Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
One straw drinking from many containers of liquid One of my friends brought up a photo:
Which sparked a debate about whether the containers closest to the end of the straw would empty first. I was just wondering if someone could explain if the closest two containers would be empty before the furthest.
| Even with a Newtonian fluid like water and sucked very slow and constant the straw distances are not the same. Thus the pressure drop at the lips would be different from each container making a very slight rate of suck difference. If not a constant rate suck it would attempt to level out on the flow back and probably ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/283183",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why are hydrogenic levels used in writing electronic configuration? I recently started taking a course in Atomic and Molecular Physics. We learned about Hartree Fock approach to solving the many-electron atom problem. If I understand correctly, the electron orbitals that we refer to as 1s, 2s, 2p etc. are eigenstates o... | The issue here is that although the atomic single-electron orbitals have the same quantum numbers as the hydrogenic orbitals (n,l,$m_l$,$m_s$), they are not hydrogenic orbitals because they result from the self-consistent (central) HF potential. This is an approximation, but quite a good one for valence orbitals (the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/283288",
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Question about oersted's experiment So I was studying my physics notes. They are on the magnetic field shown by a straight current carrying wire. To demonstrate that theres the oersted's experiment. The starting goes like this-
Insert a thick copper wire between 2 points, X and Y, in a circuit. The wire should be perp... | “The paper” is probably just meaning the table. So let's put the wire vertically going in the up-down direction. Using the right-hand-rule we obtain that the magnetic field will be circles in the plane of the table/paper.
The compass will align itself to the magnetic field lines. Therefore the rotating compass should b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/283595",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Theoretically, could there be different types of protons and electrons? Me and my friend were arguing. I think there could theoretically be different types of protons, but he says not. He says that if you have a different type of proton, it isn't a proton, it's something else. That doesn't make sense to me! There are d... | I believe you are arguing semantics. To make this clear, lets assume there are only 200 type of "particles," each with a unique set of properties. Once we give each one a name, there can't be any more of "the same thing" with a different name. For example, lets say that number 12 on this list we call it "electron" a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/283682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
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"answer_id": 10
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Could the gravitational field equations be formulated in term of the Riemann curvature tensor (as opposed to the Ricci curvature tensor)? The most symmetries and identities in Riemannian geometry are in term of the Riemann curvature tensor. One may ask why the gravitational field equations are not in term of this main ... | Sure they can. The answer comes from the Ricci decomposition and the Einstein equations.
Let $T$ be the trace of the stress-energy tensor, let $S_{ab}$ be the traceless part of the stress-energy tensor, and let $C_{abcd}$ be the Weyl tensor, let $\kappa$ be the proportionality constant for the Einstein equations $8\pi ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Help with this geometrical approach to deriving the lens equation for weak lensing All images and quotations are from Schneider, Kochanek and Wambsganss.
Here is an image of a typical weak lensing setup. Since $D_{ds}$ and $D_s$ are much larger than the extent of the lens and source plane, we can model the curvature o... | I think this is where it comes from?
Triangles $ACB$ and $ECF$ are similar so
$\dfrac {\xi}{D_d} = \dfrac {AB}{D_s} \Rightarrow AB = \dfrac {D_s}{D_d} \xi = \eta + AG$
For small angles $AG \approx \alpha D_{ds}$ and the result follows
| {
"language": "en",
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How electron get deflected in magnetic field while moving? I don't understand why electron moves this way... e.g. A light object (crampled paper) going down until gets hit by the wind will go parallel (at least a few seconds) to the wind direction ... why not with electron?
| For electrons the magnetic field is not like a "wind". The electron experiences a velocity dependent force, the Lorentz force, which is perpendicular to both the direction of the velocity and to the magnetic field direction. See, e.g., https://en.wikipedia.org/wiki/Lorentz_force .
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Finding the subsequent of motion using a gravitational field
A constant gravitational field points along the negative z-axis. If the
acceleration due to gravity is $g$, the force in the z-direction experienced
by a particle of mass $m$ is $F = −mg$. If the particle is released from
co-ordinate $z = z_0$ with th... | Forget $GM$ etc.
In the question it states that there is a "constant gravitational field" and the magnitude of that filed is $g$.
So all you need to solve is the equation $\ddot z = -g$ which you probably done may times before and got the constant acceleration kinematic equations.
| {
"language": "en",
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"source": "stackexchange",
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If energy is quantized, does that mean that there is a largest-possible wavelength? Given Planck's energy-frequency relation $E=hf$, since energy is quantized, presumably there exists some quantum of energy that is the smallest possible. Is there truly such a universally-minimum quantum of $E$, and does that also mean ... | You have to keep in mind that the relation
$$
E = hf
$$
holds only true for photons. Photons - generally - can have arbitrary energies, so they can have arbitrary frequencies as well.
When you think of quantization, you think of quantization of an observable for a specific system. An one-dimensional harmonic oscillator... | {
"language": "en",
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Promoting time to an operator In Mark Srednicki's QFT book, he talks about the fact that one of the problems with combining quantum mechanics with special relativity is that in QM, position is an operator and time is just a parameter. He then says there would be two natural ways to remedy this, either promote time to ... | For one thing, such a theory would automatically be a gauge theory, because the freedom to reparameterize the proper time in infinitely many ways would be a gauge freedom. So you'd always need to gauge fix your path integral, even for spin-0 and spin-1/2 theories, and that's always a huge mess.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Measuring very small temperature differences Can one use a thermometer with $\pm$5 mK accuracy to measure a temperature difference of 2 mK (the measurement is near 100 mK temperature on a sample on an ADR)? Using the same thermometer, I am thinking to measure temperature of the sample, heat the sample slightly, measure... | In general it's a bad idea to take two absolute measurements and subtract them from each other to find a difference that's comparable to the uncertainty in the measurements; the fractional uncertainty in the difference is much larger than in either measurement. In computer science the problem is sometimes called catas... | {
"language": "en",
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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 ... | This is in principle correct. Take the limits For $E>0$ and $E<0$. If the latter obtains, you get a negative under your square root (and k becomes imaginary) and $e^{ikx}\rightarrow e^{-kx}$, giving you the exponential solution. My guess is that there is a different sign convention in what you read, where it is assumed... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/284879",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can you experimentally determine intrinsic carrier density? I know the equation for intrinsic carrier density is
$$
n_i = BT^{3/2}e^{-E_g/2kT}
$$
Where B is a material dependent quantity. But how would you determine $n_i$ experimentally? Or if you were given an intrinsic semiconductor but no quantitative inform... | There are several experimental methods to determine the intrinsic carrier concentration of a semiconductor. Most of them are indirect. For example you can measure the conductivity of the semiconductor at relatively high temperatures where it has intrinsic properties. Then you determine the electron and hole mobilities ... | {
"language": "en",
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Young's experiment but with reflection from two thin wires? Is it possible to shine a laser beam on two thin metal wires that are really close to each other and observe a reflection interference pattern? I would like to confirm that the pattern is the same as the one obtained by transmission through a double slit, thus... | Yes I use guitar strings all the time to do these experiments. Youngs original experiment was with one human hair. My guitar strings all have different gauges and the experiments work perfectly for the fringe pattern spacings. It just depends on the wavelength of laser light, the distance from the wire to the Wall and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/285118",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is difference between operating wave function with operator of an observable and measuring for an observable? People say operator of an observable helps in measuring for an observable. We also know that measuring leads to collapse of wave function. But operator on wave function gives a number times same wave funct... | You are right in pointing out that operating with an operator on a wavefunction gives a number times the wavefunction (assuming that it is indeed an eigenfunction of the said operator). Measuring the observable collapses the wavefunction. How a wavefunction collapses is still an open question in Quantum Physics. The jo... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is Del (or Nabla) an operator or a vector? Is Del (or Nabla, $\nabla$) an operator or a vector ?
\begin{equation*}
\nabla\equiv\frac{\partial}{\partial x}\vec{i}+\frac{\partial}{\partial y}\vec{j}+\frac{\partial}{\partial z}\vec{k}
\end{equation*}
In some references of vector analysis and electromagnetism, it is consid... | I hate to play this card, but it depends on the object it acts on (and sometimes who you ask.) Example: many (professors, collegues, etc.) will insist on differentiating between writing $\vec{\nabla}$ and $\nabla$ (consider obliging if your grade/ income depends on it.) In reality, however $\nabla$ is NOT a specific... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/285317",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can (heat-related) energy $E$ be considered as the product of temperature $C$ and thermal capacity $T$? Why can (heat-related) energy $E$ be considered as the product of temperature $T$ and thermal capacity $C$?
I.e.
$$E=CT$$
I've seen this definition in one answer to an excercise in a course, but no explanation o... | Heat capacity is the increment in heat you need to increase the system's temperature by one degree, in other words, it measures system's ability to accept energy as heat
$C\equiv\frac{Q}{\Delta T}$
Where $Q$ is the amount of heat absorbed by the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/285789",
"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... | The situation is completely symmetric. Let the velocity of a frame A w.r.t another frame B is $\textbf{v}$. then from the perspective of A, the frame frame B has a relative velocity $-\textbf{v}$. From the perspective of A-observer, the clock of B-observer is slowed down and vice-versa. Note that the dialation factor d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/286038",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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... | The Reynolds-Number is the ratio between forces of inertia and forces of viscosity. The forces of viscosity are represented by the density and viscosity of the fluid.
Bodies with the same Reynolds-Number will have a similiar turbulence behavior. You can also define a critical Reynolds-Number which is related to the act... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Inclined Plane and Center of Mass Say there is a block sliding down an inclined plane that rests on a frictionless table. There is kinetic friction between the block and inclined plane. If the block slides downhill, then the kinetic friction acting on it points uphill. By Newton’s third law, the inclined plane will exp... | Treat the plane and the block as a system
When you will treat the block and the inclined plane as a system you find that the only forces which are acting on the system are in the vertical direction. therefore the center of mass of the system will accelerate ( if it does ) in a vertical line only. also the net force vec... | {
"language": "en",
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Why do odd numbers of either of the nucleons in a nucleus make it relatively unstable compared to a nucleus having even numbers of both the nucleons? Try to keep it as simple as possible, as I am still completing school. Just wanted to get an explanation.
| There is no solid theory on why the occurrence of even number of either nucleons in a nucleus of an atom is stable. Only through experimental data have we been able to observe this phenomenon and the concept of magic numbers.
Even some approximations and theories such as Semi-empirical mass formula fail to explain thi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/286701",
"timestamp": "2023-03-29T00:00:00",
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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 ... | You can get a back of the envelope notion of the energy of a inner-most orbital by just treating the problem as a hydrogen-like atom (not entirely fair and almost certainly a slight over-estimate but at least it is easy). You get
\begin{align*}
E_{1s} \approx \mathrm{Ry} * Z^2 = (13.7\,\mathrm{eV}) * Z^2 \;.
\end{align... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/286770",
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If I evaluate degree of freedom and got some number $n$, then how can I know what are those $n$ independent coordinates? Using $3N-f=d$ we can evaluate the degree of freedom or independent coordinates of a system.
But how can we know which coordinates are actually independent?
(Here $n$ = number of particles, $f$ = nu... | Technically, when you choose your $n$ generalized coordinates $q^1,\ldots,q^n,$ among the $3N$ position coordinates ${\bf r}_1,\ldots,{\bf r}_N,$ of $N$ point particles, with $n\leq 3N$, you should make sure that the $3N\times n$ rectangular matrix
$$ \frac{\partial {\bf r}_i}{\partial q^j}, \qquad i\in\{1,\ldots N\},\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/286877",
"timestamp": "2023-03-29T00:00:00",
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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... | If you formalize dimensional analysis, you end up with the set-wise product of a scalar from $\mathbb{R}$ with a free group on with n generators, where n is the number of "base units" you can talk about.
So one of your unit generators might be mass, another distance, another time, etc.
In this structure, addition is on... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/286964",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the evidence that distant galaxies are moving away from us with speeds greater than $c$, due to space expansion? I came up with this query after @Rob Jeffries's answer to a previous question of mine.
So, is there any evidence that distant galaxies are moving away from us with speeds greater than $c$, due to t... | If the galaxy was traveling away faster than the speed of light, then we wouldn't be able to see it. (obviously) By very definition, it exist outside of the "observable universe". Not only can we not "observe" it with our eyes, but no information can reach us at all. (similar to the inside of a black hole). It cannot a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/287286",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Field of a Polarized Object In Griffith's Electrodynamics, in the section 4.2, just after the equation 4.9, he writes "sleight-of-hand casts this integral into a much more illuminating form"...
I have a doubt in that. If the Gradient (or differentiation if carried out) is with respect to primed coordinates, how can var... | We need to shift from $\mathscr R$ to $r'$ because otherwise the coordinate system would keep changing as we integrate over the whole volume. Now, about that sleight of hand.
Gradient depends upon the coordinate system.
By simple definition of gradient we have :-
$dT= \nabla T.\boldsymbol{dl}$, where $\boldsymbol{dl}$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/287383",
"timestamp": "2023-03-29T00:00:00",
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Solving a problem using Newtonian mechanics and D'Alembert principle yI have to solve that problem with two methods (applying Newtonian mechanics and the D'Alembert principle.
The problem consists in two balls inside a spherical cylinder, it consists in determine the minimum value of $M$ making the tube not to knock do... | You have 2 couples countering each other.
One is the cos of the mass of two balls times 2r divided by difference the of their contact points' heights on the wall of the cylinder. And the other is overturning momentum of the cylinder.
Let's call the angle of the line connecting the center of the 2 balls A.
$A= arccos(2(... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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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.
| There have been several answers already but as a synthesis attempt :
Gravity is attractive, and in absence of repulsive counter force it causes the collapse of a massive object. The order of magnitude of the pressure needed to resist against gravitational collapse is roughly of the order of $GM^2/R^4$ where $M$ is the ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | It's a bit like when you put a thick jumper on. The inside of your clothing ends up being warmer than the outside of your clothing.
Most of the heat within the earth can be attributed to radioactive decay (of long lived isotopes like potassium). This heat is constantly being conducted out to the surface. (Yes, if you g... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | The hydrogen atom is spherically symmetric, so for any solution of the Schrödinger equation for the hydrogen atom, any rotation of that solution must also be a solution. If you do the math on how to rotate a solution, it turns out that the solutions with a particular energy $E_n$ fall into groups labeled by an integer ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/288468",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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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... | Conservation of energy occurs within a given reference frame. If you change reference frames, you cannot use those rules.
A clear example of this occurs if you consider the energy of the system when considering the Earth and an airplane flying through the air. From the perspective of an observer on the ground, the ai... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/288587",
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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... | bcs state is superconducting because excitation spectrum has a gap. which mean to create a quasi particle on ground state you need non zero energy.
creating a qp can be interperted as exciting an cooper pair. cooper pairs can be excited by scattering in lattice.
so lattice scattering of your charge carriers needs ene... | {
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What is the potential in a circuit? I have learnt that the potential in a point in an electric field is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point. However, this is in the case of an electric field. What is the potential in a circuit say, consisting... | In a circuit, you usually define potential differences with respect to a chosen (arbitrary) electrode. This is often the "mass" electrode which is connected to earth. When you measure potential differences in a circuit, you actually measure differences in electrochemical potential, not the difference in electrical pote... | {
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Difference between "Periodic motion" and "Oscillating Motion" So far I know one of them is a special case of the other: The Oscillating motion being the special case of Periodic motion. But I don't know the precise "Kinematical definition" of each one. I mean when you have an "Equation of motion" for a particle, how wi... | From what I understand, periodic motion from the physical point of view is quite general in the sense that any type of motion that repeats itself after some period of time would be term as periodic.
Where in the case of oscillation, the time period of the periodic motion is quite large, like the motion of the pendulum ... | {
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Does "Excitation" mean the value of a field rapidly changes over time at that place? I know that the definition of something called a "field" is formally defined as the presence of a quantity at every point in space. In quantum field theory, does the excitation of a field mean that the value of the field is changing ov... | The term excite in this context generally means something like to add energy to. So if we excite a field that means we add energy to it.
This can be used in either a classical or quantum context, though I'd guess it is most commonly used in quantum mechanics where it means changing a system from a lower to a higher ene... | {
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Why is the work done by some forces path independent while for others it is are path dependent? I know that by definition, forces for which the work done is independent of the path taken are known as conservative force while the forces for which the work done is path dependent are known as non-conservative forces. My q... | You can see for yourself that if a force depends only on position (not on time and speed), then it is conservative, while if it depends on speed it may not be.
Simple examples should do: take the weight force, $\vec f = m \vec g$: when something falls down from an height $h$, you have $\ W = \vec f \cdot \vec s = mgh.$... | {
"language": "en",
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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... | This comes down to a trivial integral, assuming that the relevant axis is the centre of the cylinder:
\begin{align}
I
& = \int_\Omega \rho\:r^2\:\mathrm dV
=\int_0^L\mathrm dz \int_0^\theta\mathrm d\varphi\int_0^Rr\mathrm dr \: \frac{M}{L\theta R^2/2}r^2
\\ & = \frac{2M}{R^2}\int_0^Rr^3\mathrm dr
\\ & = \frac12MR^2.
\e... | {
"language": "en",
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Non-glassy amorphous solids According to Wikipedia:
*
*A glass is any "solid that possesses a non-crystalline (that is, amorphous) structure at the atomic scale and that exhibits a glass transition when heated towards the liquid state".
*A glass transition is "the reversible transition in amorphous materials (or in... | Plastics are made if polymers, which are chains of molecules, therefore i don't think we can call it a glass even though some of them are amorphous, because they are ordered at the atomic scale.
| {
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How does the Hubbard Stratonovich transformation decouple interactions? I'm having trouble understanding how the Hubbard Stratonovich (HS) transformation decouples equations via the introduction of a field variable. The particular problem I'm facing is a derivation in Phys Rev E, 81, 021501 (2010) equations 2.4 -> 2.7,... | Probably you would have found some answers by now..
For your first question, doing integrating by parts on $(\nabla \phi)^2$, you can change it to $\phi \Delta \phi$ right? then you can complete the square as usual.
You will have something like $(\phi + A\rho) M (\phi + A\rho) + B\rho M^{-1} \rho$ with A,B some coeffic... | {
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What does the square root of Laplacian mean? There is a relation in the textbook, "Quantum Field Theory and the Standard Model, Schwartz"
$$\left \langle 0\left | \sqrt{m^2-\vec{\bigtriangledown }^2}\phi _0(\vec{x},t) \right |\psi \right \rangle=\left \langle 0\left | \int \frac{d^3p}{(2 \pi)^3} \frac{\sqrt{\vec{p}^2+m... | The square root of a differential operator indicates that the Fourier factors of that operators are taken as square roots. In this case,
$$\text{FT}(\nabla^2 \varphi) \propto p^2 \widetilde \varphi$$
$$\text{FT}(\sqrt{\nabla^2} \varphi) \propto \sqrt{p^2} \widetilde \varphi$$
The operator will then be equal to somethi... | {
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Does infinity exist in the structure of physical systems? Sometimes people fail at asking a question by being too broad, unclear like here. So I'll take a stab at what I believe to be the same question, but more concise and clearly stated:
Does infinity exist in the structure of physical systems?
To be clear I'm refe... | Infinity exists in physical theory. There are infinite-dimensional Hilbert spaces, there are cosmological solutions that are infinite in space or time, there is the infinite divisibility of space and time as modelled by the continuum of real numbers.
However, there is always the possibility that the end point of the qu... | {
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"source": "stackexchange",
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A paradox about distant galaxies When we observe a galaxy farther than 13 billion light years away, we see that galaxy as it was 13 billion years ago. But back then, that galaxy was much closer to us ,if indeed we live in an expanding and accelerating universe. The question is, why we see it so far when in fact it was ... | Have a look at this timeline of the universe:
The x axis is the time axis. After the "dark ages" there are galaxies formed, which become diluted in space as time grows.
The question is, why we see it so far when in fact it was very close to us and the time for the light to reach us was much shorter?
Because light ha... | {
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Understanding rocket problem intuitively
A rocket is trying to land on a planet. The mass of the rocket is $1\,\rm kg$, and the gravitational acceleration of the planet is $1\,\rm m/s^2$. The rocket starts the free fall at $20\,\rm m$ above the surface of the planet (initial velocity is $0$), and can use the thrust fo... | Assuming the goal is to minimise impact speed then you should time your burn so that it ends when you land.
Why? because all the time you are in flight you are gaining speed due to gravity. Burning earlier makes your flight longer and thus increases your impact speed.
| {
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"source": "stackexchange",
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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... | div E does not vanish everywhere for the dipole, you should get delta-functions in the points where there are charges.
| {
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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?
| From a slightly different, though equivalent, view...
If the line integral of a vector field is path independent, the vector field is conservative, i.e., the vector field is the gradient of a scalar field.
Thus, if $\int \mathbf{A}\cdot \mathrm{d}\mathbf{s}$ is path independent, it is the case that $\mathbf{A} = \nabla... | {
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How much information can you obtain from a pulsar-black hole system? Imagine that we have detected an interesting source in the sky that we believe is generated by a pulsar orbiting a black hole.
The challenge here is the following:
What physically relevant information could you extract from the observation of this sy... | First of all, if the pulsar is not extremely close to the black hole, we should observe almost the usual pattern of a pulsar. Let's start obtaining the distance.
The light that comes from the pulsar may encounter regions with free electrons in the interstellar medium. Those regions introduce a dispersion relation that ... | {
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Why are angular frequencies $\omega=2\pi f$ used over normal frequencies $f$? When we first studying vibrations in crystals we begin by studying the monoatomic chain, and then go onto the diatomic chain with a series of alternating masses. In studying these we look to calculate the dispersion relation, which is the ang... | Mainly because
$$\frac{\rm{d}}{\rm{d}t}\sin\left(\omega t\right) = \omega\cos\left(\omega t\right)$$
but
$$\frac{\rm{d}}{\rm{d}t}\sin\left(2 \pi f t\right) = 2 \pi f\cos\left(2 \pi f t\right)$$
All those pre-factors every time you take a derivative or an integral get to be a pain to keep track of.
As you get even more... | {
"language": "en",
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Excited State of an Electron in a 2D Box An electron in a 2D infinite potential well needs to absorb EM wave with wave length 4040 nm to be excited from $n=2$ to $n=3$. What is the length of the box if this potential well is a square($L_x=L_y$)?
My solution:
$$E_{n_x,n_y}=\frac{\pi^2\hbar^2}{2mL^2}(n_x^2+n_y^2)$$
For $... | For a 2-D well the energy is given by the following expression:
$$\boxed{E=\frac{\hbar^{2}\pi^{2}}{2m}\left(\frac{n_{x}^{2}}{L_{x}}+\frac{n_{y}^{2}}{L_{y}}\right)}$$
Since this is a case of a square well $L_{x}=L_{y}=L$.
When the electron absorbs an EM wave and gets excited it jumps from its ground state of $n=2$ to... | {
"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{... | Even though the question has already been sufficiently answered, I would like to offer the sketch of another "elegant" proof:
The space of complex $2\times 2$ matrices, denoted $M_{2\times 2}(\mathbb{C})$, is isomorphic to $\mathbb{R}^8$ via
\begin{equation}
\begin{pmatrix}
z_{11} & z_{12} \\
z_{21} & z_{22}
\end{pmatr... | {
"language": "en",
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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... | Not a physicist, but I think acceleration can be discontinuous. Consider a car travelling at constant velocity (acceleration = 0) that hits a wall. De-acceleration (negative acceleration) commences until the car comes to a complete stop. For all intents and purposes over time t acceleration starts at zero, decreases to... | {
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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!... | They are an approximation to General Relativity, so yes, they can be proven using general relativity.
| {
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"source": "stackexchange",
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4-momentum of meson in nucleon scattering Consider the nucleon scattering in scalar Yukawa theory.
Suppose that we are NOT using Feynman diagram (rules) and instead use the tedious Dyson- Wick more formal method.
How do we establish or derive this relationship between 4-momentum of meson and 4-momentum of nucleon:
$$
k... | I don't know if this answer will satisfy you completely since I'm not familiar with the Dyson-Wick formalism. But if I have scattering between two nucleons, with initial momenta $p_1, p_2$ and final momenta $p_1', p_2'$, and no additional particles in the final state, the conservation of momentum gives me
\begin{align... | {
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Is a pendulum in dynamic equilibrium? When obtaining the equation of a pendulum following classical mechanics (Virtual Work) we state that:
The work is in equilibrium, therefore $\textbf{F} = 0$ and the Virtual Work is
$$\textbf{F} · \delta \textbf{r} = 0\tag{1}$$
But, is a pendulum in equilibrium? I mean, the veloc... | Equilibrium is not a well-defined term. Loosely it means "a state in which opposing forces or influences are balanced."
Dynamic equilibrium usually means that two (or possibly more) processes are going on simultaneously but their net effect is zero. For example : in a population if the rates of births and deaths are eq... | {
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Can we think of the EM tensor as an infinitesimal generator of Lorentz transformations? I'm asking this question because I'm feeling a bit confused about how Lorentz transformations relate to the electromagnetic tensor, and hope someone can help me clear out my possible misunderstandings. Please excuse me if the answer... | The electromagnetic field strength tensor is not a Lorentz generator.
First, even when written in matrix form, the signs are wrong. The boost generators are of the form
$$ \begin{pmatrix} 0 & v_x & v_y & v_z \\ v_x & 0 & 0 & 0 \\ v_y & 0 & 0 & 0 \\ v_z & 0 & 0 & 0 \end{pmatrix},$$
which are not antisymmetric.
Second, ... | {
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Magnetic effect on AC circuits? We know that when currents in two wires move parallel to each other, they attract each other and if they are moving anti-parallel to each other, they repel each other but we cannot observe this in our daily routine; why?
I know this experiment is based on DC circuit and we cannot obse... | We absolutely observe this in daily life. Every time you see a motor running, you see the effect of the force of currents on each other. I recommend the following experiment:
Create an apparatus with two parallel conductors (fairly close together) where you can adjust the tension in the wires (like a guitar - but make ... | {
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Why is nuclear waste more dangerous than the original nuclear fuel? I know the spent fuel is still radioactive. But it has to be more stable than what was put in and thus safer than the uranium that we started with. That is to say, is storage of the waste such a big deal? If I mine the uranium, use it, and then bury th... | First, the output of a reaction is not necessarily less dangerous or at least as dangerous as it's input. Take dynamite for example(*): glycerin is a rather harmless material; nitric acid is a strong acid for sure, but still not as dangerous as the resulting nitroglycerin (active element of dynamite) that results from ... | {
"language": "en",
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Stagnation points (Body vs Tube) Can anyone please help me understand the stagnation points? If we look at the comparison between the flow of air over a wing and flow in a pitot tube, the theory says that the velocity is 0 (or very close to 0) for both cases. Having a stream hitting the wing, all the kinetic energy goe... | From what I read on Wikipedia (sorry, I'm not an expert), air doesn't flow through the tube. So its velocity is 0.
... the moving fluid is brought to rest (stagnates) as there is no outlet to allow flow to continue
| {
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Can localized wavepackets have mass? Page 31 of David Tong's notes on QFT (also in Srednicki's book while discussing LSZ reduction formula), talks about Gaussian wavepackets $$|\varphi\rangle=\int \frac{d^3\textbf{p}}{(2\pi)^{3}}e^{-i\textbf{p}\cdot\textbf{x}}\varphi(\textbf{p})|\textbf{p}\rangle$$ with $\varphi(\textb... | $$P^2 \, \int \text d ^3 \mathbf p f(\mathbf p ) \vert \mathbf p \rangle = \int \text d ^3 \mathbf p f(\mathbf p ) P^2 \vert \mathbf p \rangle = m^2\int \text d ^3 \mathbf p f(\mathbf p ) \vert \mathbf p \rangle$$
All these states are by definition on the mass shell (for each wavefunction $f$). Note that the localizat... | {
"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... | There's another reason for these pillars that is yet to be mentioned in these answers.
If you look at the picture you can see that the pillars don't hold the bridge up on their own. They extend well above the bridge deck and have many cables coming off of them for suspension.
These wires provide some force to hold the... | {
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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 energy of bound particles (in quantum systems) has two characteristics:
*
*The energy is quantized.
*The lowest allowable energy level is non-zero.
This is true of all bound particle systems, whether atoms, quantum oscillators or other.
Let us have a look at the simplest quantum system of all: the single part... | {
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Symmetric limit in Peskin and Schroeder I have a question on page 655 of Peskin and Schroeder.
The second equation of (19.23) is discussed here.
But the first equation of (19.23) is still a mystery.
$$ \underset{\epsilon \to 0}{\text{symm lim}}=\left\{\frac{\epsilon^{\mu}}{\epsilon^2}\right\} =0 $$
How can we understan... | Look at (19.27).
$$ \bar\psi(x+\varepsilon/2)\,\Gamma\,\psi(x-\varepsilon/2) = \frac{-i}{2\pi} \mathrm{tr} \left[ \frac{\gamma^{\alpha}\epsilon_{\alpha}}{\epsilon^2} \Gamma \right]\tag{19.27} $$
where the two fermion fields are contracted.
And note the first sentence of the paragraph just below (19.27) :
Because th... | {
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Why will we never run into a magnetic field that falls off as $\frac 1 {r^2}$? For example, Walter Lewin says in many lectures that we will never find a magnetic field $B\propto \frac 1 {r^2}$ - why is this?
I believe it must be related to $\nabla \times E= -\partial_t B$, but I don't see why this would make the previ... | I believe what he is implying is that there are no magnetic monopoles (that we know of), at least in classical electrodynamics. A magnet has a south and a north pole (a dipole), which produces a field (the vector potential)
$$
\mathbf{A} (\mathbf{r}) = \frac{\mu_0}{4\pi r^2} \frac{\mathbf{m} \times \mathbf{r}}{r} = \fr... | {
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What does antimatter look like? I have seen simulations of antimatter on TV. Has antimatter ever been photographed?
| Antimatter-antimatter interaction is, to the best of our knowledge of physics, chemically identical to matter-matter interactions. Any symmetry breaking is so small that it would have no observable effects at human scales.
Its interaction with photons is also identical.
The only important way it interacts differently ... | {
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Confusion between two different definitions of work? I'm doing physics at high school for the first time this year. My teacher asked us this question: if a box is slowly raised from the ground to 1m, how much work was done? (the system is only the box)
Using the standard definition, $W = Fd\cos(\theta)$, the work shou... | You have a teacher who knows his/her Physics.
the system is only the box
That statement made by your teacher immediately means that there can be no mention of gravitational potential energy as it is a system comprising of the box and the Earth which has gravitational potential energy.
A system comprising of the box... | {
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Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time? Quantum mechanics says that if a system is in an eigenstate of the Hamiltonian, then the state ket representing the system will not evolve with time. So if the electron is in, say, the first excited state then why does it ... | One way to look at this is the Fermi's Golden Rule:
If we add a time dependent perturbation to the time independent Hamiltonian,
$$
H=H_{0}+H_{1}
$$
plug it in the schrodinger's equation,
$$
(H_{0}+H_{1})|\phi(t)\rangle=i\hbar\partial_{t}|\phi(t)\rangle
$$
calculate the transition coefficients,
$$
c_{f\to i}(t)=\frac{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/295365",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "50",
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Degeneracy of two electrons on a ring The one-particle solution to the particle-on-a-ring problem is $\psi_m(\phi_j) = \frac{1}{\sqrt{2\pi}}\exp\left(-im \phi_j\right)$ for $m=0, \pm 1, \pm 2, \cdots$ corresponding to energies $E_m = \frac{m^2\hbar^2}{2I}$ where $I=MR^2$ is the moment of inertia.
I'm interested in the ... | The electrons can have different energies, so they don't both need to be in the one-particle excited state.
| {
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If a planet's core is heated by its gravitational pressure, where does that energy come from? I just saw a show about the theorized "Planet 9." One possibility is that it's an ice planet. But it could have a liquid water core from its gravitational energy crushing in the core and making it heat up. Where does the ener... | There are two sources of the heat of a planet's core:
There is the original potential energy of the asteroids that fell together to form the planet.
The material of the core is such a good insulator, that the small amount of radioactivity that occurs naturally in the core material is enough to be the input of energy ... | {
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Is general relativity a background dependent theory in five dimensions? I read the article What is a background-free theory? by John Baez and was wondering that if I add a fifth dimension to a background independent theory like general relativity I get a background dependent theory like the Maxwell's equations. The onl... | A background consists of non-dynamical data for a theory. E.g. for field theories in curved spacetimes, the metric $g_{\mu\nu}$ is a non-dynamical fixed background. In contract, for general relativity in any spacetime dimension, the metric $g_{\mu\nu}$ is a dynamically active field, and hence not a background.
For the ... | {
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Charge determines masses? Why are the masses of the $\Sigma^-$ ($1197\ \mathrm{MeV}$) and $\Sigma^+$ ($1189\ \mathrm{MeV}$) particles are not exactly equal?
$\Sigma^-$ has quark context $\rm dds$ and $\Sigma^+$ has $\rm uus$...I have been thinking that this has to do with their charge, but I am not sure how that direc... | The $\Sigma^\pm$ are not antiparticles of each other; both are baryons with a single strange quark and nonzero isospin. If isospin were an exact symmetry then they would have the same mass — but if isospin were an exact symmetry, the proton and neutron would have the same mass as well, and our universe would be very di... | {
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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.
| When doing push-ups, you are making your body into a lever! Your feet are the fulcrum. So you get the mechanical advantage that makes levers useful. It's just like how lifting the handles of a wheelbarrow (pivoting on the wheel) is a lot easier than simply picking up the contents of the wheelbarrow.
For similar reasons... | {
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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 ... | Indeed geometric interpretation of $\gamma_5$ is related to the volume form
$$
V=\frac 1 {4!} \epsilon_{\mu\nu\alpha\beta} dx^\mu \wedge dx^\nu \wedge dx^\alpha \wedge dx^\beta = \frac 1 {4!} \sqrt{-g} \varepsilon_{\mu\nu\alpha\beta} dx^\mu \wedge dx^\nu \wedge dx^\alpha \wedge dx^\beta = \sqrt{-g} dx^0 \wedge dx^1 \w... | {
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Why is there a Cardy formula in 2D CFT? In 2d CFTs, we have the Cardy formula which tells us the number of states, which can be derived from the partition function by using modular invariance. What special property of 2D CFTs make it possible to derive such formula?
| Firstly, it should be pointed out that there exist Cardy formulae for other dimensional CFT's too. See https://arxiv.org/abs/1407.6061 by Komargodski and Di Pietro and this paper by Verlinde https://arxiv.org/abs/hep-th/0008140.
But let us come to your question in 1+1 dimensional theories. The primary principle is tha... | {
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Eigenstates of Conical Potential in 3-dimensions? If we take an ordinary time-invariant Schödinger equation:
$$H|\psi\rangle = E|\psi\rangle,$$
and use a conical potential $V(r) = A r$ we get a differential equation:
$$\left[-\left(\frac{\hbar^2}{2m}\right)\nabla^2 + A r\right]\psi\left(\vec{r}\right) = E\psi\left(\vec... | See this answer of mine. In $d$ spatial dimensions, your equation reads
$$
u''(r)+2m[E-V_\ell(r)]u(r)=0
$$
where the effective potential is
$$
V_\ell=V(r)+\frac{1}{2m}\frac{\ell_d(\ell_d+1)}{r^2}
$$
with $\ell_d=\ell+(d-3)/2$. The zero-angular momentum state has $\ell=0$, and therefore in $d=3$ dimensions the equation ... | {
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Momentum and energy as a function of time If a constant force $F$ acts on a particle of rest-mass $m_0$, starting from rest at $t=0$, then what is its total momentum $p$ as a function of time? What is the corresponding energy $E$ as a function of time?
So I know $p=\gamma mu$ and $E=\gamma mc^2$
I know that $t'=\gamma ... | Your confusion is understandable. Most courses (the ones I've seen anyway) dealing with special relativity spend so much time on the Lorentz Transformation that they don't really get to much else. It was only when I took the second semester of the Electricity and Magnetism grad course that I started to feel like I ha... | {
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General Relativity and the barycenter I'm self training in physics, trying to understand as much physics as possible despite having very basic math skills and understanding. Until recently I thought I had understood the basics of gravity: A given configuration of matter distorts spacetime geometry. This distorted geom... | The concept of a barycenter, derived from Newtonian mechanics, does not generalize well to general relativity. In particular, the closed orbits you get by solving Lagrange's equation for two bodies are not solutions for full general relativity.
The most dramatic effect you get is that the orbiting bodies emit gravitat... | {
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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... | I don't think so.
*
*Looking into the past means seeing light rays that were emitted many many years ago. But you can't see light rays that are going to be emitted from some source.
*I don't completely your logic in the second statement , how can seeing the past put you in the center of the universe.
| {
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How does an ElectroDynamic Tether (EDT) clear space debris? Earlier today (9 December 2016), the Japan Aerospace Exploration Agency (JAXA) launched their Kounotori Integrated Tether Experiments (KITE) into orbit. What I understand from the description is that it will have a 20 kg weight at the end of a 700 m tether. ... |
The system comprises a long tether which is electrically conductive with devices for electron emission and collection. The system generates drag for reentry of debris by inducing an EMF along the length of the tether, caused by crossing Earth's geomagnetic field.
A current flows if there is a differential electron nu... | {
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Resonance- sound Can someone please explain resonance to me? I thought it was when an external object has the same frequency as an object, so through constructive interference, the amplitude is intensified. And maybe this has something to do with standing waves, I don't know. But can someone please further explain this... | Resonance is a property that some systems exhibit due to their specific structure, but fundamentally involves the trapping and a structural means by which energy can flow within the system between different states of energy.
The trapping of energy means that the system structure enables the system to admit at least as ... | {
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p+n reaction in nuclear fission reactors There is a recent question (Proton - neutron fusion?) about the possibility of the fusion reaction $p+n$. According to @dmckee's answer, the reaction is possible, but not useful for fusion power generation as supplying free neutrons is problematic.
My question: can this reactio... | I found an interesting answer by @Poutnik. While it does not provide a direct answer to my question here, as it discusses reactions of neutrons in a reactor with protons in water moderator, not in hydrogen, it suggests that p+n reaction in a nuclear reactor should negatively affect the performance of the reactor by rem... | {
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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.
| Partial answer:
Incident light on the solar panels will impart a momentum:
The momentum of a departing electron will be
$$p = m_e v$$
Ion thrusters use heavy ions (such as xenon ions which are 235,000 times as massive as electrons) to get a greater impulse. From this figure alone, one can see that the propulsion from ... | {
"language": "en",
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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... | The quantity you describe:
$$ S_t = \frac{T_{ref}-T_{local}}{T_{ref}} $$
is effectively just the time dilation. This is related to the spacetime geometry but does not fully describe it so time dilation alone cannot be used to calculate what happens in a gravitational field.
To see this let's take the specific example o... | {
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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 think the existing answers are making this a lot more complicated than it needs to. You are correct that the equation for the position of the center of mass is,
$$x_{cm}= \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$$
If you then take the center of mass as the origin, you set $x_{cm} = 0$, and thus $$m_1 |x_1| = m_2 |x_2|.$$... | {
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Can we get Pauli Exclusion Principle from QFT? I am learning QFT and fermion statistics.
I am confused about whether the Pauli Exclusion Principle is a fundamental rule or it can be deduced from QFT?
I saw a sentence from wiki but I don't understand.
In relativistic quantum field theory, the Pauli principle follows fro... | The spin-statistics theorem is a consequence of causality in a relativistic QFT. In order the theory to be causal, the commutator of the fields
$\left[ \Phi (x), \Phi(x^{\prime}) \right ]$
must vanish outside the light-cone, namely, for $(x-x^{\prime})^2>0$.
See the detailed discussion of the subject in Ch. 5 of Weinbe... | {
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In a "universe" where time runs backwards, is cause/effect preserved? Caveat: I'm a layman not a physicist, and this may be more semantics than physics.
In a universe where time runs backwards (think of a movie run backwards, where a vase that is shattered on the floor assembles itself and jumps up to the countertop), ... | If one considers only reversible processes or few particle physics (that is, in any case one can forget about the 2nd principle) the answer is definitely yes, the cause and effect is preserved.
Classical mechanics (including relativity) as well as quantum mechanics are indeed time-reversal symmetric.
At a mathematical... | {
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Why is the symmetry variation $\delta_s q$ different from the ordinary variation $\delta q$? I was reading about symmetry of action when I came before the symmetry variation in Particles and Quantum Fields by H. Kleinert; there he wrote:
Symmetry variations must not be confused with ordinary variations $\delta q(t)$ u... | What Kleinert calls symmetry variations and ordinary variations are used in 2 different contexts. Both are off-shell variations.
*
*Symmetry variations should leave the action invariant up to boundary terms. (In the affirmative case, one can then apply Noether's theorem to deduce a conservation law.) They have typi... | {
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How does a battery work and create a field inside it? There is an explanation of how a battery works that says that inside the battery (in the positive charge convention) there is a field and the battery does work on the positive charge against the field to move it from the negative terminal to the positive terminal an... | Batteries work by chemical reactions. The current inside a battery is an ion current. And the main point to realize is that the ion current is driven be a concentration gradient, and that it is in a direction opposite to the electric field inside the battery.
| {
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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 $\... | *
*$\lvert \psi \rvert^2 (x,t)$ is not a probability, it is a probability density which you have to integrate over smoe region of space to get a probability. The probability to find the particle in an interval $[a,b]$ is $\int_a^b \lvert \psi(x)\rvert^2\mathrm{d}x$, which is zero for $a=b$, i.e. the probability to fin... | {
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Coefficient of restitution According to Wikipedia,
The coefficient of restitution (COR) is a measure of the "restitution" of a collision between two objects: how much of the kinetic energy remains for the objects to rebound from one another vs. how much is lost as heat, or work done deforming the objects.
and the for... | Note first in your simplification in calculating the COR you cancelled the mass before and after the collision, but in general this may not be the case. If there are two masses colliding after the collision one or more may break apart, with additional masses carrying off some of the energy. Or one mass or part of that ... | {
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Let's make Jupiter a star It is known that Jupiter is mostly made of hydrogen, but that it is not massive enough to start nuclear fusion. In other words, Jupiter is not a star, but could be a star if someone added hydrogen to the planet.
How can the critical mass, where there is sufficient thermal energy at the core to... | Yes, your logic is correct, if we kept adding hydrogen to jupiter, it could eventually become a star.
See: http://www-star.st-and.ac.uk/~kw25/teaching/stars/STRUC5.pdf
So long as you understand the basic thermodynamics in there then you will be able to follow through to the end, if not, and you are not interested, then... | {
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What is the minimal discrete model of wave propagations? If one takes the step size of an $n$-dimensional symmetric random walk to be infinitesimal, then the transition probability becomes the heat kernel. Thus, symmetric random walks are discrete, or microscopic, models of heat/diffusion.
The heat equation and wave eq... | The second order forward finite difference stencil is given by
$$ f''(t) = \frac{f(t+2\Delta t)-2f(t+\Delta t) + f(t)}{\Delta t^{2}} $$
Define the update rules as
$$ P(x,t + \Delta t) = pP(x-\Delta x,t) + qP(x+\Delta x,t) $$
$$ P(x,t+2\Delta t) = p\left[pP(x-2\Delta x,t) + qP(x,t)\right] + q\left[pP(x,t) + qP(x+2\... | {
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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?
| People hope that it may be an example of AdS/CFT correspondence that can be completely understood.
AdS/CFT correspondence itself has been an incredibly important idea in the hep-th community over the past almost twenty years. Yet it remains a conjecture. In the typical situation, quantities computed on one side of th... | {
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massless rope that attaches crates , masses and blocks In exercices that involves crates , sliding , ropes and pulleys , they often say "masseless" string /rope , why ? what does it physically mean ?
| If you have two blocks connected by a string, you actually have three objects.
In a careful analysis you have to apply Newton's Laws to each one of the three objects to arrive at a dynamical equation for each object. You also have to find constraint equations that couple the dynamical equations.
I recommend that you... | {
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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... |
The earth takes 24 hours to spin around it's own axis.
Depending on the specifics (such as what it means to "spin around"), this is incorrect. To spin around exactly once with respect to distant stars (aka Sidereal day) requires 236 seconds less than 24 hours. Over half a year, this nearly 4 minute difference every... | {
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Null total spin and maximal entanglement Is it true that if the total spin of two entangled particles is 0 on all axes, then they must be maximally entangled?
| No, this isn't true. Probably the simplest example is two spin-1 particles, with both of them in the $L_z=0$ state,
$$
|\psi⟩=\left|1,0\right>\otimes\left|1,0\right>.
$$
This is completely separable, and it has zero expectation value for the total angular momentum along any axis, since
$$
\left<\psi\middle|L_x\middle|... | {
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Is $\mathbf{F}=m\mathbf{a}$ a vector field or just a vector? I've heard both yes and no.
Is $\mathbf{F}=m\mathbf{a}$ a vector field or just a vector?
I think it's ambiguous, it's always written without an argument.
For sake of clarity: I use the notation $\mathbf{F}(x,y,z)$ or $\mathbf{F}(\mathbf{r})$ for a vector fiel... | In rigid body mechanics $\bf{F}$ is not a vector field because to accelerate a rigid body (center of mass) with $\bf{a}$ you apply a force $\bf{F}$ regardless of where it is applied. The location of the force does not affect the motion of the center of mass.
On the other hand, the acceleration $\bf{a}$ is a vector fiel... | {
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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... | Let us rename your parameters in order to write the equation in a more usual form:
$$m\ddot{x}+c\dot{x}+F(x)=0 \qquad m>0,c\geq 0$$
For a suitable restoring force $F(x)$ to force the system to exert a harmonic motion.
For the sake of simpicity let the system exert small oscillations and therefore the function $F(x)$ ca... | {
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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... | Classically, a particle impinging on a potential is always reflected or transmitted. Which one occurs is determined by whether the particle's kinetic energy is less than or greater than the maximum of the potential barrier. If the particle has enough energy, it passes through the potential; if not, it rebounds.
Quant... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/300704",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
How does a transformer work? As voltage is given to primary coil, current flows through coil and consequently magnetic flux changes. Due to change in magnetic flux a back emf is also induced in the primary which opposes the applied voltage. Thus applied voltage =- induced EMF, i.e.
$$V_p=E+IR \, ,$$
and if $R=0$ then $... | A back EMF is generated but where did you learn that the back voltage from this EMF is exactly "equal" to the applied voltage? The back EMF is proportional to the time rate of change in the magnetic flux and since the magnitude of the magnetic flux and its rate of change depends, for instance, on what material is insid... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/300766",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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
$$\varphi(p)=\frac{1}{\sqrt{2\pi\hbar}}\int \mathrm dx \, e^{-i p x/\hbar} \psi(x).$$
| Let's start from scratch. Take the positions eigenvectors, $\left|x\right>$. They are such that $X\left|x\right> = x\left|x\right>$. Now, take a general ket for a wavefunction, $\left|\psi\right>$. If we want to know $\psi(x)$, that is, the wavefunction in the position representation, then we take the following scalar ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/300970",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 0
} |
Can lasers be combined to achieve higher power? For example, if an object's atoms require light with 100 nm to become ionized, can four 400 nm lasers concentrated at one point on the object achieve ionization? Or will the combined power vary based on different factors?
| Yes, very high power laser radiation can cause nonlinear effects, such as multi-photon ionization (https://en.wikipedia.org/wiki/Photoionization#Multi-photon_ionization). Actually, not only four 400 nm lasers, but also just one high-power 400 nm laser can ionize atoms that normally require 100 nm for ionization (https:... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/301233",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
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