Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why ZrO2 reservoir is useful for reducing tungsten's work function in Schottky field-emitters? Schottky emitters (field-assisted thermionic emitters) use a tungsten filament for thermionic emission, as well as barrier lowering electric field to reduce the effective work function of the filament.
Commercial tips are mad... | Because zirconium oxides increase in electrical conductivity at higher temperatures, which essentially lowers the energy barrier for electrons to move around, lowering the energy required to get them to the tip. It also preferentially lowers the work function of the tungsten (100) surface which lowers the spread of the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/291808",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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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{... | To show that $\{I, \sigma_i\}$ is a base of the complex vector space of all $2 \times 2$ matrices, you need to prove two things:
*
*That $\{I, \sigma_i\}$ are linearly independent.
*That every complex $2 \times 2$ matrix can be written as a combination of $\{I, \sigma_i\}$.
To prove point 1, you need to show that... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292102",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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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... | acceleration cannot be infinite. Things need a force to be able to accelerate an object. So to infinitely accelerate and object it needs a infinite force. Also try wording question better.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292181",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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General method of deriving the mean field theory of a microscopic theory What's the most general way of obtaining the mean field theory of a microscopic Hamiltonian/action ? Is the Hubbard-Stratonovich transformation the only systematic method? If the answer is yes then what does necessitate our mean field parameter to... | Actually Wikipedia has an answer for your question,
https://en.wikipedia.org/wiki/Mean_field_theory
which will tell you how to bulid a mean field approximation self-consistently based on the Bogoliubov inequality.
If you want to know more details about the fundamental inequality,you can go through the book,Statistic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292303",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Why do some chemicals take electrons from other chemicals? How can some chemicals, if they have an equilimbrium of electrons, take away electrons from other chemicals?
One example I believe is placing a small amount of gallium on top some alluminum and watching the alluminum melt.
Why does the gallium, if it is at equ... | There is no electron exchange when you put gallium on top of aluminum. The known observed reaction is that aluminum diffuses into the gallium because it has a very high solubility there.
The tendency of an atom/molecule to take electrons away from others is related to the concept of electronegativity. See Electronegati... | {
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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}$$
But, is a pendulum in equilibrium? I mean, the veloc... | The equilibrium Goldstein is referring to is the equilibrium between the actual force $\vec F$ acting on the particle and the inertia force $-m\vec a$, i.e.,
$$\vec F-m\vec a=0.\tag 1$$
The idea, due to d'Alembert, is to extend the applicability of the virtual work principle from statics to dynamics and in some sense t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292466",
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"source": "stackexchange",
"question_score": "3",
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Does a trumpet operate using an open air column or a closed air column Just as the title states. I could not find a coherent answer online.
Many thanks in advance
| The trumpet is a closed air column according to this source:
Closed Air Column
A closed-end instrument is an instrument in which one of the ends of the metal tube containing the air column is covered. An example of an instrument which operates on the basis of closed-end air columns is the clarinet. Some instruments wh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292669",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Young's Double Slit Experiment-Problem Can it be proved that there would be no change in the "fringe width" when the main illuminated slit(s) is shifted to a position, which makes an angle of $\Theta$ with the original position of the source slit?
My try - I first found out the fringe width in a normal double slit wher... | The fringe pattern or spacings will not change. As long as D and d and the wavelength stay the same the position or angle of the light source will not matter. The only thing that may change is the location of the maximum bright spot on the detection screen but the pattern will remain the same. I cover this on page 5 an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292826",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | The uranium that was mined was heavily diluted with other elements, and goes through an extensive refining process to produce nuclear fuel. Nuclear waste has 90%-99% of the uranium concentration of the refined nuclear fuel. Thus, it is far more radioactive than the raw mined material and the mine itself is no longer a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/292958",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "150",
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What's the reference frame for displacement when calculating work? I know that one way to calculate work is force*(displacement in the direction of the force). But what reference frame does that displacement value come from? One where the object starts at rest?
Here's an example to clarify. Imagine two identical rocket... | As matter of fact, you may use any reference frame for calculating work in general. But if you want to go with the idea of displacement, you may use any inertial frame of reference.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/293128",
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"source": "stackexchange",
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Is frequency discrete? We know that E = hv
*
*E = photon energy
*h = Planck constant
*v = frequency
We also know that photon energy E can only come in discrete values (quanta).
Does the combination of these two assumptions then determine that frequency, v can only come in discrete values as well?
======
Note on ... | You say:
We also know that photon energy E can only come in discrete values (quanta).
but this is not true. It is generally true that the energy of a bound system takes discrete values, but the energy of a free system has a continuous range and can take any value. Since for such a system the energy is not discrete it... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/293237",
"timestamp": "2023-03-29T00:00:00",
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What's the equation for frustrated total internal reflection? Could someone provide an equation for calculating frustrated internal reflection? Like for a partially reflective laser mirror or a beam splitter. I believe that it depends on the refractive indexes of a first medium and a third medium if a second medium s... | Frustrated total reflection obviously means that the usual total reflection at a surface to a medium with lower refractive index $n$ becomes less than total because the thickness of the lower $n$ medium becomes comparable to the evanescent wave damping length penetrating the lower $n$ medium.
This can be calculated by ... | {
"language": "en",
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Gravitons unaffected by gravitational lensing? Photons have energy, and so they are affected by gravitational lensing. More generally, they feel the force of gravity.
Gravitons have energy too, but it seems preposterous to assume they will swerve due to other gravitational fields. This should violate the inverse-square... | Gravitons are definitely effected by gravitational fields (i.e. there is 'back-reaction'), this is part of why general relativity is so hard to solve in general situations (e.g. numerical solutions to the field equations).
In terms of the inverse square law:
First, and most importantly, the inverse square law comes fro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/293884",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Phonons and heat conduction What is the physical picture of heat conduction in a poor conductor? In particular, I'm curious about the role of phonons in conduction in poor conductors. I know that phonons (within the harmonic approximation) move without being scattered and would lead to infinite thermal conductivity. Th... | Ballistic propagation can be observed but that needs special conditions. Normally, transport is diffusive. At low temperatures, scattering is dominated by defects in the lattice. Even isotopes have an effect, diamond with a reduced content of $^{13}$C has higher thermal conductivity than diamond with the natural isotop... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/293995",
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"source": "stackexchange",
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Small nucleus emission from a larger nucleus Like alpha decay, is there the possibility of a small (n,z) nucleus coming out of a large (N,Z) nucleus? Why lithium and beryllium don't decay out of big nuclei as helium does ?
| Yes, this is possible. It is the case of $^{223}\textrm{Ra}$ for instance, which can decay through an $\alpha$ process with a lifetime of $\sim$ 11 days, but also through the emission of a $^{14}\textrm{C}$ nucleus. However, this decay mode is extremely disfavored (branching ratio $\sim 10^{-9}$).
There are two factors... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/294125",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Partition function for classical indistinguishable particles and Bose particles We have two particles that can be in either level $E_0 = 0$ or in level $E_1$.
If we treat them as Bose particles, then the partition function will be:
$$ Z = 1 + e^{-\beta E_1} + e^{-2\beta E_1}, $$
whereas if we treat them as classical in... | It comes from the first partition, your not considering all possible 2-states. Indeed, one possible state is both are in $0$, 2 other are one is in $0$ the other in $E_1$ and finally both in $E_1$. Because they are indistinguishable you must divide the whole thing by 2!.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why will we never run into a magnetic field that falls off as $\frac 1 {r^2}$? For example, Walter Lewin says in many lectures that we will never find a magnetic field $B\propto \frac 1 {r^2}$ - why is this?
I believe it must be related to $\nabla \times E= -\partial_t B$, but I don't see why this would make the previ... | A magnetic field of the form
$$ \boldsymbol{B} \propto \frac{\boldsymbol{\hat{r}}}{r^2} $$
is impossible because
$$ \nabla \cdot \left( \frac{\boldsymbol{\hat{r}}}{r^2} \right) = 4 \pi \delta(\boldsymbol{r}), $$
so a magnetic field of this form would violate Maxwell's equations, one of which is
$$ \nabla \cdot \boldsym... | {
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How does the de Broglie-Bohm interpretation explain quantum uncertainty? I have heard recently that the de Broglie-Bohm theory, or pilot wave theory, is an acceptable alternative to the Copenhagen interpretation. But how does it explain Heisenberg's uncertainty principle? Doesn't uncertainty depend on the Copenhagen in... | It's exactly the same in Bohmian mechanics, only the reasoning is different.
From Dürr et al. (1992) - DOI: 10.1007/BF01049004:
From a general perspective, perhaps the most noteworthy consequence
of our analysis concerns absolute uncertainty (Section 11). In a universe governed by Bohmian mechanics there are sharp, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/295156",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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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... | Work is done by something, on something.
If you put the weight inside a box (so you can't see it), with the rope sticking out of the top, and you pull on the rope, you can say "I am doing work on something in the box". You don't know what the something is - gravity, a gang of minions, a very long spring, a paddle wheel... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/295245",
"timestamp": "2023-03-29T00:00:00",
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Why do excited states decay if they are eigenstates of Hamiltonian and should not change in time? Quantum mechanics says that if a system is in an eigenstate of the Hamiltonian, then the state ket representing the system will not evolve with time. So if the electron is in, say, the first excited state then why does it ... | The atomic orbitals are eigenstates of the Hamiltonian
$$
H_0(\boldsymbol P,\boldsymbol R)=\frac{\boldsymbol P^2}{2m}+\frac{e}{R}
$$
On the other hand, the Hamiltonian of Nature is not $H_0$: there is a contribution from the electromagnetic field as well
$$
H(\boldsymbol P,\boldsymbol R,\boldsymbol A)=H_0(\boldsymbol P... | {
"language": "en",
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Question on the Proof of Hohenberg -Kohn Theorem Between Equation (5) and Equation (6) of the the original paper titled as "Inhomogeneous Electron Gas" by P. Hohenberg and W. Kohn, there is a sentence stating that: "
Now clearly (unless $v'(\mathbf{r}) - v(\mathbf{r})=\text{constant}$) $\Psi'$
cannot be equal to $\... | (The notations follow the original paper by Kohn and Hohenberg.)
Suppose there are two Hamiltonian $H_1 = T+U+V_1$ and $H_2=T+U+V_2$,
where
$T = \frac{1}{2}\int\nabla \psi^\dagger\nabla \psi d^3 r $
$ U = \frac{1}{2}\int\frac{1}{|\mathbf{r}-\mathbf{r}'|}\psi^\dagger(\mathbf{r})\psi^\dagger(\mathbf{r}')\psi(\mathbf{r}'... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/295590",
"timestamp": "2023-03-29T00:00:00",
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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... | By a five-dimensional extension of general relativity that unifies it with electromagnetism, you presumably mean Kaluza-Klein theory or something very similar. As explained here, K-K is indeed background-dependent; as with string theory decades later, this is considered a problem.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Several strange phenomenon when magnetron interacts with light bulbs Is this video real or is it a hoax? What physics is going on here?
https://youtu.be/POGSEG20hkg
In the video, there appears to be a magnetron set up, and someone is using fluorescent light bulbs and potatoes to play with it.
00:18 - Eighteen seconds i... | not sure what the gas is but its same as your local neon signs there is nothing special about what he is up to this is just exciting argon rayon neon gasses and the like with a high frequency electromagnetic field. could be low frequency not my area of knowledge as to the wavelength but the basic principles are not to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296287",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Maxwell equations from Euler-Lagrange equation: I keep obtaining the wrong equation I'm deriving the Maxwell equations from this Lagrangian:
$$ \mathscr{L} \, = \, -\frac{1}{4} F^{\mu \nu}F_{\mu \nu} + J^\mu A_\nu
\tag{1}$$
My signature is $$(+ - - -)\tag{2}$$ and
$$
F^{\mu \nu} \, = \,\left(\begin{matrix}0 & -E_x & -E... | I suspect the error is in your source term: with reference to Jackson's "Classical electrodynamics", the correct Lagrangian density is
$$
{\cal L}=-\frac{1}{16\pi} F_{\alpha\beta}F^{\alpha\beta}-\frac{1}{c}J_\alpha A^\alpha\, ,
$$
which differ from yours by a sign in the source term. (The other factors $1/16\pi$ and $... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296552",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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 pushups, you're not lifting all of your body weight the full distance. Your heels don't move any appreciable amount and a point halfway between shoulders and toes only moves about half the height.
Consider an iron bar, 1m in length. Lifting the whole thing 1m requires twice as much energy as lifting it half ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296650",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "49",
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Electric field associated with moving charge I have recently started to learn about the electric field generated by a moving charge. I know that the electric field has two components; a velocity term and an acceeleration term. The following image is of the electric field generated by a charge that was moving at a cons... | According to Special Relativity, information travels at the speed of light and this case is no different. The information here refers to the position of the particle at a certain time.
Let me explain. When the charge was at x=1, its field lines were radially outward. When the charge reaches x=0, the information that t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/296904",
"timestamp": "2023-03-29T00:00:00",
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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?
| This question was just bumped to the homepage, so let me try to give a physical answer to explain why modular invariance is particular to two dimensions. The Cardy formula tells you something about the density of states of a CFT. In order to count the states of a CFT in $d$ dimensions, you naturally consider the therma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/297038",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Lorentz transformation, problem with derivation I have a question about the Lorentz transformation:
In the derivation it's said that two systems S and S' should at $t=0$ and $x=0$, overlap. We get the following transformation rules:
$t'=\gamma_0(t-v_0x/c^2)$
$x'=\gamma_0(x-v_0t)$
$y'=y$
$z'=z$
My question is: What ha... | To give a less "groupy" answer: always think first about the 3D-analogue to what you're doing in 4D. So in 3D we have these translations and rotations which are linear transforms preserving $x^2 + y^2 + z^2;$ in 4D we in addition have these "boosts" and all three are linear transforms preserving $w^2 - x^2 - y^2 - z^2$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/297123",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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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 ... | It depends on what you mean by a constant force.
If this means that the accelerating observer feels a constant force, i.e. a constant acceleration $a=F/m$, then this is the relativistic rocket problem. As discussed in this question the velocity measured by a non-accelerating observer is given by:
$$ v = \frac{at}{\sqrt... | {
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How to distinguish "system" and "environment" in quantum decoherence Quantum decoherence distinguishes the whole big system into "system" and environment, and shows how system, when density matrix is traced over environment, comes to be decoupled from environment.
But this requires distinguishing environment from syste... |
Quantum decoherence distinguishes the whole big system into "system" and environment, and shows how system, when density matrix is traced over environment, comes to be decoupled from environment.
This summary is wrong. The system is coupled to the environment. As a result of that coupling interference is suppressed a... | {
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Quasistatic and Reversible processes I'm having trouble understanding the quasistatic process concept. I understand that for any process we have well defined initial and final states and the problem is in specifying the path, and the path is important as we need to know it in order to calculate work or heat because the... | The quasistatic hypothesis is what make you use the equations, such as Gas Laws, in every point of your transition (in every point in space and in every moment in time), because you know that in every point that gas is in equilibrium. This is necessary especially when you have to integrate them and therefore you need t... | {
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"url": "https://physics.stackexchange.com/questions/297411",
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Could Dark Matter be used as reaction mass for a propulsion device? Assuming a best case scenario, where humans are able to discover a way to interact with Dark Matter, could we use dark matter like a row boat uses the water?
Assuming Dark Matter is made of WIMPs, they are going to be moving with respect to a propulsio... | Assuming there's a way to put a force on dark matter particles, then it's just an application of Newton's third law. Airplanes push air backwards to move forward an down to move up.
The problem I see is that any vehicle that interacts with dark matter to a significant degree will experience a drag force from the dark m... | {
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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. ... | Clearing (large) debris objects with current sats would take a large amount of fuel. Enough that doing more than one or two is unlikely to be possible. If you carried more fuel, doing the first one is more expensive (in fuel terms).
Electrodynamic tethers allow you to take power and electrons and use that to "push" a... | {
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Why should the perturbation be small and in what sense? In time-independent perturbation theory, one writes $$\hat{H}=\hat{H}_0+\lambda \hat{H}^\prime$$ where $\lambda H^\prime$ is a "small" perturbation.
*
*Why should the perturbation be small for perturbation theory to work?
*Both $\hat{H}_0$ and $\hat{H}^\prime... | Actually, perturbation theory can work very well even if lambda is not small. For example, the harmonic oscillator with linear potential term added yield exact results to first order in perturbation theory.
The proper way to look at it is that you assume the hamiltonian, the eigenfunctions and the energies are analytic... | {
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Sound waves: frequency, speed, and wavelength I need to understand the relationship between the three. When does the wavelength stay the same as there is a change in one of the other two variables? When does it change as there is a change in one of the other variables?
My understanding is this: If the speed changes du... | The frequency of a sound wave will stay the same when sound passes from one medium to another because each compression or rarefaction in the first medium will produced exactly one compression or rarefaction in the second medium. Typically the speed of a wave depends mainly on the properties of the medium so in this ca... | {
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An accelerating charge emits EM waves, but how can this be explained in terms of photons? I was reading this response to a question involving EM radiation due to an accelerating charge. A charge's oscillations disturb its electric field, and this effect propogates at the speed of light. If a charge is oscillating back ... | If you wiggle a charge around you has done a energy transfer to this charge. At the end, if you follow to the basics, this transfer happens by the transfer of photons (see the discussions in PSE about the touch of the hand to something). So it should not be wrong to say that the transfered photons somehow are sitting o... | {
"language": "en",
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If time dilation can slow time down, is there away to speed time up? Okay, I know the title is really confusing but I couldn't find words to explain it sorry. Pretty much what I mean is, if I can get in a lightspeed spaceship moving away from earth, time slows down for me. So one year for me will be 20 earth years or w... | No, there is not way to have the reverse effect in special relativity. This is because an object being at rest maximizes the time that elapses for it in relativity (a consequence of the lagrangian formulation of special relativity). So if your question is you have your friend sit on earth for a few (say three) months, ... | {
"language": "en",
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Is the topological index of a self-adjoint operator always zero? By the Atiyah-Singer index theorem, the index of a self-adjoint opeartor D (e.g., Hamiltonian) is given by
Index(D) = dim Ker(D) − dim Ker(D*),
where D* is the adjoint operator of D. Since D is self-adjoint, D=D*, we conclude that Index(D)=0. Is this conc... | Your conclusion is right. The index defined in the way you did, of course, can not be non-zero for self-adjoint operator. One can try to define some other index, if one wants, but I am afraid that it would have nothing to do with the Atiyah-Singer theorem.
| {
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High(very high) frequency sound waves = heat? I had this question in mind and did not quite found the answer on google. If heat is a vibration of particles in matter, and sound is pressure wave moving using particles (causing them to fluctuate), could a very high frequency sound wave raise the temperature of matter whi... | Technically speaking there is a difference between high frequency sound waves and heat, though they can have similarities. Heat is typically stochastic vibrations -- random vibrations that nobody can predict. Sound waves are typically well ordered vibrations, which still have some structure to them. Accordingly ther... | {
"language": "en",
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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... | A fermion is a state $|\vec p,\sigma\rangle$ with half-integer spin, i.e., such that
$$
J|\vec p,\sigma\rangle=\sigma|\vec p,\sigma\rangle\qquad\text{with}\qquad \sigma\in\mathbb N+\frac12
$$
where $J$ is the angular momentum operator (generator of rotations).
Therefore, upon a rotation by an angle $2\pi$ around an arb... | {
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Can a rocket with no forces acting upon it except a single push force with constant acceleration keep accelerating forever? I was wondering why a rocket with no opposing forces acting upon it couldn't keep accelerating given that it has the potential to release enough energy to maintain its acceleration at all costs. I... | "Why?"
This is the question physics can't answer. Physics describes the universe, it does not explain it. Given some postulates that you are willing to accept as true without proof or explanation, one can draw logical conclusions, but they all trace back to the unexplained postulates.
From an observer in an inertial ... | {
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Why can a red laser beam reflect in a blue surface? I've been taught that a blue object only reflects the blue fraction of light, and all the other colors are absorbed. So what happens with a red laser?
| Your teacher was oversimplifying.
A surface looks blue because it reflects more light in the blue portions of the spectrum than in other portions.
But less is not none. It's very rare for a surface to be completely non-reflective.
Your laser pointer is much brighter than the ambient light. So even if most of the light... | {
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What make an egg explode in the microwave I think it's related to the air pouch in the egg, but I'd like to have a full physics explanation. What are the forces in presence?
What are the tricks to prevent the explosion?
| Here is a layman site about explosions in microwaves
Explosion happens when
when water in the food is heated rapidly, producing steam.
When there’s no way for the steam to escape, an explosion takes place.
Anyy food that has a skin or membrane can explode in the microwave, according to Snider, a professor at the Univ... | {
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How is the frequency of a photon related to the gravitational force it exerts? I know that even though a photon has no mass it still has energy. From what i understand the mass and velocity of a photon have no bearing on the amount of energy it emits, rather its energy is dependent solely on the frequency that the part... | Yes, a photon's energy $E = \hbar \omega$ and momentum $p = (\hbar/c) \omega$ contributions to the stress-energy tensor of general relativity are both directly proportional to its frequency $\omega$.
| {
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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... | I'm not exactly sure what you're looking for, but here's how I think about this at a discrete level (this follows the Wikipedia article on the wave equation).
Consider a line of springs each of mass $m$ and length $h$, with spring constant $k$. The distance a spring, located at $x$, is displaced from equilibrium is de... | {
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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?
| The other answers already pointed out very important properties, but there is a further aspect related to black hole physics. Namely, $AdS_2/CFT_1$ is the relevant holographic description of four dimensional extremal black holes, for instance the near horizon limit of an extremal Reissner–Nordström is $AdS_2 \times S^2... | {
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Why is the natural singularity $r=0$ in Schwarzschild geometry a spacelike one? Why is the natural singularity $r=0$ in Schwarzschild geometry a spacelike one?
| Nice question. Topologically, a singularity isn't a point or set of points. It's treated as a hole in the manifold. Therefore it doesn't have its own topology or geometry. We can't even say what its dimensionality is. So if we want to define what is a spacelike or timelike singularity, we need to define it in terms of ... | {
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Diatomic molecule in an electric arc
Molecular nitrogen is heated in an electric arc, and it is found spectroscopically that the relative populations of excited vibrational levels is
$f_0/f_0=1.0; f_1/f_0=0.2; f_2/f_0=0.04; f_3/f_0=0.008; f_4/f_0=0.002$.
Is the nitrogen in thermodynamic equilibrium with respect to vi... | One can see by inspection that the vibrational occupancy numbers are an arithmetic series. A harmonic oscillator has evenly spaced energy levels, so one can conclude that the occupancy probability is given by the Boltzmann factor for some vibrational temperature. To calculate that temperature, one would need to know th... | {
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Nature of metallic bonding in solid state What is the reason behind attraction of metal kernels & free electrons in electron sea model?
| In metallic solids, the constituent particles are orderly arranged positively charged metal ions (called kernels) surrounded by a sea of free electrons. These electrons are mobile and are evenly spread throughout the crystal and flow throughout the crystal like water in sea.
These are produced from those metal atoms th... | {
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What is really instantaneous? How can a body travel at an instant and what does instantaneous speed tells us?
What really is meant by speed of an object at an instant if an object does not travel at an instant? I would like a mathematical explanation.
| Instantaneous speed (and indeed many other instantaneous concepts) is a bit of a formalism, but in layman's terms, the instantaneous speed is the ratio of distance covered to time, taken over a very small time interval. Formally, we say that the time over which the distance is measured is actually infinitesimally small... | {
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Thermodynamics Question: Does measuring the temperature of an object change its temperature? Suppose that I want to measure the temperature of an object, such as a pot of hot water. When I stick the thermometer into the pot, I know that the temperature measured by the thermometer is its own temperature when it reaches ... | Short answer is "yes" but in general is insignificant.
| {
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Algebra behind the wave function properties In lecture, for the tunnelling wave function
$$ \psi(x) = C_1\cosh(x/l)+C_2\sinh(x/l)$$
the current density is
$$ J = h/(2mi) [ \psi^*(\Delta\psi) - (\Delta\psi)^*\psi] $$
Here is my problem, lecture says that $J$ is equivalent to:
$$J=(h/m)Im[\psi^*(\Delta\psi)] \tag{1} ... | First, your expression for the current is incorrect. It should be $\nabla$ everywhere, not $\Delta$ (first derivative, not second).
To derive (1), you just use the formula $Im(z)=\frac{z-z^*}{2 i}$ for a complex $z$.
As for (2), you just substitute the expression for the wave function into (1) and evaluate for $x=0$.
I... | {
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Why do we assume weight acts through the center of mass? The weight of a body acts through the center of mass of the body. If every particle of the body is attracted by earth, then why do we assume that the weight acts through the center of mass? I know that this is true but I can't understand it. Does it mean that the... | The other answers here, which show that gravity does not exert a torque on an object, are correct. However, they rely on the following implicit step of logic to get to the answer the OP wants:
An object that has a force acting on it, but no torque acting on it appears as if it is being pulled from its center of mass.
T... | {
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How does a small object move with constant velocity when drag force is equal to its weight? When drag force ($bV$) equals to object's weight (mg) then upward and downward force becomes equal. As a result the object comes to rest. If this is true, how is a body moving with constant velocity?
| Isaac Newton:
"An object at rest will remain at rest unless acted on by an unbalanced force. An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force."
This law is often called
"the law of inertia".
| {
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How matter waves travel faster than light? I read this in my physics textbook. It says that matter waves travel faster than light. Why is it so?
Also are matter waves G-Waves?
|
I read this thing in my physics textbook.They said matter waves travel faster than light, why is it so?
Matter waves is a confusing terminology coming from the de Broglie quantum mechanical description of particles, which is what matter is at the quantum mechanical level.
Here lamda is the wavelength of the probabi... | {
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Is current density (J) in Ampere's law derivable? In Ampere's law:
$$
\nabla\times\mathbf{B}=\mu_0\mathbf{J}
+\mu_0\epsilon_0\frac{\partial\mathbf{E}}{\partial t}
$$
the current density is listed explicitly as a separate term from the change in electric field. My understanding of the history (perhaps completely wrong)... | Just by looking at the two equation that you wrote down, you get immediately that for them to be consistent you need to have $\mathbf{J}=0$. In other words the two systems of equation are not equivalent (unless you are in the trivial case $\mathbf{J}=0$).
Looking at the whole structure of Maxwell's equation + Lorentz f... | {
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Confusion with partial derivatives as basis vectors So I have seen that the directional derivative can be written as
$$ \frac{df}{d\lambda} = \frac{dx^i}{d\lambda}\frac{df}{dx^i} $$
And we can identify $ \frac{d}{dx^i} $ as basis vectors and $ \frac{dx^i}{d\lambda} $ as components. What I don't understand is why is $... | The directional derivative $\frac{df}{d\lambda}$ is not actually a vector in the space spanned by the $x^i$. What the source was trying to say was that in the abstract vector space spanned by the partial derivative operators, $\frac{d}{d\lambda}$ can be thought of as a vector.
*http://www.physicspages.com/2013/02/10/ta... | {
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How does a Galilean telescope form an enlarged image even though it has a diverging lens? I have been reading about Galilean telescope and the picture in the book is something like this:
After rays pass through the converging lens, there is a real image formed which is intercepted by the diverging lens but as I learn... | The angular magnification of a telescope $M$ is defined as the ratio of the angle subtended by the image of the object when looking through the telescope $b$ to the angle subtended by the object when looked at with the unaided eye $a$.
$$M=\dfrac ba$$
Those angles are often called visual angles and they detained the ... | {
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Why does stacking polarizers of the same angle still block more and more light? I have some sheets of polarization film. They came in a big box, all stacked at the same angle. I noticed that the entire stack of them lets almost no light through, even though they're all at the same angle.
I pulled out two, and those two... | In addition to the other answers:
Even if you had extremely clear glass (like for optical fibers), stacking them would cause them to get more quickly opaque than what would be
expected by their transmission coefficient. This is only for completeness because the effect on real polarized filters is dominated by their tra... | {
"language": "en",
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Can you touch something which is massless?
Can one touch massless things? If not then why the light get scattered by the tiny particles present in air? If light is massless how can it hit particles or dust to get scattered?
$$**OR**$$
The light do not need any medium to travel then why it changes its path by changin... | The underlying level of nature is quantum mechanical, and the theory that describes the behavior of matter is the standard model of particle physics. All classical behaviors emerge from this underlying quantum mechanical level.
The photon is a massless particle and classical electromagnetic waves , for example light, ... | {
"language": "en",
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How does the sun really produce light in terms of waves? Electromagnetic waves are caused by changing electric and magnetic fields, and these are caused by a charge possible oscillating like an antenna or a varying current etc.
My question is, with the sun, where is this source that causes the electric and magnetic fi... | This is not technically very exact since the reasoning is classical but that energy you're talking about mostly turns into heat and when something is hot it's constituents; ionic cores and electrons, move around, collide, and oscillate violently and since these constituents are charged you essentially have a bunch of o... | {
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Max damage to target by projectile
The image above is that of a past exam question.
Unfortunately I am having trouble deriving a solution, my method is as follows:
It is clear that the launch velocity for max range ($\theta = 45˚$) is:
$$
V_{max} = {(30g)}^{1/2}
$$
I assumed the landing velocity symmetric to the lau... | Your 1st equation (just before your EDIT) is correct, it must be your arithmetic which is going wrong. There is a solution for 1 bounce.
The formula for range can be written in terms of the horizontal and vertical components of velocity $v_x, x_y$ as
$R=\frac{2v_x v_y}{g}$.
After each bounce $v_y$ is reduced to $ev_y$... | {
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The position of an element on a periodic sound wave So I am looking at the equation used to locate of a small element relative to its equilibrium position on a periodic sound wave. The equation is defined as below:
$s(x, t) = A\cos(kx - wt)$
Now I understand why the use of a sinusoidal function, but the equation is exp... | It is a convention with some "method to its madness".
We often use complex notation for waves:
$$y = A e^{i(kx - \omega t)}\tag1$$
Now we know that
$$e^{i\theta} = \cos\theta + i\sin\theta$$
So it follows that the real part of (1) is a cosine function...
| {
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"source": "stackexchange",
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Example of compact operators in quantum mechanics Can anyone give an non-trivial example of compact operators in quantum mechanics? Of course, any operator on a finite-dimensional Hilbert space is compact.
| Compact operators often appear in integral equations and can be viewed as continuous generalizations of matrices, where the corresponding integral kernel must not be to singular and must decay fast enough at infinity.
An example is the Lippmann–Schwinger equation in quantum scattering theory, see https://en.wikipedia.o... | {
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Grashof number as a ratio of buoyant and viscous forces The Grashof number is supposed to be a ratio of buoyant forces to viscous forces.
I find this hard to believe, since if
$$F_b=\beta g \rho \Delta T$$
is the buoyancy force, the definition of the Grashof number,
$$\text{Gr}=\frac{\beta g\Delta T L^3}{\nu^2},$$
imp... | Don't take those intuitive notions of dimensionless numbers as ratios of forces too seriously. Those kinds of statements are to be understood as vague metaphors more than anything else.
But, clearly the expression $\frac{\rho}{L^3}\nu^2$ has the dimension of a force, and clearly this force depends on viscosity. That's... | {
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Phase Transitions and Bubble Nucleation The potential for a first order phase transition is shown below
The phase transition occurs from the spontaneous formation of bubbles. Inside the bubbles the field value is at the "true vacuum" and outside the bubble the field value is at the "false vacuum". In many texts, a se... | I will just address the question from mean-field theory with weak fluctuations, which is I think the only regime where the bubble-nucleation picture makes sense.
Below you see a picture of a Landau-Ginzburg potential (taken from Cardy's book "Scaling and Renormalization in Statistical Physics", which I highly recommend... | {
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Why does torque produce a force on the axis of rotation? If a door is rotated about its fixed axis in (outer) space, a force parallel to the door on the hinges will arise due to centripetal force on the centre of mass and conservation of momentum (Newton's third law).
But any torque on the door will create a force on ... | Pure torque does not produce any forces. So it is not true that "any torque on the door will create a force on the hinges".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/303997",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Can a ship float in a (big) bathtub? I am confused.
Some sources say it is possible at least theoretically ( http://www.wiskit.com/marilyn/battleship.jpeg ) and some say it is not true ( http://blog.knowinghumans.net/2012/09/a-battleship-would-not-float-in-bathtub.html )
Is it necessary or not that there exists an amou... | Sammy Gerbil and Pirx have already answered the question correctly. I will only include a minor statement here, since the whole confusion seems to revolve around the concept of "weight of displaced water". "Weight of displaced water" is the weight of water that would have to occupy the submerged volume of the body, if ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/304245",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Are the diffusion terms conservative? Generally the diffusion terms are of the form $$D = \dfrac{\partial}{\partial x} \left(\mu \dfrac{\partial u}{\partial x} \right) .$$
Is this this term conservative or nonconservative?
| This form is conservative in the sense that, if you approximate the right hand side with a central finite difference approximation (using $\mu$ at the boundary of each grid cell and u at the center of each cell), the finite difference approximation will automatically conserve mass.
For those of us who solve diffusive p... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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4-Vector Potential Notation How am I supposed to interpret this notation:
$$F^{uv} = \partial^uA^v-\partial^vA^u$$
I know that $\partial^u = (\frac{1}{c}\frac{\partial}{\partial t},-
\vec\nabla)$
So for example for the potential $$A=\left(\begin{matrix}
0 & 0 & 0& E_z\\ 0 & 0 & B_y & 0\\ 0 & -B_x & 0 & 0\\ E_z & 0&0&0\... | The 4-potential $A_\mu$ is a four-vector, not a matrix. Set the speed of light $c=1$ and it is defined as
$$
A^\mu = (\phi,\vec{A})\,,
$$
in which $\phi$ is the electric potential and $\vec{A}$ vector potential. The magnetic field is given by
$$
\vec{B} = \nabla \times \vec{A}\,,
$$
and the electric field is given by
... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What did the big bang "look like"? I've been reading here for a while now and something I always see is people saying "the big bang happened everywhere" or "the center of the universe is where you are", explaning that the big bang didn't happen from a single point, but everywhere at once.
The problem is that I am unabl... | The argument that there is no center of the universe is only logically valid if the universe is actually infinite in size and mass or the universe is torus(aka it loops back onto itself(you would go back to your starting point if you traveled in one direction for long enough)). If the universe has finite mass and isn't... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Momentum of an electron acting as a wave Was working on a problem with electrons acting as waves in diffraction. Part of the question asked me to calculate the momentum of the electron. Since I was dealing with waves I used the following equation:
$h=pλ \implies p = h/λ$
Since $λ = v/f$ we can substitute that in, resul... | From Einstein's famous equation we have,
$E=mc^2$
From classical mechanics we have,
$E = \frac{mv^2}{2}$
Equate both of them (both are E, right?) and you'll get
$mc^2 = \frac{mv^2}{2}$
$c^2 = \frac{v^2}{2}$
All objects in the universe are moving at $c\sqrt{2}$
Yes, they are moving FASTER than light. Oh dear! Physics do... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Why don't humans burn up while parachuting, whereas rockets do on reentry? I guess it has something to do with their being both a high horizontal and a vertical velocity components during re-entry. But again, wouldn that mean there is a better reentry maneuver that the one in use?
| The distances and speeds involved are materially different. On the scale of a parachute dive, the atmospheric density doesn't change much (and is relatively high). A parachutist quickly reaches a terminal velocity where the drag from the air matches the pull of gravity.
In a re-entry, you're approaching in a much les... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/304992",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Where does all the heat go during winter? I do not understand where actually the heat in our surroundings go during the winter season. Is it radiated out into space? I know it cannot coz global warming would not be a issue then. It might get absorbed but where? I tried figuring it myself but couldn't please help.
| Just imagine heat escaping out of Earth in all directions at the same rate. But due to the tilt of the Earth, the sun's rays hit a larger surface area of the Earth for one hemisphere and less at the other. As a result, one side would experience more heat from the sun while the experience less.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How force exerted by spring is always opposite to the direction of displacement in Hooke's law Suppose a spring lying on a horizontal table, displaced from its equilibrium length by an external agent. The external agent is removed, the spring will head back to its equilibrium length. Here, the direction of spring force... |
The external agent is removed, the spring will head back to its equilibrium length. Here, the direction of spring force and displacement will be same.
No!
$x$ is not direction of change. It is just direction.
*
*If the spring is stretched to the left, then $x$ points leftwards.
*Force points rightwards, becaus... | {
"language": "en",
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Can a (micro) black hole be used to make a microscope? We have seen that black-holes can be used as a telescope. Is there a chance that light bending from a micro black-hole can be used to create a microscope?
| Gravitational lenses would be a very poor choice for use in an optical instrument. For optical instruments we require that the lenses focus parallel rays of light to a point - the focal point:
This happens because the farther a light ray is from the optical axis the more strongly it is bent. However for a gravitationa... | {
"language": "en",
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Confusing working of lens Why do lens don't splits light into its seven constituent colors, like Prism?
*
*Why is lens left is correct, not right one?
*How does lens came to know that rays are coming from infinity or are at Focus and converge/diverge them at different point accordingly?
| All the other answers that lenses do show chromatic aberration are perfectly true, but usually they do not show it to anything like the same degree as a prism. This it's because prisms are typically operated with light at much higher incidence angles to their interfaces than for lenses. For an incidence angle of $\thet... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/305508",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Guided waves equations In Griffiths's Introduction to Electrodynamics, monochromatic guided waves are proposed to have the form
$$\mathbf{\tilde{E}}(x,y,z,t)=\mathbf{\tilde{E}}_0(x,y)e^{i(kz-\omega t)}$$
$$\mathbf{\tilde{B}}(x,y,z,t)=\mathbf{\tilde{B}}_0(x,y)e^{i(kz-\omega t)}$$
where
$$\mathbf{\tilde{E}}_0=E_x\mathbf{... | Usually, people don't use the symbol $k$ in this context so as to avoid exactly the kind of confusion you are having.
In this context, the symbol written as $k$ in Griffiths's equations is often written $\beta$ or $k_z$; it is then called the propagation constant and it depends on the geometry of the wave in the waveg... | {
"language": "en",
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How molecules radiate heat as electromagnetic wave? an object of higher temperature radiate infrared rays as a way to decrease the temperature. how a molecule produce a electromagnetic wave? in atoms electromagnetic radiation is caused by electrons. what is responsible in molecules?
| As it was correctly noted by others, molecules consist of atoms, and the radiation can be emitted as transitions between the atomic orbitals. Molecules also have other degrees of freedom, related to the rotational and vibrational motion of atoms within a molecule, their frequency being usually in infrared or even radio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/305696",
"timestamp": "2023-03-29T00:00:00",
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Does the equipartition theorem for a diatomic gas apply to the three rotations if the temperature is high enough? In a diatomic gas, there are three degrees of freedom of rotation, of which the frozen mode (the rotation around the bond axis) is ruled out because the energy spacing of frozen rotational energies is about... | Let us consider, e.g., a hydrogen molecule. The bond dissociation energy is about 5 eV (https://en.wikipedia.org/wiki/Bond-dissociation_energy). On the other hand, to initiate rotation of the diatomic hydrogen molecule around its axis you need to drive the electrons in hydrogen atoms from the ground state to higher lev... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/305809",
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"source": "stackexchange",
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Why are light rays able to cross each other? See the image first:
Why are light rays able to cross each other? Air isn't able to.
|
Why are the light rays able to cross each other
The underlying level of nature is quantum mechanical. Light is an emergent phenomenon from the quantum mechanical level of photons, where an enormous number of photons of energy $h\nu$ build up the classical electromagnetic wave which is light.
Photon–photon interaction... | {
"language": "en",
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Is there any advantage in stacking multiple images vs a single long exposure? Suppose I have a source object that is not time varying, to be concrete let's say it's a galaxy. Is there anything additional that can be learned or done with multiple short exposure images of exactly the same field as compared to a single lo... | If your exposures are short enough (a fraction of a second), you can even combat turbulence in the atmosphere. The trick is to do very many short images then pick the ones where a (bright) point source is sharpest and only stack those.
The technique is called Lucky Imaging and can deliver images as sharp as the Hubble ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/306036",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can an accelerating frame of reference be inertial? In physics problems, the earth is usually considered to be an inertial frame. The earth has a gravitational field and the second postulate of the general theory of relativity says:
In the vicinity of any point, a gravitational field is equivalent to
an accelerated ... | No. By definition an accelerating frame of reference cannot be an inertial frame of reference.
The Earth is only approximately an inertial frame of reference over sufficiently small distances and times.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/306303",
"timestamp": "2023-03-29T00:00:00",
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Is the magnetic field of a moving electron caused by length contraction in the direction of motion? Consider an electron moving relative to us. Because the space in the electron's rest frame is contracted relative to us in the direction of the electron's velocity, the electric field lines are squeezed in the same direc... | The idea is good but it is a little more complicated.
You have to work with the tensor form of the electromagnetic field $ F^{\mu \nu}$and the 4 dimensions of space-time.
The Lorentz transformation that takes an electron from rest to an electron with a constant velocity can be seen as a rotation in the 4 dimensions ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How are club-style weapons effective? The First Law of Thermodynamics states that I can't swing an object held in one hand with more energy than I can swing my arm, and the Second Law says that the total energy would probably even end up being somewhat less. And yet, a person who might not be afraid of getting punched... | There are several reasons:
*
*It is hard. That's why even wearing a knuckle duster will increase the damage you do greatly. And wearing boxing gloves decrease the damage you do.
*Humans are more strong than they are fast. I'm a bit oversimplifying, but the limiting factor in giving a strong blow is not the energy o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/306446",
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How do scientists know Iron-60 is created during supernovae? I know that the meteoroids contain Ni-60, which is formed after decaying Fe-60, and as per my study, I got to know that Fe-60 is formed during the time of a supernova. But I wonder how scientists know/find that these elements were created during that event?
| Don Clayton investigated the production of Fe-60 in his 1971 Nature paper New Prospect for Gamma-Ray-Line Astronomy (paywalled, but the abstract also hints to Arnett & Clayton 1970, also paywalled, but that abstract is unclear as to the contents being about Fe-60). This likely would have used supernova nucleosynthesi... | {
"language": "en",
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Does length of a hosepipe affect pressure/flow I have connected a hosepipe to my shower drainage plumbing (1st floor), which I am running into the garden (ground floor) as a kind of grey-water system. However, the water drains out the shower terribly slowly.
The hosepipe is 50 meters long. I'm wondering whether the le... | Yes, you are correct that the length is the problem. As a matter of fact, in an application like yours the flow rate is pretty much inversely proportional to the length of the pipe: If you cut the pipe length in half, the flow rate will roughly double. The flow rate $Q$ in $\mbox{m}^3/\mbox{s}$ is given by
$$Q=\frac{\D... | {
"language": "en",
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Relation between perturbation theory and Taylor expansion in QM So I am looking at non-degenerate perturbation theory. The idea is that the perturbing term in the Hamiltonian is small so you somehow expand the energies and wave functions in this small term and collect orders.
Now I did an exercise in which you apply pe... | I was thinking, if we write the matrix m=2 by 2 matrix. Then the $\lambda H'$ (which was treated as unknown), could be thought as the linear combination of $\lambda(H^1+\lambda H^2 + ...)$.
In a sense $\lambda$ here was $x$ in Taylor expansion, and the sequence of $H^1+\lambda H^2 + ...$, if you thought of the each of... | {
"language": "en",
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Is hermiticity a basis-dependent concept? I have looked in wikipedia:
Hermitian matrix
and
Self-adjoint operator,
but I still am confused about this.
Is the equation:
$$ \langle Ay | x \rangle = \langle y | A x \rangle \text{ for all } x \in \text{Domain of } A.$$
independent of basis?
| Symmetric operators are usually employed when working on real vector space, whereas Hermitian operators are usually employed when working on complex vector spaces.
In finite dimension, the associated matrix is symmetric in the first case ($a_{ij}=a_{ji}$ for all $i,\,j$), whereas it is equal to its complex conjugate tr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/307113",
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"source": "stackexchange",
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When is the motion oscillatory and when is it not Sometimes in physics questions we see examples in which applied force is balanced by an innate force of the body. Like in torsion balances and Cavendish's experiment. In this case we say that rotation( of coil) was up to the point where our applied force balanced the in... | For the motion to be oscillatory two conditions should be met. 1. There should be a return force that returns the system back to equilibrium. 2. The system should have an inertia, that is once it is in equilibrium position with a certain velocity it should continue to move. Inertia takes the form of inductance in a LC ... | {
"language": "en",
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What does the $j$ mean in this notation? This section of Introduction to Quantum Mechanics by Griffiths is talking about the Maxwell Stress Tensor. I don't quite understand what the $j$ means on the left side of the "$=$" sign (for either of the 2 representations).
| The $j$ represents the $j$-th component like is mentioned above. Seeing as your question is really about confusion about index notation rather than than the actual quantum mechanics, let me suggest a book to you. There is an incredible amount of books that will deal with vector and tensor notation across all different ... | {
"language": "en",
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Pauli- Villars regularization in the Electron Vertex Function: Evaluation I'm studying one loop contribution for electron vertex function form Peskin and Schroeder's book " An introduction to quantum field theory " Section: 6.3. I have some troubles with Pauli- Villars regularization and getting the final results, so a... | I only recently stumbled over the same issue, so this answer might come a bit late:
The first term in 6.56 - the 1 - appears due to the fact, that here $F_1(q^2)$ includes all corrections (to all orders), indicated by the last term, which represents terms of second order and higher in the electric coupling constant by... | {
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"source": "stackexchange",
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Wave packet expression Speaking in general about plane waves propagating along $z$ (electro-magnetic waves, for example; not necessarily particles represented as waves), a wave packet can be defined as
$$A(z,t) = \int_{\omega_1}^{\omega_2} A ( \omega ) e^{j (\omega t - kz) } d\omega$$
In particular, this expression is ... | A real-valued wavepacket solution of the dispersionless 1D wave equation can always be defined as
$$A(z,t) = \int_{\omega_1}^{\omega_2} A ( \omega ) e^{j (\omega t - kz) } d\omega, $$
where $\omega_1=-\omega_2$ and the frequency-domain amplitude satisfies $A(-\omega)=A(\omega)^*$; if this is not the case then $A(z,t)$ ... | {
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Why exactly do we say $L = L(q, \dot{q})$ and $H = H(q, p)$? In classical mechanics, we perform a Legendre transform to switch from $L(q, \dot{q})$ to $H(q, p)$. This has always been confusing to me, because we can always write $L$ in terms of $q$ and $p$ by just taking the expression for $\dot{q}(q, p)$ and stuffing i... | There's nothing stopping you from writing $L$ as a function of $q$ and $p$. In fact, you're required to write $L$ as a function of $q$ and $p$ to get the Hamiltonian! But the Euler-Lagrange equations become very ugly.
Consider the normal Euler-Lagrange equation
$$
\frac{d}{dt}\frac{\partial L}{\partial \dot q}=\frac{\p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/307794",
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Charged plasma and ion grid in interaction in ion thrusters I was just wondering .....
In this Image of an ion thruster, when the positively charged particles pass through the grids, wouldn't they just bombard the negatively charged grid(a fraction of them). This means that there must be a constant adjustment to maint... | A good high power ion thruster uses a lot of energy to accelerate ions to high energies.
The image does not include any power source, which is a serious problem if a person looking at the image wants to understand how ion thrusters work.
A simple ion thruster woks like this:
A small amount of energy is used to ionize ... | {
"language": "en",
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What is an induced electric field? I have read in many books about induced current in a coil (Faraday's law), and also the motional emf across a moving conductor in a magnetic field. But somewhere I read about induced electric field due to a time varying magnetic field.
And I think that Induction of electric field is... | Talking of "induced" fields is, again, yet more bad terminology and language that conveys a misleading notion - here, an impression of a kind of "causality" of one field upon the other - that is not part of our generally-used physical model.
What it means is this: In any case where that the magnetic field is changing i... | {
"language": "en",
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Why the electrons below the Fermi level do not conduct electricity? Physically, why is it that the electrons need to excited above the Fermi level to conduct electricity? In other words, why is the current zero when the electrons lie below the Fermi level? Does Pauli exclusion principle play any role here?
| Electron bands are symmetric about $k = 0$, so for every electron in a filled band, there exists another electron with opposite momentum which cancels out its current, resulting in zero net current flow. An infinitesimal applied electric field just tilts the bands by an infinitesimal amount, so if the whole band lies ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/308181",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is short circuit technically the same as overloading? Taking the simplest circuit: battery and resistors.
If I connect lots of resistors in parallel, wouldn't that increase the current to an extent that it would be technically be very similar to shorting the circuit?
| No, a short circuit needn't be an overload. There are circumstances (like
in current transformers) where no load, however small in resistance, is
an overload. There are ideal signal sources that are voltage sources
(i.e. low impedance), and sources that are current sources (i.e. high
output impedance), and sources ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/308261",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why is perturbation theory always implemented around $\alpha=0$? In the perturbative approach to field theory we expand whatever we are computing on a power expansion in some coupling
$$
\sum^nd_n\alpha^n
$$
then in principle we can compute all the $d_n$. This series is in general expected not to be convergent, but it... | Usually the problem is set such that $\alpha=0$ simplifies the equations: eliminates mixing / interacting terms, or allows to ignore certain effects at first order. In general, we want to get a problem that we can solve, that is the main point of perturbation theory. If we can solve the problem for some different value... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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"Bending up" $LC$-circuit to a linear antenna mathematically In introductory physics books one often finds a picture series leading from an $LC$-circuit to a simple linear antenna by "bending up" the $LC$-circuit, for example like this:
The key difference between the first and last picture is the described as that the... |
Are there any experimental measurements available which compair (in far field) the power radiated by the LC circuit
The radiation coming from a discrete inductor or capacitor will depend on the details of their construction. For example, it's possible to buy a "shielded" inductor which has a ferrite material surround... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/308447",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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