Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Two-point correlation function in Peskin's book I am reading Peskin's book on QFT and I reached a part (in chapter 4) where he is analyzing the two-point correlation function for $\phi^4$ theory. At a point he wants to find the evolution in time of $\phi$, under this Hamiltonian (which is basically the Klein-Gordon - $... | Klein-Gordon equation only determines the dispersion relation between the energy and the momentum $(p^0)^2-(\vec p)^2=0$ for free scalar field. When the interaction exists in the theory, at any time, the field $\phi$ can be Fourier expanded to the momentum space, with the operators $a$ and $a^\dagger$ explicitly depend... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Recovering the $ SU(2)$ unbroken limit by taking $m_W, m_Z \to 0$ I'm trying to compute the tree-level scattering amplitude for $e^+e^- \to q \overline{q}$ and $e^+e^- \to W^+W^-$ in unitary gauge. Both processes go through an $s$-channel photon, $Z$ and Higgs while the second process also has a $t$-channel neutrino ex... | Your question (if I understand correctly) can be summarized with:
Are the amplitudes computed in the Standard Model in the limit where the Higg's vacuum expectation value (VEV) $\rightarrow 0$ equal to those computed in the Standard Model without spontaneous symmetry breaking (i.e., either without a Higgs at all or wi... | {
"language": "en",
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Is spring force yet another force of tension? I was going through the Hooke's law and studying about Springs in general.
One question which is bugging me is whether "Force by a spring" essentially yet another force of tension (just like in a rope).
I read the following, on the following link, https://www.khanacademy.or... | Yes, the forces involved are interatomic (and so fundamentally electromagnetic) in the case of a stretched spring, as for a stretched wire or a stretched rope.
I think, though, that the passage you quote is misleading. If you formed a helical spring out of a metre of steel wire, then the extension of the spring when s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/345020",
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When is Newton's law of gravity recoverable in GR? Often in a course in GR one can recover Newton's law of gravity under certain assumptions. weak field, slow moving particles etc. Is there a general method to recover Newton's laws of gravity for an arbitrary spherically symmetric, static and asymptotically flat spacet... | A hint :
\begin{eqnarray}
-A(r) dt^2 + B(r) dr dt - C(r) dr^2 -r^2 d\Omega^2 &=& (dt^2 - dr^2 -r^2 d\Omega^2)\\
&+& (A(r)-1) dt^2 + B(r) dr dt - (C(r) - 1) dr^2
\end{eqnarray}
| {
"language": "en",
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Is there a case when it is better to use the integral form of the Maxwell equations rather than the differential form? I was wondering if there is a case where the integral form of the Maxwell equations is preferred over the differential form?
If you could provide with an example for each one of the equations I would ... | The same principles apply as when you normally want the differential form of something vs. the integral form.
It's like asking when do you want to know the total distance and time of a road trip vs. what the speed was at a particular point.
With a uniformly charged sphere, for example, you can use the integral form to ... | {
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Peskin and Schroeder spinor high-energy limit (5.26 and A.20) P&S say the high-energy limit of spinor $u^s (p)$ is
$ \sqrt{2E} {1 \over 2} (1-\widehat{p} . {\sigma}) \xi^s $ and similar for the right-handed spinor (formulae 5.26 and A.20). I can't seem to derive this. How do you get this from $\sqrt{p . \sigma }... | Don't know if anyone is still expecting a reply to this, but here is how I managed to find the result. Peskin&Schroeder found result (3.50) by doing the calculation in a specialized frame (boost along z-axis) which resulted in (3.49). If you apply the high energy limit in that same frame by setting E = p3 and rewrite i... | {
"language": "en",
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Is this an electromagnetic wave without the magnetic part? Jefimenko's Equations are:
$$
\begin{align}
&\mathbf{E}(\mathbf{r}, t) = \frac{1}{4 \pi \epsilon_0} \int \left[ \left(\frac{\rho(\mathbf{r}', t_r)}{|\mathbf{r}-\mathbf{r}'|^3} + \frac{1}{|\mathbf{r}-\mathbf{r}'|^2 c}\frac{\partial \rho(\mathbf{r}', t_r)}{\parti... | Arguably, it might be, but the sources you've provided cannot be sustained for long: since the current doesn't change in time, you have
$$
\frac{\partial^2\rho}{\partial t^2} = -\nabla \cdot\frac{\partial \mathbf J}{\partial t} = 0,
$$
i.e. if the charge density is increasing with time, then it is doing so linearly wit... | {
"language": "en",
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Is the DC/electro-optical Kerr effect usable in optical quantum computing? It seems from @EmilioPisanty's comments on this question that the AC/optical Kerr effect is impractical for use in optical quantum computers, which leads me to ask: would the DC Kerr effect work?
The major difference between the optical/AC Kerr ... | To formalize Rococo's comment as an answer: not really, no.
The electro-optic effect can be enormously useful in manipulating the propagation of light in the lab, through devices generally known as electro-optic modulators and their relatives, going all the way from precision spectroscopy down to manipulating the propa... | {
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Why don't free electrons escape from a conductor? The thermal velocity of the free electron in a metallic conductor varies from $10^5\ \mathrm{m/s}$ to $10^6\ \mathrm{m/s}$. In spite of high velocity, free electrons fail to escape from the metallic surface. Why is that?
| If a electron were able to just escape the conductor, then it would be pulled back by the positive charge left behind (An image charge potential, one could say). Due to this it would be pulled back and will not be able to escape until it is able to obtain enough energy to become completely free.
Electrons can attain e... | {
"language": "en",
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Are generalised coordinates truly independent? Say we have a system with two generalised coordinates $x$ and $y$. When we solve the equations of motion we find $x=x(t)$ and $y=y(t)$. I can invert one of these solutions to find $t=t(y)$ and therefore get $x=x(t(y))$ which therefore gives me $x(y)$. Does the equation of ... | You shouldn't try to make $t$ a coordinate; it's a label for the coordinates, over which the coordinate-dependent Lagrangian is integrated to form the action. (The most obvious problem this causes is that the momentum of time is undefined, viz. $\frac{\partial L}{\partial \dot{t}}=\frac{\partial L}{\partial 1}$.) It wo... | {
"language": "en",
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Is the pressure the same if I heat to the same temperature different closed containers with distinct ratios of water to air? Say I have 3 closed containers of 1L each. By volume, the 1st one is 50/50 air and water, the 2nd is 20% water and 80% air, and the third is 80% water and 20% air. If I heat all of them to the sa... | I'll show you how to do the calculation for 20% water and 80% air, and you can then repeat the calculations for the other mixtures. We will neglect the initial amount of water vapor in the air at 20 C. So there are 200 cc of liquid water and 0.8 l of air. The specific volume of liquid water at 20 C is 1.002 cc/gm, s... | {
"language": "en",
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When short circuits are not exactly short circuits?
Here $R1 = 2 \Omega$, $R2= 4 \Omega$ and $R3= 4 \Omega$
Though there looks to be a short circuit in this diagram, my teachers say that this circuit can easily be redrawn into simple parallel circuit. As far as I know a short circuit is an alternate way for current to... |
As far as I know a short circuit is an alternate way for current to move where there is no resistance whatsoever. So all of the current will flow through a short circuit if found.
This is correct. The part that seems to be confusing you is that this isn't a short circuit.
As stated in the other answer, you have shor... | {
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Why does the Lamb shift only affect s-states? The shift is due to interactions between atomic electrons and vacuum state fluctuations, so I would think that there would be an associated energy shift for all states, and not just s-states.
Also, is there any physical relationship between the Lamb shift and the Darwin cor... | The s-states are the only orbitals that do not vanish at the origin. This is where the coulomb field of the proton is strong enough to produce measurable vacuum polarization or Lamb shift. Hence the Lamb shift only affects s-states.
| {
"language": "en",
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Why does sugar dissolve faster in hot water compared to cold water? Why does sugar dissolve faster in hot water compared to cold water?
| I am going to have to respectfully disagree with Pranjal Rana.
The reason that sugar dissolves more quickly in hot water than in cold water has to do with the kinetic energy of the particles.
The faster (hotter) the water molecules are moving, the more energy they give to the sugar molecules when they collide with th... | {
"language": "en",
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Why is a nonlinear crystal necessary to stimulate quantum fluctuations that entangle photons? I've been reading about spontaneous parametric down conversion (SPDC). The Wikipedia article on it says:
A nonlinear crystal is used to split photon beams into pairs of photons that, in accordance with the law of conservation... | In order for photons to become entangled they must have interacted at some point. Photons don't interact in free space, but they do interact in nonlinear crystals. That is indeed why these special crystals are called nonlinear, they support some form of multi-photon interaction.
| {
"language": "en",
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Does phononic "Superconductivity" exist? Can solids be cooled to a sufficiently low temperature such that sound can travel through them without acoustic impedance?
It seems that if I had a solid in the shape of a torus, sitting in ambient vacuum, cooled to absolute zero, and then decided to introduce a compression alon... | To some extent phonons are already condensed. Usually they are thought of as the Goldstone modes of broken translational symmetry (ignore optical modes for simplicity). This means the superflow of phonons is constant movement of the crystal itself. In other words, the crystal can move at a constant velocity indefinitel... | {
"language": "en",
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In QFT, can Field Operators at different points in Space-time always be expressed as unitary Transformation of each other? Given an operator valued field $\Phi(x)$, and two points in spacetime, $x$ and $y$, can I always write down something like:
$$
\Phi(y) = U_{x,y}^{-1} \Phi(x) U_{x,y}
$$
With $U_{x,y}$ being an unit... | Depends what you call a QFT. If it is an object satisfying the definition commonly known as the set of Wightman Axioms then the property is built into it, i.e., it follows from Axiom W2 together with the trivial transitivity of the action of the Poincaré group on spacetime.
| {
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How can I use a candle to heat glass/quartz to a specific temp Excuse my ignorance of physics. Is it possible to suspend glass or quartz over a candle at a specific distance (in. or mm.) in order to heat the object to a certain temperature, say 300 C. Is there a graph anywhere for something like this? The convection he... | You can estimate the plume temperature above a fire using correlations from Heskestad or McCaffrey, listed respectively below:
$$T_0=25(\dot Q ^{2/5}_c/(z-z_0))^{5/3} + T_ \infty$$
$$T_0=22.3(\dot Q ^{2/5}_c/z)^{5/3} + T_ \infty$$
Where $T_0$ is the centreline plume temperature, $\dot Q_c$ is the convective heat releas... | {
"language": "en",
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Are the first order phase transitions always associated with a latent heat? Is the first order ferromagnetic transition below the critical temperature associated with latent heat?
For example, the transition of ferromagnetic configuration with all its spins aligned up to a ferromagnetic configuration with all its spins... | I agree with @user8153 that I don’t think entropy has to be discontinuous for the phase transition to be first order. The free energy for this case is $F=-MdH$ since the other parameter temperature is constant. At the phase transition, the first order derivative of free energy, $M = -\frac{\partial F}{\partial H}$ is d... | {
"language": "en",
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Obtaining Euler-Lagrange equation from action with constraint - Witten's topological sigma model The action of Witten's topological sigma model (defined on a worldsheet, $\Sigma$, with target space an almost complex manifold denoted $X$) takes the form
$$
S=\int d^2\sigma\big(-\frac{1}{4}H^{\alpha i}H_{\alpha i}+H^{\a... | Isn't the trick to take
$$
H^{\alpha i}={\varepsilon^{\alpha}}_{\beta} J{^{i}}_jH^{\beta j},\tag{2.5}
$$
and note
$$
H^{\alpha i}=\frac{1}{2}\left(H^{\alpha i} + {\varepsilon^{\alpha}}_{\beta} J{^{i}}_jH^{\beta j}\right)
$$
then plug this into the action to rewrite it as
$$
S=\int d^2\sigma\left(-\frac{1}{4}H^{\alpha i... | {
"language": "en",
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What is the Planck scale magnetic field strength? Using the constants $\mu_0$ (or $\varepsilon_0$), $c$, $\hbar$, $e$ and $G$, it is possible to define two quantities with units of magnetic field :
\begin{align}
B_1 &= \sqrt{\frac{\mu_0 c^7}{\hbar G^2}} \equiv \sqrt{\frac{c^5}{\varepsilon_0 \hbar G^2}} \approx 8 \times... | Planck units are found simply by multiplying together powers of certain constants; one does not consider specific physical laws to get them, which is equivalent to motivating specific multiplicative constants. (We don't do it this way because setting each Planck unit to $1$, the ultimate goal of having Planck units, wo... | {
"language": "en",
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How can a monochromatic X-Ray tube produce a spectrum in XPS? I thought that if we use monochromatic source, we can only get one peak, if it exists.
Because Photoelectric Effect allows only the electron that have the corresponding frequency(energy level) that can be excited.
appreciate your help to rectify my understan... | Because the X-rays, in the Photoelectron spectroscopy device, excite the electrons from the individual core levels out and as we know the electrons from the individual core levels reside in different energy levels. Thus the amount of energy left after the electrons overcome the individual energy barrier of each level i... | {
"language": "en",
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Expression for angular friction Consider say a door rotating about its axis. Is there, in general, any expression for the frictional hindrance to its motion? I was thinking in line with the coefficient of friction for linear motion on a surface.
| Friction only appears to stop the motion. It will not point radially but rather backwards on the sliding area. That is, it will point opposite to the door swinging direction and not towards the door hinge. Because nothing is moving/sliding in the radial direction. So, the concept of an "angular friction" is nothing mor... | {
"language": "en",
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Definition of symmetrically ordered operator for multi-mode case? As I know, Wigner function is useful for evaluating the expectation value of an operator. But first you have to write it in a symmetrically ordered form. For example:
$$a^\dagger a = \frac{a^\dagger a + a a^\dagger -1}{2}$$
For single mode case where the... | OK, I assume you are comfortable with the rules of Weyl symmetrization where you may parlay the $[x,p]=i\hbar$ commutation relation to the $[a,a^\dagger]=1$ one... the combinatorics is identical provided you keep track of the is and the ħs, etc...
So your surmise is sound. Since different modes commute with each other,... | {
"language": "en",
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Could a computer unblur the image from an out of focus microscope? Basically I'm wondering what is the nature of an out of focus image. Is it randomized information? Could the blur be undone by some algorithm?
| The goal with a camera lens system (whether a microscope or not) is to deliver light from one point on the object to one point on the sensor. This however cannot be perfectly achieved for several reasons.
*
*Light will diffract off the apeture, the smaller the apeture the more the diffraction.
*The system will only... | {
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Calculating magnetic fields by electric fields Is it possible to calculate the magnetic field due to moving charges by considering a reference frame in which they are stationary, finding electric field and then somehow relating it to the magnetic field in the reference frame where they are moving?
| Yes. To do this, you need to know the Lorentz transformations between the "lab frame" and the "charge frame", as well as how electric and magnetic fields transform between these reference frames.
To get more specific, we will denote quantities measured in the "lab frame" with primes, and those in the "charge frame" ... | {
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Why are the metric and the Levi-Civita tensor the only invariant tensors? The only numerical tensors that are invariant under some relevant symmetry group (the Euclidean group in Newtonian mechanics, the Poincare group in special relativity, and the diffeomorphism group in general relativity) are the metric $g_{\mu \nu... | The rotation group ($O(3)$ for Euclidean space, $O(1,3)$ for Minkowski signature) is defined as the group of all linear transformations that preserve the metric tensor. If there were other independent tensors, this would give additional restrictions, so it would necessarily define a subgroup of the rotation group.
Dema... | {
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How could I measure the colour spectrum of a light bulb and investigate how closely it matches a black body radiation curve? Here is my research question:
What is the colour/spectrum produced by each globe type? What is the temperature equivalence? How closely does a globe match a black body radiation curve?
I will b... |
I have been suggested to take photos of the glowing bulb then use photoshop to analyse the colour. Is that a possible solution?
No. The power spectrum of a light bulb is a continuous function $f(\lambda)$ where $\lambda$ is a particular wavelength of light and $f(\lambda)$ is the intensity of the light at just that ... | {
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Quantifying the baryon asymmetry requires normalizing the baryon number density w.r.t comoving entropy density or photon density-Why? This question has been edited a little to clarify the confusion I have.
The matter-antimatter asymmetry of the Universe quantified by the baryon asymmetry as
$$Y_B=\frac{n_B-n_{\bar{B}}}... | You have to normalize it to something because $n_B - n_\bar B$ is just the number of baryons in the universe.
I more frequently see the baryon asymmetry normalized by the number of CMB photons (e.g. this PDG table.
The Particle Data Group's review of Big-Bang cosmology says on page 12
For photons [...]
$$
d(sR^3)/dt... | {
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Mass connected to spring on a frictionless surface vibrating out of control I am not good at Physics so please bear with me. I am trying to understand harmonics and in order to do that I thought its best to ensure my understanding of the equations of motion is correct. To do this I tried to model a mass vibrating on a ... | When working with a situation like this (i.e. time-varying force), it's best to start with the differential equations
\begin{align}
\frac{{\rm d}x}{{\rm d}t}&=v \\
\frac{{\rm d}v}{{\rm d}t}&=F/m
\end{align}
rather than trying to use positions and velocities from kinematics.
The above can be re-witten using a time-stepp... | {
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How is an operator applied to a wavefunction in quantum mechanics? If you have the Hamiltonian operator written as such:
$$\hat H = -\frac{\hbar}{2m}\frac{1}{r}\frac{\partial^2}{\partial r^2}r \tag{1}$$
then to apply the Hamiltonian operator to a wavefunction, do you apply the separate operations in order from right ... | It is the same as matrix mathematics. In general quantum mechanics is linear algebra in funny hats.
That is, suppose I want to compute $\frac 12 \langle \hat X \hat P + \hat P \hat X\rangle,$ the closest Hermitian observable to the moment $\langle x p \rangle$ in classical mechanics. The relation that $[\hat X, \hat P]... | {
"language": "en",
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Can it happen that angular momentum is conserved about some points but not others? So angular momentum is conserved about a point if no external net torques act about that point. But is there any occasion when this is only true about certain points? In other words: can it happen that angular momentum is conserved about... | As you already said, angular momentum about a point is conserved if and only if the net external torque about that same point is zero. This is always true.
It might happen though that the net external torque is zero about one point and non zero about some other. In this case angular momentum is conserved about the fir... | {
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What would a Helmholz coil-like mass configuration look like? (produces locally uniform gravity field) A Helmholtz coil is an arrangement of two circular coils that produces a magnetic field in the center which is locally uniform in direction and magnitude, or at least nearly so. The configuration is optimal when the r... | Fields scale as $M/r^2$, so scaling a structure's dimensions up by $\alpha$ and decreasing its mass density by $\alpha$ leaves the field unchanged. So the field at the center of a cylinder whose diameter increases linearly along its length (I initially incorrectly suggested exponential) and whose mass-density is decrea... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Different expressions of cylindrical EM waves if derived from one dimensional or three dimensional wave equation? Consider electromagnetic cylindrical waves. Cylindrical waves can be derived from the plane waves using energy conservation consideration: since the power must be a constant the amplitude of a cylindrical w... | Also: consider the concepts of near and far field. The exact solution contains both. In the far field, only traveling waves exist ($1/r^2$ power for spherical cases) that asymptotically approach plane waves. Near field falls off faster (hence: "near"), moreover there may be phase differences with the driving oscillatio... | {
"language": "en",
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"source": "stackexchange",
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Is Bose condensation experimentally achieved for a free Bose gas? Bose-Einstein condensation is a phenomenon that theoretically happens for free Bose gases because Bose-Einstein distribution holds for free Bose gases. But in superconductors and superfluids, there are interactions between the bosons.
*
*Are supercon... | Yes, Einstein considered a purely statistical effect, where condensation occurs although interactions are absent. However, for most people the accumulation of particles in the ground state is the key point of a Bose-Einstein condensate. Therefore, most people agree that atomic, molecular, exciton-polariton and photonic... | {
"language": "en",
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Traveling Wave Equation $\sin(kx-wt)$ vs $\sin (wt-kx)$ In my textbook most if the times it uses $A\sin(wt-kx)$, but occasionally there is a problem using $A\sin(kx-wt)$
So i just changed it from $A\sin(kx-wt) \to -A\sin(wt-kx)$
but does the amplitude change to $-A$?
Is the wave going downwards first?(as negative ampli... | Using $\sin(kx-\omega t)$ or $\sin(\omega t-kx)$ does not make a difference: it is just a matter of convention. You can very legitimately change $A\sin(kx-\omega t)$ to
$-A\sin(\omega t- kx)$ without causing any damage.
Note that the full solution to the wave equation is of the form $A\sin(kx-\omega t+\phi)$. Expan... | {
"language": "en",
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"source": "stackexchange",
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Does amplitude affect time period for spring mass system? I know that with the formula $T=2\pi\sqrt{\frac{m}{k}}$ the time period is not related to the amplitude. However, would amplitude matter if i do this experiment in real life. Would a greater amplitude result in more friction of some sort?
| $2$ $pi$ frequency is root of return force/(inertia- displacement). A real spring will also have nonlinear terms in return force. The return force can be expanded in powers of displacement such as $F = ax + bx.x + cx.x.x ..$.Where $x$ is the displacement and $a,b c$ etc are constants. $b < a, c < b$ etc. The nonline... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do massive particles redshift the same way as photons in a gravitational field? Let's assume two observers $A$ and $B$ hovering in a gravitation field. $A$ sends a radio transmission of frequency $f_1$ to $B$. $B$ receives this transmission and finds it has frequency $f_2$.
As as second experiment $A$ sends an electron... | Case 1: Convert 1 kg of matter-antimatter to energy
Case 2: Lower 1 kg of matter-antimatter to a gravity well, convert it to energy there, beam the energy up to the original position.
From conservation of energy: Energy produced in case 1 = Energy produced in case 2
Energy in case2 = Energy beamed up + energy generat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/352512",
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Absorption of light I have two questions:
*
*When an atom absorbs part of spectrum from white light, why doesn't it radiate the photon back? What happens to the photon?
*How does the wave theory of light explain absorption of light?
| If an atom absorbs a photon, an electron will be raised to an excited state. For the relaxation of the excited state, we have basically two possibilities: (1) The electron jumps back to initial state where it started. Thereby it emits the "same" photon (same wavelength) it absorbed initially. However, it doesn't have t... | {
"language": "en",
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Why do objects feel heavier when held with an extended arm than with a bent arm? I do realise that this is due to torque and that torque is at maximum when the angle between the direction of the torque and the force acting on the object is 90 degrees. I would like to know if it is the angle between the forearm and the ... | I'd also say that this is due to torque. It is not the angle at the elbow. Take some weight in your hand and let it hand straight down from your shoulder. Then pull it up to your armpit. Holding it with an extended arm will be easiest because you only need to apply force in your hand.
When you have the weight in front ... | {
"language": "en",
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Short pulse of monochromatic light? (Potentially connected to this question, but could not find the answer to my particular question there.)
The frequency spread and time duration of a pulse are related by:
$$ \Delta \omega \Delta t \approx 2 \pi, $$
from which perfectly monochromatic radiation ($\Delta \omega$ = 0) wo... | Well, when you bring photons into the question, you should also bring quantum mechanics. The shutter constrains the photon's position, thereby introducing uncertainty in its momentum [equivalently, energy]. Note that this is just $\hbar$ times your original statement.
| {
"language": "en",
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What causes the phenomena of a ring appearing around the shadow of an airplane So I was sitting in an airplane and I saw a ring appearing around the shadow of the plane on the clouds. What causes this phenomena? I've added an edited image, so the effect is more pronounced.
| This is called a glory.
You can tell it apart from a circular rainbow because of the thickness of the colours relative to the radius of the turn, the repetition of the colours, and the way it seems to appear on a cloud. It's much more consistent with pictures of a glory (rainbows have a much wider circle they form due... | {
"language": "en",
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How do magnetic cores (ferrites) guide magnetic field? As far as I know, magnetic materials have magnetic dipole moments which align when they are under influence of the outside magnetic field.
Basically they increase the magnetic field strength. But people also say that they guide magnetic field. Does the magnetic fie... | Ferromagnetic materials add their own magnetic field to the external field that causes an alignment of their atomic dipoles. If the external field is from a fixed current in a solenoid, the induced field has no effect on the external external field. If the external field is from another ferro-magnet, the induced field ... | {
"language": "en",
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Does work done depend on the frame of reference? Suppose I am sitting on a bench and looking at a moving car. Force is applied on the car by its engine, and it makes it displace, hence some work is done on the car. But what if I am sitting in the car and looking at the bench? The bench covers some displacement, but who... | In a friction free world, the car moving with a certain velocity will not have any forces acting on it. If there were forces acting on the car, it would be accelerating.
There can be multiple forces acting on a body, so it's really important to specify which force are we talking about when we are calculating the work. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/353187",
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"source": "stackexchange",
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Neither a vector, nor a scalar While I was reading a book on mechanics, when introducing the vector multiplication the author stated that multiplying two vectors can produce a vector, a scalar, or some other quantity.
1.4 Multiplying Vectors
Multiplying one vector by another could produce a vector, a scalar, or some o... | If you have two vectors $\mathbf{a}$ and $\mathbf{b}$, the inner product $\mathbf{a} \cdot \mathbf{b}$ is a scalar, the cross product $\mathbf{a} \times \mathbf{b}$ is a vector and the dyadic product $\mathbf{a} \otimes \mathbf{b}$ is a matrix. It is defined as
$$\mathbf{a}\otimes\mathbf{b} = \mathbf{a b}^\mathrm{T} = ... | {
"language": "en",
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How does a free electron look like? In a simple atom say hydrogen, there is an electron cloud which is spherical in shape. What about a free electron, how big or small will that cloud be? I think the term cloud here means the likelihood the electron can be found, as for a free electron in absent of other forces does it... | Since it's isolated (and therefore has no potential energy), the quick answer is that it resembles (but is not exactly) a Gaussian distribution on the order of 10 - 50 angstroms wide. You can calculate it yourself from the equation for thermal wavelength:
$$
\Lambda = \sqrt{\frac{h^2}{2\pi m k_BT}}
$$
At room temperat... | {
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With respect to what we are saying space is homogeneous or space-time is isotropic? I don't really understand what we are talking about when we say space is homogeneous. What we are measuring? My notion is: it should depend on the entity and with respect to that entity one can decide space is homogeneous or not!
May b... | Suppose we measure the density of matter as a function of position. Then we will come up with some function for the density $\rho(r, \theta, \phi)$ where $r$, $\theta$ and $\phi$ are polar coordinates with ourselves at the origin.
*
*The density is isotropic if it is the same in all directions i.e. it is independent... | {
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Thermodynamics : Doubt in First Law I just started my study of thermodynamics. I am having problem in uderstanding a concept.
Suppose I drop an ice-cube and a rock of cube shape. Which one will reach the ground first? I know ratio of Work to Heat equals Joules Constant. Therefore any change in potential energy will res... | In your assessment of the first law of thermodynamics, you omitted certain terms in the equation that can sometimes be important. The more complete form of the first law should read $$\Delta U+\Delta (KE)+\Delta (PE)=Q-W$$In your ice cube example, $$\Delta (KE)+\Delta(PE)=0$$So, if the ice cube doesn't exchange signif... | {
"language": "en",
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Should every physical problem formulated as a differential equation have a mathematical solution? I encountered the following statement in Boyce's Elementary Differential Equations and Boundary Value Problems :
Not all differential equations have solutions; nor is the question of existence purely mathematical. If a m... | In the best of all possible worlds we know the laws of physics perfectly and can write them as differential equations (or something similar). But we do not live in that world. Instead we create models of the physical world that may not correspond to the actual laws (due to ignorance or just approximation). Good models ... | {
"language": "en",
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Nature of Work done by Forces I am confused about the possible nature of work that a conservative and non conservative force can do.
*
*Do Non conservative forces like friction only do negative or zero work and not positive?
*Can conservative force also do negative work, I know Gravitational Force is conservative f... | Work done $W$ is the dot product of a force $\vec F$ and the displacement of the force $\vec s$.
$W=\vec F \cdot \vec s$
The work done is positive if the force and the displacement are in the same direction and negative if they are in opposite directions.
You watch a lorry accelerating.
A box on the back of a lorry... | {
"language": "en",
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Why does refraction make something look closer with an incident angle of zero? The gaussian formula for a single spherical surface is defined as
$$ \frac{n}{s} + \frac{n'}{s'} = \frac{n'-n}{R}$$
When the radius of curvature, $R$, is infinite - as in the case of a planar surface, we are delt with the case
$$ \frac{n}{... | Let's say you only have one eye open and you're directly in front of the object. The thing is, your pupil has some size to it. Rays that enter are not only leaving the medium surrounding the object at 0 degrees. Your lens must change shape for the rays entering the edges of the pupil to form an image on your retina, an... | {
"language": "en",
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Time dilation for non-physicists Apologies in advance, as I'm not a physicist, and may use terms incorrectly.
In the movie Interstellar, the planet Miller has a time dilation of one hour to seven Earth years. This has brought up several questions for me:
*
*At what point would someone (outside the gravitational forc... | Re 1., gravity has infinite range, so the effect of gravitational time dilation will just grow weaker, but theoretically not go away entirely.
In the idealized case of a single source of gravity, the time dilation factor is given by
$$
\frac t{t_0} = \sqrt{\frac{1-\frac{r_s}{r}}{1-\frac{r_s}{r_0}}}
$$
where the Schwarz... | {
"language": "en",
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If we cool gates in semiconductor transistors, can we reduce the overall energy of electrons? I was reading about Moore's law and was a bit confused about why semiconductors aren't cooled down. If we have an issue with quantum tunnelling, cooling the wafer could reduce the energy level of the electrons. We might need m... | You are right that reducing the temperature will drive down leakage current, and this would lower energy waste and also increase signal fidelity.
To some extent this is already done, though not in the way you imagine. All transistors dissipate energy, so they tend to heat up. Usually heat sinks, fans, water cooling,... | {
"language": "en",
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When particles are collided some new particles come into existence. Is the field of the new particle was there before just not vibrating? I know that when two particles are collided some new particles come into existence and i know that the new particles weren't inside of the original particles. I understand that the ... | Think of tangled up wires on top of each other. Sometimes when you move one of them the right way it moves the other. Now let us say this movement is a vibration. You vibrate one and it vibrates the other. This is a cartoon picture of the mathematics. A disturbance in some field (particle A) can cause a disturbance in... | {
"language": "en",
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Relation between velocity magnitude and the pitch of the collision sound I'm doing a simulation involving collisions, I'm using glass marbles, based on testing I've noticed that the higher the magnitude of the velocity of the marble hitting another marble at rest the higher the pitch of the collision.
With a small mag... | Neat question!
First some setup. The collision of marbles is within the domain of contact mechanics. When two spheres collide their surfaces both deform. This forms a circular contact area between them, with
$$ A \propto F_n$$
The normal force $F_n$ being dependent on the velocity of the collision.
Relying on the ge... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does a calculation to count objects covering a certain area seem to give nonsensical units? Suppose you want to estimate the number of atoms in a rectangular sheet of graphene. You might estimate the sheet to have $10^{7}$ atoms along one edge and $2*10^{7}$ atoms along the other edge. Multiplying while keeping tra... | Atoms are not really a unit. They don't combine in the right way when you multiply. If you are careful, you can make them work in some situations, as both other answers show (+1 to both).
But as you saw, they don't work everywhere. Not like a length would. If the distance from atom to atom is 1 Angstrom, there is no p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/355741",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Neutrinos always travel at same speed? Neutrinos have mass, and only interact with gravitional and weak force, what make it very difficult to detect.
Neutrinos is known to travel very closer to speed of light and have very small mass altought neither have a precise measure.
Particles with no mass like photons and gluon... | The 25 detected neutrinos from supernova 1987A--168,000 light years away--arrived over a span of 13 seconds [Wikipedia, which is never wrong]. Not all neutrinos are this energetic, though.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What exactly happens in the basic QED Feynman diagram? When a photon is absorbed by an electron, I think that the following things happen:
*
*The electron changes in momentum, angular momentum and energy.
*The phase of the electron wave function changes by a fixed angle given by the coupling constant.
Is this cor... | A Feynman diagram is not depicting a physical process. Virtual particles do not exist. Strictly speaking that particle is not 'a' photon. It's just there to signify that the interaction is mediated by the electromagnetic gauge field $A^{\mu}$.
Physically, what happens is that the electron is always travelling in an are... | {
"language": "en",
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Do x-rays get emitted upon initial acceleration in this setup? Based on the diagram and the paragraph before it, the x-rays are caused by decelerating the moving electrons and thus x-rays are emitted where the diagram clearly shows it (the red arrows pointing downwards labeled "x-rays"). But does this mean that x-rays ... | The acceleration of the electrons whilst travelling between cathode and anode is very much less than the (negative) acceleration of the electrons when they hit the target atoms.
The higher the acceleration the more energetic are the emitted photons.
So the photons emitted from the interaction of the electrons with the ... | {
"language": "en",
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Where does the magnetic field energy of a charged particle moving with a uniform velocity come from? Consider a charged particle initially at rest with respect to an inertial frame.
Let a force act on it so that it gains a velocity 'v'.
It now produces a magnetic field that has some energy associated with it.
My que... | You're right that the work done on the charge is not equal to the change in the charge's kinetic energy in this case. An accelerated charged body (let's assume it's of finite size, to avoid the infinite energy problem of point charges) will have a change in its "near field", and it will send off electromagnetic radiati... | {
"language": "en",
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Analytical continuation of 2,3,4-point integrals I was reading a paper that gives a nice collection of all scalar integrals that crop up in QCD loop calculations. Such integrals are computed in some kinematic region and then the authors say the results may be analytically continued if so desired. I just wonder how is t... | This is significant: they are originate from the $+i\varepsilon$ prescription in the Feynman propagators of the original integral. The sign choices are important to obtain the correct sign for the imaginary part of the loop functions.
Note that these prescriptions are relevant only if evaluations are being made on a b... | {
"language": "en",
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Derivation of Newtons second law of motion from the principle of conservation of energy Is newton's second law a consequence of the principle of conservation of energy? How can we arrive at
net force = rate of change of momentum
using only the law of conservation of energy?
| The connection is provided by the Hamiltonian formalism, if $F = -dV/dx$ is the net force acting on a particle of mass $m$, then the quantity
$$
H(x,p) = \frac{p^2}{2m} + V(x) = E
$$
satisfies the expression
$$
\frac{dp}{dt} = -\frac{\partial H}{\partial x} = -\frac{dV}{dx} = F
$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/357186",
"timestamp": "2023-03-29T00:00:00",
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How nuking the poles of Mars would create an atmosphere? Elon Musk said one of the methods they are taking into consideration to create an atmosphere on Mars is to nuke its poles. How nuking the poles would create the atmosphere?
| Please refer here for a similar question.
The idea of nuking the poles of Mars came around when people started to seriously consider the idea of terraforming another planet. If Mars's poles were to be nuked, the Ice Caps, mainly made of carbon dioxide, would vaporize. This vapor of carbon dioxide would be the first ste... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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What is the physics behind a hard phone cover and a soft phone cover? Does hard plastic distribute forces throughout a device, similar to how the shell of an egg works, much better than a soft cover does? This is the common argument I hear for the hard cover.
How different is it from a soft plastic case? For soft plast... | One has a lower Young's modulus than the other. That's it.
| {
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Volovik's argument and superconductivity In Volovik's book he describes the Fermi surface as a vortex in energy+momentum space. Due to a winding number the Fermi surface is topologically protected.
I don't understand how the above topological protection is compatible with superconductivity, which destroys the Fermi su... | The picture is compatible with superconductivity. Because in the presence of the pairing term, we rewrite the Hamiltonian in the Nambu basis, where both particle and hole Fermi surfaces should be considered. If the particle Fermi surface corresponds to a vortex, then the hole Fermi surface corresponds to an antivortex.... | {
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Is the top of my ladder really reaching infinite velocity? Here is a classic "related rate" maths problems:
A $10$ ft long ladder rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of $1$ ft/s, how fast is the top of the ladder sliding down?
Let's represent the vertical wal... | You are making the false assumption that the ladder remains in contact with the wall. In reality, contact will be lost and the velocity remains finite.
To solve this properly you would compute the rate of rotation of the ladder, and you would notice that there isn't enough torque to keep the ladder turning as fast as y... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/358192",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What causes light to refract? The common answer to this question is that light refracts because its speed changes in different materials. But this means that the photons has internal attraction between each other. Is that the case? Otherwise is something else like density of different materials the reason why light ref... | The reason for refraction is the different speed of light in different media. This speed is determined by the refractive index $n$, which in turn can be calculated from the relative permittivity and permeability of the material:
$$n = \sqrt{\varepsilon_r \mu_r}$$
These constants simply define the response of a material... | {
"language": "en",
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How to change Pressure and Temperature "The triple point of a substance is the pressure and temperature at which all three phases coexist in equilibrium."
Take water for example.
Let's say I put some water in a rigid container and add some heat.
Then both the temperature and pressure rise because the volume is consta... | Really interesting question, the answer is yes -- the triple point exists for closed thermodynamical systems. The key word here is being closed with some volume $V$ and non-interacting with the environment except for some stimuli. Every closed thermodynamical system has a natural thermodynamical equilibrium and each ha... | {
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In quantum mechanics is momentum a vector or scalar? In quantum mechanics, is momentum a vector quantity?
| In quantum mechanics, momentum is a vector operator, but there is a subtlety. If we have a state $|\alpha \rangle$ rotated to $|\alpha' \rangle = \mathcal{D}(R)|\alpha\rangle$, for momentum to be a vector operator we must have that,
$$\langle \alpha | p_i |\alpha\rangle \to \langle \alpha'|p_i|\alpha'\rangle = \sum_j R... | {
"language": "en",
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Does String Theory predict a particle with twice the mass of the electron? As far as I know, the spectrum of any (?) String Theory is of the form
$$
M^2\propto N
$$
where $N$ is the number operator. The lightest known particle being the electron, I am led to think that we should observe particles with masses $m_e,2m_e,... | It's more complicated than that. To get the Standard Model, a standard technique is to use intersecting brane models, usually many D6s in the compact space, in which the spectrum depends on the angles between the branes and the particles comes from vibrational modes of the open strings stretched between the branes.
Rou... | {
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Can a particle have a decay width approaching its mass? Very short-lived particles have half-lives measured in terms of decay width, with the half-life calculated from the energy-time uncertainly principle.
If a particle has a decay width that approaches the mass of the particle, it never really gets a chance to "exist... | Well, "no one will ever see it" is excessively harsh. Very broad resonant states are surveyed with partial wave phase-shift analysis, although this sort of thing is more in vogue in nuclear physics these days than in particle physics. However, the fabled scalar σ resonance underlying the eponymous model of chiral symme... | {
"language": "en",
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Why are work and energy considered different in physics when the units are the same? There is a question that explains work and energy on stack exchange but I did not see this aspect of my problem. Please just point me to my error and to the correct answer that I missed.
What I am asking is this: Why in physics when ... | Perhaps a better analogy than height and width can be found in terms of money. Both the balance in your bank account and amount you pay for, say, your electricity bill are denominated in the same units (dollars where I live), but they represent separate concepts. One is measure of what is stored and the other is a meas... | {
"language": "en",
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"source": "stackexchange",
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Remove lens distorsion with intrinsic or extrinsic parameters? I'm struggling with the theoretics of camera calibration. There are the intrinsic parameters and the extrinsic parameters. I know what they are but what I'm struggeling with is to understand which of these help me getting the lens distortion removed. Not ev... | The intrinsic parameters describe the relationship between light arriving at the camera from a particular direction, and where it ends up on the sensor / focal plane. As such - once you have calibrated a camera carefully for a given focal length, those parameters are "fixed" for that camera.
But to know where something... | {
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Simple question about Schrodinger equation (time independent) For a quantum mechanical description of a system (like a small molecule) we can write:
$$\langle\psi|\hat {H}|\psi\rangle = \overline E$$
Question:
Is that energy the same as zero Kelvin energy obtained by statistical mechanics (using $E_n$ energies and par... | The average $\langle E\rangle$ you have on the right is not to be understood in the sense of statistical mechanics (and thus as a temperature).
The wavefunction $\psi$ can be a linear combination of states $\psi_n$ of definite energy of your molecule. The $\psi_n$’s are solutions of the Schrodinger equation. Thus,
\... | {
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What is Tsirelson's bound for the original bell's inequality As its well known, quantum correlations break Bell's inequalities only to a certain limit called the Tsirelson's bound. The bound was written for the CHSH inequality.
My question is what is the Tsirelson bound for the original case that Bell dealt with in his... | Tsirelson's bound for CHSH works only with matrix sum. If one uses Kronecker sum instead then the eigenvalues are -4,-2,0,2,4. So the average of CHSH can reach 4 in tensor quantum mechanics.
| {
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Understanding the equation for Potential Energy I am having a hard time understanding why Potential Energy can be calculated in the following way:
$$ \Delta U = U_f - U_i = -\int_{x_i}^{x_f} F_x dx $$
In particular, I don't understand why there is an integral in that equation. That is to say, why is it integrating the ... | Why an integral?
The integral comes from the work formula. When pushing something over a distance, you are applying work. Work is your force $\vec F$ times the displaced distance $\vec x$:
$$W=\vec F\cdot \vec x$$
If the force (or distance vector) changes along the way, then you have a problem and can't know which $\ve... | {
"language": "en",
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Can a theory gain symmetries through quantum corrections? It is well known that not all symmetries are preserved when quantising a theory, as evinced by renormalising composite operators or by other means, which show that quantum corrections may alter a conservation law, such as with the chiral anomaly, or 'parity' ano... | Maybe not the answer you are looking for but, remember that (Wilsonian) QFTs are defined at a certain scale $\mu$.For example we can take Yang-Mills theory with various matter fields added with a certain set of coupling constants/masses $a_i$. Classically this theory can be made to have conformal symmetry by choosing t... | {
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How the Hertzsprung-Russell Diagram allows us to calculate distance to stars I understand how to interpret a H-R diagram, in the sense that I know that the upper right top corner is occupied by cool stars, but they are very luminous so they must be big; and the bottom left corner are hot stars, not luminous, so they ar... | You can use an HR diagram along with calibrated evolutionary models to find the distance (and in some cases, mass and age) of individual stars. The method is known as spectroscopic parallax. This is a confusing name because it is not a parallax measurement at all.
The technique is to use spectroscopy, or less precisely... | {
"language": "en",
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What does 'massive' scalar field theory mean? I understand what scalar field theory is, it's just a theory that studies scalar fields.
But what does the 'massive' mean?, this might be a trivial question but I just wanted some clarification. Is it just a really big scalar field? If so why does the size really matter a f... | The Lagrangian density $\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-V(\phi)$ for real $\phi $ has equation of notion $\partial_\mu\partial^\mu\phi=-V'(\phi)$. When the $\phi^2$ coefficient in $V$ is $\frac{m^2}{2}$ with $m\ge 0$, $\phi$ has mass $m$. For a complex field the Lagrangian $\partial_\mu^\ast\phi\partial^\mu... | {
"language": "en",
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Use of the Kronecker Delta in Translations A translation in special relativity is, as I understand, a kind of Lorentz transformation given by:
$x^{\mu} \rightarrow \delta^{\mu'}_{\mu}(x^{\mu} + a^{\mu})$ where $ \delta^{\mu'}_{\mu} = 1$ if and only if $\mu' = \mu$.
What I fail to understand is the use of the Kronecker... | You are entirely correct; the $\delta$ in this circumstance is entirely superfluous.
It was probably chosen to emphasize a common form for all Poincaré transformations, which can be understood as a pair of a translation and a Lorentz transformation. In this particular context it means "Translations are embedded in the... | {
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What is the point of the reaction mass in the LIGO mirror suspension system? I learned from the LIGO official website that the LIGO mirror suspension system consists of a "main chain" and a "reaction chain", and there are small electric motors gently pushing the masses on the main chain (i.e., the mirror and other susp... | The vibration control systems are actuating in all the degrees of freedom of the test masses and subtracting motion from them, primarily ground motion at low frequencies.
Only when all these systems are active are the test masses "free" to the degree that the noise in these systems allows.
You can think of it as the no... | {
"language": "en",
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Does light heat transparent mediums? I was thinking that if a photon is travelling in the vacuum at $c$, then enters a transparent medium so it's speed becomes $0.8c$, the photon has lost energy. What is that energy transformed into? Is the surface being heated?
| The energy carried by light is entirely independent of the speed it travels at - it is simply given by the light's intensity, which is equal to the photon flux (number of photons carried per second) times the photon energy (equal to Planck's constant times the frequency). If the light is slowed down in a medium, then a... | {
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"source": "stackexchange",
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Hawking Radiation: Attraction of negative mass particles? My understanding of Hawking Radiation is this:
All the time, small amounts of matter and antimatter pop into existence, find each other, and annihilate. When this happens near/on the edge of a black hole, the matter particle slips out into space, while the antim... | As far as we know, antimatter does not have a negative mass, it just has an opposite electric and quantum charge (although scientists at CERN’s alpha institute are looking into the idea of antimatter having negative mass). When these two virtual particles are created, either can fall into the black hole, its not always... | {
"language": "en",
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Spring Constant Dependence on Contact Area I'm actually modeling a contact situation between an elastic cuboid (in reality it is an elastomer) and a non elastic sphere ($c_c\ll c_s$). The spring constant $c$ is defined with the young's modulus $E$, the area $A$ and the height of the cuboid $h$ with
$$c=\frac{A\cdot E}{... | It is somewhat more complicated than this. To get it right, you'll need to look at the theory of elasticity. There is a model, called the Hertzian model which deals with the force between things like two elastic spheres or a sphere and an infinite space (https://en.wikipedia.org/wiki/Contact_mechanics).
In the case o... | {
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EMF generated by a rotating rod I am confused by the following example in my textbook.
Question:-
A metallic rod of length $l$ is rotated with a angular velocity $\omega$, with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $l$, about an axis passing through t... | There are two possibilities of how you close the loop.
(Actually several possibilities, but lets consider two for now )
I have shown them in the picture.
In one case, there will be no EMF generated.
In other case, there will be EMF generated.
Two cases shown in picture below.
In both cases, the black shows initial ... | {
"language": "en",
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Are the Christoffel symbols all zero in gravity-free space? I was looking at the geodesic equation,
$$\ddot{x}^\mu + \Gamma^\mu{}_{\nu\rho} \dot{x}^\nu \dot{x}^\rho = 0,
$$
and thinking about how to identify gravity-free spaces by looking at the Christoffel symbols $\Gamma^\mu{}_{\nu\rho}$. For example, if they were ze... | No, not necessarily.
Flat space (which is what I assume you mean when you say gravity-free space) is special because it's possible to choose a global coordinate system in which all of the Christoffel symbols vanish. However, it's easy to make a choice of coordinate system (for example, spherical coordinates) for whi... | {
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Is it strange that there are two directions which are perpendicular to both field and current, yet the Lorentz force only points along one of them? By "strange" I mean 'Is there a reason for this, or is it something we accept as a peculiarity of our universe?'
I see no reason why if magnetic field is in the $+x$ direct... | You just discovered something pretty fundamental about the universe. It is conceivable that there would be a "mirror image universe" in which the laws of physics are exactly the other way around. But that's not the universe we live in.
There is an interesting Feynman lecture one the topic of symmetry - in particular, o... | {
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Does providing more heat to a pan of boiling water actually make it hotter? Sometimes my wife has a pan of water 'boiling furiously'. Is the extra heat (wasted in my opinion) actually making any difference, apart from reducing the amount of water in the pan - which could be done by pouring some away?
| Water is not going to have a temperature significantly higher than 100° C, even if you top up the gas (or whatever).
But if there is not just water, the final result can be different. For example, in a Pilaf rice (like a Paella) it is very important to time the thing so that the broth is "finished" just when the rice ... | {
"language": "en",
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How do nonlinear phenomena arise from linear theories? How is it possible that linear theories, for example maxwells equations or the schroedinger equation, produce nonlinear physics?
| One way of getting non-linear results from linear equations is to have interactions that are spread over time and/or space. This will require integration of the linear interaction, which will result in non-linear behavior. For example, if you integrate $dx/dt = kx$, you get $x=\exp(kt)$, which is clearly non-linear in ... | {
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Why is a centered parallelogram not a 2D Bravais cell, but a centered rectangle is? We had a disagreement regarding 2D Bravais lattices during a lecture. The lecturer told us that a centered rectangle forms a Bravais lattice in 2D, but a centered parallelogram isn't:
We couldn't come up with a satisfying definition of... | A centred lattice is defined [1, section 1.3.2.4.] as a sublattice formed by the integral linear combinations of independent vectors ($\renewcommand{\vec}[1]{\boldsymbol{#1}}\vec{a}$ and $\vec{b}$ on your diagrams) plus the translation of this sublattice by a finite number of so-called centring vectors. In your case, w... | {
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Energy stored in electric field and work done to change a charge configuration I had read a problem where a point charge is placed at the center of a thin grounded conducting shell. The energy for removing the shell off to infinity was asked. It was calculated by using the following expression for energy stored in the ... | It is true that the energy stored in a given system of charges is stored in its electric field.
However, it is difficult to calculate the work done in moving one positive charge in the presence of another in terms of difference in energy stored in the electric field, as the electric field energy of a point charge div... | {
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Proof quantum random walk $\sigma \propto n$? In a classical random walk, the standard deviation $\sigma \propto \sqrt{n}$, while in a quantum random walk it goes as $\sigma \propto n$.
Both discrete time and continuous time quantum random walks have been shown to display the above behaviour.
I can prove the classical ... | First note that the statement is generally true only in the translation-invariant setting.
For an elementary proof of this in the discrete time setting using Fourier techniques, see the paper by Grimmett et al. in
https://arxiv.org/abs/quant-ph/0309135
There, the weak convergence of $Q_t/t$ is proved for quantum walk... | {
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Rotations of eigenstates of $S_z$ I have a question regarding the rotation of spinors in a spin-1/2 system.
We have a Spin generator $\hat{S}$ for rotations of spinors.
A rotation around the axis $\vec{n}$ with the angle $\phi$
is generated by the operator:
$$
D_{\vec{n}}(\phi) = \exp(-i\phi \hat{S}\cdot \vec{n})
$$
... | The simplest way to think about it is by thinking of spin as a classical vector.
What kind of rotation would take a vector completely along $\hat z$ to the $\hat x$ axis? Clearly, this would be a rotation in the $xz$ plane, i.e. a rotation about $\hat y$.
The same argument will work for spin. You might care to re... | {
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Does Humid Air Rise (neglecting the effects of weather turbulence-for example in a closed environment like a sealed room) An internet search will find many people claiming that Humid Air (water vapor) rises. However, I am skeptical because if lighter molecules rose then, it follows that the air would be stratified by m... | There are no sources or sinks of oxygen or nitrogen to speak of, so there are no fluctuations in the ratios of these gasses to speak of. Water vapor, on the other hand, is constantly being added and removed--air can be dried by cooling it to condense out the water, and then reheated, for example. It is quite possible t... | {
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Feynman diagrams for eigenvalue perturbation theory I posted this question in MathOverflow but was not lucky with the answers, so wil try here.
Suppose I have a matrix given by a sum
$$A=D+\epsilon B$$
where $D$ is diagonal and $\epsilon$ is small, and I want the eigenvalues of $A$ as power series in $\epsilon$. The fi... | If you want to find the eigenvalues of a finite dimensional matrix $A$ as a Taylor series on $\epsilon$ there are well known procedures to do that. If your object $A$ is infinite dimensional things become more complicated but can be carried out in principle. (Almost) Everything you want to know on the subject can be fo... | {
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Why is it "bad taste" to have a dimensional quantity in the argument of a logarithm or exponential function? I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although I suppose i... | The other answers are correct that when you think of it in terms of unit analysis you cannot add quantities that have different units to each other. Even so, formally you can always do something like
$$f\left(\frac{x}{1\operatorname{m}}\right)$$
to get something that works, mathematically.
Where it becomes bad taste/b... | {
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Why does $2\to 2$ scattering cross-section have $E_{CM}^2$ in denominator? For $2\to 2$ scattering with equal masses we have
$$\left(\frac{d\sigma}{d\Omega}\right)_{CM} = \frac{1}{64 \pi^2 E_{CM}^2} |\mathcal{M}|^2.$$
(Schwartz's QFT eq. 5.33) Can we make the general statement that total cross section increases as $E_{... |
Can we make the general statement that total cross section increases
as $E_{CM}$ decreases for scattering processes?
If the considered QFT is unitary (at least perturbatively), there is a constraint on the cross-section following from the unitarity, called Froissart bound. It is the direct consequence of the optica... | {
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What would happen to an isolated block of material I was thinking recently about what might happen if you were to place a block of material in the middle of a complete vacuum. Obviously there's not going to be a way to ever achieve such a scenario but what would happen if you were to put a block of let's say steel at 1... | The amount of energy will depend on the mass of the block and what it is made up of. A small body will lose energy at such a slow rate that it can outlast our sun.
| {
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If I have a graph displaying the equation of elastic potential energy, why does the graph increase quadratically? I was wondering why the graph is quadratic. If one could also link me to an external source to explain this, I would be just as grateful.
| This is an addition to @Steeven's answer.
Your graph plots the distance a marker is catapulted vs. the pull-back distance on the rubber bands. We can find a theoretical prediction for how far your projectiles should go.
Assuming the markers land at the same height at which they are launched, they will travel a distance... | {
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"answer_id": 1
} |
Where will the Goldilocks zone be when the Sun becomes a red giant? In about 5 billion years, when our Sun expands into a red giant making our planet uninhabitable, where will the new Goldilocks zone be? Could life form on a new planet in the Goldilocks zone? Environment suitable for human life?
| Fortunately, our galaxy won't last that long. The Shapely-Super-Cluster is pulling hundreds of galaxies, including our Milky Way, into a large gravitational anomaly called "The Great Attractor". It's only 220 million years away... Which is pretty darn quick when compared to five billion years. The Sun will be OK for a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/365297",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 4,
"answer_id": 3
} |
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