Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Why isn't the Gear predictor-corrector algorithm for integration of the equations of motion symplectic? Okumura et al., J. Chem. Phys. 2007 states that the Gear predictor-corrector integration scheme, used in particular in some molecular dynamics packages for the dynamics of rigid bodies using quaternions to represent ... | Take a look at the notes on lectures 1 and 2 of Geometric Numerical Integration found here. Quoting from Lecture 2
A numerical one-step method $y_{n+1} = \Phi_h(y_n)$ is called symplectic if, when applied
to a Hamiltonian system, the discrete flow $y \mapsto \Phi_h(y)$ is a symplectic transformation for all sufficient... | {
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Quantum mechanics as classical field theory Can we view the normal, non-relativistic quantum mechanics as a classical fields?
I know, that one can derive the Schrödinger equation from the Lagrangian density
$${\cal L} ~=~ \frac{i\hbar}{2} (\psi^* \dot\psi - \dot\psi^* \psi) - \frac{\hbar^2}{2m}\nabla\psi^* \cdot \nabla... | Indeed, the true Lagrangian for the Schrödinger equation takes this from
$${\cal L}=i \hbar\psi^*\dot\psi-\frac{\hbar^2}{2m}|\nabla\psi|^2-V({\bf x},t)\psi^*\psi$$
and the action becomes
$$S=\int dtd^3x{\cal L}.$$
A Lagrangian for the Schrödinger equation has a meaning only in a quantum field theory context when you do... | {
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Analyticity and Causality in Relativity A few weeks ago at a conference a speaker I was listening to made a comment to the effect that a function (let's say scalar) cannot be analytic because otherwise it would violate causality. He didn't make this precise as it was a side comment, and although it intrigued me (I had ... | Analytic functions are functions which are locally given by a convergent power series.
Analyticity of a function does not does not imply that by knowing values of all derivatives one can determine value of the function in other point.
In particular, for any values of $y_0$ and $y_1$ one can construct such analytic fun... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/27318",
"timestamp": "2023-03-29T00:00:00",
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What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis? This question was listed as one of the questions in the proposal (see here), and I didn't know the answer. I don't know the ethics on blatantly stealing such a question, so if it should be deleted or be changed to ... | You may be interested in these lectures:
Entanglement and the Foundations of Statistical Mechanics
The smallest possible thermal machines and the foundations of thermodynamics
held by Sandu Popescu at the Perimeter Institute, as well as in this paper
Entanglement and the foundations of statistical mechanics.
There is a... | {
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Rigorous proof of Bohr-Sommerfeld quantization Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In particular, I suppose it gives an exact description of the large quantum number ... | perhaps it can be derived from te approximation over the density of states
$$ N(E)= \sum_{n=0}^{\infty}\theta(E-E_{n})\approx \frac{1}{2\pi \hbar}\iint_{V}\theta(E-H)dxdp $$
with $ H= P^{2}/2m +V(x) $ is the Hamiltonian of the particle and $ \theta (x) $ is heaviside step function
| {
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which letter to use for a CFT? In math, one says "let $G$ be a group", "let $A$ be an algebra", ...
For groups, the typical letters are $G$, $H$, $K$, ...
For algebras, the typical letters are $A$, $B$, ...
I want to say things such as "let xxx be a conformal field theory" and "let xxx $\subset$ xxx be a conformal inc... | There is, I think, no really standard symbol for the generic (chiral) CFT used universally, but there is within the different formalizations.
*
*When chiral CFTs are modeled by vertex operator algebras, the standard symbol is usually "$V$" (for obvious reasons) as user388027 notes in his reply..
*When chiral CFTs a... | {
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Convert state Vectors to Bloch Sphere angles I think this question is a bit low brow for the forum. I want to take a state vector $ \alpha |0\rangle + \beta |1\rangle $ to the two bloch angles. What's the best way? I tried to just factor out the phase from $\alpha$, but then ended up with a divide by zero when tryin... | You are probably dividing by $\alpha$ at some point to eliminate a global phase, leading to your divide by zero in some cases. It would be better to get the phase angles of $\alpha$ and $\beta$ with $\arg$, and set the relative phase $\phi=\arg(\beta)-\arg(\alpha)$. Angle $\theta$ is now simply extracted as $\theta = 2... | {
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How to write a paper in physics? I really like to do research in physics and like to calculate to see what happen. However, I really find it hard to write a paper, to explain the results I obtained and to put them in order. One of the reasons is the lack of my vocabulary.
*
*How do I write physics well? I think tha... | I never forgot my old lecturer Robert Barrass and his book Scientists Must Write. - He never stood a chance, with me.
I still use the basic, 'Theory, diagram, experiment, results and conclusions' approach, otherwise I am lost!
| {
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How much water is destroyed in photosynthesis, relative to the world's supply? Water is involved in the photosynthesis. How much water are we talking about compared with the total amount on water on Earth? Is it enough to have an effect on the average age of water molecules?
| According to http://ga.water.usgs.gov/edu/earthhowmuch.html the total volume of water on the earth is $1.386\times 10^9$km$^3$, which is about $1.4 \times 10^{21}$kg (I'm rounding because I don't know the average temperature and therefore density of the water).
According to http://en.wikipedia.org/wiki/Biomass_(ecology... | {
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How much more effective is it to stir in both directions? I have been told that industrial mixing machines (say, for cake batter) switch directions periodically, first stirring in one direction, then the other, because this mixes the material more thoroughly.
I imagine (but don't know for sure) that stirring in only on... | Mixing means and requires turbulence.
Single direction stirring can settle into a pretty laminar regime at least some of the time. Abruptly reversing direction would break up that order for a while. SO would abrupt stops and starts or just running the machine in a mode where the motion of the blades has a highly turbul... | {
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Did anyone claim that quantum theory meant lasers would never work I've been reading 'How the Hippies saved Physics', which describes a design for a superluminal communication device, of which the crucial part was a laser which duplicated an incoming photon many times. The reason this won't work is what is now known a... | As far as I know, initially, the main requirement for lasing was population inversion. It can easily be shown that this is not possible for a pure two (energy )level system. I suppose this is what you are referring to.
However, since then, using quantum interference in multi-level systems, one can have lasing without i... | {
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'Applications' of surface tension
What are some common applications, uses, exploitations of the properties of surface tension?
Here is what I mean. A water strider can walk on water, that is a consequence of surface tension. This is a consequence, but it is not human made.
On the other hand, I heard that in the cons... | Take a look at this paper
Tears of Venom: Hydrodynamics of Reptilian Envenomation
Reptiles use surface tension to eject venom from their fangs. See also this and this.
| {
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A certain regularization and renormalization scheme In a certain lecture of Witten's about some QFT in $1+1$ dimensions, I came across these two statements of regularization and renormalization, which I could not prove,
(1) $\int ^\Lambda \frac{d^2 k}{(2\pi)^2}\frac{1}{k^2 + q_i ^2 \vert \sigma \vert ^2} = - \frac{1}... | perhaps since your itnegral is logarithmic divergent you could do the following
$$ \int_{0}^{\infty}\frac{kdk}{k^{2}+a^{2}}\to \int_{0}^{\infty}\frac{kdk}{k^{2}+a^{2}}- \int_{0}^{\infty}\frac{dx}{x+b}+\int_{0}^{\infty}\frac{dx}{x+b} $$
then the integral $$ A=\int_{0}^{\infty}\frac{kdk}{k^{2}+a^{2}}- \int_{0}^{\infty}\f... | {
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Dielectric in a parallel plate capacitor Uniform charge: each atom has charge $q$.
Magnitude of dipole moment is $q s$, where $s$ is the distance the nucleus is shifted.
According to my notes, the charge on the surface of a dielectric in between the plates is $N q s S$, where $N$ is the number of dipoles and $S$ is the... | There are two misconceptions present in your explanation of the problem.
*
*$N$ is not number of dipoles, but their volumetric density
*$Q$ is not total charge, but equivalent charge at boundaries of the dielectric.
The idea is that (a) dielectric of the area $A$ and height $L$ polarized homogeneously along its h... | {
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This sentence makes no sense, electrostatics and electrons moving in a conductor - current
I highlighted the part where the confusion is.
The sentence said that the potential difference is 0, yet it then immediately talks about how electrons can have motion.
What are they trying to say?
| dmckee's answer has nailed it, but to try and put it more simply (and less accurately) suppose instead of electrons in a wire you were looking at gas molecules in a tube. If there's no pressure drop along the tube, i.e. no voltage drop along the wire, there will be no net flow of gas. But this doesn't stop the gas mole... | {
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X-Ray crystallography using Bragg's Law I was looking up X-Ray crystallography using Bragg's Law:
$2d\sin\theta = n\lambda$
and I can understand the values of everything except this integer value $n$.
As far as my research got $n$ is used to describe the atom spacing in the crystal lattice, but I don't understand how y... | Positive interference occurs when the waves reflected from two different "layers" differ by an (any!) integer number of wavelengths: $n$ is that integer.
| {
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What is the roaring in a roaring fire? I was just starting a barbecue fire by blowing on the smouldering coals when I realised I had no idea what the sound was actually caused by. I can make the sound by blowing at almost any flame I can think of, and I guess it is perhaps related to the increased oxygen consumption an... | The roar is indeed due to turbulence.
When a solid (or liquid) burns it isn't the solid that burns. The heat causes the solid to vaporise or emit vapour and it's the vapour that burns. When you have a steady flame the vapour burns smoothly. However, when you blow on it you make the vapour flow, and therefore the flame,... | {
"language": "en",
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How do we recognize hardware used in accelerator physics When I see a new accelerator in real life or on a picture, I always find it interesting to see how many thing I can recognize. In that way, I can also get a small first idea of how the accelerator is working.
Here is a picture, I have taken of LEIR at CERN
Help m... | Ion pump
Ion pumps are used to pump away rest gas in beam tubes at very low pressure.
http://en.wikipedia.org/wiki/Ion_pump_(physics)
| {
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On constancy of cometary orbits how are the comets able to keep to a nearly fixed orbital period, though they lose a certain amount of mass during their perihelion?
| What exactly do you mean by a "nearly fixed orbital period"? For most comets the deviations from an orbit calculated based solely on gravitational parameters are on the order of fractions of a day per apparition, but for Comet 1P/Halley it is about four days. In any case, these deviations are well observed.
The paper C... | {
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Time Reversal Invariance in Quantum Mechanics I thought of a thought experiment that had me questioning how time reversal works in quantum mechanics and the implications. The idea is this ... you are going forward in time when you decide to measure a particle. The particle then collapses to the observed state. Now if p... | No!
Time invariance holds in quantum mechanics ONLY when wave function does not collapse. This means once you did any measurements, the time invariance is destroyed. There is no time invariance in the presence of observer.
| {
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Why is the sky not purple? I realise the question of why this sky is blue is considered reasonably often here, one way or another. You can take that knowledge as given. What I'm wondering is, given that the spectrum of Rayleigh scattering goes like $\omega^4$, why is the sky not purple, rather than blue?
I think th... | All light is Rayleigh scattered, it's just that short wavelength light is scattered more. The bluest light we can see has a wavelength of about 400nm while the reddest has a wavelength of about 700nm, so there is a roughly a factor of ten increase in the scattering going from the red to the blue end of the spectrum.
So... | {
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The Planck constant $\hbar$, the angular momentum, and the action Is there anything interesting to say about the fact that the Planck constant $\hbar$, the angular momentum, and the action have the same units or is it a pure coincidence?
| Although the answers so far to this questions are very interesting and informative, I think from an analytical point of view, your question is not quite sensible.
In a mathematical structure, one could argue that there are no "coincidences", everything is related through the fundamental basis. Now in practice, the ans... | {
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How can a Photon have a "frequency"? I picture light ray as a composition of photons with an energy equal to the frequency of the light ray according to $E=hf$. Is this the good way to picture this? Although I can solve elementary problems with the formulas, I've never really been comfortable with the idea of an object... | No, sometimes photons exhibit properties of a particle, and other times it exhibits properties of a wave, therefore having a "frequency" and at the same time being a particle.
| {
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Is the classical Doopler Effect, for light shift, $1-v/c$, exact? What is it an approximation of? Is the classical doopler effect for light shift equal to $1-v/c$ exact or an approximation of a classical formula? I know that it is an approximation of the relativistic formula, but what was the corresponding classical fo... | He is comparing $\sqrt{1-v\over 1+v}$ to the classical Doppler shift $(1-v)$ (where v is the velocity divided by c, since I use units where c=1). The formula you give $1-v\over 1+v$ doesn't have a classical interpretation, and Einstein reduces to Doppler's at slow speeds.
| {
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Should any theory of physics respect the principle of conservation of angular momentum or linear momentum? Is it possible that a theory that can describe the universe at the planck scale can violate things that we now consider fundamental in nature?For example can it violate rotational and translational invariance and... | Conservation laws in theory are valid because they rest on solid and innumerable data. An experiment finding non-conservation of a law supported by theory would immediately invalidate the theory.
Our experimental experience is that the two laws you mention, conservation of angular momentum and momentum are such unive... | {
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Can every particle be regarded as being a combination of Black holes and White holes? Can the statement be regarded as true? That every particle, or element in the universe can be regarded as a combination of black hole and white hole in variable proportion.
| You first have to understand what a "white hole" is. It's the time reverse of a black hole. It was rightly pointed out in previous answers that white holes violate the second law of thermodynamics. Now, like anything in thermodynamics, this makes them unlikely but not impossible (unlikely here usually means unlikely ev... | {
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Gamma Ray Bursts What is the maximum frequency of the Gamma Rays produced during supernovae? And how are these detected by telescopes without getting some serious damage done?
| A quick Google for "gamma ray burst spectrum" found lots of hits including http://arxiv.org/abs/1201.2981, which contains a collection of spectra from gamma ray bursts in the appendix. The maximum energies detected are around 10MeV, which seems a lot but remember that the LHC accelerates particles to around a million t... | {
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Grassmann Variables Representation? It might be a silly question, but I was never mathematically introduced to the topic. Is there a representation for Grassmann Variables using real field. For example, gamma matrices have a representation, is it not possible for Grassmann Variables? The reason for a representation is,... | I think that this Wikipedia article will tells this all.
The only problem is that for $n$ (I mean $\theta_1,\theta_2,...\theta_n$) Grassmann numbers you will need to use $2^n\times 2^n$ matrices.
| {
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Is it possible to have incommensurable but equally valid theories of nature which fits all experimental data? Is it possible to have mutually incommensurable but equally valid theories of nature which fits all experimental data? The philosopher of science Paul Feyerabend defended this seemingly outrageous thesis and ma... | From your link:
if theories are incommensurable, there is no way in which one can compare them to each other in order to determine which is more accurate .
So the decision is based on accuracy, and for physical theories experimental accuracy. As time goes on, accuracy on measurements increases as well as methods of ... | {
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Lenses (refractor) or mirrors (reflector) telescope? What differentiates, in terms of practical quality, not technical implementation, a refractor from a reflector telescope?
Why would one prefer a refractor over a reflector, when reflectors come with such large diameters at a smaller price?
| Refractors suffer from fewer optical aberrations than reflectors because they have only two elements in their optical assembly, making it easier to align and maintain collimation.
The biggest problem with refractors is chromatic aberration, which can be corrected to a certain degree by Apochromatic lenses, but isn't co... | {
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Electrostatic Pressure Concept There was a Question bothering me.
I tried solving it But couldn't So I finally went up to my teacher asked him for help . He told me that there was a formula for Electrostatic pressure $\rightarrow$
$$\mbox{Pressure}= \frac{\sigma^2}{2\epsilon_0}$$
And we had just to multiply it to the ... | When charge is given to a conductor body then due to mutual repulsion between two charges on the two parts of the given conductor, a net force at a point on the surface of a charge conductor whose direction is normally outward. This mechanical force developed per unit area on the surface of charge conductor is also cal... | {
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Does friction decrease as objects move faster against each other? I was told that the faster two objects move against each other, the less the friction between them would be… compared to if they were moving slower. So does friction decrease when the body is moving faster or does it remain the same. Does the speed affec... | Friction is not a fundamental force itself, rather it is a macroscopic collective effect of the interactions between atoms and molecules of the two surfaces, dominantly electromagnetic interactions. Yet in reality, it can depend on a large number of other factors such as the relative speeds of two surfaces, the way the... | {
"language": "en",
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Entropy increase and end of the universe While taking thermodynamics our chemistry teacher told us that entropy is increasing in day by day (as per second law of thermodynamics), and when it reaches its maximum the end of the world will occur. I didn't see such an argument in any of the science books, is there any prob... | What your describing is the theory of the Heat death of the universe which is speculated about since 1850s. However, as explained here, object at astronomical scale are often self-gravitating and that gives them have unintuitive thermodynamical properties like a negative heat capacity. This usually gives more structure... | {
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Direct observations of a black hole? I'm not very knowledgeable about physics generally, but know that nothing can escape a black hole's gravitational pull, not even light (making them nearly invisible?).
My question is: What has been obtained from direct observation of a black hole to prove their existence? Please no... | This animation from UCLA's Galactic Center Group shows stars near the galactic core in images taken from 1995 to 2011. You can clearly see they are orbiting a small and massive object.
| {
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Lorentz invariance and the vacuum expectation value of fields with spin > 0 I had a question about Moduli space, which I was reading about here, but then I read this sentence:
"Lorentz invariance forces the vacuum expectation values of any higher
spin fields to vanish."
Can someone explain how exactly this happens... | There is a Lorentz transformation that maps a spacelike vector $u$ to $-u$.
If $A(x)$ is a field of spin 1 with $\langle u \cdot A(0)\rangle = c$ then applying the Lorentz transform we find $-c=c$ and hence $c=0$. Doing this for all spacelike vectors implies $\langle A(0)\rangle = 0$, and translation invariance then gi... | {
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Why/how does an electron emit a photon when decelerating? I've had two special relativity courses so far but none really gave me a clear description of the process.
| Ahhh... let's see!
Any electron that changes speeds or direction emits blue light. When an electron moves to difference valence levels emits blue and white light.
For an electron to change speed or direction it must have interaction with other particles or other EMFs. If the electron is spinning around an atom it wil... | {
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Would the rate of ascent of an indestructible balloon increase as function of it's altitude? Assume a balloon filled with Hydrogen, fitted with a perfect valve, and capable of enduring vacuum (that is to say, it would retain it's shape and so well insulated that the extremes of temperature at high altitudes and in spac... | The change in height with respect to time is given by the buoyant force divided by the viscosity, for slow rising objects, and neglecting the initial acceleration. From this differential equation we can see that, regardless of changes in viscosity, the stable attractor of this system is the height where the buoyancy is... | {
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Why do magnetic field lines go from North to South? Why magnetic lines comes from north to south out side of the magnet
is any magnetic lines comes from south to north if so in which direction
What is the reason of magnetic lineS
| A picture is worth a thousand words.
Iron filings display the "lines", like small dipoles as @PhysGrad has mentioned. The compasses are larger dipoles and the permanent magnet itself is the largest. One can imagine tiny dipoles following "lines", so in a sense they exist to the accuracy of the experiment.
The image di... | {
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How does a strobe lamp stop a fast moving object? A strobe lamp can be used to seemingly stop a fast moving object when calibrated.
Commonly used in quality assurance during production to inspect otherwise non-observable assembly line activity.
What causes this effect in observations?
| Well, it doesn't really stop the motion. If you time the strobes to coincide with the revolution period of a wheel, the wheel will make one exact revolution between strobes and will appear to be stationary. This is called sampling in signal processing (you might want to read about the Nyquist sampling rate).
On a diff... | {
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Does infrared rays pass through polarized glass? Actually I had asked in another post that "Does infrared rays pass through active shutter glass" but someone just commented that infrared rays dont pass through polarized glass. If infrared rays doesnt pass through polarized glass can someone explain the reason or give r... | Infra-red radiation will pass through a polarised medium just like visible light does i.e. the component at right angles to the plane of polarisation will be blocked. So there's nothing special about the fact the glasses are polarised.
However most materials are only transparent over a restricted range of wavelengths. ... | {
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Changing the Half-Life of Radioactive Substances Is there a way to extend or reduce the half-life of a radioactive object? Perhaps by subjecting it to more radiation or some other method.
| The simple answer is no, we can't change the half life. There's no technology available to us that can affect energy levels in the nucleus enough to make a change to the half life.
Having said that, I've always wondered if the Mossbauer effect could change the half life. Mossbauer spectroscopy measures tiny changes in ... | {
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Collision of a black hole & a white hole A black hole and white hole experience a direct collision.
What happens? What shall be the result of such a collision?
| Another amateur answer: the energy of a White Hole is convex and the energy of a Black Hole is concave, so they cannot approach each other. Two black holes can approach one another; two white holes can approach one another. But white holes and black holes are kept apart magically, in much the same ways that matter an... | {
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Distorted colors of Google StreetView photographs near electric power lines This is a followup to my question:
Cyclist's electrical tingling under power lines
Some users presented a convincing picture that the electric shocks under power lines are primarily from the electric fields, not the magnetic one, because the ... | Just discovered that the link can move around.
As following the power lines does not show this effect, it is not associated with them.
It seems to be associated with a tree line, even a tree.
either:
a) a temporary glitch in the camera program building up the picture, since it is not on all views.
b) Much less probabl... | {
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Path traced out by a point While studying uniform circular motion at school, one of my friends asked a question:
"How do I prove that the path traced out by a particle such that an applied force of constant magnitude acts on it perpendicular to its velocity is a circle?" Our physics teacher said it was not exactly a v... | I think you can prove it you can prove that the acceleration vector $\vec{a}$ is decomposed into two components
$$\vec{a} = \dot{v}\, \hat{e} + \frac{v^2}{r} \hat{n}$$
one tangential to motion along the unit direction vector $\hat{e}$ and one perpendicular to along the unit direction $\hat{n}$, with tangential speed ... | {
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Does $p=mc$ hold for photons? Known that $E=hf$, $p=hf/c=h/\lambda$, then if $p=mc$, where $m$ is the (relativistic) mass, then $E=mc^2$ follows directly as an algebraic fact. Is this the case?
| Here's another way to think about it (personally, I think this addresses the question most directly):
$E = hf$ and $p = \frac{hf}{c}$ both apply to photons. What those get you is simply that $E = pc$, so you can conclude that $E = pc$ should be valid for photons. And it is.
Now, your question is worded to ask whether y... | {
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Why isn't it allowed to use a flash when taking pictures in a certain place? When I go to, for example, a museum I try to take some pictures.
Sometimes the museum staffs forbid me to use a flash. Do you know the reason? I don't think it is related to photo-electric effect, right?
| It's actually astonishing to see how damage much a camera flash can do to black/dark colored objects!
This is a pretty good demonstration.
So, I imagine that if a photographer takes a picture with a powerful flash gun close to a black object (e.g. a dark painting) it could cause the painting to undergo combustion and g... | {
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What's the difference between Fermi Energy and Fermi Level? I'm a bit confused about the difference between these two concepts. According to Wikipedia the Fermi energy and Fermi level are closely related concepts. From my understanding, the Fermi energy is the highest occupied energy level of a system in absolute zero?... | Fermi level as a state with 50% chance of being occupied by an electron for the given temperature of the solid and at absolute zero temperature occupancy is 100%.
Fermi energy is the corresponding energy of Fermi level.
| {
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Non linear QM and wave function collapse I heard that there have been some propositions about describing the collapse of the wave-function by adding non-linear terms, but I couldn't anything in any any textbooks or even articles (probably those propositions never reached a good level of consistency). However, I'd like ... | Roger Penrose advanced the notion that gravity causes wave function collapse, giving handwavy arguments involving the Schrodinger-Newton equation (one particular flavor of the nonlinear Schrodinger equation).
The references I'm aware of:
*
*Roger Penrose, "On Gravity's Role in Quantum State Reduction", General Rela... | {
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Does regular sky clouds stops the sun's ultraviolet rays? I have an argue with an ex-Doctor of Medicine about the amount of ultraviolet light reaching us under the clear day sun and under the 100% cloudy sky.
To what extent we can say that the sky clouds stops ultraviolet light from the sun?
| Clouds don't absorb light (much), they reflect and refract it, and this applies to uv light in the same way as visible light. So a 100% cloudy sky will block uv light in the same way it blocks visible light. A quick Google suggests that heavy cloud cover will remove 80-90% of uv light. Anyone disputing this should try ... | {
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Principal value integral I am reading A. Zee, QFT in a nutshell, and in appendix 1 he has:
Meanwhile the principal value integral is defined by:
$$\int dx\,{\cal P}{1\over x}f(x)~=~ \lim_{\epsilon \rightarrow 0} \int dx\, {x\over x^2+\epsilon^2}f(x)$$
Please can someone explain to me why this is the case? As I unde... | Note that the right spelling is "principal value".
The formulae aren't identical but the results are the same whenever both definitions yield a well-defined expression. What matters is that we remove the leading logarithmic divergence on both sides from $x=0$ and we do so in a symmetric way with respect to $x\to -x$.
I... | {
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What is the ontological status of Faddeev Popov ghosts? We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they "superficially" interact over finite time periods.
*
*So, what i... | I'd say BRST ghosts have more elements of reality compared to longitudinal gauge bosons which are pure gauge. Look at the inner product structure. Physical states belong to the BRST cohomology of BRST-closed modulo BRST-exact. pure gauge longitudinal gauge bosons are BRST-exact and have zero inner product with any othe... | {
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How long was a day at the creation of Earth? Since the earth is slowing its rotation, and as far as I know, each day is 1 second longer every about 1.5 years, how long was an earth day near the formation of earth (4.5 billion years ago)?
I wouldn't assume to just do 4.5b/1.5 and subtract, because you would think the ra... | Shouldn't each day be one second longer every 1.5 years, if the Earth is rotating slower? Assuming your info is accurate, (1 sec)/(1.5 years) * (4.5 billion years) = The Number of Seconds Shorter The Day Was 4.5 billion years ago. Subtract that from the number of seconds in a day now. I would convert the final answer ... | {
"language": "en",
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Can a huge gravitational force cause visible distortions on an object In space, would it be possible to have an object generating such a huge gravitational force so it would be possible for an observer (not affected directly by gravitational force and the space time distortion) to see some visual distortions (bending) ... | Also, a neutron star, itself, is an example of this effect--it's gravity is so strong that it causes matter to begin to collapse, and protons and electrons to combine via reverse beta decay. Anything less dense than a nucleus sitting on the surface of a neutron star will eventually find itself smashed flat on the star... | {
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Friction at zero temperature? By the fluctuation-dissipation theorem (detailed-balance for Langevin equation), $$\sigma^2 = 2 \gamma k_B T$$ where $\sigma$ is the variance of noise, $\gamma$ is a friction coefficient, $k_B$ is Boltzmann's constant, and $T$ is temperature. So in principle, one can have $\gamma\neq 0$ wh... | Isn't the friction here the mechanical analogy to the resistance in a circuit? At $T=0$ the voltage noise is zero but you still have the finite property 'resistance'.
In more general terms, the dissipation is given by the imaginary part of a generalized susceptibility $\chi$ of your physical system. So as long as your... | {
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Cannon on spacecraft: hitting yourself Some Soviet space stations reportedly had anti-aircraft cannons installed. Could such a cannon hit the firing space station accidentally on a subsequent orbit? The muzzle velocity of the cannon is under 700 m/s, significantly slower than orbital velocity so the projectiles should ... | The space station could shoot itself, but it's extremely unlikely to happen by accident.
Assuming your space station is in a circular orbit you can calculate it's position in polar co-ordinates as a function of time $(r(t), \theta(t))$ very easily since $r$ is constant and $\theta = 2\pi t/\tau$ where $\tau$ is the orb... | {
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If a superconductor has zero resistance, does it have infinite amperage? If amps = volts / ohms, and ohms is 0, then what is x volts / 0 ohms?
| In the world we live in, with the accuracies we can generate it is an observed fact the R=V/I.
Infinities need careful interpretation if they happen in the physical world.
In this form when there is no current one talks of infinite resistance ( seen also on the potentiometers sold) .
When one reverses the equation to t... | {
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Are there any objective wavefunction collapse theories which are local and forbid superluminal signalling? Are there any objective wavefunction collapse theories which are local and forbid superluminal signalling? GRW is nonrelativistic and nonlocal.
| No, and there cannot be. Imagine entangling two particles, sending one of them off to a colleague on Mars, and then measuring them both at almost the same time (according to Earth's reference frame, for the sake of argument). An objective collapse theory would say that whoever measures their particle first "collapses" ... | {
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Non-Newtonian Fluid Stop a Bullet? I just saw a YouTube video about Non-Newtonian fluids where people could actually walk on the surface of the fluid but if they stood still, they'd sink. Cool stuff.
Now, I'm wondering: Could a pool of Non-Newtonian fluid stop a bullet? Why or why not?
If so, if you put this stuff insi... | BAE Systems have already done this. Annoyingly there seems to be some problem on the BAE web server at the moment, but there's a description here with links to the BAE site. Alternatively Google for something like "liquid armour site:baesystems.com".
Dilatant fluids are very good at absorbing energy as forcibly shearin... | {
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Why can't gauge bosons have mass? Clearly, a mass term for a vector field would render the Lagrangian not gauge-invariant, but what are the consequences of this? Gauge invariance is supposed to be crucial for the renormalisation of a vector field theory, though I have to say I'm not entirely sure why.
As far as removin... | Let me anwser a closely related quenstion:
Consider a U(1) gauge theory with massless gauge bosons, can any small perturbations give the gauge boson an mass.
Amazingly, the anser is NO. The masslessness of the gauge boson is topologically robust.
No small perturbations can give the gauge boson an mass.
For detail, see... | {
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How to capture electomagnetic radiation/waves? If I wanted to find out what kind of electomagnetic waves "travel" through my room at which frequency, what kind of equipment would I need? Suppose I want to view frequencies from 0 Hz to 6 GHz.
| The oscillating magnetic field associated with an EM wave will induce a voltage in any electrical conductor that it passes through. So in principle all you need to do is stretch a piece of wire across your room then measure the voltage across it. However, as usual, the devil is in the detail.
If you've ever listened to... | {
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Does gravity slow the expansion of the universe? Does gravity slow the expansion of the universe?
I read through the thread http://www.physicsforums.com/showthread.php?t=322633 and I have the same question. I know that the universe is not being stopped by gravity, but is the force of gravity slowing it down in any way?... | For most of the 20th century, it was thought that expansion slowed gravity. Many weighed in on the value of omega, it being thought that the universe was so close to critical balance it could not be determined whether it would expand forever or collapse. That mystery should have evaporated with the discovery that the... | {
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Introduction to differential forms in thermodynamics I've studied differential geometry just enough to be confident with differential forms. Now I want to see application of this formalism in thermodynamics.
I'm looking for a small reference, to learn familiar concepts of (equilibrium?) thermodynamics formulated throug... | I'm afraid that from the aesthetic side, there is not too much differential geometry to discover in (equilibrium) thermodynamics (at least on an undergrad level and if you don't want to bother with the conceptual question how to properly define the idea of heat for the most abstract situations). I suppose any book on t... | {
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What entities create a gravitational field? It is well known that masses create a gravitational field. Photons are affected by gravitation, but do they generate a gravitational field as well? What about the other gauge bosons?
Do gravitons create a gravitational field?
|
Do gravitons create a gravitational field?
There's an interesting section in MTWs "Gravitation" describing how the GR equations can be arrived at by considering massless spin-2 field ("gravitons") in flat spacetime and iterating corrections from considering that the non-zero stress-energy tensor for this field is a s... | {
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What voltages are used to "safely" shock someone (as in a carnival game) I've had this debate with some coworks. What voltage (rough order of magnitute) is used to safely shock people?
"Safe" is a vague term, but as an example, there are arcade games where you hold onto two rods and you are hit with a jolt that grows ... | In general there is not any safe voltage. The danger mostly depends on the current flowing through your body, especially the heart and the duration of the current flow.
So for any kind of trick device you want to use a relatively high voltage, so that wet or dry hands do not make a large difference and limit the durat... | {
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Which universe had a beginning? The universe or the observable universe? When we say the universe had a beginning, do we mean the entire universe or the observable universe? Or did both of them have a beginning?
| The Penrose-Hawking theorem, strictly applied, only indicates if we have a trapped null surface, which we get with an enclosing boundary larger than the Hubble radius, there has to be a singularity or closed timelike curve sometime in the past in some subregion. Strictly speaking, not even the entire observable univers... | {
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What is the physical meaning of diffusion coefficient? In Fick's first law, the diffusion coefficient is velocity, but I do not understand the two-dimensional concept of this velocity. Imagine that solutes are diffusing from one side of a tube to another (this would be the same as persons running from one side of a str... | The diffusion coefficient $D$ is a constant relating the spreading $\left\langle x^{2}\right\rangle$ and the time $t$ it spread out. This relation can be clear seen in the diffusion of a single point source as follow.
Lets consider the homogeneous diffusion equation:
$$u_t = D u_{xx} \tag{1}$$
The solution is given by... | {
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What does symplecticity imply? Symplectic systems are a common object of studies in classical physics and nonlinearity sciences.
At first I assumed it was just another way of saying Hamiltonian, but I also heard it in the context of dissipative systems, so I am no longer confident in my assumption.
My question now is,... |
Why is it worth mentioning that something is symplectic?
This question is a little like asking why it's worth mentioning that an electric field is in the room.
As an important characteristic, I'd point out that if you have a symplectic structure, you have a Poisson algebra. That means that not only can the functions ... | {
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uncertainty of fields with many harmonic modes In most basic level introduction to the quantum harmonic oscillator formulation of fields, it is assumed that the commuting variables for the fields $p_m$, $q_m$ are
$$ \lbrack p_m , q_n \rbrack = \delta_{m n} i \hbar $$
which seem to imply that each individual mode holds... | The fluctuation in a field at a point is infinite in any field theory, this is because of the reason you state. This is why you need to smear the field over a region with a test function for it to have finite fluctuation, and the reason that the fields are characterized as operator valued distributions.
If you look at ... | {
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Is there some connection between the Virial theorem and a least action principle? Both involve some 'averaging' over energies (kinetic and potential) and make some prediction about their mean values. As far as the least action principles, one could think of them as saying that the actual path is one that makes an equi... | As that lovely article linked by dfan says the virial theorem comes from varying the action $S[x]$ by $x\rightarrow(1+\epsilon)x$
$$\frac{1}{T}\delta S = \frac{1}{T}\epsilon\int_{0}^{T} dt\{m\dot{x}^2 -x\frac{\partial V}{\partial x}\}$$
This is a variation of the action and therefore must vanish up to some boundary t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/32896",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 3,
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Looking for a list of possible subatomic particle collisions This is going to be a strange question, but here we go. I'm working on a computer puzzle game that will simulate subatomic particle collisions. I am not a physicist by training, but I do dabble. I would like the game to be loosely based on reality, and I've b... | In a sense these "games" exist, need large computing power and are called high energy physics monte carlos.
These are very complicated simulations of the reality of the experiment and include all the detector effects.
At the first level of the core of these HEP monte carlos there exist tables of "complete" possibili... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How is a cathode ray tube different from beta minus radiation? In beta minus the result is one neutron in the nucleus changing to a proton, plus an electron and an anti-neutrino being sent off.
The antineutrino is indifferent to our health. So I guess what makes a beta source dangerous compared to a cathode ray tube m... | Beta emitters, or indeed most radioactive materials, aren't especially dangerous unless they get into your body. For example iodine 131 (a beta emitter) is concentrated in the thyroid and causes destruction of the thyroid and/or a cancer there. Likewise plutonium (an alpha emitter) is most dangerous when particles are ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33053",
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"source": "stackexchange",
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Ideal 2D Unicycle Kinematics A particle is connected to a massive wheel by a rigid rod. The wheel can roll without slipping on a horizontal surface. The particle is free to rotate around the centre of the wheel.
I believe the system has two degrees of freedom:
The centre of the wheel and the particle each have x- and y... | The significance of the separability of the differential equations is simple:
The difficulty involved in balancing a unicycle in 2D is independent of how fast you are going. (in 3D, you have to balance sideways as well, and only there does the wheel speed comes in handy).
Regarding the simulation, I'm not aware of any... | {
"language": "en",
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What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra o... | Feynman's Six Easy Pieces is an excellent introduction to quantum mechanics. For a more thorough analysis (and some philosophical ruminations), I'd recommend The Dancing Wu Li Masters by Gary Zukav. For an easy-to-understand discussion of the weirdness of quantum mechanics, Fred Kuttner and Bruce Rosenblum's Quantum En... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33215",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "103",
"answer_count": 19,
"answer_id": 12
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wave superposition of electrons and quarks Is quantum wave superposition of electrons and quarks possible?
If not, can different types of elementary particles be mixed in wave superposition?
| This is a good question. No experiment has shown mixing between leptons (such as the electron) and quarks. I'm using the word "mixing" here in the same you used superposition (though more often the word superposition is used to refer to energy states). There is certainly experimental evidence for the superposition o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33364",
"timestamp": "2023-03-29T00:00:00",
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Where 2 comes from in formula for Schwarzschild radius? In general theory of relativity I've seen several times this factor:
$$(1-\frac{2GM}{rc^2}),$$
e.g. in the Schwarzschild metric for a black hole, but I still don't know in this factor where 2 comes from?
| On the one hand, for nonrelativistic particle moving in an external
gravitational field, the Lagrangian has the form:
$$
L=-mc^{2}+\frac{m\mathbf{v}^{2}}{2}-m\phi,\quad\quad(1)
$$
where $m$ is a mass of particle, $\phi$ is a gravitational potential. On the
other hand, general relativity requires the following action fo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33473",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Cosmological constant of standard model of cosmology and observational data I am curious whether the current Lambda-CDM model of cosmology matches well with observational data, especially expansion of the universe.
How well does Lambda-CDM defend its established status from other models, such as quintessence (quintesse... | We don't know how the relationship between gravity and dark energy changes over time as gravity decreases (from the rest of the universe), because one cancels out the other to a degree we don't know.
It is not reasonable to assume that as the universe expands more strings of dark energy magically appear to keep the den... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33523",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Maxwell-Boltzmann distribution and total energy per unit volume We know that
$$n(E) ~=~ \frac {2 \pi (N/V)}{(\pi k_B T)^{3/2}} E^{1/2} e^{-E/(k_B T)} dE,$$
where $V$ is total volume.
If then, how do we derive total energy per unit volume from this equation?
| Integrate n(E)*E over all possible energies and divide the result by the total volume, this gives the average energy per unit volume.
Ali
| {
"language": "en",
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"source": "stackexchange",
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prove that flat shape minimizes a functional The following functional arises in an information theoretic problem that I work on currently.
$I(G(\omega)) = \int\limits_{-\kappa\pi}^{\kappa\pi}d\omega \frac{A}{G(\omega)+A}-\frac{| \int\limits_{-\kappa\pi}^{\kappa\pi}d\omega \frac{A}{G(\omega)+A}\exp(-i\omega)|^2}{ \int\l... | This hypothesis is not right. The first integral alone $\int {A\over G(\omega) +A } d\omega$ has a local minimum at the constant function (and a global minimum too), so that it's first variation is zero, but the numerator of the second term doesn't have a vanishing variational derivative, so it isn't extremal for a con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33632",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
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Non-conservative Electric Field I was watching this video from Walter Lewin and while watching these two videos, I noticed there is a "contradiction" in what he is doing. All links direct you exactly to where he begins, so you don't have to search it yourself
LR Circuit
http://www.youtube.com/watch?v=UpO6t00bPb8#t=10m2... | Lewin does appear to be using a different sign convention in the two lectures. In the first he takes a voltage drop as positive while in the second he takes a voltage drop as negative.
But it doesn't matter which convention you use as long as you are consistent. The point is that if you go round any closed loop the tot... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33692",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What are the units or dimensions of the Dirac delta function? In three dimensions, the Dirac delta function $\delta^3 (\textbf{r}) = \delta(x) \delta(y) \delta(z)$ is defined by the volume integral:
$$\int_{\text{all space}} \delta^3 (\textbf{r}) \, dV = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\... | Yes. The Dirac delta always has the inverse dimension of its argument. You can read this from its definition, your first equation. So in one dimension $\delta(x)$ has dimensions of inverse length, in three spatial dimensions $\delta^{(3)}(\vec x)$ (sometimes simply written $\delta(\vec x)$) has dimension of inverse vol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33760",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "37",
"answer_count": 2,
"answer_id": 1
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The appearance of volume $V$ in the Fourier series representation of a periodic cubic system In the textbook Understanding Molecular Simulation by Frenkel and Smit (Second Edition), the authors represent a function $f(\textbf{r})$ (which depends on the coordinates of a periodic system) as a Fourier series. I quote fro... | I) Let us just consider $1$ dimension for simplicity. (The generalization to higher dimensions is straightforward). Then the volume factor $V$ is just a length factor $L$.
II) The standard Fourier series formulas can be derived from $(12.1.7)$ and $(12.1.6)$ by taken the length $L$ to be $L=2\pi$. Then $(12.1.7)$ and $... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33817",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Topological phase Can anybody tell me, if generically any system, which is solely described by a topological field theory, resides in a topological phase? I cant find any clear notion of topological phase. Only topological phase of matter, but I mean any kind of system.
Thanks for your help.
| Topological order is a new kind of order in zero-temperature phase of quantum spins, bonsons, and/or electrons. The new order corresponds to pattern of long-range quantum entanglement. Topological order is beyond the Landau symmetry-breaking description. It cannot be described by local order parameters and long range c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there an analogue of configuration space in quantum mechanics? In classical mechanics coordinates are something a bit secondary. Having a configuration space $Q$ (manifold), coordinates enter as a mapping to $\mathbb R^n$, $q_i : Q \to \mathbb R$. The primary thing is the manifold itself and its points.
On the contr... | If you work with a path integral to define the quantum system, then the path integral sums over paths that live on the manifold. The measure of integration is given by the action, which is an integral over a given path, and it is defined without referring to a specific coordinate system.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33897",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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How can one know if a theory allow action at a distance effects or not? 1-In general, if a theory has action at a distance effects, where can that appear exactly in the theory?
2-Does it appear in the dynamical law of the theory? (does it appear in Newton's 2nd law? where can it be spotted?)
3-Does it appear in the fo... | Take a look at Newton's law in the form of gravitational potential $$\nabla^{2}\phi=4\pi G\rho$$ Let's say we change the mass density of whatever our gravitating object is. Now, the gravitational field is instantly changed - everywhere, everyone feels a different potential, and a different gravitational force.
Like yo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33977",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is Dalitz decay? What is Dalitz decay?
I know there are Dalitz $\pi^0 \to e^+ + e^- + \gamma$ decay, $w \to \pi^0 + e^+ + e^-$ decay, may be more. But is there a rule to say which decay is Dalitz and which is not?
Is there a rule to say which particle can decay by Dalitz decay and which does not?
| A particle's Dalitz decay means the particle decays to a massless gauge boson and two massless fermions. You can find this definition in 1308.0422.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it wrong to talk about wave functions of macroscopic bodies? Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not?
For example in the "Statistical Physics, Part I" by Landau & Lifshitz it is argued that such systems must be described via th... | Almost always, one cannot write a wavefunction for a macroscopic object even in principle, because if something is macroscopic, it means that it is usually entangled strongly with the environment (i.e., decohered by it, as others have pointed out). By definition of entanglement, if two systems are entangled, then the c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34084",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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"answer_id": 3
} |
Negative Mass and gravitation Since Newtonian gravity is analogous to electrostatics shouldn't there be something called negative mass? Also, a moving charge generates electric field, but why doesn't a moving mass generate some other field?
| Moving mass does generate gravitation different from stationary mass. This is the ''gravitomagnetic'' effect predicted by Lens and Thirring in the 20's and measured by Gravity Probe B:
http://en.wikipedia.org/wiki/Gravitoelectromagnetism
It is related to the ''frame dragging'' effect that you hear about with respect t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34115",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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"answer_count": 3,
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Space Expansion vs. Relative Motion Given 2 objects moving at some velocity $v$ relative to one another, is it possible to determine whether they are moving or whether the space between them is expanding?
| thinking about this question, one is eventually led to think of the initial attempts to formulate Mach principle; in that hypothesis, which predates the creation of General Relativity, but after Special Relativity was established, Ernst Mach especulated that, if there was no special frame of reference from where to mea... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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What causes a spark to move along rods that are not parallel? I took my son to a science museum where they had a gadget that many of us probably saw in movies involving a mad scientist. The gadget had two metal rods about two inches apart at the bottom. The rods were about six feet long, and four inches apart at the to... | The device you describe is called a Jacob's Ladder. You are correct that it is high voltage between the rods that produces the initial spark at the bottom of the ladder where the gap between the rods is the narrowest. Then the ionized air heats up, becoming less dense, so it rises. The current path rises as well becau... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34266",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What exactly does the holographic principle say? Does the holographic principle say given a spatially enclosing boundary satisfying the Bousso condition on expansion parameters, the log of the number of microstates in its interior is bounded by $\exp\{A/4\}$ where $A$ is its area? Or does it say something stronger, nam... | There's no a priori reason why we can't have the former without the latter. The stronger version was only introduced to resolve the black hole information loss "paradox".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34307",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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If the electron is point like, then what is the significance of the classical radius of the electron? What is the physical meaning/significance of the classical radius of the electron if we know from experiments that the electron is point like?
Is there similarly a classical radius of the photon? The W and Z bosons?
| That wiki article itself provides the answer:
In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy - not taking quantum mechanics into account.
So since the the photon is massless, and uncharged (it d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34437",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Why do photons travel? Photons travel at the speed of light.
Is there a known explanation of this phenomenon, and if yes, what is it?
Edit:
To be clearer, my question is why do photons travel at all. Why do they have a speed?
| Kind of as an expansion on what drake said, this can be explained in several ways. For example:
In electromagnetism, we know that Maxwell's equations govern electromagnetic radiation. From Maxwell's equations you can derive the EM wave equation
$$\frac{\partial^2\vec{E}}{\partial x^2} = \frac{1}{c^2}\frac{\partial^2\ve... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34595",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Parity, how many dimensions to switch? Parity is described in Wikipedia as flipping of one dimension, or - in the special case of three dimensional physics - as flipping all of them.
Is there any simple rule that generalises both for any dimension? Like: "Flip an odd number of dimensions."?
| I think David is being a bit harsh, because I had to read the Wikipedia article a couple of times to see what they were getting at.
As the article states at the beginning, a parity transformation is the flip of a single spatial co-ordinate. In effect it's like looking in a mirror: when you look in a mirror your height ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34702",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is it intuitive that the conserved quantity from time symmetry is what we know as energy? Is there an easy (aka intuitive) way to understand that the conserved quantity from time translation symmetry is just what we call energy?
In other words, we use two definitions of energy. One is with Noethers theorem, and I've be... | Answer to your side question:
Energy conservation indeed follows from symmetry properties of Lagrangian. The first law of thermodynamics is a little more than energy conservation. It says that although the heat change $\delta Q$ in the system and the work done $\delta W$ on it are inexact differentials, their sum $dU$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34819",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 4,
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Why does heterodyne laser Doppler vibrometry require a modulating frequency shift? On the wikipedia article (and other texts such as Optical Inspections of Microsystems) for laser Doppler vibrometry, it states that a modulating frequency must be added such that the detector can measure the interference signal with freq... | To talk about heterodyne interferometry in your example you would need $f_1-f_2=f_0$, this is non-practical due to optical frequencies. If you utilize directly $f_0$ then we talk about homodyne detection.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34871",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Does the uncertainty principle apply to photons? Wikipedia claims the following:
More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons. Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate and, thus... | In addition to what was discussed already, and besides the fact the Schrödinger formalism is not relevant for photons, a good place to start in my view is in Roy Glauber's work (or some other introductory text to quantum optics). There, you'd see different uncertainties arising, such as between the photon number and p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34947",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
"answer_count": 4,
"answer_id": 0
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When do the von Neumann projections occur and what causes them? (Transferred as a separate question from comments in Scott Aaronson’s gravitational decoherence question)
Reversing gravitational decoherence
The modern answer seems to be that they never occur, and that therefore nothing causes them. This leads on (or ... | I think you might find a series of blog posts that I wrote recently useful. They also point to a paper that is available on arxiv and is currently in the review pipeline. See http://aquantumoftheory.wordpress.com
The posts specifically discuss how the collapse postulate with the Born rule can emerge from unitary quantu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35047",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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Time period of torsion oscillation For the oscillation of a torsion pendulum (a mechanical motion), the time period is given by
$T=2\pi\sqrt{\frac{I}{C}}$ which is a result of the angular acceleration $\alpha=\frac{d^2\theta}{dt^2}=-(\frac{C}{I})\theta$ where $C$ is the restoring couple of the string.
Do we relate $T=\... | There are lots of different examples of oscillatory systems that have essentially the same mathematical form. Let's start by just looking at one type of differential equation:
$a = \frac{d^2 x}{dt^2} = -\omega^2 x$
This equation has a general solution (you can check this)
$x(t) = A \sin (\omega t + \phi)$
which oscill... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35213",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
How can one prove that the number of images formed by the reflecting surfaces of two plane mirrors at right angles to each other is 3? How can one prove that the number of images formed by two plane mirrors at right angles to each other is 3?
Is there a mathematical proof for the same?
| Sticking to 2D for simplicity, the transformation matrices for reflections in the x = 0 and y = 0 lines are:
$$ R_x = \left( \begin{matrix} -1 & 0 \\ 0 & 1 \end{matrix} \right) $$
$$ R_y = \left( \begin{matrix} 1 & 0 \\ 0 & -1 \end{matrix} \right) $$
Any combination of these transformations can be given by $R_x^m R_y^n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35277",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 1
} |
Why does observation collapse the wave function? In one of the first lectures on QM we are always taught about Young's experiment and how particles behave either as waves or as particles depending on whether or not they are being observed. I want to know what about observation causes this change?
| An electron, indeed any particle, is neither a particle nor a wave. Describing the electron as a particle is a mathematical model that works well in some circumstances while describing it as a wave is a different mathematical model that works well in other circumstances. When you choose to do some calculation of the el... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35328",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "27",
"answer_count": 7,
"answer_id": 4
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