Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What do we mean by charge in physics? I am drawing the comparison between electrical charge and colour charge, in electric charges they communicate with (virtual) photon and photon itself is a boson carrying no charge. How about colour charges how do they communicate with each other if they themselves are the boson?
| Charge in this context refers to the fundamental coupling between particles (either matter or gauge bosons) and gauge bosons. Let me explain, starting with the QED sector:
*
*The electron is electrically charged. This means it interacts with the photon.
*The photon is electrically neutral. This means it does not i... | {
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Problem involving gravitational potential energy
Two uniform solid spheres of equal radii $R$, but mass $M$ and $4M$ have a centre separation of $6R$. The two spheres are held fixed. A projectile of mass $m$ is projected from the surface of the sphere $M$ and towards the second sphere along the line joining the centre... | In this situation, the minimum speed is a limiting value. Anything above that will carry the projectile beyond the null point.
| {
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Does momentum conservation imply energy conservation? I was trying to figure out the situation in which energy is conserved and momentum is not and it was quite easy to find out one case which is of a stone tied to a string moving in a uniform circular motion.
Then I thought to consider the reverse situation in which m... | If you’re just considering mechanical energy, consider the case of a firework or other exploding object. The total momentum is conserved, but the kinetic energy is increased from the chemical energy of the explosion.
More formally, momentum conservation is associated with isotopic space while energy conservation is ... | {
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Time ordering of Normal ordered products in Wick's theorem I have a small doubt regarding wick's theorem.
Is it normal ordered products are time ordered?
Actually in wick's theorem we usually don't write the symbol of time ordering in front of normal ordered products that's why I asked,
In S matrix expansion for... | *
*Time-ordering and normal ordering are 2 different operator ordering prescriptions.
*It is not meaningful to apply them simultaneously, because which prescription should we then follow? However nested ordering prescriptions do make sense, cf. e.g. this Phys.SE post.
*(One version of) Wick's theorem translates bet... | {
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Difference between oscillation and radiation? Im doing this specifically in terms of the Zeeman effect, but in general I have read some stuff about osciallations and orientations that is confusing me. If we have a magnetic dipole, propagating a field in all 3 spatial directions, and then we apply an external magnetic f... | An oscillating electric charge emits electro-magnetic radiation. However, the spatial distribution of this radiation is not uniform, but has a strong preference angle
copied from here. Thus, the dipole does not radiate in the direction of its oscillation.
| {
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Fermion zero modes extra conditions? A fermion zero mode is a zero eigenfunction,
$$i\gamma^\mu(\partial_\mu-iA_\mu)\psi=0$$
The number of zero modes is apparently related to the instantons of the gauge field.
But now my question is about 'ordinary' solutions to the Dirac equation. Even if there is no gauge field and e... | The eigenvalues of the Euclidean Dirac opertor are of the form $i\lambda+m$, $\lambda,m,\in {\mathbb R}$. Instanton backgrounds can allow solutions with $\lambda=0$, but if $m\ne 0$ you cannot get $i\lambda+m=0$. Your confusion comes from the fact that the Euclidean Dirac operator with hermitian $\gamma^\mu$ obeying... | {
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The Vertical Launch of a Rocket From Q7 on Pg.22 of "Upgrade Your Physics" by BPhO/Machacek
A rocket of initial mass $M_0$ is being launched vertically in a uniform gravitational field of strength $g$.
(a) Calculate the final velocity of the rocket 90 % of whose launch mass is propellant, with a constant exhaust veloc... | As you say :
$$M(t) = M_o - \alpha t$$
But you must know that at time $\tau$ after start the object now has $0.1M_o$ mass (since it consumed all of it's fule).
Therfore
$$0.1M_o = M_o - \alpha \tau \tag 1$$
$$\Rightarrow \tau = \frac {0.9M_o}{\alpha} \tag 2$$
After substituting $(1)$ and $(2)$ into your equation we g... | {
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Conceptual freshman year physics question about acceleration A particle moves along the x-axis.
When its acceleration is positive,
A. its velocity must be positive
B. it must be speeding up
C. it must be slowing down
D. its velocity must be negative
E. none of the above is always true
The answer to this is $E$, but ac... | Two examples should illustrate why answer "E" is the correct answer.
When you work a physics problem, you get to decide which direction is positive. Accordingly, when you are driving down the road, it is valid to state that the direction that is in front of your car is the positive direction.
Example 1: You are starti... | {
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What is meaning of negative frequency got from Doppler equation? If a observer is moving away from a stationary sound source with a velocity V' then observed frequency is (1-V'/v)f where v is the speed of sound and f is the frequency observed when at rest. Now if V'>v what will happen actually? What is the meaning of n... | This will be easier to picture with you in a boat on a lake with a wave source.
Say you travel away from the source, but slower than the waves propagate. Then the waves will travel past you and hit your boat from behind. In your formula for the doppler frequency, this will give a positive frequency.
If you speed up to... | {
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Antimatter and quantum mechanics This question could have a very simple answer but I could not find that answer anywhere. My question is since electrons, protons, etc they all have their antiparticles, why are not they mentioned in Quantum Physics? And if they are real, should not they be included into Schrödinger equa... | The non-relativistic behavior of antiparticles can be understood with the Schrodinger equation. For example, anti-hydrogen is approximated by the Schrodinger equation to the same accuracy as hydrogen is. This is often never mentioned in an introductory Quantum Mechanics course.
But the relationship between particles an... | {
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What is the reason to believe that the laws of physics are same in all frames of reference? The first postulate of Special Relativity is that the laws of physics must be the same in all frames of reference i.e. invariant of coordinate transformations. I know this might be moot to ask but after reading a critique's pape... | The laws of physics being the same in all inertial reference frames is an idea that originates not with Einstein but Galileo, who noted if you're in a sealed windowless room on a ship you can't tell whether the ship is moving (though you can tell if it's accelerating, such as when it bobs). Special relativity differs f... | {
"language": "en",
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What happens when the amplitudes of interfering waves is different in the phenomenon of beats? I had read that for the formation of beats, two waves must interfere such that they have similar frequencies but not identical, and their amplitudes should be identical. I don't understand why should their amplitudes be ident... | Beat frequency is as you say when the difference in frequency is low enough for us to make out a beat. When the beats occur the signal is ideally interfered into $0\%$ amplitude. If the amplitudes of the two signals however are very different we'd have a reduction in intensity but not an attenuation to $0\%$ but maybe ... | {
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Entropy change in the free expansion of a gas Consider the adiabatic free expansion of a gas since there is no external Pressure hence Work done on the system is 0 and since the walls are insulated (hence adiabatic) the heat absorbed is 0. However since this is a irreversible process then entropy change > 0 hence dQ > ... | Substitute the irreversible spontaneous expansion with an appropriate reversible process. This can be done thanks to entropy being a state function.
Since in the spontaneous expansion the temperature remains constant, you can choose a reversible isothermal expansion with the same initial and final state as in the spont... | {
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Conservation of Energy stored in electric field? Let's say due to some particle process, an electron is created at time $t >0$. And from this moment on, the electric field will start to propagate to infinity at the speed of $c$. But we know that the energy stored in the electric field is proportional to the volume inte... | No energy conservation is not violated because for creating an electron,energy is required.In this case without specifying any source you have violated the law of conservation of charge.
| {
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Does friction do work or dissipate heat? I know there are a bunch of similar questions but I read through them all and they don't answer my question.
Let's say I give a box on a floor an initial "kick" of force such that it has kinetic energy $KE$. Due to friction between the box and the floor, the box will slide to a ... | This is an answer to the original title:
Is friction work or heat?
Neither work nor heat. Friction is a force:
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.2 There are several types of friction
In physics one has to be accurate... | {
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Why is law of conservation of angular momentum (seemingly) being violated over here?
Description of the system
Assume two point masses one at the point $C$ and the other on the circumference of the circle with radius $R$. They are attracting one another gravitationally and no external forces are acting on them. The po... | For circular motion ${\bf r} \times {\bf p} = rp$ as these are perpendicular vectors and $\sin 90=1$. So angular momentum is constant hence conserved. There is no torque with respect to the centre of the circle. Of course angular momentum is not conserved with respect to any other position. The reason is that there is ... | {
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Conduction band and free electron I have learnt that at room temperature there are some free electron(not bound to any nucleas) in a conductor and when an electric field is applied they form an electric current.I am quite comfortable with this theory but then I am introduced to band theory which talks of valence and co... | Solids contain a huge no of atom packed closely together, when such a atom is isolated then it is discrete set of electronic energy levels and when the isolated atom brought together their outermost electronic level overlap and the form energy bands to preserve the Pauli exclusion principle.
When the distance between a... | {
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What makes a wheel spin? I don't fully grasp what makes a wheel much easier to move than to push a solid block.
The pressure at the point of contact between a wheel and the ground must be pretty enormous compared to the pressure created by a block of same material and mass as the wheel.
Friction is defined as the pro... | Some of the other answers are correct, but too high of a physics level to be appropriate to the question. This needs a low-tech answer.
First, consider how much easier it is to walk than it would be to drag yourself across the ground. The reason is because you're not dragging anything - you lift a foot up, you move it ... | {
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How do I find the equilibrium points in an electric field created by three or more charges? I know that for two charges $q_1$ and $q_2$ of the same polarity, the neutral point will be at the internal section of the segment by the ratio of $\sqrt q_1$:$\sqrt q_2$, and if they are of opposite polarity the point will be a... | There is in general no simple closed formula for the positions of the neutral points of a system of 3 or more charges. The centre-of-mass formula does not apply because the neutral points have no connection with the centre of mass. There can be several neutral points but only one centre of mass.
If charges $Q_i$ are p... | {
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Does polarisation matter in double slit experiment? So I am studying diffraction, in particular the diffraction of electromagnetic waves using a double slit set up. However, there seems to be no mention of the polarisation of electromagnetic waves and I wondered would the experiment differ if the polarisation was diffe... | Polarisation can matter in real two slit experiments. If metal is used for the slit then the boundary conditions are different for perpendicular and parallel polarization. The difference becomes important when the slit width and separation are comparable to the wavelength, so for large diffraction angles.
| {
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Unique characterization of Ideal gas In Thermodynamic state - Wikipedia, it defines a thermodynamic state as:
A thermodynamic state of a system is its condition at a specific time, that is fully identified by values of a suitable set of parameters known as state variables.
In the part explaining state functions, it s... | The ideal gas law reads
$$
p V = n R T
$$
where $R$ is a constant or alternatively, $p V = N k_B T$, where $k_B$ is a constant. Thus, if three of the four variables are given, you can use this equation to determine the fourth variable.
How to derive this law statistically, was discussed here.
| {
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Three-Dimensional Picture from 2D tiles The CMS Silicon Pixel detector can create three-dimensional pictures of a particle's trajectory. It specifically says that "because the detector is made of 2D tiles, rather than strips, and has a number of layers, we can create a three-dimensional picture."
Why the emphasis on "r... | To get a trajectory in space you need an (x,y,z) . The two dimensional panels provide the (x,y) of their location ( with error their width) and the layers the z variable from their z location . A strip has only one dimension in the panel plane, so cannot give two coordinates. From the description of strip detectors a c... | {
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Solution to infinite particle creation in EM by classical sources In this question: Peskin and Schroeder "Particle Creation by a Classical Source"
particle creation by a classical source is discussed. Doesn't this mean that a static constant source would create infinite energy? I heard that QFT solves this problem by q... | A classical charge $|Q|\gg e$ (source) is neutralized gradually by the oppostely charged particles of the created pairs. So the number of pairs created is less than $|Q/e|$.
| {
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How does the current remain the same in a circuit? I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.
Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the ... | @Farcher answer, particularly the last paragraph, sums it up perfectly. The positive work done by the electric field on the charge giving the charge kinetic energy equals the negative work done by the lattice structure that takes away the kinetic energy of the charge increasing the internal energy of the structure. Ult... | {
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What are the eigenfunctions of Hamiltonian of a free particle? From my actual understanding of quantum physics observable are operators, when we measure some observable we will find an eigenvalue of such operator, and the system will collapse in the eigenstate.
The Hamiltonian is the operator related to energy, just li... | $ψ(x)=Ae^{ikx}+Be^{−ikx}$ is the correct general eigenfunction for a given eigenvalue $E$:
But there is the boundary condition that $ψ(x)$ must go to zero at plus and minus infinity. In order to follow it, $E$ can not be a fixed value, but a continuous interval $[E_1,E_2]$.
And $ψ(x)$ must be a Fourier integral.
| {
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Is it possible to build a quantum logic circuit that has feedback loop? Using classic logic gates, it is possible to make circuits with loops, i.e. with feedback. I wonder whether that is still the case using quantum gates. I do not mean sequential circuits that are synchronized using clock, but simple logic circuits w... | Using the output of a gate as input of another, in the quantum case, amounts to applying something like a CNOT operation. Unless you want classical feedback (e.g. the decision of what ist the next gate being conditional to a previous measurement result), in which case the evolution ceases to be unitary (which doesn't m... | {
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Graph of periodic motion due to wave Wave is a disturbance in a medium, due to this disturbance the particles in the medium oscillate. Due to this oscillation we say that the wave is sinusoidal because the motion of the particle is periodic. So we REPRESENT the motion in sine wave.
Periodic motion can be represented by... | Re.
Due to this oscillation we say that the wave is sinusoidal because the
motion of the particle is periodic
Sinusoidal motion is not required for oscillation. For example square waves or triangular waves oscillate.
So if instead of representing in sine graph can we represent it as
square (instead of curves) p... | {
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Relation between grand potential and expected number of particles in an energy state? During the review of my lecture notes I stumbled upon an equation that gives me some trouble understanding.
The big task that motivates the following is to express the entropy $S$ with the expected number of particles in an energy sta... | The trick is to use the definition of a derivative of a logarithm. Lets do the calculus for the FD case:
$$-\frac{1}{\beta}\ln \mathcal{Z}_G \stackrel{?}{=} \sum_i (E_i-\mu)\langle n_i\rangle$$
If you see in the right side of the equation, you have a case $\frac{f'(x)}{f(x)}=\frac{d(\ln f(x))}{dx}$. Remember the defini... | {
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Is the commutation relation in quantum mechanics right? $$[ \hat X, \hat P_x\hat F(x)\hat P_x] =\frac{\hbar}{i}[\hat F(x)\hat P_x+ \hat P_x\hat F(x)]$$
It's given in the book "Basic Quantum Mechanics" by R.L. White.
Maybe I am doing something wrong.
What I am getting is:
$$[ \hat X, \hat P_x\hat F(x)\hat P_x] =-\frac{... | I think you can try using the identity $[\hat{A},\hat{B}\hat{C}\hat{D}]=[\hat{A},\hat{B}]\hat{C}\hat{D}+\hat{B}[\hat{A},\hat{C}]\hat{D}+\hat{B}\hat{C}[\hat{A},\hat{D}]$. Then, according to your question, we have
$$ \begin{align*}
[\hat{X},\hat{P}_{X}\hat{F}(\hat{X})\hat{P}_{X}]\Psi&=[\hat{X},\hat{P}_{X}]\hat{F}(\hat{X}... | {
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If different wavelengths of light have different speeds, how can they move together as a white light in air? My question is with respect to Newton's experiment of using two identical glass prisms [in which one is inverted with respect to the first one]. When he allowed all the colors of the spectrum to pass through the... | The speed of light in a vacuum is constant for all wavelengths. In other media (like glass), it can vary. The speed of light in a particular medium doesn't depend on its history, only on what the medium is. Questions such as " Will it speed back up to the speed of light?" don't make sense - the speed of light depends o... | {
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Why isn’t the center of the Earth cold? If the pressure of the Earth is keeping the inner core solid, keeping it rigid to take up the least space, and temperature is dependent on how much the atoms are moving, why isn’t the inner core cold? If the pressure is so high that it’s forcing the inner core to be solid then th... | I'll answer by analogy with a spring:
*
*Temperature <=> Energy in vibration of spring
*Pressure <=> Compression of spring
*Phase state (solid or liquid) <=> Movement of the spring
Temperature is basically the energy of the moving particles.
If you take our analogous spring and have no weight on it (no pressure)... | {
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Why is the von Neumann entropy maximised when $p_n=1/N$? For example, $\hat \rho=\sum_{\substack{n}} p_n |E_n \rangle \langle E_n|$ is a stationary mixed state of a given quantum system, where $|E_n \rangle$ are eigenstates of the Hamiltonian $\hat H$ with the eigenvalues $E_n$.
In every book that I read on quantum in... | I'm assuming you meant the say that $p_n=1/N$ is the maximal value of the von Neumann entropy without constraining the mean energy (otherwise the statement is not true).
One way to see it is using Lagrange multipliers. You want to maximise $S(\mathbf p)\equiv-\sum_i p_i \log p_i$ in the hyperplane $\sum_i p_i=1$. For t... | {
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How strong would the electromagnetic field of the earth and the planets would have to be, in order to mimic the effects of gravity? How strong would the combined forces of electromagnetism on the earth and planets need to be, to mimic, and therefore, replace gravity?
| The gravitational force between the Earth and Sun is easily calculated to be about $3.5\times10^{22}$ newtons.
If the Earth and the Sun had opposite charges of magnitude $3.0\times10^{17}$ coulombs, their electrostatic attraction could "replace" this gravitational attraction. (Unequal charges would also work as long as... | {
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Difference between adding Force Vectors and adding Velocity Vectors Consider the following two situations.
Case I
I am able to solve this question. The answer to this question is = 5 m/s. I have attached the solution in the end.
This is not the doubt. Kindly read further to understand the theoretical doubt.
Case II... | The velocities add exactly like the forces, her to about 7,21m/s not to 5.
the solution you give is wrong. Do you really believe , that the net velocity is exactly the size and direction of v1? The equation which gives you sin(theta)=0 is wrong.
may be you just add the two vectors graphical to see it?
| {
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Direction of average acceleration in circular motion I know that the instantaneous acceleration is always directed towards the center of the circle.But what about average acceleration.
In the above figure my book says place change in velocity along the line that bisects angle $r$ and $r'$ and observe that it is directe... | Since the average acceleration is along Δv (a=Δv/Δt), the average acceleration is perpendicular to Δr. We already know that, since the path is circular, v is perpendicular to r and so is v' to r', according to the figure given by you. (Since the velocity vectors v and v' are always perpendicular to the position vectors... | {
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Why traditional turbulence theory concerns so much about statistics such as correlations? I have been wondering why the traditional turbulence theory, e.g., Kolmogorov's 1941 theory, concerns so much about things like two-point correlations, structure functions, their scalings, and so forth. I saw somebody says that, I... | *
*The average two point correlation tels us how large are the phenomena appearing in the flow. Theory actually shows us that turbulence quickly becomes a cascade of similar phenomena but at a smaller and smaller length scale. Turbulence is an mechanism of transferring energy from macro to micro scales much more effic... | {
"language": "en",
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Are the boundary and initial conditions only effecting parameters make turbulence unpredictable? The book that I used to study turbulence states that "in a laboratory experiment initial and boundary conditions can not be fully under control, despite all the effort there will be infinitesimal variations between experimen... | This is just a long comment. The idealization must include instruments that have infinite precision, in a world without thermal fluctuations. In such case yes, if everything is exactly equal (including the position and velocity of every molecule) the predictions will be too. All these assuming a classical world, becaus... | {
"language": "en",
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Is the movement of heated gas via combustion considered "work" and thus a form of mechanical energy? I'm teaching middle school kids about energy, but I got curious for my own education:
Does heated gas, as a product of combustion, produce mechanical energy or is this conversion (from chemical to mechanical) too neglig... | It is chemical energy, and it can be transformed into heat and from here to work, like in an Otto engine. Here the efficiency is limited by the Carnot efficiency. Alternatively, it can be transformed directly into work, like in molecular engines, or fuel cells, which in general are more efficient. I might be wrong on ... | {
"language": "en",
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Why do springs have a linear relationship? Why does:
F = k*(change in position)
Why can't the relationship be quadratic or higher ordered?
| Springs do not always follow Hooke's law. Hooke's law is a very good law, and it handles a lot of cases, but it's not The Law.
As J.G. points out in his answer, Hooke's law can be seen as an approximation that's good for small changes. As it turns out, for the way springs deform, its a very good law because springs t... | {
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Why Pauli matrices are the same in any frame? On page 157 of Schwartz's QFT book, He write that “$\sigma_i$ do not change under rotations”.
If so, changes in $\psi$ and $B$ cancels, so we can get that $(\vec{\sigma} \cdot \vec B)\psi$ is rotationally invariant.
But why Pauli matrices are the same in any frame?
Any hint... | Pauli matrices is sets of numbers, they don't transform under rotations in contrast of vector $\vec{B}$ or field $\psi$!
See for details An introduction to spinors around (31).
Another useful reference Spin, topology, SU(2)$\to$ SO(3). See around (7).
Main idea:
Using therms like $(\sigma^i B^i)$ one can convert rotati... | {
"language": "en",
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"source": "stackexchange",
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Splitting a single particle wave function The wikipedia article on the double slit experiment contains the following animation:
https://upload.wikimedia.org/wikipedia/commons/transcoded/a/a0/Double_slit_experiment.webm/Double_slit_experiment.webm.180p.vp9.webm
Here we can see that part of the wavefunction is reflected ... | When a single electron is fired it will not give the full probability function that you see in the animation, in fact there are other paths of low probability that are not even shown. Any particle has a chance of going anywhere, that's why we can say a single particle many has possible paths or wave functions. The sing... | {
"language": "en",
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How can I determine the mean size (area) of the surface reconstruction domains from a LEED (low energy electron diffraction) pattern? How can I determine the mean size (area) of the surface reconstruction domains from a low-energy electron diffraction (LEED) pattern?
The cross-section of the electron beam is definitely... | Focus your beam to a spot size smaller than the domain size and scan the intensity of a peak that is due to the surface reconstruction.
| {
"language": "en",
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Why bound currents cannot be detected in experiment? In today's group meeting about anomalous Nernst effect, I learned that bound currents cannot be detected in experiment. Why?
| While finding the vector potential due to piece of magnetized material with magnetization M ,it is turn out that it is same as potential produced by a volume current and a surface current called bound current. Physical interpretation for them that in uniform magnetized material there tiny current loops which produces ... | {
"language": "en",
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How to find the magnetic field of a current using the differential form of Maxwell's equations? To find the magnetic field produced by a long straight wire, one would ise either Biot-Savart law or Ampere's Law in integral form. How do you find this simple result starting from $\nabla \cdot \vec{B} = 0$ and $\nabla \tim... | As others already pointed out, it is hard
to solve this problem in cartesian coordinates
and from the differential Maxwell equations.
But anyway, here is a rough sketch
without going too much into the details.
The current density $\vec{J}$ is zero everywhere,
except in the wire (at $x=0, z=0$) where it is
infinite and ... | {
"language": "en",
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Orthogonality of a Lorentz Boost Matrix in terms of an invariant I have been doing questions recently involving Lorentz boosts. However I was wondering if the Lorentz boost matrix $Λ$ is orthogonal.
$$
\left[\begin{array}{cccc}\hat {ct} \\ \hat x\end{array}\right] =
\left[\begin{array}{cccc}{\cosh \varphi} & {-\sinh \v... | Yes your statement is correct. Rotations are isometries of 3D Euclidean space: they preserve the inner product defined using the Euclidean metric. Rotations + boosts are isometries of 4D Minkowski space: they preserve the inner product defined using the Minkowski metric (technically this isn't an inner product since it... | {
"language": "en",
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Doubt related to the use of Gaussian Surfaces My textbook says we need to take care not to let the Gaussian Surface pass through any discrete charge. However, the Gaussian Surface can pass through a continuous charge distribution.
Why so?
| Point charges correspond to a discontinuous charge distribution. For instance if your surface is a sphere of radius $r$ enclosing a uniform charge distribution $\rho_0$, then the enclosed charge is perfectly defined ans is a continuous function of $r$ ($Q(r) = 4/3 \pi r^3 \rho_0$) so when using the macroscopic Gauss eq... | {
"language": "en",
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"source": "stackexchange",
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Effective action for ferromagnetism and ferroelectricity In Three Lectures On Topological Phases Of Matter section 2.1 mentioned, that:
$$
I^\prime = \int dt d^3x \; \left(\vec{a}\vec{E}+\vec{b}\vec{B}\right)
$$
correspond to ferromagnetism and ferroelectricity. And that
$$
I^{\prime\prime} = \int dt d^3x \; \left(a_{i... | The energy of an electric dipole moment $\bf{p}$/magnetic dipole moment $\bf{m}$ in the external field is proportional to it, $W = -\bf{p\cdot E}$ or $W = -\bf{m\cdot B}$. In a ferromagnetic sample the local magnetic dipole moment is propotional to element of volume $d^3x$. This is just the same as you have in the expr... | {
"language": "en",
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Clarification of the concept "less resistance means less heating" in a wire So my textbook says that the reason cables that are suppose to carry high currents, are thicker that those that are meant to carry lesser current, is that "less resistance (of the wire) means less heating..."? Is this even true?
Isn't CURRENT ... |
If we decrease resistance, more current flows
You're talking about the resistance of the transmission wires that carry electric current from the generating station (or other power supply) to the load. Normally those things are sized such that the power dissipated in the transmission line is much less than the power d... | {
"language": "en",
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What can cause a steam condensate pipe to oscillate and is this normal? I was visiting an industrial site not too long ago and I noticed an interesting phenomenon involving one of their steam condensate pipes. This (insulated) pipe was suspended from the ceiling. It hung down about 20 feet, supported by a series of s... | This is common in piping systems carrying steam and connected to big boilers and turbines, for the following reasons.
A boiler generates a strong random "rumble" while operating, which comes from the boiling process inside it. When connected to piping systems which possess compliance and inertia, those pipe runs are dr... | {
"language": "en",
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How to find the critical exponent of some directional dependent correlation length? I am working on a two dimensional anisotropic system with correlation length diverging with different critical exponent in different directions. And I am wondering if there is any theoretical prediction on what exponent characterize the... | When you refer to there being two different correlation lengths in two orthogonal directions, I assume what you mean is that the correlation functions take the form
$$
G(x,y) = \exp\left[ - x/\xi_x - y/\xi_y \right]
$$
at long distances (let me know if you have something else in mind). Now, if you consider the decay of... | {
"language": "en",
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Gravity, matter vs antimatter I have a simple question regarding matter-antimatter gravity interaction.
Consider the following though experiment:
If we imagine a mass $m$ and an antimass $m^-$, revolving around a large mass $M$
the potential energy of mass $m$ should be:
$$ U_1=-\frac{GmM}{R} $$
and the potential energ... | There are also constraints on antimatter gravitational coupling from studies of neutral mesons. In the Standard Model, neutral kaons (down-antistrange and strange-antidown) can oscillate into one another via weak interactions. By measuring the decays of the kaon beam, you can put very accurate constraints on the rate o... | {
"language": "en",
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Velocity after applying a force in the vacuum I’m sorry for so simple question, but I just need to be sure.
I understand, that the changing of the speed occurs only when the force is applied, I understand that if one punch a ball in the free space it will infinitely move with a constant velocity
Some point-like body wi... | Firstly, the body will only accelerate while the force is being applied, and it will move at a constant velocity the instant the force stops being applied.
Your final equation is just a variation on
$$x=\frac12at^2$$
Why that factor of ½ arises can be shown using elementary calculus, or by a geometrical argument.
Both... | {
"language": "en",
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The Enigma of Universal Gravitation Forces This is taken from a book called "Physical Paradoxes and Sophisms" by V. N. Lange.
1.22. The Enigma of Universal Gravitation Forces
The law of gravitation can be written $F=\gamma\frac{m_1m_2}{R^2}$.
By analyzing this relationship we can easily arrive at some interesting ... | We have the power to overcome this near infinite force of gravity because the electromagnetic forces generated by our muscles is much much stronger.
Every cell in our body burns on the order of 1 to 10 million molecules of ATP every second.
That’s when those cells are at rest.
During periods of high intensity, that ATP... | {
"language": "en",
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What does Heisenberg's uncertainty principle tell about nature? I agree with the fact that the principle points out to the inaccuracy in the measurement of the two quantities of the particles (momentum and position).
But measurements apart, does it explain anything about how nature works, in general? As in, I think the... | Look at a neutron star. The particles are under so much compression that all position locations will be occupied. Since we don't see matter more dense than this we assume that the position locations approach maximal definition.
This constraint means, according to the Heisenberg Uncertainty Principle that the momenta o... | {
"language": "en",
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Is a pseudo-Goldstone boson always a pseudoscalar particle? There are several examples of pseudo-Goldstone bosons which are CP-odd particles, such as the pion, as well as many axion-inspired models.
If we invert the logic,
Are all pseudo-Goldstone boson of CP-odd type? Or, can they be CP-even too? Is there a known exa... | I'm not sure why you would think all (pseudo-)Goldstone bosons have to be CP odd. This would be the result if the spontaneously broken symmetry is a chiral symmetry ($SU(2)_A$ for pions, $U(1)_{\text{PQ}}$ for axions), but of course you can spontaneously break other kinds of symmetries too.
For example, consider a comp... | {
"language": "en",
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Intuitive explanation why rate of energy transfer depends on difference in energy between two materials? The temperature of an object will decrease faster if the difference in temperature between the object and it's surroundings is greater.
What is the intuitive explanation for this?
| You know that temperature is related to the microscopic kinetic energy of the atoms and molecules that make up a material. For simplicity, let's assume the two materials consist of monatomic ideal gases with one having a higher temperature than the other. Then the temperature of the two gases is a measure of the averag... | {
"language": "en",
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Number of electrons in an orbital How do we know number of electrons per element since electrons do not have shape and volume? Isn't an electron just quantized fluctuating probability wavefunction? Is there an experimental study supporting the idea that electrons are the moving particles in orbitals?
| When we solve the hydrogen atom Hamiltonian, we get quantised energy states that are allowed for an electron. These states correspond to the wavefunction of the electron and are called orbitals. And since these orbitals are stationary states, the number of electrons in the ground state is constant. So when you say:
Is... | {
"language": "en",
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Symmetry breaking and higgs representation I was wondering if there is a criterion for the representation the Higgs should change under or if it's a case by case scenario.
For instance, electroweak symmetry breaking is done with a higgs in the fundamental representation of SU(2). Using an adjoint representation does n... | Table III of the legendary 1974 paper by Ling-Fong Li, required canonical reading for theory students, details which low-lying Higgs representations break SU(n) groups to what subgroup and why.
The "job" is to SSBreak 12 of the 24 symmetry directions of SU(5) so the remaining 12, so far unbroken at this stage, comprise... | {
"language": "en",
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Why does charge on a capacitor remain constant when dielectric is fully inserted between the plates of the capacitor? We have a capacitor let's say of capacitance C and is charged by Voltage say V. Then the voltage is disconnected and a dielectric of dielectric constant say k is inserted fully between the plates of par... |
why does charge stored in capacitor remain constant.
Because you disconnected the voltage source. It's meant to be implied that the capacitor is disconnected from all external circuits. Therefore there's nowhere for the charge to go. And since charge is a conserved quantity, that means the charge on the capacitor pl... | {
"language": "en",
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Power Spectrum Density of real valued time series data There are real valued time-series data X(t) and corresponding auto-correlation function ACF(t)=$\left<X(0)X(t)\right>$. As written in wikipedia, Power Spectrum Density (PSD) can be calculated using either of X(t) or ACF(t). If one choose to calculate PSD using ACF,... | The autocorrelation function is defined as:
$$
r_{a b}\left( i, j \right) = E\left[ a_{i} \ b_{j}^{*} \right] \tag{0}
$$
where $a(b)$ is an arbitrary time series signal and $i(j)$ is the corresponding index, respectively. The $E\left[ x \ y \right]$ term is the expectation value between $x$ and $y$ and the asterisk in... | {
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Can momentum never be zero in quantum mechanics? I have seen Zetilli's QM book deals with $E>V$ and $E< V$ (tunnelling) in case of the potential wells deliberately avoiding the E=V case, so I thought maybe something is intriguing about this and made this up.
Suppose the total energy of the particle is equal to its pote... | I would like to add two points to the accepted answer:
*
*If you use the periodic boundary conditions trick to normalize the momentum eigenstates, then all the momentum eigenstates become normalizable, including the zero momentum eigenstate.
*The discussion of tunneling in QM books is usually within the quasi-class... | {
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Can elementary particles be explained adequately by a wave-only model? I have been watching quantum mechanics documentaries and reading a layman's book called "The Quantum Universe". I believe I understand why the double slit experiments exclude a particle only model. However I do not understand why the particle port... | Sort of, yes.
The many-worlds interpretation of quantum mechanics essentially says that there aren't actually any particles, just the quantum waves and our observations of them - the "particles" are just our limited observations of a small slice of the complete quantum waveform. As a result, you could say that they're ... | {
"language": "en",
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How do we know not all photons are absorbed? Only those of specific energies? When a photon hits an electron in an atom, its energy has to be equal to the difference in energy between the current shell and a shell with a higher energy level, otherwise it is not absorbed at all.
How do we know not all photons are absor... | We can shoot photons of different energies at atoms and see what goes thru and what is absorbed. only the specific energy photons will be absorbed. And no part of the energy will not. This is one of the results from quantum mechanics. The first excitation energy of hydrogen is 10.2 ev. If you shoot photons of energy ... | {
"language": "en",
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Vector Helmholtz Equation In my recent exercise book I've derived the following equation that needs solving: $\nabla^2\vec{u} + k^2\vec{u} = 0.$ The deformation vectors points only in the $\hat{e}_r$ direction. I didn't want to write out the Laplace in spherical coordinates, so I tried using what I learned in my PDE co... | Yes, indeed you can use your knowledge of the scalar Helmholtz equation. The difficulty with the vectorial Helmholtz equation is that the basis vectors $\mathbf{e}_i$ also vary from point to point in any other coordinate system other than the cartesian one, so when you act $\nabla^2$ on $\mathbf{u}$ the basis vectors a... | {
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Is the electromagnetic field a real physical entity? Up till now, I always thought that electric and magnetic fields are mathematical constructs which aid our understanding. What was a one-step process of particle $A$ exerting force on a particle $B$ is replaced by a two-step process of the particle $A$ creating a fiel... | You should consider electromagnetic fields to be just as “real” as matter because both have energy, momentum, and angular momentum.
“Reality” is a vague concept and isn’t what is important here. What is important is that energy, momentum, and angular momentum can only be locally conserved if the EM field transports the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536169",
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How does the baryon asymmetry control temperature fluctuations of CMB? The temperature fluctuations of the Cosmic Microwave Background (CMB) have a sensitive dependence on the quantity of baryon asymmetry of the universe. In fact, analysis of CMB fluctuations is one of the ways of inferring the amount of baryon asymmet... | I am afraid this will not be a complete answer; also, there is a similar question on the site [How does the CMB constrain the baryon asymmetry? ].
If the universe were uniformly occupied by equal amounts of matter and antimatter, it is reasonable to imagine that the CMB spectrum would take note of the frequent annihil... | {
"language": "en",
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Why is the speed of light in vacuum a universal constant? While getting familiar with relativity, the second postulate has me stuck. "The speed of light is constant for all observers". why can't light slow down for an observer travelling the same direction as the light?
| Speed of light is constant in all inertial frames in a vacuum, this is a postulate of Special theory of Relativity. There was no assumption that Speed of light is the fastest traveling speed in the Universe but if you study Special theory of Relativity closely, you will understand that particles having zero mass can on... | {
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"answer_id": 6
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Action of quantum Fourier transform on two-fermion states In section 2.2 of the paper https://arxiv.org/abs/1807.07112, there appears a Fourier transformation named $F_k^n$ that comes out of a matrix called $F_2$,
$$
F_2 = \begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1/\sqrt{2} & 1/\sqrt{2} & 0\\
0 & 1/\sqrt{2} & -1/\sqrt{2} & ... | It's the beamsplitter unitary (a.k.a. the QFT in two dimensions, a.k.a. the Hadamard gate), represented via its action on two-mode Fermion states.
With two modes, there are four possible fermionic states: $|11\rangle\equiv c_1^\dagger c_2^\dagger |\text{vac}\rangle$ (one fermion per mode), $|01\rangle\equiv c_2^\dagger... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536851",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Harmonic waves: direction left or right? Consider $E(x,t)=A\sin(kx-\omega t)$ where $k=2\pi / \lambda$, with $\lambda$ the wave length and $A$ its amplitude. We have
$$E(x,t)=A\sin(k(x-vt))$$
so this wave is going to the right. Now, if I want to make it going to the left, I just have to change the sign of $v$ which lea... | The Plane progressive harminic wave of the form
$$E(x,t)=A\sin(kx-\omega t)$$
where $\omega =kv$ , represents the wave with speed $v$ travelling in $+x$ direction. While $$E(x,t)=A\sin(kx+\omega t)$$
represent the wave with speed $v$ travelling in $-x$ direction. Now Let I change the sign of $k$ form first equation.
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537089",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why complex numbers are used in electronics? The impedance of a capacitor or an inductor is imaginary. How do we know these quantities are imaginary?
| Using complex numbers means you are trying to describe a value in a different domain and in complex number systems, the Imaginary number doesn't mean that the value of capacitor is imaginary. The imaginary number helps to signify the vector rotation when voltage is applied across it or when current flows through it.
I... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537446",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
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Why can vector components not be resolved by Laws of Vector Addition? A vector at any angle can be thought of as resultant of two vector components (namely sin and cos).
But a vector can also be thought of resultant or sum of two vectors following Triangle Law of Addition or Parallelogram Law of Addition, as a vector ... | Because they have nothing to do with vectors and their addition. They are simple sketches or representations of algebraic objects, elements of vetoor spaces.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537550",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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"answer_id": 6
} |
Does the magnetic field for only two particle exist? I have read the article about the relationship between electric fields and magnetic field, which involves special relativity. But i wouder does the effect of relativity always take place?
When a single electron is flying by another single electron, and when their dis... |
When a single electron is flying by another single electron, and when their distance minimizes, the displacement between two electrons is perpendicular to the direction of the speed, so the distance between two electrons should not be affected by relativity, which means the force between them can be simply derived by ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537877",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Solving TDSE for molecular alignment I'm doing my thesis, and I have to solve a TDSE for molecular alignment - non-adiabatic and non-resonant laser induce alignment. And I really need your help to solve it. I tried split operator method to solve it but I was unable to solve it:
$$i\frac{\partial\Psi_{JM}(\theta,\phi,t)... | Split-operator is going to work perfectly fine for non-resonant alignment simulations. The drifting normalization is probaby due to not small enough time-step or an implementation error. In rigid rotor alignment simulations the direct exponentiation of the molecule+field hamiltonian in spherical harmonics basis is also... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538130",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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Why can a partial derivative be added to a hamiltonian in canonical transformations? In canonical transformations, how come we allow hamiltonian to change by a partial derivative of time?
$$H'(P, Q, t) = H(p, q, t) + \frac{\partial F}{\partial t}.$$
Here $F$ is the generating function.
I mean geometrically that is not ... | A more geometric approach is to consider the $(2n+1)$-dimensional contact manifold ${\cal M}$ with coordinates $(q^i,p_j,t)$. The Hamiltonian action functional is
$$S_H[\gamma]~=~\int_I \gamma^{\ast} \Theta, \qquad \Theta~=~p_j \mathrm{d}q^j -H \mathrm{d}t, \tag{1}$$
where $\gamma:I\to {\cal M}$ is a curve. This acti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538253",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why are some energies dependent on reference frame, and some are not? And why is transfer between them possible? For example the chemical energy of a kilogram of gasoline is 44-46 MJ/kg. It is only dependent on its chemical structure, which stays the same, whether the gas tank moves or stays still relative to the obser... | All energy is more or less frame-dependent. This is obvious in the case of the kinetic energy of a moving car, but less so for a quantity of gasoline. An illustration: let's say the chemical energy of 1 kg gasoline is 45 MJ at rest. If you put this gasoline in motion so it moves at 1000 m/s, the total energy will now b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538791",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 5,
"answer_id": 4
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What is the flux through a square plane cointaining a point charge? Consider a square plane of finite area A and let a point charge q be placed on the plane.
What is the electric flux through the plane due to point charge?
I reckon it to be zero as all electric field lines in the plane are parallel to the plane but my ... | Its easy, consider the point having charge as P over the sheet we can draw 3d radial field lines all around it you can notice apart from parallel field lines(to the sheet), there are other field lines originating through the surface(IMAGINE A 3D SPHERE with point P) hence flux is not zero it is infact q/E0(E0 = epsilon... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538914",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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The integral in centre of mass (one dimension) This is the integral for finding the centre of mass in one dimension:
$$X=\frac{1}{M}\int xdm.\tag{1}$$
But I was wondering whether we could do it by taking x as the integrating variable:
A homogenous rod of length $X$ is split into $N$ regions of width $\Delta x$.
Let $m... | Your equation (2) is wrong. To use $x$ as the integrating variable you need to change $x\,dm$ into $x\,\dfrac{dm}{dx}\,dx$. This means we need to define $m$ as a function of $x$, and the most reasonable way to do that while keeping the original meaning of $dm$ is to let $m(x)$ be the mass of the section that goes from ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/539996",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 0
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Special relativity and tensile stress If an observer studies a cubic structure crystal from a moving frame of reference while speeding towards the crystal, he would expect to measure the atoms in the crystal closer together in the direction of his travel compared to distance of atoms in a perpendicular direction.
How w... |
How would this observer explain the tensile stress force he observes on the crystal which someone standing next to the crystal will not detect?
Stress is the space-space components of the stress energy tensor. For the stationary observer the stress energy tensor is
$$\left( \begin{array}{cccc}
\rho & 0 & 0 & 0 \\
0 ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540056",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Symmetry transformations: a doubt about the relations that we assume true When we deal with symmetry transformations in quantum mechanics we assume true that,
If before the symmetry transformation we have this
$ \hat A | \phi_n \rangle = a_n|\phi_n \rangle,$
and after the symmetry transformation we have this
$ \hat... | *
*This is not an assumption, it is a requirement for consistency. The symmetry transformation acts on operators and states, it does not act on numbers. So the equation $A\lvert \psi_n \rangle = a_n\lvert \psi_n\rangle$ simply becomes $A'\lvert \psi_n'\rangle = a_n\lvert \psi_n'\rangle$ after applying the transformati... | {
"language": "en",
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How do we know that one particular solution for the velocities of a two-body elastic collision is the correct one over the other? Assuming there is a 1-D collision between two bodies, having masses $m_1$ and $m_2$, if we conserve energy and momentum, we get two solutions.
$$
v_{1,i} = v_{1,f} \\
v_{2,i} = v_{2,f}
$$
... | In 1 dimension, in the center-of-momentum frame, there are only 2 types of elastic scattering:
(1) Forward scattering:
$$ v'_i = v_i $$
for $i \in \{1, 2\}$ which looks like no collision at all.
(2) Backward scattering:
$$ v'_i = -v_i $$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540239",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Does Pascal's Law hold true in this scenario? In the attached image, it has been told that the pressure at point A is equal to the pressure at point B(both at the same height).
My question: Can this be justified using Pascal's Law? Whether yes or no, how is it justified?
To clarify, the outline represents the boundary... | For the liquid to stay like that, it has to be held in place by a container on top (or some other forces), or else $h_1$ and $h_2$ would be the same because the water would level out.
Lets assume that the top of the water column on point $B$ is at atmospheric pressure. For things to remain balanced, the pressure at th... | {
"language": "en",
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How can a red light photon be different from a blue light photon? How can photons have different energies if they have the same rest mass (zero) and same speed (speed of light)?
| "different color" is a feeling in your brain. Red and blue is different feeling, the root of the different feeling is some different property of the photon that can result in different feelings.
In the case of human eye, the property that make the difference of feeling is the frequency/energy of the photon. Photons wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "29",
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Is Stokes' law, for drag force in fluids, accurate? In high school, I was taught that Stokes' law is dependent on assumption that drag force is proportional to velocity, viscosity and radius of the sphere (and the powers/exponents are evaluated using dimensional analysis). Is Stokes' law proven or is it just an assumpt... | As indicated, Stokes' law applies when the inertial effects of the fluid are negligible. The pressure forces compensate the viscosity forces. It can be shown that this is true when the Reynolds number is less than 1.
In the general case, with reasonable assumptions, dimensional analysis can justify that the drag force ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540590",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Decoupling of ghost fields in axial-gauge QCD After quantizing QCD using the Faddeev-Popov "prescription", we end up with the original QCD Lagrangian plus the gauge-fixing term,
\begin{equation}
-\frac{1}{2\alpha}(n\cdot A)^2,
\end{equation}
and the ghost fields action
\begin{equation}
S_\mathrm{g}(\phi,\bar{\phi},A)=
... | In the path integral with a $R_{\xi}$-gauge-fixing term ${\cal L}_{GF}=-\frac{\chi^2}{2\xi}$, the axial gauge-fixing condition $\chi=n\cdot A\approx 0$ is only imposed in a quantum average sense. In general the gauge-fixing condition may be violated by quantum fluctuations, except in the Landau gauge $\xi=0^+$, where s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540696",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Finite barrier. Constant including minus or not? For a finite potential barrier of magnitude $V_0$ between $x=-a$ and $x=a$ we know that the time independent schrodinger equation is $\Psi'' +\frac{2m}{\hbar}E\Psi=0$ for $x<-a$. Let $E<V_0.$ Normally we set $k_1^2=\frac{2mE}{\hbar^2}$ and get $\Psi''+k_1^2\Psi=0$ which ... | The difference is in the sign of $E$.
The definition $k_2^2=-2mE/\hbar^2$ with $E>0$ implies that $k$ is pure imaginary $k_2$, i.e $k_2=i k_1$ with
$k_1^2=+2mE/\hbar^2>0$. Then $e^{k_2 x}= e^{ik_1 x}$.
On the other hand the definition $k_1^2=+2mE/\hbar^2$ gives $k_1$ real so again
$e^{i k_1x}$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540866",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Indefinite integral of a density function Suppose that $\rho(x)=\frac{dm}{dx}$ is the linear density of a rod. Can we find the mass at each point of the rod by integrating $\rho(x)$, so that:$$m(x)=\int\rho(x)dx.$$ Can we do the same with probability density in quantum mechanics, so that:$$P(x)=\int|\Psi|^{2}dx$$ (assu... | It's neither possible to find the mass of a point nor the (quantum) probability in such a point.
It is possible to find the mass of a small interval $\delta x$, located at $x$ as:
$$m(x,x+\delta x)=\int_x^{x+\delta x}\rho(x)\text{d}x$$
Similarly:
$$P(x,x+\delta x)=\int_x^{x+\delta x}|\Psi|^{2}\text{d}x$$
Note that in b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541072",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do not we consider the topological term in Abelian gauge theory? The second Chern form $\epsilon^{\mu\nu\rho\sigma} F_{\mu\nu}F_{\rho\sigma}$ is topological in 4-dimensional spacetime. However, we usually only consider this term in non-Abelian gauge theory, but not in Abelian gauge theory. Is this term vanishing id... | For Abelian gauge theory $$\epsilon^{\mu\nu\lambda\rho}F_{\mu\nu} F_{\lambda\rho}=\epsilon^{\mu\nu\lambda\rho}\partial_\mu(A_\nu F_{\lambda\rho}).$$ Thus, the term in the action coming from this term can be converted to a surface integral of $A_\nu F_{\lambda\rho}$, which vanishes since $F_{\lambda\rho}$ vanishes on th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541223",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Mass in different inertial frames EDIT: In standard textbooks on classical mechanics I know after the notion of mass of a body is introduced, it is tacitly assumed that in all inertial frames the mass of a body is the same.
Does this fact follow from other basic principles of classical mechanics (like the Galileo pri... | The idea from early treatments of special relativity that mass increases with velocity was superseded in general relativity and is better not used. It is a fundamental principle that the laws of physics are covariant - they are formulated using tensor (& vector & scalar invariant) quantities so as to be the same for al... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541322",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do electrostatic air filters maintain their charge? 3M meets the N95 filtration specification on disposable respirators by constructing them with "electrostatically charged microfiber filter media."
How does air filter fabric stay charged? Fun grade school demonstrations involving everything from balloons to Van d... | The fibres are made from a high resistivity synthetic polymers called electrets which can maintain a permanent dipole moment both on the surface and in the bulk. In many ways they are the electrostatic equivalent of permanent magnets.
They are charged with excess charge on the surface and by producing permanent bulk ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541382",
"timestamp": "2023-03-29T00:00:00",
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Fourier Optics - Impulse Response of Free Space from Fresnel Transfer Function I am currently reading the chapter "Fourier Optics" in the book "Fundamentals of Photonics" by Saleh and Teich. However I am not able to follow one specific mathematical derivation.
On page 111 the transfer function of free space is derived ... | Remeber that for $a>0$ the Fresnel integral is
$$
\int_{-\infty}^{\infty} e^{iax^2} = e^{i\pi/4} \sqrt{\frac \pi{a}},
$$
because of the need to push the contour off the real axis with $x= e^{i\pi/4}t$.
Your integral has the product of two Fresnel integrals $x$ times $y$ and so you have
$$
\left[e^{i\pi/4} \sqrt{\frac ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541467",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What is the best way to imagine the difference between vectors and one-forms? I am studying the GR and reading the Schutz.
He is defining the one-form as $\widetilde{p} = p_{\alpha}\widetilde{w}^{\alpha}$, and a vector $\vec{A} = A^{\beta}\vec{e}_{\beta}$
such that
$$\widetilde{p}(\vec{A}) = p_{\alpha}A^{\beta}{w}^{... | To keep it simple, think of vectors (contravariant vectors) as column matrices and think of one-forms (covariant vectors) as row matrices (the dual space), and the inner product as a multiplication between row matrices and column matrices.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541571",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Derivation of Optical Absorption Coefficient in Semiconductors I have been researching how to derive an expression for the absorption coefficient in semiconductors. I know the absorption coefficient can be expressed as such $$\alpha = A(hf-E_g)^{n}$$ with $n = \frac{1}{2}$ and $n = 2$ for direct band gap and indirect b... | Starting with parabolic bands.
The absorbed photon has energy $h\nu$ and generates an electronic and hole at energy levels $E_2$ and $E_1$ respectively. Energy and moment balance imply,
$$ h\nu = E_2 - E_1 = E_c(k) - E_v(k)$$
where $k$ is the momentum of the photo-generated electron and hole (it’s the same for both car... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541669",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is the answer different with energy conservation vs forces?
Q) An insect crawls up a hemispherical surface very slowly.The coeffiecient of friction is $\mu$ between surface and insect.If line joining the centre of hemispherical surface to the insect makes an angle $\alpha $ with the vertical, find the maximum poss... | The difference in energy between the two static equilibrium positions may only be some potential energy difference. You may assume the friction force is $F=\mu N$ during sliding, where $\mu$ is the kinetic friction coefficient (taken equal to the static friction coefficient) but since this force is non conservative, th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541882",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Solving the geodesic equation for a Schwarzschild metric Using the Schwarzschild solution is there a simple differential equation describing the four position of a particle influenced by a Schwarzschild metric using the geodesic equation. How would the simplest form look like?
| In the Scharzschild solution, we can write the geodesic equation in the form of the equations of motion
$$ r^2 \dot\phi = h = \mathrm {const}$$
$$ {\dot r}^2 = {2\mu\over r} - \bigg(1-{2m\over r}\bigg){h^2\over r^2} $$
Einstein showed that solving these equations perturbs the Newtonian equations and results in orbita... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542012",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What do the fixed points of a RG equation mean and what are its importance? Can somebody explain to me what the fixed points of a renormalization group mean? What is their physical significance in the sense that why do we study them and what do we get to know from them?
| Chiral anomaly gave an excellent answer in QFT language but I'll provide a more physical way of thinking about fixed points.
Consider two distinct physical systems (for example Ni or Fe magnet) that flow to the same fixed point under RG, then near the critical point, they have similar behaviors in heat capacity or mag... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542183",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Interesting generalisation about a parallel ray between 2 mirrors I have been self studying from home nowadays and came across a result in a video lecture on 'Ray Optics'
If an incident ray is parallel to one of the 2 mirrors kept an angle $\theta$ = $\frac{\fracπ2}n$ where $n \in N$, then the ray will fall normally ... | For a simple 'geometrical' answer the following sketch may suffice. Red lines represent the first mirror, and its images. The blue lines represent the second mirror and its images.
I think the diagram is self-explanatory to confirm that there are $2n-1$ reflections, and that the 'middle' one is perpendicular to the mir... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542347",
"timestamp": "2023-03-29T00:00:00",
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Is boiling once more effective than boiling twice half the amount? In a real-life (non-ideal) situation, is boiling 1 litre of water in a kettle the same as boiling two times 500 millilitres in terms of consumed energy? In the latter, I assume the kettle is still hot from the previous boiling.
| Intuition tells me that the only difference is due to heat loss while at high temperature. Assuming the same kettle the rate of loss from the kettle should be the same at given temperature. Because the smaller volume heats faster, I think it will spend less time at high temperature, and the net energy loss will be less... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542585",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Energy stored in an electric field I know the mathematical proof that $U=\frac{\epsilon_0}{2}\int\vec{E}^2dv$ is the energy stored in a particular volume in space due to an electric field, but I don't get what it actually means. I lack the physical intuition to this result. For example, if I want to calculate what work... | One needs to perform work in order to construct a charge distribution. Doing work is an energy transfer and this energy is stored in the form of the electric field.
An easy example is a parallel plate capacitor. Its capacitance is $$C=\frac{\epsilon_0A}{d},$$ whereas the energy built by moving the charge from one plate... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542797",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Physics of the trikke tricycle I love my trikke, but I still do not understand what propels it forwards.
It is very clear that the energy comes from my legs and not from my arms (I only have to touch the handle bar ever so lightly), but I do not see how my shifting weight from side to side can result in a forward point... | See the technical studies at http://www.lastufka.net/trikke/. The main physical principle is angular torque via angular momentum transfer from the body to the Trikke. The generation of motion is very much like cross country skiing according to skiers. Both legs and arms can contribute to the angular momentum transfer. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542899",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 3,
"answer_id": 2
} |
Incident and reflected waves Let's consider a transversal wave on a string, which is reflected on a wall. I understand that the velocity of the incident and reflected wave are equal. However, I don't understand why the frequencies of both waves are the same. Can anyone please explain this fact?
| The spatial boundary conditions on the fields must hold for all times, something not possible unless the incident, reflected and transmitted waves have the same temporal part that “cancels out” for all times. You have a spatial boundary (or obstacle) so this changes the spatial part of the wave, but why should it chan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542995",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
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