instruction stringlengths 31 24.3k |
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I grasped my head around this topic a lot and I want to ask if my interpretation of the problem is now correct in the most clear way.
I'm trying to measure time dilation using the spacetime interval but adding the ingredient of the proper time, the measurable time, being compared between two observers (this part is usu... |
This feels like it could be a undergrad/grad-school quantum mechanics course level problem, or potentially something pretty interesting. I'd be happy with either answer, but I don't know which one is true.
Consider spin-1/2 quantum spins, and let us denote the Pauli operators as $X_i$, $Y_i$, and $Z_i$ etc. for the $i$... |
Why is the speed of light $c$ used to determine the value of permittivity in free space?
|
I recall Feynman explaining time dilation in a moving spacecraft using a clock which counts reflecting light. As I understand it, to a stationary observer the path the light takes is longer than it is to the observer aboard the ship and this accounts for slower clocks and indeed all processes, so this causes time dilat... |
I am trying to understand the concept of waveguiding, scattering, and total internal reflection. I have a question regarding the optical waveguides.
Let's consider an optical waveguide transmitting light via total internal reflection. If one takes its photo, and if the color of the guided light can be easily seen on th... |
Assume we have a point charge $Q$ moving with velocity $\vec{v}$ with respect to an observer at rest and is in the presence of magnetic field $\vec{B}$. $\vec{B}$ and $\vec{v}$ are perpendicular to each other.
For the observer at rest, the charge would start doing a circular motion in the plane which contains the veloc... |
If I understand Roger Penrose's Conformal Cyclic Cosmology correctly, the previous eon comprised a universe conformal to ours with a smaller size and time-frame, at a finite point in the past.
If we add up the time duration of the infinite previous eons in the CCC model, do we arrive an asymptotically finite time in th... |
Imagine an astronaut is practicing with a standard official basketball on an orbiting space station. Assume everything is in free fall so I wonder would it consume less or more effort to dribble compared to at 1g?
|
backscattering is already part of Compton scattering for X-rays.
Compton scattering is directly proportional to the density of the material i.e. as the density increases as the Compton scattering increases.
This should suggest that high-density materials would backscatter more radiation than lower-density materials, bu... |
I am very well aware that chemical potential or concentration is typically said to be the reason for molecular diffusion but consider a case,
We have a cube filled with gas containing minor amount of nitrogen, say nitrogen is a solute and other molecules are solvents, opposite faces of cube are maintained at different ... |
I have this partial differential equation which models the diffusion of a contaminant substance in a 1-dimensional river. The terms represent the following:
The first term represents the diffusion effect with the diffusion constant $D$
The second term represents the convection effect with a flow rate $v$
The third ter... |
Let $t$:time, $r$:distance, and $u=t-r$.
Since any massless particle should propagate along u=const. , we need to change the asymptotic infinity of a massless scalar from time infinity to null infinity. This implies that the quantization of a massless scalar must be adjusted accordingly. For example, I think the LSZ fo... |
Suppose there are two protons ( as we have in LHC). One proton is coming from +ve z axis and other from -ve z axis toward the collision point(origin). Both proton collide with equal velocity. Now as collision happen at very high velocity. So lot of particles will be produced due to various scattering processes.
My ques... |
There are three blocks - a big block (C) above a horizontal surface that is smooth. A block (A) of mass m is resting on block C, and is also connected to another block (B) of mass m through an ideal string running through a pulley (the pulley is fixed on the upper right corner of the block C).
The question is to find t... |
My textbook has the following question:
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $ \sigma/2\epsilon_0$ $\hat{\mathbf{n}}$, where $\hat{\mathbf{n}}$ is the unit vector in the outward normal direction, and $\sigma$ is the surface charge density near the... |
If I warmed two cups of water from 20 °C to 90 °C, one in a microwave and one over a flame. Is there a test that could be performed to determine how each cup was warmed? Are there residual effects from different types of "warming"? We can assume 30 seconds pass after removing from the heat sources before testing.
Do no... |
For anyone who has studied the book 'An Introduction to General Relativity Spacetime and Geometry' by Sean Carroll, can I study chapters 1 to 4 (which do differential geometry & field equations it seems) and then skip straight to chapter 8 which is the cosmology section? Or must I study the chapters in between which ar... |
In all textbooks on quantum optics I can reach (Scully, Leonhardt, Walls, etc), the Glauber-Sudardhan $P$-representation $P(\alpha)$ is introduced in the following two ways:
Fourier transform of $\mbox{Tr}(\hat\rho \mbox{e}^{\alpha \hat a^\dagger}\mbox{e}^{\alpha ^*\hat a})$.
"Diognal element" of density operator in t... |
I am currently investigating the response of a specific system to an external electric field and have encountered a question that has puzzled me for a long time.
Consider a system subjected to alternating electric fields represented by $\vec{E}(t) = \int \rm{d} \omega \vec{E}(\omega) e^{i \omega t}$. Expanding the ener... |
This is the motivation behind my question; what would the longest line therein translate into on a $p$-$V$ curve? It is evident that the horizontal line is an isothermal process and the vertical line is an adiabatic (isentropic) process. But what kind of process is represented by the third line?
|
I was looking at this answer which eventually stated this about the proper acceleration (when $\vec v$ is parallel to $\vec a$):
$$
\vec \alpha =\gamma^3 \vec a = \gamma^3 \dfrac{d\vec v}{dt}=\dfrac{du}{dt}=\dfrac{d}{dt}\dfrac{d\vec x}{d \tau}
$$
Now, I'm programming a relativistic integrator and to do this I used the ... |
Consider the action $S = \int dt \sqrt{G_{ab}(q)\dot{q}^a\dot{q}^b}.$
Now for computing the Euler-Lagrange equations, we need the time derivative of $\frac{\partial L}{\partial \dot{q}^c} = \frac{1}{\sqrt{G_{ab}(q)\dot{q}^a\dot{q}^b}}G_{dc}(q)\dot{q}^d$.
Do we also need to take the time derivative of the denominator? I... |
In this reaction:
$$\require{mhchem}
\ce{^6_2He ->{^6_3Li}}$$
in the initial state there are two neutrons in the $1p_{3/2}$ that coupled (for the Pauli's principle) with antiparallel spin, so $J_i=0$, when the He decay the neutron transform in proton that occupy the same state but with parallel spin, so $J_f=1$. This r... |
I am currently working on an applied maths project in which I have modeled the forces at play when a rollercoaster travels down a slope and comes to a stop over a distance $d$ with the use of brakes. For my final challenge I need to figure out the force applied by the brakes when the rollercoaster is on the flat plane.... |
I was reading Schwartz's QFT, I came across a lagrangian density,
$$ \mathcal{L} = -\frac12 h \Box h + \frac13 \lambda h^3 + Jh ,\tag{3.69} $$
Calculating the Euler-Lagrange equation,
$$ \partial_{\mu} \frac{\partial \mathcal{L}}{\partial(\partial_{\mu}h)} - \frac{\partial \mathcal{L}}{\partial h} = 0 \tag{1}, $$
the e... |
Suppose I want to solve for some Langevin dynamics. Let us consider a single particle:
$$m\ddot {\mathbf r}=-\eta\dot{\mathbf r}+\mathbf F$$
where $\mathbf r$ is position, $\eta$ is viscosity force and $m$ is mass. Usually $\mathbf F =\mathbf F(t)$ (only depends on time) is some Gaussian random force. However, is there... |
I am studying about the center of momentum from Wikipedia. It is defined as the frame in which the total linear momentum of the system of particles vanishes and that the center of mass is but a special case of it. There it is given the following:
If $S$ is the laboratory frame and $S'$ be the center of momentum frame. ... |
In Polchinski's String Theory volume 2, appendix B, on page 433 (in the section on Spinors and SUSY in various dimensions, specifically the subsection on Majorana spinors) he says:
"It follows from eq B1.18 that the spinors $\xi$ and $B^{-1}\xi^*$ transform in the same way under the Lorentz group, so the Dirac represen... |
I am wondering if one can extend the radiography outside the visible range (ordinary cameras), X-ray band (x-ray photos), IR-band (infrared images), and microwave region. Can one construct imaging units that capture images in the other regions such as the lower-energy range of radiofrequencies?
Thanks
|
I've recently been watching this lecture series on Condensed Matter. The part I'm currently on covers band theory for the tight-binding model in a few different scenarios. We covered two different models in one-dimension. The first had a Hamiltonian given by
$$H = -t \sum_i c_i^\dagger c_{i+1} + c_{i+1}^\dagger c_i,$$
... |
When two balls collide directly, the impulse of the collision acts along the line of centers, so the momentum along this direction is not conserved. Therefore, I can only use the conservation of momentum perpendicular to this direction:
But in this question (A is twice mass of B):
I had to use conservation of momentu... |
This question is for the review portion of a thermodynamics class:
A small hot-air balloon has a volume of $15.0 m^3$ and is open at the
bottom. The air inside the balloon is at an average temperature of
$75^{\circ}C$, while the air next to the balloon has a temperature of
$24^{\circ}C$, and a pressure, on average, of... |
Every object wants to reduce its potential energy, but why is that so? Does it have an explanation, or is it just a law we accept?
|
And, here's the solution my teacher gave: read from top to bottom (and note that the angle $θ$ is the instantaneous slope at that point) and ignore the green highlighting, I apologize for the poor picture quality.
According to his answer, no matter what the path of the particle is, as long as it is acted upon by an e... |
Can a Strontium target be deposited on a substrate utilizing asymmetric-bipolar pulsed-dc magnetron sputtering?
|
I know that the Gaussian integral over complex vectors $\mathbf{u}=(u_1,\dots u_N)$, where $u_i$ are complex valued, is
$$\int \mathcal{D}[\mathbf{u}^*,\mathbf{u}] e^{-\mathbf{u}^* A\mathbf{u}+\mathbf{a}^*\cdot\mathbf{u}+\mathbf{u}^*\cdot\mathbf{b}} = \pi^N \mathrm{det}(A^{-1}) e^{-\mathbf{a}^* A^{-1} \mathbf{b}}$$
Now... |
We have a system of two unequal opposite point charges, of which $q_2$ is smaller and $d$ is the distance between charges. There is an equipotential spherical surface of potential $V=0$ that encloses a charge of lesser absolute value. The task is to find parameters of that spherical surface, or more precisely circle, s... |
First of all, I understand that this will be mostly a mathematics questions. However, I'm asking this in the context of General Relativity, which comes with its own language, conventions and applications. Furthermore, understanding diffeomorphisms and coordinate changes is one of the most important theoretical aspects ... |
For a U(1) symmetric Hamiltonian, the current operator can be derived simply by taking the time derivative of the density operator. I wonder how can one obtain a supercurrent operator for U(1) broken Hamiltonian like Bogoliubov de Gennes Hamiltonian? I am only asking about the continuum limit.
|
There is something that is confusing me about the Stoner-Wohlfarth model. Looking at the wiki page, one sees this picture for the hysteresis loop:
The angles denoted are the angles between the field and the easy axis. Notice how the larger $\theta$ is, the smaller $m_h$ is at $h=0$. But now here is the condition for t... |
I recently enrolled in a structural dynamics course, and am frustratingly trying to grasp the so called 'D'Alembert's principle'. I have probably now checked close to 10 structural dynamics books about the subject, and essentially every single one just states the principle, as 'adding inertia forces', followed by doing... |
Let's consider an ideal gas that expands in vacuum and it is thermally isolated from the surroundings. Since it is isolated, it does not exchange heat with the exterior $Q=0$. Since it is expanding against the vacuum, it does no work $W=0$. From the first principle we get that the change in internal energy is zero.
$$\... |
I am supposed to find the proper time of a particle whose worldline is given by:
$$\begin{align}
x(t) &= \frac{3}{2} a t^2\\
y(t) &= 2 a t^2\\
z(t) &= 0
\end{align}$$
where $a = const$ and $0 \leq t \leq t_0$ for some $t_0$.
I found $\gamma (t) = \frac{1}{\sqrt{1-\frac{25 a^2 t^2}{c^2}}}$.
To find the proper time $\tau... |
In the schoolbook physics example of a generator, the wire loop rotating in a constant (both in space and time) magnetic field, we can measure a non-zero voltage between the loop's two terminals due to the EMF. Since the magnetic field is constant in time, by the Maxwell-Faraday equation the rotation of $E$ vanishes:
$... |
My question is about the transition from discrete to continuous quantum mechanics, which amounts to losing the restriction of bounded compact operators on a Hilbert space. When one introduces these kind of operators into quantum mechanics, tipically through the momentum and position operators, it is costumary to write ... |
Consider a particle of mass $m$ attached to a massless string (fixed at one end) in a lift going down with acceleration $g$. What minimum velocity $v_0$ should be given to it so that it performs complete circular motion?
Since it is going with an acceleration $a$ downwards the tension in the string is 0, so will it reg... |
Lets say that a car engine can output a maximum power of $P$. Now initially, the car starts from rest would have zero velocity.
Now the tires start slipping and a force of $f_k = \mu mg$ will act on the car accelerating it forward where $\mu$ is the friction coefficient between the ground and the tires.
Now the car sta... |
I'm trying to derive the following equation using a Riemann sum formulation only $$ \frac{d}{d t}e^{A(t)} = \int_0^1 ds \,\,\,\,e^{sA(t)}(\frac{d A(t)}{dt})e^{(1-s)A(t)}. $$
The book is using einstein notation on the indices. What I've done so far is make sure I understand how to take the derivative of $e^{A(t)}$ for m... |
I need help!
I'm trying to calculate the Power Spectral Density of a quantum operator ($\delta \hat{n}(t)$) given by:
$$ \delta \hat{n}(t) = A(t)\delta\hat{a}(t)+A^{*}(t)\delta\hat{a}^{\dagger}(t) $$
$\delta\hat{a}(t)$ is a wide-sense stationary process and $A(t)$ is a complex time-dependent deterministic factor. To c... |
Is there any kind of way/equipment that can change the air refractive index? For example, a mirage is hot air refracting light in a certain way, making it look like water.
The best I could think of were using a heat gun (basically a hair dryer), a water humidifier or an infrared laser. Aside from the water humidifier, ... |
I am using a gyro-kinetic simulation tool 2103.16457 which solves the 3D Fokker-Planck equation for the electron population in tokamak plasmas and evolves plasma parameters self-consistently. In many cases, there can be relativistic electrons (runaway electrons) in these populations. I use the code in 1D space and 2D m... |
The more precisely we want to locate a particle in space, the more energy we will need to expend. does this statement have a mathematical formulation? When studying quantum mechanics, I often found this statement in textbooks where examples of the uncertainty relation are given: the Heisenberg microscope, when estimati... |
I see that Nagaoka magnetism is a low-temperature quantum effect from "minimizing" the energy of the system, but that explanation, while erudite, doesn't really explore any specifics - nearly all low temperature quantum effects happen as the system finds a lower energy state and lots of those have nothing to do with ma... |
I wanted to ask for book or literature in general recommended for control volumes in Fluid Mechanics. Particularly about non inertial and deformable CV which is a topic that basic Fluid Mechanics books tend to explain shallowly.
|
Imagine we have a circuit with an extremely long wire (like some light years). Usually, the electric field from the battery would cause electrons in the wire to move thus creating a magnetic field and the energy would be transported through the Poynting vector from EM waves. But when the wire is too long, the battery’s... |
I am currently studying fluid mechanics and one of the most important concepts we come across is that of shear stress. I understand that it is a force that is acting on the fluid in a direction that is tangential to the surface, as opposed to normal stress that is perpendicular to the surface. I can perfectly understan... |
How did I get here?
While drafting my question, I found this very similar question on our site.
Three days ago, I happened upon the concept of supertranslations and superrotations in General Relativity while reading the comment section of a well-known blog. I decided to try to understand this idea. I even opened up a f... |
For $$I_1=\int \sqrt{-g}C_{abcd}C^{abcd}d^4x,$$ where $C_{abcd}$ is the Weyl tensor. If we neglect the Gauss-Bonnet term this can be reduced to $$I_2=2\int \sqrt{-g}(R^{ab}R_{ab}-\frac {1}{3} R^2)d^4x.$$ My question is, does the variation of $I_1$ yield the Bach tensor or the variation of $I_2$ give the Bach tensor? I'... |
So a negatively charged sphere and a sphere S which has been attracted to it(the electrons have been repelled to the right, and the positive charges are in its left side). They are now "stuck" to each other and are touching. An earth wire is touched to S. I understand that the negative charges in the right side of S w... |
I'm trying to derive the following equation using a Riemann sum formulation only
$$\frac{d}{d t}e^{A(t)} = \int_0^1 ds \quad e^{sA(t)}(\frac{d A(t)}{dt})e^{(1-s)A(t)}$$
What I've done so far is make sure I understand how to take the derivative of $e^{A(t)}$ for matrix $A$ and continuous parameter $t$:
$$\frac{d}{dt}e^{... |
A map from $(q,p)$ to $(Q,P)$ is called an extended canonical transformation if it satisfies
$$
\lambda(pdq-H(q,p,t)dt)-(PdQ-K(Q,P,t)dt)=dF
$$
Here, to include the change of $t$, let us use
$$
\lambda(pdq-H(q,p,t)dt)-(PdQ-K(Q,P,t')dt')=dF
$$
instead.
Time reversal map is defined by
$$
t'=-t,\quad Q(t')=q(t),\quad P(t')... |
This is a simplified version of a recent question I asked. My hope is that this simplified version will be easier to tackle. The motivation behind both of these questions is roughly to ask "Given that a Hamiltonian acts simply on each state in some subspace, can it be identified with a single simple operator when actin... |
I came across this question which asked about the reading of the ammeter and voltmeter. I tried to solve it and deduced that the centre and right resistors are in series while the left one is in parallel, thinking that this is an ideal case and that the resistance of the ammeter and voltmeter in an ideal case is zero ... |
In class 11 physics ncert
Reynolds number
Re= ρA(v^2)/ (ηAv/d)
Where inertial force = ρA(v^2)
And viscous force is = ηAv/d
In the book d is described as dimensions of the pipe
But they don't mention what A is at all.
As far as I understand the only way ρA(v^2) is the inertial force if A is the cross-sectional area of t... |
Impossibly hypothetical, but to communicate the question: when the universe "ticks" a plank second, what does a particle do? I'd imagine the natural conception that it moves from position a to position b instantly, like a frame in a movie, is wrong. If I were "watching" the particle at the time, what would I "see"? Wha... |
A Hamiltonian system is a dynamical system driven by a Hamiltonian $H$, i.e.
$$ \dot{q}=\nabla_p H,~~~~ \dot{p}=-\nabla_q H. $$
These systems have nice properties like being symplectic as well as the flow being a semigroup.
Recently, after overhearing a conversation, a non-science family member asked me what a Hamilton... |
Consider the following general setup:
Assume have a chain of atoms (of mass $m=1$) in one dimension interacting with their nearest neighbor through a interaction potential $U$, and which are in an external potential $V$. Assume that the interparticle potential is such that the particles do not cross each other and so ... |
A water tank has two pipes installed on the outside near the bottom which point upwards towards the open top of the tank. One is a nozzle the other a diffusor. According to the hydrostatic pradox, they shoot the water out to the same height as the water level in the big tank. How come? Why doesn't the law of continuity... |
We’re told the universe was very hot and energetic immediately after the Big Bang, and just shows H2O was present early on. Yet, it is not considered to be a primordial element. Why is that?, and what theories might suggest that H2O formed from Big Bang nucleosynthesis?
|
Why the voltage across an ideal pn junction diode remains 0.7 volts, even when the applied voltage exceeds 0.7 volts? Shouldn't it be the applied voltage minus the 0.7 V?
|
I am studying a bit about statistical mechanics for a course at my university.
My book introduces first the Boltzmann entropy $S = k_b lnW$, and then the Gibbs one, $S=k_b \sum p_i lnp_i$, in what seems a derivation from the previous formula. I was confused about the meaning of this last one, in particular my book in t... |
Is it determined that light is a wave or a particle or it still exists as a dual nature?
because young's experiment said that light is a wave but still I hear people saying that light shows both wave and particle nature.
please answer my question in a layman's language as I am still not introduced to technical terms.
|
I want to understand why (what is the mechanism behind) lowering the time to echo (can we actually have T1-weighted Zero Time to Echo images) increases the Signal to Noise Ratio in (nuclear) Magnetic Resonance Imaging and why increasing the time to repetition decreases the Signal to Noise Ratio (can we have Zero Time t... |
I've been looking up the history and evolution of the seven base units and am currently checking out the ampere. What I've found is that 1A is defined as the current in a wire which would experience a force equivalent to this formula:
$$F=\frac{\mu_0 I_1 I_2l}{2\pi r}$$
which is $2\times 10^{-7}$N when all other values... |
While I acknowledge that this topic has been discussed extensively, and I've read numerous similar questions along with their respective answers, I am still struggling to comprehend why all the eigenvectors of the harmonic oscillator are non-degenerate.
My confusion stems from a particular proof presented in the book "... |
The context is that there is a charge $q$ moving with velocity $\vec{V}$ in magnetic field $\vec{B}$. The angle between $\vec{V}$ and $\vec{B}$ is given as $30^{\circ}$
The formula to calculate the radius helical path of the charge is $r= mV / QB$.
My question is, do I consider the perpendicular component of Velocity i... |
I have two questions:
When dealing with simple DC circuits, it is often said that the electrons in the wire move because the charge density of the surface charges decreases. Is that due to the fact that the amount of electric field of the battery decreases with distance?
I don't understand why the potential differenc... |
I'm trying to expand an arbitrary operator using creation/annihilation operators following this post, where $|m\rangle \langle n|$ is expressed as
$$
|n\rangle \langle m|~=~\sum_{k\in\mathbb{N}_0} c^{nm}_k (a^{\dagger})^{n+k} a^{m+k},
$$
and $c^{nm}_k$ is solution of
$$
\delta_k^0~=~\sum_{r=0}^k c^{nm}_{k-r} \sqrt{ \f... |
In Van der Pauw method, two resistances are measured in orthogonal directions to each other. These are used to calculate sheet resistance from the Van der Pauw equation. Why is it that resistances are measured specifically in mutually orthogonal directions? I tried finding an answer in different papers, online sources ... |
This is the question I get confused:
Initially, the system of objects shown in Figure P5.93 is held motionless. The pulley and all surfaces and wheels are frictionless. Let the force F be zero and assume that m1 can move only vertically. At the instant after the system of objects is released, find
(a) the tension T in ... |
There is a certain sign mismatch between the time translation operator and time evolution operator in quantum field theory which I hope someone can illuminate.
From my understanding, a Poincaré transformation is a transformation:
$$x \to x' = \Lambda x + a,$$
for some Lorentz $\Lambda$ and vector $a$ . The transformed... |
Why does a body(especially cylindrical) when immersed completely in liquid (density of liquid >density of object) floats back up to the surface of water in horizontal Orientation regardless of it's initial orientation underliquid.is this because of less friction on surface of water and some air resistance? Centre of ma... |
In equation (3.24) of QFT and the Standard Model by Schwartz, he uses the notation $\frac{\delta \phi}{\delta \alpha}$ in the context of Noether's theorem(s) and their applications. I did my Master's dissertation on Noether's theorem last year, and I often saw this notation being used, without any clarification on the ... |
Despite Chen-Ning Yang's objections, the Circular Electron Positron Collider (CEPC) project is progressing. The CEPC research team officially released its Technical Design Report (TDR) for the accelerator complex on December 25, as detailed in the CEPC Technical Design Report, with the first operation anticipated aroun... |
I was studying quantum information from Nielsen and Chuang's book and I got a little bit confused because sometimes they use the terms "spectral decomposition" and "orthonormal decomposition" for what seems to me to be the same thing.
Correct me if I'm wrong but the spectral decomposition of, let's say, the density mat... |
Suppose, we have an arrangement as shown in the diagram(same fluid):
Pressure at point A is Pa= Atmospheric Pressure (Patm). Similarly, Pressure at point C is Pc = Patm.
We have been told that pressure at same horizontal level within same static fluid, is equal. Therefore, Pressure at point B (Pb) should also be equal... |
I was trying to solve the following problem and I realised that there are some things I do not understand:
An atom with only one electron and mass $M$ is at rest. Its electron is in an excited state with energy $E_i$. At some point, is goes to its ground state, whose energy is $E_f$, emitting a photon that moves in th... |
My question is going to be a bit sketchy so please forgive me.
Imagine the following experiment:
-We have a particle that is in a superposition of space, such that $\psi(x)$ has the form of two gaussians at $p_0$ and $-p_0$(suppose the gaussians are concentrated enough around their center).
-Now we make the two gaussi... |
If we apply potential difference through wire we know that there is an electric current which is the flow of electrons.I want to know how do electrons move do they move within wire like in the picture below or do they move only through its surface? . If it moves only through its surface why is there n which is number o... |
Two objects of varying mass, but of the same surface area, are dropped from the same height. Which will strike the ground earlier?
|
Consider a rectangular wire frame with a sliding wire of length l. When the frame is dipped in soap solution, a soap film is formed over it. Assume that there is no friction between the arms and the sliding wire and let S be the surface tension. Now, a force S×2l is applied to pull the wire outwards so as to increase t... |
Neutrinos are only observed to have a left handed chirality and anti neutrinos are only observed as having a right chirality. In some beyond the standard model hypotheses neutrinos of right chirality are modeled as being much bigger than left chiral neutrinos with a potential mass as large as $10^{15}$ GeV, if these ev... |
When we are defining the entropy we have been used two isolated system not a heat bath with a small system, to ensure that entropy is defined as an energy variable dependent. My question why is the entropy defined as (E, V, N) variables not the (T, V, N)?
The same as for Helmholtz free energy is defined as (T, V, N) va... |
Given a smooth (differentiable) manifold $M$ and intervals $I_1,I_2\subset\mathbb{R}$, two curves
\begin{equation}
\gamma_1:I_1\to M\quad\text{and}\quad\gamma_2:I_2\to M~~,
\end{equation}
are tangent at $p\in M$ if there exists $\lambda_0\in I_1\cap I_2$ such that
\begin{equation*}
\gamma_1(\lambda_0)=p\quad\text... |
I am still confused about how HBT interferometry for star angular size works after reading about it on the internet and in papers. Mathematics usually does not help before I do not catch the way the experiment is done in hardware and what type of data is obtained.
Let us consider the image below.
Can someone explain s... |
Solid, liquid, and gas are all states of matter. However, I have never seen a rigorous definition of what a state of matter is. Is there such a definition somewhere? I would like to see such a definition.
|
The opposite is quite common such as EWSB, SUSY or GUT. Is there any example where a certain symmetry emerges from a low energy effective theory but is not present in the high energy theory?
|
I know up to some degree how spinfoam models and LQG work, but there are some details that i still miss since i have still a naif knowledge.
In the literature it as often said that an open problem is the luck of a proof that those are equivalent theories.
Of course one is concerned with a 3D Hamiltonian description whi... |
I am having troubles understanding whether $$\vec F=-\nabla U_{effective}$$ or $\vec F=-\nabla U$ with $$U_{eff}=U(r)+\frac{1}{2}\frac{L^2}{\mu r^2}$$ being $\mu=\frac{m_1 m_2}{m_1+m_2}$ the "reduced mass" of a 2-body-problem. My teacher says it is the $\vec F=-\nabla U(r)$ the one that is the integral of the force but... |
Some nonlinear optical materials, such as for example glass doped with As2Se3 or As2S3, are able to generate supercontinuum if a single mode laser pulse, in range of a few watts, is launched into the glass. However, will the supercontinuum be also generated if a continuous wave of a low power (a few miliwatts) is launc... |
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