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28583 | What is negative about negative energy states in the Dirac equation? | This question is a follow up to What was missing in Dirac's argument to come up with the modern interpretation of the positron? There still is some confusion in my mind about the so-called "negative energy" solutions to the Dirac equation. Solving the Dirac equation one finds the spectrum of allowed energies includes b... | What is the physical interpretation of negative energy solutions in the Dirac equation, and how does the concept of the Dirac sea reconcile these solutions with observable particle behavior in quantum electrodynamics (QED)? | 36,055 | cqadupstack-physics |
47328 | Reference request for the Aharonov-Bohm effect | I am looking for a good reference to an online source or book, on the magnetic Aharonov-Bohm effect. I have read the appropriate sections from the book by Griffiths and Ballentine, and still haven't understood it properly. The reference should also contain topological arguments. I have done QM on the order of 4 chapter... | What is the quantitative difference in the magnetic vector potential experienced by a charged particle in a region with a non-zero magnetic field and in a region where the magnetic field is zero, as described by the Aharonov-Bohm effect? Please explain how this difference manifests in the interference pattern observed ... | 17,178 | cqadupstack-physics |
131769 | How do gauginos and scalars gain masses after gauge-mediated symmetry breaking? | In the minimal-GMSB model, the messenger fields transform under the MSSM gauge group and connect a so-called hidden sector to the visible sector. These meesenger fields (left-handed chiral supermultiplets in this case) break SUSY and introduce the soft terms in the MSSM. I do not understand how to integrate out these f... | In the minimal-GMSB model, how do the masses of gauginos and scalars in the MSSM arise from the integration of messenger fields, specifically through one-loop and two-loop contributions? Can you provide a quantitative example or reference that illustrates this process? | 15,702 | cqadupstack-physics |
34440 | Dimensions of obstacle needed to block light? | How many dimensions are required minimum for an object to block light? in 1d I doubt it's possible. in 2d I think it could do it if only the light was limited to a dimension perpendicular to the 'thickness' dimension in 3d I think it could do it no matter what dimension the object was looked at in. Clarification: 3d ->... | What is the minimum number of dimensions required for an object to effectively block light in an n-dimensional space, and how does this compare to the blocking properties of 1D, 2D, and 3D objects? | 35,967 | cqadupstack-physics |
21038 | Identifying hue, brightness and chroma of color and reaction time | If someone knows how identify hue, brightness, and chroma of color, please let me know. I am a PhD student at Educational Linguistics UNM. | What are the quantitative relationships between hue, brightness, and chroma in color theory, and how are they measured using the CIE color space? | 3,944 | cqadupstack-physics |
72941 | RGEs of the MSSM - problems with Mathematica | I'm having some troubles with the trilinear soft couplings of the MSSM RGEs. I've used the ones written in Martin's supersymmetry primer and I run them using mathematica, if I do so without taking into account the soft trilinear terms (by putting them to zero at all scales and not considering that they get generated ev... | What are the conditions under which the trilinear soft coupling terms in the MSSM renormalization group equations can significantly alter the behavior of gauge coupling constants and Yukawa couplings, and how can errors related to dimensionality in Mathematica be resolved when simulating such systems? | 11,272 | cqadupstack-physics |
1572 | How to determine the (n,m) dimensions of a carbon nanotube? | I've been reading about nanotubes lately, and I keep seeing the $ (n,m) $ notation. How does this describe a nanotube's structure? How do I determine which is $n$ and which is $m$ ? I'm familiar with matrix notation referring to rows and columns, but I couldn't connect it with the nanotube structure which is, albeit pr... | What is the relationship between the indices \( (n,m) \) in the notation for carbon nanotubes and their physical properties, and how can you calculate the diameter of a nanotube given \( n \) and \( m \)? | 14,585 | cqadupstack-physics |
79632 | Why an extra path difference of wavelength/2 is added when light reflects? | In my textbook it is given that in thin film interference a path difference of wavelength/2 is added up to the reflected light from the upper surface. But, how does that happen? No physics textbook of mine gave an answer on this. So, please help. My thoughts:I know that reflection is actually electrons absorbing and re... | In thin film interference, when light reflects off a boundary where the second medium has a higher refractive index, why is there a phase shift of λ/2 (180 degrees) introduced for the light reflecting from the upper surface of the film? Can you explain the underlying physics and how this affects the path difference for... | 2,615 | cqadupstack-physics |
40886 | Could someone jump from the international space station and live? | Felix Baumgartner just completed his breathtaking free-fall skydiving jump from $120,000\,\text{feet} = 39\,\text{km}$ above the Earth, breaking the speed of sound during the process. I was wondering if the next step could be jumping from the international space station. The person would have to overcome the orbital ve... | What would be the terminal velocity of a human in free fall from the International Space Station, and what factors would influence the survivability of such a jump? | 34,537 | cqadupstack-physics |
69601 | Suggestions of a non-linear example for a small research project on numerical solution of ODEs? | I'm a first year undergrad and I'm doing a small research extension on numerically solving ODEs. I have done the main ODE course at my university, as well as physics. The second part of the project constitutes using a method (linear multistep in my case) to solve a system of our choice and writing a report about it. I ... | Can you provide an example of a nonlinear ordinary differential equation (ODE) that describes a fluid dynamics problem, preferably one that is relevant to plasma physics? | 26,039 | cqadupstack-physics |
13606 | Does rotational energy have effect on gravity/metric? | Intuitively, if energy can be stored in rotational motion, it has to obey $E=mc^2$. Does rotation of typical stellar-sized objects - BHs, pulsars, binaries - have measurable effect on their overall gravity? (I'm not talking about nearby effects, like frame dragging described by Kerr metric, the effect on measurements f... | How does the rotational energy of a stellar-sized object, such as a black hole or pulsar, influence its gravitational effects on surrounding objects at a measurable distance, given the principles set forth by relativistic physics? | 29,362 | cqadupstack-physics |
95847 | How do I calculate the work done by snow when stopping a person from falling from a plane? | I have the following data: Assume a man falling from a plane from a height of 370 m ($=h$) high (Straight down). The man falls into a pile of snow and creates a 1.1 m ($=d$) deep crater. The man has a mass of 88kg ($=m$) and his velocity right before hitting the snow was 45 m/s ($=v$). What is the amount of work done... | Calculate the amount of work done by the snow when stopping a man with a mass of 88 kg who falls from a height of 370 m and creates a 1.1 m deep crater, reaching a velocity of 45 m/s just before impact. | 15,023 | cqadupstack-physics |
72022 | Show that charge conservation $\partial_\mu J^\mu = 0$ implies global U(1) invariance? | The $U(1)$ global gauge symmetry of electromagnetism implies - via Noethers theorem - that electric charge is conserved. Actually, it implies a continuity equation: $$ \psi \rightarrow e^{i\theta}\psi \quad\Rightarrow\quad \partial_\mu J^\mu = \frac{\partial}{\partial t} \rho + \vec\nabla\cdot\vec j = 0 $$ Is it possib... | How can I demonstrate that the $U(1)$ symmetry is implied by the continuity equation $\partial_\mu J^\mu = 0$? Specifically, could you provide a derivation that links the conservation of charge to this symmetry, possibly through Noether's theorem? | 10,286 | cqadupstack-physics |
127309 | Why does blowing on hot coffee cool it down? | And will it cool off faster if you blow across the top of the cup or directly into the coffee? Does it have to do with the fact that when you blow across the top of the cup the velocity of the air increases which causes an area of low pressure above the cup, resulting in steam from the coffee to be forced up and out of... | In an experiment, you have two identical cups of hot coffee at the same temperature. In one case, you blow directly into the coffee, and in the other, you blow across the top of the cup. Which method results in a greater rate of cooling for the coffee, and what are the underlying physical principles that explain this d... | 33,064 | cqadupstack-physics |
101754 | Information about newton's third law | Well I am still small student of physics, but as far as I know, Newton's Third Law states that, > "For every action there is equal and opposite reaction." Now let me tell you how I understood this, Suppose there are two bodies A & B initially at rest (w.r.t the earth), now if A makes collision with B, of course there w... | In a collision between two bodies A and B at rest, if the force exerted by body A on body B is \( F_{ab} \), what is the force exerted by body B on body A according to Newton's Third Law, and how does static friction influence the forces acting between the two bodies before they begin to move? Consider the forces invol... | 21,715 | cqadupstack-physics |
92262 | Moment of weight of leaning beam |  Having trouble with a FBD moment. The problem is: > _How big can the force couple C (looks like a G in the pic) be in order for > the disk to not spin? The disc has mass m and the beam also has mass m. All > other variables are given._ > > _Let point A... | In a system where a beam of mass \( m \) is tilted at an angle \( \alpha \) and is resting on a disc of mass \( m \), how do you determine the point at which the center of mass of the beam is located, and how does this affect the moment equilibrium about the bottom point of the disc (point A)? Assuming the distance fro... | 24,573 | cqadupstack-physics |
129427 | What physical phenomenon occured in this experiment? | I noticed a strange behavior of my experiment. I have a glass container with a fully saturated solution of CuSO4, which I use to grow CuSO4 crystals, by waiting for the water to evaporate. Recently I noticed that crystals were build above water surface and outside of the container. After some time I noticed that half o... | What physical phenomena could explain the behavior of a saturated CuSO4 solution creeping out of its container, particularly in relation to capillary action and the properties of the solution? Additionally, what factors could influence the rate at which the solution escapes from the container? | 23,540 | cqadupstack-physics |
24053 | missing dark matter? | A recent arXiv article measures the variation of gravitational potential in a local region around the solar system, and from that it tries to infer the mass density. Are there any valid counterarguments to their conclusion, i.e: that there is no dark matter near our vicinity? | What is the estimated mass density of matter in the local region around the solar system, and how does it compare to the expected density if dark matter is present? | 9,607 | cqadupstack-physics |
61915 | Some questions about anyons? | **(1)** As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" Hilbert space $V$ would be $V=W_0\oplus W_1\oplus W_2\oplus W_3\oplus...$ , and further we can define creation and anni... | Is it possible to construct a Hamiltonian model in three dimensions that incorporates both local operators and spatially extended operators, resulting in the existence of point-like quasiparticles and knot-like quasiparticles with nontrivial mutual statistics? If so, what would be an example of such a model? | 8,299 | cqadupstack-physics |
130067 | Looking for lists of student difficulties with electromagnetism, circuits (DC and AC) | I'm trying to help with an Instructor's Guide for an introductory calc-based physics text, and it would really help if I could locate some lists of typical student difficulties with topics like ... flux induced E and B fields Faraday's law Lenz's law DC circuits AC circuits Is there a better approach than just Googling... | What are the common misconceptions or difficulties that students encounter when learning about Faraday's Law and Lenz's Law in electromagnetic induction? | 32,691 | cqadupstack-physics |
44390 | Help: 3D visualization of magnetic field around moving point charge | The diagrams I'm able to find online only show the concentric field lines in the particle's plane, perpendicular to the motion, which of course generalizes to the cylindrical shape around a conductor. Can someone share a nice representation of the three-dimensional magnetic field all around a moving point charge? | What is the mathematical expression for the magnetic field around a moving point charge in three dimensions, and how does it vary with distance from the charge? Please include the formula used to calculate the magnetic field. | 31,846 | cqadupstack-physics |
32281 | On the naturalness problem | I know that there are several questions about the naturalness (or hierarchy or fine-tunning) problem of scalars masses in physics.stackexcange.com, but I have not found answers to any of the following questions. Suppose that we add to the SM Lagrangian the following piece: $(\partial b)^2-M^2 \, b^2-g\, b^2 \, h^2+ \, ... | Given the context of the discussed scalar field contributions to the Higgs mass, what is the relationship between the physical mass of the Higgs boson \( m_P \) and the mass scale \( M \) of a new scalar field \( b \), specifically in terms of how \( m_P \) varies when \( M \) is much larger than the Higgs mass (\( m_P... | 24,969 | cqadupstack-physics |
112113 | What is the difference between Biot-Savart law and Ampere's law? | What is the difference between these laws? Which law is more useful? When to use Ampere's law and when to use Biot-Savart law? | Given a straight current-carrying wire with a current of 5 A and another scenario involving a circular loop of radius 0.1 m carrying the same current, calculate the magnetic field (in teslas) at a point located 0.2 m directly to the side of the wire using both Ampere's Law and the Biot-Savart Law. Which method provides... | 6,605 | cqadupstack-physics |
134856 | Units of Hubble Time and Hubble Constant? | When we have Hubble constant and it's inverse Hubble Time (1/H) what units are they measured in? I know Hubble constant is in "km/s per Mpc" but is there any other units which are popular used with it, and if so is there any conversion between the two? And would Hubble Time unit still be in billion years, seeing it is ... | What are the units of measurement for the Hubble constant and its inverse, Hubble time, and how would you convert between these units, particularly in terms of expressing Hubble time in billions of years? | 23,874 | cqadupstack-physics |
65752 | Short-duration forces | In **circular motion** , it is said that the centripetal force acts only for a very very short period of time, hence is able to only change the direction but not magnitude of the velocity. Similarly in a collision, the impulsive-collision forces act for a very short period of time, but they are able to change the direc... | In a scenario where a 1 kg mass undergoes circular motion with a speed of 100,000 m/s at a radius of 1 m, the centripetal force acting on it is calculated to be equal in magnitude to a collision force of 100,000 N during an instantaneous collision. Given that both forces are equal in terms of impulse, explain mathemati... | 12,727 | cqadupstack-physics |
24002 | Is a closed system receiving heat guaranteed to have entropy below maximum? | Isolated system will preserve its entropy unchanged (for fully reversible system) or it will increase its entropy (for system with irreversible processes). For a closed system, it can receive energy in form of heat. Does this always imply, that its entropy will be below maximum? Is it possible to add heat in such a way... | In a closed system receiving heat, under what specific conditions can the entropy remain unchanged, and what is the theoretical maximum value of entropy for such a system? Provide an example of a process that illustrates these conditions. | 23,608 | cqadupstack-physics |
23550 | Why does your car lurch toward an oncoming truck as it passes you? | I notice that the larger the truck the greater the magnitude of the lurch. Can anyone give a physical explanation to this? | What is the relationship between the mass of a truck and the amplitude of its lurch when navigating a turn, and how can this relationship be explained using Newton's laws of motion? | 36,458 | cqadupstack-physics |
106159 | Impact of Ag nano-particle size on OPV efficiency : simulation | I would like to simulate the impact of gold nano particles size on the efficiency of Organic photovoltaic devices(inverted ofcourse) looking for any simulation plateform where this idea could be done any sugguestions ? | How does the size of gold nanoparticles affect the efficiency of inverted organic photovoltaic devices, and what is the optimal nanoparticle size for maximizing this efficiency? | 7,172 | cqadupstack-physics |
18396 | Who is right? Force exerted on a body. Me or my friend? | > Three masses $m_1 = 3\text{ kg}$, $m_2 = 9\text{ kg}$ and $m_3 = 6\text{ > kg}$ hang from three identical springs in a motionless elevator. The > elevator is moving downward with a velocity of $v = -2\text{ m/s}$ but > accelerating upward with an acceleration of $a = 5\ \mathrm{m/s^2}$. (Note: > an upward acceleratio... | What is the force exerted by the bottom spring on the bottom mass when three masses \( m_1 = 3 \, \text{kg} \), \( m_2 = 9 \, \text{kg} \), and \( m_3 = 6 \, \text{kg} \) are hanging from three identical springs in a motionless elevator that is moving downward with a velocity of \( v = -2 \, \text{m/s} \) while acceler... | 34,039 | cqadupstack-physics |
30015 | why the difference between $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is NOT zero? | Well, the difference between the two expressions $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is exactly $\Delta p^2$ , i.e. the squared uncertainty (variance) of the momentum, where the $\hat p$ is momentum operator and uncertainty on the momentum operator is defined by: $$\Delta p= \sqrt {\... | Why is the difference between the expectation values $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ not equal to zero, and how does this difference relate to the concept of uncertainty in momentum $\Delta p$? | 24,723 | cqadupstack-physics |
120043 | Understanding What A Wakefield Describes? | I am trying to understand the some of the properties of wakefields, namely the energy change. So, as a preface I am interested in primarily the wakefield due to electron beams as they progress through a curved section (the eletcrons radiate strongly when they are in circular motion). There are two main/simple regimes: ... | If we assume a constant wakefield regime where the change in energy per distance traveled along a curved trajectory is given by \(\frac{dE}{ds}(z)\), and integrate this expression from \(0\) to \(L\) (the total path length), what is the total energy change \(E_{\text{total}}(z)\) as a function of \(z\)? Furthermore, fo... | 8,598 | cqadupstack-physics |
77737 | Why depolarization of light by scattering | I am trying to understand the concept of depolarization of light by various particle shapes. For example, depolarization light scattered (re radiated) from a sphere illuminated with vertically polarized light. Is my picture an accurate representation of why light is depolarized? Essentially are the electrons on the 'ed... | What is the fraction of the light scattered by a 1-micron diameter sphere that remains polarized when illuminated by vertically polarized light at a wavelength of 623.8 nm? Assume the refractive index of the sphere material is 1.5. | 3,129 | cqadupstack-physics |
130470 | (Un)countability in QFT | I am a mathematician self-studying physics, and a currently working on QFT with Srednicki's book. One thing that bothers me is that for a scalar field (in the Hamiltonian version) there is a harmonic oscillator at every point of momentum space. These all commute with each other, which means that they can be observed si... | In quantum field theory, does a generic field state correspond to a countably infinite number of particles, or can it have an uncountably infinite number of particles? How does this relationship manifest in the transition from a quantum field to a classical field in the classical limit? | 33,637 | cqadupstack-physics |
64126 | What is the smallest existing thing in theory and law? | What is the smallest existing thing in theory and law? | What is the smallest particle in the universe according to current scientific understanding, and what is its significance in the context of particle physics? | 29,176 | cqadupstack-physics |
111414 | When rotating a liquid-filled jar what determines how much force goes to spinning the specimen floating inside? | Another way of stating it: When you have leaves in a (cylindrical) tea cup, if you rotate the cup (eg clockwise), the leaves largely stay in place relative to the table, but spin clockwise a little. What factors go into determining how much force (spin? torque?) transfers to the tea leaves (or to a neutrally buoyant ob... | How does the torque applied to a cylindrical tea cup affect the angular displacement of neutrally buoyant objects (like tea leaves) within it, and what factors determine the amount of spin transferred to these objects? | 10,167 | cqadupstack-physics |
109080 | Some question about symplectic transformation | I read Arnold's book **Mathematical Methods of Classical Mechanics** and come across with three problems in page 229. > 1.Let $\lambda$ and $\bar{\lambda}$ be simple (multiplicity 1) eigenvalues > of a symplectic transformation $S$ with $|\lambda|=1$. Show that the two- > dimensional invariant plane $\pi_\lambda$ corre... | Let \( S \) be a symplectic transformation with simple eigenvalues \( \lambda \) and \( \bar{\lambda} \) that have a modulus of 1. If the eigenvalue \( \lambda \) corresponds to a positive definition according to \( [S\xi, \xi] > 0 \) for a vector \( \xi \) in the invariant plane \( \pi_\lambda \), can you derive the c... | 9,981 | cqadupstack-physics |
66818 | Why myopic people see this picture differently? | I found the following picture in the Internet and I am curious how from a physicist point of view to explain it.  Basically the idea is the following. If you are a normal person - you suppose to see Einstein here, but if you are myopic, then you will se... | How does the resolution of the human eye and the effects of visual perception explain why a person with normal vision sees one image while a myopic person sees a different image from the same picture? Quantitatively, at what distance does the perceived image transition from one figure to another for both normal and myo... | 16,163 | cqadupstack-physics |
64716 | How does an earthen pot keep water cool? | I understand that evaporative cooling takes place thanks to small pores contained in the pot and that allow some water to go through and evaporate. However I couldn't understand clearly whether water inside the pot stays at its original temperature or would it cool further? If it will become cooler then how? | When water evaporates from a porous pot, what is the change in temperature of the water inside the pot, assuming the initial temperature is 25°C and the evaporation rate is 0.1 kg/h? Calculate the new temperature of the remaining water after one hour, considering the heat of vaporization of water is approximately 2260 ... | 30,835 | cqadupstack-physics |
10372 | Inflating a balloon (expansion resistance) | I am doing a quick calculation on how to calculate the pressure needed to inflate a perfectly spherical balloon to a certain volume, however I have difficulties with the fact that the balloon (rubber) has resistance to stretching and how this affects the pressure needed. It has to do with the E-modulus of the material ... | What is the relationship between the pressure required to inflate a spherical rubber balloon to a specific volume and the elastic modulus of the rubber material? Can you derive a formula that includes these factors? | 22,696 | cqadupstack-physics |
102409 | Naive visualization of space-time curvature | With only a limited knowledge of general relativity, I usually explain space- time curvature (to myself and others) thus: _"If you throw a ball, it will move along a parabola. Initially its vertical speed will be high, then it will slow down, and then speed up again as it approaches the ground._ _"In reality, the ball ... | Is the statement that a ball thrown near the Earth's surface appears to follow a parabolic trajectory due to the curvature of space-time, while in reality moving in a straight line at constant velocity, a correct interpretation of general relativity? What principles of physics support or refute this claim? | 29,088 | cqadupstack-physics |
21611 | Origin of field deduced from potential | > Related: Tubelights+power lines pictures? I would've edited this into the above question, but I realized that there' enough to it to qualify as a new one. Plus this seems to be a confusion of many people (including me). I've already been able to explain part of this, so I'll put that explanation first just to make th... | In a circuit containing a capacitor, what is the origin of the electric field that exists between the plates, and how does it differ from the field in the surrounding wires when the capacitor is charged? Additionally, for a power line carrying AC or DC current, how is the electric field generated along the wire, partic... | 24,231 | cqadupstack-physics |
9992 | Any resources to learn how to interpret formulae/diagrams? | Are there any materials exploring intermediate levels (of any sub-subject) which give plain English descriptions along side formulas/equations//diagrams/notations? | What are three intermediate-level materials in physics that provide clear English explanations alongside relevant formulas and diagrams? | 25,526 | cqadupstack-physics |
44449 | Interacting representation of the Poincaré group | In his QFT book, Weinberg claims what follows (Vol I, pag. 144-145): given a (free) representation of the Poincaré group with generators $\bf P$ (spatial translations), $H_0$ (time translations), $\bf J$ (rotations), and ${\bf K}_0$ (boosts), one obtains another (interacting) reprentation by replacing $H_0$ and ${\bf K... | What are the conditions under which the Poincaré group generators can be modified to obtain an interacting representation from a free representation, specifically regarding the self-adjoint operator density $\mathcal{H}({\bf x}, 0)$, and can you provide a rigorous proof of this transformation? | 4,048 | cqadupstack-physics |
129533 | What does centre of lift depend on? | I've read in many places that centre of lift is about quarter chord of the wing and that post-stall lift (the part developed on lower surface) has centre midchord. The later makes sense; the pressure is distributed more or less uniformly (or at least symmetrically) on the lower surface. But what determines the centre o... | What factors determine the position of the center of pressure on the upper surface of a wing, and how does this position vary between different airfoil shapes, such as a flat plate versus a supercritical airfoil? | 9,672 | cqadupstack-physics |
68214 | what happens to the angular velocity of star in star-black hole system? | What happens to the rotational and revolutionary angular velocities of star in star-black hole system as the star loses mass ? | How does the loss of mass from a star in a star-black hole system affect its rotational and revolutionary angular velocities, and can you calculate the change in angular momentum using the conservation of angular momentum principle? | 36,259 | cqadupstack-physics |
62834 | How would you determine whether an object is at equilibrium? | How would you determine whether an object is at equilibrium or not? What is the definition of equilibrium? | Given an object subjected to multiple forces, describe the conditions necessary for the object to be in a state of equilibrium. Support your answer with a calculation involving the forces acting on the object, ensuring that the resultant force is zero. What is the mathematical expression that defines this condition? | 33,222 | cqadupstack-physics |
23946 | Why is glass a good conductor of heat? | AFAIK Glass is insulator, it doesn't have free electron. It's said metal is a good conductor of heat because it has free electron, glass doesn't have free electron, why it is a good conductor of heat? | Considering that glass is generally an insulator and lacks free electrons, how does its thermal conductivity compare to that of metals, which are known to be good conductors of heat due to the presence of free electrons? Provide quantitative data to support your answer. | 19,275 | cqadupstack-physics |
25892 | Temperature of WIMPs | As a dark matter candidate, what should be the temperature and kinetic energy (or also the speed) of the WIMPs (weakly interacting massive particles) to agree with the observed distribution of dark matter and not to accumulate so much in the inner part (40 AU radius) of the Solar System that the change in the orbits of... | What is the maximum kinetic energy of weakly interacting massive particles (WIMPs) that would prevent them from significantly affecting the orbits of planets within 40 AU of the Solar System, assuming they are in equilibrium with the microwave background radiation? | 26,738 | cqadupstack-physics |
130119 | Diffusion in the standard map | Consider the standard map (also known as Chirikov map): $$ p_{n+1} = p_n + K \sin(\theta_n) \\\ \theta_{n+1} = \theta_n + p_{n+1} $$ I know that the diffusion coefficient according to the Einstein relation is defined through the relation: $$ \sigma^2 = 2Dt $$ being $\sigma$ the variance of the position in the case of t... | In the context of the standard map, where the equations of motion are defined as \( p_{n+1} = p_n + K \sin(\theta_n) \) and \( \theta_{n+1} = \theta_n + p_{n+1} \), explain how the diffusion coefficient \( D \) can be expressed as \( D = \lim_{n \rightarrow \infty} \frac{<(p_n - p_0)^2>}{n} \). Specifically, why is the... | 15,757 | cqadupstack-physics |
79745 | Why same formula describing Doppler effect in the case of light in different situations? | I made comparison between Doppler effect in light and sound and one interesting thing that I saw was that in the case of sound there are different formulas to find the apparent frequency in different situation (like observer moving,source moving,both moving etc) due to Doppler effect but in the case of light there is o... | Explain why the Doppler effect for sound requires multiple formulas to account for different observer and source motions, while the Doppler effect for light can be described with a single formula. How does the constancy of the speed of light in all reference frames contribute to this difference? | 19,274 | cqadupstack-physics |
98439 | Some questions about the large-N Gross-Neveu-Yukawa model | Consider the following action with a fermionic field $\psi$ and a scalar field $\sigma$, $S = \int d^dx \\{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}[ \frac{(\partial_\mu \sigma )^2 + m^2\sigma^2 }{2g^2 } + \frac{\lambda \sigma^4 }{4!g^4 } ] \\} - (N'-1)Trln(\gamma^\mu \partial_\mu + \sigma )$ A... | Given the action \( S = \int d^dx \left\{ -\bar{\psi}(\gamma^\mu \partial_\mu +\sigma )\psi + \Lambda^{d-4}\left[ \frac{(\partial_\mu \sigma )^2 + m^2\sigma^2 }{2g^2 } + \frac{\lambda \sigma^4 }{4!g^4 } \right] \right\} - (N'-1)Tr\ln(\gamma^\mu \partial_\mu + \sigma ) \), it has been concluded that a non-trivial soluti... | 15,804 | cqadupstack-physics |
67713 | How to estimate the physical size of a molecule? | I'm reading some chemistry-related papers that employ concepts of droplet evaporation. Since I am no chemist, I am wondering: How can I estimate the actual size of a molecule, say succinic acid? An order of magnitude would suffice. I'm aware of the fact that most molecules can not be approximated by simple assuming tha... | What is the approximate size of a molecule of succinic acid in nanometers? Please provide an order of magnitude estimate. | 33,059 | cqadupstack-physics |
83534 | Are length contraction and time dilation physical? | Are length contraction and time dilation real physical phenomena, or are they just a measurement issue? | What is the relativistic equation for calculating length contraction, and how does it quantitatively compare an object's length when measured at rest versus when it is moving at 0.8c (where c is the speed of light)? | 36,398 | cqadupstack-physics |
98011 | Binary Star system with one star stationary? | Can a Binary Star system be possible where in one star is stationary and the other star revolves around it? (Just like a planet revolving a star. i.e planets in the system and the star revolving around their own center of masses to balance the system). | In a binary star system, if Star A is stationary and Star B revolves around it, what would be the relative masses of the two stars for the system to remain stable, considering that the center of mass of the system must lie within Star A? Calculate the minimum mass of Star B if Star A has a mass of 2 solar masses. | 25,438 | cqadupstack-physics |
93225 | How 4-vector nature of the value is connected with it's conservation law? | In electrodynamics Poynting vector and energy flux of field don't create 4-vector. Also they aren't conserved independently from substance (conservation law includes summand connected with current density). In linearized gravity mass density and mass current density as components of stress-energy tensor also aren't con... | Explain how the non-conservation of the Poynting vector in electrodynamics relates to the absence of a 4-vector nature in its representation, and provide an example of a physical quantity in linearized gravity that also fails to exhibit conservation. | 7,184 | cqadupstack-physics |
35486 | Is there a thought experiment which brings to light the contradiction between General Relativity and Quantum Mechanics? | I've been told that GR and QM are not compatible, is there an intuitive reason/thought experiment which demonstrates the issue? (Or one of the issues?) | What is the energy of a photon emitted by an electron transitioning from the second energy level to the first in a hydrogen atom, and how does this relate to the compatibility issues between Quantum Mechanics and General Relativity? | 5,953 | cqadupstack-physics |
92549 | The most general procedure for quantization | I recently read the following passage on page 137 in volume I of 'Quantum Fields and Strings: A course for Mathematicians' by Pierre Deligne and others (note that I am no mathematician and have not gotten too far into reading the book, so bear with me): > _A physical system is usually described in terms of states and o... | What is the relationship between symplectic diffeomorphisms and ordinary diffeomorphisms on a manifold, particularly in the context of Hamiltonian mechanics, and how do they influence the quantization process of classical systems? | 6,200 | cqadupstack-physics |
56446 | List of all past comet passes and area it was visible? | Is there a database/website which shows all comets which have passed Earth and have been viewed? Is there any country specific viewing database as well? I would like to do a search on the lines of : Show me all comets were visible from India during 1950 to 1960? Any searches on Google have not returned anything, so que... | Can you provide a list of all comets that were visible from India between 1950 and 1960, along with their dates of visibility? | 15,229 | cqadupstack-physics |
11782 | how does a helicopter get forward thrust? | Just passed a helicopter on my way to work. We have read in some detail how an airplane gets forward thrust and lift by deflecting air. How does a helicopter with horizontal fans achieve that ? | How does the rotor configuration of a helicopter generate lift and thrust by manipulating airflow, and what principles of physics are involved in this process? | 20,321 | cqadupstack-physics |
99698 | What are qubits made of in Wen's string-net theory? | In Prof. Xiaogang Wen's theory, photons and electrons are described as quasi- particles appeared as a result of the existence of the string-net liquid, which is the topological order of the qubits that form the space. This is a little confusing to me. Consider when we talk about other quasi-particles, for example, phon... | In the context of Prof. Xiaogang Wen's theory, can you explain the quantitative relationship between the number of qubits required to represent a certain volume of space and the emergent properties of quasi-particles such as photons and electrons? Additionally, how does this relate to the understanding of quasi-particl... | 2,586 | cqadupstack-physics |
23186 | Maximum range of a projectile (launched from an elevation) | > If a projectile is launched at a speed $u$ from a height $H$ above the > horizontal axis, and air resistance is ignored, the **maximum** range of the > projectile is $R_{max}=\frac ug\sqrt{u^2+2gH}$, where $g$ is the > acceleration due to gravity. > > The angle of projection to achieve $R_{max}$ is $\theta = \arctan ... | What is the expression for the maximum range \( R_{max} \) of a projectile launched from a height \( H \) at an initial velocity \( u \) with no air resistance, and how can the angle of projection \( \theta \) that achieves \( R_{max} \) be derived? | 10,755 | cqadupstack-physics |
27008 | From Manifold to Manifold? | Tensor equations are supposed to stay invariant in _form_ wrt coordinate transformations where the metric is preserved. It is important to take note of the fact that invariance in form of the tensor equations is consistent with the fact that the individual components of the tensor may change on passing from one frame t... | What mathematical principles ensure the invariance of tensor equations in the transition between different manifolds, particularly when the preservation of the metric does not hold? | 28,088 | cqadupstack-physics |
131500 | Green's function for moving solidification front | Consider a liquid solid interface $z =\zeta(x,t)$ moving at constant speed $v$, for a two dimensional problem. Due to solidification interface is changing it position. For simplicity heat conductivities, heat capacity of liquid and solid are assumed to be the same. Heat conduction equation in the liquid and solid regio... | Given the heat conduction equation under the assumption of equal thermal properties for the liquid and solid phases, can you derive the equation for temperature distribution at the moving liquid-solid interface considering the provided form of the Green's function? Specifically, explain how the interface velocity \(v\)... | 13,596 | cqadupstack-physics |
81315 | Do primary first class constraints change the electric field in the Hamiltonian form of Maxwell's theory? | In my understanding of Dirac's theory of constrained Hamiltonians, the primary (and also the secondary) first class constraints are generators of canonical transformations that do not change the physical state: the electric field is part of the physical state so it has zero response to a primary first class constraint.... | What is the expression for the response of the electric field \( E_r \) to the primary first class constraint \( G \) as derived from the Poisson bracket, and how does this contrast with the expectation that this response should be zero? | 14,054 | cqadupstack-physics |
130432 | Must length equal distance? | In his book The Elegant Universe, Brian Greene points out that when a foot ruler is laid out by an observer on a spinning “Tornado” ride (a disk) that a “A shorter ruler means that he will have to lay it out - head to tail - more times to traverse the whole circumference” and that the total physically measured distance... | In the context of special relativity, if a muon travels a distance of 1,000 meters in the Earth's rest frame in a time of 1 microsecond, calculate the corresponding distance in the muon's frame according to the gamma factor, assuming the muon's speed is 0.98c. What is the length contraction experienced by the muon as o... | 23,414 | cqadupstack-physics |
73144 | Derive that $P = I^2R$ | As our homework, we were asked to derive $P = I^2R$. Now, I started off with the basic relation $P = \frac{W}{T}$. I was not able to think of anything from here, so I started plugging in random formulas from a purely algebraic point of view. I tried the one for voltage $V = \frac{W}{q} \implies Vq = W$ and got $P = \fr... | How do the definitions of voltage and current relate to the total energy consumed by electrical appliances, and how can we reconcile the different interpretations of work and time in the context of calculating power using the formula \( P = I^2R \)? | 20,193 | cqadupstack-physics |
131748 | Is something beyond the material needed to solve the Von Neumann Chain? | A problem has been presented that goes like this: Particles normally exist as several mathematical possibilities rather than one actual object. It is said that in the absence of observation, particles exist in a superposition of possibilities rather than one actual thing. But when we look they are not in such an indefi... | In the context of quantum mechanics and the concept of decoherence, what implications does the measurement problem have on the existence of reality as a definite state, and can you quantify the number of entangled particle measurements required to arrive at a definitive state in a Von Neumann chain? | 19,107 | cqadupstack-physics |
78071 | Optical Raytracing by using Adiabatic Hamiltonian Method | I'm looking into raytracing a Lüneburg Lens which is a gradient index (GRIN) optical element with a radially varying refractive index: $$ n(\rho)=n_0\sqrt{2-\left(\frac{\rho}{R}\right)^2}, 0<\rho<R $$ The good paper by Hanhong Gao et.al, "Design of thin-film photonic metamaterial Lüneburg lens using analytical approach... | What is the expression for the focal length of a Lüneburg lens with a maximum refractive index \( n_0 \) and radius \( R \), given the radial refractive index profile \( n(\rho) = n_0\sqrt{2 - \left(\frac{\rho}{R}\right)^2} \)? | 34,780 | cqadupstack-physics |
65207 | Is the 125 GeV Higgs boson some kind of a "almost-commutative graviton" at the electroweak scale? | The clumsy "almost-commutative graviton" is provocative. I use it on purpose, to ask two questions in one : * **Is the observation of only one Higgs and no supersymmetric particle below 8 TeV (up to now) a sufficient evidence to substantiate the almost commutative spectral model?** * **Can physicists consider now t... | What evidence exists to support the claim that the observation of only one Higgs boson and no supersymmetric particles below 8 TeV can validate the almost-commutative spectral model of gravitation and Yang-Mills-Higgs interactions? | 36,769 | cqadupstack-physics |
47297 | Can an orbit be calculated using two points and transit time? | Working in only two dimensions and assuming that the central body is at the origin of the coordinate system, given two points in space and knowing the transit time between those points, as well as the direction of motion, is it possible to calculate a body's orbit? It seems to me that there should be enough information... | Given two points in polar coordinates, \((\theta_0, r_0)\) at time \(T=0\) and \((\theta_1, r_1)\) at time \(T=T_1\), along with the transit time \(T_1\) and the direction of motion, can you determine the specific orbital path of a body around a central focus located at the origin? If so, what mathematical approach or ... | 3,039 | cqadupstack-physics |
71864 | Understanding the argument that local U(1) leads to coupling of EM and matter | I'm trying to better understand the argument that U(1) local gauge invariance implies a coupling of EM and Dirac fields. I understand the math, but I'm not sure about the chain of logic. You start with $\mathcal{L}_\mathrm{Dirac} = \bar\psi ( i\hbar \partial_\mu - m)\psi $ and the following transformations: $$ \psi \ri... | Consider a Dirac field described by the Lagrangian density $\mathcal{L}_\mathrm{Dirac} = \bar\psi ( i\hbar \partial_\mu - m)\psi$. If we assume a transformation of the form $\psi \rightarrow \psi' = e^{i\theta}\psi$ and corresponding transformation for the gauge potential $A_\mu \rightarrow A'_\mu + \partial_\mu \chi$,... | 21,829 | cqadupstack-physics |
44629 | Elastic Collision And Momentum | The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = 5.00~m$ above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repel... | Two blocks are allowed to slide along a frictionless track. Block \( m_1 \) with a mass of 4.98 kg is released from a height of 5.00 m, while block \( m_2 \) with a mass of 9.40 kg is at rest. When \( m_1 \) approaches \( m_2 \), they repel each other due to identical north poles of magnets attached to them, preventing... | 17,643 | cqadupstack-physics |
10592 | Would a car tow rope withhold an adult person? | I am not exactly sure how the physics work here. If we take a car tow rope, which is manufactured for towing a 3500 kg car and we actually start towing such a car on this rope, what force do we really apply to the rope? Could the same rope **safely** withhold an adult person (100 kg) hanging on it? | What is the maximum tensile force that a tow rope, designed for towing a 3500 kg car, can safely withstand? Additionally, would this rope be able to support an adult person weighing 100 kg hanging from it without breaking? | 13,419 | cqadupstack-physics |
31222 | Why are subjects upside down when I look through my door peephole? | There is a convex lens 3/4" on the outside and 1 1/2" convex lens on the inside. Each lens has one flat side facing out and one convex side facing in. What can be done to correct this image? | What is the focal length of a lens comprised of an outer convex lens with a diameter of 3/4" and an inner convex lens with a diameter of 1 1/2", given that both lenses have one flat side facing outward? | 17,329 | cqadupstack-physics |
117426 | What limits of integration do Landau and Lifshitz use here? | In "Mechanics" book by Landau and Lifshitz, $\S18$ "Scattering", problem 7 on deducing the form of scattering field given the effective cross-section as a function of scattering angle an equation is obtained: $$-\pi\text{d}\log w=\text{d}\left(\frac s w\right)\int_0^{s^2/w^2}\frac{\chi'(x)\text{d}x}{\sqrt{\frac{s^2}{w^... | What are the correct limits of integration for the variable upper limit in the equation $$-\pi\text{d}\log w=\text{d}\left(\frac s w\right)\int_0^{s^2/w^2}\frac{\chi'(x)\text{d}x}{\sqrt{\frac{s^2}{w^2}-x}}$$ when switching the order of integration, and how does this affect the validity of the integral in the context pr... | 38,066 | cqadupstack-physics |
127470 | Why do hydraulic jumps form? | I know that a hydraulic jump is formed when a zone of supercritical flow discharges into a zone of subcritical flow, but why exactly is a hydraulic jump formed? From a mechanical point of view, are the only forces acting in the diagram weight and friction?  into a subcritical region (flow velocity less than the wave speed). If the flow rate is 10 m³/s and the width of the channel is 2 m, determine the height difference (in meters) between the supercritical and su... | 27,193 | cqadupstack-physics |
61554 | Potential of a Body | I have a doubt about the electric potential of a body. Well, I know that given a continuous distribution of charge we can find the potential at a point $a$ using the following relation: $$V(x,y,z)=\frac{1}{4\pi\epsilon_0}\iiint_{S} \rho(a') \frac{1}{|a-a'|}dV'$$ However, this gives a function that at each point tells m... | What is the difference in electric potential between the surfaces of two concentric spheres with uniform charge densities, where the inner sphere has a radius \( a \) and the outer sphere has a radius \( b \)? Assume both spheres carry the same charge \( Q \). Calculate this difference. | 9,217 | cqadupstack-physics |
61228 | Asymmetric uncertainties | Inspired by these two question on tex.SX * Asymmetrical tolerancing * Asymmetric uncertainties with siunitx package I'd like to ask for a nice explanation for these kind of uncertainties, like $10_{-2}^{+6}$. I never saw them in real life. I'd like to give some question that may be stupid or redundant to each other... | How do you interpret the asymmetric uncertainties represented as \( x_{-a}^{+b} \), and can you provide a real-life example illustrating how this type of uncertainty affects the determination of a physical quantity? Additionally, how would you compute these asymmetric uncertainties from experimental data? | 35,715 | cqadupstack-physics |
123753 | How effective is speeding? | At a simple level, speeding in a car attempts to minimize the time required to travel a distance by utilizing the basic relationship: $$d=st$$ So for a given distance, time should be inversely proportional to speed: the faster you go the less time it takes. My question is, on a practical level, does this actually help ... | If a driver exceeds the speed limit by 5 mph while maintaining a constant speed, how much time would they save on a journey of 20 miles compared to driving at the speed limit? Additionally, consider how traffic conditions, such as stoplights or congestion, might affect this time savings in a practical scenario. | 31,498 | cqadupstack-physics |
100249 | From Dirac to Klein-Gordon in curved spacetime | Is there an easy/elegant way of showing that "squaring" the Dirac equation in curved spacetime yields the Klein-Gordon equation, just like it happens in Minkowski space? A brute force approach would require a lot of tedious algebra dealing with the spin connection, the veilbein formalism and the Dirac matrices. | What is the relationship between the Dirac equation in curved spacetime and the Klein-Gordon equation, and can you derive the Klein-Gordon equation by squaring the Dirac equation in a systematic way? | 18,486 | cqadupstack-physics |
110930 | Proof of equivalence of different representations of the $\gamma$-matrices in the Dirac equation | This question concerns the Dirac equation and the $4\times4$ $\gamma$-matrices. The task is to prove that a similarity transformation of the standard $\gamma$-matrix conserves the commutation relation $$ \\{\gamma^\mu,\gamma^\nu\\} ~=~ 2g^{\mu\nu}, $$ where $2g^{\mu\nu}$ is the metric tensor $\text{diag}(1,-1,-1,-1)$, ... | Do all unitary matrices commute with the metric tensor \( g^{\mu\nu} \) defined as \( \text{diag}(1, -1, -1, -1) \)? If they do, can you provide a straightforward proof or explanation for this? | 38,012 | cqadupstack-physics |
1067 | Is it guaranteed that wavefunction is well behaved everywhere? | I don't really know much about Quantum mechanics, but would like to know one simple fact. The state function $\Psi(r, t)|$ whose magnitude gives the probability density of the position of the particle and the magnitude of its ($\Psi(r, t)$) fourier transform gives probability density of its momentum. Is there any rule ... | Is the wave function $\Psi(\mathbf{r}, t)$ in quantum mechanics required to be infinitely differentiable everywhere, and if so, what implications does this have for the physical properties of the system? | 11,781 | cqadupstack-physics |
122754 | For what rare events was the LHC built? | I understand that for low cross-section events a very high luminosity is necessary in order to obtain enough data to produce meaningful statistics. That is why the LHC was built. But which are these event which we are interested in? What are the events which would hint at new physics or would confirm theoretical models... | What specific low cross-section events at the LHC might provide evidence for new physics or validate existing theoretical models, and how does the required luminosity for these events compare to that of high cross-section events? | 31,147 | cqadupstack-physics |
371 | How about an exact solution for the position of a planet as a function of time? | Recently I was surprised to discover that no exact solution for the position of a planet as a function of time exists. I am referring to the two-body problem in a gravitational field where Newtons law of gravity holds. Well known are proofs that the planet will move in an ellipse, Keplers laws can be derived fairly eas... | In the context of the two-body problem in classical mechanics, can you explain why an exact analytical solution for the position of a planet as a function of time does not exist, while the orbit can still be described as an ellipse according to Kepler's laws? Additionally, what are the implications of this on the predi... | 9,349 | cqadupstack-physics |
55324 | Question about the derivation of an equation in full replica symmetry breaking solution | Using replica method and saddle point method, the free energy of a magnetic system can be expressed as $$-\beta[f]=\lim_{n\to0}\\{\frac{-\beta^2J^2}{4n}\sum_{a\ne b}q_{\alpha\beta}^2-\frac{\beta J_0}{2n}\sum_\alpha m_\alpha^2+\frac{\beta^2J^2}{4}+\frac{1}{n}\log\operatorname{Tr}e^L\\}$$ $$L=\beta^2J^2\sum_{\alpha<\beta... | If we assume that \( J_0, h, \) and \( m_\alpha \) are all equal to 0, how can you derive the equation for \( \beta[f] \) using the provided expression for the free energy of a magnetic system, specifically focusing on the expansion to fourth order? What are the coefficients and terms involved in this expansion? | 16,181 | cqadupstack-physics |
131861 | Why do the $1/2$ factor appear in the Majorana mass Lagrangian? | In case of Dirac neutrino there is no $1/2$ factor in the mass Lagrangian but for Majorana type neutrino there is a half factor in the mass Lagrangian. | How does the mass Lagrangian differ between Dirac neutrinos and Majorana neutrinos in terms of the presence of the $1/2$ factor? Specify the significance of this factor in relation to the neutrino masses. | 24,436 | cqadupstack-physics |
112840 | New focal point of converging light through a concave lens | Suppose I pass rays of already converging light through a concave lens. The rays are equally centered on the lens such that the original focal point is through the lens and centered on the lens axis. My understanding is that the lens will bend the incoming rays, such that they all focus on a new focal point closer to t... | If the original focal length of the converging rays is \( f_o \) and the focal length of the concave lens is \( f_c \), can you derive a formula to determine the location of the new focal point \( f_n \) for the rays after passing through the concave lens? What would be the numerical value of \( f_n \) if \( f_o = 20 \... | 17,119 | cqadupstack-physics |
104052 | Is Λ-CDM and no inflaton field compatible with the observed value of the scalar spectral index? | From the cosmic microwave background, one can extract the scalar spectral index $n_s$. It is measured to be smaller than 1 by several standard deviations. Wikipedia says that it is a parameter of the Λ-CDM model. This is puzzling me. I thought that Λ-CDM includes a cosmological _constant_ (i.e. no inflaton field necess... | What is the scalar spectral index \( n_s \) measured from the cosmic microwave background, and how does it relate to the parameters of the Λ-CDM model? Additionally, could you explain if the inclusion of a cosmological constant in Λ-CDM necessitates an inflaton field or if it's possible for this model to be valid witho... | 21,642 | cqadupstack-physics |
133063 | Work done against a resistive force | My past year exam paper had a question about work done against the resistive force, where the answer key said it was resistive force * distance. As I understand it, work done is a measure of impact a force has on an object, but why is the resistive force, which is in the opposite direction of the direction of motion us... | When calculating the work done against a resistive force, how do we account for both the magnitude of the resistive force and the distance over which it acts, given that the force opposes the direction of motion? Provide a mathematical expression for this scenario and explain the significance of the negative sign in th... | 15,937 | cqadupstack-physics |
118870 | Frequency spectrum and histogram of white noise | I haven't been able to find any images with, so here goes: In the frequency/Fourier spectrum, how does white noise look like ? Is that just random dots all over the place, making it very hard to filter out ? And the same with the histogram, how does it look ? Is it just a flat line, containing more or less the same amo... | What is the expected shape of the histogram for white noise, and how does its intensity distribution compare to a Gaussian distribution? | 3,738 | cqadupstack-physics |
11222 | Thought experiment that seems to involve something growing at twice the speed of light. Is anything wrong? | Let foo be some unit of distance and bar be some unit of time which have been chosen so that the speed of light c = 1 foo/bar. Position several observers along a line each separated by one foo, and place light sources some distance apart amongst the observers, initially off. All observers and light sources are stationa... | Given a scenario where two light sources, L and R, are ignited simultaneously at time 0 bars and are 10 foo apart from each other, with observers positioned at each foo along a line, calculate the maximum distance \( r \) (in foo) that encompasses all observers who have seen both light sources by time 7 bars. Assume al... | 406 | cqadupstack-physics |
17624 | What are some interesting coupled harmonic oscillators problems? | That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks. | What innovative classical mechanics project could I design that goes beyond the typical textbook examples, and what specific physical principles would it demonstrate? | 5,907 | cqadupstack-physics |
134395 | How to find optical toy models of entangled quantum mechanical systems? | I recently read Arnold Neumaier's lectures on uncovering classical aspects of quantum mechanics: * Classical and quantum field aspects of light * Optical models for quantum mechanics * I can't find the third lecture, probably it doesn't exist yet. I guess it will elaborate more on the **thermal interpretation** ,... | In the context of simulating quantum systems using optical models, how can a complex superposition of polarized monochromatic plane waves be designed to represent a 2-qubit quantum system, and what specific measurements can be performed in this setup to verify its quantum characteristics? | 29,359 | cqadupstack-physics |
55254 | Two mirrors facing each other | What happens when you place two mirrors facing each other? Is it possible to have an infinite amount of reflections? | If two mirrors are placed facing each other and a single object is placed between them, how many reflections of that object can be observed, and under what conditions might these reflections appear to be infinite? | 7,666 | cqadupstack-physics |
51332 | Relationship between current through a motor and it's load | When a motor, connected to a battery that has a constant voltage, spins without a load it's speed is higher than with load. I'm told that because of back emfs the current is very small when there's no load because of the higher speed. And so when there is a load the back emf is less as the motor spins slower, and so th... | What is the equation that describes the back electromotive force (back EMF) in a DC motor, and how does it relate to the motor's speed and current when a load is applied? Additionally, if the torque increases due to a load, how does this affect the input current if the motor is operating at a constant voltage? | 197 | cqadupstack-physics |
43740 | Most sophisticated experiment you could perform in your garage? | What are some of the most elegant/complex/sophisticated physics experiments one could perform in his garage, if he has enough spare time and technical/theoretical know-how, but a relatively limited budget? Say, a retired emeritus physics professor? These could be either novel or reproductions of known experiments, eith... | What are the key measurements and calculations involved in reproducing the double-slit experiment to demonstrate the wave-particle duality of light using a budget of $100, and what results can be expected? | 25,519 | cqadupstack-physics |
4935 | Is there a relativistic (quantum) thermodynamics? | Does a relativistic version of quantum thermodynamics exist? I.e. in a non- inertial frame of reference, can I, an external observer, calculate quantities like magnetisation within the non-inertial frame? I'd be interested to know if there's a difference between how to treat thermodynamics in a uniformly accelerated re... | In a uniformly accelerated reference frame, how would the temperature of an ideal gas change according to an external inertial observer compared to the temperature measured within the accelerated frame, assuming the gas is contained in a box that also accelerates with the same uniform acceleration? | 33,364 | cqadupstack-physics |
82172 | Why does a bicycle (without any support of stand) falls down being at rest, but not under motion? | I have always seen a bicycle not standing without any support, it either falls down to the right or to the left, may even to some other direction. But,the same two wheeler when under motion,moves balanced, without falling to either side,even it not falls, when the two wheeler is bent to left or right by the driver, lik... | What are the forces and principles at play that allow a bicycle to maintain balance while in motion, and how do these differ from the forces acting on a stationary bicycle that cause it to fall? | 27,359 | cqadupstack-physics |
71385 | Identify the coefficients of Operator Product Expansion (OPE) | Sorry I have a stupid question in Polchinski's string theory book vol 1, p46. For a holomorphic function $T(z)$ with a general operator $\mathcal{A}$, there is a Laurent expansion $$T(z) A(0,0) \sim \sum_{n=0}^{\infty} \frac{1}{z^{n+1}} \mathcal{A}^{(n)}(0,0). \tag{2.4.11}$$ Under transformation $\delta \mathcal{A}=-\e... | What is the form of the operator product expansion (OPE) for a holomorphic function \( T(z) \) with a general operator \( \mathcal{A} \) under the transformation \( \delta \mathcal{A} = -\epsilon v^a \partial_a \mathcal{A} \), and how do you derive the terms involving \( \frac{h}{z^2}\mathcal{A}(0,0) \) and \( \frac{1}... | 29,189 | cqadupstack-physics |
61641 | Transforming an equation to the co-vector version | Ok, this question is more a result of my lack of knowledge of how to manipulate equations involving index notation rather than about physics... I have the geodesic equation with $U^\lambda\equiv\dot{x}^\lambda$:- $$ \dot{U^\lambda} + \Gamma^\lambda_{\mu\nu} U^\mu U^\nu $$ And I want to transform to the co-vector $U_\mu... | In the context of general relativity, consider a particle moving along a geodesic described by the geodesic equation
\[
\dot{U^\lambda} + \Gamma^\lambda_{\mu\nu} U^\mu U^\nu = 0,
\]
where \( U^\lambda \) is the four-velocity, \( \dot{U^\lambda} \) is the derivative with respect to proper time, and \( \Gamma^\lambda_... | 13,176 | cqadupstack-physics |
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