is often claimed that POVMs represent the most general measurement statistics possible. But what is the justification for this claim? Textbooks and university courses generally try to build up to the claim starting from the measurement postulate, which can either be from the perspective of measurement of observables... | Okay, so I need to figure out why POVMs are considered the most general type of quantum measurements. The user mentioned some approaches in textbooks, like using unitary interactions and ancilla systems or starting with general measurements, but they aren't convinced these rule out non-POVM statistics. Let me try to un... | The assertion that POVMs (Positive Operator-Valued Measures) represent the most general quantum measurement statistics arises from foundational principles of quantum mechanics and mathematical theorems that constrain all physically realizable measurement processes. Here is a consolidated justification:
### **1. Linear... | 19,653 | stackexchange-physics | <think>
Okay, so I need to figure out why POVMs are considered the most general type of quantum measurements. The user mentioned some approaches in textbooks, like using unitary interactions and ancilla systems or starting with general measurements, but they aren't convinced these rule out non-POVM statistics. Let me t... | [
{
"from": "human",
"value": "It is often claimed that POVMs represent the most general measurement statistics possible. But what is the justification for this claim? Textbooks and university courses generally try to build up to the claim starting from the measurement postulate, which can either be from the ... |
The Romanian physicist Proca formulated his famous Lagrangian to describe a hypothetical massive photon. From it we derive, as equations of motion, the relations that the electric and magnetic fields must obey (the analogous of Maxwell's equations for massive photons). We know that Einstein deduced the Lorentz transfor... | Alright, let me try to work through this problem. So, the user is asking about Proca's theory for a massive photon and how it makes sense given that Einstein's derivation of Lorentz transformations relies on the constancy of the speed of light. Also, they're confused because if the photon has mass, then the speed of li... | The Proca hypothesis, which posits a massive photon, remains consistent with the principles of special relativity and Lorentz invariance. Here's a structured explanation:
### 1. **Lorentz Transformations and the Role of \( c \):**
- Lorentz transformations are derived from the principles of relativity, isotropy, an... | 36,594 | stackexchange-physics | <think>
Alright, let me try to work through this problem. So, the user is asking about Proca's theory for a massive photon and how it makes sense given that Einstein's derivation of Lorentz transformations relies on the constancy of the speed of light. Also, they're confused because if the photon has mass, then the spe... | [
{
"from": "human",
"value": "The Romanian physicist Proca formulated his famous Lagrangian to describe a hypothetical massive photon. From it we derive, as equations of motion, the relations that the electric and magnetic fields must obey (the analogous of Maxwell's equations for massive photons). We know t... |
I know that for standard QCD with quarks, chiral symmetry breaking occurs for around 4 - 5 light/active quarks - i.e. pions, or generally pseudoscalar goldstone bosons, definitely appear in the spectrum for $N_f=1,2,3,4$.
My question is, within $N_f=1,\ldots, 4$, how does the pion decay constant vary with respect to $N... | Okay, so I need to figure out how the pion decay constant, F_π, varies with the number of quark flavors, N_f, in QCD when there are between 1 and 4 light quarks. The user mentioned that chiral symmetry breaking occurs for N_f in this range, leading to Goldstone bosons like pions. But the specific dependence of F_π on N... | The pion decay constant, \( F_\pi \), decreases as the number of light quark flavors \( N_f \) increases from 1 to 4 in QCD. This trend arises because the dynamics of chiral symmetry breaking weaken with higher \( N_f \), influenced by the following key factors:
1. **QCD Coupling Strength**: For larger \( N_f \), the ... | 25,210 | stackexchange-physics | <think>
Okay, so I need to figure out how the pion decay constant, F_π, varies with the number of quark flavors, N_f, in QCD when there are between 1 and 4 light quarks. The user mentioned that chiral symmetry breaking occurs for N_f in this range, leading to Goldstone bosons like pions. But the specific dependence of ... | [
{
"from": "human",
"value": "I know that for standard QCD with quarks, chiral symmetry breaking occurs for around 4 - 5 light/active quarks - i.e. pions, or generally pseudoscalar goldstone bosons, definitely appear in the spectrum for $N_f=1,2,3,4$.\nMy question is, within $N_f=1,\\ldots, 4$, how does the ... |
For the following Lagrangian:
$$\mathcal{L}= \overline \psi \left(i \gamma^{\mu}D_{\mu} - m \right)\psi -\frac{1}{2}\left(F_{\mu\nu}\right)^2,$$
I'm trying to find the Feynman rules. I know that the second derivative of the generating functional gives me the propagators and the third derivative gives me the vertices of... | Okay, so I need to figure out the Feynman rules for the given Lagrangian, which is a combination of a Dirac field and an electromagnetic field. The Lagrangian is:
$$
\mathcal{L}= \overline \psi \left(i \gamma^{\mu}D_{\mu} - m \right)\psi -\frac{1}{2}\left(F_{\mu\nu}\right)^2,
$$
where $D_\mu = \partial_\mu + i e A_\m... | To derive the Feynman rules for the given Lagrangian:
$$\mathcal{L}= \overline \psi \left(i \gamma^{\mu}D_{\mu} - m \right)\psi -\frac{1}{2}\left(F_{\mu\nu}\right)^2,$$
we start by separating the Lagrangian into free and interacting parts. The free parts are the Dirac and Maxwell terms, while the interaction term is ... | 29,308 | stackexchange-physics | <think>
Okay, so I need to figure out the Feynman rules for the given Lagrangian, which is a combination of a Dirac field and an electromagnetic field. The Lagrangian is:
$$
\mathcal{L}= \overline \psi \left(i \gamma^{\mu}D_{\mu} - m \right)\psi -\frac{1}{2}\left(F_{\mu\nu}\right)^2,
$$
where $D_\mu = \partial_\mu + ... | [
{
"from": "human",
"value": "For the following Lagrangian:\n$$\\mathcal{L}= \\overline \\psi \\left(i \\gamma^{\\mu}D_{\\mu} - m \\right)\\psi -\\frac{1}{2}\\left(F_{\\mu\\nu}\\right)^2,$$\nI'm trying to find the Feynman rules. I know that the second derivative of the generating functional gives me the prop... |
Electrons are incredibly small, and the "size" of photons (or the distance away from one required to not interact with it) is also incredibly small. Yet photons still interact with electrons all the time. Are they attracted to each other in some way, does it have to do with the wave of the electron being larger than ... | Okay, so the user is asking about why photons and electrons interact so much despite both being incredibly small. Let me start by recalling what I know about electrons and photons. Electrons are elementary particles with a point-like structure, meaning they don't have a physical size in the traditional sense. Photons a... | The interaction between electrons and photons arises from fundamental principles in quantum electrodynamics (QED), not their physical size. Here's a breakdown of the key factors:
1. **Electromagnetic Interaction**:
Electrons carry electric charge, and photons are the quanta of the electromagnetic field. Their int... | 22,488 | stackexchange-physics | <think>
Okay, so the user is asking about why photons and electrons interact so much despite both being incredibly small. Let me start by recalling what I know about electrons and photons. Electrons are elementary particles with a point-like structure, meaning they don't have a physical size in the traditional sense. P... | [
{
"from": "human",
"value": "Electrons are incredibly small, and the \"size\" of photons (or the distance away from one required to not interact with it) is also incredibly small. Yet photons still interact with electrons all the time. Are they attracted to each other in some way, does it have to do with ... |
I am a complete novice in physics beyond the high school level, so please excuse anything wrong in my question.
So I have recently read that according to General Relativity, the presence of mass in spacetime causes spacetime to become curved and that is how gravity arises.
Does vacuum spacetime have an inherent curvatu... | Okay, so I need to figure out whether spacetime has inherent curvature even in a complete vacuum, right? Let me start by recalling what I know about General Relativity (GR). From what I understand, Einstein's theory says that mass and energy curve spacetime, and this curvature is what we experience as gravity. So, if t... | In General Relativity (GR), spacetime curvature is determined by the distribution of mass and energy through Einstein's field equations:
\[
G_{\mu\nu} + \Lambda g_{\mu\nu} = 8\pi T_{\mu\nu},
\]
where \(G_{\mu\nu}\) (Einstein tensor, encoding curvature), \(\Lambda\) (cosmological constant), and \(T_{\mu\nu}\) (stress... | 21,081 | stackexchange-physics | <think>
Okay, so I need to figure out whether spacetime has inherent curvature even in a complete vacuum, right? Let me start by recalling what I know about General Relativity (GR). From what I understand, Einstein's theory says that mass and energy curve spacetime, and this curvature is what we experience as gravity. ... | [
{
"from": "human",
"value": "I am a complete novice in physics beyond the high school level, so please excuse anything wrong in my question.\nSo I have recently read that according to General Relativity, the presence of mass in spacetime causes spacetime to become curved and that is how gravity arises.\nDoe... |
I saw the following problem in a book:
In S.T.P., a balloon of diameter 1.004m has to be filled with H2 gas.At 27°C,a cylinder with volume 1 m^3 is filled with H2 gas having 2000 kPa pressure.How many balloons can be filled with the gas in the cylinder?
The volume of the gas at S.T.P. in the cylinder comes out to be 17... | Okay, let's see. I need to figure out why the volume of the gas at STP is larger than the cylinder's volume and why we can't take out all the gas. Hmm. So, the problem is about filling balloons with hydrogen gas from a cylinder. The cylinder has a volume of 1 m³, is at 27°C, and the pressure is 2000 kPa. They calculate... | To address your questions:
1. **Why is the gas volume at STP larger than the cylinder's volume?**
The gas in the cylinder is under high pressure (2000 kPa) and at 27°C. When expanding this gas to STP (100 kPa, 0°C), the **same number of moles** occupies a much larger volume due to reduced pressure and temperature... | 17,629 | stackexchange-physics | <think>
Okay, let's see. I need to figure out why the volume of the gas at STP is larger than the cylinder's volume and why we can't take out all the gas. Hmm. So, the problem is about filling balloons with hydrogen gas from a cylinder. The cylinder has a volume of 1 m³, is at 27°C, and the pressure is 2000 kPa. They c... | [
{
"from": "human",
"value": "I saw the following problem in a book:\nIn S.T.P., a balloon of diameter 1.004m has to be filled with H2 gas.At 27°C,a cylinder with volume 1 m^3 is filled with H2 gas having 2000 kPa pressure.How many balloons can be filled with the gas in the cylinder?\nThe volume of the gas a... |
I have a $\text{i2c}$ GPS module I got working yesterday, and here are my co-ordinates.
Latitude: 44.901354999999995
Longitude: -68.97112333333333
What I am having trouble figuring out is that position: what size is it, with 14 significant figures? Is it 1 square foot, or the head of a pin?
Granted, the polling pr... | Okay, so the user has a GPS module that gives coordinates with 14 significant figures. They're wondering how precise that is—like, is it a pinhead size or a square foot? Let me break this down step by step.
First, I need to recall how GPS coordinates work. Latitude ranges from -90 to 90 degrees, and longitude from -18... | With 14 significant figures in GPS coordinates, the theoretical precision is extraordinarily high—on the order of **nanometers** (1.11 nm for latitude, ~0.79 nm for longitude). This level of precision is **far beyond the physical capabilities of any real-world GPS system**, including specialized scientific equipment. C... | 2,781 | stackexchange-physics | <think>
Okay, so the user has a GPS module that gives coordinates with 14 significant figures. They're wondering how precise that is—like, is it a pinhead size or a square foot? Let me break this down step by step.
First, I need to recall how GPS coordinates work. Latitude ranges from -90 to 90 degrees, and longitude ... | [
{
"from": "human",
"value": "I have a $\\text{i2c}$ GPS module I got working yesterday, and here are my co-ordinates.\n\nLatitude: 44.901354999999995 \nLongitude: -68.97112333333333\n\nWhat I am having trouble figuring out is that position: what size is it, with 14 significant figures? Is it 1 square foot,... |
In the book "Combustion Theory" for Forman Williams, appendix A, and also in the book "Combustion Physics" for C.K. Law, chapter 1, the following derivation can be found for the chemical equilibrium criterion:
$$\sum_{i} \mu_i dN_i = 0.$$
The derivation starts by stating out the first law of thermodynamics as:
$$\delta... | Okay, let me try to unpack this. The user is confused about the derivation of the chemical equilibrium criterion from the first and second laws of thermodynamics as presented in Williams and Law's books. The key point of contention is whether the result ∑μ_i dN_i ≤ 0 is general or if it requires constant temperature an... | The derivation presented in Williams and Law is indeed correct and general, though it requires careful interpretation within the framework of thermodynamic potentials and their natural variables. Here's the breakdown:
1. **General Thermodynamic Inequality**:
Combining the first and second laws for any process giv... | 30,045 | stackexchange-physics | <think>
Okay, let me try to unpack this. The user is confused about the derivation of the chemical equilibrium criterion from the first and second laws of thermodynamics as presented in Williams and Law's books. The key point of contention is whether the result ∑μ_i dN_i ≤ 0 is general or if it requires constant temper... | [
{
"from": "human",
"value": "In the book \"Combustion Theory\" for Forman Williams, appendix A, and also in the book \"Combustion Physics\" for C.K. Law, chapter 1, the following derivation can be found for the chemical equilibrium criterion:\n$$\\sum_{i} \\mu_i dN_i = 0.$$\nThe derivation starts by stating... |
While reminiscing of his discovery of the quantum of action Planck writes in his "Scientific Autobiography" [1]:
Thus the nature of entropy as a measure of probability, in the sense indicated by Boltzmann, was established in the domain of radiation, too. This was made especially clear in a proposition, the validity of... | Okay, so I need to figure out what Planck and Laue meant by the entropy of a "coherent pencil of light." Let me start by recalling some basic concepts. Entropy in thermodynamics is a measure of disorder or randomness, and in statistical mechanics, it's related to the number of microstates corresponding to a macrostate,... | Planck and von Laue's discussion of the entropy of "coherent pencils of light" refers to the thermodynamic implications of coherence in radiation, particularly in the context of interference phenomena. Here's a structured breakdown:
### **Key Concepts**
1. **Entropy and Probability**:
Entropy, as formulated by Bo... | 20,937 | stackexchange-physics | <think>
Okay, so I need to figure out what Planck and Laue meant by the entropy of a "coherent pencil of light." Let me start by recalling some basic concepts. Entropy in thermodynamics is a measure of disorder or randomness, and in statistical mechanics, it's related to the number of microstates corresponding to a mac... | [
{
"from": "human",
"value": "While reminiscing of his discovery of the quantum of action Planck writes in his \"Scientific Autobiography\" [1]:\n\nThus the nature of entropy as a measure of probability, in the sense indicated by Boltzmann, was established in the domain of radiation, too. This was made espec... |
Diamagnetic materials repel magnetic fields because freely moving electrons or cooper pairs within the material can form eddy currents in response to a changing magnetic field.
It is natural to wonder “what happens if we pump up the number of electrons available” by say using a van de graff generator to electrically ch... | Okay, let's try to figure out whether charging a diamagnetic metal like copper with a van de Graaff generator would change its diamagnetic properties. So, the user is asking if adding more electrons (by charging the metal) would strengthen the eddy currents (and thus diamagnetism) or maybe fill up orbitals and make it ... | Charging a diamagnetic metal like copper with a net electric charge using a van de Graaff generator would **not significantly alter its diamagnetic properties**. Here's the breakdown:
1. **Negligible Electron Addition**:
The number of electrons added by a van de Graaff generator (microcoulombs to millicoulombs) i... | 16,774 | stackexchange-physics | <think>
Okay, let's try to figure out whether charging a diamagnetic metal like copper with a van de Graaff generator would change its diamagnetic properties. So, the user is asking if adding more electrons (by charging the metal) would strengthen the eddy currents (and thus diamagnetism) or maybe fill up orbitals and ... | [
{
"from": "human",
"value": "Diamagnetic materials repel magnetic fields because freely moving electrons or cooper pairs within the material can form eddy currents in response to a changing magnetic field.\nIt is natural to wonder “what happens if we pump up the number of electrons available” by say using a... |
Holed up at home, I was distracting myself by shining my green laser pointer around. Something particularly interesting happened when I pointed the laser at a reflective black plastic surface. The reflected beam would show first as a dot, but rapidly start to spread out and achieve a sort of halo shape. Waiting longer ... | Okay, let's try to figure out what's going on here. The user is shining a green laser pointer at a reflective black plastic surface, like a fan casing, and observes a reflected beam that starts as a dot but then spreads into a halo and concentric rings. They noticed that leaving the laser on for a while actually alters... | The intriguing phenomenon you observed with your green laser pointer and the black plastic surface can be explained by a combination of thermal effects and optical interactions. Here's a detailed breakdown:
### 1. **Laser Absorption and Localized Heating**
- **Black Plastic Properties**: The black color indicates h... | 37,304 | stackexchange-physics | <think>
Okay, let's try to figure out what's going on here. The user is shining a green laser pointer at a reflective black plastic surface, like a fan casing, and observes a reflected beam that starts as a dot but then spreads into a halo and concentric rings. They noticed that leaving the laser on for a while actuall... | [
{
"from": "human",
"value": "Holed up at home, I was distracting myself by shining my green laser pointer around. Something particularly interesting happened when I pointed the laser at a reflective black plastic surface. The reflected beam would show first as a dot, but rapidly start to spread out and achi... |
My quantum mechanics book has this proof of Ehrenfest theorem: let $A$ be an observable and $\hat{A}$ the operator that represents it. Then we have
$$\frac{d}{dt}\langle \hat{A}\rangle=\frac{i}{\hbar}\langle [\hat{H},\hat{A}]\rangle+\left\langle \frac{\partial \hat{A}}{\partial t}\right\rangle.$$
The proof is:
\begin... | Okay, so I need to figure out how the Ehrenfest theorem proof works, specifically the step where they take the time derivative of the expectation value of an operator A. The user mentioned that when you have a multiplicative operator like the potential, the product rule is straightforward, but they're confused about ho... | To prove the Ehrenfest theorem, we start by considering the time derivative of the expectation value of an observable \( A \), represented by the operator \( \hat{A} \). The expectation value is given by \( \langle \hat{A} \rangle = \langle \Psi | \hat{A} \Psi \rangle \). Taking the time derivative, we apply the produc... | 9,931 | stackexchange-physics | <think>
Okay, so I need to figure out how the Ehrenfest theorem proof works, specifically the step where they take the time derivative of the expectation value of an operator A. The user mentioned that when you have a multiplicative operator like the potential, the product rule is straightforward, but they're confused ... | [
{
"from": "human",
"value": "My quantum mechanics book has this proof of Ehrenfest theorem: let $A$ be an observable and $\\hat{A}$ the operator that represents it. Then we have \n$$\\frac{d}{dt}\\langle \\hat{A}\\rangle=\\frac{i}{\\hbar}\\langle [\\hat{H},\\hat{A}]\\rangle+\\left\\langle \\frac{\\partial \... |
I am a little confused about this question. I cannot imagine that it is possible to rise through a rope (assuming inextensible) that isn't fixed in its upper end. But when I solve this problem, I see that it is possible.
If the person exerts downwards force of $F$ on the rope, according to the third law of Newton, the... | Okay, let me try to work through this problem step by step. The question is whether a person can climb up a rope that's not fixed at the top, meaning the rope is free to fall. At first glance, it seems impossible because if the rope isn't anchored, how can pulling down on it lift you up? But when I tried to analyze the... | To determine if a person can rise through a free-falling rope, we analyze the forces and accelerations involved:
1. **Forces on the Person**:
- The person exerts a downward force \( F \) on the rope.
- By Newton's third law, the rope exerts an upward force \( F \) on the person.
- The gravitational force acti... | 36,609 | stackexchange-physics | <think>
Okay, let me try to work through this problem step by step. The question is whether a person can climb up a rope that's not fixed at the top, meaning the rope is free to fall. At first glance, it seems impossible because if the rope isn't anchored, how can pulling down on it lift you up? But when I tried to ana... | [
{
"from": "human",
"value": "I am a little confused about this question. I cannot imagine that it is possible to rise through a rope (assuming inextensible) that isn't fixed in its upper end. But when I solve this problem, I see that it is possible.\n\nIf the person exerts downwards force of $F$ on the rope... |
If I put charged particles in the center of long hollow cylinder shaped electromagnet, in a vacuum, would it accelerate them? Is this how particle accelerators work? If so are there formulas I could use to calculate the acceleration(my grandfather might be able to help me, he's an engineer)
| Okay, so I want to figure out if putting charged particles in the center of a long hollow cylinder-shaped electromagnet in a vacuum would accelerate them. The user also asked if this is how particle accelerators work and if there are formulas to calculate the acceleration. Let me start breaking this down step by step.
... | **Answer:**
1. **Acceleration by a Hollow Cylinder Electromagnet:**
Placing charged particles in the center of a **static** hollow cylinder electromagnet (solenoid) will **not accelerate them** (i.e., increase their speed). The magnetic field (\(\mathbf{B}\)) exerts a Lorentz force (\(\mathbf{F} = q(\mathbf{v} \t... | 17,338 | stackexchange-physics | <think>
Okay, so I want to figure out if putting charged particles in the center of a long hollow cylinder-shaped electromagnet in a vacuum would accelerate them. The user also asked if this is how particle accelerators work and if there are formulas to calculate the acceleration. Let me start breaking this down step b... | [
{
"from": "human",
"value": "If I put charged particles in the center of long hollow cylinder shaped electromagnet, in a vacuum, would it accelerate them? Is this how particle accelerators work? If so are there formulas I could use to calculate the acceleration(my grandfather might be able to help me, he's ... |
In Doppler or Hubble red shift, the wavelength reached us is longer than the original wavelength, as a result, according to the Planck relation, its energy has decreased. Where does this energy go? Isn't this against the law of conservation of energy?
The idea that I have for this question is that energy is a geometric... | Alright, so I'm trying to figure out where the energy goes when light gets redshifted due to the expansion of the universe. The user mentioned the Planck relation, which I remember is E = hc/λ, right? So if the wavelength λ increases because of redshift, the energy E should decrease. But energy is supposed to be conser... | The apparent loss of energy in redshifted photons due to the universe's expansion does not violate the law of conservation of energy because **global energy conservation is not a strict requirement in general relativity (GR)**. Here's a structured explanation:
1. **Cosmological Redshift vs. Doppler Effect**:
- In... | 37,815 | stackexchange-physics | <think>
Alright, so I'm trying to figure out where the energy goes when light gets redshifted due to the expansion of the universe. The user mentioned the Planck relation, which I remember is E = hc/λ, right? So if the wavelength λ increases because of redshift, the energy E should decrease. But energy is supposed to b... | [
{
"from": "human",
"value": "In Doppler or Hubble red shift, the wavelength reached us is longer than the original wavelength, as a result, according to the Planck relation, its energy has decreased. Where does this energy go? Isn't this against the law of conservation of energy?\nThe idea that I have for t... |
I am trying to thoroughly solve the infinite spherical well potential problem that is introduced in Griffith's Introduction to QM, Chapter 4. To solve the Radial part of the equation, one must solve the Bessel equation, which I know is:
$$\frac{d^2Y}{dx^2}+x\frac{dY}{dx}+(x^2-\nu^2)Y=0$$
To arrive at this, I begin mani... | Okay, let me try to work through this step by step. So, I'm trying to solve the radial part of the Schrödinger equation for an infinite spherical well. The potential is zero inside the well and infinite outside, right? That means we only need to consider the region where r is less than the radius a of the well.
Start... | To solve the radial part of the Schrödinger equation for an infinite spherical well, we start with the radial equation:
$$
\frac{d}{dr}\left(r^2\frac{dR}{dr}\right) + \left(k^2 r^2 - l(l+1)\right)R = 0
$$
where \( k^2 = \frac{2mE}{\hbar^2} \). Using the substitution \( u(r) = rR(r) \), the equation transforms into:
... | 24,029 | stackexchange-physics | <think>
Okay, let me try to work through this step by step. So, I'm trying to solve the radial part of the Schrödinger equation for an infinite spherical well. The potential is zero inside the well and infinite outside, right? That means we only need to consider the region where r is less than the radius a of the well.... | [
{
"from": "human",
"value": "I am trying to thoroughly solve the infinite spherical well potential problem that is introduced in Griffith's Introduction to QM, Chapter 4. To solve the Radial part of the equation, one must solve the Bessel equation, which I know is:\n$$\\frac{d^2Y}{dx^2}+x\\frac{dY}{dx}+(x^2... |
I've been following the derivation from Ch. II-31 of Feynman's Lectures, and there is a bit that I don't understand. We start from the relation between the strain $T_{ij}$ and the stress $S_{ij}$, $$T_{ij}=\sum_{k,l}\gamma_{ijkl}S_{kl}.$$ Feynman's argument is as follows:
How can the components of $\gamma_{ijkl}$ be i... | Okay, so I'm trying to understand why Feynman says that for an isotropic material, the tensor γ_ijkl must be expressible in terms of the Kronecker delta δ_ij. And then he mentions two specific combinations: δ_ijδ_kl and δ_ikδ_jl + δ_ilδ_jk. Hmm, let's break this down step by step.
First, isotropy means that the materi... | To address why the components of $\gamma_{ijkl}$ must be expressible in terms of $\delta_{ij}$ for an isotropic material, we consider that isotropy implies the material's properties are invariant under any rotation. This requires the tensor $\gamma_{ijkl}$ to be isotropic. The only second-order isotropic tensor is the ... | 14,735 | stackexchange-physics | <think>
Okay, so I'm trying to understand why Feynman says that for an isotropic material, the tensor γ_ijkl must be expressible in terms of the Kronecker delta δ_ij. And then he mentions two specific combinations: δ_ijδ_kl and δ_ikδ_jl + δ_ilδ_jk. Hmm, let's break this down step by step.
First, isotropy means that th... | [
{
"from": "human",
"value": "I've been following the derivation from Ch. II-31 of Feynman's Lectures, and there is a bit that I don't understand. We start from the relation between the strain $T_{ij}$ and the stress $S_{ij}$, $$T_{ij}=\\sum_{k,l}\\gamma_{ijkl}S_{kl}.$$ Feynman's argument is as follows:\n\nH... |
PROBLEM 1 : A 2.14 kg block is dropped from a height of 43.6 cm onto a spring of force constant k = 18.6 N/cm as shown in fig:12-19.find the maximum distance the spring will be compressed.
solution :::: Let the spring get compressed a distance x. If the object fell from a height h= 0.436 m . then conservation of energy... | Alright, so I have these two physics problems here, both involving springs and potential energy, but they seem to be solved differently. In the first problem, when calculating the maximum compression of the spring after a block is dropped onto it, the solution uses the conservation of energy and includes both the gravi... | In Problem 1, the block is dropped from a height **above the spring**, so the total gravitational potential energy lost includes both the initial drop \( h \) and the spring's compression \( x \). The conservation of energy equation \( 0.5kx^2 = mg(h + x) \) accounts for both distances because the reference point for g... | 35,529 | stackexchange-physics | <think>
Alright, so I have these two physics problems here, both involving springs and potential energy, but they seem to be solved differently. In the first problem, when calculating the maximum compression of the spring after a block is dropped onto it, the solution uses the conservation of energy and includes both t... | [
{
"from": "human",
"value": "PROBLEM 1 : A 2.14 kg block is dropped from a height of 43.6 cm onto a spring of force constant k = 18.6 N/cm as shown in fig:12-19.find the maximum distance the spring will be compressed.\nsolution :::: Let the spring get compressed a distance x. If the object fell from a heigh... |
I'm currently reading Sean Carroll's book on general relativity. In the first chapter, he states something like:
In a moving frame, we can find the components of $p^\mu$ by performing a Lorentz transformation; for a particle moving with three-velocity $v = dx / dt$ along the $x$ axis, we have $$p^\mu = (\gamma m, v \... | Okay, so I'm trying to understand how Sean Carroll gets from the expression for the four-momentum \( p^\mu = (\gamma m, v \gamma m, 0, 0) \) to \( p^0 = m + \frac{1}{2}mv^2 \) when the velocity \( v \) is small. The user is confused because if \( v \) is small, then \( \gamma \) should be approximately 1, which would m... | To reconcile the expression for \( p^0 = \gamma m \) with the classical expectation of rest energy plus kinetic energy when \( v \) is small, we perform a Taylor expansion of the Lorentz factor \( \gamma \):
1. **Expand \( \gamma \) for small \( v \):**
\[
\gamma = \frac{1}{\sqrt{1 - v^2}} \approx 1 + \frac{1}{2... | 32,903 | stackexchange-physics | <think>
Okay, so I'm trying to understand how Sean Carroll gets from the expression for the four-momentum \( p^\mu = (\gamma m, v \gamma m, 0, 0) \) to \( p^0 = m + \frac{1}{2}mv^2 \) when the velocity \( v \) is small. The user is confused because if \( v \) is small, then \( \gamma \) should be approximately 1, which... | [
{
"from": "human",
"value": "I'm currently reading Sean Carroll's book on general relativity. In the first chapter, he states something like: \n\nIn a moving frame, we can find the components of $p^\\mu$ by performing a Lorentz transformation; for a particle moving with three-velocity $v = dx / dt$ along th... |
If you have a Hilbert space $\mathcal{H}$, you can make a projective Hilbert space by modding out by the $U(1)$ group action of multiplying by a phase, $\mathcal{H}/U(1)$.
While we usually talk about states as vectors in a Hilbert space, really they are rays in a projective Hilbert space because phases are unobservable... | Okay, so I'm trying to understand how state addition works in a projective Hilbert space. Let me start by recalling what a projective Hilbert space is. If we have a Hilbert space H, then the projective Hilbert space is obtained by identifying vectors that differ by a scalar multiple of a phase, right? So, we're modding... | In a projective Hilbert space $\mathcal{P}(\mathcal{H}) = \mathcal{H}/U(1)$, states are equivalence classes (rays) of vectors in $\mathcal{H}$ modulo global phase. While $\mathcal{P}(\mathcal{H})$ itself is not a vector space (addition of rays is not inherently defined), the linear structure of $\mathcal{H}$ enables su... | 35,292 | stackexchange-physics | <think>
Okay, so I'm trying to understand how state addition works in a projective Hilbert space. Let me start by recalling what a projective Hilbert space is. If we have a Hilbert space H, then the projective Hilbert space is obtained by identifying vectors that differ by a scalar multiple of a phase, right? So, we're... | [
{
"from": "human",
"value": "If you have a Hilbert space $\\mathcal{H}$, you can make a projective Hilbert space by modding out by the $U(1)$ group action of multiplying by a phase, $\\mathcal{H}/U(1)$.\nWhile we usually talk about states as vectors in a Hilbert space, really they are rays in a projective H... |
Two persons A, B are uniformly accelerating in the positive z direction by amount $g$.
$A$ flashes two pulses of light with an interval $T_a$.
The time interval between two flashes of light in $A$ frame is $T_a$ and correspondingly this event has a time interval $T_b$ in $B$ frame.
We can prove that $T_b$>$T_a$ using... | Okay, let me try to figure out this problem. So, the question is about gravitational redshift and how the equivalence principle applies when we're talking about light coming from a star with a strong gravitational field to Earth, where the gravitational field is much weaker. The confusion arises because the original ar... | The gravitational redshift observed when light from a star (with a strong gravitational field) reaches Earth arises due to the difference in gravitational potential between the star's location and Earth's location, even though Earth is not within the star's gravitational field. Here's the breakdown:
1. **Equivalence P... | 19,283 | stackexchange-physics | <think>
Okay, let me try to figure out this problem. So, the question is about gravitational redshift and how the equivalence principle applies when we're talking about light coming from a star with a strong gravitational field to Earth, where the gravitational field is much weaker. The confusion arises because the ori... | [
{
"from": "human",
"value": "\nTwo persons A, B are uniformly accelerating in the positive z direction by amount $g$.\n$A$ flashes two pulses of light with an interval $T_a$.\nThe time interval between two flashes of light in $A$ frame is $T_a$ and correspondingly this event has a time interval $T_b$ in $B... |
The electric energy supplied by the cell for a unit charge to move from any point in the circuit and come back to the same point by traversing the entire circuit along with the cell is called the electromotive force of the cell.
Now, if I move a unit charge from A to A, by traversing the entire circuit, shouldn't the ... | Okay, let's try to figure this out. The user is confused about electromotive force (emf) because when you move a unit charge from point A back to point A in a circuit, the potential difference is zero. So why does the cell provide energy (emf) if there's no potential difference? Hmm, that does seem contradictory at fir... | The confusion arises from conflating electrostatic potential difference with electromotive force (emf). Here's the breakdown:
1. **Electrostatic Potential Difference**: When a charge moves from point A back to A in a circuit, the net electrostatic potential difference is indeed zero (\(V_A - V_A = 0\)). This aligns wi... | 5,738 | stackexchange-physics | <think>
Okay, let's try to figure this out. The user is confused about electromotive force (emf) because when you move a unit charge from point A back to point A in a circuit, the potential difference is zero. So why does the cell provide energy (emf) if there's no potential difference? Hmm, that does seem contradictor... | [
{
"from": "human",
"value": "\nThe electric energy supplied by the cell for a unit charge to move from any point in the circuit and come back to the same point by traversing the entire circuit along with the cell is called the electromotive force of the cell.\nNow, if I move a unit charge from A to A, by tr... |
The Klein–Gordon Equation in Minkowski space says $\partial_\mu \partial^\mu \phi+ m^2 \phi = 0$.
The solution has modes $e^{ikx}$, $e^{-ikx}$ scaled by creation and annihilation operators $a^{\dagger}(k)$, $a(k)$.
When using an arbitrary diffeomorphism $(x,t) \rightarrow (x’,t’)$, we will get some sort of “modified” K... | Okay, so I need to show that under a Lorentz transformation, the beta coefficients in the Bogoliubov transformation vanish. Let me start by recalling what the Bogoliubov transformation is. When you have two different sets of creation and annihilation operators, say \( a_i, a_i^\dagger \) and \( b_j, b_j^\dagger \), the... | To show that the Bogoliubov coefficients \(\beta_{ij}\) vanish under a Lorentz transformation, we start by noting that Lorentz transformations are symmetries of Minkowski spacetime and preserve the causal structure, including the splitting of solutions into positive and negative frequency modes.
1. **Transformation o... | 27,834 | stackexchange-physics | <think>
Okay, so I need to show that under a Lorentz transformation, the beta coefficients in the Bogoliubov transformation vanish. Let me start by recalling what the Bogoliubov transformation is. When you have two different sets of creation and annihilation operators, say \( a_i, a_i^\dagger \) and \( b_j, b_j^\dagger... | [
{
"from": "human",
"value": "The Klein–Gordon Equation in Minkowski space says $\\partial_\\mu \\partial^\\mu \\phi+ m^2 \\phi = 0$.\nThe solution has modes $e^{ikx}$, $e^{-ikx}$ scaled by creation and annihilation operators $a^{\\dagger}(k)$, $a(k)$.\nWhen using an arbitrary diffeomorphism $(x,t) \\rightar... |
I have a question after I read the second postulate of relativity. Is the velocity of light is constant for moving bodies also? suppose, a body at rest emit a photon from its frame of reference and another body is moving with half the velocity of light observes the velocity of photon from its frame of reference. So, m... | Okay, so I just read about the second postulate of relativity, which says that the speed of light in a vacuum is constant for all observers, regardless of their motion relative to the light source. That's pretty mind-blowing, but now I have a question. Let me try to work through it step by step.
First, let me restate ... | The second postulate of special relativity states that the speed of light in a vacuum, \( c \), is constant for all inertial observers, regardless of their relative motion. This means that even if an observer is moving at half the speed of light (\( 0.5c \)) relative to a light source, they will still measure the speed... | 1,363 | stackexchange-physics | <think>
Okay, so I just read about the second postulate of relativity, which says that the speed of light in a vacuum is constant for all observers, regardless of their motion relative to the light source. That's pretty mind-blowing, but now I have a question. Let me try to work through it step by step.
First, let me ... | [
{
"from": "human",
"value": "I have a question after I read the second postulate of relativity. Is the velocity of light is constant for moving bodies also? suppose, a body at rest emit a photon from its frame of reference and another body is moving with half the velocity of light observes the velocity of ... |
Can we prove that if, for a system of particles, the centre of mass is at origin then the summation of $xy$ over all the particles of the system is zero, where $x$ and $y$ are the respective coordinates of $i^\text{th}$ particle.
I tried to fix the any one coordinate, say $x$, but the summation of $y$ coordinates of th... | Okay, so the problem is asking whether we can prove that if the center of mass of a system of particles is at the origin, then the sum of the products of the x and y coordinates (i.e., Σxy) over all the particles is zero. Hmm, let me think about this.
First, let's recall that the center of mass (COM) being at the orig... | The problem asks whether we can prove that if the center of mass of a system of particles is at the origin, then the summation of \(xy\) over all the particles is zero.
First, recall that the center of mass (COM) being at the origin means:
\[
\sum m_i x_i = 0 \quad \text{and} \quad \sum m_i y_i = 0
\]
where \(m_i\) a... | 26,139 | stackexchange-physics | <think>
Okay, so the problem is asking whether we can prove that if the center of mass of a system of particles is at the origin, then the sum of the products of the x and y coordinates (i.e., Σxy) over all the particles is zero. Hmm, let me think about this.
First, let's recall that the center of mass (COM) being at ... | [
{
"from": "human",
"value": "Can we prove that if, for a system of particles, the centre of mass is at origin then the summation of $xy$ over all the particles of the system is zero, where $x$ and $y$ are the respective coordinates of $i^\\text{th}$ particle.\nI tried to fix the any one coordinate, say $x$,... |
I have an $x-t$ graph (position-time) which its equation is $x=e^t$.
If we get derivative of it, the velocity's equation will be $e^t$ too.
How can a particle's position and velocity be the same? what does it mean when position and velocity are the same? is there any real examples of it?
| Okay, so I have this position-time graph where the equation is x equals e to the power of t, right? So, x(t) = e^t. And if I take the derivative of that with respect to time, I get the velocity, which is also e^t. Wait, that means the position and velocity are the same function? That seems kind of weird. How can a part... | Given the position-time graph with the equation \( x(t) = e^t \), taking the derivative with respect to time gives the velocity \( v(t) = e^t \). This means both the position and velocity are the same function.
To understand this physically, we note that in kinematics, position and velocity have different units (mete... | 1,736 | stackexchange-physics | <think>
Okay, so I have this position-time graph where the equation is x equals e to the power of t, right? So, x(t) = e^t. And if I take the derivative of that with respect to time, I get the velocity, which is also e^t. Wait, that means the position and velocity are the same function? That seems kind of weird. How ca... | [
{
"from": "human",
"value": "I have an $x-t$ graph (position-time) which its equation is $x=e^t$.\nIf we get derivative of it, the velocity's equation will be $e^t$ too.\nHow can a particle's position and velocity be the same? what does it mean when position and velocity are the same? is there any real exam... |
I was reading the book called "Gravitation: Foundations and Frontier" by T.Padmanabhan, there in chapter 1 he defined the 3-volume element of a 3-surface in 4-dimensions, as shown in the above Image in (1.58), I understand why this definition works, but I want to know the motive behind such a construction.
My question... | Okay, so I need to figure out how to construct the volume element for a 3-surface in 4-dimensional spacetime. The user mentioned equation (1.58) from Padmanabhan's book, which I don't have in front of me, but based on the context, I can guess that it's something involving the normal vector to the 3-surface. Let me try ... | To construct the volume element of a 3-surface embedded in 4-dimensional spacetime, the key steps involve leveraging the Levi-Civita tensor and the normal vector to ensure covariance and geometric intuition. Here's a structured derivation:
### 1. **Hypersurface Parametrization**:
Consider a 3-surface parametrized b... | 24,496 | stackexchange-physics | <think>
Okay, so I need to figure out how to construct the volume element for a 3-surface in 4-dimensional spacetime. The user mentioned equation (1.58) from Padmanabhan's book, which I don't have in front of me, but based on the context, I can guess that it's something involving the normal vector to the 3-surface. Let... | [
{
"from": "human",
"value": "\nI was reading the book called \"Gravitation: Foundations and Frontier\" by T.Padmanabhan, there in chapter 1 he defined the 3-volume element of a 3-surface in 4-dimensions, as shown in the above Image in (1.58), I understand why this definition works, but I want to know the mo... |
We all know the example where we say that a massless box containing photons has inertia, because the photons exert pressure of the inner walls of the box.
But my question is about a single photon traveling freely. Can it have inertia?
An aspect of this property is the tendency of objects to keep moving in a straight l... | Okay, so the user is asking if photons have inertia. Let me start by recalling what inertia is. Inertia is the property of an object to resist changes in its state of motion. If an object is at rest, it stays at rest, and if it's moving, it keeps moving at the same velocity unless acted upon by an external force. In Ne... | **Answer:**
Yes, photons possess inertia, but this conclusion requires a relativistic understanding of inertia that transcends the classical notion tied solely to rest mass. Here's the breakdown:
1. **Inertia in Relativity:**
Inertia is the resistance of an object to changes in its state of motion. In Einstein’s... | 35,945 | stackexchange-physics | <think>
Okay, so the user is asking if photons have inertia. Let me start by recalling what inertia is. Inertia is the property of an object to resist changes in its state of motion. If an object is at rest, it stays at rest, and if it's moving, it keeps moving at the same velocity unless acted upon by an external forc... | [
{
"from": "human",
"value": "We all know the example where we say that a massless box containing photons has inertia, because the photons exert pressure of the inner walls of the box.\nBut my question is about a single photon traveling freely. Can it have inertia?\n\nAn aspect of this property is the tenden... |
Is this video real or is it a hoax? What physics is going on here?
https://youtu.be/POGSEG20hkg
In the video, there appears to be a magnetron set up, and someone is using fluorescent light bulbs and potatoes to play with it.
00:18 - Eighteen seconds into the video, a fluorescent light bulb seems to turn on when the mag... | Okay, so I need to figure out if this video is real or a hoax and explain the physics involved. Let's start by breaking down each of the user's questions.
First, at 00:18, the fluorescent bulb lights up when the magnetron touches the glass. I know that fluorescent bulbs require a gas inside that gets ionized to conduc... | The video demonstrates real physics phenomena, albeit in a highly dangerous and unsafe manner. Here's the breakdown of each effect:
### 1. **Fluorescent Bulb Illumination (00:18)**
- **Physics Explanation**: The magnetron emits **2.45 GHz microwaves**, which penetrate the glass of the fluorescent bulb. These micr... | 10,444 | stackexchange-physics | <think>
Okay, so I need to figure out if this video is real or a hoax and explain the physics involved. Let's start by breaking down each of the user's questions.
First, at 00:18, the fluorescent bulb lights up when the magnetron touches the glass. I know that fluorescent bulbs require a gas inside that gets ionized t... | [
{
"from": "human",
"value": "Is this video real or is it a hoax? What physics is going on here?\nhttps://youtu.be/POGSEG20hkg\nIn the video, there appears to be a magnetron set up, and someone is using fluorescent light bulbs and potatoes to play with it.\n00:18 - Eighteen seconds into the video, a fluoresc... |
For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low energy excitations via the following two approaches:
(1)Jordan-Wigner (JW) transformation, we get $H\approx H_f=\sum \omega_... | Alright, let me try to work through these questions. So, the user is asking about two different approaches to studying the low-energy excitations of a 1D ferromagnetic Heisenberg chain: the Jordan-Wigner transformation, which leads to fermionic excitations, and the Holstein-Primakoff transformation, which results in bo... | **Answer:**
### (1) Elementary Excitations and Duality:
In the 1D spin-1/2 ferromagnetic Heisenberg chain, the Jordan-Wigner (JW) and Holstein-Primakoff (HP) transformations yield seemingly contradictory descriptions of low-energy excitations as fermions and bosons, respectively. However, these results are consistent ... | 22,570 | stackexchange-physics | <think>
Alright, let me try to work through these questions. So, the user is asking about two different approaches to studying the low-energy excitations of a 1D ferromagnetic Heisenberg chain: the Jordan-Wigner transformation, which leads to fermionic excitations, and the Holstein-Primakoff transformation, which resul... | [
{
"from": "human",
"value": "For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\\sum_{i=1}^{N}\\mathbf{S}_i\\cdot\\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low energy excitations via the following two approaches:\n(1)Jordan-Wigner (JW) tra... |
When I had a Mac back at JPL in the 80's, I had software that allowed me to enter the mass and X, Y velocity vectors for a number of bodies. It was fun to play with. Is there anything like that out there now? I've seen N-body software for 3D but I really wanted to play with 2D. Much easier to visualize.
| Okay, the user is looking for a 2D gravity simulation similar to what they used on a Mac at JPL in the 80s. They mentioned it allowed entering mass and X, Y velocity vectors for multiple bodies and was fun to play with. Now they want something modern but still 2D for easier visualization. They’ve seen 3D N-body softwar... | There are several modern 2D gravity simulators and tools that align with your JPL-era nostalgia while offering updated features. Here’s a curated list of options, ranging from simple browser-based tools to coding frameworks:
---
### **1. Browser-Based Simulators (Instant Play)**
- **PhET Gravity Force Lab (University... | 32,907 | stackexchange-physics | <think>
Okay, the user is looking for a 2D gravity simulation similar to what they used on a Mac at JPL in the 80s. They mentioned it allowed entering mass and X, Y velocity vectors for multiple bodies and was fun to play with. Now they want something modern but still 2D for easier visualization. They’ve seen 3D N-body... | [
{
"from": "human",
"value": "When I had a Mac back at JPL in the 80's, I had software that allowed me to enter the mass and X, Y velocity vectors for a number of bodies. It was fun to play with. Is there anything like that out there now? I've seen N-body software for 3D but I really wanted to play with 2D. ... |
Further in my textbook it is stated that the ends of all three resistors are under the same potential difference. how is that possible?
| Okay, so I need to figure out how the ends of all three resistors can be under the same potential difference. Let me start by recalling what I know about resistors and circuits.
First, resistors in a circuit can be connected in series or parallel. In series, the same current flows through each resistor, and the total... | The situation described in your textbook occurs when the three resistors are connected in **parallel**. Here's why:
1. **Parallel Connection**: In a parallel circuit, each resistor is connected between the same two points (nodes) in the circuit. This means both ends of every resistor share the same two electrical node... | 11,328 | stackexchange-physics | <think>
Okay, so I need to figure out how the ends of all three resistors can be under the same potential difference. Let me start by recalling what I know about resistors and circuits.
First, resistors in a circuit can be connected in series or parallel. In series, the same current flows through each resistor, and t... | [
{
"from": "human",
"value": "\nFurther in my textbook it is stated that the ends of all three resistors are under the same potential difference. how is that possible?\n"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out how the ends of all three resistors can be under the same... |
I have searched everywhere I know to look but I cannot find out how Hamilton's equations deal with non-conservative forces. In my understanding, Lagrangian mechanics deals with this as follows: the Euler-Lagrange equations no longer have a zero on the right, they have a term $$\Sigma F_q$$ that is the sum of all the no... | Okay, so I need to figure out how Hamilton's equations handle non-conservative forces like friction. I know that in Lagrangian mechanics, when you have non-conservative forces, you add them as a generalized force on the right side of the Euler-Lagrange equations. But Hamilton's equations are based on the Hamiltonian, w... | In Hamiltonian mechanics, non-conservative forces are incorporated by modifying the momentum equation to include a generalized force term \( Q \), analogous to the treatment in Lagrangian mechanics. Here's the detailed breakdown:
### Modified Hamilton's Equations with Non-Conservative Forces:
1. **Position Equation** ... | 14,714 | stackexchange-physics | <think>
Okay, so I need to figure out how Hamilton's equations handle non-conservative forces like friction. I know that in Lagrangian mechanics, when you have non-conservative forces, you add them as a generalized force on the right side of the Euler-Lagrange equations. But Hamilton's equations are based on the Hamilt... | [
{
"from": "human",
"value": "I have searched everywhere I know to look but I cannot find out how Hamilton's equations deal with non-conservative forces. In my understanding, Lagrangian mechanics deals with this as follows: the Euler-Lagrange equations no longer have a zero on the right, they have a term $$\... |
In $N$-body simulations, there is a Hubble constant $H$ in equation of motion.
when we integrate the equation of motion, does this constant H also change with the simulation time?
or it is just a constant of present Hubble constant in simulation.
Most simulations seems use $H = 100$ h KM/s/Mpc, where normalized h is us... | Okay, let's try to tackle this question about the Hubble constant in N-body simulations. The user is confused because they know that in reality, the Hubble parameter H depends on time as the universe expands, but in simulations, they often see H written as a constant, like H = 100 h km/s/Mpc with h being around 0.5. So... | In cosmological N-body simulations, the Hubble parameter \( H(t) \) in the equations of motion **is time-dependent** and evolves with the simulation's cosmic time. However, its evolution is governed by the Friedmann equations, which depend on the cosmological model (e.g., matter density \(\Omega_m\), dark energy \(\Ome... | 32,589 | stackexchange-physics | <think>
Okay, let's try to tackle this question about the Hubble constant in N-body simulations. The user is confused because they know that in reality, the Hubble parameter H depends on time as the universe expands, but in simulations, they often see H written as a constant, like H = 100 h km/s/Mpc with h being around... | [
{
"from": "human",
"value": "In $N$-body simulations, there is a Hubble constant $H$ in equation of motion.\nwhen we integrate the equation of motion, does this constant H also change with the simulation time?\nor it is just a constant of present Hubble constant in simulation.\nMost simulations seems use $H... |
Suppose that I have three non-interacting spin-1/2 particles such that I can represent the combined system in a basis of
\begin{align}
D^{(1/2)}_1 \otimes D^{(1/2)}_2 \otimes D^{(1/2)}_3
& =\left(D^{(1)}_{12} \oplus D^{(0)}_{12}\right)\otimes D^{(1/2)}_3
\\ & =
\left(D^{(1)}_{12} \otimes D^{(1/2)}_3\right) \oplus \left... | Okay, so I need to figure out how to calculate the energy eigenvalues for a system of three non-interacting spin-1/2 particles using the group theory representation provided. The basis is given as a combination of direct products and direct sums of irreducible representations (irreps) of SU(2), I think. Let me start by... | To calculate the energy eigenvalues for a system of three non-interacting spin-1/2 particles using the group theory representation, we decompose the Hilbert space into irreducible representations (irreps) of SU(2). The decomposition is given as:
\[
D^{(1/2)}_1 \otimes D^{(1/2)}_2 \otimes D^{(1/2)}_3 = D^{(3/2)}_{123} ... | 30,957 | stackexchange-physics | <think>
Okay, so I need to figure out how to calculate the energy eigenvalues for a system of three non-interacting spin-1/2 particles using the group theory representation provided. The basis is given as a combination of direct products and direct sums of irreducible representations (irreps) of SU(2), I think. Let me ... | [
{
"from": "human",
"value": "Suppose that I have three non-interacting spin-1/2 particles such that I can represent the combined system in a basis of\n\\begin{align}\nD^{(1/2)}_1 \\otimes D^{(1/2)}_2 \\otimes D^{(1/2)}_3\n& =\\left(D^{(1)}_{12} \\oplus D^{(0)}_{12}\\right)\\otimes D^{(1/2)}_3\n\\\\ & =\n\\l... |
I am here to clarify myself about the role of the observer in Gödel's solution (1949) of Einstein's field equations.
The Universe we are dealing with is anisotropic, since the axis of rotation defines a directional preference, while still homogeneous, as every observer is equivalent. The last fact is driving me crazy,... | Okay, so I'm trying to wrap my head around Gödel's universe and the role of the observer, especially regarding closed timelike curves (CTCs) and how homogeneity plays into this. Let me start by recalling what I know.
Gödel's solution to Einstein's field equations describes a rotating universe that's homogeneous but an... | In Gödel's rotating universe, the interplay between homogeneity, anisotropy, and closed timelike curves (CTCs) leads to intriguing conceptual challenges. Here's a structured breakdown of the key points to clarify the role of observers and CTCs:
### 1. **Homogeneity and Anisotropy**
- **Homogeneity**: Every point in... | 26,854 | stackexchange-physics | <think>
Okay, so I'm trying to wrap my head around Gödel's universe and the role of the observer, especially regarding closed timelike curves (CTCs) and how homogeneity plays into this. Let me start by recalling what I know.
Gödel's solution to Einstein's field equations describes a rotating universe that's homogeneou... | [
{
"from": "human",
"value": "I am here to clarify myself about the role of the observer in Gödel's solution (1949) of Einstein's field equations. \nThe Universe we are dealing with is anisotropic, since the axis of rotation defines a directional preference, while still homogeneous, as every observer is equi... |
I often see in slo-mo explosions, whether underwater or in air, the medium expanding outward before imploding, at which point the flash of the explosion happens. I used to think this was a cool movie trope, but I see in many cases, like this and this the phenomenon is very real. Even this nuke shows a kind of implosion... | Okay, so the user is asking about explosions, both in air and underwater, where there's an expansion followed by an implosion, and then a flash. They mentioned specific examples, like some videos and a nuclear explosion. They used to think it was just a movie effect but realized it's real. They want to know what causes... | The phenomenon you observe in slow-motion explosions—expansion followed by implosion and a flash—is rooted in the physics of shockwaves, pressure dynamics, and energy release. Here's a breakdown:
### 1. **Initial Expansion**
When an explosion occurs, a massive amount of energy is released almost instantaneously. Thi... | 7,580 | stackexchange-physics | <think>
Okay, so the user is asking about explosions, both in air and underwater, where there's an expansion followed by an implosion, and then a flash. They mentioned specific examples, like some videos and a nuclear explosion. They used to think it was just a movie effect but realized it's real. They want to know wha... | [
{
"from": "human",
"value": "I often see in slo-mo explosions, whether underwater or in air, the medium expanding outward before imploding, at which point the flash of the explosion happens. I used to think this was a cool movie trope, but I see in many cases, like this and this the phenomenon is very real.... |
There's been plenty of discussion on here about the Blackbird as featured in this video. I get that it harvests energy from the relative velocity of air to ground. But I still can't wrap my head around it in the reference frame of the vehicle.
In that frame, the wind speed is already zero or backwards. Let's say we'... | Okay, so I need to figure out why the Blackbird works when, in its own reference frame, the air is stationary, and yet it can still extract energy from the wind. The user is confused because in the vehicle's frame, the air is either at rest or moving backward once the vehicle is at wind speed. They mention that the pro... | The Blackbird's operation can be understood by analyzing energy transfer in its reference frame and recognizing how it exploits the relative motion between the ground and air. Here's the breakdown:
### Key Concepts:
1. **Energy Source**: The Blackbird extracts energy from the *relative motion* between the ground (movi... | 20,736 | stackexchange-physics | <think>
Okay, so I need to figure out why the Blackbird works when, in its own reference frame, the air is stationary, and yet it can still extract energy from the wind. The user is confused because in the vehicle's frame, the air is either at rest or moving backward once the vehicle is at wind speed. They mention that... | [
{
"from": "human",
"value": "There's been plenty of discussion on here about the Blackbird as featured in this video. I get that it harvests energy from the relative velocity of air to ground. But I still can't wrap my head around it in the reference frame of the vehicle.\nIn that frame, the wind speed is... |
The answers to this question explain that ice is less dense than water because it has a "crystal structure", but they dont explain what exactly that is and why this happens, also I saw this answer from another site stating that not all ice is less dense than water.
What is the "crystal structure" that ice has? Why is i... | Okay, so I need to figure out why ice is less dense than water, and what this "crystal structure" is all about. Let me start by recalling what I know. Water expands when it freezes, which is why ice floats. But why does that happen? The answer mentions a crystal structure. I remember that in liquid water, molecules are... | The unique properties of ice and water arise from hydrogen bonding and molecular arrangement. Here's a structured explanation:
### 1. **Crystal Structure of Ice (Ice Ih):**
- **Hexagonal Lattice:** Under normal conditions (1 atm, 0°C), water freezes into **ice Ih** (hexagonal ice). Each water molecule forms four hy... | 2,434 | stackexchange-physics | <think>
Okay, so I need to figure out why ice is less dense than water, and what this "crystal structure" is all about. Let me start by recalling what I know. Water expands when it freezes, which is why ice floats. But why does that happen? The answer mentions a crystal structure. I remember that in liquid water, molec... | [
{
"from": "human",
"value": "The answers to this question explain that ice is less dense than water because it has a \"crystal structure\", but they dont explain what exactly that is and why this happens, also I saw this answer from another site stating that not all ice is less dense than water.\nWhat is th... |
After being absorbed by an electron, does a photon continue to behave like a particle, or like a wave, or both?
| Okay, so the question is: After being absorbed by an electron, does a photon continue to behave like a particle, or like a wave, or both? Hmm, let me try to work through this.
First, I need to recall what happens when a photon is absorbed by an electron. From what I remember, photons are the quanta of electromagnetic... | After a photon is absorbed by an electron, the photon ceases to exist as a distinct entity. Its energy and momentum are transferred to the electron, which may then transition to a higher energy state. Since the photon no longer exists post-absorption, it does not continue to behave as a particle, a wave, or both. The q... | 7,383 | stackexchange-physics | <think>
Okay, so the question is: After being absorbed by an electron, does a photon continue to behave like a particle, or like a wave, or both? Hmm, let me try to work through this.
First, I need to recall what happens when a photon is absorbed by an electron. From what I remember, photons are the quanta of electro... | [
{
"from": "human",
"value": "After being absorbed by an electron, does a photon continue to behave like a particle, or like a wave, or both?\n"
},
{
"from": "gpt",
"value": "<think>\nOkay, so the question is: After being absorbed by an electron, does a photon continue to behave like a particle, ... |
based on the paradox resolved at A relativistic meter stick and a thin disk
if in the place of a relativistic stick, was a relativistic man whose length is the same as that of a stick, and instead of an end of a hole, was a bullet. In the man's frame, would he die(Does the bullet effectively hit the man?)? and in the r... | Okay, let's try to figure out this physics problem. So, the original paradox involved a relativistic meter stick and a disk with a hole. Now, they're replacing the meter stick with a man of the same length and the end of the hole with a bullet. The question is: in the man's frame, would the bullet hit him, meaning woul... | In the scenario presented, based on the resolution of the relativistic meter stick and hole paradox, we analyze the outcomes in both the man's frame and the hole's (lab) frame:
1. **Hole's (Lab) Frame**:
- The man is moving at relativistic speed and is length-contracted.
- The bullet (analogous to the hole's... | 33,094 | stackexchange-physics | <think>
Okay, let's try to figure out this physics problem. So, the original paradox involved a relativistic meter stick and a disk with a hole. Now, they're replacing the meter stick with a man of the same length and the end of the hole with a bullet. The question is: in the man's frame, would the bullet hit him, mean... | [
{
"from": "human",
"value": "based on the paradox resolved at A relativistic meter stick and a thin disk\nif in the place of a relativistic stick, was a relativistic man whose length is the same as that of a stick, and instead of an end of a hole, was a bullet. In the man's frame, would he die(Does the bull... |
In Schrödinger picture operators do not depend on time explicitly. Consider a free scalar field with Lagrangian density
$${\cal L} ~=~ \frac{1}{2}\partial_{\mu} \phi\partial^{\mu}\phi-\frac{m^2}{2}\phi^2,$$
where $\phi=\phi(t,x,y,z)$. In quantum field theory we take it as an operator. Is this operator Schrödinger or He... | Okay, so I need to figure out whether the scalar field operator φ in the given Lagrangian is in the Schrödinger picture or the Heisenberg picture. Then, I also need to express the free field Lagrangian in both pictures. Let me start by recalling what I know about the Schrödinger and Heisenberg pictures in quantum mecha... | In quantum field theory, the scalar field operator \(\phi(t, x, y, z)\) given in the Lagrangian is in the Heisenberg picture because it explicitly depends on time. In the Schrödinger picture, operators are time-independent, and the time evolution is carried by the states.
To express the free field Lagrangian in both ... | 32,622 | stackexchange-physics | <think>
Okay, so I need to figure out whether the scalar field operator φ in the given Lagrangian is in the Schrödinger picture or the Heisenberg picture. Then, I also need to express the free field Lagrangian in both pictures. Let me start by recalling what I know about the Schrödinger and Heisenberg pictures in quant... | [
{
"from": "human",
"value": "In Schrödinger picture operators do not depend on time explicitly. Consider a free scalar field with Lagrangian density\n$${\\cal L} ~=~ \\frac{1}{2}\\partial_{\\mu} \\phi\\partial^{\\mu}\\phi-\\frac{m^2}{2}\\phi^2,$$\nwhere $\\phi=\\phi(t,x,y,z)$. In quantum field theory we tak... |
The electric strength between two parallel plates does not depend on its separating distance, and only depend on the number of charges the two plates carried. Therefore $\epsilon$ cannot be calculated by a random combination of $\Delta$V and r with this formula below:
$${\epsilon} =\frac{\Delta V}{r}$$
Therefore is it ... | Okay, let me try to work through this. So the question is about the electric field between two parallel plates and how it relates to the voltage difference and the separation distance. The user is confused because they know that the electric field (which they refer to as "electric strength") between parallel plates doe... | The electric field (E) between two parallel plates can be analyzed in two distinct scenarios:
1. **Fixed Charge (Isolated Capacitor):**
When the charge \( Q \) on the plates is constant, the electric field \( E \) is determined by the surface charge density \( \sigma \):
\[
E = \frac{\sigma}{\epsilon_0} =... | 24,056 | stackexchange-physics | <think>
Okay, let me try to work through this. So the question is about the electric field between two parallel plates and how it relates to the voltage difference and the separation distance. The user is confused because they know that the electric field (which they refer to as "electric strength") between parallel pl... | [
{
"from": "human",
"value": "The electric strength between two parallel plates does not depend on its separating distance, and only depend on the number of charges the two plates carried. Therefore $\\epsilon$ cannot be calculated by a random combination of $\\Delta$V and r with this formula below:\n$${\\ep... |
$$\partial_{\mu} \frac{\partial(\partial_{\alpha}A_{\alpha})^2}{\partial(\partial_{\mu}A_{\nu})} = \partial_{\mu}\left[2(\partial_{\alpha}A_{\alpha})\frac{\partial(\partial_{\beta}A_{\gamma})}{\partial(\partial_{\mu}A_{\nu})} g_{\beta\gamma}\right]$$
I assume the metric comes from differentiating a vector wrt to anothe... | Okay, so I need to figure out why the left-hand side of this equation is equal to the right-hand side. Let me start by understanding what each part of the equation means. The original expression is a partial derivative with respect to ∂μ of the partial derivative of (∂αAα)² divided by the partial derivative of ∂μAν. Th... | To understand the equality of the given equation, we start by analyzing the left-hand side and right-hand side separately and then show how they are equivalent.
1. **Left-Hand Side Analysis**:
- The term \((\partial_{\alpha} A_{\alpha})^2\) is the square of the divergence of the vector field \(A\). Expanding this, ... | 13,266 | stackexchange-physics | <think>
Okay, so I need to figure out why the left-hand side of this equation is equal to the right-hand side. Let me start by understanding what each part of the equation means. The original expression is a partial derivative with respect to ∂μ of the partial derivative of (∂αAα)² divided by the partial derivative of ... | [
{
"from": "human",
"value": "$$\\partial_{\\mu} \\frac{\\partial(\\partial_{\\alpha}A_{\\alpha})^2}{\\partial(\\partial_{\\mu}A_{\\nu})} = \\partial_{\\mu}\\left[2(\\partial_{\\alpha}A_{\\alpha})\\frac{\\partial(\\partial_{\\beta}A_{\\gamma})}{\\partial(\\partial_{\\mu}A_{\\nu})} g_{\\beta\\gamma}\\right]$$... |
We say that light has magnetic and electric fields ossilating perpendicular to each other.What causes the those fields to exist and why does the light as a whole does not get affected in the presence of other charges or magnetic fields.
| Okay, so I need to figure out why light has these oscillating electric and magnetic fields and why light itself isn't affected by other charges or magnetic fields. Hmm. Let me start by recalling what I know about electromagnetic waves. Light is an electromagnetic wave, right? So according to Maxwell's equations, changi... | Light, as an electromagnetic wave, consists of oscillating electric and magnetic fields that are generated by accelerating charges. When charges accelerate, they disturb the electromagnetic field, creating a self-propagating wave. According to Maxwell's equations, a time-varying electric field generates a magnetic fiel... | 30,114 | stackexchange-physics | <think>
Okay, so I need to figure out why light has these oscillating electric and magnetic fields and why light itself isn't affected by other charges or magnetic fields. Hmm. Let me start by recalling what I know about electromagnetic waves. Light is an electromagnetic wave, right? So according to Maxwell's equations... | [
{
"from": "human",
"value": "We say that light has magnetic and electric fields ossilating perpendicular to each other.What causes the those fields to exist and why does the light as a whole does not get affected in the presence of other charges or magnetic fields.\n"
},
{
"from": "gpt",
"value"... |
Say a red colour with 400nm mixes with blue colour with 700nm, but out of phase by a little. What would be the resultant colour?
I would know how to represent the resulting wave mathematically, but what colour is it? Is the colour only determined by the resulting wavelength?
| Okay, so the user is asking about mixing a red color with 400 nm and a blue color with 700 nm, but they are out of phase by a little. They want to know the resultant color. Hmm, wait, first off, red and blue colors with those wavelengths? Let me check the visible spectrum. Normally, red light has longer wavelengths, ar... | When mixing light of different wavelengths, the resultant color perceived by the human eye is determined by **additive color mixing**, which depends on the stimulation of the eye's cone cells (S, M, L) by the wavelengths present. Here's the breakdown for your scenario:
### Key Points:
1. **Wavelengths Clarified**:
... | 26,194 | stackexchange-physics | <think>
Okay, so the user is asking about mixing a red color with 400 nm and a blue color with 700 nm, but they are out of phase by a little. They want to know the resultant color. Hmm, wait, first off, red and blue colors with those wavelengths? Let me check the visible spectrum. Normally, red light has longer wavelen... | [
{
"from": "human",
"value": "Say a red colour with 400nm mixes with blue colour with 700nm, but out of phase by a little. What would be the resultant colour?\nI would know how to represent the resulting wave mathematically, but what colour is it? Is the colour only determined by the resulting wavelength?\n"... |
Say we add infinitely many waves (states of definite momentum) so as to produce a function that gives a very well-defined position, does that addition(using Fourier series) make that function periodic? I mean, if the added waves are themselves periodic(in Fourier they are harmonic), does that mean that the resulting fu... | Okay, so I need to figure out whether adding infinitely many waves with definite momentum (which are periodic) using Fourier series results in a periodic function. The user is asking specifically about constructing a function with a very well-defined position, like a Dirac Delta function, and whether that function woul... | When constructing a function by superposing waves (momentum eigenstates), the periodicity of the result depends on whether you use a **Fourier series** (discrete sum) or a **Fourier transform** (continuous integral):
1. **Fourier Series (Periodic Case):**
If you add discrete harmonic waves (e.g., with momenta \(k... | 35,457 | stackexchange-physics | <think>
Okay, so I need to figure out whether adding infinitely many waves with definite momentum (which are periodic) using Fourier series results in a periodic function. The user is asking specifically about constructing a function with a very well-defined position, like a Dirac Delta function, and whether that funct... | [
{
"from": "human",
"value": "Say we add infinitely many waves (states of definite momentum) so as to produce a function that gives a very well-defined position, does that addition(using Fourier series) make that function periodic? I mean, if the added waves are themselves periodic(in Fourier they are harmon... |
Let there be a system and surroundings. Let the system undergo an irreversible process. I understand that to calculate the entropy change of the system, one can use a reversible path between the initial and final states instead because entropy is a state function.
What I don't understand is why you must use the actual... | Okay, so I need to figure out why the entropy change for the system is calculated using a reversible path, but for the surroundings, we use the actual (irreversible) heat flow. Hmm. Let me start by recalling what entropy is. Entropy is a state function, right? That means the change in entropy between two states depends... | The entropy change for the system and surroundings is calculated differently due to their distinct roles in thermodynamic processes:
1. **System's Entropy Change**:
Entropy is a state function, so $\Delta S_{\text{system}}$ depends only on the initial and final states, not the process path. For an **irreversible ... | 26,420 | stackexchange-physics | <think>
Okay, so I need to figure out why the entropy change for the system is calculated using a reversible path, but for the surroundings, we use the actual (irreversible) heat flow. Hmm. Let me start by recalling what entropy is. Entropy is a state function, right? That means the change in entropy between two states... | [
{
"from": "human",
"value": "Let there be a system and surroundings. Let the system undergo an irreversible process. I understand that to calculate the entropy change of the system, one can use a reversible path between the initial and final states instead because entropy is a state function. \nWhat I don't... |
When an AC voltage U is put onto a loss less capacitor C the capacitor will require a certain reactive power Q (current 90 degress out of phase with the voltage):
$Q=UI = \omega C U^2$ in VAr (Only reactive power, no real power)
I can also determine the reactive power strating from the stored energy in a capacitor:
$E=... | Alright, so I'm trying to figure out why there's a discrepancy when calculating the reactive power of a capacitor using two different methods. Let me start by recapping what I know.
First method: When an AC voltage U is applied across a lossless capacitor C, the reactive power Q is given by Q = U * I. Since the curren... | The discrepancy arises from a mix-up between peak and RMS values when relating reactive power to stored energy. Here's the step-by-step resolution:
1. **Reactive Power via Voltage and Current:**
- Using RMS voltage \( U_{\text{rms}} \), the reactive power is \( Q = \omega C U_{\text{rms}}^2 \).
2. **Energy Stored ... | 10,977 | stackexchange-physics | <think>
Alright, so I'm trying to figure out why there's a discrepancy when calculating the reactive power of a capacitor using two different methods. Let me start by recapping what I know.
First method: When an AC voltage U is applied across a lossless capacitor C, the reactive power Q is given by Q = U * I. Since th... | [
{
"from": "human",
"value": "When an AC voltage U is put onto a loss less capacitor C the capacitor will require a certain reactive power Q (current 90 degress out of phase with the voltage):\n$Q=UI = \\omega C U^2$ in VAr (Only reactive power, no real power)\nI can also determine the reactive power stratin... |
Basically the title. Light can go into my room through some lenses so that I can see it, but light can't escape my room so that people outside? The article about peepholes on Wikipedia doesn't elaborate at all about how this works.
| Okay, so the user is asking about how peepholes work, specifically why light can enter their room through lenses allowing them to see outside, but light can't escape so people outside can't see in. The Wikipedia article on peepholes didn't explain the mechanism, so they want a clear explanation.
First, I need to recal... | The one-way visibility of a peephole (or door viewer) relies on **optical principles** and **light intensity differences**, not mirrors or electronic components. Here's how it works:
### 1. **Lens Design: Fisheye + Small Aperture**
- Peepholes use a **wide-angle (fisheye) lens system**, typically a combination of c... | 4,987 | stackexchange-physics | <think>
Okay, so the user is asking about how peepholes work, specifically why light can enter their room through lenses allowing them to see outside, but light can't escape so people outside can't see in. The Wikipedia article on peepholes didn't explain the mechanism, so they want a clear explanation.
First, I need ... | [
{
"from": "human",
"value": "Basically the title. Light can go into my room through some lenses so that I can see it, but light can't escape my room so that people outside? The article about peepholes on Wikipedia doesn't elaborate at all about how this works. \n"
},
{
"from": "gpt",
"value": "<... |
I have a question about gravity
So as we know gravity is significantly less on high mountains or tall buildings and increases as we lose height
☕ My question is that if we have 2 objects with the same volume and mass, 1 falls on a mountain and one falls on a beach ( note that they are released from the same height base... | Okay, so the user is asking about gravity and whether two objects dropped from the same height but on different surfaces—like a mountain and a beach—will hit the ground at the same time. Let me break this down step by step.
First, they mentioned that gravity is weaker at higher elevations, which is correct. The gravit... | The two objects will **not** reach the ground at the same time, and their speeds will differ. Here's why:
### Key Factors:
1. **Gravitational Acceleration (g):**
Gravity decreases slightly with altitude. For example, on a tall mountain, \( g \) is marginally weaker than at sea level (e.g., ~9.78 m/s² vs. ~9.81 m/... | 39,864 | stackexchange-physics | <think>
Okay, so the user is asking about gravity and whether two objects dropped from the same height but on different surfaces—like a mountain and a beach—will hit the ground at the same time. Let me break this down step by step.
First, they mentioned that gravity is weaker at higher elevations, which is correct. Th... | [
{
"from": "human",
"value": "I have a question about gravity\nSo as we know gravity is significantly less on high mountains or tall buildings and increases as we lose height\n☕ My question is that if we have 2 objects with the same volume and mass, 1 falls on a mountain and one falls on a beach ( note that ... |
I'm relatively new to astronomy and I would like to better understand why we need filters.
I understand the concept of the filter, I just can't understand we they are so useful.
In other words, what can you do with them that you can't do without them?
Thank you in advance
| Okay, the user is new to astronomy and wants to understand why filters are so useful. They get the basic concept but don't see the practical applications. Let me start by recalling what I know about astronomical filters.
First, light pollution. Right, filters can block out certain wavelengths from city lights, which u... | Astronomical filters are essential tools that enhance observations and imaging by selectively allowing specific wavelengths of light to pass through. Here's why they're indispensable, organized by key use cases:
### 1. **Combating Light Pollution**
- **What they do**: Block wavelengths emitted by artificial light... | 25,853 | stackexchange-physics | <think>
Okay, the user is new to astronomy and wants to understand why filters are so useful. They get the basic concept but don't see the practical applications. Let me start by recalling what I know about astronomical filters.
First, light pollution. Right, filters can block out certain wavelengths from city lights,... | [
{
"from": "human",
"value": "I'm relatively new to astronomy and I would like to better understand why we need filters.\nI understand the concept of the filter, I just can't understand we they are so useful. \nIn other words, what can you do with them that you can't do without them?\nThank you in advance\n"... |
Let's say we somehow speed up the moon's rotation. (I'm thinking about a big asteroid smashing into it, but I'm open to better ideas.) Here are some questions:
How fast could we get the moon to spin before gravity stopped holding it together? (An answer in revolutions per minute would be nice.)
At half that speed, wha... | Okay, so I need to figure out how fast the Moon could spin before gravity can't hold it together anymore. Then, at half that speed, what would happen to the Moon, space missions, and Earth? Also, how many asteroids would be needed to get it spinning that fast. Let me start breaking this down.
First, the maximum rotati... | **1. Maximum Spin Rate Before Disintegration**
The Moon's critical rotation speed—where centrifugal force at the equator equals gravity—is calculated to be **~0.00924 RPM** (one full rotation every ~108 minutes). At this speed, material at the equator would begin to escape into space.
**2. Consequences at Half Criti... | 18,405 | stackexchange-physics | <think>
Okay, so I need to figure out how fast the Moon could spin before gravity can't hold it together anymore. Then, at half that speed, what would happen to the Moon, space missions, and Earth? Also, how many asteroids would be needed to get it spinning that fast. Let me start breaking this down.
First, the maximu... | [
{
"from": "human",
"value": "Let's say we somehow speed up the moon's rotation. (I'm thinking about a big asteroid smashing into it, but I'm open to better ideas.) Here are some questions:\nHow fast could we get the moon to spin before gravity stopped holding it together? (An answer in revolutions per minut... |
The QM spin operator can be expressed in terms of gamma matrices and I am trying to do an exercise where I prove an identity which uses $\gamma^5$ and ${\mathbf{\alpha}}$:
$$\mathbf{S}=\frac{1}{2}\gamma^5\mathbf{\alpha}$$
In my first attempt I did this directly in the Dirac representation but the exercise states that I... | Okay, so I need to prove that the spin operator **S** in quantum mechanics can be expressed as (1/2) times γ⁵ times the α vector. The user mentioned that they initially tried doing this directly in the Dirac representation but were told not to. Hmm. Let me recall some properties of gamma matrices and the α matrices.
F... | To prove the identity \(\mathbf{S} = \frac{1}{2} \gamma^5 \mathbf{\alpha}\) without resorting to a specific representation, we can use the properties of the gamma matrices and the given definitions.
1. **Definitions and Properties**:
- The alpha matrices are defined as \(\alpha^i = \gamma^0 \gamma^i\).
- The spi... | 33,406 | stackexchange-physics | <think>
Okay, so I need to prove that the spin operator **S** in quantum mechanics can be expressed as (1/2) times γ⁵ times the α vector. The user mentioned that they initially tried doing this directly in the Dirac representation but were told not to. Hmm. Let me recall some properties of gamma matrices and the α matr... | [
{
"from": "human",
"value": "The QM spin operator can be expressed in terms of gamma matrices and I am trying to do an exercise where I prove an identity which uses $\\gamma^5$ and ${\\mathbf{\\alpha}}$:\n$$\\mathbf{S}=\\frac{1}{2}\\gamma^5\\mathbf{\\alpha}$$\nIn my first attempt I did this directly in the ... |
Let's say I stay at point $x=0$ in vacuum. When I move my arm forward such that it will have a positive $x$ position (say $x=5$) will the rest of my body move backward such that it will have a negative $x$ position (like $x=-1$)?
| Okay, let's try to figure this out. So the question is, if I'm at rest at point x=0 in a vacuum, and I move my arm forward to x=5, will the rest of my body move backward to like x=-1? Hmm. I remember something about conservation of momentum from physics class. Let me think.
First, in a vacuum, there's no air resistanc... | When you move your arm forward in a vacuum (where no external forces act), the **conservation of momentum** and **center of mass** principles ensure that the rest of your body moves backward to keep the system's center of mass stationary. Here's the breakdown:
1. **Initial State**: Your entire body (arm + rest) is at ... | 10,307 | stackexchange-physics | <think>
Okay, let's try to figure this out. So the question is, if I'm at rest at point x=0 in a vacuum, and I move my arm forward to x=5, will the rest of my body move backward to like x=-1? Hmm. I remember something about conservation of momentum from physics class. Let me think.
First, in a vacuum, there's no air r... | [
{
"from": "human",
"value": "Let's say I stay at point $x=0$ in vacuum. When I move my arm forward such that it will have a positive $x$ position (say $x=5$) will the rest of my body move backward such that it will have a negative $x$ position (like $x=-1$)?\n"
},
{
"from": "gpt",
"value": "<thi... |
Everyone knows that the mass of a system is less than the mass of its components, with the equation:
$M = \sum_i m_i - BE(M) $
Now, if we consider a general decay, lets say
$A \rightarrow \sum_i B_i$
then, for the conservation of the first component of the four-vector momentum we obtain a necessary condition for the de... | Okay, so I'm trying to understand this problem about mass in particle decays and how it relates to binding energy. Let me start by restating the issue to make sure I get it.
The user mentions that the mass of a system is less than the sum of the masses of its components because of the binding energy. The equation giv... | The apparent contradiction arises from a misunderstanding of the systems being compared. Here's the resolution:
1. **Binding Energy and Mass Defect**:
The mass of a bound system (e.g., a nucleus) is given by \( M = \sum_i m_i - BE \), where \( \sum_i m_i \) is the total mass of its free components (e.g., nucleons... | 37,158 | stackexchange-physics | <think>
Okay, so I'm trying to understand this problem about mass in particle decays and how it relates to binding energy. Let me start by restating the issue to make sure I get it.
The user mentions that the mass of a system is less than the sum of the masses of its components because of the binding energy. The equa... | [
{
"from": "human",
"value": "Everyone knows that the mass of a system is less than the mass of its components, with the equation:\n$M = \\sum_i m_i - BE(M) $\nNow, if we consider a general decay, lets say\n$A \\rightarrow \\sum_i B_i$\nthen, for the conservation of the first component of the four-vector mom... |
My Text Book says the Lagrangian for a one-dimensional relativistic harmonic oscillator can be written as
$$L = mc^2(1-\gamma) - \frac12kx^2$$
but I've learnt it as;
$$L = -mc^2/\gamma - \frac12kx^2$$
how is this possible?
| Okay, so my textbook says the Lagrangian for a one-dimensional relativistic harmonic oscillator is L = mc²(1 - γ⁻¹) - ½kx². But I remember learning it as L = -mc²/γ - ½kx². Hmm, how can both of these be correct? Let me think through this step by step.
First, I need to recall what a Lagrangian is in the context of rela... | The two Lagrangians provided are indeed equivalent for describing the relativistic harmonic oscillator, differing only by a constant term that does not affect the equations of motion. Here's the breakdown:
1. **Lagrangian Forms**:
- **Textbook Version**:
\[
L = mc^2(1 - \gamma^{-1}) - \frac{1}{2}kx^2
... | 17,065 | stackexchange-physics | <think>
Okay, so my textbook says the Lagrangian for a one-dimensional relativistic harmonic oscillator is L = mc²(1 - γ⁻¹) - ½kx². But I remember learning it as L = -mc²/γ - ½kx². Hmm, how can both of these be correct? Let me think through this step by step.
First, I need to recall what a Lagrangian is in the context... | [
{
"from": "human",
"value": "My Text Book says the Lagrangian for a one-dimensional relativistic harmonic oscillator can be written as \n$$L = mc^2(1-\\gamma) - \\frac12kx^2$$\nbut I've learnt it as;\n$$L = -mc^2/\\gamma - \\frac12kx^2$$\nhow is this possible?\n"
},
{
"from": "gpt",
"value": "<t... |
I'm trying to solve this problem from Halliday & Resnick in a creative way:
A block is projected up a frictionless inclined plane with initial speed $v_0 = 3.50$ m/s. The angle of incline is $\theta = 32.0°$. (a) How far up the plane does the block go? (b) How long does it take to get there? (c) What is its speed when... | Okay, so I just solved this physics problem from Halliday & Resnick about a block sliding up a frictionless inclined plane. I used an analogy to projectile motion where instead of gravity acting straight down, it's acting along the incline with acceleration g sin θ. Surprisingly, it worked perfectly, and I got the righ... | The success of modeling the block's motion on an incline using projectile motion equations with adjusted acceleration stems from the following key principles:
### 1. **Component of Gravity**:
The acceleration along the incline is \( a = g \sin\theta \), which acts opposite to the block's initial motion. This is d... | 19,876 | stackexchange-physics | <think>
Okay, so I just solved this physics problem from Halliday & Resnick about a block sliding up a frictionless inclined plane. I used an analogy to projectile motion where instead of gravity acting straight down, it's acting along the incline with acceleration g sin θ. Surprisingly, it worked perfectly, and I got ... | [
{
"from": "human",
"value": "I'm trying to solve this problem from Halliday & Resnick in a creative way:\n\nA block is projected up a frictionless inclined plane with initial speed $v_0 = 3.50$ m/s. The angle of incline is $\\theta = 32.0°$. (a) How far up the plane does the block go? (b) How long does it t... |
What is the exact meaning of the wave function of a particle?
| Okay, so I need to figure out the exact meaning of the wave function of a particle. Hmm, I remember from my physics class that the wave function is related to quantum mechanics. Let me start by recalling what I know.
In classical physics, particles have definite positions and velocities, but in quantum mechanics, thi... | The wave function of a particle is a fundamental concept in quantum mechanics, serving as a mathematical description of the particle's quantum state. Here is a structured breakdown of its meaning and role:
1. **Mathematical Representation**:
- The wave function, typically denoted as Ψ (psi), is a complex-valued fu... | 13,359 | stackexchange-physics | <think>
Okay, so I need to figure out the exact meaning of the wave function of a particle. Hmm, I remember from my physics class that the wave function is related to quantum mechanics. Let me start by recalling what I know.
In classical physics, particles have definite positions and velocities, but in quantum mechan... | [
{
"from": "human",
"value": "What is the exact meaning of the wave function of a particle?\n"
},
{
"from": "gpt",
"value": "<think>\nOkay, so I need to figure out the exact meaning of the wave function of a particle. Hmm, I remember from my physics class that the wave function is related to quan... |
I was reading the treatment of the large $N$ limit of the Non-Linear Sigma Model (NLSM) in Peskin & Schroeder, Sec. 13.3, and I noticed something strange in the evaluation of the path-integral by steepest descent.
P&S are evaluating the NLSM euclidean partition function:
$$Z_E=\intop \mathcal D n \,\delta [n^2 -1]\exp... | Okay, let's try to unpack this step by step. So, the problem is about the large N limit of the Non-Linear Sigma Model (NLSM) as treated in Peskin & Schroeder. The confusion arises when they introduce an auxiliary field α to enforce the delta function constraint n²=1. Initially, α is introduced with an "i" in front, whi... | The confusion arises from the interplay between the representation of the constraint via an auxiliary field and the saddle point approximation in the large \( N \) limit. Here's the breakdown:
1. **Auxiliary Field Introduction**: The auxiliary field \( \alpha \) is introduced as a real field to enforce the delta funct... | 23,878 | stackexchange-physics | <think>
Okay, let's try to unpack this step by step. So, the problem is about the large N limit of the Non-Linear Sigma Model (NLSM) as treated in Peskin & Schroeder. The confusion arises when they introduce an auxiliary field α to enforce the delta function constraint n²=1. Initially, α is introduced with an "i" in fr... | [
{
"from": "human",
"value": "I was reading the treatment of the large $N$ limit of the Non-Linear Sigma Model (NLSM) in Peskin & Schroeder, Sec. 13.3, and I noticed something strange in the evaluation of the path-integral by steepest descent.\nP&S are evaluating the NLSM euclidean partition function: \n$$Z_... |
I am considering the calculation of the black hole entropy, given the MTZ solutions for the mass and temperature (https://arxiv.org/abs/hep-th/0406111):
$$M=\frac{\sigma r_+}{4\pi G}\left(\frac{r_+}{\ell}-1\right)$$
$$T=\frac{1}{\pi \ell}\left(\frac{r_+}{\ell}-\frac{1}{2}\right)$$
where $\ell$ is the AdS length, $\sigm... | Okay, so I need to figure out why the entropy formula S = σ/(4G) * R²(r_+) makes sense, especially why σ R²(r_+) is considered the area within the event horizon. Let me start by recalling what I know about black hole entropy and the MTZ solutions.
First, the general formula for black hole entropy in Einstein gravity i... | The entropy formula \( S = \frac{\sigma}{4G} R^2(r_+) \) in the MTZ black hole solution generalizes the Bekenstein-Hawking entropy \( S = A/(4G) \), where \( A = \sigma R^2(r_+) \) is the area of the event horizon. Here's the breakdown:
1. **Metric Structure**: The black hole metric includes a radial function \( R(r) ... | 36,036 | stackexchange-physics | <think>
Okay, so I need to figure out why the entropy formula S = σ/(4G) * R²(r_+) makes sense, especially why σ R²(r_+) is considered the area within the event horizon. Let me start by recalling what I know about black hole entropy and the MTZ solutions.
First, the general formula for black hole entropy in Einstein g... | [
{
"from": "human",
"value": "I am considering the calculation of the black hole entropy, given the MTZ solutions for the mass and temperature (https://arxiv.org/abs/hep-th/0406111):\n$$M=\\frac{\\sigma r_+}{4\\pi G}\\left(\\frac{r_+}{\\ell}-1\\right)$$\n$$T=\\frac{1}{\\pi \\ell}\\left(\\frac{r_+}{\\ell}-\\f... |
Background:
When learning about BCFW recursion I am shown the deformation equation:
$$\hat{p_1}=p_1 -zq \hspace{5mm}; \hspace{5mm} \hat{p_n} = p_n +zq$$
This deformation represents a $\langle1n]$ shift and $q$ is defined as $q=\lambda^\dot{\alpha}_1 \lambda^\alpha _n $
To check under which circumstances $\lim _{z \to ... | Okay, let's try to figure out why ⟨1̂ 2̂⟩ equals ⟨12⟩ when we do this BCFW shift. The problem mentions that we're doing a ⟨1^- 2^-] shift, which I think means we're shifting the spinors of particles 1 and 2. From the deformation equations given earlier, the shifted momenta are:
p̂₁ = p₁ - z q
p̂₂ = p₂ + z q ?
Wait, ... | The key steps to show that ⟨1̂ 2̂⟩ = ⟨12⟩ under the ⟨1^- 2^-] shift are as follows:
1. **Shift Definition**: For a ⟨1^- 2^-] shift, the spinor λ₁ of particle 1 is deformed as:
\[
\hat{\lambda}_1 = \lambda_1 - z \lambda_2
\]
while particle 2's spinor λ₂ remains unchanged (only its λ̃₂ is shifted).
2. **Spi... | 14,337 | stackexchange-physics | <think>
Okay, let's try to figure out why ⟨1̂ 2̂⟩ equals ⟨12⟩ when we do this BCFW shift. The problem mentions that we're doing a ⟨1^- 2^-] shift, which I think means we're shifting the spinors of particles 1 and 2. From the deformation equations given earlier, the shifted momenta are:
p̂₁ = p₁ - z q
p̂₂ = p₂ + z q ?... | [
{
"from": "human",
"value": "Background:\nWhen learning about BCFW recursion I am shown the deformation equation:\n$$\\hat{p_1}=p_1 -zq \\hspace{5mm}; \\hspace{5mm} \\hat{p_n} = p_n +zq$$ \nThis deformation represents a $\\langle1n]$ shift and $q$ is defined as $q=\\lambda^\\dot{\\alpha}_1 \\lambda^\\alpha ... |
I am working with a condensed matter system in terms of charge and spin bosonic fields $\phi_c$ and $\phi_s$, respectively. I am trying to reach a diagonal Hamiltonian by diagonalizing the following matrix:
$$
M=
\begin{pmatrix}
\frac{V_c}{2K_c} & \frac{\Delta}{4} & 0 & 0 \\\\
\frac{\Delta}{4} & \frac{V_s}{2K_s} & 0 & ... | Okay, so I'm working on this condensed matter problem involving charge and spin bosonic fields, phi_c and phi_s. The goal is to diagonalize the matrix M given in the problem. I managed to diagonalize it, and I got these new dynamical variables expressed in terms of the original fields and their conjugate momenta. But n... | To address the problem of preserving canonical commutation relations after diagonalizing the matrix \( M \), we must ensure the transformation is symplectic. Here's the step-by-step solution:
### Key Issue
The diagonalization process neglected symplectic conditions, which are necessary to preserve the canonical commut... | 31,750 | stackexchange-physics | <think>
Okay, so I'm working on this condensed matter problem involving charge and spin bosonic fields, phi_c and phi_s. The goal is to diagonalize the matrix M given in the problem. I managed to diagonalize it, and I got these new dynamical variables expressed in terms of the original fields and their conjugate moment... | [
{
"from": "human",
"value": "I am working with a condensed matter system in terms of charge and spin bosonic fields $\\phi_c$ and $\\phi_s$, respectively. I am trying to reach a diagonal Hamiltonian by diagonalizing the following matrix:\n$$\nM=\n\\begin{pmatrix}\n\\frac{V_c}{2K_c} & \\frac{\\Delta}{4} & 0 ... |
I've been trying to slog through Quantum Physics for Dummies, but can't even get past the first chapter. There's a lot of talk of Bras, Kets, and Hilbert spaces, but I feel I'm missing the mathematical underpinnings that would make it understandable.
Can anyone recommend a good book to build up my mathematical foundat... | Okay, so I need to find a good math book to understand the foundations for quantum physics. The user is struggling with bras, kets, and Hilbert spaces in "Quantum Physics for Dummies," so they need a stronger math background. Let's think about what math is involved in quantum mechanics.
First off, linear algebra is c... | To build a strong mathematical foundation for quantum physics, particularly understanding bras, kets, and Hilbert spaces, the following resources are recommended based on their clarity, depth, and practical problem sets:
### 1. **"Mathematical Methods in the Physical Sciences" by Mary L. Boas**
- **Why?** This bo... | 28,109 | stackexchange-physics | <think>
Okay, so I need to find a good math book to understand the foundations for quantum physics. The user is struggling with bras, kets, and Hilbert spaces in "Quantum Physics for Dummies," so they need a stronger math background. Let's think about what math is involved in quantum mechanics.
First off, linear alge... | [
{
"from": "human",
"value": "I've been trying to slog through Quantum Physics for Dummies, but can't even get past the first chapter. There's a lot of talk of Bras, Kets, and Hilbert spaces, but I feel I'm missing the mathematical underpinnings that would make it understandable.\nCan anyone recommend a goo... |
I was going through working of a real transformer and saw that there are two different branches of currents in the primary, one to magnetize the core I(m) and another whose flux links with the secondary I'(2). Is my qualitative understanding correct or does this mean anything else?
| Okay, so I'm trying to understand how a real transformer works, specifically the currents in the primary side. The user mentioned two different branches: one for magnetizing the core (I_m) and another whose flux links with the secondary (I'_2). Let me break this down step by step.
First, in an ideal transformer, all t... | Your qualitative understanding is correct. In a real transformer, the primary current (\(I_1\)) consists of two components:
1. **Magnetizing Current (\(I_m\)):**
This is the current required to establish the mutual magnetic flux (\(\Phi_m\)) in the core. It accounts for the finite permeability and core losses (hy... | 7,518 | stackexchange-physics | <think>
Okay, so I'm trying to understand how a real transformer works, specifically the currents in the primary side. The user mentioned two different branches: one for magnetizing the core (I_m) and another whose flux links with the secondary (I'_2). Let me break this down step by step.
First, in an ideal transforme... | [
{
"from": "human",
"value": "I was going through working of a real transformer and saw that there are two different branches of currents in the primary, one to magnetize the core I(m) and another whose flux links with the secondary I'(2). Is my qualitative understanding correct or does this mean anything el... |
I have read this great answer (first one) by joshphysics:
Are Newton's "laws" of motion laws or definitions of force and mass?
It cleared all my confusion regarding what mass actually is and how we define force. What is missing though is how has Newton reached these three observations? For example, what experiment coul... | Okay, so I need to figure out how Newton might have come up with his three laws of motion, especially the part about the ratio of accelerations being constant when two objects interact. The user mentioned the first law, but the question seems to focus more on how Newton determined that the acceleration ratio is constan... | Newton's derivation of his laws of motion, particularly the observation that the ratio of accelerations between interacting objects is inversely proportional to their masses, relied on careful experimentation and insights from earlier scientists. Here's a concise breakdown of the methods and reasoning he likely used:
... | 14,208 | stackexchange-physics | <think>
Okay, so I need to figure out how Newton might have come up with his three laws of motion, especially the part about the ratio of accelerations being constant when two objects interact. The user mentioned the first law, but the question seems to focus more on how Newton determined that the acceleration ratio is... | [
{
"from": "human",
"value": "I have read this great answer (first one) by joshphysics:\nAre Newton's \"laws\" of motion laws or definitions of force and mass?\nIt cleared all my confusion regarding what mass actually is and how we define force. What is missing though is how has Newton reached these three ob... |
I have a question on paper "https://doi.org/10.1038/nature02054".
In this paper, the CNOT gate is realized using a beam displacer for higher stability. The figure below shows a 1:1 mapping from (a) to (b). In (a), the interference where C1 meets with T0 is needed for a CNOT gate. This interference happens when the two ... | Okay, let me try to work through this problem step by step. So the user is referring to a specific CNOT gate implementation using beam displacers as described in the paper by Nature (doi:10.1038/nature02054). The main confusion seems to be about how interference occurs in the setup depicted in figures (a) and (b), espe... | The concern about temporal distinguishability due to beam displacers in the CNOT gate setup is addressed through careful optical design ensuring that the interfering paths have identical optical path lengths. Here's the breakdown:
1. **Beam Displacer Functionality**: Beam displacers are birefringent crystals that spat... | 21,213 | stackexchange-physics | <think>
Okay, let me try to work through this problem step by step. So the user is referring to a specific CNOT gate implementation using beam displacers as described in the paper by Nature (doi:10.1038/nature02054). The main confusion seems to be about how interference occurs in the setup depicted in figures (a) and (... | [
{
"from": "human",
"value": "I have a question on paper \"https://doi.org/10.1038/nature02054\".\nIn this paper, the CNOT gate is realized using a beam displacer for higher stability. The figure below shows a 1:1 mapping from (a) to (b). In (a), the interference where C1 meets with T0 is needed for a CNOT g... |
The wave equation is an example of an equation for which there are simple transparent boundary conditions. We can factorize the wave operator
$$\partial_t^2 -\partial_x^2 = (\partial_t - \partial_x)(\partial_t + \partial_x)\,.$$
The physical interpretation of this operator is that each factor is responsible for propaga... | Okay, so I need to figure out how to implement transparent boundary conditions for the Klein-Gordon equation. Let me start by recalling what transparent boundary conditions (TBCs) are. From the wave equation example, the idea is to factor the differential operator into parts that correspond to waves moving in specific ... | To implement transparent boundary conditions (TBCs) for the Klein-Gordon equation, we need to account for its dispersive nature, which complicates the factorization approach used for the wave equation. The Klein-Gordon operator \(\partial_t^2 - \partial_x^2 + 1\) does not factorize into simple first-order operators. In... | 27,650 | stackexchange-physics | <think>
Okay, so I need to figure out how to implement transparent boundary conditions for the Klein-Gordon equation. Let me start by recalling what transparent boundary conditions (TBCs) are. From the wave equation example, the idea is to factor the differential operator into parts that correspond to waves moving in s... | [
{
"from": "human",
"value": "The wave equation is an example of an equation for which there are simple transparent boundary conditions. We can factorize the wave operator\n$$\\partial_t^2 -\\partial_x^2 = (\\partial_t - \\partial_x)(\\partial_t + \\partial_x)\\,.$$\nThe physical interpretation of this opera... |
If the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then would the Gauss Law still be valid?
I infer that the $r^{-2}$ term in the Electric field comes as a result of solid angle in 3 dimensions. Would this be valid in higher dimensions? The flux would depend on the spatial dimension... | Okay, so the user is asking whether Gauss's Law would still be valid if the electric field due to a point charge varies as r^{-2.5} instead of r^{-2}. Hmm. Let me start by recalling what Gauss's Law actually states. From what I remember, Gauss's Law relates the electric flux through a closed surface to the charge enclo... | If the electric field due to a point charge varies as \( r^{-2.5} \) instead of \( r^{-2} \), **Gauss's Law would not hold** in three-dimensional space. Here's a structured explanation:
---
### **1. Gauss's Law and the Inverse-Square Dependence**
Gauss's Law states:
\[
\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\t... | 14,956 | stackexchange-physics | <think>
Okay, so the user is asking whether Gauss's Law would still be valid if the electric field due to a point charge varies as r^{-2.5} instead of r^{-2}. Hmm. Let me start by recalling what Gauss's Law actually states. From what I remember, Gauss's Law relates the electric flux through a closed surface to the char... | [
{
"from": "human",
"value": "\nIf the electric field due to a point charge varies as $r^{-2.5}$ instead of $r^{-2}$, then would the Gauss Law still be valid?\n\nI infer that the $r^{-2}$ term in the Electric field comes as a result of solid angle in 3 dimensions. Would this be valid in higher dimensions? Th... |
In 3D interacting Boson system, the condensate leads to a gapless spectrum and superfluidity. The same gapless spectrum for 2D with quasi-condensate (correct me if it is wrong ).
I am wondering if it is a necessary condition? I remember the correct way to define superfluidity is to show superfluid density non-zero. Is ... | Okay, so I need to figure out whether a gapless spectrum is necessary for having a non-zero superfluid density. The user mentioned that in 3D Bose-Einstein condensates (BEC), the condensate leads to a gapless spectrum and superfluidity. In 2D, there's a quasi-condensate with a gapless spectrum as well. The question is ... | In a 3D interacting Bose system, the condensate leads to a gapless spectrum and superfluidity. In 2D, a quasi-condensate also results in a gapless spectrum. The question is whether a gapless spectrum is necessary for a non-zero superfluid density, which is defined using Landau's formula for superfluid density, \(\rho_s... | 17,365 | stackexchange-physics | <think>
Okay, so I need to figure out whether a gapless spectrum is necessary for having a non-zero superfluid density. The user mentioned that in 3D Bose-Einstein condensates (BEC), the condensate leads to a gapless spectrum and superfluidity. In 2D, there's a quasi-condensate with a gapless spectrum as well. The ques... | [
{
"from": "human",
"value": "In 3D interacting Boson system, the condensate leads to a gapless spectrum and superfluidity. The same gapless spectrum for 2D with quasi-condensate (correct me if it is wrong ).\nI am wondering if it is a necessary condition? I remember the correct way to define superfluidity i... |
First, please tell me if following logic and assumptions are correct. The 4 forces of the universe generate all the changes in velocity of particles in the universe. The particles in the universe behave in such a way that entropy increases over time. Therefore, the 4 forces of the universe increase entropy.
But that ra... | Okay, let me try to work through this. The user is asking if their initial logic is correct. They said that the four fundamental forces cause all changes in velocity (so acceleration) of particles, and since particles behave in a way that increases entropy, then the forces must be the reason entropy increases. Then the... | Your questions touch on the interplay between fundamental forces, entropy, and the second law of thermodynamics. Let’s break this down step by step:
---
### **1. Initial Assumptions: Forces and Entropy**
Your starting logic is partially correct but incomplete. The four fundamental forces (gravity, electromagnetism, s... | 38,952 | stackexchange-physics | <think>
Okay, let me try to work through this. The user is asking if their initial logic is correct. They said that the four fundamental forces cause all changes in velocity (so acceleration) of particles, and since particles behave in a way that increases entropy, then the forces must be the reason entropy increases. ... | [
{
"from": "human",
"value": "First, please tell me if following logic and assumptions are correct. The 4 forces of the universe generate all the changes in velocity of particles in the universe. The particles in the universe behave in such a way that entropy increases over time. Therefore, the 4 forces of t... |
My textbook states Boyle's law without a proof. I saw Feynman's proof of it but found it to be too handwavy and at the same time it uses Boltzmann's equipartition theorem from statistical mechanics which is too difficult for me now.
So to state roughly what Boyle's law is, it states that at a constant temperature and m... | Okay, so I need to figure out how to prove Boyle's law using Newtonian mechanics without relying on other gas laws or statistical mechanics. Let me start by recalling what Boyle's law states: for a fixed amount of gas at a constant temperature, the product of pressure and volume is a constant. So, PV = k.
First, I sh... | To prove Boyle's law using Newtonian mechanics, we consider the relationship between the pressure exerted by gas molecules and the volume of the container. Here is a step-by-step explanation:
1. **Pressure from Molecular Collisions**:
- Pressure \( P \) is defined as force per unit area. For a gas in a container, ... | 16,985 | stackexchange-physics | <think>
Okay, so I need to figure out how to prove Boyle's law using Newtonian mechanics without relying on other gas laws or statistical mechanics. Let me start by recalling what Boyle's law states: for a fixed amount of gas at a constant temperature, the product of pressure and volume is a constant. So, PV = k.
Fir... | [
{
"from": "human",
"value": "My textbook states Boyle's law without a proof. I saw Feynman's proof of it but found it to be too handwavy and at the same time it uses Boltzmann's equipartition theorem from statistical mechanics which is too difficult for me now.\nSo to state roughly what Boyle's law is, it s... |
What is the difference between emission spectrum and diffraction pattern? I known that emission spectrum is the plot of the energy of beams in function of wavelength when I give energy to a material (--> electrons go up from a low energy level to a high energy level) and then electrons go down from a high energy leve... | Okay, so I need to figure out the difference between an emission spectrum and a diffraction pattern. Let me start by recalling what I know about each.
First, the emission spectrum. From what I remember, when you give energy to a material, like heating it or passing an electric current through it, the electrons in the... | The **emission spectrum** and **diffraction pattern** are distinct phenomena, though they both involve light and can be analyzed using tools like diffraction gratings. Here's a concise breakdown of their differences:
### **Emission Spectrum**
- **Origin**: Arises from energy transitions in atoms or molecules. When ele... | 31,928 | stackexchange-physics | <think>
Okay, so I need to figure out the difference between an emission spectrum and a diffraction pattern. Let me start by recalling what I know about each.
First, the emission spectrum. From what I remember, when you give energy to a material, like heating it or passing an electric current through it, the electron... | [
{
"from": "human",
"value": "What is the difference between emission spectrum and diffraction pattern? I known that emission spectrum is the plot of the energy of beams in function of wavelength when I give energy to a material (--> electrons go up from a low energy level to a high energy level) and then ... |
The title of my question basically is what I want to know. In Bragg's law, $nλ = 2 d \sin{\theta}$, if we want to find, let's say, $d$, and know only $\lambda$ and $n$, but not $\theta$, what could be the possible values of $d$? Does it depend on $n$? Because if we were to calculate the limits of $d$, then the smallest... | Okay, so I need to figure out the possible values of d in Bragg's law when I only know the wavelength λ and the order n, but not the angle θ. Let me start by recalling Bragg's law: nλ = 2d sinθ. Right, this equation relates the wavelength of incident X-rays, the distance between crystal lattice planes (d), the angle of... | In Bragg's law, \( n\lambda = 2d\sin\theta \), if we want to determine the possible values of \( d \) given \( \lambda \) and \( n \), but not \( \theta \), the key constraint arises from the range of \( \sin\theta \). Since \( \sin\theta \leq 1 \), rearranging Bragg's law gives:
\[
d \geq \frac{n\lambda}{2}.
\]
**Ke... | 12,797 | stackexchange-physics | <think>
Okay, so I need to figure out the possible values of d in Bragg's law when I only know the wavelength λ and the order n, but not the angle θ. Let me start by recalling Bragg's law: nλ = 2d sinθ. Right, this equation relates the wavelength of incident X-rays, the distance between crystal lattice planes (d), the ... | [
{
"from": "human",
"value": "The title of my question basically is what I want to know. In Bragg's law, $nλ = 2 d \\sin{\\theta}$, if we want to find, let's say, $d$, and know only $\\lambda$ and $n$, but not $\\theta$, what could be the possible values of $d$? Does it depend on $n$? Because if we were to c... |
Magnets's atoms are vital for the strength of its magnets. The magnetic fields are the most crowded at the pole of the magnets which is the reason why the poles have the maximum magnetic attraction.
Suppose we imagine a small button magnet and keep it on one of its faces. So, is it possible that we can adjust a it... | Okay, so the user is asking if it's possible to make a magnet where one half of its face has weaker magnetic force and the other half retains its original strength. They mentioned something about adjusting the atoms or using a material to block part of the magnetic field. Let me break this down.
First, magnets work be... | Yes, it is possible to create a magnet where one half of its face exhibits weaker magnetic attraction while the other half retains its original strength. Here are the primary methods to achieve this, along with their feasibility:
### 1. **Magnetic Shielding**
- **Concept**: Use a high-permeability material (e.g.,... | 35,114 | stackexchange-physics | <think>
Okay, so the user is asking if it's possible to make a magnet where one half of its face has weaker magnetic force and the other half retains its original strength. They mentioned something about adjusting the atoms or using a material to block part of the magnetic field. Let me break this down.
First, magnets... | [
{
"from": "human",
"value": "Magnets's atoms are vital for the strength of its magnets. The magnetic fields are the most crowded at the pole of the magnets which is the reason why the poles have the maximum magnetic attraction. \nSuppose we imagine a small button magnet and keep it on one of its faces. ... |
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