Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Confusion regarding the finite square well for a negative potential Consider the finite square well, where we take the potential to be $$V(x)=\begin{cases}
-V_0 & \text{for}\,\, |x| \le a \\
\,\,\,\,\,0 & \text{for}\,\, |x|\gt a
\end{cases}$$ for a positive constant $V_0$.
Within the square well the time-independent ... | You are just looking at the general solutions of Schroedinger equation inside and outside the well. In principle, however, you have to solve the eigenvalue problem to find the allowed energy eigenvalues E and wavefunctions for the whole system. For this, you have to use the boundary conditions at the well boundaries an... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Must all types of clocks agree on the time that has passed since the spaceship started accelerating? The above would be true if the spaceship were not accelerating, because SR says that the physical laws are all same in inertial frames of references. If there were a gap in the time of the 2 clocks, a person on the spac... | This depends on exactly what you are asking. Clocks at different heights in an accelerating spaceship run at different rates. This is discussed in the question Which clock is the fastest inside an accelerating body?.
All clocks are affected by the time difference in the same way, so it doesn't matter whether the clock ... | {
"language": "en",
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Why do bands arise from a lattice of two-site "atoms"? What is the basic reason why an “atom” with a trapping potential with two bound states becomes a system with two bands when a large number of such atoms are assembled into a lattice?
| If you couple a large number N of identical atoms with two energy levels so that they can interact, the energy levels will split up into a closely spaced energy level band with N levels each. This is analogous to the classical case of two coupled identical oscillators where the oscillation frequencies split into two fr... | {
"language": "en",
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When is the free charge density zero at the boundary of dielectrics It is known that across the interface of two different dielectrics, the electric displacement field must satisfy
$$(\mathbf{D}_2-\mathbf{D}_1)\cdot\mathbf{\hat{n}}=\sigma$$
where $\sigma$ is free surface density charge in the boundary.
My question is: ... | In dielectrics with different permittivities but no conductivity, there will be no free charge at the interface upon application of en electric field. However, if the dielectrics also possess different conductivities, which leads to a current flowing across the interface, in general, a free interface charge will accumu... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can we concentrate magnetic (electromagnetic) field in same way we concentrate light into laser? Sorry if that question is too noobish but i wonder- we can make laser beam and it can go far in distance without loosing much of its power.
To my understanding magnetic field just propagates around its source (like magnet).... | There is no way you can keep a large volume with a magnetic field lines going straight to infinity. Field lines are nothing like a laser, the laser is a wave (propagates according to wave equations) and field lines are abstract concepts that link points with the same value of magnetic field.
However, you can make those... | {
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To normalize in a given length, should the wavefunction at the endpoints be zero? I have an assignment question:
A free particle is moving in $+x$ direction with a linear momentum $p$. What is the wave function of the particle normalized in a length $L$?
Do I need to use the boundary condition that $f(0)=f(L)=0$?
| No, when you normalize to a length $L$ that only means you should use a region of length $L$ to do the normalization integral.
$$\int_{x_0}^{x_0 + L} \lvert\psi(x)\rvert^2\,\mathrm{d}x = 1$$
Here $x_0$ can be anything. It shouldn't matter what it is because, presumably, you are assuming the wavefunction is periodic wit... | {
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Why Does Electric Potential Approach Zero at Infinity: Boundary Conditions for Infinite Conducting Sheets Imagine an infinitely long conducting "trough," as shown in the figure. The two sides are grounded, and the bottom strip is maintained at potential $V_0$. Suppose we want to know the electric potential everywhere b... | If you solve Laplace equation outside the trough, you will see that a large part of the electric field lines emerging from the ground plane will end on the sidewalls. Therefore, as you say, the potential goes to zero faster than in the case of a line charge. You would have a similar case with two closely spaced line ch... | {
"language": "en",
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If I only roll my object, what angular velocity value will change? Question 1
I know this is a simple question but I just need clarification. This is an honest question so if anyone could help reorientate my brain I would appreciate.
Let say I have a body like this:
Yaw Pitch Roll
If I only try to roll, which angular ... | There is a difference between the net angle change (roll, pitch, and yaw) and angular velocity which is primarily that angular velocity has dependence on time (that is, keeping track of time is essential for calculating it) while roll (or pitch and yaw) can just be calculated at regular intervals of time, where it is j... | {
"language": "en",
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If we were on the Moon would Earth appear to be in motion or at rest? If we were on the moon would earth appear stationary or would it appear to move. I think it must be stationary because moon is in sychronous rotation with earth.
| Because the Moon is tidally locked the Earth will be in a nearly fixed place in the sky, while the sun rises and sets once every orbit (about once a month). There's a really cool animation/video from NASA that shows the moon undergoing libration as it orbits the Earth. From the point of view of the moon, the Earth woul... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/285887",
"timestamp": "2023-03-29T00:00:00",
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Why the clock at rest runs faster, while another clock slows when moving? I have observed from my first question that it is hard for me to study the special relativity from every frame of reference. But, there is one most important question in my head right now that time runs slower for moving body if observe from rest... | Einstein's postulates entail SYMMETRICAL time dilation - either clock is slow as judged from the other clock's system. Instead of honestly deriving this in 1905, Einstein derived, fraudulently and invalidly of course, ASYMMETRICAL time dilation - in his 1905 article the moving clock is slow and lags behind the stationa... | {
"language": "en",
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bubble/drop Reynolds number The bubble/drop Reynolds number makes me confused and I hope someone can help me on this please!
Normally (as I read in every books and papers) that when a bubble or drop rises in a fluid, the bubble/drop Reynolds number is calculated by:
Re = ρUD/μ
where U is particle velocity, D can be par... | In some cases Reynolds number is used to decide whether the flow of the fluid is laminar or turbulent. So it is the fluid which is important and not the objects (your bubble) which is important.
So the density and the viscosity of the fluid are contained in Reynolds number.
If the flow is not turbulent analysis is a l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/286285",
"timestamp": "2023-03-29T00:00:00",
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Near Earth vs Newtonian gravitational potential Newton's Law of Universal Gravitation tells us that the potential energy of object in a gravitational field is $$U ~=~ -\frac{GMm}{r}.\tag{1}$$
The experimentally verified near-Earth gravitational potential is
$$U ~=~ mgh.\tag{2}$$
The near-Earth potential should be an a... | Given a force $F$, the work done on an object over a distance between two points $s_0$ and $s_f$ by that force is
$$W=-\int_{s_0}^{s_f} Fds$$
In the case of gravity,
$$F=\frac{GMm}{r^2},\quad ds=dr$$
Thus, in the case where $U=W$, $s_0=0$ and $s_f=r$, so
$$U=\frac{GMm}{r}$$
Now, over small distances by the Earth's surf... | {
"language": "en",
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Is the gravitational effect of distant galaxies lost forever? Hubble's law is usually expressed by the equation
$$v = H_0D$$
According to this equation, the space between us and very distant galaxies,
is expanding with a speed greater than the speed of light $c$.
As a result the light from these galaxies can no long... | The influence of gravity and gravitational waves are thought to travel at the speed of light. So what goes for light also goes for gravity.
Galaxies that we see now can already be receding at greater than the speed of light. As Thriveth says in his comments, this is the case for galaxies at redshift more than 1.4. We s... | {
"language": "en",
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What would be the atomic number of the atom whose 1s electron moves nearly at the speed of light? What would be the atomic number of the atom (may be hypothetical) whose $1s$ electron moves at $0.99c$ (the speed of light)?
Quantum mechanics might have an answer, but I do not know the necessary maths to calculate. I am ... | Gold has a strong absorption line at 200-300 nm which is for blue photons. The complement of that blue is yellow, so the reflected light looks yellow to the eye.
Yes, the effect is due to special relativity, but it is slightly different for different elements. The line for gold is the 5d to 6s transition, and the rela... | {
"language": "en",
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How exactly do I distingish an interpretation from computation? Feynman wrote this in his Quantum Mechanics and Path integrals
To summarize: we compute the intensity ( ... ) of waves which would
arrive in the apparatus at x and then interpret this intensity as the
probability that a particle will arrive at x
I ha... | I think you're getting a bit mixed up over the meaning of the word interpret as it is used in two ways in quantum mechanics.
The word interpret isn't a precise scientific term, and in everyday use it means something like assign a meaning to. This is the sense in which Feynmann is using the word. Quantum mechanics is (l... | {
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Should zero be followed by units? Today at a teachers' seminar, one of the teachers asked for fun whether zero should be followed by units (e.g. 0 metres/second or 0 metre or 0 moles). This question became a hot topic, and some teachers were saying that, yes, it should be while others were saying that it shouldn't be u... | Golly, in my opinion, when we are told to count it should be by starting from zero whereby no units need apply. Zero would have some meaning before being sent to work. We better state units for zero when it comes up in description of temperature: "temperature" is just a description of the units to follow such as Fahren... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/286964",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "72",
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Where does the extra kinetic energy of the rocket come from? Consider a rocket in deep space with no external forces. Using the formula for linear kinetic energy
$$\text{KE} = mv^2/2$$
we find that adding $100\ \text{m/s}$ while initially travelling at $1000\ \text{m/s}$ will add a great deal more energy to the ship th... | Assume the rocket without fuel has weight $M$, the fuel has weight $m$, and the rocket engine works by sending the fuel instantaneously backwards with velocity $v_e$ relative to the initial velocity of the rocket. Thus, by conservation of momentum, the speed gain of the rocket is
$$
\Delta v_\text{rocket} = \frac{m}{M... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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In car driving, why does wheel slipping cause loss of control? When driving a car on ice, there is a danger of slipping, thereby losing control of the car.
I understand that slipping means that as the wheels rotate, their circumference covers a total distance larger than the actual distance traveled by the car. But why... | As all the answers have mentioned the reason for slippage is change of friction coefficient form higher to lower when going from static to dynamic friction. the reason for skidding and loss of control is two parts:
The physics of motion and the driver's over steering.
1- Tires have treads and indentations designed... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/287160",
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Is energy relative or absolute? Does gravity break the law of energy conservation? Imagine a meteor, with a mass of 1 kg, traveling towards the earth at a velocity of 1 mile/hr. It is having very little energy, as it can easily be brought to rest. Now as it enters earth's gravitational field, its velocity increases. No... | The statement that gravitational potential energy is $U=mgh$, with the height $h$ measured relative to some arbitrary vertical zero, is an approximation.
The potential energy associated with the gravitational interaction between two masses $M$ and $m$ is given by
$$
U(r) = -G \frac{Mm}{r},
$$
where $G$ is an empirical ... | {
"language": "en",
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How to get pressure from continuity equation for an incompressible fluid? The initial formulation of continuity equation for in-compressible fluids does not contain initially pressure.
$$\nabla \cdot \vec v = 0$$
I have seen, in some books it is assumed that pressure is calculated from continuity equation. How can we ... | You solve two equations: continuity and Navier Stokes equation, to find two unknowns: velocity vector field and (scalar) pressure field. Solving only Navier Stokes equation gives you velocity field as a function of pressure. Then the pressure field must be such that the resulting velocity field satisfies continuity equ... | {
"language": "en",
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Could one see his hands in a dark moonless night in Sahara desert? If you were standing in a place on earth on a moonless night where there was no other light to be seen except starlight, could you see your hand held in front of your eyes?
| Most likely that you will see it, especially after your eyes are adapted to darkness. However, the main reason seems to be not the light from the stars but other sources. See here, for example:
http://www.skyandtelescope.com/astronomy-blogs/why-we-can-see-in-the-dark/
| {
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Spin representation in 3D How do you represent $S_x$ and $S_y$ and $S_z$ as a 3D matrix? Can someone explain how $$\left[ J_x,J_y \right] = i\hbar\epsilon_{ijk}J_k,$$ comes out in 3D also? How does it relate to $S_x$ $S_y$ $S_z$? And how can I write $S_x$ and $S_y$ and $S_z$ in Dirac notation in 3D.
Here is the 3D mat... | It sounds like what you're asking is: how do you construct a representation of SU(2) in terms of 3x3 matrices on a real 3-dimensional vector space? (This representation is also known as the "spin-1" representation, as it's used to describe the spin of spin-1 particles.)
The H you mention, which appears to be some kind... | {
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Why are planets not crushed by gravity? Stars can be crushed by gravity and create black holes or neutron stars. Why doesn't the same happen with any planet if it is in the same space time?
Please explain it in simple way. Note: I am not a physicist but have some interest in physics.
| You must understand that there are two factors involved here, first one is gravity that is trying to bring the planet closer and crush it and the second factors tries to resist this crushing e.g. pauli exclusion principle leads to repulsion sometimes, nuclear reaction also resist crushing in stars . So this play of two... | {
"language": "en",
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Why doesn't the heat of the Earth's core diffuse to the surface? The Earth has a crust, mantle, outer core and the inner core with each one getting hotter than the next. How come, over millions and millions of years, the heat that is at the center of the Earth hasn't conducted throughout the planet's material so that t... | The pressure at the core is higher, so higher temperatures are thermodynamically more favourable there.
More importantly, the Earth is not in thermal equilibrium. Heat can't move outward from the core nearly so efficiently as from the surface off the planet, for example, so the surface cools a lot more quickly.
There ... | {
"language": "en",
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"source": "stackexchange",
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Can Hydrogen Fusion via CNO Cycle Occur in First Generation Stars CNO cycle requires the presence of carbon, nitrogen and oxygen to undergo hydrogen fusion. Does this mean that for first generation stars, no matter how big they are, can't undergo hydrogen fusion by CNO cycle because there is no carbon, nitrogen and oxy... | The CNO cycle does take place in the earliest massive stars, but only once a significant amount of helium has been burned into carbon by the triple alpha reaction.
Massive population III stars ($>20 M_{\odot}$) cannot be supported on the "main sequence" by pp hydrogen burning alone. What happens is that they collapse u... | {
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Why is electric field lines away from (+) and toward (-)? I have a questions about the electric field lines.
Well in the basic learning, we know that:
*
*The electric field lines extend away from a positive charge
*They move forward a negative charge
Let's take parallel plates, which make a uniform electric fiel... | The direction of the field is defined to be the direction of the force on a positively charged test particle. Positive charges always move away from other +ve charges and towards -ve charges.
As @Charlie says, it is a convention, like driving on the right (or left), or which pin on a plug is "live". So that everyone ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/288172",
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Where do symmetries in atomic orbitals come from? It is well established that:
'In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit.
There are also many graphs describing this fact:
http://en.wikipedia.org/wiki/Electron:
(hy... |
How do these symmetries shown in the above article occur? What about the 'preferable' axis of symmetries? Why these?
For atoms subject to no net external electric of magnetic fields the orientation of the axes is arbitrary. This shows up clearly in the math because adding up all the spherical harmonic contributing to... | {
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Why is energy not conserved in this situation Suppose there are three masses that are still relative to each other in space. They are positioned in an equilateral triangle. Let's accelerate one mass towards the other two with a force. The energy added to this system should be $F\cdot{ds}$. However, according to the par... | Ok I think there are 2 distinct problems here. firstly it is that I cannot apply the same equations for energy in an accelerating coordinate system. It only works for inertial reference frames. Secondly it is that even under galilean transformations work done is not (and doesn't need to be) invariant which is what was ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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BCS state and its superconductivity I've learned in BCS theory about its ground state by applying Bogoliubov annihilation operator on it to be zero; however, in the textbook the total momentum of electrons is set to be zero. It's okay to me for this state to be a ground state for the effective Hamiltonian; however, I c... | Now even though I haven't derive a concrete solution to what happens when applying external electric field to BCS superconductor, I eventually get an explanation of why gapped BCS states has relation with superconducting.
Considering the excitation energy spectrum as illustrated (gapped):
And then considering an imp... | {
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Standard Model Proton Decay Rate The electro-weak force is known to contain a chiral anomaly that breaks $B+L$ conservation. In other words, it allows for the sum of baryons and leptons to change, but still conserves the difference between the two. This means that the standard model could have a channel for protons to ... | Electroweak instantons violate baryon number (and lepton number) by three units (all three generations participate in the 't Hooft vertex). This is explained in 't Hooft's original paper. As a result, the proton is absolutely stable in the standard model. The lightest baryonic state that is unstable to decay into lepto... | {
"language": "en",
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Why can't we make Carnot heat engine in real life? Question is obvious: Why can't we make Carnot heat engine in real life?
I read Wikipedia and Fundamentals of Physics (Halliday) but I haven't found anything on my question. There are explanations about formulas and how it works but no obvious answer why it can't be mad... | A Carnot engine has to be perfectly reversible. This means zero friction, and perfect thermal conductivity between reservoirs*.
In practice neither of these things are possible so you will only ever get "close".
* As was pointed out by David White, reversibility requires zero temperature difference between the reservo... | {
"language": "en",
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"source": "stackexchange",
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The dimensional analysis of the GR geodesic equation The geodesic equation parametrized by the proper time contains two terms:
$$
{d^{2}x^{\mu } \over ds^{2}}=-\Gamma ^{\mu }{}_{{\alpha \beta }}{dx^{\alpha } \over ds}{dx^{\beta } \over ds}\
$$
The dimensions of the different elements of the previous expresion are
$$
[... | The Christoffel symbols are obtained by differentiating with respect to $x^\alpha$, and since the metric is dimensionless if we write the dimensions we end up with:
$$ \left[{d^{2}x^{\mu } \over ds^{2}}\right] =\left[\frac{d}{dx^\alpha}\right]\left[{dx^{\alpha } \over ds}\right]\left[{dx^{\beta } \over ds}\right] $$
So... | {
"language": "en",
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Given that ice is less dense than water, why doesn't it sit completely atop water (rather than slightly submerged)? E.g.
*
*If we had a jar of marbles or something else of different densities and shook it, the most dense ones would go to the bottom and the less dense ones to the top.
(Image Source)
*If I put a cube... | I'll try to explain this using some mathematics.
Let us have an ice cube floating in water. Let the density of water be $ \rho_1 $ and that of ice be $\rho_2$. Let the volume of the ice cube be $v$. Let the submerged volume be $v'$. If you consider the forces on the ice block:
$$ \rho_2 \cdot v \cdot g = \rho_1 \cdot... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/289495",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "58",
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How can I calculate the improper integral appearing in the BCS gap equation for obtaining the critical temperature? To estimate the critical temperature of the BCS theory, when the gap is zero, one has the following improper integral:
$$\int_0^\infty \frac{\ln(x) }{\cosh^{2}(x)} dx $$
Many books and articles (includin... | Mathematica gives the result that you are trying to get, but with the opposite sign.
You are calculating sums of diverging series. This procedure requires accuracy. Looks like you can get the Mathematica's result if, say, you take the sum 1-1+1-1+... equal to 1/2 (Cesaro summation).
| {
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Deriving a formula for the moment of inertia of a pie slice of uniform density Say you have a right cylinder of radius $R$, and you take a pie slice of angle $\theta$ at the origin with mass $M$. How can you determine the moment of inertia?
My teacher says it is impossible to derive its moment of inertia given those tw... | Assuming that the axis of rotation is the axis of symmetry of the cylinder, then the moment of inertia (MI) is the same as that of the cylinder which it came from, ie $\frac12 MR^2$ where $M$ is now the mass of the 'pie slice' rather than the mass of the 'whole pie' (= cylinder).
The explanation is the Stretch Rule, wh... | {
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What is an instant of time? If we say that an instant of time has no duration, why does a sum of instants add up to something that has a duration? I have a hard time understanding this.
I think of one instant as being a 'moment' of time. Hence, the sum of many instants would make a finite time period (for example 10 mi... | Perhaps it's useful here to differentiate between a specific time (as in, a one dimensional representation of a specific instant or location in time) and a duration, which is the measure of difference between two specific times.
In this case hat you refer to as a summable 'instant' may actually refer to a delta of dura... | {
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Where does gravitational energy come from? We've all heard mass tells space how to curve and curved space tells matter how to move. But where does the energy to curve space come from? Likewise where does the energy that curved space uses to push planets around come from? I mean if I tell my son to clean his room, an... | Asking where energy comes from is like asking about the origin of the universe. Did it all spontaneously pop into existence out of nothing, completely violating every existing law of nature, or has it always been there just waiting to expand out of the singularity when god himself gave the command. The answer is we don... | {
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How can voltmeter still measure potential difference if it has very large resistance? I am just confused how can a voltmeter which has a very large resistance and hence small current or in ideal condition zero current still measure potential different because as far as I know voltmeter is modified galvanometer and a ga... | Voltmeters come in many forms and as their implies they measure a difference in potential between two points.
One important characteristic of a voltmeter is that it does not alter the potential difference it is trying to measure and this usually means that its resistance is much higher than the resistance in the circui... | {
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Phase transition in 2D Heisenberg model When we study the two-dimensional isotropic Heisenberg Model using Mean Field Theory or by Monte Carlo simulation we observe a phase transition at a temperature not equal to zero. This is opposed to Mermin Wagner theorem.
Interestingly this ordering happens only in z direction. C... | If you simulate with angles you shouldn't take theta and phi uniform random numbers. In here
http://mathworld.wolfram.com/SpherePointPicking.html
explained why. If you take random theta and phi uniformly, you oversampled in poles and your spins are a lot more up an down (like Ising).
| {
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Constancy of temperature in a closed system Consider a thermodynamical classical isolated system, made by a small subsystem and a way large reservoir. The two could exchange heat.
Usually in such situation we say that the system is closed or is a $(N,V,T)$ system.
What perplexes me is that for the $(N,V,T)$ system, $N... | The thermodynamic parameters $N, V, T$ are all mentioned at the equilibrium states only. So, when your system is in contact with a heat bath, there causes an exchange of energy between the system. According to the definition of a heat reservoir, its temperature is not affected by any slight exchange of heat. Hence the ... | {
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Solenoidal electric field In electrostatic electric field in a system is always irrotational ∇×E=0. And divergence of electric field is non zero ∇.E=ρ/ε but in some cases divergence of electric field is also zero ∇.E=0 such as in case of dipole I had calculated and got that ∇.E=0 for a dipole
So in case of this... | For better understanding of an irrotational and rotational field I am attaching two video links about Vorticity(Vorticity is the curl of velocity of fluid flow) which cleared my concept to a good extent. The term here to emphasise is CURL and not rotation, using the word rotation gives the vague sense of it but curl ac... | {
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Why does the Pauli exclusion principle not apply to bosons? The Pauli exclusion principle states that two fermions cannot have the same quantum state simultaneously, but why does this not apply to bosons with whole integer spins?
| This is a legitimate question but one for which you probably won't get any real, satisfying answer rather than just "because that's how nature works".
You can "derive" the impossibility for two fermions to have the same quantum numbers from the requirement for many-fermion states to be antisymmetric with respect to the... | {
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Line integral of a vector potential From the theory of electromagnetism, the line integral $\int {\bf A}\cdot{d{\bf s}}$ is independent of paths, that is, it is dependent only on the endpoints, as long as the loop formed by pair of different paths does not enclose a magnetic flux.
Why is this true?
| It's a straightforward application of Stokes' theorem:
Given two paths $\gamma_1,\gamma_2$ with the same starting and end points, let $\gamma := \gamma_1 - \gamma_2$ be the loop obtained by going from the starting point along $\gamma_1$ to the end point, and then in the reverse direction along $\gamma_2$. Let $S$ be a ... | {
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Are there any recent experiments demonstrating retrocausality? I was wondering if there are any recent experiments outside of the typical quantum mechanics single particle realm that demonstrate that retrocausality is more than pseudo-science?
| Probably not what you have in mind, because it's hard to interpret quantum experiments without making additional assumptions. The entanglement experiments that violate Bell-inequalities can be interpreted as evidence for either retrocausality or nonlocality. If you assume a local reality in space and time, then they ... | {
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Different hydrostatic pressure on sphere I want to ask a question that I can't answer it for about 1 year. Does the sphere rotate if we have the sphere or a cylinder that has an point of rotation in the center of the shape holding by a rotatable rod when the liquid no.1 and no.2 is water with different height as shown ... | I think that it will never rotate whatever you do with the different liquids because the different hydrostatic pressure forces along the circumference of the cylinder are all directed towards the axis so that no torque necessary for rotation can result.
An additional argument against rotation is conservation of energy ... | {
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What is a logarithmic divergence? I am reading about renormalisation in QED and I come across the term logarithmic divergence several times. Can somebody explain to me about it in simple terms?
| The term 'logarithmic divergence' is normally used for integrals of the type
$$
F(x) = \int_{x_0}^x \frac{1}{\xi}\mathrm d\xi
$$
(or possibly of the form $F(x) = \int_{x_0}^x \frac{1}{\xi}f(\xi)\mathrm d\xi$ where $f(\xi)$ approaches some finite limit when $\xi\to\infty$). In these cases, the integral diverges to infin... | {
"language": "en",
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How do one show that the Pauli Matrices together with the Unit matrix form a basis in the space of complex 2 x 2 matrices? In other words, show that a complex 2 x 2 Matrix can in a unique way be written as
$$
M = \lambda _ 0 I+\lambda _1 \sigma _ x + \lambda _2 \sigma _y + \lambda _ 3 \sigma_z
$$
If$$M = \Big(\begin{... | And yet another answer.
Pauli matrices $\sigma_1,\sigma_2$ and $\sigma_3$ evidently form a base of the 3-dimensional real vector space of the 2 by 2 traceless Hermitian matrices. Since every Hermitian matrix is the sum of a traceless Hermitian matrix and the real multiple of the identity matrix, $\sigma_1\sigma_2,\sigm... | {
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Is acceleration continuous? The extrapolation of this Phys.SE post.
It's obvious to me that velocity can't be discontinuous, as nothing can have infinite acceleration.
And it seems pretty likely that acceleration can't be discontinuous either - that jerk must also be finite.
All 4 fundamental forces are functions of di... | With respect, I think you're splitting hairs.
Before the wall, the velocity is constant, and a = 0. After the wall, the velocity is constant at 0, and a = 0. In between velocity is decreasing to 0, acceleration is the derivative of the velocity as a function of time, at some non-constant value of un-changing sign (si... | {
"language": "en",
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Can Newton's laws of motion be proved (mathematically or analytically) or are they just axioms? Today I was watching Professor Walter Lewin's lecture on Newton's laws of motion. While defining Newton's first, second and third law he asked "Can Newton's laws of motion be proved?" and according to him the answer was NO!... | If you want to prove something, you have to start with axioms that are presumed to be true. What would you choose to be the axioms in this case?
Newton's Laws are in effect the axioms, chosen (as others have pointed out) because their predictions agree with experience. It's undoubtedly possible to prove Newton's L... | {
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Dielectric material problem I read about dielectric just 2 days ago and come across something about what polarization means: how a neutral object can be created to be a dielectric under external electric field, etc.
Then I read about the electric field in a dielectric material and there I found two terms: one is surfac... | One way of thinking about the divergence of a vector field is that it is the flux of that vector quantity in or out of a unit volume.
I think what you are calling ${\bf p}$ is the polarisation field, which is the electric dipole moment per unit volume, with units of charge times length. If you take the divergence of th... | {
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Regarding the Dirac Hamiltonian's use of summation notation: Einstein summation notation, as I understand it:
By writing $A_i B^i$ one implicitly means a sum over elements of the rank 1 tensors A and B. The key is the contraction of an "up" and a "down" index. In a formalism where a metric raises/lowers we should see t... | As it was pointed out, we are in Euclidean space, so the metric is the unit matrix $I$, if you are in Minkowski space, similar things hold with $g_{\mu\nu} =\pm(+,-,-,-)I$ (don't care about the sign as long as you stick to one convention). There can be other metrics in general relativity, but as long as you are not in ... | {
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Magnetic quantum number for d orbitals Online one can find many pictures of d-orbitals.
I know that these states correspond to :
n = 3, l = 2, m = -2, ...,2
but I don't know which one is which and I couldn't find a clear asignment anywhere. What are the magnetic quantum numbers for each of the above displayed states?
... | I got this one. Does this help ?
The subscript of d represents the m value.
Link :http://study.com/academy/lesson/electron-orbital-definition-shells-shapes.html
| {
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Color confinement and integer electric charge? Quarks have electric charges proportional to one third of the elementary electric charge, but both mesons and baryons have integer electric charge.
Is there some deep explanation from a more fundamental and generalizable conservation law that any state that forms an $SU(3)... | It may help noticing that the normalization of the $U(1)$ charge is arbitrary. The only meaningful information that one can have is the ratios
of the charges of the particles in the model (2:(-1) for the case of the quarks). They can always be defined to be all integer numbers.
If you want to know why the charge of the... | {
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Is there oscillating charge in a hydrogen atom? In another post, I claimed that there was obviously an oscillating charge in a hydrogen atom when you took the superposition of a 1s and a 2p state. One of the respected members of this community (John Rennie) challenged me on this, saying:
Why do you say there is an osc... | The superposition of eigenstates in a hydrogen atom results in an oscillating wave function in time with a frequency corresponding to the difference of energies of the eigenstates. Schrödinger considered for a time the wave function squares as charge density which resulted in an oscillating charge distribution. As this... | {
"language": "en",
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What is the role of pillars in bridges?
As I can see in the picture, there are so many pillars which are holding the bridge. This picture gave a question to me that what are these pillars doing below the bridge?? An appripriate answer could be "these are providing support to bridge".
I tried to get the answer as foll... | Not only do the pillars need to bear the weight of the bridge but the bridge itself also needs to bear it's own weight (i.e. Not snap). For this reason, lots of pillars can be used to support the bridge in more places, stopping this from happening.
Further, the more pillars, the less weight each pillar holds itself. If... | {
"language": "en",
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If an electron is in ground state, why can't it lose any more energy? As far as I know, an electron can't go below what is known as the ground state, which has an energy of -13.6 eV, but why can't it lose any more energy? is there a deeper explanation or is this supposed to be accepted the way it is?
| The existence of a minimum energy follows from the wave-like aspects of matter.
The allowed values of energy are those corresponding to stationary wave states, so the trite answer to your question is that where you have a set of allowed energy values one of them has to be a minimum.
To get some physical insight into ... | {
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Necessary and sufficient condition for Bernoulli's theorem For an ideal fluid, if the vorticity is $\vec{\omega}=\nabla \times \vec{v}$, then Euler's equations can be rewritten as:
$$\rho \dot{v}_i = \rho \epsilon_{ijk} v_j \omega_k - \frac{1}{2} \rho \partial_i v^2 - \partial_i p $$
Any textbook will then tell you th... | The actual derivation of the Bernoulli equation comes from the vorticity form of the incompressible Navier-Stokes equation. In terms of vorticity, the Navier-Stokes equation take the form,
$$ \frac{\partial \vec{V}}{\partial t} + \vec{\omega} \times \vec{V} = -\nabla\left(\frac{p}{\rho} + \frac{|\vec{V}|^2}{2} + k\righ... | {
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Beta decay form factors I'm trying to understand formula from Anthony Zee qft in nutshell for beta decay:
$$\langle p'|{J_5}^{\mu} |p\rangle = \bar u(p')\left[\gamma^\mu\gamma^5F(q^2) +q^\mu\gamma^5G(q^2)\right]u(p)$$
it is stated, that term with $$(p' + p)^\mu \gamma^5 A(q^2)$$
is missing because of some charge and ... | it seems, that one can use one of the Gordon identities:
$$0 = \bar u(p')\left[(p' + p)^\mu\gamma^5 +iq_\nu\sigma^{\mu\nu}\gamma^5\right]u(p)$$
to replace $(p' + p)^{\mu}$ with $q_\nu\sigma^{\mu\nu}\gamma^5$, which would correspond to positive G-parity term of the current, while only negative are allowed for this react... | {
"language": "en",
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What does antimatter look like? I have seen simulations of antimatter on TV. Has antimatter ever been photographed?
| Antimatter looks just like matter. Experimentally, there is no difference between the spectral lines of antihydrogen and of ordinary hydrogen. Same emission spectrum.
The photon is its own antiparticle. It interacts in the same way with matter as with antimatter.
PS: Very recent Nature article by Ahmadi et al gives an ... | {
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Moving camera and special relativity Consider a rigid inertial coordinate system $K$.
A photo camera is located on the point $O=(0,0,0)$ and in $t=0$ it captures a picture from the light rays of the physical objects at rest wrt $K$. Let's suppose that the capture takes an infinitesimal time.
Consider the two cases:
... | *
*Light will be red- or blueshifted due to the Doppler effect. https://en.wikipedia.org/wiki/Redshift#Doppler_effect
*The size of the objects in the direction in which the camera is moving will be affected by length contraction, and the shape will also be affected if we consider where light has to come from to reach... | {
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Confusion between two different definitions of work? I'm doing physics at high school for the first time this year. My teacher asked us this question: if a box is slowly raised from the ground to 1m, how much work was done? (the system is only the box)
Using the standard definition, $W = Fd\cos(\theta)$, the work shou... | For a system with no internal degree of freedom (such as a point mass), work is equal to the change in kinetic energy:
$$W=\int_{\mathcal L} \vec F \cdot d \vec x = \Delta E_k$$
The $\vec F$ in the above equation is the net force. This is a very important point.
Let's model our box as a point mass. At the initial time,... | {
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Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time? Quantum mechanics says that if a system is in an eigenstate of the Hamiltonian, then the state ket representing the system will not evolve with time. So if the electron is in, say, the first excited state then why does it ... | The hydrogen atom in an excited state is not really in an energy eigenstate.
There are two ways of looking at it. One way is to recognize that the atom is not isolated. It is always coupled to the electromagnetic field. Even if field itself is in the ground state, there are "zero-point" fluctuations in the field a... | {
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What is "quantum" in topological insulators? When I'm looking at descriptions of topological insulators, (non interacting just in case anybody ascribes interactions), I'm essentially looking at single particle quantum mechanics on a lattice.
What made quantum mechanics special to me was entanglement and measurement. If... | Perhaps what makes these systems quantum is the fact that they must be Fermionic, and one must use the Pauli exclusion principle (an inherently quantum phenomenon) in order to fill the Fermi sea and get the Fermi projection. If it weren't for quantum mechanics, you wouldn't have such a Fermi projection and hence no top... | {
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Will there be translation + rotational motion? If a rod is on a frictionless plane, and a force is applied on one of it's end, will there be both, translation + rotation motion?
Also, if only a single force is applied on a body that does not pass through Centre of Mass, will it always produce rotation + translation?
| Suppose that you have a force $\vec F$ acting at a point $A$ on the rod as shown in the diagram below.
Add two forces of equal magnitude but opposite in direction whose line of action is parallel to the original force but with those forces acting at the centre of mas.
This results in a force $F$ (red) acting through t... | {
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Why are explanations of the Aharonov–Bohm effect based on trajectories? Every explanation of the Aharonov–Bohm effect that I have seen seems to justify the phase that shows up due to different paths that the particles (electrons) take to reach some point in space.
How does this make any sense in (standard = Kopenhagen)... | The Bohm-Aharonov effect (well, really the double-slit experiment) does not concern one single path, but rather a sum over all paths, each being weighted by a phase (of unit modulus). That is what gives the interference pattern. The presence of a magnetic vector potential with non-zero circulation about a particular re... | {
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Equivalent form of Bianchi identity in electromagnetism In electromagnetism, we can write the Bianchi identity in terms of the field strength tensor $F_{\mu \nu}$ as,
$$ \partial_{\lambda} F_{\mu \nu} + \partial_{\mu} F_{\nu \lambda}+ \partial_{\nu} F_{\lambda \mu} = 0,\qquad \mu,\nu,\lambda=0,1,2,3. \tag{1}$$
Now, in ... | Let's start by contracting the first equation with the 4-dimensional totally antisymmetric tensor $\epsilon^{\alpha\lambda\mu\nu}$. Thanks to the properties of $\epsilon^{\alpha\lambda\mu\nu}$ we then have
$$ \epsilon^{\alpha\lambda\mu\nu} \partial_{\lambda} F_{\mu\nu} = 0 . $$
Next we separate the Faraday tensor into ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296164",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
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What is the difference between classical correlation and quantum correlation? What is the difference between classical correlation and quantum correlation?
| It feels like the answer was that "any correlation that is not classical is quantum". That is correct but it doesn't really explain where the quantum nature comes from and what it really is. In quantum mechanics, as opposed to classical mechanics, the outcome of an observable doesn't have to always be the same value. T... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Meaning of Fock Space In a book, it says, Fock space is defined as the direct sum of all $n$-body Hilbert Space:
$$F=H^0\bigoplus H^1\bigoplus ... \bigoplus H^N$$
Does it mean that it is just "collecting"/"adding" all the states in each Hilbert space? I am learning 2nd quantization, that's why I put this in Physics ins... | Suppose you have a system described by a Hilbert space $H$, for example a single particle. The Hilbert space of two non-interacting particles of the same type as that described by $H$ is simply the tensor product
$$H^2 := H \otimes H$$
More generally, for a system of $N$ particles as above, the Hilbert space is
$$H^N :... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296391",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Summer Winter cause As far as I understand, there are two main reasons for having lower temperatures in winter :
*
*shorter days, so the sun has less time to heat the earth
*smaller angle of incidence, so the energy from the sunlight is absorbed in a larger area on the ground
Which of these has a bigger effect? D... | The smaller angle of incidence should have the greater effect, otherwise during the summer the northernmost regions (in the boreal emisphere) would be hotter than the southern ones, and, believe me, northern Scotland in August is still colder than southern Italy in March. Or think about the Poles: they have six months ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296566",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is bench pressing your bodyweight harder than doing a pushup? Why does bench pressing your own bodyweight feel so much harder than doing a push-up?
I have my own theories about the weight being distributed over multiple points (like in a push-up) but would just like to get a definite answer.
| While doing push-ups, you don't push your whole body weight. You have your toes on the ground, so your body weight is distributed between your feet and your arms.
While benching, you have no support from feet. You hold the whole weight with your arms, so benching your body weight is always tougher.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296650",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "49",
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Covariant gamma matrices Covariant gamma matrices are defined by
$$\gamma_{\mu}=\eta_{\mu\nu}\gamma^{\nu}=\{\gamma^{0},-\gamma^{1},-\gamma^{2},-\gamma^{3}\}.$$
The gamma matrix $\gamma^{5}$ is defined by
$$\gamma^{5}\equiv i\gamma^{0}\gamma^{1}\gamma^{2}\gamma^{3}.$$
Is the covariant matrix $\gamma_{5}$ then defined ... | *
*by the definition of the $\epsilon$ symbol:
$-\frac{i}{4!} \epsilon_{\mu\nu\rho\sigma} = -\frac{i}{4!}(\gamma^0\gamma^1\gamma^2\gamma^3 - \gamma^0\gamma^1\gamma^3\gamma^2 + ... + \gamma^3\gamma^2\gamma^1\gamma^0) = i\gamma^0\gamma^1\gamma^2\gamma^3 = \gamma_5$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Electric field associated with moving charge I have recently started to learn about the electric field generated by a moving charge. I know that the electric field has two components; a velocity term and an acceeleration term. The following image is of the electric field generated by a charge that was moving at a cons... | No such exist in reality... Electrons or charged atoms never move in constant velocity and to stop one, one must apply electric o magnetic field...
Also electric field of an electron never changes regardless of how it is moving...
Isolated hypothetical cases are useless because one cannot prove it right or wrong... Rea... | {
"language": "en",
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"source": "stackexchange",
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2D time-independent Schrödinger Equation I'm considering the time-independent Schrödinger equation in two dimensions,
$$\frac{-\hbar^2}{2m}\left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} \right)\psi + U(x,y)\,\psi = E\,\psi \ \ .$$
Textbooks usually consider the case of a constant or zero pote... | The following article may be relevant: L. P. Eisenhart, "Enumeration of potentials for which one-particle Schroedinger equations are separable", Phys. Rev. 74, 87-89 (1948) I read it a few years ago, but I don't have immediate access to it right now. I remember it contained a long list of potentials where separation of... | {
"language": "en",
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Why is the electron self-energy gauge dependent? Let $\psi(x)$ be the field of the electron. Its Fourier transformed two-point function reads
$$
\langle\psi\bar\psi\rangle=\frac{1}{\not p-m-\Sigma(\not p)}.
$$
If we calculate $\Sigma(\not p)$, we observe that it depends on the gauge parameter $\xi$, which in principle ... | The propagator $S(p)$ is the Fourier transform of the two-point function
$S(x,y)=\langle\psi(x)\bar\psi(y)\rangle$,
$$
S(p) = \int \frac{d^p}{(2\pi)^4} \, \exp(-ip\cdot(x-y)) \, S(x,y)\, .
$$
Note that because of Lorentz invariance $S(x,y)$ does not depend on $x+y$. Clearly, the two-point function is non-local and n... | {
"language": "en",
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Higher-Order Derivatives in the Lagrangian I am trying to derive the equations of motion for a Lagrangian which depends on $(q, \dot{q}, \ddot{q}).$ I proceed by the typical route via Hamilton's Principle, $\delta S = 0$ by effecting a variation $\epsilon \eta$ on the path with $\eta$ smooth and vanishing on the endpoi... | You have to impose that
$\eta(t_0)=\eta(t_1)=\dot{\eta}(t_0)=\dot{\eta}(t_1)=0$ where $t_0$ and $t_1$ are the endpoints of the time interval over which you are integrating. Then, the last term is:
\begin{equation}
\int_{t_0}^{t_1}\frac{d^2}{dt^2}
\left(\frac{\partial L}{\partial\ddot{q}}\eta\right)dt =
\left[\frac{d}{d... | {
"language": "en",
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Can a telescope look into the future? If a telescope can see the past, can it look into the opposite direction and see the future?
I suppose I am trying to put time into a single line. (timeline) with a beginning and end, and we are in the middle.
If I can look out in any direction and see the photons that are billi... | When you see or hear anything you are perceiving the past. Any sound, any lightwave, takes a finite amount of time to travel from its source to its receiver. The telescope is just a fancy version, for light waves, of a hearing horn used by deaf people before electronics.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can the entropy of the universe increase when undergoing an irreversible process? So there’s something about entropy that I just can’t wrap my head around. So: we saw in class that when undergoing a reversible process, the entropy change of the universe (so of the system + the environment) is 0. And we saw that to ... | Consider an irreversible process between states a and b,
We write $dU = dQ_{irr} - dW_{irr}$
For a reversible process between a and b,
$dU = TdS - dW_{rev}$
Sine dU is the same for both, we have
$dS = \frac{dQ_{irr}}{T} + \frac{( dW_{rev} - dW{irr})}{T}$
It is obvious that the second term is non negative at all times.... | {
"language": "en",
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Would an Electron Gun create thrust in space? Using solar panels, and the resulting electrical energy, could an electron gun provide a suitable level of renewable thrust, better than an Ion thruster? If it would even create thrust at all that is.
| There is another aspect to this, that is the level of energy imparted to the electrons, and the quantum state they are in.There will come a time, when we have the ability to impart near relativistic velocities to particles, and to change the way they behave. Bunching electrons into large Bose Einstein condensates will ... | {
"language": "en",
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If time dilation can slow time down, is there away to speed time up? Okay, I know the title is really confusing but I couldn't find words to explain it sorry. Pretty much what I mean is, if I can get in a lightspeed spaceship moving away from earth, time slows down for me. So one year for me will be 20 earth years or w... | Being in a gravitational field is equivalent to accelerated frame... So we may accelerate towards the earth (in 0 g surrounding, so that acceleration causes us to experience gravity pulling us back in direction opposite to that of we are accelerating towards), so that while we experience the flow of time normally, time... | {
"language": "en",
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"source": "stackexchange",
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Concept of strain as applied to time What if we were to measure gravitational force as a function of strain in time $S_t$ as defined by $S_t=\frac{T_\mathrm{ref}-T_\mathrm{local}}{T_\mathrm{ref}}$ where $T_\mathrm{ref}$ is the rate of time at a massless reference clock at infinite distance from mass and $T_\mathrm{loca... | It's an interesting questions, Schwarzschild radii (SR) could be used as unit you are looking for since space and time warp relative to that and not distance as you are suggesting.
One SR away from a black hole will have the same time dilating effects and gravitational potential no matter what the size of the black ho... | {
"language": "en",
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Why center of mass formula is $m_1 r_1 = m_2 r_2$ for a two particles system? In this website, it states that if we have a two particles system and measure from centre of mass, then the following equation holds:
$$m_1 r_1 = m_2 r_2$$
where $m_1, m_2$ are masses of the two objects and $r_1, r_2$ are distances from cent... | I am not so sure about that expression; a definition of the CM system is that $$m_1 r_1^{cm}+m_2 r_2^{cm}=0.$$So $$m_1 r_1^{cm}=-m_2 r_2^{cm}$$ holds. This can also be shown in the laboratory system with the $x_{cm}$ definition (which directly follows form the first eq. I wrote).
Looking at the picture on the page I... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/298478",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Can a rocket with no forces acting upon it except a single push force with constant acceleration keep accelerating forever? I was wondering why a rocket with no opposing forces acting upon it couldn't keep accelerating given that it has the potential to release enough energy to maintain its acceleration at all costs. I... | To accelerate a body in space one need a thrust. Since nothing is faster the electromagnetic radiation all you can do is to accelerate your rocket with light. This indeed is possible, so sealing with the lights pressure from the sun is technical makeable. Using a light projector you can also accelerate a rocket.
But e... | {
"language": "en",
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Without the Michelson-Morley experiment, is there any other reason to think speed of light is the universal speed limit? If the Michelson-Morley experiment hadn't been conducted, are there any other reasons to think, from the experimental evidence available at that time, that Einstein could think of the Special Theory ... | The strongest current experimental evidence is the standard model of particle physics, the beautiful symmetries of SU(3)xSU(2)xU(1) with the plethora of data that produced them, would fall on their face if c were not the limiting velocity, i.e. if special relativity did not hold.
Every single mass measurement in the pa... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "47",
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Confusion about probability of finding a particle The wave representation of a particle is said to be $\psi(x,t)=A\exp\left[i(kx−\omega t)\right]$.
The probability of the particle to be found at position x at time t is calculated to be $\left|\psi\right|^2=\psi \psi^*$ which is $\sqrt{A^2(\cos^2+\sin^2)}$. And since $\... | It is not true that the probability of finding the particle at $x$ is $|\psi|^2$ (think of it as if you have a continuum of possible values, what is the probability of obtaining an specific value?). As it has been pointed out, $|\psi|^2$ can be interpreted as a probability density, so the probability of finding a parti... | {
"language": "en",
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"source": "stackexchange",
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Electron emission from insulators? can electron emission happen from insulators? I mean can the electrons in an insulator jump into the vacuum around them when sufficiently large electric fields are applied like in conductors?
| Yes it can. In an insulator, electrons are bound on Atoms, but do not form an electron gas as in metals. With electromagnetic Radiation of high intensity, electrons can be emitted from the Atom. A photon with frequency $\nu$ carries an energy $E=h \nu$. An electron of the exterior Atom hull will be emitted if the photo... | {
"language": "en",
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Why are hollow conductors used for signals of a certain frequency? So this question is really about skin depth. I have been introduced to the skin depth by a simple model (simple equation for electrons in a metal with a damping term) of polarisability for a metal. In this calculation, using the dilute form of the class... | For microwaves the skin depth is too small and it does not conduct efficiently, so you have to design it and use it as a waveguide. For lower frequencies the skin depth causes the conduction to be near the surface. See the answer and comments already given at Does electricity flow on the surface of a wire or in the in... | {
"language": "en",
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Are volume of solids & liquid totally independent of pressure In my book it is written as
$GASEOUS$ $STATE$ : The state is characterized by sensitivity of volume change with change of pressure and temperature.
Now my doubt is that are volume of $solids$ & $liquid$ totally independent of pressure??
I searched on intern... | No, the volume of liquids and solids does depend on pressure. However, the volume of gases is drastically more sensitive to pressure. (This property is known as compressibility.)
In most contexts, the dependence of volume on pressure for liquids and especially solids is considered negligible (that is, most liquids and ... | {
"language": "en",
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Why is Sachdev-Ye-Kitaev (SYK) Model model important? In the past one or two years, there are a lot of papers about the Sachdev-Ye-Kitaev Model (SYK) model, which I think is an example of $\mathrm{AdS}_2/\mathrm{CFT}_1$ correspondence. Why is this model important?
| SYK model provides us with the simplest example of holography which is much easier to study than canonical $AdS_5 \times S^5$ case due to much lower dimensionality. It was the initial motivation for Kitaev to study this model. Here is a set of 2 lectures in which he briefly discusses it.
Because of its simplicity, it i... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why wouldn't the part of the Earth facing the Sun a half year before be facing away from it now at noon? The Earth takes 24 hours to spin around its own axis and 365 days to spin around the Sun. So in approximately half a year the Earth will have spun around its axis 182.5 times.
Now take a look at the following pictu... | Our clocks are set so that 24 hours is the time for the Sun to appear in the same part of the sky. What this means in terms of the Earth's orbit and rotation is that the Earth does slightly more than a complete rotation in 24 hours.
Let's say that your picture is drawn from the perspective above Earth's north pole. Ear... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/300146",
"timestamp": "2023-03-29T00:00:00",
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Different frictional forces- damped harmonic motion What classifies as damped harmonic motion? All of the books/Web pages I have looked at about damped harmonic motion have used a damping force that is proportional in magnitude to the velocity, even if it is not appropriate for a particular problem. For example the equ... | As far as I understand differential equations and simple harmonic motion, the reason that your solution doesn't display decaying amplitude is simple. you assumed that the force F is constant for all time t, and a system of spring force with an additional constant force, simply doesn't have decaying amplitude (you can t... | {
"language": "en",
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Tunnel Effect and wave in classical mechanics and in quantum mechanical My question is: from the point of view of classical mechanics, when a wave encounters a barrier, it is totally transmitted through the barrier, while in quantum mechanical there is also a part of the wave that is reflected? Or is it the opposite? I... | If you have a particle wave impinging on a finite width potential barrier, you will always have a quantum mechanical reflection and transmission, for a particle energy below or above the barrier height. Classically, there is only a transmission for an energy above the barrier height and only a reflection for an energy ... | {
"language": "en",
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Why Weyl's (infinitesimal geometry) theory of gravity is physically unreasonable? It is usually mentioned that Weyl theory is generalization of the Einstein’s gravity that included Electromagnetism.
In the same time, they saying that it is physically unreasonable and inconsistent with QM. Is it possible to explain in a... | I hope it is clear to OP that the validity of physical models can only be judged by experimental verification.
Weyl's theory explains electromagnetism through an extended affine connection. Parallel transport with respect to this extended connection no longer preserves the interval $g_{\mu \nu}(x) v^{\mu} v^{\nu}$ of t... | {
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Can someone give me an intuitive meaning of the term "moment of area".? Moment if inertia is the rotational analogue of mass. But I can't get the idea of the term "moment of area". What does it mean?
| In general, a moment is a quantity that describes the shape and position of something. In statistics, the mean and standard deviation are the first and second moments of a distribution; they are numbers that tell the reader approximately where the distribution is located (the mean) and approximately how wide it is (the... | {
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Momentum state of a particle Why is the momentum state of a particle in quantum mechanics given by the Fourier transform of its position state? For instance, in one dimension given by
$$\varphi(p)=\frac{1}{\sqrt{2\pi\hbar}}\int \mathrm dx \, e^{-i p x/\hbar} \psi(x).$$
| In general, a Fourier transform takes functions on a group $G$, or a space $X$ on which $G$ acts, and decomposes them in terms of characters of the group, such as $\chi : G \to S^1$, and the coefficients of the decomposition are encoded in the transformed function in the Pontryagin dual $\hat G$ of $G$.
Now for Euclide... | {
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How to get the force constant? Suppose we have a spring with a difference . When it is streched by x , the restoring force is not proportional to x instead ,
F = $x^3$ + $x^2$ + $x$
Now , for normal springs F = kx
where k : Spring constant
If we want to find out the spring constant for the given spring then how wi... | Yes indeed: we need the definition of spring constant for such cases. For small enough $x$ you can neglect the $x^2$ and $x^3$ so that
$$
F\approx x
$$
which means that $k=1$. For a more general force, we can always define
$$
k\equiv \lim_{x\to x_\mathrm{eq}}\frac{\mathrm dF}{\mathrm dx}
$$
where
$$
F(x_\mathrm{eq})\e... | {
"language": "en",
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What is really instantaneous? How can a body travel at an instant and what does instantaneous speed tells us?
What really is meant by speed of an object at an instant if an object does not travel at an instant? I would like a mathematical explanation.
| Instantaneous (linear) speed isn't that helpful. In planar rigid body mechanics instantaneous rotational speed and the point about which the body is rotating is extremely helpful as it describes the velocity of the body at every other point (ie. describes the motion completely).
For example see my answer in Rotation o... | {
"language": "en",
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Evolution of neutrinos flavor states What do we mean by saying that neutrino flavor states do not satisfy the schrodinger equation? How does the time evolution of states look like?
| Neutrino's flavor states evolve with time by a process called oscillation in which the three definite mass eigenstates that each flavor has associated with it exist in superposition.
A neutrino may be created in one flavor, an electron neutrino for example, and be considered in a super position of electron, muon, and ... | {
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Why do we assume weight acts through the center of mass? The weight of a body acts through the center of mass of the body. If every particle of the body is attracted by earth, then why do we assume that the weight acts through the center of mass? I know that this is true but I can't understand it. Does it mean that the... | As a point of clarification which perhaps has not been made as clearly in the other answers: No, the weight of a body does not act through the center of its mass, and no such assumption is necessary. However, one can show (see the answer by @tomph) that the sum of all gravitational forces (which indeed do act on any sm... | {
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} |
How do Faddeev-Popov (FP) ghosts help path integrals? How does the inclusion of Faddeev-Popov ghosts in a path integral help to fix the problem of over counting due to gauge symmetries?
So, after exponentiating the determinant for the inclusion of either anti-commuting or bosonic variables and the corresponding extens... | The ghosts are not so much inserted, as they naturally arise. The path integral of a gauge theory naively defined will integrate over all fields, including those related by a gauge symmetry, which are seen by the theory as being equivalent.
The Faddeev-Popov procedure provides a means to split our integration over phys... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/301966",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 2,
"answer_id": 1
} |
Solar panel frequency range What is a solar panel's frequency range (i.e. from THz to THz)? Is there a way to capture energy that exceeds that frequency range, either more towards IR or UV? If so, you could produce energy from sound, considering its frequency is 20-20,000Hz.
| Currently the best way to generate electricity from sound is a piezoelectric transducer. You can find these in some microphones. Your garden-variety piezo buzzer (such as the little black cylindrical "speakers" in desktop computers) is capable of generating current from sound, though it's generally used to produce soun... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/302301",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
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