Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Anisotropy in spin chain hamiltonian The Hamiltonian of XY Spin Chain on a lattice of N sites can be written as
$$
H = -J\sum_{i=1}^N \left(\frac{1+\gamma}{2}\sigma_i^x\sigma_{i+1}^x + \frac{1-\gamma}{2}\sigma_i^y\sigma_{i+1}^y + \lambda \sigma_i^z\right)
$$
where $J$ is exchange interaction and $\gamma$ is anisotropy.... | You can write the Hamiltonian for the Heisenberg model as:
$H = - J_x \sum_i \sigma_i^x \sigma_{i+1}^x - J_y \sum_i \sigma_i^y \sigma_{i+1}^y - J_z \sum_i \sigma_i^z \sigma_{i+1}^z$
where $J_x, \ J_y$ and $J_z$ are the three exchange terms. In the isotropic Heisenberg model (or the $XXX$ model), all three of these term... | {
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"timestamp": "2023-03-29T00:00:00",
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How do rocks store information about Earth's magnetic field? When a particular rock is being formed in a rift (by the solidification of magma, which is composed of ferromagnetic materials), the rock "stores information" about the Earth's magnetic field at the time of its formaiton.
My textbooks talk about the material... | The field direction is stored in the magnetization direction of ferromagnetic minerals in the bedrock when it cools down. Those minerals are typically iron oxides like magnetite Fe$_3$O$_4$ etc or iron sulphides like pyrrhotite Fe$_7$S$_8$, with admixtures of other elements.
Such minerals are often not really hard ferr... | {
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Why do $x - ct = 0$ and $x' - ct' = 0$ imply that $(x - ct) = \lambda (x' - ct')$ in special relativity? From the book, Relativity: The Special and General Theory (PDF) by Albert Einstein - Appendix 1:
A light-signal, which is proceeding along the positive axis of $x$, is transmitted according to the equation $$ x = ... | All the book is saying (at this stage) is that this is obviously a solution. There is no suggestion at this stage that it is the only solution.
Equally obviously $(x-ct) = λ(x'-ct')^n$ is also a solution for any non-zero value of λ and any non-zero value of n. Many other solutions are also available.
Any addition o... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How does momentum/'forward' thrust affect an object inside a vehicle in space? Apologies if this is a worn-out question, but I'm curious about this: if you're inside a vehicle in space, and that vehicle begins to move in a direction under its own power, would you 'drift' towards the origin of the thrust of the vehicle?... | The acceleration caused by the thrusters would produce the effect of gravity pulling you towards the floor, and in fact, you wouldn't be able to tell the difference from "real gravity" as the inside occupant. You can read more here: https://en.wikipedia.org/wiki/Equivalence_principle
I hope this helps.
| {
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Josephson junction: why do we need a capacitance in parallel to the inductance in the description? To start: I am really a huge beginner in Josephson junction. I need to understand the electrical equations associated to it, I don't need to go in the superconducting physics and I would like to stick on this if possible ... | As you pointed out, the small-signal model derived from the two Josephson relations is a perfect inductor.
Any parallel capacitance in the model is not derived from the Josephson relations at all, but only used to approximate AC impedance measurements of actual physical Josephson junctions. Since I am not after the bou... | {
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Can I have one single molecule of water? Is it possible detach one single molecule of water into vacuum lab?
| One can certainly separate water molecules at low temperature on a surface, as demonstrated by STM images. In Hossain et al. 2003 they show that the molecules stick to C defects on the surface. In (Shin et al 2010) they have nicer pictures of dissociated molecules on the surface.
I suspect one can also make free-flyin... | {
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If a ball is thrown to a person standing on a frictionless surface, is the impulse of the thrower equal to that of the catcher? If a person throws a ball, exerting a given impulse does the person that catches the ball receive the same impulse assuming that the catcher moves. Is the impulse that the catcher receives les... | The change in the ball's momentum when caught will be smaller than when thrown, since its speed will not go all the way back to zero. Since $J=\Delta p$, this means the impulse imparted by the ball on the catcher will be smaller than the impulse imparted on the ball by the thrower. This is why, if (say) a baby falls fr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How can one be sure that type-Ia supernovae have constant properties in time? In this Wikipedia article there can be much read about type-Ia supernovae. One can read:
This type Ia category of supernovae produces consistent peak luminosity because of the uniform mass of white dwarfs that explode via the accretion mecha... | There are some researchs about stars's metalicities that point that we can't use Supernovae Ia as standard candles as they dont explode always the same way. You can check some of this works in Arxiv.
Anyway this is true or not, the dark energy is not only backed up in Supernovae Ia.
Microwave background radiation meas... | {
"language": "en",
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Conduction band and free electron confusion When an electron is said to be in conduction band is it completely detached from the atom to act as free electron and conduct electricity as per free electron sea model?Do a jump from valence to conduction actually imply ionisation of atoms?Please clarify me about conduction... | The electrons at the bands are not free. What happens is that their wave functions can't be adequately described considering only the Coulomb potential of one nucleus. But they can't also be adequately described as a free particle. In a way their wave function combine both situations. According to Bloch's theorem:
\... | {
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What does the arbitrary constant in cosine equation of displacement in S.H.M say? The phase and phase constant in a displacement time equation show from where the particle has started.
In my school textbook, first the displacement equation was given as :-
$$x= A\sin(\omega t+\phi)$$
where $\phi$ i... | OK, you already understood the most important part. This is that
$$
\sin{(wt + \frac{\pi}{2})}
= \cos{(wt)}
$$
This implies, that the two following equations are equally valid
*
*$x(t) = A \sin{(wt + \phi)}$ or
*$x(t) = A \cos{(wt + \phi^\prime)}$
to define the position of an oscillator. If we like to start at t... | {
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Torsional Pendulum: Deriving an expression with time Period, Suspension Length, Moment of Inertia and Rigidy Modulus Constant I have been looking for the derivation/place where I can quote the formula $T=\frac{2\pi}{r^2}\sqrt{\frac{2IL}{\eta\pi}}$ from as I remember seeing in class but can't seem to find it online to q... | For relatively small (see Note) angular twists of the wire, the torque $\tau$ which restores the wire to its untwisted position is proportional to the angle $\theta$ through which the end of the wire is rotated : $$\tau=-\kappa \theta$$
$\kappa$ is called the torsion constant of the wire. The minus sign indicates that ... | {
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$V$-$I$ characteristic of a solar cell please explain the VI characteristics of a solar cell. The characteristics is given in my book without any explanation. How can the Voltage decrease on increasing current shouldn't it be opposite.
Solar Cell I-V characteristics
(Image from Electrical 4 U - Characteristics of a S... | If I invert your graph and change the direction of the current axis I get the graph in the middle.
That is an $IV$ characteristic which looks very like that of a forward biassed diode and in fact the solar cell is a diode which is designed to act as a current source when illuminated with light, the current delivered... | {
"language": "en",
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How do the unit vectors in spherical coordinates combine to result in a generic vector? I might be missing the obvious, but I can't figure out how the unit vectors in spherical coordinates combine to result in a generic vector. In cartesian coordinates, we would have for example $ \mathbf{r} = x \mathbf{\hat{i}} + y \m... | A vector space is a space that fulfills the vector axioms, closure under vector addition and scalar multiplication being the ones pertinent to this case. With all of the vector space axioms, any finite dimensional vector space has a basis set such that every vector can be written as a linear combination of the basis ve... | {
"language": "en",
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How does the current remain the same in a circuit? I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.
Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the ... | The circuit in its whole will settle into an equilibrium state.
If you were to shoot a very short pulse of electrons through your lamp, then indeed, the current would decrease right after the lamp.
But if you have a constant flow, then, as another user illustrated, you'd have electrons bunch up right before the lamp, w... | {
"language": "en",
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Can the Higgs particle escape a black hole? The higgs particle or field is what gives mass to everything. It's said that nothing can escape a black hole. If that is true how can the black hole "tell" its mass as even the higgs would not be able to escape? If higgs particles are able to escape, will eventually all matte... | The basic answer to your question is no, a Higgs particle cannot escape from the event horizon of a black hole, just like everything else. Although the underlying Higgs field is a (small, but important) source of mass for leptons, quarks, and the weak bosons ($W^{\pm},Z^0$), this essentially does not affect the discuss... | {
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Can any sum of infinitesimal canonical transforms on phase space be obtained from evolution under a static Hamiltonian? Suppose I have a canonical transformation on phase space, which is obtained by evolving a classical Hamiltonian system from time $t=0$ to $t=T$, with some arbitrary time-dependent Hamiltonian $H(t)$. ... | Maybe this is too naive a picture, but under your time-dependent Hamiltonian you can define a unitary time-evolution operator:
$U(T,0) = {\cal T} \left( e^{-i \int_0^T H(t') dt'} \right)$
where $\cal T$ signifies the time-ordering operator. As $U$ is a unitary operator, you can express it in terms of a hermitian operat... | {
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If magnetic field lines don't exist, what are these iron filings doing around a magnet? Obviously the iron filings can be seen aligning themselves along the virtual magnetic field lines produced by the permanent magnet, the virtual magnetic field line is made of electromagnetic field due to the alignment of electrons i... | When we say that magnetic field lines don't exist we mean that there is no physical form of them. Magnetic field lines just represent the direction of force which a ferromagnetic substance like iron would experience in the vicinity of a magnet (the pattern formed by iron filings).
The specific lines or pattern is form... | {
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Heisenberg's principle in classical world I have a ball with me and I have been observing it's position which remains constant at a place only, hence it must be largely localised, further as it remains on the same place from so long, it's velocity must be largely localised to 0 only.
Now with both momentum and position... | What we call uncertainty is the expected value of the standard deviation of position and momentum.
From statistical theory, if the standard deviation of a random variable with normal distribution is $\sigma$, the standard deviation of the mean is: $\sigma_{\mu} = \frac{\sigma}{\sqrt{n}}$, where $n$ is the number of el... | {
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First derivative of the moment of inertia in time as a physical parameter My question is addressed to the reputable community of physicists in connection with the ignorance of some of the subtleties of mechanics. Perhaps it will be interesting to other users.
Moment of inertia of a three-dimensional rigid body relative... | Since you're asking about physical intuition, I'd start with a simpler, more intuitive formula:
$$L = I\omega$$
in a suitable coordinate system (i.e., origin at the center of mass, coordinate axes chosen such that the rotation is an a plane). A change in the moment of inertia would contribute to the change in angular ... | {
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Charge Renormalization in Peskin and Schroeder I'm working on the charge renormalization in Peskin(page 252).
However I don't understand how he got infinite bare charge $e_0$.
According to $$\frac{e^{2}-e_{0}^{2}}{e_{0}^{2}}\approx-\frac{2 \alpha}{3 \pi \epsilon}$$
Solve this equation and we get $$e_0^2=\frac{3 \pi\ep... | You should remember that $\alpha = e^2/4\pi$, and that your expressions should all be determined perturbatively in $e$. Since you have only computed corrections to your theory to order $e^4$, the solution to the equation should really be written
$$
e_0^2 = \frac{3 \pi \epsilon}{3 \pi \epsilon - e^2/2\pi} e^2 \approx e^... | {
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If sound passes through material, vibration is produced. So are electromagnetic waves produced too? Sound means vibration of molecules and vibration produces electromagnetic waves. So, this means that sound produces electromagnetic waves directly.
Is this possible?
| Physically vibrating atoms with a sound wave will technically accelerate the charges, but the radiation emitted will be very weak. However secondary effects from the sound wave are a different matter.
Indeed, sound waves in water can create light. This is called sonoluminescence. In the lab it's done with ultrasound pa... | {
"language": "en",
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Observing from a true stationary point in space is there a "True time" we can observe? Aren't all points on planets, in solar systems, in galaxies moving through space subject to different amounts of time dilation due to gravity and velocity when observed from a stationary point in space? Do we generally have a mathema... | There is no such thing as a stationary point in space, so there is no universal time.
| {
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Torque and force Does the force due to torque on the edge of a wheel depend on the mass of the the wheel or is it always $\tau / R$?
| Force due to torque will not depend on the mass of the wheel.
If the mass of the wheel is more, more amount of work needs to be done on the wheel. But we are not caring about that.
Remember here we have produced the torque ( tau) ( that is the initial condition provided to us), now your formula will always be valid.
| {
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Why does the same proportion of a radioactive substance decay per time period? (half life) Just wondering, if decay is random, why does the activity half every half life, as in, why does it have to reduce by the same proportion in the same time period?
| You're asking the wrong question.
There is no magical notion by which it decays by half. That is why "half-lives" vary so much. "Half-lives" are simply the chosen method of measurement.
Your question is analogous to asking "why all cars travel in hourly increments?" just because we measure speed in km/h.
The notion i... | {
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Integrating acceleration - wrong choice of bounds in textbooks? I've noticed in my physics textbook (and in a lot of other popular sources), that the process of integrating non-constant acceleration to get to a velocity formula, the integrating bounds imposed on the velocity-part seem wrong.
In the above snippet, they... | I think you are getting confused by notation. A cleaner way of writing 3-34 would be $$ \int_{v_0}^{v} d\tilde{v} = \int_{t=0}^{t} a(\tilde{t}) d\tilde{t} $$ then the LHS is $ [\tilde{v}]_{v_0}^{v}$ which does become $v-v_0$ (the tilde is just a a technique to distinguish between a variable and a parameter - a dummy v... | {
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"source": "stackexchange",
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Double slit for electrons (two beams or one)? I understand the double slit for waves but for electrons do we have a beam for each slit so each beam is responsible le to shoot electrons through its own slit.
Or do we have just one beam? Which slit do we place the beam to? If it’s in the middle, wouldn’t all the electro... | This is not a direct answer to the question, because the question is built on some misconceptions:
*
*There's nothing special about "double slit" interferometry. All that's required to produce interference fringes is for two waves from the same source to be superimposed at an angle. This occurs in Young's double-s... | {
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Emf induced by a changing electric field Is there a law/formula that relates the rate of change of electric flux with the induced electromotive force? i.e. similar to what Faradey's law of induction states for the magnetic field.
| Let $L$ be a closed area with boundary $\partial L$. If it helps, you can imagine $\partial L$ to be a loop of wire. Now suppose we send a time-varying electric field through $L$. We seek to relate this electric field $\textbf{E}$ traveling through $L$ with the (induced) magnetic field $\textbf{B}$ in $\partial L$.
To ... | {
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Fringing of electric field I have read that in a capacitor with charged parallel plates the electric field lines are parallel in the middle, but they tend to bend outwards (causing a "fringe") towards the ends of the parallel plates. Can someone explain why this really happens? Does it happen due to the lack of symmetr... | There are many ways of answering your question but I think one of the simplest is as follows:
Assume there is no fringe field when a capacitor is storing charge.
Move a positive charge from the outside of the negative plate to the outside of the positive plate.
Since there is no fringe field, the work done in moving th... | {
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Different expression of $\Delta(x, m^2)=(2\pi)^{-3}\int e^{ip \cdot x}\theta(p^0)\delta(p^2+m^2)d^4p$ Let $$\Delta(x, m^2)=(2\pi)^{-3}\int e^{ip \cdot x}\theta(p^0)\delta(p^2+m^2)d^4p.$$
Here $\theta$ is the step function at $0$.
I would like to show that this is the same as
$$\Delta(x, m^2)=(2\pi)^{-3}\int \frac{e^{i... | I assume that there is a misprint, argument of delta-function should be $p^2-m^2$.
Consider case $p^0>0$, so the integral becomes
$$\int d^4p\delta(p^2-m^2)e^{ipx}=\int dp_0\int d^3p\delta(p_0^2-p^2-m^2)e^{ip_0t}e^{ipx},$$
where zeros of delta-function are
$$p_0=\pm\sqrt{p^2+m^2},$$
and delta function becomes
$$\delta(... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532540",
"timestamp": "2023-03-29T00:00:00",
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How is a 25-year-old can of soda now empty without having been opened or poked? I just discovered in my parents' basement a Sprite can from 1995* and also a Coca-Cola can probably from the same year.
Both cans are unopened and have no visible damage or holes. The Coca-Cola can feels "normal", but the Sprite can is emp... | My vote is that the can was accidentally shipped empty. This does actually happen - I myself happen to have a nearly-brand-new unopened Pepsi can which is empty (and I once encountered another, but I foolishly opened it to confirm the fact, thus rendering it just another empty can). I also have an old tub of Wendy's ... | {
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"timestamp": "2023-03-29T00:00:00",
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Angular velocity, angular acceleration and it's observer
I was solving the problem above and realized that I was wrong somewhere.
I did two approaches but one didn't work well.
1. let one end which is at hold be the point we calculate torque.
Then, $\frac{1}{2}lmg=\frac{1}{3}ml^2\alpha$ (here $\alpha$ denotes $\frac... | $\alpha$ is not observer dependent. Now as far as l/2 is considered , it is used because the motion is such that the person which is holding the rod acts as a stationary centre for the motion of the body which is at a distance of $l/2$ from the centre.
| {
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Problem in derivation of Smoluchowski Equation I am trying to derive Smoluchowski equation using Fokker Planck equation. I am following the book ''Non Equilibrium Statistical Mechanics'' by Robert Zwanzig. I am attaching a screenshot of a few pages of the book.
I am having issues with going from Equation 2.51 to 2.52. ... | Set the left hand side of 2.50 to zero which is what "dropping the second derivative on the left hand side" means and solve for dx/dt.
| {
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Ionizing radiation in thermal radiation According to the black-body radiation equation, the spectrum extends to infinitely high frequency (although its intensity gets small quickly towards high frequency).
(1) How do you roughly estimate the ionizing radiation power in common high power thermal sources like a 2KW heate... | Planck's law says:
$$B_\nu(\nu, T) = \frac{2h\nu^3}{c^2} \frac1{\exp\left(\frac{h\nu}{kT}\right) - 1}.$$
This is the power emitted by a black body of temperature $T$ at frequency $\nu$. If we consider a black object (thus highest possible purely thermal emission) of temperature $700°\mathrm C$ (an estimate of temperatu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Solving projectile motion using least action principle and level sets I'm trying to compute 1D projectile motion -- basically throwing a ball up and catching it in the same hand. I want to use Lagrangian dynamics and find a numerical solution out of interest.
I started trying to compute a trajectory that minimizes the... | FWIW, the simplest is probably to graph the mechanical energy $(y,\dot{y})\mapsto \frac{m}{2}\dot{y}^2 + mgy $ rather than the Lagrangian. Because of energy conservation the stationary paths would then be level sets.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Does Another Universe Where Time Runs Backwards Revive the Idea of a Cyclical Universe? https://www.pbs.org/wgbh/nova/article/big-bang-may-created-mirror-universe-time-runs-backwards/
This article talks about a new theory where the big bang happened in one direction for us and the other direction where time is going ba... | Perhaps it does. But I would also stipulate that the two-sided inversion is also overlaid, meaning that we cannot disconnect from the other side, meaning that we need a mirror side of reality to make sense of existence, and meaning that there are likely lesser mirrors (e.g., an actual mirror, the condition called situs... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Clarification of the concept "less resistance means less heating" in a wire So my textbook says that the reason cables that are suppose to carry high currents, are thicker that those that are meant to carry lesser current, is that "less resistance (of the wire) means less heating..."? Is this even true?
Isn't CURRENT ... | You can regard a power supply in series with a load as a constant current source. At a constant current, the $I^2R$ losses in the cable reduce with resistance.
However, your concerns are valid in the event of a short circuit, and this is a thing in the design of resilient power distribution networks. Thicker cables mea... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Do black holes move through space? I know it was already asked here:
Does a black hole move through space? What happens to other things around it?
And it might be a very stupid question, but here it is:
From a relativistic perspective, do black holes move through space, or is it the space around them that is curved in... | Consider a black hole with lots of stuff in orbit around it. For example, most galaxies are like this (they have a big black hole at the centre, or, at least, there are good reasons to think that this is so). When all the orbiting stuff moves along together (while still orbiting), surely it makes sense to say the black... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Dumping hot liquid water in sink When I make pasta or potatoes, I dispose of the hot water (around 80-100°C) in a metal sink.
Am I justified to first pour regular hot tap water on the sink to reduce the amount of steam generated, or is this pure superstition ?
If it's not, what is the physical explanation ?
| If you fill the sink with colder water there will not be much steam, but if you just pour a layer of colder water it will not have much effect. The reason is that the mass of boiling water is much larger than the layer, so the temperature reduction will be much smaller than for mixing it with an about equal volume of c... | {
"language": "en",
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"source": "stackexchange",
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Torque cross product Torque is the cross product of force and distance. Almost all the resources I find online have the formula as $\vec\tau=\vec d\times \vec F$, yet my professor (and I've seen some other sources do this) insists on using $\vec\tau=\vec F\times \vec d$. From what I've learned, swapping the two vecto... | $\vec \tau=\vec r \times \vec F$ is consistent with the right-hand grip / right-hand corkscrew rule.
| {
"language": "en",
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Infrared divergency in the correction to the electron vertex Function in QED/ Question to Schwartz "Quantum Field Theory and the Standard Model I'm currently studying Mathew Schwartz's "Quantum Field Theory and the Standard Model". In the chapter on Infrared divergences (Page 359 (7th edition, hard cover))
he calculate... | It's actually possible to do the integral explicitly. To do so, it's convenient to decouple the x- and y-integration. Thus introduce $ \tilde{x}=1-x$ and $y= \tilde{x} \tilde{y}$ and define $r \equiv \frac{m^2_{\gamma}}{-Q^2}$. The integral reads now (dropping the tildes)
$$ \int_0^1 dx \frac{-x}{1-x-r} \int_0^1 dy \fr... | {
"language": "en",
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The Enigma of Universal Gravitation Forces This is taken from a book called "Physical Paradoxes and Sophisms" by V. N. Lange.
1.22. The Enigma of Universal Gravitation Forces
The law of gravitation can be written $F=\gamma\frac{m_1m_2}{R^2}$.
By analyzing this relationship we can easily arrive at some interesting ... | It is just a math exercise about limits:
$F = \frac{GMm}{R^2}$.
If $\rho$ is the density of the body with mass $M$ (supposed spherical for simplicity):
$F = \frac{G\rho m 4\pi R^3}{3R^2}$.
So: $F = \frac{G\rho m 4\pi R}{3}$ goes to zero when $R$ goes to zero!
| {
"language": "en",
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What does Heisenberg's uncertainty principle tell about nature? I agree with the fact that the principle points out to the inaccuracy in the measurement of the two quantities of the particles (momentum and position).
But measurements apart, does it explain anything about how nature works, in general? As in, I think the... | From vector algebra we know that
$$ |\vec{u}|\,|\vec{v}| \geqslant \vec{u} \cdot \vec{v}$$
This can be generalized for inner products :
$$
\langle \mathbf {u} ,\mathbf {u} \rangle \cdot \langle \mathbf {v} ,\mathbf {v} \rangle
\geqslant
|\langle \mathbf {u} ,\mathbf {v} \rangle |^{2}
$$
That general principle is known... | {
"language": "en",
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Time period of piston performing SHM Suppose I have a closed piston-cylinder system which contains an ideal gas,and it is being compressed adiabatically by the piston which has a vertical orientation,and in doing so,the piston is actually undergoing SHM. Now if I use a similar piston in a horizontal orientation (keepin... | It is straightforward to show that if $$pV^\gamma =\text{constant}$$
then
$$\frac{dp}{dV}=-\gamma \frac pV$$
Therefore for small changes, $\Delta V$, in volume, giving rise to small changes, $\Delta p$, in pressure, we have to first order,
$$\frac{\Delta p}{\Delta V}=-\gamma \frac pV$$
$p$ and $V$ are the equilibrium p... | {
"language": "en",
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Is there any relation between turn on voltage of LED and the colour emitted?
It is evident from the above V-I graph that longer the wavelength of the light emitted lower is the turn on voltage. I know that turn on voltage is voltage required to have significant current that can give a detectable brightness.And light i... | The voltages you see there are based on what is required to make the material emit light. Its based on the particular material properties that are required to make each color.
And if you look, you can see that yellow is nestled between green and orange, so they aren't in spectrum order.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Characterization of states for "-wave" in discrete lattice system Assuming there exists four states, i.e. $|1\rangle, |2\rangle,|3\rangle,|4\rangle$, localized in four sites, which satisfy $C_4$ symmetry:
And we can characterize the combination of them via the eigenvalue of $J_z$, i.e. $e^{-iJ_z\theta/\hbar}|m\rangle=... | You are doing quantum mechanics around the clock in a clock of only 4 hours (period 4). Apart from an excessive square root in your normalizations (which I suspect should be just 1/2), your are Discrete Fourier Transforming your "hour" states $| 1\rangle, | 2\rangle,| 3\rangle,| 4\rangle,$ (the discrete analog of posit... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Gauge symmetries not from promotion of global symmetries The most intuitive example of a gauge symmetry is such where you take a theory that has some global symmetry, and ask what needs to be done for this symmetry to be local. This procedure involves the introduction of new fields. For example, when a global phase sym... | A theory invariant under some spacetime-dependent transformations is automatically invariant under the constant transformations. So there's always a group of global symmetries that resemble the local ones. Usually these global symmetries are not treated as gauge symmetries. The transformations they induce are physic... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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If we ignore energy and talk about force, Why do objects bounce lower when they hit a softer surface? If an object hits a soft surface it will bounce lower compared to the object hitting a hard surface, isn't the impulse in the first case equal to the impulse in the second case, so why does the object bounce lower when... | Why do you assume that the impulse is the same in both cases? Impulse is equal to the change of momentum, so clearly it is not the same. There is an equal and opposite force in both cases, but these forces are not the same in one case as in the other (indeed the meaning of "soft" is a smaller equal and opposite force d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535442",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Why would this evaporation-based perpetual motion machine not work? This morning I was struck by an odd thought:
*
*Hydroelectric power stations get energy by dropping water from a height. The greater the height difference between top and bottom, the more energy can be gained.
*To evaporate 1 gram of a boiling liqu... | The scenario you describe is more or less how hydroelectric plants operate in the first place, but they use a power source- the sun- to do the evaporation work and to generate the winds that move the humid air around.
If there were no energy input from the sun, evaporation and global circulation of the atmosphere woul... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535604",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Periodicity of the solution of the wave equation In a few references, I have found that if I have a wave equation
$$
\nabla^2 E=\left[\frac{n(x,t)}{c}\right]^2\frac{\partial^2E}{\partial t^2}
$$
where the refractive index is periodic in space and time
$$
n(x+\Lambda,t)=n(x,t) \\
n(x,t+T)=n(x,t)
$$
then, also the electr... | It is because electric field is function of medium refractive index :
$$
\mathbf {E} (n(z,t)) =\operatorname {Re} \!\left[\mathbf {E} _{0}e^{i(2\pi (n(z,t)+i\kappa )z/\lambda _{0}-\omega t)}\right]
$$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is a simple argument to prove that the stars in the sky are further away from the Earth than the Moon? How do we know, without using modern equipment, that the stars are further away than the moon in the night sky? Further, is there a simple and actionable argument to prove that this is indeed the case? Additional... | Compare angular sizes of stars and sun. Sun has angular size of $\approx 32 \,'$ and our closest star Alpha Centauri A has angular diameter of $0.007\,''$. This gives of angular size ratio between them as about $270\,000$ times, which correlates very well with real distance ratio between them and Earth. You don't need ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536244",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 7,
"answer_id": 4
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Why is the speed of light in vacuum a universal constant? While getting familiar with relativity, the second postulate has me stuck. "The speed of light is constant for all observers". why can't light slow down for an observer travelling the same direction as the light?
| It does seem strange at first, it sounds like you're asking "If I'm moving towards a source of light won't I see the light travelling faster than c?". If you picture yourself standing still, watching someone drive past you on a car, if they throw a tennis ball in the direction they're driving the speed of the tennis ba... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536432",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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If work is a scalar measurement, why do we sometimes represent it as the product of force (a vector) and distance (scalar)? Consider an object being pushed 3/4 of the distance around a circular track. The work done on the object would be the distance of 3/4 the track’s circumference times the force applied to the objec... | The general definition of work is
$$W=\int\mathbf F\cdot\text d\mathbf x$$
Which essentially says, "Add up all of the dot products between the vector force $\mathbf F$ and the vector displacement $\text d\mathbf x$ along the path the object travels on." Since we are adding up dot products, which are scalar quantities,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536688",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Why is the action of lowering operator on the ground state of a harmonic oscillator to give a 0 wave function? In quantum mechanics of the harmonic oscillator, when we use the operator method to find out the solutions, we find that the action of $\hat{a}$ is to lower the energy of a state by $\hbar\omega$ and the actio... | The eigenstates of the operator $N = a^\dagger a$ can be labeled by their eigenvalues, i.e. $N \phi_n = n \phi_n$, where $n$ is an integer. Note that
$$n = \langle \phi_n,N\phi_n\rangle = \underbrace{\langle\phi_n,a^\dagger a \phi_n\rangle = \langle a \phi_n,a\phi_n\rangle}_{a \text{ and } a^\dagger\text{ are mutually... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In circular motion why is the vector $\mathbf v_f$ minus the vector $\mathbf v_i$ equal to the vector $\Delta \mathbf v$? What is the vector $\Delta \mathbf v$ ? and why does equal $\mathbf v_2 - \mathbf v_1$.
notice: I knew about calculus, my question is not generally but it is about circular figure, vectores confused... | Delta v is just an abbreviation for v2-v1 so it is the little green vector in your picture
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537193",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Does no-level-crossing theorem (aka avoided crossing) always hold in perturbation theory? In perturbation, J.J. Sakurai Modern Quantum Mechanics Second Edition page 310 stated a no-level-crossing theorem stated that
"a pair of energy levels connected by perturbation do not cross as strength of perturbation is varied"... | Firstly the N-2 condition is simply a constraint that gives you a number of equations without enough degrees of freedom to solve them. By having a manifold that can support more degrees of freedom this is indeed possible and is exactly what happens when a crossing is analytically continued into the complex plane as a f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537262",
"timestamp": "2023-03-29T00:00:00",
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Could a Dyson Sphere-like object be made to encase a black hole without collapsing? In this question, I'm not asking about the feasibility of building a black hole Dyson Sphere or the effectiveness, I simply want to know if an object could stay in a locked position encasing a black hole without collapsing in on itself.... |
… if an object could stay in a locked position encasing a black hole without collapsing in on itself.
Yes.
Solutions for a thin static spherical shells around a nonrotaing black hole have been considered in the following paper:
*
*Frauendiener, J., Hoenselaers, C., & Konrad, W. (1990). A shell around a black hole,... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why can vector components not be resolved by Laws of Vector Addition? A vector at any angle can be thought of as resultant of two vector components (namely sin and cos).
But a vector can also be thought of resultant or sum of two vectors following Triangle Law of Addition or Parallelogram Law of Addition, as a vector ... | Suppose you are attempting to find a point on a map given a starting point. Which do you prefer:
*
*4 km north and 3 km east of your current location
*7 km north and 4.2 km southeast of your current location
We can use whatever non-parallel vectors we want to describe an offset in two dimensions. Is it now clear ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537550",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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A bar moves to the right with a velocity $v$ in a uniform magnetic field. What is the induced current? I know that a change in a magnetic field produces a current, as $-\frac{\partial}{\partial t}\int B\text{d}a = \int E \text{d}l$. In this case however, the magnetic Flux stays constant through the loop so there should... | I see that I misinterpreted the question. For some reason I thought of the whole circuit moving, while actually only the bar moves. Thus the flux through the circuit does indeed change, and because of Lenz's Law there will be a current flowing clockwise (opposite to the B field). If is negative, the flux will decrease... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537665",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is a Lorentz transformation of a Lorentz transformation also a Lorentz transformation? Why is a Lorentz transformation of a Lorentz transformation ($x''$,$y''$,$z''$,$t''$) also a Lorentz transformation?
| You're asking the wrong question. You don't apply a Lorentz transformation (LT) to a transformation, you apply a Lorentz transformation to an inertial reference frame (1) to get a description of an event (or events) in another inertial reference frame (2). That LT will preserve the space-time quantity $$c^2t_1^2-r_1^2 ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537873",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Do gravitational waves carry momentum? We know from the idea of wave-particle duality that electromagnetic waves are photons which have the property of momentum. It stands to reason that gravitational waves would have similar duality. Would the particle form of gravitational waves carry momentum the same as a photon ... | Yes. Gravitational waves carry energy, momentum, and angular momentum, just like electromagnetic waves. This is classical field behavior; you don’t have to quantize either field to have this effect. If you do, you can understand the energy, momentum, and angular momentum in terms of gravitons and photons, at least in t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537993",
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"source": "stackexchange",
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Partition function for quantum Ising model I have hamiltonian for fermionic field as
$${\cal H}_F=E_0+\int dx[\frac{v}{2}(\Psi^\dagger\frac{\partial \Psi^\dagger}{\partial x}-\Psi\frac{\partial \Psi}{\partial x})+\Delta\Psi^\dagger\Psi]\tag{1}$$
And partition function is
$$\mathcal{Z}=Tre^{-\frac{H_F}{T}}=\int D\Psi D\... | As you can see the action is a sesquilinear form in $\Phi, \Phi^\dagger$. This means that you can write
$$
S = \Phi^\dagger G \Phi.
$$
Now you realize that the partition function is a gaussian (infinite dimensional) integral over Grassmann variables, i.e.
$$
Z = \int D\Phi D\Phi^\dagger e^{- \Phi^\dagger G \Phi }.
$$
T... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Regarding Law of Conservation of Energy If a force is applied on a body in an isolated system, it gets accelerated, which means its velocity and hence its Kinetic Energy will go on increasing. How does law of conservation of energy holds for this increase in Kinetic Energy?
| The notion required here is the concept of system. A system is a set of parts that interact.
So, asking "If a force is applied on a body in an isolated system" is an ill-formed question. If the system is isolated, an external force cannot be applied to one of its parts. If an external force is applied to the system, t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538238",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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New orbit of Jupiter after the death of the Sun When our sun finally ceases to exist as a red giant, 7 billion years from now, the outer layer of the star will get blown off in huge clouds of gas and dust known as planetary nebulae, leaving behind a very dense core, that cools down to form a white dwarf (approx.. 6000k... | A Study to Show : Jupiter : Our Next Star
My 11th grade research paper 2018
Final Answer under -
Jupiter’s Orbit during Thermal Pulse 4 ,
pg32
(New orbit - 11.620 Billion km from the white dwarf)
| {
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"timestamp": "2023-03-29T00:00:00",
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CFT dual to a black hole AdS/CFT is famous correspondence between gravity and CFT.
What one can say about black holes using this correspondence?
What CFT object correspondent for black hole? For charged black hole? Rotating black hole?
What kind of information about black hole one can extract from this correspondence?... | When a Black Hole is present in a bulk, it gives the background some temperature due to Hawking radiation. Thus a stable spacetime in presence of a generic BH has a fixed tempertature $T$. The dual CFT theory also has thermal states. It has been recently shown that these thermal states have one-to-one correspondence wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538782",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The electric field should be in circular coil. But why do current flows in whole circuit? We know changing magnetic flux induces electric field which makes current to flow .here in the below picture the flux is changing through only circular coil bout not through the rectangular part.so what induces electric field in r... | When you move the magnet through the loop, you induce a collective shift of electrons in the metal wire. At one end of the loop there is an excess of electrons and at the other end there is a shortage of electrons. This potential difference is equalized over the whole wire, you get a current.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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} |
Energy conservation in reflection of light from a perfect mirror I came across a question where a light source is shined on a mirror attached to a spring which is attached to a rigid support. The question goes:
A perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular f... | The mass of the mirror is given to make you think this is a frame-of-reference problem. It is not. That, or it's required to derive the spring constant $k$ from the oscillator frequency $\Omega$. Let's suppose that is done.
Now the situation is in equilibrium with the mirror displaced by a distance $x$, which requires ... | {
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"timestamp": "2023-03-29T00:00:00",
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Applying force in zero seconds? How is this possible? $F\,\Delta t=m\,\Delta v$, is the equation of impulse. Let's say that I push a wall with my hands, we can have $0$ change in velocity; therefore, $F\,\Delta t=0$, since I'm pushing the wall there is force, the only way the equation equals zero is that $\Delta t$ equ... | Beware of blindly applying equations.
In thinking about the velocity of the wall, then for $F\Delta t=m\Delta v$, $F$ is the net force acting on the wall. If $\Delta v=0$, then we know that $F=0$ (and the same is true vice versa).
Note that this is just Newton's second law: $F=m\frac{\Delta v}{\Delta t}=ma$. If $a=0$ ... | {
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How to formalize taking line integral by a reversible or irreversible path? In thermodynamics work can be done by moving alone a reversible or irreversible path. Physical definitions of reversible and irreversible processes is uncommon in thermodynamics textbooks. The main idea is that I have to imagine something I can... |
Does this mean that some curves have the property of being
reversible paths and some don't?
Yes. The work done by a reversible process between the same two equilibrium states will be greater than for the same process carried out irreversibly between the same two equilibrium states. Each has a different shape "curv... | {
"language": "en",
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"source": "stackexchange",
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Calculating formula prep using thermodynamics I suspect there is a very simple mathematical formula for preparing formula (forgive the pun) that simply mixes a combo of freshly boiled water and room-temp water.
To be specific, if I need to prepare an n mL feed, I would like to:
*
*Mix x mL room temp (r) water + y mL... | The problem gives us three equations:
$$ z \, T_r + (x + y) \, 70^\circ \text{C} = n \, 45^\circ \text{C} $$
$$ y \, T_r + x \, 100^\circ \text{C} = (x + y) \, 70^\circ \text{C} $$
$$ x + y + z = n $$
With $T_r$ beeing room temperature.
From this I get:
$$ x = n \, \frac{\frac{45^\circ \text{C}}{T_r} - 1}{(1 + \frac{30... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540329",
"timestamp": "2023-03-29T00:00:00",
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How do we know that a non-rechargeable battery obeys the law of conservation of energy? For a rechargeable battery, I can show that energy is conserved by
*
*Discharging the battery.
*Measuring the energy required to charge the battery.
*Measuring the energy I get out from a second discharge.
For a non-rechargeab... | I don't think it's experimentally feasible, but if one could measure its change in mass precisely enough, it will change by $1/^2$ times its change in potential energy, which will will be the energy produced during discharge.
If you discharged it through a resistor, then the total energy as heat generated by the resis... | {
"language": "en",
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Relativity and mass increase Consider a long bridge which can marginally tolerate the weight of a car when it is parked on it. If this car has to go over this bridge with relativistic speed which increases its mass/weight above what the bridge can hold, what would happen? Will the bridge collapse (pedestrian view) or r... | SPOILER ALERT: The following is probably not the answer you wanted, but as a recovering ex-engineer I can't help myself:
In practical terms, the bridge will not collapse, because the residence time of the relativistic car on the bridge will be insufficient for the applied stresses (the weight of the car) to propagate t... | {
"language": "en",
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Gauss' Law in 2D? At first I thought it was $$∮E.dl=Q/ϵ.$$
So i've read through some sources here and on the internet and most of them said that
$$∮E.dl=2πq.$$
But I'm confused. Can anyone explain where does the $2πq$ come from?
Also someone answer this question with a result: $$∮E.dl=λ/ϵ.$$ So does this means that $λ... | In 2D one can define an entity analogous to flux by the integral of $E\cdot dl$ where the $dl$ is a segment of curve in the vicinity of a charge and is represented by a vector perpendicular to the curve and directed away from the charge. (No area is involved.) In 2D the $E$ field is spreading in two directions rather ... | {
"language": "en",
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Which configuration is better in terms of elastic stiffness?
Which one deforms more when subjected to the same torque? I am having trouble thinking about this mathematically and with equations. Don't know what to do...
| I will assume that you are talking about the twist of a slender bar.
In that case, you can consider that the torsional stiffness is written as
$$
\kappa_0 = J_0 G_0 + J_1 G_1 = \frac{\pi G_0 (r_1^4 -r_0^4)}{2} + \frac{\pi r_0^4\, G_1}{2}\, ,
$$
for one case, and
$$
\kappa_1 = J_0 G_1 + J_1 G_0 = \frac{\pi G_1 (r_1^4 -r... | {
"language": "en",
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Why a ball doesn't stop when it collides with a wall? If a ball collides with a ball of same mass the first ball stops and the second ball gets the velocity of first ball.The first ball stops due to the reaction force acting on it. But when a ball collides with a wall why doesn't it stop due to the reaction force?
|
I'll let the animation speak for itself.
The blue arrow shows the force on the object.
For this scenario to happen it is important that the collision is elastic (all energy is conserved). I used a force that is proportional to penetration depth. This way the balls feel a force that is the same during the deceleration ... | {
"language": "en",
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If an observer changes their velocity, is it equivalent to a momentum shift? Suppose we have a world with one massive free particle and one observer. If the observer changes their velocity with respect to the particle, will this have the same effect on $\lvert\Psi(r,t)\rvert^2$ as if $\langle p\rangle$ was changed loca... | No $|\psi(x,t)|^2$ will not change.
Reason Schrodinger equation is invariant under Galilean transformation.
See this Galilean invariance of the Schrodinger equation
| {
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Newton 3rd law of motion If I took both hands and hold as I am greeting someonei.e.namaste. Now, I push both hands with same force say 10N , there is no change in position.But Newton 3rd law has said,equal and opposite forces are on different bodies and they never cancel each other (action reaction). So, why they don't... | I think you are confusing two ideas (commonly confused). Equilibrium forces (which cancel) and reactive forces, which may or may not cancel depending on the situation.
Think of a book on the table. You push on the book. The book pushes back on you with an equal and opposite reactive force. If you push hard enough, the ... | {
"language": "en",
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Application of work energy principle an open garage door as it closes
According to the solution to the related example problem in the book, points B and D have no linear velocity when the door is fully closed, that is, when point E strikes the floor, because they are at the lower limit of their respective motion range... | The garage door is an example of constrained motion. End A is constrained to move in a horizontal line. Points B, D are constrained to move in a vertical line and to stay in a rigid position relative to A, C and C, E respectively.
The object dropped from a height is not constrained while it is freely falling.
A fairer... | {
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What is the physical interpretation of the Helmholtz free energy for an isothermic, irreversible process? $$dF=-SdT-pdV$$
For an isotherm, $dF=-pdV$, so $\Delta F=-\int^{V_1}_{V_2}pdV$. Thus, a change in the free energy tells us how much work has been done by or on the system. However, at this point the textbook I've b... | Partial answer: This certainly does only hold true for quasi-static processes (the reversiblity in your textboox is an even stronger condition), as only for these processes a pressure is defined throughout the process.
| {
"language": "en",
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What saves bike rims when one rises before hitting small obstacles at full speed? When riding a road bike with thin tires over small obstacles such as tree roots, there is a risk of damaging the tires.
Cyclists argue that rising off the saddle will all but eliminate the risk of rim damage.
Why does rising save the rims... | The answer to 2, is that the 70kg of the rider is decoupled from the bike mass which effectively pivots at the pedal crank, which is approximately midway between the wheels. Forces acting on either wheel simply pivot the 10kg of bicycle about the crank pivot, significantly reducing the effective moment of inertia.
If t... | {
"language": "en",
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Potential energy of a single point-mass in an upright object Does a point-mass on one end of an object sitting upright have gravitational potential energy?
An example would be a balanced pencil. Does a point-mass on the top end of the pencil have gravitational potential energy?
|
The potential energy is:
$$U=-mgL $$
With:
$$mg=\dfrac{mMG}{\left( R+L\right)^2}\approx\dfrac{mMG}{R^{2}}$$
Thus $g=\frac{MG}{R^2}$
And
$$U=-mMG\left( \dfrac{L}{R^{2}}\right) $$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Deriving Unitarity of $S$-matrix in 1D Quantum Mechanics I was studying about scattering across a one-dimensional unknown potential ( pretty elementary Quantum Mechanics) and how, if we know the $S$-matrix of such a system, we can deduce an awful lot of information about the potential. Also, the $S$-matrix satisfies so... | The reason for the equality of the currents is particle conservation. You can start with the continuity equation $$\partial_t |\psi(x,t)|^2+ \partial_x j(x,t)=0;$$ integrating it over the central region we get
$$\int_{x_L}^{x_R}dx \partial_t |\psi(x,t)|^2 +
\int_{x_L}^{x_R}dx \partial_x j(x,t) =
\frac{dQ(t)}{dt} +j(x_... | {
"language": "en",
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How to calculate the fraction of light rays reflected?
The smooth surface is air-liquid interface and the rough surface is let's say a t-shirt.
The image above shows the probability of each reflection, and the $p$ value is the probability of the light rays totally reflected by the air-liquid interface. So this means $... | Lambertian phase function is,
$$
\Phi(\theta) = \cos(\theta)
$$
This means at normal $\theta=0$ maximum intensity is reflected form the cloth surface, which falls of to zero when $\theta=\pi/2$.
Reflection from the surface is diffuse, meaning that a beam of light entering at a constant angle, will be reflected into all... | {
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Derivation of Torque on Loop of Wire For a loop of wire in a uniform magnetic field, the torque is given by the following equation:
$\vec{\tau}$ $=$ $\vec{m}$ $\times$ $\vec{B}$
where $\vec{m} = I\vec{A}$ is the magnetic moment of the loop and $\vec{B}$ is the magnetic field. How can you prove this, especially for an a... | as your 1st question---
$\vec{\tau}$ $= $ $\vec{m}$ $\times$ $\vec{B}$
well this derivation could be found on any website, just google it you will get it, or please state what to ask specifically in its derivation
now your 2nd question---
$\vec{m}$ $=$ $I\vec{A}$ is the magnetic moment of the loop and
is the magnetic... | {
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On the prefactor in the path integral formulation The propagator $K$ from ($x_a,t_a$) to ($x_b,t_b$), as defined by Gottfried, can be written as
$$ K(b,a) = F(t_b-t_a)\exp\left(\frac{i}{\hbar}S_{c}(b,a)\right) $$
where $S_c$ is the classical action and $F(t_b-t_a)$ is the integral over all paths from the origin and bac... | There is certainly a mathematical reason:
*
*The external force $f$ appears in the term linear in the position variable $x$ of the action $S[x]$.
*When we split the path integral variable $x~=~x_{\rm cl}+ y$ in a classical path $x_{\rm cl}$ plus quantum fluctuation $y$, we know that the action $S[x]~=~S[x_{\rm cl... | {
"language": "en",
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Functional Derivative In Chapter 1 of Lancaster's Quantum Field Theory for the Gifted Amateur, he gives an example of taking the derivative of a functional but doesn't show much work. I was confused how he got the answer.
$$\int g[f(x) + \epsilon \delta(x - x_0)] dx= \int (g[f(x)] + \epsilon \delta(x - x_0) g'[f(x)])dx... | The best way to think about this is to think about the definition of a derivative. Start with $$g(x + h) \approx g(x) + h\times g'(x).$$ In the limit as $h$ goes to zero, this is the definition of a derivative of a function. Now, replace $x$ with $f(x)$ and replace $h$ with $\epsilon \delta(x-x_0)$. You get: $$ g(f(x +... | {
"language": "en",
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QFTs without Lagrangian I have been reading other questions in this site, but I have not found answers to all my questions about theories without Lagrangians.
What do we mean exactly when we say that they do not have a Lagrangian? Do they still have an action but this action cannot be defined as the integral of a local... | *
*That a set of equations does not have a variational formulation means that there does not exist an action functional, cf. e.g. this Phys.SE post.
*The existence of a local functional is typically a separate issue, which is usually required in fundamental physics.
| {
"language": "en",
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Where does normal force shift to?
"A block of side length $a$ and mass $m$ resting on a ground with a coefficient of friction $\mu $. A force $F$ is applied on the upper edge of the block (think of the cross-section and one of the topmost vertices). How much force should be applied to topple the block?"
In the solut... | The magnitude of the normal force is sufficient to prevent the block from accelerating downward. As long as the material does not yield, it will equal the weight of the object.
The location of the normal will shift to prevent rotation. If you apply a torque $\tau$, the normal will shift sufficiently to oppose the rot... | {
"language": "en",
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Tensor product of representations of Lorentz group Where is the rules for tensor product of representations of Lorentz group $(a,b)\otimes (c,d)$ without decomposition of one of these in orthogonal sum?
| Your answer is there for the appreciating in WP 3.2.1.2, and all you need is understand the notation. (Several people attach to Ch. 5, of v I of Weinberg's QFT text.) There may be a confusion of the tensor product ⊗ used in both linking the Lorentz Group left ideal A to the right one B but also, again with common rot... | {
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What are Inertial and non-inertial forces? What are inertial and non-inertial forces? I looked them up.
One of the websites says that an inertial force is a force that can be observed/measured in an inertial frame. In this case, do we have a Force that we can't observe or measure in an inertial frame? Aren't forces fr... |
Inertial reference frame implies, if two co-ordinate systems are in a constant relative speed respective to each other, then their relative speed is zero. Let us assume co-ordinate_1 and co-ordinate_2 are in constant speed relative to each other. Their relative speed is zero. A force here will follow the newton's 2nd ... | {
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Quantum circuit calculating sum of two quantum states $|a\rangle + |b\rangle$ What is the simplest quantum circuit which takes states $|a\rangle$ and $|\rangle$ as its input, and outputs their (normalized) sum $c (|\rangle+|\rangle$)? Here $c$ is a normalization constant to make the output a valid quantum state. The us... | Such a circuit cannot exist. To see why, assume $|b\rangle = e^{i\phi}|a\rangle$. Then, the input $|a\rangle|b\rangle$ is mapped to $|a\rangle + e^{i\phi}|b\rangle=(1+e^{i\phi})|a\rangle$, which (i) is not normalizable independent of $\phi$, (ii) is identically zero for $\phi=\pi$, and (iii) whose output normalization,... | {
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Does wave function always mean position in time? Does wave function always mean position in time? If we take an entangled state wave function $\frac1{\sqrt2} (|0>|0>+|1>|1>)$, we see nothing about position and time.
| Strictly the wave function is a function of position at given time, but it also has arguments of other quantum numbers, such as spin. If we are interested in spin and not position, then it is common just to write the spin components of the wave function and to still refer to it as the wave function. This is typically ... | {
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Neglecting the gravitational term in an equation of acoustic wave It appears that one can derive a wave equation if the gravitational force is considered in its derivation by using
$$\frac{\partial p_0}{\partial x} = -\rho_0 g.$$
Here, $\rho_0 = \rho(p_0)$ and $p_0 = p(\rho_0)$ are the density and pressure respectivel... | Straight from Euler equation you may write:
$$ \rho_{0} \frac{\partial v}{\partial t}=-\mathbf{\nabla} p=-\rho_{0} g - \nabla \tilde{p}$$
So you end up comparing $\rho_{0} g$ with $\nabla \tilde{p}$.
With the state equation, you may write:
$$ \tilde{p}= \rho_{0}c^{2}$$
So $\nabla \tilde{p}$ is of the order of $\tilde{p... | {
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What is the dynamical $\phi^4_3$ model in quantum field theory and what does it mean intuitively? I'm a math student studying the SPDE: $u_t = \Delta u - \kappa u^3 +\dot{W}(t)$, where $\dot{W}(t)$ is space-time white noise. In many papers I'm reading(here for example), I see references to a model in quantum field theo... | The theory $\varphi^4_3$ describes a quantum scalar field in dimension $2+1$ (two spatial and one time dimension). Its $3+1$-dimensional counterpart is physically relevant as the foremost example of a simple but realistic scalar theory (such type of quartic self-interaction should be the one of the Higgs boson if I rec... | {
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Fraunhofer line width What sets the width of Fraunhofer lines on the solar spectrum ?
I first thought of Doppler broadening, but numerical applications result in much too high temperatures. For instance, using these data, I find a $\Delta \lambda =$ 0.01nm line width on the 630.25nm line of iron, corresponding to a te... | The only reference I could find is a 1925 (!) paper criticizing the idea that a Doppler broadening could explain Fraunhofer lines width ; but it doesn't suggest a quantitative way to analyze the line profile...
http://adsabs.harvard.edu/full/1925MNRAS..85..732S
| {
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Direction of forces due to pressure If I understood correctly then if you have a 'pressure field' and you have a pressure difference between two points in it, then there is a force acting. (This is the explanation of Archimedes principle , the upthrust is due to pressure difference at top and bottom of immersed object)... | Taking a small cube of liquid in equilibrium, oriented according an arbitrary cartesian axis: $F_z(z + \Delta z) + \delta B_z - F_z(z) = 0$, where $\delta B_z$ is the component of a body force (the weight for example) in $z$ direction.
For a generic material, $F_z$ would produce normal and shear stresses. For a liquid... | {
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Uniqueness of final velocities in law of conservation of momentum Let's suppose that an object $A$ of mass $1\ \mathrm{kg}$ is moving with a velocity of $2\ \mathrm{m/s}$ and another object $B$ of mass $2\ \mathrm{kg}$ is moving with a velocity of $-1\ \mathrm{m/s}$ (in the opposite direction with respect to the motion... | The final velocities are indeed not unique. The final limiting factor is kinetic energy. Let's call the initial velocities $u_1,u_2$ and the final momenta $u_1',u_2'$ (otherwise the subscripts are going to get crowded). The condition of momentum conservation can be written as
$$m_1u_1+m_2u_2=m_1u_1'+m_2u_2'.$$
If no e... | {
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} |
Particle in a box wavefunction derivation I tried solving the particle in a box problem and I came to a result that's different than what I find online. I solved the Schrödinger equation and I found the analytical form of $\psi$:
$$ \psi(x) = Ae^{ikx} + Be^{-ikx}
$$
Then I set the boundary conditions
$$\psi(0)=0\,\... | Normally, when doing this problems you put every constant you encounter inside one "common" constant only, namely $A$.
The thing is that you didn't put $2i$ inside of it, and that wouldn't be a problem, normalization takes that into account.
So in the end you have $\psi(x)=\frac{2i}{\sqrt{2L}}\sin\left(\frac{n\pi}{L}x\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545169",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Why does frictional force depend on normal reaction and not the weight of a body? One possible explanation I came across for this was that if you have an external force and you press on the body, the body's frictional resistance to motion increases and hence it should depend on normal reaction and not weight.
| If the body rests on a horizontal surface with a coefficient of friction of μ, then the force normal to the surface equals the weight (mg) of the body and the friction force is μW.
But not all friction problems involve horizontal surfaces. If a block is placed on an incline plane with a coefficient of friction μ, and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545638",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
Graphical explanation for length contraction I can understand the mathematical explanation for the reason why there should be a length contraction, but I fail to understand it intuitively. That is why I tried to explain it using spacetime diagrams, but for some reason, I was unable to do so.
Let us use the following ... | You are using wrong metric. The relation $t_2=\sqrt{L_0'^2+(t_2')^2}$ is correct on your sheet of paper (I would advice using prime for all quantities measured in primed frame). This is not correct in spacetime. In spacetime, the relation is $$t_2=\sqrt{-L_0'^2+(t_2')^2}=\sqrt{-v^2+1}t_2'$$
which is consistent with you... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545736",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 1
} |
Wavefunction of many particles Suppose that we have $N$-many identical particles, whose space-spin-coordinates are given by $x_{1}, x_{2},...x_{n}$ and whose composite system is represented by $|\Psi\rangle$. Then, according to the textbook, the wavefunction of these particles can be represented by:
$$\Psi(x_{1}, x_{2... | You should think of $|\Psi\rangle$ as a vector and $\Psi(x)$ as the vector components. Compare this to a regular vector $\vec v$. If you have a basis $\{\vec e_i\}$ then you can decompose $\vec v$ into vector components: $\vec v=\sum_i v^i\vec e_i$. If you change the basis you get different components but the overall v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545881",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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