Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What's the Coulomb Branch and why is it important? I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the Coulomb branch. I have searched the concept but I always find very long and complex explanations. Could anyone... | If the vacuum of the theory is supersymmetric - i.e. SUSY is not broken - then it is annihilated by the SUSY generators. On the other hand, using the SUSY algebra one can show that the hamiltonian can be written in terms of the SUSY generators. This implies that the vacuum $|0\rangle$ is supersymmetric if and only if ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102272",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Why are free electrons free? This is what I understand so far: in a conductor, the ions have a weak pull on the valence electrons. So when an electric field is applied, the free electrons are able to easily move about. Makes sense.
In a neutral conductor with no electric field, the free electrons aren't bound to any io... | An atom in isolation offers a potential well, and electrons form bound states in the well. The energy of those bound states can be calculated exactly in the case of a single-electron (hydrogen-like) atoms or by variational computational methods for more complicated cases.
Now when you put several atoms together in a ti... | {
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "3",
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Convert $\text{mm}^2$ to $\text{m}^2$ Stuck on a very very basic concept.
I have $1750\text{ mm}^2$ and need to get into $\text{m}^2$.
I figured $1750\text{ mm}^2 = (1750\text{ mm}) \cdot (1750\text{ mm})$, but I know this isnt right.
| What you need to do is realize how many $\text{mm}$ fit into one $\text{m}$. The answer is $1000=10^3$. Therefore: $1 \text{m}=10^3 \text{mm}$, or equivalently, $1 \text{mm}= 10^{-3} \text{m}$.
$$1750 \text{mm}^2=1750 (10^{-3}\text{m})^2=1750 * 10^{-6} \text{m}^2$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102400",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does a thin film of soap help defog bathroom mirrors? We often find bathroom mirrors get fogged while hot water is used. Looking this up on the internet, we find several easy solutions:
*
*use a hot air blower
*use a heater behind the mirror
*vinegar + water mixture
*thin film shaving cream/foam lather
*thin... | If you look at condensation fog through a strong magnifier, you'll notice that the fog is actually composed of a large number of hemispherical water droplets. The optical effect is caused by the fact that the tiny droplets act like lenses, scattering the light. On a vertical glass panel like a mirror, the maximum stabl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102609",
"timestamp": "2023-03-29T00:00:00",
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What may be effect of air friction to the velocity of satellite? What is the effect of air friction to the velocity of satellite? I have heard satellite's speed increases with air friction. But I'm in confusion how is it possible?
| Air friction (simply a form of friction) as we observe in our everyday life opposes the motion/state of the body (in this case motion of satellite ).
It's true that air friction is responsible for decreasing the speed of the satellite, thereby decreasing the kinetic energy and ultimately the total energy of satellite.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102699",
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Understanding fields and their correlation to forces I seem to be confused between the concept of a "force", and a field.
Now let's assume there is a magnetic field of $1$ $\mathrm{Tesla}$, what does that mean in relation to force?
Finally, if field is $1$ $\mathrm{Tesla}$ does that always mean, the force at that field... | No, magnetic field does not determined force alone. Force depends on other things. If the force discussed is magnetic force on a moving eletric charge, the force is given by
$$
q \mathbf v\times \mathbf B
$$
in SI units. Here $q$ is electric charge of the particle, $\mathbf v$ its velocity and $\mathbf B$ is magnetic ... | {
"language": "en",
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Why would spacetime curvature cause gravity? It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with i... |
When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve.
Even when at rest in space, the apple still advances in space-time. Here is a visualization of the falling apple in distorted space-time:
http://www.youtube.com/watch?v=DdC0QN6f3G4
| {
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Bogoliubov transformation with a slight twist Given a Hamiltonian of the form
$$H=\sum_k \begin{pmatrix}a_k^\dagger & b_k^\dagger \end{pmatrix}
\begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \omega_0\end{pmatrix} \begin{pmatrix}a_k \\ b_k\end{pmatrix}, $$
where $a_k$ and $b_k$ are bosonic annihilation operators... | This is an eigenvalue problem.
Let's assume your Bogoliubov transformation is of the form: $(a_k,b_k)^T=X(c_k,d_k)^T$. What this transformation do is let your Hamiltonian become: $H_k=w_1c_k^\dagger c_k+w_2 d_k^\dagger d_k$, with the anti-commute relation holds for new field operators $c_k$ and $d_k$.
Now you can check... | {
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Prove EM Waves Are Transverse In Nature Why we say that EM waves are transverse in nature? I have seen some proofs regarding my question but they all calculate flux through imaginary cube. Here is My REAL problem that I can't here imagine infinitesimal area for calculating flux because em line of force will intersect (... | I am going to try to "unconfuse" you.
Let's start with a picture of ocean waves; as seen from the side, they look like "sine" waves (just like BMS's red EM wave); as seen from the top, the crests and troughs make lines (not points). The same thing happens with the E and B waves (make lines), and since they are perpendi... | {
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"url": "https://physics.stackexchange.com/questions/103171",
"timestamp": "2023-03-29T00:00:00",
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Can someone please explain the "infrared catastrophe"? In my readings I've run into this idea of an "infrared catastrophe" associated with 1/f noise. As far as I can tell it is because when you graph the periodogram of the 1/f signal you see the PSD goes to infinity as frequency goes to 0. Not sure what that means pr... | $1\over f$ noise does have finite energy. It does not have an infrared catastrophe. The infrared catastrophe was the (unrealistic) result of an attempt to theoretically explain blackbody radiation. The result implied that blackbody radiation were infinitely powerful in the infrared. This did not appear to be the case, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103212",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Effect of linear terms on a QFT I was told when first learning QFT that linear terms in the Lagrangian are harmless and we can essentially just ignore them. However, I've recently seen in the linear sigma model,
\begin{equation}
{\cal L} = \frac{1}{2} \partial _\mu \phi _i \partial ^\mu \phi _i - \frac{m ^2 }{2} \phi ... | Linear terms can be thought as source terms. They are important to define the effective potential (which is the Legendre transform of the (log of) the partition function with respect to the source).
I'm not sure why one would say that one can forget about them, since, for instance, they imply a non zero value of $\lang... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103328",
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Difference between positron and electron scattering in Coulomb field In first order of perturbation theory the S-matrix amplitude for electron scattering in the Coulomb field will be (up to normalization factors)
$$
S_{fi} = \frac{iZ q^2}{\sqrt{2E_{f}2E_{i}}}\bar {u}(p_{f}, s_{f})\gamma_{0}u (p_{i}, s_{i}) \int \frac{d... | For positrons there is an overall minus sign and the spinors are the positron spinors. But to calculate the cross section you need to take the square of the S- matrix, so the sign does not matter. If you are going to calculate the unpolarized cross section you need to sum over the spins. In this case spinor parts are g... | {
"language": "en",
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Derivation of the general Lorentz transformation The standard Lorentz transformation or boost with velocity $u$ is given by
$$\left(\begin{matrix} ct \\ x \\ y \\ z \end{matrix}\right) = \left(\begin{matrix}
\gamma & \gamma u/c & 0 & 0 \\
\gamma u/c & \gamma & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{matrix}\righ... | To apply the Lorentz transformation to some vector $\vec v$, having a $L_x$ matrix, but doing it along another axis $\vec q$, you can temporarily change coordinates so that the vector is parallel to $\vec e_x$:
$$\vec v'=U\vec v.$$
Now your intermediate result would be
$$L_x\vec v'=L_x U\vec v.$$
But it's still in the ... | {
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Why don't the leaves of an electrometer repel each other in water? A normal electrometer filled with air will repel like it should do for electrostatic demonstration, but what if it is filled with water instead or even oil, what will happen?
My guess is that the water is charged too, making the net repelling force equ... | There are a few options.:
A) the liquid is a conductor and the electrometer is discharged.
B) the liquid is non conductive, but it's viscosity is too high, so the leaves will not move
C) if the viscosity is low enough, the leaves will move
In normal water you will get A.
As coulomb forces are usually not that big, ... | {
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What is the exact relation between $\mathrm{SU(3)}$ flavour symmetry and the Gell-Mann–Nishijima relation I'm trying to understand how the Gell-Mann–Nishijima relation has been derived:
\begin{equation}
Q = I_3 + \frac{Y}{2}
\end{equation}
where $Q$ is the electric charge of the quarks, $I_3$ is the isospin quantum num... | The Gell-Mann–Nishijima relation arises from electroweak symmetry breaking. If we vev our Higgs SU(2) doublet,
$$
\langle(\phi^+, \phi^0)\rangle = (0, v/\sqrt{2}),
$$
we find that the theory remains invariant under a combination of the diagonal, Cartan SU(2) generator, the weak hypercharge, and the hypercharge, $Y$, be... | {
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Surface current and current density I want to know when I am asked to find the surface current density and the space current density what should I do? Also what is the difference between the surface and space current? Can the space current density help me to find the latter if I know it?
| The following discussion refers to electrodynamics in three dimensions.
Definitions.
Let a two-dimensional surface $\Sigma\subset\mathbb R^3$ be given, then a surface current density on $\Sigma$ is a function $\mathbf K:\Sigma\to \mathbb R^3$. In other words, it is a vector field on the surface. For each point $p$ on... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103803",
"timestamp": "2023-03-29T00:00:00",
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Should water cool faster if is inserted metal canister with ice inside either mix only with ice? Let's say that we have two canister first bigger (metal canister 2l) with 1l of water at 100C, and second smaller (metal canister 1l) with 1l of ice. And we want to cool down boiled water to 50C. So we will insert ice (only... | If the cold canister you insert has more surface area than all the ice cubes that you would otherwise insert, then we would presume (for most circumstance) that the canister will perform a cooling action more quickly.
A variance occurs if the canister is filled with ice cubes. Then you have two surface-area problems;... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/103861",
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Current through two inductors after a long time I'm having trouble with visualizing the following problem, which is asking me for the final, steady current in both inductors $L_{1}$ and $L_{2}$. I was thinking that after a long time, essentially the current will be stable and thus there will be no induced current in th... | try taking a look at this page it goes in to good detail about inductors in a dc circuit.
http://www.ibiblio.org/kuphaldt/electricCircuits/DC/DC_15.html
| {
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Do photons make the universe expand? I have a problem understanding the ideas behind a basic assumption of cosmology. The Friedmann equations follow from Newtonian mechanics and conservation of Energy-momentum $(E_{kin}+E_{pot}=E_{tot})$ or equally from Einsteins field equation with a Friedmann-Lemaitre-Robertson-Walke... | The fallacy here is assuming conservation of energy. See, Noether's theorem ensures the energy is conserved if the hamiltonian of the system is time invariant. But the universe is expanding, so the very frame in which you describe it is changing over time, therefore you cannot apply energy conservation.
It is, however,... | {
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"url": "https://physics.stackexchange.com/questions/104041",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Will a sound composed of the frequencies 450Hz, 650Hz 850Hz have a clearly defined musical pitch? Why? According to my lecturer, the perceived pitch of a sound composed of the following harmonics: 750Hz, 1000Hz, 1250Hz is equal to the fundamental frequency which is the highest common factor of the harmonic frequencies;... | The brain is quite good at filling in for a few missing harmonics. For example music still sounds reasonable on a smartphone speaker even though that speaker is incapable of creating low frequencies. This Wikipedia article explains the phenomenon (thanks to Glen for the link).
So it's possible that if you heard the 2nd... | {
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Galilean, SE(3), Poincare groups - Central Extension After having learnt that the Galilean (with its central extension) with an unitary operator
$$ U = \sum_{i=1}^3\Big(\delta\theta_iL_i + \delta x_iP_i + \delta\lambda_iG_i +dtH\Big) + \delta\phi\mathbb{\hat1} = \sum_{i=1}^{10} \delta s_iK_i + \delta\phi\mathbb{\hat1}... | The central extensions are classified by the second cohomology group:
http://en.wikipedia.org/wiki/Group_extension .
If this group is trivial then each central extension is semidirect (and hence in some sense trivial). In particular, this is the case for the Poincare group but not for the Galilei group.
However, if you... | {
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"url": "https://physics.stackexchange.com/questions/104442",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Temperature of gases I can't find any law that states this (maybe the combined gas law does and I'm misinterpreting it?), but Feynman said that if you compress a gas, the temperature increases. This makes sense, for example, a diesel engine (or gas engine with insufficient octane or too high a compression ratio). Also,... | Just for completeness, when a gas expands its temperature does not necessarily change. The temperature of the gas only changes if it does work on something, for example its container as discussed in Danu's answer. If a gas is expanding into a vacuum it does no work and (to a first approximation) its temperature does no... | {
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When combining three spin $\frac{1}{2}$ particles what are the corresponding states? I want to combine three spin half particles and this is what I have so far.
I used the lowering operator $J_{-}$ on the top states and found the following states fine:
$$|\frac{3}{2},\frac{3}{2}\rangle , |\frac{3}{2},\frac{1}{2}\rangle... | No, it is not equivalent. The Spin $s = S = 3/2$ particle will have spin projections between $S_3 = 3/2$ and $-3/2$, as you have worked out. That is it, it will just be a multiplet with 5 members.
The three particles with spin $s = 1/2$ can also have a combined spin with $S = 3/2$ which will form the same 5-multiplet. ... | {
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Help understanding proof in simultaneous diagonalization The proof is from Principles of Quantum Mechanics by Shankar. The theorem is:
If $\Omega$ and $\Lambda$ are two commuting Hermitian operators, there exists (at least) a basis of common eigenvectors that diagonalizes them both.
The proof is:
Consider first the ca... | When $\lambda_1$ is an eigenvalue of a matrix and $v_1$ and $v_2$ are the components of the corresponding eigenvector, then the following equation holds:
$\begin{pmatrix} a-\lambda_1 & b \\ c &d-\lambda_1 \end{pmatrix}\begin{pmatrix} v_1 \\ v_2 \end{pmatrix}=\begin{pmatrix} 0 \\ 0 \end{pmatrix}$
Now when you scale up t... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Proving a step in this field-theoretic derivation of the Bogoliubov de Gennes (BdG) equations In derivation of the BdG mean field Hamiltonian as follows, I have a confusion here in the second step:
$H_{MF-eff} = \int d^{3}r\psi_{\uparrow}^{\dagger}(\mathbf{r})H_{E}(\mathbf{r})\psi_{\uparrow}(\mathbf{r})+\int d^{3}r\psi... | Write the differential operator $\nabla^2$ in terms of derivatives as $\nabla^2=\partial^2_x+\partial^2_y+\partial^2_z$. Write each derivative as a limit (i.e.: $\partial_x f(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} $). Rearrange the fields by putting $\psi_\downarrow (r')$ on the left, of course keep track of fermi... | {
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"source": "stackexchange",
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Can effect of gravity be broken (counteracted) by electric force? Can we make a jacket using an electronic circuit that uses electric force to cancel the effect of gravity so that we get lifted in air.
| Short answer not really.
There are 2 3 ways to cancel gravity,
-one you create anti gravitation particles which no human scientist has ever produced,
let alone observed. (or where they its own antiparticle i don't remember)
-two you propel your self with air,
so basically if with electronic jacket you mean a electri... | {
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Collection Efficiency of Photon I am currently reading this paper:
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.116802#references
In the second column of text in page 2, the author makes various claims about the number of photons detected and the collection efficiencies of different optical components. ... | 2.6 million counts, with each count producing a dead time of 90 nsec, gives a total dead time of .234 seconds / second. So the total number of counts should be 3.4 million counts (2.6 / (1 - .234), assuming no dead time. Since each QD emits 770 million photons per second, the detector efficiency is 3.4 / 770 (which I g... | {
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Symmetry Breaking And Phase transition
*
*Is every phase transition associated with a symmetry breaking? If yes, what is the symmetry that a gaseous phase have but the liquid phase does not?
*What is the extra symmetry that normal $\bf He$ has but superfluid $\bf He$ does not? Is the symmetry breaking, in this case,... | The classical situation with no symmetry breaking is the case of the, so-called, isostructural transitions. The word "isostructural" is misleading, since what is meant is "isosymetric". However, historically the term emerged. There is a number of examples of such transiotions. One is the alpha-alpha' transitions in the... | {
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"url": "https://physics.stackexchange.com/questions/105166",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
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Scattering geometry question While reading up on light scattering I came across this slide:
My vector maths is a bit rusty and I am having trouble understanding the last term (scattering geometry).
What is the significance of $\hat{r} \times \hat{E_{i}} \times \hat{r}$
| you have three terms in the equation, which together define the scattered wave. the first two define the amplitude at any given time and place along the vector $\hat{r}$, which points the direction you're interested in.
$\hat{r}\times\hat{E}\times\hat{r}$ tells you that the wave is going to be perpendicular to $\hat{r}... | {
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What happens when we bring an electron and a proton together? I have a couple of conceptual questions that I have always been asking myself.
Suppose we have an electron and a proton at very large distance apart, with nothing in their way. They would feel each the other particle's field - however weak - and start accele... | To rephrase: an electron approaches an cation.
Most likely result: a photon is emitted and the electron is captured.
Added: The way I see it: an ion and an electron at a large distance apart. This would probably be an electron in a very high orbital of the ion. As the electron approaches, all the natural forces affect ... | {
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Uncertainty principle in Quantum mechanics The Uncertainty principle says that "△x△p>h/2"; we cannot precisely obtain both position $x$ and momentum $p$ simultaneously.
Is this because the uncertainty is the natural characteristic or it is because we do not know additional values? (ex. like additional 11 dimensions in ... | "△x△p>h/2" is a simple consequence of the fundamental principle of using wavefunctions ("Amplitudes") to determine the probability of finding a particle.
A plane wave is evenly spread over all space and is the eigenfunction of one precisely known value of p.
In order to get anything other than such complete indetermina... | {
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Non-Hermitian operator with real eigenvalues? So we know that in Quantum Mechanics we require the operators to be Hermitian, so that their eigenvalues are real ($\in \mathbb{R}$) because they correspond to observables.
What about a non-Hermitian operator which, among the others, also has real ($\mathbb{R}$) eigenvalues... | For Hermitian matrices eigenvectors corresponding to different eigenvalues are orthogonal. This guarantees that not only are the eigenvalues real, expectation values are too.
| {
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Why is QM maximally predictive? Let's suppose I'm in the lab and I claim that I can predict more than QM can, specifically, I can predict exactly at which moment in time a particle decays. You don't believe me (naturally) so I set up the experiment, provide a piece of paper with a time written on it, and start the clo... | Particle decay is not a good example here bc a lot of the stochastics come from not following the nuclear dynamics closely. A better example might be the decay of a metastable state in an atom. There we have an atom that is not in an energy eigenstate by itself but the whole system is. There are well studied toy models... | {
"language": "en",
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Total Electrical potential energy of two particle system I recently have been studying Electro-statics and I couldn't understand properly how the potential energy of two particle system is found.
Suppose you have two particles with charges $Q_1$ and $Q_2$ respectively. The distance between them is $r$. What is the to... | If a positive charge $Q_1$ is fixed at some point in space and another positive charge $Q_2$ is brought close to it, it will experience a repulsive force and will therefore have potential energy.
Now to find this potential energy, we assume that the potential energy with respect to that point at infinity is $0$. So if ... | {
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Quantum Mechanics - Rectangular Potential Barrier - Normalisation I have a quick question regarding the normalisation of the wave function of a particle incident on a potential barrier specifically regarding the normalisation of the wave functions.
The problem is set up as on this webpage:
https://www.ntmdt.com/spm-ba... | They are not normalisable because they either come from, or extend to infinity. This essentially means that the probability density blows off and gives non-physical results.
| {
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Does field line concept explain electric field due to dipole? Consider an electric dipole consisting of charges $-q$ and $+q$, separated by a distance $2a$ and placed in free space. Let $P$ be point on the line joining the two charges (axial line) at a distance $r$ from the centre of $O$ of the dipole.
You can obse... | At any point the electric field is the vector sum of the fields from the two charges. So while the fields from $A$ and $B$ are indeed in opposite directions at your point $p$ you just add them (well, subtract their magnitudes since they're in opposite directions) and this gives you the net field.
I wouldn't take the fi... | {
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Why does the topological entropy scale with $\log(L)$ in 1D? Why, in one dimension, does the topological entropy scale with the size of system as $S \sim \ln L$, while in a 2D system it scales with $S \sim L$? Why does dimensionality play such an important role here? I mean, is there any simple but straightforward ide... | In a 1D system, all you can do is vary the size of a subset, which only ever gives $\propto L$ possibilities. Then the entropy takes the logarithm, and we have $\propto \ln L$.
In higher dimensions however, you can also vary the shape, and that is combinatorially much more powerful: you have exponentially many possibil... | {
"language": "en",
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Which temperature to evaluate fluid properties in pipe? I am always confused about which temperature to evaluate fluid properties at. Let's say I have a helical pipe and I know the inlet temperature, outlet temperature, and surface temperature and the inlet Reynold's number. I must determine the length of the pipe need... | Changes are huge, I would recommend to re-derive the pipe flow rate with a (linear) temperature dependent formula for viscosity and density. You'll get $Q(T)$, from this can get the heat flux and thus will have a nonlinear differential equation for $T(x)$, which you can integrate numerically. Then find the intercept of... | {
"language": "en",
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Why Do Sausages Always Split Lengthwise? Sausages universally split parallel to the length of the sausage. Why is that?
| I'll have to take a page from my EE background and say it's because of the path of least resistance. If you look at the end of a sausage, there is already tension along that plane, in multiple locations:
A chain is only as strong as its weakest link (see what I did there? :) ), so it's natural for a hot dog/sausage to... | {
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Speed of light originating from a star with gravitational pull close to black-hole strength? Imagine you have a star which is on the brink of turning into a black hole. Lets say it is infinitely close to become a black hole, but not there yet.
Since there is no event horizon, but a great gravity pull. Will the speed of... | I assume you don't mean the speed of light, but you are essentially asking: Will light escape that strong gravitational pull?
If this is your question then first:
Direct quote from wikipedia -> "An object whose radius is smaller than its Schwarzschild radius ($r_s = \frac{2GM}{c^2}$) is called a black hole. The surfac... | {
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Centrifugal force when there is no friction Assume that a coin is placed on circular disk and now a disk is rotated with constant angular velocity.
If there is no friction between the surfaces of a disk and coin, according to theory the coin will move away from centre of disk. But I have confusion here that the centrip... | The coin will not move.
First, to differentiate between centrifugal and centripetal, I'll start by stating the definitions first.
Centrifugal force is the apparent force that draws a rotating body away from the center of rotation. It is caused by the inertia of the body as the body's path is continually redirected.
Cen... | {
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force on a moving charge in magnetic field Need help in understanding the direction of magnetic force in the magnetic field!Totally confused by directions.
Why is it that magnetic force is perpendicular to the direction of magnetic field and velocity of charged particle.
Why is it(force) not in the same direction as th... | A magnetic field exerts a force on a moving charge. Given a magnetic field, $\vec{B}$, and a charge, $q$, moving with velocity, $\vec{v}$, the magnetic force, $\vec{F}$, on the charge is:$$\vec{F}= q(\vec{v} \times \vec{B})$$
The directions of these with respect to one another can be found using the right hand rule. Se... | {
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If I drop a leaf twice from the height of a tree in a completely controlled environment, will the trajectory in each case be the same? Putting my question in other words, can earth form again if a similar initial universe condition is given? The uncertainty principle says that we cannot tell with certainty the position... | From my understanding of your questions, you are confusing the "scientific method" and the "uncertainty principle. The scientific method says that "given the same starting conditions, within a controlled environment, etc., the "results" should be the same (ei. repeatable within some degree of accuracy). The uncertain... | {
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How to express magnetic field vector in terms of force on current I am preparing for an exam and one of the questions I have come across asks:
Define the electric field $\mathbf{E}$ and the magnetic flux density $\mathbf{B}$, in terms of the force on charges and currents.
By the Lorentz force law we have:
$$\mathbf{F... | You might be interested in this. Lets look in case where $\vec E=0$. If you know $q \vec v$, $\vec F$ and $\alpha=\angle(\vec B;q \vec v)$ you can actually find $\vec B$.
$$\vec F=q \vec v \times \vec B$$
$$\vec B=\frac{|F|}{ q|v| sin \alpha} \left (\frac{q \vec v cos \alpha}{q |v|}+\frac{q\vec v \times \vec F sin \al... | {
"language": "en",
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Electrostatic and gravitational forces? Electrostatic force between two charged particles depends on the magnitude of the charges and the distance between them. If the charges have mass $m$ and $m'$ then, what will be the total force including gravitational and electrostatics forces? Distance between them is $d$.
| Seeing your comment, it seems you are concerned about group of charges with certain mass. Then you need to apply Gauss law for the cases where it becomes difficult to apply coulombs law or principle of superposition. In case of gravitational force, find the center of masses of either configuration and you can proceed t... | {
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Would QM be detectable in a all boson universe If there was a universe with the same laws as this one, but there were only bosons in it, would QM 'do anything'?
Would there be any QM effects - such as an energy level (but that would require fermions..).
| WSC - Not all matter is made of fermions. Things such as helium-4 and carbon-12 are bosons, and there are are many other composite particles and molecules that are actually composite bosons. Any composite particle with an even number of fermions, and thus with an integer value of spin, is boronic, which to me seems a l... | {
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Finding friction forces of stacked boxes on a table Consider the following system. The given friction coefficients are for static. Let $g=10$ (meter per square second).
If the $F(t)=10t$, for example, determine the friction forces $f_{AB}(t)$ (between the boxes $A$ and $B$) and $f_{BF}(t)$ (between the box $B$ and the... | $f_{AB}(t)$ will be on the left side and $f_{BF}(t)$ on the right.
Maximum $f_{BF}(t)=\mu (m_A+m_B)g=(0.6)(30)(10)=180N$
So, $F(t)$ will have to be greater than $180N$ so that $B$ can move. When it does, $A$ will experience a pseudo force say $F'(t)$ in the left direction. If $B$ accelerates at $a_B$, then $$F'(t)=m_Aa... | {
"language": "en",
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Why do rocket engines have a throat? Diagrams of rocket engines like this one,
(source)
always seem to show a combustion chamber with a throat, followed by a nozzle.
Why is there a throat? Wouldn't the thrust be the same if the whole engine was a U-shaped combustion chamber with a nozzle?
| The whole point to the throat is to increase the exhaust velocity. But not just increase it a little bit -- a rocket nozzle is designed so that the nozzle chokes. This is another way of saying that the flow accelerates so much that it reaches sonic conditions at the throat. This choking is important. Because it means t... | {
"language": "en",
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Force exerted on ceiling by a simple mecahnical system I have a simple static mechanical system, but I reach a conclusion that seems to me counter-intuitive:
There is a pulley fixed to the ceiling and there is a weight fixed to a rope which goes through the pulley and is fixed to a point on the floor. I denote by $T$ ... | If there is no air drag, the pulley and the rope are frictionless and massless, the rope is not slacking anywhere, the rope is unstretchable and the rope is attached at exactly the centre of mass of the object so that no torque is produced, yes.
How is it counter-intuitive? It may seem like that it would require an exa... | {
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Sum of acceleration vectors If a point mass has some accelerations $\mathbf{a_1} $ and $\mathbf{a_2} $, why is mathematically true that the "total" acceleration is $\mathbf{a}= \mathbf {a_1}+\mathbf {a_2}$?
| This is due to the superposition principle: when several forces act upon a body, the net force is the sum of the individual forces: $$\vec F_{net} = \sum \vec F_i $$
However, this is only true when the relation between the force and the acceleration is linear.
Let's take the gravitational force as an example: say you... | {
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Why is the periodicity of fields in finite temperature QCD consequence of Trace in the action? In finite temperature QCD, the gauge fields must be periodic in temporal direction. They say this is the consequence of trace in the action for gauge fields. How does trace imply that the fields must be periodic?
| A derivation is given for the case of a scalar field in these lecture notes. The same arguments apply for gauge fields in QCD.
The idea is that when calculating the partition function, which is equivalent to the euclidean action of the quantum field theory, we take the trace of the exponential of the hamiltonian $\hat{... | {
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Behavior of Saha and Boltzmann So I'm just wondering why the Saha and Boltzmann distributions behave differently as temperature increases?
I know one is for ionization levels while the other is for energy levels but is that the answer?
| It's likely due to a combination of two reasons, one of which you already mentioned:
*
*As you state, the Saha equation relates the ionization levels while the Maxwell-Boltzmann distribution deals with the energy levels
*The Saha equation incorporates quantum mechanical effects in deriving it's equation while the ... | {
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Electric field in a sphere with a cylindrical hole drilled through it Suppose that you have a sphere of radius $R$ and uniform charge density $\rho$; a cylindrical hole with radius $a$ ($a\ll R$) is drilled through the center of the sphere, leaving it like a "necklace bead".
I would like to find a function for the elec... | For a cylinder:
$$dV=\pi a^2dr\\dq=\rho dV=\rho\pi a^2dr\\dE=Kdq/r^2=K\rho\pi a^2dr/r^2\\E=\int dE=K\rho\pi a^2\int_{r_0}^{r_0+l} dr/r^2=\frac{K\rho\pi a^2l}{r_0(r_0+l)}$$
In case inside of it as in the figure the field due to $R-x$ length cylinder is cancelled by a similiar one in the opposite side thus the resul... | {
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Sign convention for EMF When we define the field generate by EMF, why there is not negative sign in $\mathcal{E} = \oint \vec{E} \cdot d\vec{l}$?
Usually we talk about potential, there should be a negative sign, right?
| The conceptual problem here is that of EMF, $\mathcal{E}$ vs Electric Potential, V. They aren't really the same thing despite being measured in the same units. For instance the EMF is caused by an external agent that isn't the conservative electrostatic field, like say a chemical reaction in a battery or a solar cell. ... | {
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About the recent discovery of tetraquark boundstates I am referring to this,
http://home.web.cern.ch/about/updates/2014/04/lhcb-confirms-existence-exotic-hadron
So how does this work if we stick to keeping quarks in the 3 dimensional fundamental representation of $SU(3)$?
This bound-state seems to have 2 anti-quarks ... | Antiquarks can be distinguished from quarks, so you only need to antisymmetrize two at a time. That's no problem, and even if you had 3 quarks it wouldn't be. Furthermore, you only need the total state to be antisymmetric. You could have antisymmetry in space, symmetry in spin and symmetry in color, and the whole thing... | {
"language": "en",
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Experimental evidence for the relic neutrinos What are the experimental (indirect) evidence for the cosmic neutrino background? Where can I read more about this?
The discussion on the wikipedia page about the C$\nu$B seems to me to be more about the evidence of the number of generation of neutrinos, than about the cos... | We have, at this time, no tools capable of detecting neutrinos at the very low energies of the cosmic neutrino background, and if such tools existed they would have to contend with numerous backgrounds making the experiment ferociously difficult.
| {
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De Broglie Wavelengths I have a working knowledge of wave-particle duality, I think. I know the de Broglie wavelength is a sort of probability of finding a particle in a specific position, and is calculated by $\lambda=\frac{h}{\vec{p}}$. I have a couple questions I'm hoping to have cleared up, though.
First, since $\v... | I have never seen de Broglie's relation written with vector quantities. A quick search online reveals a lack of vectors as well. In the relation
$$\lambda = \frac{h}{p}$$
it is implied that the quantity $p$ is the magnitude of the momentum $\left | \vec{p} \right |=p.$ Yes, the word momentum in a strict sense refers to... | {
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What is the notion of a spatial angle in general relativity? Is there a notion of spatial angles in general relativity?
Example:
The world line of a photon is given by $x^{\mu}(\lambda)$. Suppose it flies into my lab where I have a mirror. I align the mirror in such a way, that I measure a right angle between the incom... | As a geometric quantity, the value of an "angle" can be determined and expressed in a coordinate-free way:
Given three pairwise space-like events, "$A$", "$B$" and "$C$", and given the positive real numbers
$\frac{s^2[ A C ]}{s^2[ A B ]}$, $\frac{s^2[ A C ]}{s^2[ B C ]}$ and $\frac{s^2[ B C ]}{s^2[ A B ]} = \frac{s^2[ ... | {
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Could Charles-Augustin de Coulomb measure the charge in Coulombs?
*
*Did Charles-Augustin de Coulomb know:
*
*Coulomb's constant
*Coulomb (as a unit)
if not then what was the first time it was measured?
| No, Coulomb did not know the Coulomb as a unit. According to this page, the Coulomb was defined at the 9th CGPM (General Conference on Weights and Measures) conference, in 1948. Wikipedia gives the same date.
Coulomb could not measure charges, but he could create a charge and then halve it, quarter it, etc by letting t... | {
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Constant of motion An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one-dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where
$$
u(q,p,t)=\ln(p+im\omega q)-i\omega t
$$
and $\omega=(k/m)^{1/2}$. The demonstration is easy but the physical significance of the constant of motion is not s... | The quantity inside the natural log seems to be proportional to the classical analog of the raising operator in quantum mechanics:
$$
a_{+}= \frac{1}{\sqrt{2m}}\bigg(\frac{\hbar{}}{i}\frac{d}{dx}+im\omega{}x\bigg)\\
a_{+}= \frac{1}{\sqrt{2m}}\bigg(\hat{p}+im\omega{}q\bigg)
$$
Where $\hat{p}$ is the quantum mechanical m... | {
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An identity for spinor helicity formalism I have a question about the spinor helicity formalism from arXiv:1308.1697
Denote the massless spin-1/2 fermions as Eqs. (2.10)-(2.11) in that paper
$$v_+(p)= \begin{pmatrix} |p]_a \\ 0 \end{pmatrix} $$
$$v_-(p)= \begin{pmatrix} 0 \\ |p \rangle^{\dot{a}} \end{pmatrix} $$
$$... | The problem is sloppy (but convenient) notation. The objects,
\begin{equation}
\left| k \right] ^a , \quad \left| p \right\rangle ^{ \dot{a} }
\end{equation}
are two component spinors while $
\gamma_\mu$ is a 4x4 matrix. So its not even clear what the brakets mean. When we write the braket,
\begin{equation}
\left[ k... | {
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How do I simulate this simple quantum circuit in MATLAB? I want to simulate a circuit similar to the one below in MATLAB. If you have a state matrix describing the state of 3 qubits, I understand that you could apply a CNOT matrix tensored with and identity matrix to $\psi_{0} $ get $\psi_{1}$, but if you want to apply... | I think this will answer your question. How does the CNOT between qubits one and three work?
$$\left|000\right\rangle \to \left|000\right\rangle$$
$$\left|001\right\rangle \to \left|001\right\rangle$$
$$\left|010\right\rangle \to \left|010\right\rangle$$
$$\left|011\right\rangle \to \left|011\right\rangle$$
$$\left|100... | {
"language": "en",
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Why maximum energy transfer at natural frequency even if max amplitude occurs below $f_0$ This is a paragraph from my book:
"For a damped system, the resonant frequency at which the amplitude is a maximum is lower than the natural frequency.However, maximum transfer of energy, or energy resonance always occurs when app... | Your question has been answered by following standard mathematical procedures. Nonetheless, your concern about intuitive sense is quite fair. On one hand, the idea that energy transfer should be maximum at a frequency below the natural frequency $\omega_0$ is not wrong at all. The work done by the external force over o... | {
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Is the molecule of hot water heavier than that of cold water? We know that the molecule of hot water($H_2O$) has more energy than that of cold water (temperature = energy)
and according to Einstein relation $E=mc^2$ ,this extra energy of the hot molecule has a mass.
Does that make the hot molecule heavier?
| According to http://www.verticallearning.org/curriculum/science/gr7/student/unit01/page05.html , the average velocity of a water molecule at 20C is approximately 590 m/s:
If you now calculate the difference in mass between water molecules "at rest" and moving at 590 m/s, this ratio is given by
$$\gamma=\sqrt{\left(1-\... | {
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What would we observe from thompson's lamp thought experiment? The thought experiment goes like this:
Say there is some circuit which turns a lamp on/off with just a flick
of a switch. Say its off; you flick it, it turns on; flick it again it
turns off, and so on.
So say you are conducting the experiment for two... | The lamp would be "on", but with a reduced luminous flux output. This is very similar to pulse-width modulation, which is used to control the brightness of LEDs in various applications.
| {
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What is charge? I know this isn't the right place for asking this question, but in other places the answers are so awfull.. I'm studying eletricity, so, I start seeing things like "charges", "electrons has negative charges",etc. But I didn't quite understand what charge is. I search a little bit on the internet and fou... |
Ans 1: Charge is the physical observable corresponding to a conservation of a certain symmetry.
-
Ans 2: The electric charge or Electromagnetic charge is due to the electromagnetic U(1) gauge symmetry.
-
See also this post: Is there any theory for origination of charge?
| {
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How is "Band Intensity" related to absorption coefficient I am interested in the linear absorption of $762\,\rm nm$ light near a transition of molecular oxygen. I need to find some experimental numbers that will tell us how far the $762\,\rm nm$ light will propagate before getting absorbed. Specifically, I want to know... | What the question refers to as "band intensity" is also referred to a "line strength" $S$. To calculate an absorption coefficient $k$ from $S$, a line shape function $f(\nu - \nu_0)$, where $\nu_0$ is the center of the line.
$$k = Sf(\nu - \nu_0)$$
Then "optical depth" = $ku$, where $u$ is called "path length" but i... | {
"language": "en",
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Range of poissons ratio I know the range of poisson's ratio is -1 to 0.5 but how do you arrive at this expression? I am a 11th grade student and I am not too familiar with advanced physics
| Poisson's ratio can be expressed in terms of Young's modulus $E$, Bulk modulus $K$ and Shear modulus $G$. I hope you know how do arrive at these relationships;
$$ G=\frac{E}{2(1+\nu)}$$
$$ K=\frac{E}{3(1-2\nu)}$$
$E, K$ and $G$ and all NOT less than zero.
From the equation of $G$ you can see that it's the value of $v=-... | {
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Could you theoretically map the internal distribution of mass in a black hole using Hawking radiation? Assuming you could measure the qualities of the radiation emanating from all around a black hole, could this be used to determine the internal geometry or makeup of the mass inside?
| The answer is no, if our current understanding of Hawking radiation is correct. The problem is that Hawking radiation is thermal. This means that it comes in a statistical ensemble of quantum states. In particular it can't carry information about the evolution of quantum states you dropped into the black hole. This is ... | {
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Why does Hawking Radiation not add up to zero? First off: I am not familiar with the details of quantum mechanics or relativity.
My understanding of Hawking radiation is as follows: Pairs of particles and anti-particles can and will spontaneously form in space and when that happens near the event horizon of a black hol... | What do you mean, "cancel out"? Even if a particle and its antiparticle annihilate, energy is still conserved, e.g. an electron annihilating with a positron gives two photons (well, depending on their energy). The radiated energy can't just vanish without a trace.
| {
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Optics biconvex and plano convex What is the resultant focal length If a biconvex lens is cut into half and then the resulting 2 plano-convex lens arranged in such a way that the plane surface of one faces the curved surface of the other plano-convex lens considering the focal length of the plano-convex lens to be f.
| Let f' be the focal length of the biconvex lens initially & let 'f' be the focal length of the two plano convex lens each.
Then, by Gullstrand's Equation,
P'=P1+P2-P1P2d
or, in terms of focal length,
$$1/feq=1/f1+1/f2-d/f1f2$$ (for separated lens)
or, $$1/feq=1/f1+1/f2-d/nf1f2$$ (for thick lens)
Here, P' is the power ... | {
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Why do He-3 atoms repel each other much more strongly than electrons? Is there a simple answer to this question ? see last line of this paragraph
http://en.wikipedia.org/wiki/Fermionic_condensate#Fermionic_superfluids
| The following may be more clear:
The BCS theory can be applied to 3He, as well as to electrons. However, the Cooper pairs for 3He are much more complex creatures than the those in a conventional superconductor. Due to the hard-core repulsion of the helium nuclei, the two 3He atoms in the Cooper pair feel a greater nee... | {
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Finding Tension in an Elastic String? I know that this is a homework type question and I'm not asking a particular physics question, but I'm really desperate for help.
Here's the question:
I tried to divide the string to 2 parts with $O$ as the mid-point of $AB$.
Let $AO$=$T_{1}$ and $OB$=$T_{2}$, then $T_{2}-T_{1}=m... | Six years later:
We are given that the natural length of the string is $2l$.
When the mass is suspended at the midpoint, $O$, of the string, the extension perpendicular to $AB$ is $x$. Let $M$ be the position of the mass at perpendicular extension $x$.
Then the extended length of the string from $A$ to $M$ (the hypoten... | {
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How might eddy currents and terminal velocity be broken down? This is a branch from this question.
With regards eddy currents and terminal velocity I have located a homework question but would appreciate more detail (and translation of the symbols described therein) about the forces at play.
Eddy currents are generate... | Yes, faraday law and eddy current will cause terminal velocities to exist for falling objects outside of any other friction consideration. The most widely used example to show it is this setup:
These are two connected rails of width $l$ with a third rail freely gliding along the two main rails. The whole setup can be ... | {
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Lorentz invariance? What exactly is meant by Lorentz invariance?
Is it just an experimental observation, or is there a theory that postulates it?
What quantities do we expect to be Lorentz invariant?
Charge? Charge densities? Forces? Lagrangians?
| Lorentz invariant is a short-hand for "invariant under action of the Lorentz transformation". It is used to classify quantity that has value that is the same in all inertial frames. For example, electric charge of any electron, or the quantity $\Delta x_\mu \Delta x^\mu$ of any two events.
| {
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Are there two different ways to express the position operator $x$ in terms of the creation and annihilation operator? As we known, to express the position operator $x$ in terms of the creation and annihilation operator $a^{+}$ and $a$, one way is:
$$x= \sqrt{\frac{\hbar}{2\mu\omega}}(a^++a);$$
$$p= i\sqrt{\frac{\mu\hba... | You are just dealing with the unitary transformation
$$U : L^2(\mathbb R) \to L^2(\mathbb R)\:.$$
defined by the unique linear continuous extension of
$$U|n\rangle := i^n |n\rangle\:,$$
which implies
$$ U ^\dagger a U = i a\:,\qquad U ^\dagger a^\dagger U = -i a^\dagger\:,$$
The two pairs of operators $x,p$ are relat... | {
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Is gravitational time dilation different from other forms of time dilation? Is gravitational time dilation caused by gravity, or is it an effect of the inertial force caused by gravity?
Is gravitational time dilation fundamentally different from time dilation due to acceleration, are they the same but examples of dif... | Well, the answer is "no" time dilation is always the same effect and is due to velocity! Indeed, when an object is located in a gravitational field it is falling. Even when you sit on your chair you are falling in the Earth's gravitational field, otherwise you would float in the air as in the ISS! Let's equate the fact... | {
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Why does squeezing a water bottle make the water come out? This seems natural, but I can't wrap my head around it when I think about it.
When I squeeze an open bottle filled with water, the water will spill out. When I squeeze a bottle, the material collapses where I squeeze it, but expands in other areas, resulting in... | jdj081's answer is good. I just want to address where I think you originally went wrong.
Your confusion lies in using the word "volume" in two different ways. You should differentiate between volume of the container (capacity is a better term, as jdj081 states) and volume of the liquid.
The liquid's volume doesn't cha... | {
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Why electrons have less energy than photons with the same wavelength? I am studying quantum physics and I have a question: what is the physical explanation for electrons having less energy than photons with the same wavelength?
Energy of a photon : $E = h ... | The energy of the particle is proportional to the oscillation frequency of its wavefunction, $E=h\nu$. A photon always moves at the speed $c$, so its wavelength is related to the frequency in the usual way for a traveling wave, $\lambda = c/\nu = hc/E$.
A massive particle moves more slowly than the photon, so its wave... | {
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Do I need to take weight of the rocket into account when calculating escape velocity? Here there is the old problem.
I know from the old problem that the work $W_v$ that I need to make a rocket fast enough to reach the escape velocity is
$$W_v= G \frac{mM}{r}$$
therefore because $$W_v=F\cdot S = G \frac{mM}{r} \right... | Escape Velocity doesn't depend on mass(but work depends on mass) of a rocket, Escape Velocity equation looks like this:
$$
v=\sqrt{\frac{2GM_{earth}}{r}}
$$
And Work is just change in kinetic energy $\Delta KE$ or $KE_{final}-KE_{initial}$, So Work equation looks like this:
$$
W=\frac{m_{rocket}v_{final}^2}{2}-\frac{m_... | {
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How does band gap vary with the cell volume? How does band gap vary with the cell volume? is there a relation?
If the volume is compressed, the interaction between atoms would be more, therefore the perturbation is higher hence the splitting would be more. Is my assumption right?
What is the mathematical backgrou... | Let's assume, you take a one-dimensional chain of atoms and compress it.
In order to investigate the bandstructure, you will need to determine the electronic wavefunctions of quantum-mechanically allowed states. If you know your wavefunctions for the initial condition, before you compress your chain of atoms, you need ... | {
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Magdeburg Hemispheres The Magdeburg Hemisphere experiment was the experiment that showed the effect of pressure differences on a vacuumed sphere.
We know that the Force caused by pressure is $\Delta p A$ and so you can calculate the force by using the area of the base of one of the hemispheres of the the vacuumed ball... | Integrating the force over the surface of the half-sphere yields
$$F=\int_\text{C}\Delta p\hat{\mathbf{n}}dS=\int_0^{\pi/2}\int_0^{2\pi}\Delta p\left(
\begin{array}{c}
\sin (\theta ) \cos (\phi ) \\
\sin (\theta ) \sin (\phi ) \\
\cos (\theta ) \\
\end{array}
\right)R^2\sin(\theta)\,d\phi d\theta=\left(
\begin{array... | {
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Effect of wavelength on photon detection When some photon detector detects a photon, is it an instantaneous process (because a photon can be thought of as a point particle), or does the detection require a finite amount of time depending on the wavelength of the photon?
EDIT: I guess what I am wondering is if a photon ... | The wavelength of a photon is closely related to the minimum possible uncertainty in its position. So, for a photon has a wavelength of $3x10^8m$, and if we assume that before the detection we already know as much about the photon as is possible, we still won't know exactly when it will be detected, and the uncertaint... | {
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The choice of pivot point in non-equilibrium scenarios It is true that under equilibrium condition, no matter what pivot point one choose, the resulting net torque will always be zero. I wonder if this principle apply to non-equilibrium scenarios as well, namely, the net torque of the system being the same regardless o... | Yes only on equilibrium the choice of point where moments are summed is arbitrary. This is because to move from one point to another the moment vector transformation is
$$ \sum\vec{M}_A = \sum\vec{M}_B + \vec{r}_{AB} \times \sum\vec{F} $$
and if $\sum \vec{F} = 0$ (static equilibrium) then
$$ \sum\vec{M}_A = \sum\vec{... | {
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Why fermions have a first order (Dirac) equation and bosons a second order one? Is there a deep reason for a fermion to have a first order equation in the derivative while the bosons have a second order one? Does this imply deep theoretical differences (like space phase dimesion etc)?
I understand that for a fermion, w... | Spin-1/2 admits first order equations simply because
$
(\mathbf{1/2,1/2})\otimes (\mathbf{0,1/2})
$
contains the representation $(\mathbf{1/2,0})$ so that a linear equation for free particles can be written (i.e. it contains a derivative acting on one field and returning one field).
The first term in the product is th... | {
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How does a spinning electron produce a magnetic field? I learned in my undergraduate physics class that atoms have magnetic fields produced by the orbit of electrons and the spin of electrons. I understand how an orbit can induce a magnetic field because a charge moving in a circle is the same as a loop of current.
Wh... | Electron is not like a ball, as it has no volume at all. So it can not spin like a ball. Magnetic moment comes "as is" from quantum mechanics, which do not explain its nature.
| {
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"source": "stackexchange",
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"answer_id": 7
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Isotropy of Space Weinberg writes in his Cosmology text "Likewise,isotropy requires the mean value of any three-tensor $t_{ij}$ at $x=0$ to be proportional to $\delta_{ij}$ and hence to $g_{ij}$, which equals $a^2\delta_{ij}$ at $x = 0$"
May someone please illuminate the point.
| Since we have local isotropy, if I zoom in enough the space-time has rotational invariance. In other words, at any local point in space, the mean value of any tensor must be rotationally invariant, i.e. under rotation, we must have
$$
\langle t_{ij} \rangle \to R_i{}^k R_j{}^l\langle t_{kl} \rangle = \langle t_{ij} \ra... | {
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Is there an equation to calculate the average speed of liquid molecules? I seem to remember from first year physics that we can calculate the RMS speed of a stationary, ideal gas with $v=\sqrt{\frac{3RT}{M}}$. Does a similar equation exist for liquids?
| If you are looking for root mean square velocity, it can be very high (relative to long range velocity).
If treat water as gas (which it is not) velocity comes around 650 m/s http://www.madsci.org/posts/archives/2007-07/1184005380.Bc.r.html
For order of magnitude calculation velocity in liquid water is about 8 times sl... | {
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Heat generated on thin disc plate in magnetic field There are the eddy currents in thin circular copper plate thickness h and radius a, in a harmonic magnetic field which is perpendicular to plate and the effect of auto-induction is negligible. Now we must get average heat generated on it.
As I said, I have final equat... | In macroscopic EM theory, we can calculate heat being evolved due to electric current in unit time in region $V$ by
$$
\int_V \mathbf j \cdot \mathbf E\,dV.
$$
If you express electric field in terms of $B_0$ and $\omega$ and assume Ohm's law $\mathbf j = \frac{1}{\gamma}\mathbf E$ where $\gamma$ is resistivity, you s... | {
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A question about a complex integration in Peskin's QFT textbook In page 27 (2.52), the integration is
$$\int_{-\infty}^{\infty}dp \frac{p e^{ipr}}{\sqrt{p^2+m^2}}$$
He says that there are two branch cuts starting from $\pm im$
But I learn in complex analysis that $\sqrt{z^2+m^2}$ has only one branch cut from $-im$ to... | Remember this all start from the fact that $\left(z^2+m^2\right)^{-\frac{1}{2}}=\left(z+im\right)^{-\frac{1}{2}}\left(z-im\right)^{-\frac{1}{2}}.$
So you have two branch points: one in $-im$ and one in $im.$
Let's now consider the branch cuts as on the image you posted. If you rotate upper branch of $\pi$, so is direc... | {
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Why wasn't the meter defined using a round-number fraction (like 1/300 000 000) of the distance travelled by light in 1 second? We know that 1 meter is the distance travelled by light in vacuum within a time interval of 1/299,792,458 second. My question is why we didn't take a simpler number like 1/300,000.000 or why n... | Because $299\,792\,458\ \mathrm{m/s}$ is the speed of light. By using $300\times10^6$ we won't get one meter
after $1/300\times10^6\ \mathrm{s}$.
We could change the speed of light and set it to $300\times10^6\ \mathrm{m/s}$ by changing either the
definition of second or the previous definition of meter. However, it ... | {
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Description of the heat equation with an additional term I have the following equation:
$$\frac{\partial U}{\partial t}=k\frac{\partial^2 U}{\partial x^2}-v_{0}\frac{\partial U}{\partial x}, x>0$$
with initial conditions:
$$U(0,t)=0$$
$$U(x,0)=f(x)$$
In the problem is requested to give an interpretation of each of the ... | The heat equation is an example of a convection-diffusion equation.
Your problem is one-dimensional in space (only $x$), which simplifies it a bit. The term on the left hand side is the time-rate of change of the internal energy $U$ (often a multiple of the temperature).
The second term is a diffusion term, as, in time... | {
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Taylor expansion of the metric Consider a coordinate change
$$
x^a\mapsto \tilde x^a=x^a+\epsilon y^a
$$
In the note I am reading, the author calculate the change of metric by
$$
g_{ab}(x) = \tilde g_{ab}(\tilde x)=\tilde g_{ab}(x^a+\epsilon y^a)=\tilde g_{ab}(x^a)+\epsilon\mathcal{L}_Y\tilde g_{ab}(x^a)+\cdots
$$
My q... | I'm not quite sure what you are doing in your post. It is not true that
$$
g_{ab}(x) = {\tilde g}_{ab}({\tilde x})
$$
The correct equality as I pointed out is
$$
{\tilde g}_{ab}({\tilde x}) = \frac{ \partial x^c}{ \partial{\tilde x}^a} \frac{ \partial x^d}{ \partial{\tilde x}^b} g_{cd}(x)
$$
where ${\tilde x}^a = x^a +... | {
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Amateur's question on Black Holes Black holes are caused by massive curvature of the fabric of space-time. Is it right in believing theoretically that forces of electromagnetic origin could also lead to distortion of the fabric of space-time, (though it may not be as tremendous as the extent to which distortion is brou... | Electromagnetic effects do lead to a curvature of spacetime, as gravitation couples to any quantity in the stress-energy tensor, as dictated by the Einstein field equations. Specifically, the tensor is given by,
$$T^{ab}=-\frac{1}{\mu_0}\left( F^{ac} F_{c}^b +\frac{1}{4}g^{ab}F_{cd}F^{cd}\right)$$
where $F$ is the fiel... | {
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} |
If I'm floating in space and I turn on a flashlight, will I accelerate? Photons have no mass but they can push things, as evidenced by laser propulsion.
Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practi... | This does not directly answer your question, but this is related. If you are floating in space the photons that hit you are also exerting a force. When you float in space a large number of photons emitted by the sun will hit you. These photons exert a force, this mechanism is referred to as radiation pressure. This for... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/112866",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "60",
"answer_count": 4,
"answer_id": 1
} |
Single Photon Hits A Linear Polarizer, What Happens? If a linear polarized single photon strikes a linear polarizer such that its polarization is at 45 degrees to the polarization axis of the polarizer, what happens?
There is a nearly 50% chance that the photon is transmitted, and assuming it is transmitted, it somehow... | Since you are talking about photons, you are also talking about quantum mechanics. In the language of QM, the incoming photon induces a transition to a virtual state of a molecule in the polarizer. When the molecule returns to the ground state, a photon of rotated polarization is emitted.
This transition to a virtual... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113017",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Find the points where potential is null Let's say we have two charges called $q_1$ and $q_2$, respectively $20 \, C$ and $-40\,C$, at a distance $d=1\,m$
We want to find all the points where electric potential is null.
I solved the equation
$$\frac{q_1}{4\pi\epsilon_0r_1} + \frac{q_2}{4\pi\epsilon_0(d-r_1)}=0$$
For $r_... | Let's draw the setup:
The expression for $V(r)$ is simply (I'll set $\kappa$ to 1 for convenience):
$$ V(r) = \frac{20}{r} - \frac{40}{r+1} $$
so the potential is zero when:
$$ \frac{20}{r} = \frac{40}{r+1} $$
Only this isn't quite right because the potential for each charge is symmetric so the potential due to charge... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113091",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why does light travel in straight paths? Why light travels in straight paths? What's the real cause that makes light photons to go in a straight line? and what are the factors that could change the path of light externally? (I'm excluding reflection, refraction and deviation here.)
| I'll give other ways of getting to the same answer.
First of all, the wonderful path integral formulation (which can be found in Feynman's excellent book, "QED"):
In order to consider the probability of a particle from going to a point $A$ to a pont $B$, you consider ALL the possible paths. Each path has a probability ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113135",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Does the Standard Model require neutrinos to be massless? I am an undergraduate student in Physics, I have a basic understanding of Particle Physics and Quantum Mechanics but none whatsoever of Quantum Field Theory.
I know that Neutrino mixing requires neutrinos to be massive (but why? Physically, couldn't neutrinos mi... | Your question is addressed in this paper. The Standard Model as is can accomodate massive neutrinos but if the neutrinos have a mass, and no right handed neutrinos are added, the model becomes non-renormalisable. Adding right handed neutrinos fixes this.
The Standard Model doesn't make any predictions of neutrino mass,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113242",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 3,
"answer_id": 0
} |
Wrapping plastic in aluminium foil to protect it from heat Does it make any sense to wrap the plastic handle of a pan in aluminium foil to protect it from overheating when placing it to the hot oven?
| Everything will want to go to equiliberium for temperature in the oven.
Aluminium foil is not a good insulator.
Suggest three courses of action:
*
*Remove plastic handle
*find a different pan with a metal handle and use an insulator (i.e. oven mitten) when removing pan from oven
*find a material with a good insula... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/113364",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 2
} |
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