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It is implied, per QM, that the behavior of subatomic particles cannot be precisely predicted. However, these indeterministic effects do have defined probabilities. By the law of large numbers, they can “average” out and result in approximately deterministic laws.
For this reason, I presume, we can predict with pinp... | [
"\nWhen thinking about the entirety of the Universe in terms of QM you will very quickly run into paradoxes. That's why I don't think we are at a point when your question can be meaningfully answered. For instance, the Universe is by definition a closed system (there is nothing else but it). So it must be in a pure... |
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"\nThis answers only address part of the problem, i.e., assuming that local and global stand for properties of function/vectors/tensorial obejects defined on spacetime. If you look at spacetime as a [manifold](https://en.wikipedia.org/wiki/Manifold) $M$, then local means that the property/definition under considera... |
I understand that superconductors have zero resistivity, however, I wonder if there is a relation between resistivity and the work function of a specific material so that a superconductor has zero (or a low value) work function. If so, photons with very long wavelengths can release electrons from the surface of a supe... | [
"\nThe work function is a measure of how much energy it takes to completely remove an electron from a material and send it into **free space**, and costs on the order of 1000-5000 meV of energy. The resistance is a measure of how much energy is needed to move electrons infinitesimally ($\\omega\\sim0$) **within the... |
In quantum mechanics, the probability, say, that a radioactive atom will decay is well defined. By the Born Rule, it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. However, the actual decay point and the actual measurement outcome are indi... | [
"\nAlthough the outcomes of the measurement of a quantum phenomenon might be **probabilistic**, that **does not mean that the outcome could be anything**. For a large enough ensemble, one can predict with a high degree of accuracy what the outcome of the experiment will be. E.g., the spin of a fermion in the [Stern... |
[](https://i.stack.imgur.com/JJpO9.jpg)
I just start learning Physics, and so many strange questions come across my mind. Here is one:
The picture shows the ISS orbiting Earth. Suppose now we (or rather say God) put a baseball behind ISS, Will thi... | [
"\nIt is all about the *sideways speed* of the object.\n\n\n* The ISS and also your baseball is falling towards Earth constantly. If you just let go of the ball up there, then it will fall down and crash on the ground underneath.\n* Push it a bit sideways while letting go and it still crashes but a bit more to the ... |
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"\nIn a refrigerator or freezer without a circulating fan to stir the air around, it isn't possible to get a uniform temperature in it except by waiting a long time. however, there is another effect which may be important here, as follows.\n\n\nIf you cool down a very pure water sample in a very clean container whi... |
It is implied, per QM, that the behavior of subatomic particles cannot be precisely predicted. However, these indeterministic effects do have defined probabilities. By the law of large numbers, they can “average” out and result in approximately deterministic laws.
For this reason, I presume, we can predict with pinp... | [
"\nWhen thinking about the entirety of the Universe in terms of QM you will very quickly run into paradoxes. That's why I don't think we are at a point when your question can be meaningfully answered. For instance, the Universe is by definition a closed system (there is nothing else but it). So it must be in a pure... |
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"\nThis answers only address part of the problem, i.e., assuming that local and global stand for properties of function/vectors/tensorial obejects defined on spacetime. If you look at spacetime as a [manifold](https://en.wikipedia.org/wiki/Manifold) $M$, then local means that the property/definition under considera... |
I understand that superconductors have zero resistivity, however, I wonder if there is a relation between resistivity and the work function of a specific material so that a superconductor has zero (or a low value) work function. If so, photons with very long wavelengths can release electrons from the surface of a supe... | [
"\nThe work function is a measure of how much energy it takes to completely remove an electron from a material and send it into **free space**, and costs on the order of 1000-5000 meV of energy. The resistance is a measure of how much energy is needed to move electrons infinitesimally ($\\omega\\sim0$) **within the... |
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"\n\\*\\*\\* Why is it the square of the amplitude and not 1/4 or 1/8?\n\n\nIt's essential that the description of quantum phenomena use probability amplitudes that have the feature that they are complex numbers and can be negative. The amplitudes allow for interference, etc. We take the square modulus for the prob... |
[](https://i.stack.imgur.com/JJpO9.jpg)
I just start learning Physics, and so many strange questions come across my mind. Here is one:
The picture shows the ISS orbiting Earth. Suppose now we (or rather say God) put a baseball behind ISS, Will thi... | [
"\nIt is all about the *sideways speed* of the object.\n\n\n* The ISS and also your baseball is falling towards Earth constantly. If you just let go of the ball up there, then it will fall down and crash on the ground underneath.\n* Push it a bit sideways while letting go and it still crashes but a bit more to the ... |
**This question already has an answer here**:
[If I jump will I land in the same spot? [duplicate]](/questions/80090/if-i-jump-will-i-land-in-the-same-spot)
(1 answer)
Closed 3 hours ago.
The answer to this question may differ from what we directly observe because the Earth is spinning.
| [
"\nSee the link for the answer.\n[enter link description here](https://zhuanlan.zhihu.com/p/652945463)\n\n\n",
"-1"
] |
I don't have any physics background aside from intro physics so apologies if my question sounds very shallow.
If lens power is based on focal length, but our eyes adjust its focal length based on the distance of the object we are observing, how do we know that our lens prescription is correct for all distances? Most... | [
"\nAn \"ideal\" eye can adjust its optical system from the *near point*, $25\\,\\rm cm$ (least distance of distinct vision) from the eye, to the *far point* at \"infinity\" (largest distance of distinct vision).\n\n\nWhen things go wrong that range might change and the optical system has to be adjusted by using ext... |
Consider the following system:
[](https://i.stack.imgur.com/2aksP.jpg)
I am thoroughly confused about certain aspects of the situation described in this diagram in which a block is placed on a wedge inclined at an angle θ. (Assume ***no friction everywhere***) ... | [
"\nRather than answer your individual questions I will give you an overview and then discuss some of the points that you have raised. \n\nThere are many ways of tackling such problems but drawing a few FBDs together with some coordinate axes is always a good to start.\n\n\n[![enter image description here](https://... |
Let's consider a satellite which is moving in an elliptical orbit. The velocity of the satellite is $v\_1$ at the perigee, and the distance of the perigee from the centre of the Earth is $r\_1$.
Is it possible to calculate the change in orbital velocity of the satellite required to change its orbit to a circular orbit... | [
"\nYour approach is on the right track, and you could use the law of conservation of angular momentum, but you also need to consider the conservation of mechanical energy to *fully* solve this problem.\n\n\nLet's denote the following variables:\n\n\n* $v\\_1$ = Velocity of the satellite at perigee.\n* $r\\_1$ = Dis... |
In many formulations of Bohmian mechanics, researchers seem to claim that 1) measurements of observables such as spin are just measurements of the position of a *pointer variable*, such as the Stern-Gerlach experiment apparatus and 2) measurements of position reveal the position of particles. This effectively removes ... | [
"\nIn Bohmian mechanics, the entire trajectory of all particles through space as a function of time is well-defined. So they have both a position and a momentum at all times.\n\n\nYes, you are correct that measurements never reveal the exact position or momentum. So what?\n\n\n",
"0"
] |
Context
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In the derivation of the Boltzmann factor and the canonical partition function based essentially on Lagrange multipliers presented [here](https://en.wikipedia.org/wiki/Partition_function_(statistical_mechanics)), the equalities,
\begin{align\*}
p\_j &= \frac{1}{Z} e^{\frac{\lambda\_2 E\_j}{k\_B}} \\
... | [
"\nImo, your doubt is related to the assumption that the partial derivative of the energy of a microstate, $(E\\_j$), with respect to the total energy, $(U$), is zero, i.e., $(\\frac{\\partial E\\_j}{\\partial U} = 0$).\n\n\nIn the context of statistical mechanics, the assumption $(\\frac{\\partial E\\_j}{\\partial... |
I recently encountered this question:
>
> *How long would an someone need to spend on the ISS so that
> their biological clock would be one day younger than their twin who stayed on Earth? The ISS is orbiting the Earth at an altitude $h$.*
>
>
> *Hint: Consider the twins born on a hypothetical stationary Alien s... | [
"\n\n> \n> I thought that maybe you need to take into account the Earth's rotation or something, but then you would need to make an assumption about whether they are moving in the same direction or not.\n> \n> \n> \n\n\nSince the hint says both twins are moving, you indeed need to take into account the Earth's rota... |
Applying the Ampere-Maxwell law for a point charge moving:
$$\nabla × \vec{B} = \mu\_{0} \vec{J} + \mu\_{0}\epsilon\_{0} \frac{\partial \vec{E}}{\partial t}$$
Since differentiation at a point requires continuity, and at r=0 jefimenkos equation show that the electric field is not continuous nor defined, how can we ... | [
"\nTerms in this equation need not have finite value at position of the point charged particle, and some of them certainly don't ($\\vec{J}$).\n\n\nThe equation term $\\vec{J}$ becomes singular (of infinite magnitude) at that position. The equation still makes sense at all other points, which is often enough to mak... |
[](https://i.stack.imgur.com/h8luK.png)
The small ball attached by a thin string is in uniform circular motion as shown in the picture (vertical plane). There are two forces acting on the ball, Gravitational force $F\_g$ and Tension force from the s... | [
"\nFor uniform circular motion, acceleration and force are directed toward the center.\n\n\nHere you have another component. The ball will slow as it rises on the circular trajectory. On the other side, it will speed up.\n\n\nAs the speed varies, the component of force and acceleration toward the center will vary. ... |
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"\nIf you think of the minima, you always need two elementary wave starting in the slit and in a direction to have another wave with way difference $\\lambda\\over2$ this is the case if you think of the two rays at the edges of the slit having a difference of $\\lambda$sin so the angle to the slit is $sin(\\alpha)=... |
I used to read the term "pure energy" in the context of matter-antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass?
Basically, what does "pure energy" in the context of matter-antimatter annihilation refer to?
| [
"\nIf I ruled the world, I would ban the phrase \"pure energy\" in contexts like this. There's no such thing as pure energy!\n\n\nWhen particles and antiparticles annihilate, the resulting energy can take many different forms -- one of the basic principles of quantum physics is that any process that's not forbidden... |
When a fluid-filled container containing an ideal liquid is rotated about its central axis with angular velocity $\omega$, the surface of the liquid forms a paraboloid shape. Now when we derive the equation of the parabola formed by taking a cross section through the midpoint of the paraboloid, using the standard tech... | [
"\nYes, of cause you can do it from the ground frame. You need a centripetal force to keep the fluid particles on a circle. So on the particle you have the weight $mg$ and the force $m·\\omega^2·r$ perpendicular to the slope; together they give the centripetal force.\n\n\n",
"1"
] |
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"\nLet $H$ be the harmonic oscillator Hamiltonian.\n$$\nH=\\frac{\\hat p^2}{2m}+\\frac{m\\omega^2\\hat x^2}{2}\n$$\n\n\nLet $K(b,a)$ be the propagator for the harmonic oscillator.\n\\begin{equation\\*}\nK(b,a)=\\langle x\\_b|\\exp\\left(-\\frac{iHt}{\\hbar}\\right)\n|x\\_a\\rangle\n\\tag{1}\n\\end{equation\\*}\n\n\... |
[Homework-like questions](https://physics.meta.stackexchange.com/q/714) and [check-my-work questions](https://physics.meta.stackexchange.com/q/6093) are considered off-topic here, particularly when asking about specific computations instead of underlying physics concepts. Homework questions can be on-topic when... | [
"\nConsider using MathJax when typing formulas. Yes your reasoning is correct. Another way to get it directly is to notice that the entropy of the system is conserved by reversibility of the Carnot cycle. The total entropy is:\n$$\nS = C\\_1\\ln T\\_1+C\\_2\\ln T\\_2\n$$\nwith $C\\_1,C\\_2$ the respective heat capa... |
I've kept a ball between one fixed and another mobile surface of same height (say two books one which functions as a fixed support while other is moved on about by me). While I pull one of the books, the ball starts coming down which implies that $mg$ overpowers normal by the surfaces.
Well then at some instant, I s... | [
"\nI don't think that the normal due to the contact surface prevents the ball from falling, but it is the one which provides necessary friction to balance out the weight of the given ball.\n\n\nWhen you remove the contact surface(book in this case), then the necessary friction required to prevent the ball from fall... |
The no-hair theorem states that we can't detect scalar fields outside a black hole, meaning that the solution for the KG equation is trivial, but in fact, we can solve it (for instance for a Schwarzchild BH) and the solution is not trivial, what am I missing?
| [
"\n\n> \n> … what am I missing?\n> \n> \n> \n\n\nYou are missing the meaning of (various) no-hair theorems. Those theorems are talking about *equilibrium* configurations corresponding to end points of gravitational collapse and thus about *static* or *stationary* solutions to Einstein equations with various kinds o... |
If I understand correctly, the rate of radioactive decay depends on the amount of the radioactive element. How then can it be constant, if it depends on concentration?
| [
"\nThe rate of radioactive decay depends on the statistical probability that any random *single* nucleus will decay in a unit of time. That probability does not depend on the number of atoms present in a sample, which is a piece of information that the nucleus of an atom does not have any sort of access to in the f... |
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This question appears to be about **engineering**, which is the application of scientific knowledge to construct a solution to solve a specific problem. As such, it is off topic for ... | [
"\nIt's impossible to say. The unknown geometry of the antenna element inside the stick matters, and the computer and attached wiring are also part of the antenna. The environment is full of reflectors and diffractors, so it's not a clean \"wave in empty vacuum\". situation.\n\n\nThe resulting link signal/noise wil... |
Is there a proof from the first principle that for the Lagrangian $L$,
$$L = T\text{(kinetic energy)} - V\text{(potential energy)}$$
in classical mechanics? Assume that Cartesian coordinates are used. Among the combinations, $L = T - nV$, only $n=1$ works. Is there a fundamental reason for it?
On the other hand... | [
"\nWe assume that OP by the term *first principle* in this context means [Newton's laws](http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion) rather than the [principle](http://en.wikipedia.org/wiki/Principle_of_least_action) of [stationary action](http://www.scholarpedia.org/article/Principle_of_least_action)$^... |
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"\n\n> \n> How are we supposed to take the component of a component ?\n> \n> \n> \n\n\nThere is no reason why you cannot do this - it is just a mathematical procedure. In this case it makes sense because the component of the block's weight perpendicular to the slope is balanced by the normal force from the slope, s... |
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"\nIn the case of a vertical nonlinear spring, the effect of gravity can indeed influence the behavior of the spring and the motion of an object attached to it. Unlike a linear spring, where the relationship between force and displacement is linear, nonlinear springs have force-displacement relationships that are n... |
I found this proof of Kepler's first law of planetary motion online [here](https://radio.astro.gla.ac.uk/a1dynamics/ellproof.pdf). Running through the text I found nothing wrong.
However, a warning message at the top the the page saying that "this proof is not examinable!". So what is missing in that proof?
| [
"\nThe proof you've provided is indeed a valid derivation of Kepler's first law of planetary motion, which states that planets move in elliptical orbits with the Sun at one of the foci. The proof correctly derives the equation of an ellipse in polar coordinates and identifies the key parameters, such as the semi-la... |
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[What happens to the energy when waves perfectly cancel each other?](/questions/23930/what-happens-to-the-energy-when-waves-perfectly-cancel-each-other)
(14 answers)
Closed yesterday.
I have been wondering if the energy changes when two waves inter... | [
"\nGiven their fundamental differences(mechanical waves need a medium to interact in, while their electromagnetic counterparts do not), it is not common for mechanical and electromagnetic waves to directly interfere with each other in the traditional sense of wave interference(ie constructive and destructive interf... |
Recently I have been reading Berkeley Physics Course - Mechanics. In Chapter 12 (page 350 - 352), author gave a very good example that original definition of momentum $P = mv$ is not working by showing the y-axis' total momentum is not conserved before and after collision. Because:
$$-Mv'\_y(1) + Mv'\_y(2) \neq Mv\_... | [
"\nIn the original analysis, when you're using the non-relativistic momentum definition $P = mv$, you indeed encounter a problem with momentum conservation in the y-axis, which indicates that the classical momentum definition is not adequate in special relativity. This leads to the introduction of the corrected def... |
Last winter I started toying with the galaxy gravitational rotation curve graphs. I started modifying the exponent of $r$ that in effect change the $1/r^2$ law and therefore correct the mismatch, just to see where it will lead me.
[](https://i.stack... | [
"\nBy eye this curve doesn't seems like a good one. Try to study the residues of the $\\chi^2$.\n\n\nIn principle for a good fit they should be gaussian, but since this is an approximation you can partially ignore that.\n\n\nNonetheless they should at least be symmetric about zero and, at least by eye, that's not y... |
Let's consider a glass slab ABCD.
Now a light ray is incident on the near end of the air-glass interface AB and is emerging from the glass-air interface BD. In such a manner:
[](https://i.stack.imgur.com/G5N3D.png)
Is there something wrong how I have made my... | [
"\nThere is a potential problem.\n\n\nThe critical angle $c = \\sin^{-1}\\left ( \\frac 1 n\\right)$, where $n$ is the refractive index of the glass.\n\n\nAt the first interface $r\\le c$ and at the second interface $i\\_2 \\le c$ for there to be refraction\n\n\nHowever, $i\\_2 + r= 90^\\circ$, and so only if $n\\l... |
Let's consider a glass slab ABCD.
Now a light ray is incident on the near end of the air-glass interface AB and is emerging from the glass-air interface BD. In such a manner:
[](https://i.stack.imgur.com/G5N3D.png)
Is there something wrong how I have made my... | [
"\nThere is a potential problem.\n\n\nThe critical angle $c = \\sin^{-1}\\left ( \\frac 1 n\\right)$, where $n$ is the refractive index of the glass.\n\n\nAt the first interface $r\\le c$ and at the second interface $i\\_2 \\le c$ for there to be refraction\n\n\nHowever, $i\\_2 + r= 90^\\circ$, and so only if $n\\l... |
Boltzmann's entropy formula:
$S=k\_{\mathrm {B} }\ln \Omega$
where $\Omega$ is the number of real microstates corresponding to the gas's macrostate.
Let's assume that we are talking about an ideal gas in a fixed close isolated space, with $n+1$ atoms.
It seem that the number of possible microstates of the follow... | [
"\nYou're comparing the two microstates incorrectly.\n\n\nScenario Uno\n\n\n* There are $n$ atoms with energy $x$ each.\n* There is one atom with energy $y$.\n\n\nScenario Dos\n\n\n* There are $n$ atoms with energy $x/2$ each.\n* There is one atom with energy $y + nx/2$.\n\n\nNow, let's analyze these scenarios in t... |
In Polchinski's exposition of the RNS formalism for the superstring (String Theory: Volume II, chapter 10), in page 8, he mentions the worldsheet fermion number operator, which he calls $F$. He then goes on to define
\begin{equation}
(-1)^F = e^{i \pi F}.\tag{10.2.19}
\end{equation}
To my best knowledge, this object i... | [
"\nRecall that\n$$\\{ \\psi\\_r^\\mu , \\psi\\_s^\\nu \\} = \\eta^{\\mu\\nu} \\delta\\_{r,-s}. \\tag{1}$$\nLet's start by trying your definition,\n\\begin{equation}\n\\begin{split}\n[ F' , \\psi\\_r^\\mu ] &= \\sum\\_s [ \\psi\\_s^\\nu \\psi\\_{-s,\\nu} , \\psi\\_r^\\mu ] \\\\\n&= \\sum\\_s \\psi\\_s^\\nu \\{ \\psi... |
Let the differential cross section of a scattering experiment given by $\frac{\text{d}\sigma\_{c}}{\text{d}\Omega\_{c}}(\vartheta\_{c})$, where $\vartheta\_{c}$ describes the scattering angle in the center of mass frame. The relation between $\vartheta\_{c}$ and the scattering angle in the laboratory frame is given by... | [
"\nAfter an Odyssey up the reference tree i found the answer in\n\n\n\n> \n> W. K. Chu, J. W. Mayer, and M. -A. Nicolet, Backscattering Spectrometry (Academic Press, New York, 1978)\n> \n> \n> \n\n\nSo you don't have to search it here it is:\n\n\nStarting with the formula:\n$$\n\\frac{\\text{d}\\sigma}{\\text{d}\\O... |
From the following [image](https://www.eigenplus.com/wp-content/uploads/2022/12/isotropic_material-2048x1444.jpg), why do we still call it isotropic? if the density at A and B differ, I don't think it's enough to call it isotropic. In my opinion, material is only isotropic if when we choose some point, around it in al... | [
"\nFor a system to be isotropic w.r.t. a point of reference it has to appear the same in all directions. Say if I'm located at a point $p$ and from there I find the system isotropic then this just means that the system has the same property at a fixed radius $r$. In particular, it does not need to have the same pro... |
I don't understand why the nuclear decay formula is derived with logarithms.
if $t=T\_{1/2}$ then
$N=N\_0\cdot\frac{1}{2}$
if $t=2T\_{1/2}$ then
$N=N\_0\cdot\frac{1}{2^2}$
if $t=3T\_{1/2}$ then
$N=N\_0\cdot\frac{1}{2^3}$
and so on... so the formula can be expressed in this form
$N=N\_0\cdot \frac{1}{2^... | [
"\nThe decay graph can be described in a number of ways each with a parameter which is a characteristic of the decay.\n\n\nYour description the characteristic parameter is the *half-life*, $\\tau$ and so $N(t) = N\\_0\\,2^{-t/\\tau}$.\n\n\nAnother often used parameter is the *decay constant*, $\\lambda$ which is th... |
[Homework-like questions](https://physics.meta.stackexchange.com/q/714) and [check-my-work questions](https://physics.meta.stackexchange.com/q/6093) are considered off-topic here, particularly when asking about specific computations instead of underlying physics concepts. Homework questions can be on-topic when... | [
"\nThe reason your professor considers 𝐽 = 0 outside the wire (𝑟 ≥ 𝑅) is related to the assumption that the current is confined to the wire itself. In the context of solving for the magnetic field generated by an infinite wire carrying current, there's typically an implicit assumption that the current is flowing... |
Do [Boltzmann brain](https://en.wikipedia.org/wiki/Boltzmann_brain) thought experiments suggest literally anything can form randomly?
What are the limitations to what random fluctuations can form? Literally any physical, material object?
Lastly, I am curious as to how this compares to an object with a high degree ... | [
"\nA very handy way of looking at the statistical mechanism of a system is by looking at its so-called [phase space](https://en.wikipedia.org/wiki/Phase_space) (read as state space).\n\n\nConsider a [microstate](https://en.wikipedia.org/wiki/Microstate_(statistical_mechanics)#:%7E:text=Treatments%20on%20statistical... |
This is my first post and also the first time I've ever tried understanding a physics concept by approaching it with my own math logic so tips on trying to do this more effectively are also welcome
I’m trying to understand the link between a force experienced by a wire in a homogenous magnetic field and the magnetic... | [
"\nThe combination of magnetic fields is sometimes called the *catapult field* as illustrated below.\n\n\n[](https://i.stack.imgur.com/Qquir.jpg)\n\n\nThe name catapult field comes from the idea that magnetic field lines are always in a state of te... |
I am trying to understand the implementation of POVMs on a Hilbert space by using unitary operations and projective measurements in a larger Hilbert space. In A. Peres' *Quantum Theory: Concepts and Methods*, Section 9.6, he claims that a POVM on a Hilbert space $H$ of dimension $n$, consisting of rank-1 elements
$$ {... | [
"\n### Naimark dilation for arbitrary POVMs\n\n\nAny POVM $\\{\\mu\\_b\\}\\_{b=1}^{m}$ can be implemented as a computational basis projective measurement in an enlarged space via the Naimark's construction. Restricting our attention to finite-dimensional spaces, let's assume without loss of generality that the rele... |
I recently came across a paper that argues that we can substitute a qubit for arbitrarily large number of bits in a physical system (<https://arxiv.org/abs/quant-ph/0110166>).
The notion of bit represent classical information. This then implies qubit can hold a huge amount of information. On the other hand, we have ... | [
"\n\n> \n> So if a qubit represent the quantum memory how can we compare its size with classical memory ?\n> \n> \n> \n\n\nYou can think of a quantum computer as being an analogue computer - the state of a qubit is like the angle of a wheel or the level of water in a tube in an analogue computer. In principle you c... |
If we have a sealed piston-cylinder with gas inside and we heat it from the outside, the temperature changes. At the same time, if we look at it as a control mass system,the volume increases as the gas expands. Mass remains same. Hence specific volume changes too. So how can temperature and specific volume always be i... | [
"\nTake gas in a box with a fixed size and heat it. The temperature increases, but the specific volume remains fixed. This is also a perfectly reasonable physical situation thatwe could easily achieve. Comparing this situation with the one in your question, we conclude that while I *can* increases the temperature a... |
Take the following standard setup and calculation for a Faraday disk:
A metal disk of radius $a$ rotates with angular velocity $\omega$ about a vertical axis, through a uniform field of magnitude $B$, pointing up along the vertical axis. A circuit is made by connecting one end of a resistor to the axle and the other... | [
"\nIf only a sector of the disk is in uniform magnetic field, then there can't be equilibrium of charge in the disk, because in the frame of the disk, the charge experiences time-dependent force, due to moving in and out of the magnetic field. The disk will experience electric currents in its frame, and thus dissip... |
I'm aiming to use differential equations to simulate thermal transfer between different materials in a 3D space, however, my physics knowledge is lacking. Is there a formula that can give the rate of thermal transfer between two different materials (e.g copper, aluminium) with a two-dimensional area of contact?
| [
"\nYou could use a formula known as Fourier's Law, which essentially states that\n\n\n$Q = -k \\cdot A \\cdot \\frac{dT}{dx}$\n\n\nWhere:\n\n\n* Q is the rate of heat transfer (in watts, W).\n* k is the thermal conductivity of the material (in watts per meter-kelvin, W/(m·K)).\n* A is the cross-sectional area throu... |
I think I am misunderstanding something elementary. Supposing a scenario where you have a negative charge enclosed in a Gaussian surface, why would the presence of outside charges not affect the flux?
In scenario 1 there are no outside charges, so there will be field lines coming in from infinity and none going out ... | [
"\n\n> \n> And the more positive charges you have, the more field lines that end in the negative charge?\n> \n> \n> \n\n\nThe number of field lines chosen to describe the amount of charge is purely arbitrary and doesn't follow any physical laws. They are simply used to depict the magnitude of charge on individual c... |
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"\nYou are just asking notation. The Fourier transform comes with a choice of where and how to put the $2\\pi$, unless you start with the most mathematically natural version.\n\n\nFirst, you should rewrite your transformation with the usual symbols, $k$ instead of $\\omega:$\n$\n\\begin{align}\n\\tag1f(x)=\\frac1{2... |
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"\nIt is important to know that for the data you've provided- there would be more than simply electrostatic and gravitational forces at play. Since the velocity of particles is of the order of 10% of the speed of light, *relativistic* effects would also come into play. Even in the simplest solution (where i will as... |
I don't understand how to explain why kinetic energy *increases* using Faraday's Law as a charged particle reaches the end of a magnetic bottle.
I know that along the field line in the bottle, the magnetic moment of the particle is conserved (first adiabatic invariant) which leads to $v\_{\perp}$ icreasing as $v\_{\... | [
"\nI suspect you know that the total energy doesn't change; the kinetic energy due to the velocity perpendicular to the axis of the magnetic bottle, $1/2 m v\\_\\perp^2$ increases at the expense of the remaining kinetic energy term $1/2 m v\\_{||}^2$. As the particle moves into a region of higher magnetic field, th... |
It's well known that the basic formula for the angular magnification of an optical telescope is
$$ |M| = \frac{f\_{ob}}{f\_{oc}} $$
where $f\_{ob}$ is the focal length of the objective, and $f\_{oc}$ is that of the ocular (the *eye-piece*).
So, if $f\_{ob}$ of the objective increases, so will $M$ of the telescop... | [
"\nA couple of problems:\n\n\n1. Your formula assumes the telescope is short compared to the distance to the object you're imaging. An infinitely long telescope violates that assumption.\n\n\nBut more seriously:\n\n\n2. You're using a ray optics approximation, ignoring diffraction. With diffraction, what happens as... |
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"\nThe trick is,\nmultiply the integrand by $\\exp(-\\epsilon r)$, solve the integral,\nthen let $\\epsilon\\rightarrow0$.\n\n\nFor example, consider the following momentum transfer function\nwhere $\\breve p=p\\_a-p\\_b$.\n$$\nv(\\breve p)=\\frac{4\\pi\\hbar}{\\breve p}\n\\int\\_0^\\infty \\sin\\left(\\frac{\\brev... |
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[Why does a ball rolling without slipping stop due to friction? [duplicate]](/questions/410708/why-does-a-ball-rolling-without-slipping-stop-due-to-friction)
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I have been reading about rolling motion and I seem to have... | [
"\nIf there were no drag or losses, then you're correct. The sphere would move forward and rotate indefinitely.\n\n\nBut assuming the surfaces are not completely smooth and there is air in the room, then there will be drag forces on the sphere. These forces slow down the sphere relative to the surface.\n\n\nOn a fr... |
Let's assume that a cylindrical magnet is clamped by an horizontal arm extending out of the wall. The top of the magnet is its north pole and the smooth face facing down is its south pole. If I bring another cylindrical magnet and position it perfectly in line below the fixed magnet, with its top being its north pole ... | [
"\nEarnshaw's theorem doesn't say that you can't have equilibrium; it says that you can't have *stable* equilibrium.\n\n\nThere's a point below the fixed magnet where the attraction it exerts on the \"floating\" magnet exactly cancels out the force of the floating magnet's weight. But if the floating magnet is pert... |
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"\nThe pressure from a lightening strike is not due to a lot of electrons hitting the target (some strikes are opposite polarity), but because of the explosive heating of the air in the discharge.\n\n\nOne way of estimating the pressure is the ideal gas law: $PV=nRT$. In lightening $T$ increases from ca 300 K to ab... |
I wanted to explain to a person knowing some very very basics of physics, why the force of attraction on two charges $Q\_1=3nC$ and $Q\_2=-1nC$ are the same. Of course my interlocutor thought that $3nC$ charges should experience larger attraction force.
Well, how can you explain that to somebody that didn't fully co... | [
"\nSimple, partial answer\n----------------------\n\n\nOne way to explain this is that there are two contributions to the force, that get multiplied together. A way to express this is:\n$$\nF = q E\n$$\nwhere $q$ is the charge that the force acts on, and $E$ is the (magnitude of the) electric field at the location ... |
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"\nHere are some typical one dimensional problems you might solve in quantum mechanics, and some ways they serve as toy models for more realistic problems. The one dimensional problems often display some interesting behavior. When more complex problems can be solved analytically, it is often by transforming them in... |
The Carter constant for the [Kerr Newman](https://en.wikipedia.org/wiki/File:Kerr-Newman-Orbit-1.gif#Equations) metric
$$ \rm C = p\_{\theta}^{2} + \cos^{2}\theta \ \Bigg[ a^2 \ (m^2 - E^2) + \left(\frac{L\_z}{\sin\theta} \right)^{2} \Bigg] $$
with (in $[+---]$ signature)
$${{\rm E = -p\_t}=g\_{\rm tt} \ {\rm \d... | [
"\n[Here](https://arxiv.org/pdf/0707.0409.pdf) is a paper that gives the Conformal Killing-Yano tensor for any member of the Plebanski–Demianski family of solutions. This is the most general family of type D vacuum solutions to the Einstein-Maxwell equation with cosmological constant, which includes the Kerr-Newman... |
so I recently came across the term 'virtual mass' and when I looked up more about it, it just gave me some stuff about fluid mechanics that I dont understand properly. My understanding of virtual mass is that when a body is pushed through a fluid (let's say water) it moves slower than usual and behaves like hoe a big ... | [
"\n*Virtual mass*, or *added mass*, is a concept of fluidodynamics related to the enhanced inertia acquired by a body in a fluid. A short description of the concept can be found on [this Wikipedia page](https://en.wikipedia.org/wiki/Added_mass).\n\n\nIt is an effect due to the coupling between a body in a fluid and... |
I hope that my question will be suitable for this forum: I would like to understand the difference between the so called consistent history approach to QM and several other interpretations. In [this](https://physics.stackexchange.com/questions/3862/is-the-consistent-histories-interpretation-of-qm-a-many-worlds-interpr... | [
"\nFrom a birds-eye view, all three of these are quite similar. (Consistent Histories = CH, Relational Quantum Mechanics = RQM, and QBism= QB.)\n\n\nWhen Rovelli [first published](https://link.springer.com/content/pdf/10.1007/BF02302261.pdf) his take on RQM (1996), he explicitly compared it to CH, and didn't see mu... |
It is given that $\frac{ds}{dt} = \frac{d\theta}{dt}$, i.e. the time derivative of s and $\theta$ are equal to each other.
Does it follow that for small values of $t$, $\Delta s ≈ \Delta \theta$? My thought process for this was that if I multiply $dt$ on both sides, I am left with just the value of $ds=d\theta$, whi... | [
"\nThe answer depends on a necessary clarification: does the equation\n\n\n$$\\frac{ds}{dt} = \\frac{d \\theta}{dt}$$\n\n\nhold for **all** $t$, or just for a **particular** value of $t = t\\_{0}$?\n\n\nIf the equations holds for **all** $t$ then the equation can be integrated and we will have\n\n\n$$ s(t) = \\thet... |
I was reading Fermi's 1932 paper "[Quantum Theory of Radiation](http://fafnir.phyast.pitt.edu/py3765/FermiQED.pdf)". I was able to understand the paper until this particular derivation (*which was excluded*).
>
> [](https://i.stack.imgur.com/b8TQ3... | [
"\nThis is likely using the fact that $[\\hat{H},\\vec{r}] = -i\\frac{\\hbar}{m}\\vec{p}$, which you can verify by direct computation. (Here, I am using $\\vec{r}$ for the position vector, replacing $X$ in the paper.) By replacing the momentum operator with the commutator, you can expand out the commutator and act ... |
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[Is mechanical energy conserved in all Inertial frames? (Newtonian Mechanics)](/questions/575865/is-mechanical-energy-conserved-in-all-inertial-frames-newtonian-mechanics)
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I am aware there are similar questions alread... | [
"\nIn classical mechanics, Galilean transformations (we'll assume a non-relativistic problem) relate the coordinates of events as measured in two different inertial reference frames that are related by a constant relative velocity $v$ along a straight line. The Galilean transformations for space and time coordinate... |
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"\nA propagator is the amplitude for a particle to go from $x\\_a$\nat time $t\\_a$ to $x\\_b$ at time $t\\_b$.\n\n\nLet $K(b,a)$ be the propagator\n$$\nK(b,a)=\\langle x\\_b|\\exp[-iH(t\\_b-t\\_a)/\\hbar]|x\\_a\\rangle\n$$\n\n\nwhere $H$ is the free particle Hamiltonian\n$$\nH=\\frac{\\hat p^2}{2m}\n$$\n\n\nBy the... |
In Griffith's EM, section 7.2.1 includes following pictures to talk about Faraday's law , where by Faraday's law I will be referring to its differential form rather than integral form.
[](https://i.stack.imgur.com/iWRE6.jpg)
In the images (b) and ... | [
"\nThe case a) is different: here EMF in the circuit is not due to induced electric field $\\mathbf E\\_i$ (which is negligible here), but due to motion of part of the circuit in external static magnetic field, thus it is better called *motional EMF*. The motional force per unit charge is $\\mathbf v\\times\\mathbf... |
This question is made up from 5 (including the main titular question) very closely related questions, so I didn't bother to ask them as different/followup questions one after another. On trying to answer the titular question on my own, I was recently led to think that scale transformations and addition by a total time... | [
"\nRather than answering the question point-by-point, I am going to cut to the essence.\n\n\nSuppose that we are given $n$ independent variables $x=(x^i)=(x^1,\\dots,x^n)$, $m$ \"dependent variables\" $y=(y^\\sigma)=(y^1,\\dots,y^m)$ and also their \"formal derivatives\" eg. $y^\\sigma\\_i$, $y^\\sigma\\_{i\\_1...i... |
In "conventional" quantum mechanics, in the presence of electromagnetic fields, we use minimal substitution in the Hamiltonian in the simplest case. I.e.
$$H=\frac{\vec{p}^2}{2m}\rightarrow \frac{(\vec{p}+e\vec{A}/c)^2}{2m}$$
What if one wants to consider more complicated gauge fields $$\vec{A}=\vec{A}^\alpha t\_\alph... | [
"\n\n> \n> But I don't know how the wavefunction would transform in QM when we introduce, say, an 𝑆𝑈(𝑁)gauge field. I guess maybe the question should have been \"how do quantum states transform in an 𝑆𝑈(𝑁)\n> gauge theory?\"\n> \n> \n> \n\n\nLook at your hamiltonian in electromagnetism,\n$$H=\\frac{\\vec{p}^2... |
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"\nIf you set $t=0$ in C-6, you get\n$$\n\\psi(\\vec{r}) = \\frac{1}{(2\\pi)^{3/2}}\\int d^3 k\\ g(\\vec{k}) e^{i\\vec{k}\\cdot\\vec{r}}\n$$\nThen it is clear that $g(\\vec{k})$ is the Fourier transform of $\\psi(\\vec{r})$, which is the \"initial state\" or if you prefer \"initial condition\" for the wave function... |
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