Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Are there other properties besides lower boiling point that make isobutane a better refrigerant than butane? Asked differently, if -1C is low enough for the application is there any reason not to use butane rather than isobutane as the working fluid in a refrigeration system?
| They have different pressure curves:
But to answer the question: yes, there are other properties that make isobutane preferred over n-butane. The most widely
used refrigerants in household appliances are isobutane and R134a according to "Evaluation of N-Butane as a Potential Refrigerant
for Household Compressors" by P... | {
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Red-shifting due to emitting gravitational waves Light waves exert their own gravitational pull and must be emitting gravitational waves, losing energy in the process. Does this mean that light becomes red-shifted as it travels even without the effects of universal expansion?
| This does not directly answer your question about redshift, but does clarify some points: Do photons and cosmic rays radiate energy through gravitational waves? If not, why not?. A key point here is that the photon must be accelerated for it to emit a gravitational wave, a photon simply travelling through empty space f... | {
"language": "en",
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Static temperature A Professor of Fluid Mechanics a told that the static temperature is the temperature observed when the relative speed between observer(thermometer) and fluid is zero.
I have trouble understanding as to how will the temperature of fluid depend on the reference frame since temperature is a quantity whi... | Moving fluid has kinetic energy which will be converted to internal energy if the flow changes. This is straight-up first law.
So you might consider air blowing through a venturi for instance; if you were to insert a thermometer at different points along the airflow, you would measure different temperatures as the airf... | {
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Equivalence between ghosts? Ok. I'm trying to get the terminology right about the term ghost in physics. Is there any equivalence between these terms?
*
*Faddeev-Popov ghosts
*Paul-Villars ghosts
*Landau ghost
*The vanishing Goldstone bosons in electroweak symmetry breaking
Does any of these terms encapsulates on... | All they have in common is being unphysical. Faddeev-Popov ghosts can't be observed as particles because they violate the spin-statistics tension; Pauli-Villars ghosts are negative-norm states; the Landau pole tells you your theory must give way to another at high energies; Goldstone ghosts represent an unphysical arte... | {
"language": "en",
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Does a charged particle travelling with uniform velocity induce a magnetic field? Does a charged particle, an electron say, travelling with uniform velocity induce a magnetic field? I believe it doesn't. In primary school, we all learned how to induce a magnetic field into an iron nail by wrapping coils of wire aroun... | A straight wire does have a magnetic field. It circles around the wire instead of going in a straight line like in a coil.
Picture source: http://coe.kean.edu/~afonarev/physics/magnetism/magnetism-el.htm
On the left is a straight wire with the magnetic field curling around it. The middle shows a single loop of wire. N... | {
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EM Plane wave, the changing electric field is in all directions right? I just want to confirm this, because this type of diagram seems pretty popular.
The electric field and magnetic field actually surround in all directions orthogonal to x axis, right? It is not just 2d pointing only in the y direction and z direction... | Yes, the fields are everywhere surrounding the direction of propagation. But it would be linearly polarized, in the same direction as the vectors in the figure. If one only draws the E-field vectors, it could be a representation like this: https://commons.wikimedia.org/wiki/File:Linear_Polarization_Linearly_Polarized_L... | {
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What would happen if Jupiter collided with the Sun? This question is inspired by a similar one asked on Quora. Let's say a wizard magicked Jupiter into the Sun, with or without high velocity. What happens?
The Quora question has two completely opposed answers: one saying "nothing much happens" and the other saying "the... | I would definitely lean towards "nothing" happening.
The "goes dark for 200 years" answer makes an awful lot of assumptions, some of which seem unfounded to me. In particular, it assumes that Jupiter will evenly spread over the surface of the sun, and will remain on top without mixing with the bulk of the sun.
At one o... | {
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AP physics 1 rotation problem could someone help me with this problem?
the correct answers are a and d. one issue i have with it is that i just don't understand what the problem is asking. like what spool? what table? i tried making some sense of the question and the answers, but i can only see d moving the wheel clo... | This question is written very poorly. I would recommend using a different source for questions unless this is one that your teacher is making you do.
I think that by "to the right" it means clockwise, although in physics we call clockwise rotation either "clockwise" or "negative", we don't use linear direction for rota... | {
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Could dark matters massive gravity create areas of slowly released expanding space left over from the big bang? I am not a physicist and apologize if this wastes anyone's time. I follow progress in most theoretical fields of physics and understand the premises but not how they are realised. The question I posed has bee... | *
*dark matter has not been directly observed, but its presence is implied by for example the gravitational effects that visible matter cannot cause
*mostly when observing galaxies, without dark matter they would fly away and not rotate
*dark matter makes up most of the mass in the universe, so to your question yes,... | {
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Will the weight of a man standing on a scale changes if he throws something straight up? If a man enclosed inside a chamber and the chamber is on a weighing scale and if he throws a ball straight up in air will the weight of the whole system changes or not? If yes, then what is the weight change at
1) just moments aft... | In order to throw the ball up in the air, you must apply a force to give the ball a greater acceleration then the downwards force from gravity. By Newtons third law, the ball will exert a force of equal magnitude and opposite direction on the person. So since you are giving the ball a force in the upwards direction, yo... | {
"language": "en",
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Is *Conservation of Distinction* a true conservation law in mainstream physics? Both Leonard Susskind and Francis Heylighen have written about the Conservation of Distinction but it seems Susskind more closely connects this (law?) with unitarity in quantum mechanics. Heylighen doesn't mention unitarity from what I've r... | Here's an article by Heylighen on this; it appears he's interested in theorising causality judging from the abstract:
Equal causes have equal effects is reformulated as a distinction conserving relation. Unpredictable, respectively irreversible processes are analysed as processes in which distinctions are created, res... | {
"language": "en",
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Stress in rotating 'rigid' body? I have some trouble understanding the rotating rigid body motion. Consider a cube made of very high elastic modulus homogeneous material (which can be approximated as 'rigid' body), it is rotating about axis-z with constant spin speed $\Omega$.
I wonder if the is internal stress or str... | The internal stress in the cube does exists - it keeps the cube from falling apart due to the rotation or, we can say, due to the centrifugal forces.
The diagram below shows a possible way to estimate the stress at any given point $P$ inside the cube.
The force (stress) acting on an infinitesimally narrow vertical sli... | {
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Is it possible to measure the number of spacetime dimensions? My question is pretty straightforward to be stated but I don't know whether the answer is as easily reported. It is remarkable and very interesting that Physics work in (almost) any number of spacetime dimensions, but is it possible to actually measure the d... | I think your hypothetical observer can be sure of the dimensionality of the space he occupies by figuring out the minimum number of measurements required to specify the location of an object relative to some fixed reference frame. I get 3.
This requires some assumptions about space being 'well-behaved.' It seems to be ... | {
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Can an electromagnetically induced dipole be explained with photon interactions? An incident electromagnetic wave will cause a dipole moment in the medium it passes through, displacing positive and negative charges in accordance with the EM field. How much of this interaction (if any) can be explained via the particle ... |
An incident electromagnetic wave will cause a dipole moment in the medium it passes through, displacing positive and negative charges in accordance with the EM field. How much of this interaction (if any) can be explained via the particle nature of light, i.e. photons?
This depends on the level of abstraction. At a h... | {
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Are avalanches caused by the shift from static to kinetic coefficient of friction? I was thinking about avalanches, and how they form, when it occurred to me to be quite likely that avalanches occur when a mass of snow gains enough momentum to push more snow through static friction into kinetic, gaining enough momentum... | My info on this comes from the book Snow sense: a guide to evaluating snow avalanche hazard, by Fredston and Fesler.
The physics of avalanches seems to be pretty complicated. Fredson and Fesler classify avalanches into four main types: "loose snow slides, slab avalanches, cornice collapses, and ice avalanches." They de... | {
"language": "en",
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Law of vector addition In one (Why is heat a scalar quantity?) of the questions I answered, I came across this:-
https://physics.stackexchange.com/a/404287/181020
or
A vector quantity should obey the law of vector addition.
But I don't think it is true. Consider a y junction circuit containing 3 identical wires. If i ... | Vectors do follow vector addition; your Y-junction is not a counterexample to this, because you're applying the concept of "addition" to vectors in different places, which is not what is meant by "vector addition".
Vector addition for current fluxes means this:
*
*Suppose you run a current i through a wire
*Keep th... | {
"language": "en",
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What is the difference between electrons and holes in silicon? Electrons and holes behave differently in a silicon semiconductor (e.g. mobility of holes is one order of magnitude smaller than that of electrons, the collection time of holes at the same electric field is larger than for electrons... ). I was wondering, i... | One qualitative way to understand this concept is by thinking about the orbital origins of the conduction band and valence band.
For example, let's assume the conduction band is primarily coming from hybridized $s$-orbitals, while the valence band comes from hybridized $p$-orbitals. As you might guess, particles in the... | {
"language": "en",
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How can a horizontally fired bullet reach the ground the same time a dropped bullet does? I studied projectile motion and now I know that we can treat each component of motion independently. Since gravitational acceleration acts on both a horizontally launched bullet and a vertically dropped bullet in free fall, they b... | Since I'm impatient I'll suggest one way you could be surprised: if
*
*You are comparing the carry time of a rifle bullet to a dropped bullet and
*The rifle sights have been zeroed in for non-trivial distances
then the barrel is not level when aimed at a target the same height at the firing point, but instead ... | {
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Time Evolution of a Maximally Entangled State My question is basically this:
Does a maximally entangled state stay maximally entangled under the time evolution?
Assume our Hilbert space is $\mathcal{H}_A \otimes \mathcal{H}_B$. At the time $t=0$, the states is $\rho_{AB}$ such that $\text{Tr}_A \rho_{AB}=\frac{1}{n_A... | General time evolution can generate a general, i.e., arbitrary, unitary transformation. This can map any quantum state to any other state. Thus, no state is special, including maximally entangled ones.
The situation is different if the Hamiltonian acts on the two parts separately. Then it creates a unitary evolution... | {
"language": "en",
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Reason for body attached to a string being in free fall? This is a question I found in a book:
A string is wrapped around a uniform cylinder as shown in diagram. When cylinder is released string unwraps without any slipping and the cylinder comes down.
I assumed that an equation $T - mg = ma$ could be formulated an... | The cylinder is not in free fall. It rolls down the string without slipping.
A cylinder which rolls without slipping down an inclined plane accelerates less than an identical cylinder which slides without rolling. In the same way the cylinder in your question accelerates less than an identical cylinder which slides do... | {
"language": "en",
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If the 3-Body force problem hasn't been solved, how do rocket scientists plan orbits of spacecraft? What methods would they use to predict what would happen in a situation when a probe is being acted upon by the gravity of two stars, say?
|
What methods would they use to predict what would happen in a situation when a probe is being acted upon by the gravity of two stars, say?
For that matter, what methods do they use to predict what would happen in a situation when a probe is being acted upon by the gravity of a single star plus eight planets, a large ... | {
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Change of wavefunction due to relativistic speed Imagine a spacecraft which is moving at a speed comparable to the speed of light relative to a reference frame with a hydrogen atom at it's origin. How would the probability distribution function of an electron in 1s orbit look relative to an observer inside the spacecra... | The Schroedinger equation is only invariant under galilean boosts. Under such a boost with velocity $v$ we have
$$
\psi(x,t) \mapsto \tilde \psi = e^{i(mvx- \frac 12 mv^2t)}\psi(x-vt).
$$
The extra phase factors are because seen form the moving frame the s-wave electron has an extra momentum $mV$ and extra energy $\fr... | {
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Why is $ \frac{\vec{r}}{r^3} = \frac{1}{r^2} $? I know it's surely a beginner's question but I don't see why you can write
\begin{align}
\frac{\vec{r}}{r^3} = \frac{1}{r^2}\cdot \frac{|\vec{r}|}{r}
\end{align}
Could someone explain it please? It would help understand quite a few things ...
| Another possibility is: being $\overline r= r\mathbf{\widehat r}$, then
$$\frac{\overline r}{r^3}=\frac{r\mathbf{\widehat r}}{r^3}=\frac{\not r\mathbf{\widehat r}}{r^{\not 3\,2}}=\frac{\mathbf{\widehat r}}{r^{2}}.$$
| {
"language": "en",
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Bragg Reflection While reading about the experiment of x-ray spectrum and Bragg reflection, I saw somewhere that it is more accurate to measure the crystal lattice constant when considering the largest measurable Bragg angle. That choosing this angle minimize the error in the calculation of the lattice parameter.
My qu... | The Bragg equation is $2d \sin \theta=n \lambda$, so you write
$d={n \lambda \over 2 \sin \theta}$
if you measure the angle $\theta$ you get a measurement of the lattice spacing $d$. You presumably know $\lambda$ very accurately so the uncertainty on the measurement of $d$ comes from the uncertainty on the measurement ... | {
"language": "en",
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Is there a charge buildup on elecrodes in DC glow discharge? In the figure below, direct current (DC) discharge occurs at and after some breakdown voltage, $V_{\text{breakdown}}\,,$ when the plasma pressure $P_{\text{plamsa}}$ is within a range observed to include $\left[0.01,\, 10\right]\,\mathrm{Torr}$, as electrons ... | For a small capacitance a small charge suffices to create a large voltage, since $V=Q/C$.
| {
"language": "en",
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Modifying the Bohr Model for Muonic Hydrogen I am trying to find the energy between the $n=2\leftrightarrow3$ transition for Muonic Hydrogen. My approach was to modify the Bohr model for standard hydrogen but taking the mass of the Muon $m_\mu\approx 207m_e$ instead of the mass of the electron $m_e$ and then substituti... | In order to obtain the energy levels of muonic hydrogen you can simply replace the reduced mass corresponding to the proton and electron with the reduced mass corresponding to the proton and the muon particle as you have already indicated.This should give you the correct Rydberg constant for the spectrum of this atom. ... | {
"language": "en",
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Why can a wave be expressed with a sine function? I see many expressions which express waves with the sine function like $y=\sin(kx-\omega t)$.
Waves really look similar to the shapes of a sine or cosine function, but does this guarantee that expressions that show wave-like movement are sine or cosine functions or is t... | There's no rule that waves have to be sinusoidal in nature. Some waves show different waveforms, and tonnes of waves aren't even continuous and hence aren't described by sine functions.
But it's useful to model most continuous waves in this manner because trigonometric functions are the easiest periodic functions (easi... | {
"language": "en",
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What are the physical conditions for general ohms law? A problem presents Ohm's law as $$\vec{J}=\sigma \vec{E}$$ where $\sigma$ is the conductivity given by a scalar. The problem asks what physical conditions must be satisfied for the equation to hold.
I understand that the material must be isotropic for the conductiv... | The most general form of the ohm law would be $J_i = \sigma_{ij}(x) E_j$. In the most general case, the conductivity is a tensor that depends on the position. Note that in the most general case, $J$ and $E$ are not parallel.
If the material is isotropic, then $J$ and $E$ are parallel and $\sigma$ is just a scalar func... | {
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Help with D. Tong example on Noether in QFT In this lectures, example 1.3.2 on page 14 concludes that the Noether current is
But how can the current be a two index object when it is defined in eq. (1.38), which is
as a one index object? If I apply the formula I obtain something of the form $j^\mu$. Can someone mak... | I think it is explained somewhat in David Tong's notes.
The symmetry under consideration is spacetime translation in a direction $\varepsilon^\mu$. For example, $\varepsilon^\mu=(1,0,0,0)^\mu$ would be the time translation symmetry. To draw an analogy with David Tong's notes, $\epsilon^\mu=\lambda \varepsilon^\mu$ woul... | {
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Sound Relationships Whats the relationship between amplitude, volume, and wave energy. I have tried many websites but none have helped me yet and I believe maybe someone on here can help me.
| The Intensity is the power delivered by a wave per unit area.
It is proportional to the square of the amplitude of the wave.
The Loudness, is measured in decibels as a relative intensity, L = 23.03 ln(I/Io)
The energy in terms of the intensity is,
E = IAt
(by the definition of intensity.)
If you were looking for equati... | {
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Connecting a charged capacitor to an uncharged capacitor
I was attending a lecture about capacitors and something confused me.
If I charge a capacitor using a DC supply, the capacitor will gain charge $Q_0$.
Now, if I discharged it along an uncharged capacitor in this arrangement, according to the lecture notes, the c... | What you suggest would be true if the upper component were a battery, which maintains a certain definite voltage and can act as a supplier of charge. But a capacitor has only a finite charge, here $Q$, and as it flows off to the other capacitor it is not replenished.
The usual confusion with this particular circuit is ... | {
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Is the equation of motion for a spring-damper system the same whether oriented upward or downward? So every spring-damper system I've found online has the equation of motion:
$$mx''+cx'+kx=0$$
I can understand how this is derived when downwards is positive, but what about when upwards is positive? Wouldn't it be
$$mx... | Yes.
This is because your 2nd equation should read as
$$ -mx''-cx'-kx=0 $$
since the sense where positive $x$ is has switched. This means a sign change for $x$, $x'$ and $x''$.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Potential due to line charge Is it possible to calculate the electric potential at a point due to an infinite line charge? Because potential is defined with respect to infinity.
| It is possible. Electrosatic potential is just a scalar field whose negative gradient is the electric field. Due to this defintion it is indeterminate to the extent of an additive constant. (if you increase it everywhere equally, its slope remains the same everywhere) Only the potential difference between two points is... | {
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Earthing a system of parallel plates our sir has taught us that when in a system of conducting infinite plates kept parallel to each other, when any one of them is earthed, then the charges present on the free ends(i.e. the open sides of the parallel plates at the 2 ends) will become zero!
Say we have 3 infinite condu... | It happens to minimize the energy content of the system.
The electric field stores energy in the form of electrostatic potential energy. Remember, you have to do work to bring the system in the state explained in question. This work is stored as energy (1st law of thermodynamics). Earthing opens the path to redistribut... | {
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Energy of massless particles with the example of Magnon Consider this situation.
I am told that: at low temperatures magnons, the elementary excitations of a ferromagnetic ground state, can be treated as a gas of non-interacting, massless, spin-0 bosons with a dispersion relation $ω$ = $α$$k^2$ where $α$ is a constant.... | The relation $E = pc$ for massless particles comes from Lorentz invariance, specifically by requiring that the "length" of the 4-momentum, $E^2 - (pc)^2$ should be the same in all reference frames. Therefore, it only holds for fundamental particles, which magnons are not. Magnons do not occur in vacuum, they occur in s... | {
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Is presure inversely related to velocity? .
I’m not sure if that picture worked or not but it’s a question from my textbook that was asking what factors would cause velocity of blood in an artery to decrease. It says in the answer at the bottom that apparently a lower pressure would
Cause this, but I thought pressure ... | The Bernoulli equation uses the energy of the fluid before and after traveling through different cross sectional areas. This is a link to a good explanation of the principle. In general, when a fluid's speed increases, its pressure decreases, that's why planes can fly so well, the lower pressure, faster moving air abov... | {
"language": "en",
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Time evolution of momentum wave function when initial position wave function is in an eigenstate (i.e., a delta function of position) In The Dirac-delta function as an initial state for the quantum free particle,
Emilio Pisanty
states that if an object's position wave function, $\Psi(x,0)$, is a delta function (at $t =... | What you have is a free particle propagator (also called Green's function of the free particle Hamiltonian). This is an auxiliary mathematical concept to express time evolution of a general normalizable $\psi$ function. But propagator itself is not a normalized $\psi$ function, the usual theorems valid for normalized $... | {
"language": "en",
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Data - Monte Carlo Correction techninques in Particle physics It is said that the data does not always match with the Monte Carlo simulations in particle physics.(I guess even in the Higgs to gamma gamma channel, the peak in real data was at about 127GeV and thus it was corrected) .Thus,I wished to know what are the di... | If certain distributions of variables don't agree, then you can reweight the MC sample to match data (typically either using a nice clean control sample or s-weighted signal). There are a variety of reweighting techniques e.g. histograms, kernel-density estimators, boosted decision trees.
If resolution doesn't agree, y... | {
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Meaning of crystal orientation If I have a crystal, say (001)-oriented ABO3, what does the 001 imply, from an experimental perspective? I understand that the 001 is referring to a plane as described by Miller indices, but what is it about this plane that is relevant? Is it that this plane is the same plane as the surfa... | It depends on context. In a surface science experiment, it would be the surface. In experiments on bulk properties, the surface could be irrelevant and rough, but one would measure some property along a cubic axis (or maybe paricularly along the c-axis), like velocity of sound or conductivity, etc.
| {
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$\phi\phi\to\phi\phi$ scattering in $\phi^4$-theory and Feynman diagrams at the tree-level What are the tree-level Feynman diagrams for $\phi\phi\to\phi\phi$ scattering in $\phi^4$-theory? I know that there are four diagrams at tree-level (zero loop). But each diagram is considered only once. Why is that? There are one... | Consideration of correlation functions in an interacting QFT (i.e one in which you wish to describe a scattering event) means you can neglect disconnected diagrams order by order in the perturbative expansion. Formally, this amounts to a generating functional with connected diagrams 'exponentiated' but that is a detail... | {
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How strict are the boundaries that divide dimensions? Is a single-layer sheet of graphene 2D or 3D? I would like to know if there is any theory that describes a set of rules that define the boundaries of dimensions.
For example, does a single layer sheet made of graphene considered a two or a three dimensional object?
... | As others have pointed out, even a single atom exists in three dimensions. However, there's an alternative, and mathematically rigorous, sense in which you should regard a sheet of graphene (or two sheets of stacked graphene, or four sheets of stacked graphene) as 2D.
In condensed matter, one is often interested in the... | {
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Phase Transitions (Statistical Mechanics) Book Recommendation I am Studying Phase Transitions, starting from simple VdW equation up to Mean-Field&Landau Theory. I have many books such as Huang Kerson-Statistical mechanics, Yeomans- Statistical Mechanics of phase Transitions, Lubensky, Kardar and they've covered me so f... | The statistical physics book by Linda Reichl is easy to read and has some of the advanced material. A good complement for the renormalization aspect are Goldenfeld's Lectures On Phase Transitions And The Renormalization Group.
| {
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Why does plasmon have higher erngy than phonon? In my mind plasmon is movement of electrons and phonon is movement of atoms in an lattice. movement of atoms should have a large energy because atom is larger.
| The phonon describes the vibrational motion in a solid.
The plasmon is a quasi particle, describing the plasma oscillation.
These quantized excitations have different energy levels, phonons in the meV range, and plasmon in the eV.
As you write you are wrong, because phonons energy is 3 orders of magnitude higher.
The d... | {
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If there is friction and everything stops on earth why does earth not stop due to friction? Why do planets revolve around the Sun if there is a force called frictional force? Why do planets not stop rotating while the objects in motion stop after a while? Why are they continuously moving? Why are planets not affected b... | The answers here seem to address all but one of the questions -- Why do planets not stop rotating while the objects in motion stop after a while?
Note that there is no net external torque on the planet, at least not due to friction inside it, and hence its angular momentum is conserved. So long as the shape of the plan... | {
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Which pole will electrons flow towards in a changing magnetic field (generator) In a generator a magnet spins in the middle of a coil of wire and the changing magnetic field causes current to flow, but the current changes direction whenever fields from a new pole of the magnet cross a point on the wire, so will the cur... | (a) "when you use current to magnetize something the north end of the magnet is the end that was negative" I'm afraid that this suggests a misunderstanding. The direction of magnetisation is determined by the direction of current around the coil, not along its length. You need to consult a textbook and learn about the ... | {
"language": "en",
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Energy conservation on expanding universe Due to the expansion of the universe, the photons emitted by the stars suffer redshift, Its mean that the energy is lowered a little bit. Does this mean that the energy is lost? Does the expansion of the universe violate some conservation principles according to Noether's theor... | Actually it is possible to speak of energy conservation in curved spacetime in the presence of a timelike Killing vector $K$, since the contraction of it with the stress energy tensor is a conserved current from Killing equation and symmetry of $T^{ab}$:
$$\nabla_a (K_bT^{ab}) =(\nabla_a K_b) T^{ab} + K_b \nabla_aT^{ab... | {
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Electron Microscopy: Are photons smaller than electrons? So, I'm told that electron microscopy provides greater resolution than traditional photo/optical (i.e. visible light) microscopy, due to the (ahem) "fact" that "electrons are physically smaller than photons".. Which I'm pretty sure is not necessarily true, (or st... | Here is a basic overview- experts are invited to add detail.
Subatomic particles like electrons actually possess a wavelength that is related to their energy, even though they behave most of the time like tiny point particles and not like waves. By accelerating a beam of electrons to very high energies, their waveleng... | {
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Should we take the elevator instead of the stairs to save energy? In our university there's a posted sign that encourages students to take the stairs instead of the elevator to save the university electricity during the hot NYC summers.
When you climb the stairs you generate something like 8x your mechanical energy in ... | Accepting that climbing stairs generates heat equal to 7 times the mechanical energy (one part goes into you lifting yourself), how much energy does it take to remove that heat?
The 2nd Law of Thermodynamics says the best you can do is
$W = Q \frac {T_h - T_c}{T_c} \sim Q \frac{\Delta T}{T}$
Where $\Delta T$ is the dif... | {
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Trying to check current conservation under symmetry transformation
Consider a simple scalar field and its Lagrangian $L=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi$. Then say you have the following transformation
$$x^{\mu}\rightarrow e^{\omega}x^{\mu},\tag{1}$$
$$\phi\left(x\right)\rightarrow e^{-\omega}\phi\left(... | Why did you write $\frac{\partial L}{\partial (\partial_\mu\phi)}=-\phi\partial^\mu\phi$?
It should be $=\partial^\mu\phi$.
update: everthing's correct, $\partial_\mu\phi\partial^\mu\phi$ vanishes because it is equal to $\partial_\mu\partial^\mu\phi$ up to a surface term. Whenever equation of motion is satisfied ($\pa... | {
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Will wind blowing perpendicular to the path of motorbike, topple a slow moving bike or fast moving bike? So, I am riding a Motorbike on a windy day.
I am traveling from North to South and winds were blowing from East to west.
Should I drive slow or fast to avoid getting toppled down by the winds?
Also, is there a way t... | High speed makes a bike more stable whether you deal with a wind or with other disturbances.
One of the factors is a gyroscoping effect of the wheels: the greater the speed, the more difficult it is to change the orientation of the wheels and therefore of the bike.
Another factor is the ease of correction. If, due to ... | {
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Does the fact that $j^\mu$ is a 4-vector imply $A^\mu$ is, as argued by Feynman? Let
\begin{equation}
\boldsymbol{\Phi}=\Bigl(\dfrac{\phi}{c},\mathbf{A}\Bigr)
\tag{01}
\end{equation}
the electromagnetic 4-potential. We know that if its 4-divergence is zero
\begin{equation}
\dfrac{1}{c^{2}}\dfrac{\partial \phi}{\partia... |
under these conditions is the 4-potential a 4-vector ??? I ask for a proof or a reference (link,paper,textbook etc) with a proof.
No, not necessarily.
It is convenient to choose it as a 4-vector in relativistic theory.
But Maxwell's equations together with the Lorenz constraint do not imply that 4-tuple $(\varphi/c,... | {
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Trying to prove the Hadamard gate leaves a state unchanged It is known that the Hadamard gate is the equivalent of doing a 180 degree rotation about the x + z axis.
I am therefore trying to prove that applying the gate on the state cos pi/8 |0> + sin pi/8 |1>, which lies on the x + z axis unchanged.
So, on applying the... | Note that
$$\sin(x\pm\pi/4)=\frac{1}{\sqrt2}(\sin x\pm\cos x).$$
It follows that
\begin{align}\cos(\pi/8)+\sin(\pi/8) &= \sqrt2 \sin(3\pi/8), \\
\cos(\pi/8)-\sin(\pi/8) &= \sqrt2 \sin(\pi/8).
\end{align}
You should be able to reach the conclusion from here.
| {
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Can we (in principle) obtain molecular bound systems by modelling fundamental particles and their interactions? Is it possible, at least in principle, to start with the Schrodinger/Dirac/Klein-Gordon equations to model elementary particles and their interactions and to obtain in the end molecular bound systems? In othe... | Yes, but due to the difference in time and space scales, we have specific models for specific problems to model. Some examples are: First principles modelling (ab-initio approaches), DFT, molecular dynamics; the first two start with Schrodinger's equations and work their way up, molecular dynamics is used in bigger sys... | {
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Why is linear momentum not conserved for a particle in a central force? I am studying a two-body central force system in which the two particles, one of mass $m$ and one of mass $M$, experience a force directed along the line connecting the two particles.
We can reduce this to a system of just one fictitious particle ... | Suppose that I know that $p$ is conserved and $q$ is not. Now suppose I define the new variable
$$p' = p + q.$$
If you weren't paying attention, you might conclude that $p'$ is also conserved, because it has the same letter as the conserved quantity $p$. But that's clearly wrong. The similarity is just superficial. Not... | {
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Finding the equation of a chain hanging between two points Say I have a connected at either end to two points, $A(x_A, y_A)$ and $B(x_B, y_B)$ of length $l$, where $l \leq \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}$, how would I go about finding an equation of its shape?
I guess the chain would be of the form $y = \alpha \c... | The general shape is
$$ y(x) = y_c + a \left( \cosh \left( \frac{x-x_c}{a} \right)-1 \right) $$
where $(x_c,y_c)$ is the lowest point on the curve (sag point) and $a = \frac{H}{w}$ is the catenary constant. Here $H$ is the horizontal tension shared along the cable, and $w$ is the unit weight (that is weight over length... | {
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Sign of work done by friction In Goldstein's classical mechanics (3rd ed.) we read:
"The independence of W12 on
the particular path implies that the work done around such a closed circuit is zero,i.e.
$$\oint \textbf{F}.d\textbf{s}$$
Physically it is clear that a system cannot be conservative if friction or othe... | Perhaps I misunderstand the context of Goldstein's writing, but work due to friction should be negative:
Friction always acts antiparallel to the displacement/velocity. So, when computing work from friction, drag, etc, you find that
$$ W = \oint \mathbf{F} \cdot d\mathbf{r} = \oint (F\cos\theta) dr, $$
where $\theta$ i... | {
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Is there an intuitive reason as to why there is no phase transition to get to a degenerate Fermi gas? Cooling a bosonic gas leads to a phase transition into the Bose-Einstein condesate. This is characterised by a symmetry broken ( U(1), by choosing a specific phase for the macroscopic wavefunction) and by discountinuou... | In terms of phase transitions, interactions are the main source of intuition. You can imagine a collective field which biases the order parameter. For non-interacting bosons, the collective field is coming from the statistics instead of an interaction (an energy). Thus, it’s hard to identify the collective field as ... | {
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Interaction of Magnetic field with light Can there be any interaction of a varying magnetic field with light? (Please explain using electromagnetic waves as both are)
(Say we have an alternating current of 60Hz and He-Ne laser (632.8 nm wavelength)
What all different kinds of interaction may happen? In free space or i... | If you've wanted to mean the change of direction of the light beam by the word 'interaction' ,then the answer is no, because a photon of a light ray goes with a very high speed so if there will be a varying magnetic field then the work done by that varying magnetic field will be 0.
| {
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"source": "stackexchange",
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Do the ladder operators $a$ and $a^\dagger$ form a complete algebra basis? It is easy to construct any operator (in continuous variables) using the set of operators $$\{|\ell\rangle\langle m |\},$$ where $l$ and $m$ are integers and the operators are represented in the Fock basis, i.e any operator $\hat M$ can be writt... | @Accidental reminds you this is a theorem. To actually see it in your terms, use the infinite matrix representation of $a, \quad a^\dagger$ of Messiah's classic QM, v 1, ChXII, § 5. Specifically, your vacuum projection operator has a 1 in the 1,1 entry and zeros everywhere else.
The operator you chose is freaky to re... | {
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Misunderstanding of the functioning of the reflective diffraction grating Suppose we have a sawtooth diffraction grating, as depicted below:
where the angle $\beta$ is the angle of inclination of the 'teeth' of the grating with respect to the plane of the grating and incident plane monochromatic waves normal to the pl... |
shouldn't the two parallel incident waves (incident at an angle β )
be simply reflected from the face of the 'saw-tooth' at exactly the
same angle, in accordance with the law of reflection?
This is a useful approximation of what actually happens, but in reality the behavior of light is a little more complicated.... | {
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Why do scientists think that all the laws of physics that apply in our galaxy apply in other galaxies? I like watching different videos about space. I keep seeing all these videos saying scientists found so and so at 200 billion light years away or this happened 13 billion years ago.
My question is why do scientists t... |
What if, say at 135 billion light years away, all of a sudden the time space relationship changes drastically.
Well, it could.
Science is built on reasonable, well-founded assumptions, and a good scientist is open to the possibility of those assumptions being broken at some point in the future when more data becomes ... | {
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How come I can kick a football further when it's moving towards me? If a ball is moving towards me, I can kick it further than if I were to kick it if it was stationary. But surely if the ball is moving in the opposite direction, it should take more force to kick it the same distance as I am accounting for the initial ... | If a ball is moving toward you it will exert a force on you.If you kick it in opposite direction of its its inital direction it will require more force for same distance in case it was moving away from you.You hit it.Now the ball will cover same distance with less force than first case as by now there is already a forc... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Hose pressure when the valve is closed To add to the interesting threads on hoses, here's one from someone with no physics knowledge. Please be patient with this basic question!
If you open your hose valve and press the trigger on the nozzle of the hoze, I understand that thanks to the pressure of gravity from the wate... | Water escapes at great velocity briefly.
Hoses are elastic. Some stretch more, some less, but that elastic stretch keeps the original pressure in the hose until you open the outlet. The force due to elastic hose then pushes out water, initially at the same pressure hence same high speed.
But water is leaving the hose,... | {
"language": "en",
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Is potential Difference Really a Measure of Electromotive force? If I separate some amount of positive and negative charge a certain distance I will create some voltage. If I then separate the same amount of positive and negative charge a longer distance I will create an even bigger voltage since more work would've bee... | The electric field is a measure of the "push" acting on an electric charge. The voltage (aka electrical potential) is a measure of the energy required to move an electric charge from one location to another location in an electric field. There is an analogy with gravity: the gravitational field at your location is a me... | {
"language": "en",
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How is a quantum gate constructed in the real world? I've been reading a lot about quantum mechanics and arrived at entanglement. I understand these things and I understand how to perform computation on qbits if they are represented as vectors and the transformations as matrices.
However I have not seen any physics ab... | The specific details about how to apply quantum gates depend on the system you are looking at. For example, in a photonic system, you could apply some gates by beam splitters, polarizers, mirrors, waveplates and $\cdots$ . Or in spin systems you can tune the Hamiltonian of the system by changing the electric and magnet... | {
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Definition of an operator in quantum mechanics In J.J. Sakurai's Modern Quantum Mechanics, the same operator $X$ acts on both, elements of the ket space and the bra space to produce elements of the ket and bra space, respectively. Mathematically, an operator is simply a map between two spaces.
So, how can the same op... | The action (to the right) on the ket space naturally induces an action (to the left) on the bra space. The bra space is the dual space of the ket space (that is the space of linear functionals over the kets). We can simply define $\left< \psi \right| X$ by its action on kets (or, since it's linear, on a basis of ket sp... | {
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What's the reaction force on a charge moving in a magnetic field? According to newtons third law, all forces occur in pairs. What is the reaction force that the third law predicts when a magnetic force acts on a charged particle moving in a magnetic field?
| It is induced emf.
According to Lenz's law, in a magnetic field as flux linked with the object changes ,an emf is induced in it such that it opposes its very own cause.
Mag. Flux = B.A
emf=-change in flux/time
Example: Suppose you move a magnet with its north pole ahead through a single turn coil from left to right. T... | {
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How do fusion reactors deal with blackbody radiation? The plasma of the ITER reactor is planned to be at 150 million K. Using the Stefan-Boltzmann law, setting the surface area as $1000\,\mathrm{m}^2$ (the plasma volume is $840\,\mathrm{m}^{3}$ so this is being generous), and the emissivity as $0.00001$ (emissivity is ... | The plasma in a fusion reactor is typically "optically thin"; the radiation isn't really in equilibrium with itself and the plasma particles.
Generally, instead of just modeling the plasma as a black body, people look at specific radiation processes. Kenneth Gentle (UT) has a nice set of slides that works through that.... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What does vector addition of voltages mean? So I was studying LCR Circuits in Alternating Current and I found something pretty weird. We are treating the voltage as a vector (phasor) and then vectorially adding them to get the net voltage.
But this thing doesn't make sense to me: What does it mean to add voltages whic... | If you have an LCR series circuit connected to an alternating voltage supply then at an instant of time the current through each component in the circuit is the same and the variation of current with time is represented by the top graph in the diagram below.
The addition of voltages in the circuit is complicated th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Weird Reflection Pattern in Reading Glasses While fidgeting with a pair of reading glasses, I noticed a strange reflection pattern (shown in video and photo).
I would appreciate it if anyone that knows more about this could help me figure out why there were eight dots in the reflection instead of four, and why there we... | The colors are due to antireflection and/or anti-abrasion coatings on the lenses. The doubling of each light image is due to internal reflection from the lens surfaces. The 3D effect is due to the fact that the lens surfaces are curved. If you look at the reflection of a light in a Christmas tree ball, you will see ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electron Splitting in Peskin and Schroeder I am confused by formula (17.88) and (17.89) on page 578 in P&S. They are computing the matrix element for electron splitting ($e^-\rightarrow e^-+\gamma$) in the massless limit.
They call $z$ the fraction of energy of the initial electron that is carried off by the photon an... | A left-handed electron moving the 3 direction has the 2-component spinor (0,1), and a left-handed photon moving in the 3 direction has the polarization vector $\epsilon^* = \frac{(1,i, 0)}{\sqrt{2}}$. However, in this problem, the outgoing electron and photon are not moving exactly in the 3 direction. They are moving... | {
"language": "en",
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Physical intuition behind Poincaré–Bendixson theorem The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour can only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that canno... | An important characteristics of chaotic dynamics is that they are recurring, i.e., any trajectory will eventually come arbitrarily close to its starting point.
Suppose there is a chaotic dynamics with continuous time in a two-dimensional phase space. Let’s look at the trajectory starting from some point A. Since the dy... | {
"language": "en",
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Do gravitational waves lose energy through interaction with i.e. matter or magnetic fields? Gravitational waves dilute while traversing space like any other radiation, and their amplitudes are proportional to r-2, that's a basic. But do they lose energy while traversing through matter or something else (i.e. space with... | Your question is very original, and I have never seen it addressed, so here are my own hastily prepared thoughts on the matter. Caveat lector.
You can gain some insight into the fate of gravitational waves by pursuing the analogy with electromagnetic waves, which get both scattered and absorbed. EM waves get scatter... | {
"language": "en",
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can heat radiate from a cold to hot body? if you have 2 bodies (A,B), with Temperature of B>A, can you have heat transfer from A to B through radiation?
In particular if A reflects the wavelengths that B is emitting the radiation at would this be possible?
And if so is this process independent of the temperature of B... | Yes, some times it is possible
This is happening in refrigerator.
In this case some energy must be supplied to complete this transaction
| {
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"source": "stackexchange",
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When will velocity and acceleration vectors be perpendicular?
Suppose a particle is moving in the $xy$ plane with
$$x=at, \quad y=at(1-bt),$$
where $a$ and $b$ are positive constants. When will the velocity vector and acceleration vector be perpendicular?
I know that these vectors are perpendicular in circular mo... | Another approach uses $v\cdot a=\frac{d}{dt}(v^2/2)$, so orthogonality is equivalent to $v^2=\dot{x}^2+\dot{y}^2=a^2+(a-2abt)^2$ being constant. This is equivalent to $a=0$ or $b=0$.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why are photo electrons emitted instantly from metal surface just nanoseconds after the light falls upon it? Why are photo electrons emitted instantly from metal surface just nanoseconds after the light falls upon it? How does the quantum theory of radiation explain it? Why can't classical physics explain this?
| According to quantum mechanics
The energy is transmitted by photon to electrons by the collision between the two. Only those photons can eject electrons which have energy more than or equal to a minimum required energy (threshold energy). Since energy is transferred in a lump, the ejection is instantaneous.
According t... | {
"language": "en",
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"source": "stackexchange",
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Why is a fermion field complex? The Lagrangian of a fermion field is
\begin{equation}
\mathcal{L} = \overline{\psi} (i\gamma_{\mu} \partial^{\mu} - m)\psi
\end{equation}
It is said that the fermion field $\psi$ is necessarily complex because of the Dirac structure. I don't quite understand this. Why is the fermion fiel... | Any type of field can be complex, not only the fermions. The reason is the $U(1)_{EM}$ symmetry, i.e., the electromagnetic interactions.
The electric charge is the conserved quantity of the $U(1)_{EM}$ gauge symmetry in nature. A transformation of this symmetry is such that
$$
\phi(x) \mapsto e^{iq\theta (x)} \phi (x) ... | {
"language": "en",
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Why does this paper use 1/cm for units of frequency? Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency.
Here is an excerpt:
It doesn't seem like wave number, as they clearly call it frequency. What's going on here?
$^*$ Sievers III, A. J., and M. Tinkham. "Far infrared antiferromagnetic reso... | People working in the infrared or optical region tend to sometimes, depending on what school of thought they come from, use a unit called wavenumber, which is the reciprocal wavelength in centimeters, $\frac{1}{\lambda_{centimeter}}$.
This is still a frequency, but instead of oscillations per second, it is oscillations... | {
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Why does an atom in an oscillating electric field behave like an electric dipole? How can I understand that an atom subjected to an oscillating electric field (e.g., $\vec{E}=\hat{i} E_0\cos\omega t$) behaves like an oscillating electric dipole? What is the underlying picture that comes out of the quantum mechanical de... | Well, let’s start with a static electric field: the electrons would move in the opposite direction of it and the nucleus in the same direction. But the nucleus’ and the electrons’ attractive force counteracts this process, thus forming a (steady) dipole.
I know, the picture I painted is very classical, but that’s suffi... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is a current carrying loop considered a dipole? I am unable to understand why a current carrying loop is considered a dipole. Why exactly is it called a "dipole", which two poles are we referring to and how do those two poles function as the north and south pole of a magnet?
| A long way away from the current loop, compared with its characteristic linear dimension (for example its diameter) the magnetic field, $\vec{B}$, follows an inverse cube law and is exactly the same in magnitude and direction as the field due to a small dipole (of suitable strength and orientation) whose poles give ris... | {
"language": "en",
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"source": "stackexchange",
"question_score": "4",
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$SO(3)$, orbital angular momentum, vector product I have a big confusion with group theory terminology. I know that orbital angular momentum (OAM) is $\mathrm{SO}(3)$-symmetric in 3D-space. Let's define QM orbital angular momentum (OAM) conventionally:
$$\pmb{L} = -i \pmb{r} \times \pmb{\nabla}$$
This definition can al... | I don't know if I've understood your question well. The math may be too complicated for me, but the ideas are
*
*The usual definition of OAM satisfies the conmutation rule
$$\left[\frac{L_x}{\hbar}, \frac{L_y}{\hbar}\right]=i \frac{L_z}{\hbar}$$
*This means that they are infinitesimal generators of rotations in ... | {
"language": "en",
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Suppose the speed of individual photons reduced over time. Would that explain the apparent speeding up of distant galaxies? The observation that distant galaxies seem to be speeding up has led to the theory of dark energy.
However if the speed of individual photons actually reduced over ( very long ) periods of time wo... | I think we define distance by light signals, so perhaps the answer is yes, and perhaps the two are in a way equivalent.
On the other hand, the CMB shows us that the size of the fluctuations on the celestial sphere have stretched since the CMB was released. According to what you are saying, while the photons would indee... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What allows dividing equations in 1D finite potential well? So I was reading the lecture notes of 8.04 at MIT on the classic finite potential well problem of QM, until I reach this part in page 8:
Let us finally complete the construction. We must impose the continuity of the wavefunction and the continuity of $\psi'$ ... | You're not dividing by zero, so it's fine. The cosine may not obviously be non-zero, but it's equated to an exponential, which obviously is non-zero.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How does tilting a bike make it turn sharper? Note that my question is not why do you tilt your bike when on a curve. It's about the reduction in turning radius when one tilts the bike inwards.
Short to-the-point answers are welcome.
| There is an effect is due to geometry.
Turn the front wheel of a bike to the left by thirty degrees, say.
Now lean the bike into the turn.
For simplicity, suppose that you could lean the bike completely on its side while the tires maintain contact with the ground.
Having done so you will find that the turning radius... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/419353",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "52",
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What does it mean if the dot product of two vectors is negative? If the dot product gives only magnitude, then how can it be negative?
For example, in this calculation:
$$W = \vec{F}\cdot\vec{r} = Fr\cos\theta = (12\ \mathrm{N})(2.0\ \mathrm{m})(\cos 180^\circ) = -24\ \mathrm{N\,m} = -24\ \mathrm{J}$$
Why is there a ne... | $$W = \vec{F}\cdot\vec{r} = Fr\cos\theta$$
So this is negative when $\frac{\pi}{2}<\theta<\frac{3\pi}{2}$.
It's telling you that the two vectors are pointing in more or less the opposite direction. Or more precisely, if you projected $\vec{F}$ onto $\vec{r}$, the projection would be in the opposite direction from $\vec... | {
"language": "en",
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DBI action expansion for non-abelian brane worldvolume I am trying to reproduce the results of the (famous) Myer's paper "Dielectric Branes" https://arxiv.org/abs/hep-th/9910053. In eq (33),
when he expands the determinant factor for a flat-space background, there is a 1/4 in the first term that, says me, should be 1/... | Hint: If we write
$$ Q^i{}_j ~=~\delta^i_j -C^i{}_j\qquad\Leftrightarrow\qquad Q~=~{\bf 1} -C , \tag{A}$$
then
$$\ln \det Q ~=~ {\rm tr}\ln Q~\stackrel{(A)}{=}~{\rm tr}\ln ({\bf 1} -C)~=~-\sum_{n=1}^{\infty}\frac{1}{n}{\rm tr}(C^n)~=~-\underbrace{{\rm tr}(C)}_{ = 0 } -\frac{1}{2}{\rm tr}(C^2) + {\cal O}(C^3),\tag{B}
$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/419877",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does $\Lambda^{-1}_{\frac{1}{2}}\gamma^\mu\Lambda_{\frac{1}{2}}=\Lambda^\mu_{\phantom{\mu}\nu}\gamma^\nu$ mean? \begin{equation}
\Lambda^{-1}_{\frac{1}{2}}\gamma^\mu\Lambda_{\frac{1}{2}}=\Lambda^\mu_{\phantom{\mu}\nu}\gamma^\nu
\end{equation}
In P&S, p. 42:
Equation (3.29) says that the $\gamma$ matrices are inva... | This is just an example of an important property of the GL(N) Lie Group tensor operators. It means that the tensor operator $\gamma^{\mu}$ transforms like a 4-vector under conjugation.
Please see my answer to "Do the Dirac matrices form a proper four-vector?" which might have been better posted here.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/419977",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 2
} |
Is general relativity about Lorentzian manifolds only? General relativity is often used in context of Lorentzian manifolds. But the texts which describe Einstein Field Equations discuss them in context of general pseudo-Riemannian manifolds.
It seems natural that general relativity be restricted to Lorentzian manifolds... | The spacetime in general relativity is defined as an $n$-dimensional Lorentzian manifold. Lorentzian manifolds are a type of pseudo-Riemannian manifold (Since they are manifolds of signature $(p,q)$, a Lorentzian manifold is just a pseudo-Riemannian manifold with $p = 1$), which is why you find the term occasionally in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/420162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Euler equations in primitive form for a real gas For an ideal gas, it is relatively easy to express the Euler equations in primitive form (variables $\rho$, $u$, $p$), starting from their expression in conservative variables ($\rho$, $\rho u$, $E$).
I did not find any example of such derivation for a general real gas, ... | Yes it can always be done. I assume you can write the general case in conservation form. so you already have one primitive variable, Then
$$u_t=\rho^{-1}((\rho u)_t-u\rho_t)$$
and$$i_t=\rho^{-1}[(\rho i+\rho u^2/2)_t-(i+u^2/2)\rho_t-\rho uu_t]$$
where i is specific internal energy. Generalization to more dimensions is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/420291",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why $\rm Pt$-$\rm Ir$ Alloy or Tungsten is used for the tip in scanning tunneling microscopy? Just want to know the properties which qualify these materials to be used as the same.
| For topography scanning purposes, especially for an undergrad experiment the pre-requisites are the robustness and stability in ambient conditions. Both PtIr and W make hard, and, with quite some practice, sharp tips which are ideal for STM.
Moreover, W tips, when chemically etched are the go-to in most STM labs [1].
[... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/420527",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
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does tension in the string affect its equilibrium? In my textbook (Sears and Zemansky's University Physics), it is written that the vector sum of the forces on the rope is zero, however the tension is 50 N. Then is tension different than the force? And if not, then why force is zero while tension is not?
A body that h... | Assuming the block isn’t accelerating, the sum of the external forces on the rope is zero. But tension is an internal force. You know it exists because if you cut the rope the Mason will go flying. To determine the amount of tension force, you can cut the string removing one end, say the block end, and replace it with ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/420708",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
What solid elements, if formed into their thinnest possible 'sheet', would be translucent? Would this have to be experimentally done or is there some manner to estimate translucency based on molecular properties?
| Every solid object, deposited in a smooth film a single monolayer thick on a transparent substrate, transmits some/most visible light (even metal, graphene and other carbon allotropes, and resonant molecules). In fact it’s more difficult to think of a material/color combination for which most of the light is absorbed.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/420819",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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Stars filling up the night sky Due to the huge number of stars in the universe, will there ever be a time that the night sky is filled up completely with stars such that the night sky is as bright as it is in the daytime?
| I think the best answer as far as we know, is dissipation of light energy. The electromagnetic phenomena known as light, is a wave of alternating electric and magnetic fields. It is a 3 dimensional wave, so if you have a point source the wave travels outwards like ever increasing spheres. The surface of the spherical w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421052",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
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What is the value of the mass gap in QCD? Is there any estimation either from experiments or numerical simulations for the value of the mass gap in QCD?
| As Lubos says in his answer here, there are theoretical proposals fo the mass gap in lattice QCD and other theoretical models.
Searching for "lattice QCD and the mass gap" this paper came up, and they do give a formula for the mass gap (number 22), but in dimensionless numbers!!
It is not a simple concept in the QCD f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421333",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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What does electrical potential at a point mean? From my understanding, potential difference (or voltage) between point A and point B is the difference in electrical potential at the two points. The potential difference is also, the work done per unit charge in moving charges from point A to point B.
But apparently, the... | You have understood the concept of potential difference between two points A and B. But you are confused as to why there is a potential at a single point, say P. When we talk about the potential at a point P, we usually refer to the potential difference between infinity and the point P. That is, the potential at point ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421510",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 2
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How is work transferred to the system recognised? For example, a potato initially at room temperature $25 \sideset{^{\circ}}{}{\mathrm{C}}$ is baked in an oven that is maintained at $200\sideset{^{\circ}}{}{\mathrm{C}}.$
I made potato as the system and the outer surface of the skin as the system boundary. While the ove... | The First Law of Thermodynamics says that changes to the internal energy of a thermodynamic system into two ways of energy transfers.
Work refers to forms of energy transfer, which can be accounted for in terms of changes in the macroscopic physical variables of the system, e.g. energy which goes into expanding the v... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
What is the difference in conditions of a free electron in metal and a isolated free electron in space-time? I am asking that what environment does the free electrons in metal have,what is net electric fields,force experienced by them.does they have transitions like valence electrons.can they be compared to an isolated... | The free electron model (FEM) was derived mostly by Sommerfeld in 1927. It does not yield band structures, so there's no energy bands, i.e. it cannot predict the existence of insulators and semiconductors. For such a description, one has to look at the nearly free electron model, which is able to describe energy bands.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421851",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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A slipping cylinder comes into contact with friction Suppose a cylinder is slipping rigidly on a frictionless horizontal surface. Then, at $t=0$ it reaches a different ground. The coefficient of friction between the cylinder and this new type of ground is $\mu$. What happens?
- assuming usual high-school friction to b... | You can simplify the problem by looking at a box sliding on rough table, slowing to full stop. When sliding, friction is constant $\mu mg$. Once stopping, friction is zero.
However, the transition is actually from constant kinetic friction force to gradually reducing static friction force.
A rolling / sliding cylinde... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421904",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Classical theory fails to explain quantization of motions?
I understand everything written here.
But the last point, I cannot get, at all.
How does it point towards Quantization of the two motions, since the energy change is not sudden, but gradual?
And if anything is wrong with the given image, please tell what it is... | The "wrong" thing in this picture is an illusion of "horizonality" of some parts of this curve. According to the Maxwell distribution $\propto \text{exp}(-mv^2/2kT)$, in the volume there are always high velocity molecules capable to get rotational and vibrational excitations, thus the curve has always a slope as a func... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/422075",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 1
} |
Was the universe already expanding before inflation occured? Was the universe already expanding before inflation occured or did inflation cause the universe to start off expanding?
By “cause it to start off expanding” , I mean the cause of the initial expansion.
| Here is a link discussing cosmological models, as one has to keep in mind that the models develop in order to fit/explain observations using current physics theories, classical and quantum mechanical.
The current mainstream model can be seen here, and your question is about what happens at the quantum era, before $10^... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/422296",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 1
} |
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