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10172 | Would dark matter absorb gravitational waves? | Would the vast and seemingly diffuse clouds of dark matter floating around our galaxy (and most others) absorb gravitational waves? Is this perhaps why we haven't detected any yet? | What is the estimated mass density of dark matter in the vicinity of our galaxy, and how would this affect the propagation of gravitational waves through these regions? | 23,325 | cqadupstack-physics |
70707 | Adiabatic theorem and Berry phase | As far as I can check, the adiabatic theorem in quantum mechanics can be proven exactly when there is no crossing between (pseudo-)time-evolved energy levels. To be a little bit more explicit, one describes a system using the Hamiltonian $H\left(s\right)$ verifying $H\left(s=0\right)=H_{0}$ and $H\left(s=1\right)=H_{1}... | What is the condition for the energy levels \(\varepsilon_i(s)\) and \(\varepsilon_j(s)\) in a quantum system for the adiabatic theorem to hold, and how does this relate to the emergence of the Berry phase when these energy levels are nearly degenerate? | 28,082 | cqadupstack-physics |
93589 | Approximating evolution as occurring in a two-dimensional subspace | Suppose you have a quantum system with a Hamiltonian having some number (greater than 2, possibly infinite) of eigenfunctions, and that the system is prepared in the ground state. When can you approximate it as by two-level system (using just the ground state and first excited state)? Is there some property that will m... | In a quantum system described by a Hamiltonian with an infinite number of eigenstates, what is the minimum energy gap between the first excited state and the second excited state required for the system to be well approximated as a two-level system using only the ground and first excited states? Illustrate how this ene... | 14,199 | cqadupstack-physics |
36181 | Driving a solution of optical isomer molecules with the resonant frequency | What happens when we drive a solution of optical isomer molecules (enantiomers) with a microwave radiation in resonance with the tunneling frequency of the molecules (the frequency of the transition between the eigenstates of the Hamiltonian)? I expect it will become a racemic mixture. Is that correct? Update: Any refe... | If a solution of optical isomers (enantiomers) is exposed to microwave radiation at the resonance frequency corresponding to the tunneling transition between their eigenstates, what specific temperature and frequency threshold must be met to achieve the racemization of the enantiomers? Please provide any experimental e... | 14,128 | cqadupstack-physics |
55722 | Could we survive if the sun were a black hole? | Ignoring the impossibility of the sun suddenly collapsing, and the energy release (which would kill us): If the sun suddenly turned into a black hole, could we survive if we had sufficient energy for heat, light, etc? | If the sun were to suddenly transform into a black hole with the same mass but no longer emitted light or heat, how far away would Earth need to be to maintain a temperature capable of supporting life, assuming we had a sufficient energy source that provided necessary heat and light? | 38,299 | cqadupstack-physics |
90928 | Virtual Higgs boson? | Can particles emit a virtual Higgs boson in a similar manner to the way a virtual photon is emitted? | What are the conditions under which particles can emit a virtual Higgs boson, and how does this process compare quantitatively to the emission of virtual photons? | 32,655 | cqadupstack-physics |
73720 | Graphene's Tight Binding Hamiltonian | Graphene has two atoms in its primitive unit cell. This makes it intuitive to see that the tight binding Hamiltonian can be constructed as a $ 2 \times 2 $ matrix $H$ acting on a spinor $S$ that consists of the wavefunction from an atom in sublattice A and B. $H_{monolayer}=\gamma \cdot \begin{pmatrix} 0 & k_x-ik_y \\\... | What is the form of the tight binding Hamiltonian for bilayer graphene when expressed in a two-component basis that includes only one atom per layer, and how do the matrix elements of this Hamiltonian relate to the physical hopping parameters between the atoms? | 460 | cqadupstack-physics |
111274 | Perception of sound in varying temperature | If one disregards situations like explosions (where air is heated) etc. and also disregards humidity – does _temperature_ affect sound in any way for the observer? Say for example one listens to a song/speech/sound from a loud speaker in 40°C and the same in -50°C. $$v_{40{^\circ}{\mathrm C}} = 331\tfrac{m}{s} \sqrt{\f... | How does the temperature of the air influence the speed of sound, and what would be the difference in the time it takes for sound to travel 1 kilometer at 40°C compared to -50°C? | 35,249 | cqadupstack-physics |
76824 | Proper Time with a non-zero Initial Velocity | I have a question regarding how to find the proper time for a body with an initial velocity to slow down to 0. For example, the equation I have been working with looks like: $$\int^\tau_0 d\tau=\int^t_0\frac{1}{\sqrt{1+\frac{(\alpha t+v)^2}{c^2}}}dt$$ Where $t$ is equal to the coordinate time for the rocket to slow dow... | Given the equations provided and considering a rocket undergoing constant proper acceleration $\alpha$ with an initial velocity $v$, can you derive the correct expression for the proper time $\tau$ needed for the rocket to come to a complete stop (i.e., velocity becomes zero) and verify if the previously mentioned rela... | 22,579 | cqadupstack-physics |
4314 | Studying electrodynamics problems | Suppose an advanced undergraduate student has reached a moderate level of understanding on electrodynamics. Where should he **focus** on, to sharpen his **problem-solving skills**? * Practicing integrals and/or other **mathematical tools**. * Studying **theoretical results**. * Working on the **physical meaning**... | What specific mathematical tools or concepts should an advanced undergraduate student prioritize practicing to effectively enhance problem-solving skills in electrodynamics, and why are they beneficial? | 27,464 | cqadupstack-physics |
130254 | Crystal Momentum in a Periodic Potential | I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. There is an associated reciprocal lattice with lattice vectors $\textbf{K}$ such that $\textbf{K} \cdot \textbf{R} = 2\pi ... | Consider a one-dimensional crystal lattice with a lattice constant \( a \). The corresponding reciprocal lattice has a reciprocal lattice constant \( b = \frac{2\pi}{a} \). A particle in this lattice has a wavefunction given by
\[
\psi_{n\textbf{k}}(x) = e^{i k x} u(x)
\]
where \( u(x + a) = u(x) \). If the crystal ... | 16,580 | cqadupstack-physics |
108983 | Rotation operator for a point in a coordinate system linearly derived from Cartesian coordinates | For some experimental and practical reason, I have created a new coordinate system in the form $$x^\prime_i=T_{ij}x_j$$ where $T_{ij}$ **isn't** a square matrix. $x_i$ is standard Cartesian coordinates, and $x^\prime_j$ is a point in the new system. I have to mention that the new system's axes **are not linearly indepe... | How can I derive a 4x4 rotation matrix that applies a rotation to a point in my new coordinate system defined by the transformation \( x'_i = T_{ij} x_j \), given that the specific transformation matrix \( T_{ij} \) is not square and the axes are not linearly independent? | 9,151 | cqadupstack-physics |
44143 | What does the velocity of a wave mean? | I know that the velocity of a wave is given by $v=\lambda f$ but what does this velocity represent in the physical sense. For instance, if I am told a car moves at a velocity of 5 $m/s$ I know that the car itself will cover 5 meters in displacement every second. What part of the wave is moving at velocity $v$? | In the context of wave mechanics, if a wave has a wavelength of 2 meters and a frequency of 3 Hz, what is the velocity of the wave, and what physical quantity does this velocity represent in relation to the wave itself? | 21,274 | cqadupstack-physics |
44175 | Thomas-Fermi approximation and the dielectric function (+ small bit on graphene) | 1) With the dielectric function, which is a function of wavenumber and frequency,how is it possible to take the limit of either to zero without changing the other one? I thought that frequency and wavenumber are linked, also am I right in thinking that they are both for the 'probe'? 2)What exactly is meant by the 'stat... | How does the Thomas-Fermi approximation apply to systems where the electron wavenumbers are close to the Fermi wavevector, such as in impurity scattering in a metal, and why might it still be considered valid in materials like graphene? | 2,410 | cqadupstack-physics |
13777 | Pair production kinematics | In the process $A\rightarrow B+C$ If we know the energy and momentum four vectors of B and C, then how can we find the momentum three vector of A. The particular proces I have in mind is pair production $\gamma\rightarrow e^+ + e^-$ 4-vectors for electron is $(E_1,\vec{p_1})$ and for positron it is $(E_2,\vec{p_2})$. T... | Given the pair production process $\gamma\rightarrow e^+ + e^-$, if the momentum three vectors of the electron and positron are known as $\vec{p_1}$ and $\vec{p_2}$ respectively, how can you determine the three-component momentum vector $\vec{p}$ of the photon? Assume the conservation of momentum applies to the process... | 17,452 | cqadupstack-physics |
122929 | Lagrangian depends on second derivative of field | In case of the gauge-fixed Faddeev-Popov Lagrangian: $$ \mathcal{L}=-\frac{1}{4}F_{\mu\nu}\,^{a}F^{\mu\nu a}+\bar{\psi}\left(i\gamma^{\mu}D_{\mu}-m\right)\psi-\frac{\xi}{2}B^{a}B^{a}+B^{a}\partial^{\mu}A_{\mu}\,^{a}+\bar{c}^{a}\left(-\partial^{\mu}D_{\mu}\,^{ac}\right)c^{c} $$ (for example in Peskin and Schröder equati... | In the context of the gauge-fixed Faddeev-Popov Lagrangian, can you derive the classical equations of motion for the ghost fields and their adjoints, specifically focusing on confirming or disproving the last equation: $$ f^{abd}\left(\partial_{\sigma}\bar{c}^{a}\right)A^{\sigma}\,^{b}=0 $$ and relating it to the expre... | 33,436 | cqadupstack-physics |
106454 | Number of wave modes in a cavity | I'm trying to calculate the number of acoustic modes that can exist in a room in a certain range of frequencies. I thought of using the Rayleigh-Jeans formula for the electromagnetic standing wave modes possible in a cavity ($\frac{dN}{d\nu}=\frac{8\pi V}{c^3}\nu^2$), dividing by two to account for the fact that longit... | How do you determine the number of acoustic modes in a non-cubical cavity using the Rayleigh-Jeans formula, and what adjustments need to be made for the differences in dimensions if any? Specifically, can you explain if the formula $\frac{dN}{d\nu}=\frac{8\pi V}{c^3}\nu^2$ is valid for arbitrary geometries and what the... | 35,889 | cqadupstack-physics |
29550 | How are the CPU power and temperature caculated/estimated? | 1. From Wikipedia > The power consumed by a CPU, is approximately proportional to CPU frequency, > and to the square of the CPU voltage: $$ P = C V^2 f $$ (where C is > capacitance, f is frequency and V is voltage). I wonder how that is derived from basic circuit theory? How is a CPU modeled as a circuit? Why is it mod... | In a CPU's power consumption model represented by the formula \( P = C V^2 f \), if the capacitance \( C \) is considered constant, how would the power consumption change if the frequency \( f \) is halved and the voltage \( V \) is decreased to \( 0.8V \) of its original value? Calculate the new power consumption as a... | 24,853 | cqadupstack-physics |
26068 | Recommended first accessories for starblast 4.5 | My son got an orion starblast 4.5 for Christmas. It comes with orion explorer II 17mm and 6mm eyepieces. We are looking at some additional accessories and wondering what you would recommend as "first accessories" to get the most out of the telescope. Our initial inclination is towards: 1. A barlow lens. Probably the ... | What is the theoretical maximum magnification achievable with the Orion StarBlast 4.5 telescope when using the 17mm eyepiece and a 2x Barlow lens? | 4,573 | cqadupstack-physics |
66616 | Heat transfer in a pipe | I have a gas (assuming air) at T = 500 K that enters a cylindrical pipe. The outlet target temperature is 330K. There will be heat transfer via: Forced convection from the gas to the inside of the pipe, conduction through the pipe thickness, convection to the ambient air environment ($T_{\infty} = 300 K) $ and radiatio... | What is the expected temperature variation along the length of a cylindrical pipe through which air at 500 K flows, given that the outlet temperature is set to 330 K and heat transfer occurs via forced convection, conduction through the pipe, convection to the ambient air at 300 K, and radiation from the pipe surface? | 16,933 | cqadupstack-physics |
93310 | What is the difference between the words transparent and translucent? | Merriam Webster defines **_transparent_** as: > Having the property of transmitting light without appreciable scattering so > that bodies lying beyond are seen clearly. And **_translucent_** as: > Transmitting and diffusing light so that objects beyond cannot be seen > clearly. Now if you see any object through a lens ... | Given that the definitions of **transparent** and **translucent** can affect how we perceive objects through materials like lenses or water bottles, could you quantify the levels of light transmission for a typical glass lens and a frosted glass bottle? Specifically, what percentage of light do these materials transmit... | 30,005 | cqadupstack-physics |
75917 | positron / electron annihilation - where is the invariant? | Electron and a positron are headed towards each other with same kinetic energies - observed from _center of mass_ (COM) system. After the colission two photons are emitted and are headed in opposite directions with the same momentum. hat are photon wavelengths? In almost every pair production problem we have to use Lor... | In a collision between an electron and a positron, each with the same kinetic energy, two photons are emitted in opposite directions. Given that the rest mass energy of the electron (and positron) is \( E_0 = m_e c^2 \) and the total kinetic energy of the system in the center of mass frame is \( KE \), how would you ap... | 31,196 | cqadupstack-physics |
78776 | Relation between decay probability and the energy of particle | Is there any way to find the energy of a particle through its decay probability? | How can the energy of a particle be calculated using its decay probability, and what is the relationship between these two concepts? | 25,267 | cqadupstack-physics |
21278 | Discrete point particles stress energy tensor | I am trying to solve an exercise in Sean Carroll's GR book "Spacetime and Geometry". Basically we need to derive the stress-energy tensor of a perfect fluid (ie $T^{\mu\nu}=(\rho +p)U^{\mu}U^{\nu} + p\eta^{\mu\nu}$) from the stress-energy tensor of a discrete set of particles (ie $T^{\mu\nu}=\sum_a \frac{p^{\mu}_a p^{\... | How can we derive the pressure of a perfect fluid from the stress-energy tensor of a discrete set of particles, specifically relating the density distribution \(\rho\) to the four-momentum \(p^{\mu}\) using the integral approximation for a continuous fluid? What is the mathematical relationship that connects these quan... | 32,037 | cqadupstack-physics |
127451 | Strength of strong nuclear force vs distance? | Is there at least an approximation of the decrease in strong nuclear attraction vs distance from the center of the nucleus? | What is the approximate relationship between the strength of strong nuclear force and the distance from the center of the nucleus, and how does this impact the stability of atomic nuclei? | 36,654 | cqadupstack-physics |
116813 | AdS Space Boundary and Geodesics | I'm new to working with AdS space and am primarily concerned with black holes. I'm just playing round with the metric for AdS$_4$ $$ds^2=-f(r)dt^2+f^{-1}(r)dr^2+r^2d\zeta^2$$ for $f(r)=r^2+m $, $\space\space\space\zeta=d\theta^2+\sin^2\theta d\phi^2$. My problem is trying to understand the boundary; specifically when c... | How can I mathematically demonstrate that null geodesics in AdS space correspond to straight lines reaching the boundary, and how does this relate to the derived equation \(\frac{dr}{d\lambda}=k\) for a radial path, given the metric \(ds^2 = -f(r)dt^2 + f^{-1}(r)dr^2 + r^2d\zeta^2\) where \(f(r) = r^2 + m\)? Additional... | 14,307 | cqadupstack-physics |
17072 | Are there irreducible tensors of half integral degree in quantum mechanics? | According to Ballentine, an irreducible tensor of degree k can be defined as a set of $2k + 1$ operators $\\{T_q^{\;\;(k)}:(-k \le q \le k)\\}$ satisfying the following commutation relations: $$ [J_\pm, T_q^{\;\;(k)}] = \hbar \left( (k \mp q)(k \pm q + 1) \right)^\frac{1}{2} T_{q \pm 1}^{\;\;(k)} $$ $$ [J_z, T_q^{\;\;(... | Is it possible to construct an irreducible tensor of half integral degree, specifically for \( k = \frac{1}{2} \)? If so, can you provide a simple example of such a tensor? | 25,557 | cqadupstack-physics |
30800 | on what fundamental force is a black hole based on? | what fundalmentel force does a black hole based on? It seems people is very unfamilar with black holes. I will take a guess, is it electromantic force? please explain. | What is the fundamental force that black holes primarily rely on, and how does it influence their formation and behavior in the universe? | 35,065 | cqadupstack-physics |
82625 | Curie temperature and magnetization? | If an ferromagnetic object is heated and reaches Tc the magnetization gradually drops as we get closer to Tc or it's a instant drop? Can I assume as I heat the object, the magnetization is weakening gradually? Likewas as it cools? | At what temperature range does the magnetization of a ferromagnetic material begin to decrease as it approaches the Curie temperature (Tc), and what is the nature of this change—gradual or sudden? Additionally, how does the magnetization behave as the material cools back down through Tc? | 29,884 | cqadupstack-physics |
87560 | Does a radio receiver add a load to the transmitter? | If I have a dynamo connected to a switch and a load (such as a light bulb), the load on the dynamo is increased when the switch is closed and the light comes on. The dynamo gets harder to turn. Is the same true for a radio transmitter and receiver? If the receiving aerial is initially not connected to a circuit and the... | When a receiving aerial in a radio receiver circuit is connected, can the transmitting end detect a change in load due to this connection? If so, what principles govern this detection, and how does this differ from the increased load on a dynamo when a light bulb is switched on? | 29,926 | cqadupstack-physics |
12418 | How Can We Measure The Mass Of Particle? | As we know, the mass of well known particles are below. $m_{n}\approx0.0000000000000000000000000016749286[kg]$ $m_{p}\approx0.0000000000000000000000000016726231[kg]$ $m_{e}\approx0.00000000000000000000000000000091093897[kg]$ I roughly know the way how to measure the electron's mass, but I don't know rest two of them. A... | What is the ratio of the mass of a neutron to the mass of a proton, using the approximated masses given: \(m_{n} \approx 1.675 \times 10^{-27} \, \text{kg}\) and \(m_{p} \approx 1.673 \times 10^{-27} \, \text{kg}\)? | 8,535 | cqadupstack-physics |
21353 | Why no basis vector in Newtonian gravitational vector field? | In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a three dimensional gradient$$\mathbf{g}=-\mathbf{\nabla\phi}=-\left(\frac{\partial\phi}{\partial x},\frac{\partial\phi}{\p... | Given the gravitational potential field \(\phi = \frac{-Gm}{r}\), derive the gravitational field \(\mathbf{g}\) using the gradient operator \(\nabla\). What is the expression for \(\mathbf{g}\) in terms of the variables \(G\), \(m\), and \(r\)? | 16,124 | cqadupstack-physics |
118410 | On conservative forces | We say if we calculate the work done by a force in going from 1 to 2 following a path say A is equal to -1 times the work done by the same force in getting from 2 to 1 following a path say B then work done by the force along any path to get to 2 from 1 is the same and the work done is hence path independent while the f... | How can we mathematically demonstrate that the work done by a conservative force is path independent, and what conditions must be satisfied for a force to be classified as conservative? | 9,626 | cqadupstack-physics |
114109 | Conservation of energy (or lack thereof) in Doppler cooling | I did not find my question answered elsewhere, so here it is. I'm doing a project in my first optics course, and we are reading a bit about Doppler cooling. I understand that a laser is tuned to a frequency where the photon energy $E_p = h \nu$ corresponds to an energy slightly below the energy $E_{abs}$ required to ex... | In a Doppler cooling experiment, a laser is tuned to a frequency slightly below the energy required to excite gas atoms, allowing atoms moving towards the laser to absorb photons and slow down. If an atom initially moving towards the laser with speed \( v \) absorbs a photon of frequency \( \nu_1 \) and then re-emits i... | 3,733 | cqadupstack-physics |
131028 | What is a good textbook to learn how to ray trace light through an optics system in 3d? | I can do 2d problems easily, but I need to learn more to do a 3D ray trace. Can you guys point me towards a textbook? I'm having trouble dealing with the normal and incident rays in 3D | What are the steps to calculate the reflection and refraction of a ray of light striking a transparent sphere at an angle of incidence of 30 degrees, given that the refractive index of the sphere is 1.5? | 918 | cqadupstack-physics |
115217 | Is battery capacity proportional to Ampere-hour in every case? | Suppose I have two batteries one inside the laptop with 2.5 AH giving a backup for around 2 hours. The battery is external inside a UPS system with 7.5 AH. Since it has thrice the capacity of the previous one, can I conclude it will give backup for 6 hours? | If a laptop battery with a capacity of 2.5 AH can provide a backup for 2 hours, what would be the expected backup time of an external UPS battery with a capacity of 7.5 AH, assuming both batteries discharge at the same rate? | 14,539 | cqadupstack-physics |
104097 | Quantum computing records (storage times) | Long storage times for qubits will be integral in the construction of a scalable quantum computer. This leads me to ask the current state of affairs in our ability to store qubits. Namely, what is the **record** storage time for a qubit at **any** temperature? Upon searching for the record storage time I found the foll... | What is the longest recorded storage time for a qubit, and how does this storage time vary with temperature? | 16,154 | cqadupstack-physics |
107320 | Gravity and acceleration | I've imagined this little scenario to help me conceptualize things. Let's say we have a doughnut-shaped object with a hole whose diameter is greater than that of a sphere. Let's say that the sphere is vertically aligned with the center of the doughnut and is horizontally gravitating towards it according to Newton's law... | If a sphere with a mass of 1 kg is aligned vertically through the center of a toroidal doughnut-shaped object with an inner diameter of 10 cm and a mass of 5 kg, how far would the sphere travel toward the doughnut before the gravitational force causes it to reverse direction, assuming only gravitational forces are acti... | 19,821 | cqadupstack-physics |
66550 | Conceptual difficulty in understanding Fourier's Law of heat conduction | I am having a bit of difficulty understanding the statement of Fourier's law of heat conduction. As mentioned in Georg Joos , Theoretical Physics > The quantity of heat passing per second through unit area of a surface > normal to the direction of flow, is proportional to the negative of the > temperature gradient. My ... | How does Fourier's law of heat conduction represent the flow of heat in terms of a temperature gradient, and can you provide a mathematical example of how the heat transfer rate varies with different temperature differences across a surface? | 21,913 | cqadupstack-physics |
80028 | What does the complex electric field show? | We have a complex electric field. Is there any definition for absolute and imaginary part of a complex electric field? What do they stand for? | What are the absolute and imaginary parts of a complex electric field, and how do they relate to the physical properties of the field? | 28,513 | cqadupstack-physics |
6897 | Why didn't Newton have a cosmological constant | Einstein initially added the Cosmological Constant because (if I get this right) it seemed to him that the universe should be static. I agree that back then this would have been an obvious assumption. I'm curious now, before Hubble, where there any opinions/debates about whether the universe would be expanding or contr... | What evidence existed before Hubble's observations to support the idea that the universe was either expanding or contracting, and how did this shape early 20th-century cosmological theories? | 12,655 | cqadupstack-physics |
94317 | Is there a way to increase the speed of light itself? | When light enters materials it slows down due to its refractive index (due to absorbing and re-emission of photons). But, is there a way to increase the speed of light itself? Can there be some material which would increase rather than decrease the speed of light? | In a vacuum, light travels at a speed of approximately \(3.00 \times 10^8\) m/s. If a hypothetical material were developed that could allow light to travel faster than this speed, what fundamental physical principles would need to be considered, and what implications would it have on our understanding of causality? | 33,036 | cqadupstack-physics |
55918 | Newtonian Gravity on a Riemannian $3$-Manifold | To solve the Poisson equation for the Newton Potential, say $\phi$, one can use the divergence theorem, such that $$\int_U \nabla^2 \phi \sqrt{g}~ dV= \int_{\partial U} <\nabla \phi,n> \sqrt{g_\Sigma}~ d\Sigma=1,$$ where $\sqrt{g_\Sigma}$ represents the induced metric on the border. Considering that $\phi$ is classic i... | In the context of Riemannian manifolds, can you derive the relationship between the minimized energy and the geodesic distance from a point source? Specifically, under what conditions do equipotential surfaces correspond to curves of equal energy rather than equal distance? Please provide examples to illustrate your ex... | 8,613 | cqadupstack-physics |
129175 | Transformer leakage reactance | In practical transformers there is always a leakage reactance. If it is possible to construct such a transformer (ideally thinking) having zero leakage reactance will the transformer action work? or not. Edited: Probably my approach was wrong for that question I actually wants to ask. Now I'm trying to say it clearly. ... | If a transformer could be constructed such that no magnetic flux links either the primary or secondary coil, resulting in zero magnetic coupling, what would be the consequence for the transformer action? Would it still be able to induce an electromotive force (EMF) in the secondary winding, and why or why not? | 35,322 | cqadupstack-physics |
9274 | Can one see radioactive substances with an X-ray detector? | I was wondering the other day an X-ray detector (like the ones used at airports) can detect gamma-rays lets say from a sample of uranium. I know its all electro-magnetic waves but I'm really unsure about how it works in practical terms. **Edit** Now out of curiousity, if you got an beta-radiator, might that go unnotice... | What is the minimum energy threshold of gamma-rays required for detection by a standard X-ray detector, and how does this compare to the energy of beta particles emitted from a typical beta-radiating source? | 29,580 | cqadupstack-physics |
22204 | Lorentz invariance of the 3 + 1 decomposition of spacetime | Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example $$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$ ($N$ is called lapse, $N_a$ is the shift vector and $q_{ab}$ is the spatial part of the metric.) in order to arrive at a Hamiltonian formulation of GR? H... | In the decomposition of the spacetime metric into temporal and spatial parts as shown by the equation $$ds^2 = (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b,$$ where $N$ is the lapse function, $N_a$ is the shift vector, and $q_{ab}$ is the spatial metric, how can one mathematically ensure that the resulting Hamilto... | 8,332 | cqadupstack-physics |
28700 | Auxiliary field and loop expansion | Something bugs me with the use of auxiliary fields in QFT. On one side I understand that they are nothing more than Lagrange multipliers and should be replaced by their equation of motions in the action, and this works perfectly on-shell (by definition) but what about this replacement at the quantum level, where the eq... | In a quantum field theory with one physical field and one auxiliary field, if you perform a loop expansion first by eliminating the auxiliary field and then by retaining it, will the calculated quantities at each order of perturbation be identical? Can you provide a proof or reasoning for your answer? | 30,699 | cqadupstack-physics |
86815 | EM attenuation in free space at different frequencies | Can anyone explain intuitively why electromagnetic radiation (according to the basic path loss equation in communications) experiences more attenuation at higher frequencies? The equation states that the path loss $ L $ is proportional to $ d\times f $, where $ d $ is the distance the wave has propagated and $ f $ is t... | What is the path loss in decibels experienced by an electromagnetic wave with a frequency of 5 GHz when it has propagated a distance of 100 meters? Use the basic path loss equation \( L = d \times f \), where \( d \) is in meters and \( f \) is in GHz. | 30,630 | cqadupstack-physics |
103083 | Changing the resistance of a circuit | I am wondering, when we change the resistance in a circuit, does the voltage tend to increase or the ampere decrease? More specifically, under what conditions does what happen? E.g. If we have a high-resistance voltmeter, does increasing the resistance of the circuit itself necessary increase the reading, or might the ... | In a simple electrical circuit with a fixed voltage source, how does increasing the total resistance affect the current through the circuit, and what is the relationship between resistance, voltage, and current as described by Ohm's Law? Provide a quantitative example using specific resistance values and initial curren... | 4,020 | cqadupstack-physics |
29542 | interpretation of Green function | Is there a physical interpretation of the existence of poles for a Green function? In particular how can we interpret the fact that a pole is purely real or purely imaginary? It's a general question but I would be interested in the interpretation in quantum systems. | How does the presence of real or imaginary poles in a Green function indicate the stability of quantum states in a quantum system, and what specific physical interpretations can be drawn from these poles in terms of energy levels and system behavior? | 7,183 | cqadupstack-physics |
99094 | Using 2D position, velocity, and mass to determine the parametric position equations for an orbiting body | I have a gravity-related question. I am programming an orbit simulator. I have everything up and running, but I would like to render the smaller body's orbital path (the larger body is fixed). To do this, I need the parametric equations for the body's position for any given time (i.e. I need an $x(t)$ and $y(t)$ functi... | Given the positions and velocities of a smaller body orbiting a larger body, how can I derive the parametric equations $x(t)$ and $y(t)$ for the smaller body's orbital path, assuming the larger body is fixed and using only the provided initial conditions? Additionally, what conservation laws or principles should I cons... | 16,973 | cqadupstack-physics |
29501 | How do gravitational waves sustain and propagate large scale spacetime curvature? | I understand that gravity in GR is a manifestation spacetime curvature dictated by the field equations by the principle that objects follow the geodesic path in spacetime. And, I get how gravitational radiation travels like waves because there are wave equations in the field equations. But, I have trouble reconciling g... | If a massive object like Earth were to suddenly disappear, how would you mathematically quantify the propagation of the resulting change in spacetime curvature, specifically regarding the speed and characteristics of the gravitational waves emitted, assuming an initial Schwarzschild metric? | 25,702 | cqadupstack-physics |
98502 | How many unequivalent Seifert surfaces appear in a AdS/CFT extension? | When introducing the 't Hooft diagrams from Feynman diagrams on a torus has there been a classification in terms of knots and Seifert surfaces? | What is the relationship between 't Hooft diagrams and knot theory in the classification of Feynman diagrams on a torus, specifically regarding Seifert surfaces? | 31,841 | cqadupstack-physics |
89558 | Is it possible to harness energy from the exothermic reaction of changes of state of matter? | Since a substance emits heat as it transitions from a high energy state (gas) to a lower energy state (solid), is it possible to devise a method to capture this heat and convert it to usable energy? I'm not sure how economical this would be, but consider the exothermic reaction of water freezing. The heat of fusion for... | If 1 cubic meter of water freezes and releases $3.33 \times 10^8$ J of heat energy, what is the total energy output in megajoules, and how might this energy capture compare in efficiency to traditional methods of energy generation? | 10,623 | cqadupstack-physics |
111239 | Would dropping large blocks of ice into the ocean mitigate global warming? | This amusing Futurama sketch 'solves' global warming by dropping increasingly larger blocks of ice into the ocean. Presumably the blocks of ice are harvested from a different planet. Would this theoretically be effective? My understanding is that by global warming, we mean an increased amount of energy in Earth's atmos... | If we drop a block of ice with a mass of 1000 kg into the ocean, how much energy in joules is absorbed by the ocean as the ice melts, assuming the initial temperature of the ice is -10°C, the melting point of ice is 0°C, and the specific heat capacity of ice is 2.09 J/g°C? Additionally, how does this energy transfer po... | 9,391 | cqadupstack-physics |
41672 | A man on a boat, with something in his hand | > **Possible Duplicate:** > Basic buoyancy question: Man in a boat with a stone A man is on a boat, in the middle of a quiet lake. He has something in his hands (anything you like) He throws the "something" in the water. Does the water level increases or decreases? And if the answer is "it depends", on what it d... | A man is in a boat on a lake, holding a stone that weighs 5 kg. While in the boat, the stone causes the water level to rise by a certain volume. If he throws the stone into the water, what happens to the water level in the lake? Calculate the change in water level, assuming the boat and man displace a total volume of 0... | 18,067 | cqadupstack-physics |
87821 | Symmetries of a Uniform Magnetic Field | Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel to it. This system also has rotational invariance in the plane perpendicular to the electric field. What about a uniform... | What is the most symmetric choice for the vector potential \(\vec{A}\) in a uniform magnetic field, and how does this choice affect the system's symmetries compared to a uniform electric field? | 28,420 | cqadupstack-physics |
62929 | Time Dependent HydroHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? gen Wave Function | 1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? go about writing the time dependent wave function given the wavefunction at $t=0$? Suppose How would I go about writing the time dependent wave function given the wavefunction at $t=0$? an electron is in a superpo... | Given the normalized wavefunction of an electron in a superposition state in the hydrogen atom at time \( t = 0 \):
\[
\psi(r, \theta, \phi) = A(2R_{10}Y_{00} + 4R_{21}Y_{1,-1}),
\]
what is the time-dependent wavefunction \(\Psi(r, \theta, \phi, t)\) for this state, considering that the corresponding energy eigenvalu... | 31,962 | cqadupstack-physics |
77419 | When studying electrodynamics do we assume Maxwell's Equations or derive them? | This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like Coulomb's law in electrostatics and so on, and then manipulate those things to derive Maxwell's Equations. After that we could then use Maxwell's Equations at will. Now, I'm conf... | Why is it often more practical to start from Maxwell's Equations rather than deriving them from fundamental concepts like Coulomb's law, despite the historical development of electromagnetism? Can you quantify the implications of using the equations directly in terms of their predictive power or applications in electro... | 18,280 | cqadupstack-physics |
16282 | Critics of Mannheim's Conformal Gravity Theory? | I'm looking for more articles/reactions/critiques/support for Philip Mannheim's recent conformal gravity theory. See here: http://arxiv.org/abs/1101.2186v1 Any ideas on where to start? | What are the key predictions of Philip Mannheim's conformal gravity theory, and how do they differ from predictions made by general relativity in a specific experimental scenario? | 32,820 | cqadupstack-physics |
70209 | How is energy extracted from fusion? | I understand that combining deuterium and tritium will form helium and a neutron. There are three methods to do this (1) tokamak (2) lasers and (3) cold fusion. I would like to know after helium is formed. How is that energy extracted from tokamak and stored? | What are the mechanisms involved in extracting and storing energy from helium produced during deuterium-tritium fusion in a tokamak reactor? | 11,622 | cqadupstack-physics |
21146 | The energy of electric interaction between these dipoles? | I'm a physics tutor. This is not a homework problem. I'm unable to solve this problem. The energy of electric interaction between these dipoles will be:  Choose the correct answer from: ... | Given two electric dipoles \( \mathbf{p_1} = q_1 \mathbf{d_1} \) and \( \mathbf{p_2} = q_2 \mathbf{d_2} \), calculate the potential energy of the system when the dipoles are positioned in a uniform electric field \( \mathbf{E} \) and oriented at an angle \( \theta \) with respect to the field. Provide your answer in te... | 25,010 | cqadupstack-physics |
70822 | Magnification, and it's application | I'm having a problem with a very trivial thing- magnification makes things bigger. But if it doubles or triples the size AND distance away, why does it even help? I think I'm just ignoring something about how we see, but I don't understand why making a small object twice as tall but twice as far away would help at all. | If an object is magnified to twice its original height and positioned twice as far away from the observer, what effect does this have on the angular size of the object as perceived by the eye? Calculate the change in angular size in degrees, assuming the original height of the object is 2 cm and the original distance i... | 13,056 | cqadupstack-physics |
43909 | Is $kg_f$ the same everywhere in the universe? | A textbook question says that a vehicle weighs $25kg_f$ on Earth, and asks us to consider certain issues related to its behaviour on the moon. My question is, does the unit kilogram-force $kg_f$ need to be converted to match the gravitational pull of the moon, or is it $25kg_f$ everywhere in the universe? I read up on ... | If a vehicle weighs 25 kg_f on Earth, what would its equivalent weight be in newtons on the Moon, where the gravitational acceleration is approximately 1.62 m/s²? | 12,576 | cqadupstack-physics |
74271 | Equations of motion for a pendulum and spring system | The question is available here:  I've modeled the building as a rod on a torsional spring (with a pendulum hanging from the top). $\phi$ is the angle from the centre for the pendulum and $\theta$ is the angle from the centre for the building. Taking the... | In a system where a pendulum hangs from a torsional spring modeled as a rod, the pendulum has a moment of inertia of \( mL^2 \) and the building (rod) has a moment of inertia of \( \frac{mh^2}{3} \). If \( \phi \) is the angle of the pendulum and \( \theta \) is the angle from the center of the building, derive the equ... | 22,241 | cqadupstack-physics |
128802 | How can a detector distinguish between a photon and a gluon | 1. Considering that both gluons and photons have no mass, no charge and spin 1, I was wondering how one can tell the difference, if they hit a detector after a collision at the LHC. 2. I know that gluons are supposed to have a color, but I have never heard, that someone measured the color. How can you measure the col... | How can the presence of color charge in gluons be experimentally identified in a detector after a collision at the Large Hadron Collider, given that gluons and photons both have no mass, no charge, and are spin-1 particles? | 17,491 | cqadupstack-physics |
92903 | Polarisation of light is a wave concept or applicable to photons as well? | I have a very fundamental question. We explain polarisation of light assuming wave nature of light. Is it still valid if we assume light as photons? Or in other words, polarisation is a wave concept or applicable to individual photons as well? May be this is my wrong concept! I feel some confusion here. | How can the phenomenon of light polarization be explained in terms of individual photons, and what implications does this have for our understanding of light as both a wave and a particle? | 35,812 | cqadupstack-physics |
90558 | Interpretation: probability form probability amplitude (free particle) | If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you will find it to be given by $$ \mathcal{M} = \left\langle x_N \right| \text{e}^{-\frac{\text{i}}{\hbar} \frac{P^2}{2m}(t... | Can you explain why the probability density \( P \) of detecting a free non-relativistic particle in one dimension does not depend on the distance \( (x_N - x_0) \) and what this implies about the likelihood of detecting the particle at different positions over time? | 18,910 | cqadupstack-physics |
82310 | Photons angular momentum / spin | I have a textbook that says that photons have a spin of absolute value $\hbar$ and at some other point, they say that it has angular momentum of absolute value $\hbar$. Now, since they are different things, I was asking myself: Is it maybe right to say, that it is a spin that is transformed into angular momentum when t... | What is the relationship between the spin of a photon, which has an absolute value of $\hbar$, and its angular momentum when it interacts with matter, particularly during absorption? Are these quantities equivalent, and if so, how do they relate in the context of quantum mechanics? | 12,618 | cqadupstack-physics |
38984 | a positive potential as $ x \rightarrow \infty $ | let us suppose i can calculate the asymptotic of any potential $ V(x) $ in one dimension , and that i manage to prove that $ V(x) \ge 0 $ as $ x \rightarrow \infty $ could i conclude taht if or big 'x' the potential is POSITIVE that for big 'n' the enegies will be also POSITIVE $ E_{n} \ge 0 $ ?? as $ n \rightarrow \in... | If a potential \( V(x) \) in one dimension satisfies \( V(x) \ge 0 \) as \( x \rightarrow \infty \), can you determine whether the energies \( E_n \) are also positive for large \( n \)? Specifically, what conditions must be met for this to hold true in the context of the asymptotic behavior of \( V(x) \) and the WKB a... | 18,782 | cqadupstack-physics |
63399 | Non reciprocal light propagation | In search for some explanation in why magneto-optical materials (like the one used in the Faraday rotator and, consequently, in the "optical diode") act in such a "strange" way, I saw that this kind of materials break the time- reversal symmetry and a different kind of reciprocity is applicable, the Rayleigh-Carson one... | How does the interaction of polarized light with a magneto-optical material, such as the Faraday rotator, lead to a rotation of the polarization vector, and what would be the expected angle of rotation for a light beam passing through a sample with a thickness of 1 cm and a Verdet constant of 0.1 rad/T·m in the presenc... | 31,447 | cqadupstack-physics |
65822 | Why are the magnetic moment and the angular moment related? | I've always read everywhere that they are related but found nowhere a satisfactory explanation of the cause | What is the biochemical basis for the relationship between genotype and phenotype, and how can this be quantitatively measured in a controlled experiment? | 10,680 | cqadupstack-physics |
102395 | Coupled mass spring system with damping and initial values | After researching through the web, I can't figure out how to express into a differential equation a coupled mass spring system with damping and initial values. Two masses and two springs, no external forces, just gravity because of vertical position. I know that $mx''+cx'+kx=f(t)$ is used for single spring systems, but... | Given a coupled mass-spring system with two masses, where the first mass is attached to a spring with spring constant \( k_1 = 3 \, \text{N/m} \) and damping coefficient \( c_1 = 1 \, \text{Ns/m} \), and the second mass is attached to a spring with spring constant \( k_2 = 1 \, \text{N/m} \) and damping coefficient \( ... | 13,154 | cqadupstack-physics |
110073 | How to derive quantum Fourier transform from discrete Fourier transform (DFT)? | I am interested in Shor's algorithm, and I am reading several papers that related to the quantum Fourier transform (QFT). I know the there is a difference between the output of QFT and DFT (DFT). But I do not know how to derive QFT from DFT. I do not know how to link from QFT and DFT, and maybe I have not comprehend al... | Can you explain the differences between the Quantum Fourier Transform (QFT) and the Discrete Fourier Transform (DFT), and provide a step-by-step derivation that links the two transformations? | 30,968 | cqadupstack-physics |
69258 | Derivation of impact free Boltzmann equation | When deriving the impact-free boltzmann equation ( $\frac{\partial f}{\partial t} + \vec{v} \cdot\frac{\partial f}{\partial \vec{x}} + \vec{a} \cdot \frac{\partial f}{\partial \vec{v}} = 0$) I have a question about the notion. Basically we are looking at the change in particles in a given volume $V$ which is given by: ... | How can we mathematically interpret the term \( f(\vec{x}, \vec{v}, t) d\vec{A} \) in the context of the flux of particles through the surface of a volume \( V \), and how does multiplying this term by the vector \( (\vec{v}, \vec{a}) \) relate to the particle interactions at the boundary of \( V \)? | 18,562 | cqadupstack-physics |
101822 | How is the scale factor from the FLRW equation used with Volume? | I'm trying to put a spreadsheet together that shows the co-moving volume of the universe from the time soon after the Big Bang through the present and then as predicted into the future. I am pretty sure that all I have to do is use the scale factor $a(t)$ as derived from the FLRW equations (I suppose this is what the s... | How do you calculate the co-moving volume of the universe, \( V(t) \), using the scale factor \( a(t) \) derived from the FLRW equations? Specifically, is it correct to use the formula \( V(t) = V_0 a(t)^3 \), \( V(t) = V_0 a(t) \), or should I first determine the radius \( R(t) = a(t) R_0 \) before calculating \( V(t)... | 19,440 | cqadupstack-physics |
58178 | Work done by friction | Suppose we have a block of mass $M$ and we are moving it up a curve, very slowly ($a=0$). The surface is not smooth, and coefficient of friction is $\mu=\mu_s=\mu_k$. To move the block we apply a force $F$ to the block tangential to the surface(on which the block is, at that time). If we take the angle of slope to be $... | Given a block of mass \( M \) moving up a slope with an angle \( \theta \), where the coefficient of friction is \( \mu \), derive the expression for the work done by friction as the block moves a vertical height \( h \) and a horizontal distance \( x \). How does this work relate to the external force \( F \), and doe... | 14,070 | cqadupstack-physics |
122952 | Work done in pulling a rope from a boat | > _A boy sitting on a boat pulls on a rope with a constant force $F$ over a > duration of time $t$. The other end of the rope is either tied to a bridge > or to another freely floating boat of equal mass. Does the boy do more work > in the case of the bridge, or in the case of the other freely floating > boat?_ Here's ... | When a boy sitting on a boat pulls on a rope with a constant force \( F \) for a duration of time \( t \), and the rope is either tied to a bridge or to another freely floating boat of equal mass, how does the work done by the boy in each case compare quantitatively? Specifically, calculate the work done in both scenar... | 4,454 | cqadupstack-physics |
101853 | Photoelectric effect with protons | Is it possible to make a metal plate emit protons (not electrons) when it is illuminated with light? If possible, how? | Is it feasible to use a specific wavelength of light to induce a metal plate to emit protons, and if so, what parameters would influence the efficiency of this proton emission? | 26,208 | cqadupstack-physics |
81712 | How does enthalpy help us to find the state of equilibrium? | For an adiabatic system with constant external (generalized) forces, in a state out of equilibrium we have: $$\delta H\leq 0 $$ If I understand correctly, derivation of this inequality does not rely on the second law of thermodynamics, which states how systems evolve toward equilibrium. Here is the derivation: Having c... | In an adiabatic system with constant external forces, the inequality \( \delta H \leq 0 \) is derived without using the second law of thermodynamics. Can you explain the physical principle that justifies this inequality and how one can deduce that the system evolves toward equilibrium without reference to the second la... | 37,820 | cqadupstack-physics |
78915 | Efficiency of Stirling engine and Carnot's theorem | I want to calculate the efficiency of this Stirling cycle for an ideal gas $pV = nRT$  The mechanical work is $$ \Delta W_{12} = - \int_{V_1}^{V_2} p(V) \mathrm{d}V = -nRT_2 \ln \fr... | Given an ideal Stirling cycle operating between two temperature reservoirs at temperatures \( T_1 \) and \( T_2 \), with the respective heat exchanges and work done expressed as follows:
- Input heat:
\[
\Delta Q = n R T_2 \ln \frac{V_2}{V_1} + C_V (T_2 - T_1)
\]
- Total mechanical work:
\[
\Delta W = -nR(T... | 38,281 | cqadupstack-physics |
1716 | In photo-electric experiment, if the light is exposed to a metal plate for a long enough interval, does the plate become lighter? | I know from the book that electrons will be kicked out from the metal plate if the light of appropriate wavelength is exposed to the metal plate. My mental model says if we let the light expose the plate in a long enough interval, the plate will have no electrons anymore. So what happens on the plate? Does it still loo... | If a metal plate is continuously exposed to light of an appropriate wavelength, causing the photoelectric effect, how does the loss of electrons affect the mass and surface properties of the plate over time? Would the plate become noticeably lighter, and would there be any observable changes in its appearance? | 33,486 | cqadupstack-physics |
34679 | Anti particles: What exactly is inverted? | http://en.wikipedia.org/wiki/Antiparticle says "Corresponding to most kinds of particles, there is an associated antiparticle with the same mass and opposite electric charge." and What is anti-matter? goes along with that. But. Reading about the Standard Model I see several things sometimes called XXX- charge, like bar... | What are the specific quantum numbers that change sign when comparing a particle and its corresponding antiparticle, and how does this relate to the principles of the Standard Model? | 10,534 | cqadupstack-physics |
106699 | Quantum Mechanics: Momentum operator questions | I'm asked to determine $\hat{P}|\Psi_0\rangle$, $\langle{\hat{P}}\rangle$, and $\langle\hat{P}^2\rangle$ for $$\Psi_0(u) = \psi_0 + 2\psi_1$$ I understand how to make the matrix for $P$ in regards to the original $\psi_0$ and $\psi_1$ functions, but I'm clueless for the $\Psi $ function that contains the two. | How do I calculate the expectation values $\langle\hat{P}\rangle$ and $\langle\hat{P}^2\rangle$ for the state function $\Psi_0(u) = \psi_0 + 2\psi_1$, given that I already have the matrix representation of the operator $\hat{P}$ for the individual functions $\psi_0$ and $\psi_1$? | 26,805 | cqadupstack-physics |
21573 | Quantum perpetual motion | > Perpetual motion describes hypothetical machines that operate or produce > useful work indefinitely and, more generally, hypothetical machines that > produce more work or energy than they consume, whether they might operate > indefinitely or not. (Source:Wikipedia) With this definition in mind, particularly the "oper... | Can quantum mechanics allow a hypothetical machine to operate indefinitely without doing work, and what are the implications of energy quantization on such a scenario? | 36,171 | cqadupstack-physics |
70896 | How "things" radiate electromagnetic radiation? | How things radiate electromagnetic radiation? I don't ask why they radiate (higher temperature than 0K) but how they radiate this electromagnetic waves? | How can the intensity of electromagnetic radiation emitted by a black body at a temperature of 500 K be calculated, and what equation is used to determine the relationship between temperature and emitted radiation? | 32,888 | cqadupstack-physics |
75184 | Why does a mirage disappear as you approach it? | Related: why do mirages only appear on hot day? The title says it all: why does a mirage disappear as you approach it? The related question does not answer this. | What is the relationship between the temperature of the ground and the formation of a mirage, and how does this effect change as the observer approaches the mirage? | 2,701 | cqadupstack-physics |
72059 | Does the particle vibrate in 3D space? | As far as I know, particles vibrate with a frequency and wavelength determined by their energy level. Is this vibration in 3D space? | In the context of quantum mechanics, describe how the vibration of particles is related to their energy levels and determine if this vibration can be described as occurring in three-dimensional space. What are the implications of this for the wave function of a particle in a three-dimensional potential well? | 907 | cqadupstack-physics |
79047 | Determine resultant velocity of an elastic particle-particle collision in 3d space | So I have two particles that have collided in 3 dimensional space. I want the particles to rebound off of each other in an elastic manner. How do I determine the resultant velocity vector if I know: Both particles' initial velocity vector, their masses, and their initial position vectors relative to the origin. I tried... | How can I calculate the resultant velocity vectors of two particles after an elastic collision if I know their initial velocity vectors, masses, and initial position vectors in three-dimensional space? Additionally, can you explain the process without using polar coordinates, and clarify the conventions for angles if p... | 28,901 | cqadupstack-physics |
57455 | Tunneling v. Hopping | Can someone explain the difference between hopping and tunneling? The context I'm considering is conduction in semiconductors, specifically between impurity states within the bandgap. It's always been my understanding that hopping _is_ tunneling. Variable range hopping and nearest neighbor hopping, as I understand it, ... | What is the quantitative difference in conductivity between variable range hopping and nearest neighbor hopping in semiconductors, and how does this difference manifest in the electron transport mechanism within the bandgap? | 11,005 | cqadupstack-physics |
67824 | Question about Lagrangian mechanics | I have a question about the Lagrangian-formalism; they state that the holonomic constraints are expressed as: $$f_\alpha(x_1,y_1,z_1,...,x_n,y_n,z_n,t) = 0 $$ where $\alpha = 1,...,L$ They state now that these constraints may not contain irrelevant information. They express this by saying: $$rank(\frac{\partial{f^{\alp... | Given a system described by holonomic constraints \( f_\alpha(x_1, y_1, z_1, \ldots, x_n, y_n, z_n, t) = 0 \) with \( \alpha = 1, \ldots, L \), if the rank of the Jacobian matrix \( \left( \frac{\partial f^\alpha}{\partial x_k}, \frac{\partial f^\alpha}{\partial y_k}, \frac{\partial f^\alpha}{\partial z_k} \right) \) i... | 9,480 | cqadupstack-physics |
94354 | Uncertainty on a single observable measurement | Heisenberg Uncertainty Principle states (in the form of the Robertson- Schroedinger Formula) that measurement of two non-commuting observables has a limiting precision, even for flawless measurement devices. Okay, no problem with this. But what about a measurement on a single observable, does Quantum Mechanics imposes ... | What is the minimum uncertainty associated with the measurement of a single observable in quantum mechanics, and how is it quantitatively expressed in relation to the properties of quantum states? | 18,096 | cqadupstack-physics |
105407 | Alice and Bob moving in a circular ring of radius $R$ | Alice and Bob are moving in opposite direction around a circular ring of Radius $R$, which is at rest in an inertial frame. Both move with constant speed $V$ as measured in that frame. Each carries a clock, which they synchronize to zero time at a moment when they are at the same position on the ring. Bob predicts that... | Alice and Bob are moving in opposite directions around a circular ring of radius \( R \) with constant speed \( V \). After one complete revolution, what will be the readings on their synchronized clocks when they meet again, and why do both of their predictions regarding time dilation fail to hold true? Provide a deta... | 31,941 | cqadupstack-physics |
63151 | Spaceship split near event horizon | Lets say there's two astronauts, Alice and Bob, going on a space trip to a super-massive black hole. So large that they wouldn't notice any significant spaghettification forces at the event horizon. Alice is sitting on the left, and Bob on the right. They go so close to the event horizon, that Bob enters the event hori... | If Alice is moving faster than the escape velocity of the super-massive black hole and remains outside the event horizon, while Bob crosses the event horizon, what would Alice observe about Bob's movement as he approaches and crosses the event horizon? Additionally, what would Bob perceive about Alice's position as he ... | 30,656 | cqadupstack-physics |
67561 | If subatomic particles pop into existence all the time, why don't I gain weight? | Watching Discovery's first episode of the first season of Curiosity (entitled "Did God Create the Universe?" by Stephen Hawking), I heard this information: > [...] _you enter a world where conjuring something out of nothing **is** > possible (at least, for a short while). That's because at this scale > particles, such ... | If virtual particles can spontaneously appear and disappear in empty space according to quantum mechanics, how does the conservation of mass-energy ensure that the weight of an object, like my body, remains constant despite these fluctuations? | 33,873 | cqadupstack-physics |
51573 | Gravitational redshift derivation | When we derive gravitational potential it is dependant only on (rest) mass $m$, but i have seen a derivation of gravitational redshift equation placing relativistic mass $\widetilde{m}$ instead of rest mass $m$ like this: $$ \begin{split} W_1 &= W_2\\\ h\nu_1 + 0 &= h \nu_2 + \left(-\frac{GM \widetilde{m}}{r}\right)\\\... | What is the relationship between gravitational potential energy and the rest mass of an object in a gravitational field, and how does this differ when considering the concept of relativistic mass? Specifically, how does gravitational redshift relate to rest mass versus relativistic mass for massive particles and massle... | 27,566 | cqadupstack-physics |
7189 | 3D Minimum uncertainty wavepackets | Based on the 1D case mentioned in Griffiths, I decided to try looking at the features of 3D Gaussian wavefunctions, i.e. (position basis) wavefunctions of the form $\psi(\mathbf{r}) = Ae^{-\mathbf{r}^\dagger\mathsf\Sigma\mathbf{r}/4}$, where _A_ is a normalization constant, **r** is position, Σ is a positive-definite s... | Given the condition for minimum uncertainty such that \((\operatorname{Tr}\mathsf\Sigma)(\operatorname{Tr}\mathsf\Sigma^{-1})=1\) and the requirement that \(\mathsf\Sigma\) be a positive-definite symmetric matrix, what specific form must \(\mathsf\Sigma\) take such that it yields both minimum uncertainty with respect t... | 9,627 | cqadupstack-physics |
66866 | Maximum angular velocity to stop in one rotation with a known torque | I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that applying maximum torque will stop the rotation of the object within one rotation. If I know my torque and moment of inertia... | Given an object with a known torque \( \tau \) and moment of inertia \( I \), what is the formula for calculating the maximum rotational velocity \( \omega_{\text{max}} \) that allows the object to stop in exactly one full rotation when maximum torque is applied? | 18,841 | cqadupstack-physics |
74614 | Why are the classical electron radius, the Bohr radius and the Compton wavelength of an electron related to each other? | Using the definition of the fine-structure constant $\alpha = \frac{4 \pi \epsilon_0 \hbar c}{e^2}$ and the Compton wavelength of an electron $\lambda_c = \frac{h}{m_e c}$ the classical electron radius $r_e$ and the Bohr radius $a_0$ can be expressed like $$r_e = \alpha \frac{\lambda_c}{2\pi}$$ $$a_0 = \frac{1}{\alpha}... | Given the equations for the classical electron radius \( r_e = \alpha \frac{\lambda_c}{2\pi} \) and the Bohr radius \( a_0 = \frac{1}{\alpha} \frac{\lambda_c}{2\pi} \), calculate the ratio of the classical electron radius to the Bohr radius in terms of the fine-structure constant \( \alpha \). What numerical value do y... | 31,599 | cqadupstack-physics |
54720 | Restriction on vector fields | The 2D vector field (x,-y) does not transform like a vector under rotation(Arfken Vol. 1)! Does this mean we cannot have such a vector field physically? | In a rotating frame of reference, how does the vector field (x, -y) transform, and what are the implications of this transformation on its physical representation in a real-world scenario? | 38,046 | cqadupstack-physics |
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