Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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$k$-dependence of the energy in solid state physics In a crystal, the electrons are subject to a periodic potential due to the fact that the atoms form a periodic lattice. From this periodicity we can obtain the Bloch theorem, and get a general formula for the electron wave function, known as the Bloch function.
Throug... | I think your question is confused, the quantum numbers $k$ and $n$ denote a wavefunction with a particular spatial dependence $\psi(x)$ and energy $E_{n,k}$. So in that sense, the energy does sensitively depend on $x$. One should note that this is the same result as that of the simple harmonic oscillator, which has sta... | {
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Help understanding Einstein notation This is basically the same question as this one. I have the same problem with the sign. In the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi = 0$, the term $i\gamma^{\mu}\partial_{\mu}$ is:
$$i\gamma^{\mu}\partial_{\mu} = \sum_{j=0}^{3}i\gamma^{j}\partial_{j}$$
However, the Ei... | We use the metric $[\eta]=\mathrm{diag}(+,-,-,-).$
Note first that
$$X^\mu Y_\mu=X^0Y_0+X^1 Y_1+X^2Y_2+X^3Y_3 \tag{1},$$
but also
$$X^\mu Y_\mu=\eta^{\mu\nu}X_\mu Y_\nu=\eta^{00}X_0Y_0+\eta^{11}X_1Y_1+\eta^{22}X_2Y_2+\eta^{33}X_3Y_3, \tag{2}$$
which, using the components of the metric gives
$$X^\mu Y_\mu=X_0Y_0-X_1Y_1-... | {
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Relation between critical temperature and density of states The BCS theory predicts that the critical temperature of the superconducting transition is given by
$$
T_c \approx \theta \exp \left (- \frac{1}{U D(\epsilon_F)} \right )
$$
where $\theta$ is the Debye temperature, $U$ is the coupling constant of the electron-... | It is an experimental fact that HTS superconductors generally show large temperature-independent Pauli susceptibility, indicating high DOS near the Fermi surface. See e.g. here.
| {
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Why intensity of light reaching the sensor or film with a particular lens directly proportional to $\frac{D^2}{f^2}$? The following is quoted from my book:
"The intensity of light reaching the sensor or film is proportional to the area viewed by the camera lens and to the effective area of the lens. The size of the are... | The first term, proportional to $D^2$, is rather simple: The larger your lens aperture, i.e. the larger the area that collects light, the more photons you get.
The second term is a bit misleading. Actually, the smaller the focal length $f$, the larger the angle of view $\alpha$ that the camera sees, both in the horizon... | {
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Why is the number of isotopes of an element bounded? Is there a known reason why any given element has finitely many isotopes? Here I mean both stable and unstable isotopes.
If we know this, do we have a reason why, for a given element, are the isotopes limited to that particular number?
| In the comments you clarify your question by asking, as an example, about hydrogen isotopes.
If you look at a Table of Nuclides, you will see that there are at least 7 hydrogen isotopes which have been identified so far. There are links attached to each entry in the table that give data on the reactions for creating th... | {
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What is the basic physics of current-electricity? Why current decreases when length of resistor increases and How the speed of electricity is almost $c$ (speed of light)?
| The field due to the battery sets up a surface charge in the wire. The surface charge is negative near the negative pole of the battery, and positive near the positive terminal, and varies more or less linearly along the wire. The surface charge in turn sets up inside the wire an electric field which is constant acro... | {
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Does mass have an effect on Centripetal Acceleration? I am using an online simulation for a lab concerning Centripetal Acceleration. When I change the mass the graph indicates that the magnitude of the acceleration is constant. According to the Centripetal Acceleration formula: $a=v^2/r$, this is true because no mass i... | If you change the mass, then either the acceleration or the centripetal force must change as well (or both). That is what we see from Newton's 2nd law.
The simulator you are using seems to adjust the force. That's why you see no acceleration change. That is just a choice by the software developers or possibly something... | {
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Why is this result no contradiction to length contraction? Let's consider 2 events in an inertial system $S$:
$$x_1=(0,0,0,0) \quad \quad \quad x_2=( \Delta t, \Delta x,0,0)$$
If we assume the two events occur in the same place we have: $\Delta \bar{t}= \gamma \Delta t$ for every other inertial system, also known as ti... | Let me start by saying that $x_2=( \Delta t, \Delta x,0,0)$ is not an event.
It's somewhat confusing. If you state that $\Delta x=\gamma x'$ you must put $\Delta t'=\frac{1}{\gamma}\Delta t$. You didn't do this though. Let me explain.
The Lorenz transformations are:
$$x'=\gamma(x-vt)$$
$$t'=\gamma(t-\frac{vx}{c^2})$$
F... | {
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How does physics "remember" that there's an EM wave when $E, B = 0$? I don't understand this subject well but I'll try to explain what I mean. In case of a pendulum or other macro oscillators you can calculate the "next" state from position/angle and velocity/angular velocity. They give you the entire description of th... | For the photon in a box with the right distance between the walls as a multiple of the wavelength, the E and B fields are out of phase and a sketch looks like this:
Here it is obvious that the photon has a constant energy content. Which also corresponds to our intuition.
| {
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In which frame (with respect to which object) velocity is taken in Bernoulli equation?
Duplicate: Bernoulli's equation and reference frames
why we need to take velocity of air in tunnel with respect to train & velocity of train with respect to earth (inertial frame) (here we are comparing pressure difference between ... | I seem to understand your problem. I feel u are having difficulty in understanding how is V = 4/3.Vtrain.
If so then it is very simple. See this relationship is achieved by equation of continuity and in that we have to consider the velocity of fluid w.r.t pipe. Thus :-
V. 3A( as out of 4A ,A Is blocked by train) = Vtra... | {
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Value of $\Omega(0)$? If we define $\Omega$ as the following, where $E_r$ is the energy in state $r$,
$$\Omega(E)=\int...\int d^{3N}p\ d^{3N}q\ \delta(E-E_r) \tag{1}$$
Then the laplace transform of $\Omega$ is the canonical partition function $Z(\beta)$,
$$L\{\Omega(E)\}=\int_{0}^{\infty}\Omega(E)e^{-\beta E}dE=Z(\beta... | You are mixing equations from the microcanonical and canonical ensemble.
For clarity, let us write :
$$\beta_*(E) = \frac{\partial \ln \Omega}{\partial E}(E)$$
for the temperature in the microcanonical ensemble and $E_*(\beta)$ for the average energy in the canonical ensemble.
Then equation $(4)$ is rewritten :
$$\Omeg... | {
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Are the properties of anti-hydrogen opposite to those of hydrogen? In the series Crisis of Infinite Earths, the whole story is that there is a wave of antimatter rampaging through the multiverse. So I got interested and googled "how to create antimatter", and I found out that when an antiproton and a positron are prese... | The properties of anti-matter in general are very similar to properties of matter. Richard Feynman considered the problem of if we made radio contact with an alien civilization, how would we be able to tell if they were made of matter or anti-matter? It turns out to be a complicated process. See 52-8.
Anti-hydrogen is ... | {
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How to generate electric current without a permanent magnet? The question is pretty simple:
Can we build a device that coverts mechanical work in electric current1 without employing a permanent magnet and without access to any external source of current?
The restrictions in place seem to rule out the possibility of c... | Doesn't a battery do this? Also, capacitors.
EDIT: With the edit, it looks like the premise of your question could be satisfied by a Van de Graff generator:
https://en.wikipedia.org/wiki/Van_de_Graaff_generator
which uses friction to strip electrons from a substance, and create an electrostatic potential.
| {
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Can soneome help me understand this part of the Feynman's Lost Lecture? Feynman's lost lecture
So at 17:38, 3Blue1Brown states:
We know that once the planet has turned an angle $\theta$ off the horizontal with respect to the sun, that corresponds to walking $\theta$ degrees around our circle in our velocity diagram, si... | On the right diagram, there are 4 sections, each section is an equal angle of 15 degrees, so 60 degrees around the orbit.
On the left velocity diagram, it said earlier that the tips of the velocity vectors are equally spaced, so 4 of those sections is a fraction of 4 out of 24 'steps' around the circle or 60 degrees ag... | {
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What is the problem with a rotating singularity? In most cases, people ask how can a point spin, resulting in a 'ringularity' as an answer. But I'm not quite sure why a point can't spin. After all, it's like saying how can something with mass have no volume, or how can a ringularity spin if each frame of its rotation i... | I guess that you're asking about the question How can a singularity in a black hole rotate if it's just a point?, and this highly upvoted answer.
The answer is just wrong. The angular momentum of a black hole is not "in" the singularity, but rather in the shape of the whole spacetime manifold, so there isn't really a p... | {
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Does energy of a capacitor means energy stored in both plates? I've a doubt in this,
Does the term potential energy of a parallel plate capacitor means the energy stored in both the plates or a single plate, since the formula $E=Q^2/2C$ , $Q$ is the charge of only one plate?
Please help me in this.
| It is the energy for the entire system. It is the energy required to put $+Q$ on one plate and $-Q$ on the other plate.
| {
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Does the $H_2$ in cosmic clouds virtually not radiate? I am reading the lecture notes of a friend. He has written about the cold (3-20 K) molecular $H_2$ cosmic gas, that "practically doesn't radiate, due to symmetry". Can someone confirm that $H_2$ has this feature of radiating much less electromagnetic radiation than... | Yes, it is correct that cold $H_2$ radiates much less electromagnetic radiation than other molecules (for example, carbon monoxide).
Here's one way to think about this intuitively. On macroscopic scales, electromagnetic radiation is produced when charged objects accelerate. The atoms in a hydrogen molecule consist of... | {
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Are charged particles cold? Are charged particles colder than neutral ones?
If a charged particle is vibrating due to temperature, it will release some of its energy as electromagnetic waves. So that means it's losing energy, cooling itself off. Is there an error in my logic?
| There are two main errors:
Single particles don't have a temperature. Temperature is a statistical feature of bulk matter.
Single particles don't emit EM radiation when they move. Instead their energy is quantised. Under Classical theories all atoms would quickly collapse as their electrons radiate all their energy awa... | {
"language": "en",
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If photons have also particle properties why should they not collide with each other? If photons have also particle properties why should they not collide with each other? Collisions between fermions are possible as collisions between fermions and photons(bosons) except collisions between photons (that are described by... | Having particle properties does not mean that a photon is a small sphere traveling at the speed of light. Collisions in quantum mechanics mean that particles interact and modify their free-particle behavior.
Quantum electrodynamics predicts an electron-electron interaction, electron-photon interaction, but also a photo... | {
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When I walk down the stairs where does my potential energy go? When I leave my room I walk down three flights of stairs releasing about 7kJ of potential energy. Where does it go? Is it all getting dispersed into heat and sound? Is that heat being generated at the point of impact between my feet and the ground, or is it... | There is a nice answer by @annav, I would like to add something none of the answers mention, that is atmospheric pressure.
However small the atmospheric pressure is changing when you walk down the stars, it does change, and it means that as you descend, your body must take more pressure.
At low altitudes above sea lev... | {
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Conventions for graded wedge product in supergeometry There are two conventions for the graded exterior product on superspace (see https://ncatlab.org/nlab/show/signs+in+supergeometry):
$$\alpha \wedge \beta = (-1)^{pq+|\alpha||\beta|}\beta\wedge\alpha \;(\text{Deligne})\tag{1}$$
$$\alpha \wedge \beta = (-1)^{(p+|\alph... | TL;DR: The confusion seems to be that the notation $|\cdot|$ somewhat misleadingly sometimes denotes the Grassmann-grading and sometimes the total grading.
*
*In the Deligne convention $|d|_g=0$, the form-degree $|\cdot|_f$ and the Grassmann-grading $|\cdot|_g$ are two independent gradings. This leads to eqs. (1) & (... | {
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Simultaneity of timelike separated events It can be easily shown that if we have two time-like separated events which are not simultaneous in one frame then they cannot be made simultaneous by Lorentz transformation. But, if those events are simultaneous in one frame then they can be made non-simultaneous by Lorentz tr... |
if we have two time-like separated events...But, if those events are simultaneous in one frame then they can be made non-simultaneous by Lorentz transform
If two events are both time-like separated and simultaneous then the two events have the same spacetime coordinates and will be simultaneous in all frames.
Further... | {
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Shor's algorithm entanglement verification I would like to ask whether the entanglement verification is necessary in Shor's algorithm
In the paper, Nature Photon 6, 773–776 (2012), they mentioned that they tried to factorize 21 to avoid the entanglement verification, but I'm not sure why this verification can be avoide... | In the abstract of this paper they say
The algorithmic output is distinguishable from noise, in contrast to
previous demonstrations.
The previous demonstrations seem to be claims to have factored $15$.
Shor's algorithm works (slowly) even if your "quantum" computer has a coherence time of zero. The reason is that it ... | {
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Group velocity is zero at zone boundaries The E-k diagram derived in Kronig Penney model looks like:
As we can see that slope of this curve is zero at all zone boundaries as well as k=0, which makes group velocity zero at these points. Why is it so? Why group velocity is zero at these points?
| At the boundaries of the Brillouin zone, the wavelength is an integer multiple of the lattice constant. Therefore, strong reflected waves are generated and they are mixed with the traveling wave. Eventually, the waves become standing waves and do not have group velocity.
| {
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Does Motional EMF depend on the shape of path taken or depends on the shortest distance between given two points?
A semi-circular conducting wire of radius 2m is rotated in a uniform magnetic field $B=0.1\text{ T}$ ($\vec k$) about point $O$ with angular speed $\omega=10\text{ rad/s}$ as shown in the figure. The axis ... | The given solution uses the fact that a closed loop that encloses a constant amount of magnetic flux has no e.m.f. Let $\alpha$ denote the path $\overset{\Huge\frown}{OM}$ and $\beta$ the straight line $\overline{OM}$. By Lenz's law,
$$ \oint \mathbf{E}\cdot \text{d}\mathbf{r} = \int_\alpha \mathbf{E}\cdot \text{d}\mat... | {
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Explain the theory behind this problem(if possible using number line or graph or any other method of pictorial representation) In a situation in which data are known to three significant digits, we write 6.379 m = 6.38 m and 6.374 = 6.37 m. When a number ends in 5, we arbitrarily choose to write 6.375 m = 6.38 m. We co... | You are looking for a value $x$ such that
$\displaystyle \frac x {100} = \frac{1000} x
\\ \Rightarrow x^2 = 10^5
\\ \Rightarrow x = \sqrt{10^5} = 100\sqrt{10} \approx 316$
| {
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If an antimatter-matter reaction is a perfect transfer of matter to energy (light), is there a perfect transfer of energy to matter? I am aware that two photons can combine to form an electron and positron pair, but if any matter and antimatter can annihilate to form photons, shouldn't there be a way for photons, or an... | Gamma rays are photons of very large energy. Technology has advanced to the point of talking of gamma gamma colliders, so yes, the electromagnetic energy will be used to create a lot of elementary particles for study.
Photon beams can be made so energetic and so intense that when brought into collision with each other... | {
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How do sound waves cause air molecules to oscillate? I would like to clear up some confusion about the mechanics of air particles that are propagating a sound wave.
I understand that there is no net movement of air molecules when a sound wave passes through air. Instead, the particles oscillate and the wave is propagat... | Sound waves are referred to as pressure waves, and if you understand this, it should answer your question.
When sound waves propagate, they form alternate regions of high pressure, called compressions, and low pressure, called rarefactions in the air. The air molecules move toward and away from these regions as the wav... | {
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Why is difference of points not a valid definition for a vector in curved space? In page-49 of MTW (1973 edtn), the following picture is shown:
After seeing this picture, the question which arose in my head is why exactly can we not define a vector as difference of points in curved space?
| The short answer is that vectors must satisfy the eight axioms of a vector space in order to qualify as vectors.
Flat space is professionally known as affine space, which I have described in my answer here. In affine space, one can subtract two points to obtain a vector. By defining an origin and position vectors, one ... | {
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If $E=mc^2$, then why do different substances have different calorific values? Today during a classroom discussion, I realised that if we consider the equation $E=mc^2$, then we are establishing a relation between energy and mass but we often observe that different substances produce different amount of energy when the... | If you converted 1 pound of fuel completely into energy it would be the same as converting 1 pound of wood completely into energy.
But when you burn wood, you get leftover mass in two forms: smoke and ashes. When you burn gas, you get leftover mass in exhaust ($CO_2$, $CO$, etc.)
The energy you get from burning a subst... | {
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Functional integrations We often see functional versions of Gaussian integrations $$ \int_{-\infty}^{\infty} d^dx e^{-x^{T}Mx} = \frac{1}{\sqrt{2\pi^d \det M}} \to \int[\mathcal{D}X] e^{-i\int X \mathcal{O}X} = (\det{O})^{-1}$$
where $\mathcal{O}$ is some hermitian operator. The map to convert a gaussian integral into ... | The second integral's functional equivalent, say
\begin{equation}
\int \mathcal{D}X e^{-i \int \mathcal{O} X}
\end{equation}
is just a Lagrange multiplier on the operator $\mathcal{O}$ so you'll just get a delta function on whatever the operator $\mathcal{O}$.
If you'd like to make this into a more precise answer, ... | {
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Computing the metric tensor from its Killing vectors? On page. 139 of Carroll's GR book, during the discussion of Killing vectors, he quotes an explicit coordinate basis representation for the Killing vectors on $S^2$:
\begin{array}{l}
R=\partial_{\phi} \\
S=\cos \phi\,\partial_{\theta}-\cot \theta \sin \phi\,\partial_... | You're going to need some sort of extra assumption in order to make this idea work, because not every spacetime even has a single global Killing vector, much less enough Killing vectors to span the spacetime.
| {
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Quantum volume required to break a 2048 bit number used in RSA encryption I am curious as to whether there is a specific amount of quantum volume that will allow a quantum computer to break a 2048 bit number used in RSA encryption, and if so, what that number is. (within a realistic time frame of less than 1 hour)
Than... | To perform integer factorization on a quantum computer sucessfully depends mainly on number of available qubits and their quality (low noise and long decoherence time). Of course, quantum volume is linked to these two parameters.
According to the article this article dissused here, some millions of qubits are necessary... | {
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"timestamp": "2023-03-29T00:00:00",
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Can you exit the event horizon with a rocket? The reason given in most places about why one cannot escape out from an event horizon is the fact that the escape velocity at the event horizon is equal to the speed of light, and no one can go faster than speed of light.
But, you don't really need to reach the escape veloc... | The force of gravity is small. But it's a small force on a thing that contains zero energy. So the force gravity is infinite in a sense.
The rocket lost all of its energy when it was lowered to the event horizon.
It may be worth mentioning that the rocket motor burns fuel at infinitely slow rate. That has some effect o... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Quantum mechanics and logical statements I am a math student and currently working on my bachelor thesis with a philosophy professor. The subject is paraconsistency and thus also dialetheism which is the believe that a statement can be true and false at the same time.
I had a general/introductory course to QM and one e... | There's a difference between paraconsistent and quantum logics (there's more than one of each, and there is some overlap). In paraconsistent logics, the explosion theorem $(p\land\neg p)\to q$ fails in general. In quantum logics, the distributive laws $p\land(q\lor r)=(p\land q)\lor(p\land r)$ and $p\lor(q\land r)=(p\l... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Expansion of $\Gamma(-\epsilon)$ and $\Gamma(1-\epsilon)$ I'm currently trying to do some loop calculations in QFT and have come to a point where I need to expand a product of $\Gamma$-functions. Let $\epsilon$ be the parameter introduced in the $\overline{\text{MS}}$-regularization scheme that we want to let go to zer... | $\Gamma(1-\varepsilon)$ is the easier one since we know that $\Gamma(n)=(n-1)!$ so $\Gamma(1)=0!=1$; so
$$\Gamma(1-\varepsilon)=1-\varepsilon\Gamma'(1).$$
The derivative of Gamma function is related to another special function called $\psi$ function defined by
$$\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}=(\ln\Gamma(x))'.$$
B... | {
"language": "en",
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Why is everything not invisible if 99% space is empty? If every object is $99$% empty space, how is reflection possible? Why doesn't light just pass through?
Also light passes as a straight line, doesn't it? The wave nature doesn't say anything about its motion. Also, does light reflect after striking an electron or at... | It depends on what you are calling "empty".
Electrons are point particles. Or maybe they are not, but their size is probed down to 10^-22 m and found to be less than this already pretty much little value.
Atomic nuclei are not points. They are made of protons and neutrons that are not points either. But protons and neu... | {
"language": "en",
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"source": "stackexchange",
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Can I apply the Born rule to a Dirac spinor? How does a Dirac spinor such as:
$$
\psi = \pmatrix{a_0+ib_0\\a_1+ib_1\\a_2+ib_2\\a_3+ib_3}
$$
Connect to a probability?
Can one apply the Born rule of this object?
| The Born rule, in its simplest form, tells us that the probability (density) of finding a particle at a given point is the square of the particle's wave function at that point. That is, $$\rho = \mid \psi (x,t)\mid^2$$ which is always a positive real number.
As such, the Dirac spinor is not a wave function. They do not... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Magnetic field induced by a rotating charged disk Let's assume that there is a disk of total electric charge $Q$ rotating about its axis with a
constant angular velocity $\vec{\omega}$. I know that one can easily compute the magnetic field
generated on the axis of the rotation of the disk, which is possible due to the ... | Your rotating charged disk can be thought of as many concentric rings of current. Each ring can be thought of a many short elements of current, each of which contributes to the magnet field at any chosen point as predicted by Biot-Savart. Not being a mathematician, if I had to do this I would let a computer do a nume... | {
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Do Newton's laws of motion hold true in non-inertial frames of reference? My book derived the formula for the acceleration of a rocket at any instant in the following way:
$v_r=$ velocity of gas released from the nozzle relative to the rocket
$dt=$ infintesimal time interval
$dm=$ mass of the gas released from the nozz... | The derivation that you show is not calculated from the perspective of the rocket. It is calculated from the perspective of a stationary outside observer. The calculation simply uses the relative velocity of the gas to calculate what force the rocket will experience.
Newton's laws are valid in non-inertial reference fr... | {
"language": "en",
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How does a string pulls pulley at both the ends?
For an Atwood's machine, why does the string exert a downwards force on the pulley that is twice its tension? I'm neither able to understand nor imagine this scenario.
How does a wrapped string with tension $T$ pull a pulley downwards with a force of $T$ at each end?
In... | At one level the answer is trivial- the pulley is subject to two parallel forces T, so the resultant force is 2T.
If, however, your question is exactly how is the force applied to the pulley, the answer is that it is the vertical component of the normal force integrated over the surface of the pulley.
To see that, imag... | {
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What interval to use when proving orthogonality of wavefunctions? When proving that $\psi_1=\sin(n\pi x/a)$ and $\psi_2=\cos(n\pi x/a)$ are orthogonal to each other in a 1D box, the main problem that I am facing is what to use as the domain of integration. If I take the interval $[0,a]$ as we use in the Schrodinger wav... | There is no rule, it depends on what the author of the exercise wants to use. However, the solutions $\psi_1$ and $\psi_2$ will also come out slightly differently, depending on the setting chosen in the exercise. If the solutions satisfy the Schröedinger equation for the correct potential, they will automatically come ... | {
"language": "en",
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"source": "stackexchange",
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Block on an accelerating wedge
In the above figure, the wedge is been accelerated towards right as shown in figure. According to my teacher it is possible to keep the block at rest or even accelerate it in the upward direction along the the inclined plane of wedge. To explain he taught us about pseudo forces. Stating ... | In the laboratory frame, The equation of motion given by
$$N\cos\theta-mg=0$$
$$N\sin\theta =ma$$
In Accelerating frame, The equation of motion given by
$$N\cos\theta-mg=0$$
$$N\sin\theta-ma=0$$
Both are equivalent.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Relative Circular Motion
Four particles $P_1, P_2,P_3,P_4$ are moving in a plane. At $t=0$, they are at the four corners of a square $ABCD$ of edge length $l$. Each of the particles has a constant speed $v$. The velocity of $P_1$ is always directed to $P_2$, that of $P_2$ is always directed to $P_3$, that of $P_3$ is ... | Hint: Try putting 4 dots on the paths after a short time.
Join the 4 dots and see what happens.
There is a nice simple answer to this...
| {
"language": "en",
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Does real life have "update lag" for mirrors? This may sound like a ridiculous question, but it struck me as something that might be the case.
Suppose that you have a gigantic mirror mounted at a huge stadium. In front, there's a bunch of people facing the mirror, with a long distance between them and the mirror.
Behin... | When I read a few answers to this question, I noted how everyone wants to emphasize that it is a small effect because light moves so quickly. So that set me pondering whether we can find an example with longer distances.
If we look out into the depths of space, we don't see mirrors but we do see something that acts to ... | {
"language": "en",
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Electric flux due to a charge on a square surface
what is the flux through the square if a charge q is placed on the surface of the square ?
Now,
according to me if we use the solid angle method
the flux should be
$$([q/\epsilon]*2\pi)/4\pi$$
as the solid angle is $2\pi$
however I'm not sure if this is correct :(
.
No... | If the charge is in the surface, the electric field vectors are also parallel to the surface, due to symmetry. Then
$$\Phi_E=\int \vec E\cdot d\vec A=\int \vec E\cdot \vec n d A=0$$
because of $\vec E\cdot \vec n=0$. No need for solid angles to get that result.
The electric field of a point charge at the origin is (in ... | {
"language": "en",
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Can we cool Earth by shooting powerful lasers into space? In a sense, the climate change discussion revolves around the unwanted warming of the earth's atmosphere as a whole.
It seems a bit too obvious to be true, but could we cool the atmosphere by simply shooting that unwanted energy somewhere else?
Energy might be c... |
... could we cool the atmosphere by simply shooting that unwanted energy somewhere else?
Yes, but only by making our problems worse than they are already. A heat pump removes unwanted heat (that is how a refrigerator works) but it takes energy to make a heat pump work. Either this energy comes from non-renewable reso... | {
"language": "en",
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"source": "stackexchange",
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On existence of orthonormal basis for each subsystem in Separable state A separable state in $\mathcal{H}_{a}\otimes\mathcal{H}_{b}$ is given by
$$\rho_{s}=\sum_{\alpha,\beta}p(\alpha,\beta)|\alpha\rangle\!\langle\alpha|\otimes|\beta\rangle\!\langle\beta|.$$
Now, my question is, can what can we say about the existence ... | No, such a decomposition does not always exist.
To see this, we need two facts:
(1) The set of all separable state has the same dimension as the set of all density operators (it is a finite-volume subset) -- that is, it has $\approx D^4$ real parameters (if both systems have dimension $D$).
(2) The family you descibe i... | {
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Equation of motion of a gas's center of mass due to heating So here's a pretty basic question that I don't know how to solve within standard thermodynamics.
Let's say I have a container with a gas in it. I transfer heat, $Q$, to the gas from the bottom of the container. Let us assume the local equilibrium hypothesis is... | The natural convection problem you are envisioning can be solved for the time- and spatial variations of the temperature, the velocity, and density using the basic spatially differentiated transport equations (Navier-Stokes equations {with typically a linearized buoyancy term} in conjunction with the continuity {mass ... | {
"language": "en",
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"source": "stackexchange",
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Gravitational wave and 1st law of thermodynamics Introduction:
A prediction of the general relativity is that any moving mass produces fluctuation in the space-time fabric, commonly referred as Gravitational-Wave.
This prediction was recently confirmed by the LIGO experiment.
The generation of such gravitational waves ... | The objects that are radiating gravitational waves must be losing the energy and angular momentum they had in their orbits. For example, when two black holes spiral in toward each other, they radiate away this energy and angular momentum as their orbit decays and they eventually merge.
How does a system, for instance ... | {
"language": "en",
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Does the physical singularity of the Reissner-Nordstrom metric have a ring structure? The physical singularity of the Kerr metric has a ring structure due to the axi-symmetric nature of the metric.
The Reissner-Nordstrom metric is the solution for a non-spinning, electrically charged black hole, and has two horizons: a... | The singularity in a Reissner-Nordström geometry is at $r = 0$. With a little assistance from Mathematica I find the Kretschmann scalar to be:
$$ K = \frac{56r_q^4}{r^8} - \frac{48 r_q^2 r_s}{r^7} + \frac{12 r_s^2}{r^6} $$
and this is finite everywhere except at $r = 0$.
theoretically, the existence of the Kerr singu... | {
"language": "en",
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Proton Electron Merger Can somebody explain what would happen if an electron & a proton, very close to each other are left to "fall" to each other in a straight line?
| I wish to point out that electrons are LEPTONS, and protons are HADRONS (forgive the SCREAMING). All protons are made up of 3 quarks (u u d). Neutrons have (u d d) quarks. Leptons have 0 quarks and do not participate in strong force interactions which are mediated by gluon exchanges between the hadron's component quark... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Bloch functions vs. Bloch state vectors Let
$$\hat{H}=\frac{\hat{\mathbf{p}}^2}{2m} + V_L(\mathbf{r})$$
where the lattice potential $V_L(\mathbf{r})=V_L(\mathbf{r}+\mathbf{R})$ for any lattice vector $\mathbf{R}$, and let $\hat{T}_{\mathbf{R}}$ denote translation by $\mathbf{R}$. Skipping the details for now, we can de... | The trick is to replace the $\mathbb C$-valued function $\exp(i\mathbf k\cdot\mathbf r)$ by the operator $\exp(i\mathbf k\cdot\hat{\mathbf r})$ (which no longers depend on $\mathbf r$.
More explicitely, you are defining $u$ by :
$$ u_{n\mathbf{k}}\left(\mathbf{r}\right)=\exp\left(-i\mathbf{k}\cdot\mathbf{r}\right)\psi_... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/651420",
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True or False: energy is conserved in all collisions Using introductory physics, how would you answer this question? (I have a disagreement with my instructor and I’m curious to hear your input)
One of us says true because the question doesn’t specify “kinetic energy,” or a “system” and all energy is always conserved. ... | In any situation you will encounter, most notably using mere introductory physics, it is "true".
Energy is always conserved, but gets quite handily transmuted between different forms. As a last resort, energy becomes simple thermal heat. But it is still energy, and is conserved.
In the typical teacher's mind, the answe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the difference between elastic force and restoring force?
Elasticity is the ability of a material to return to its original shape after being stretched or compressed. When an elastic material is stretched or compressed, it exerts an elastic force.
The restoring force is a force that acts to bring a body to i... | This is a matter of semantics, but I’d say that an elastic force is a specific type of restoring force, in the context of a physical elastic/spring type system. A restoring force is any general force that opposes an applied force, usually describing harmonic oscillation. A different type of restoring force could be ele... | {
"language": "en",
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Inclined Stationary Bike Why would it make you work harder if you incline a stationary exercise bike? What's the physics involved? Assuming all other factors remain constant and only the incline changes, why would you burn more calories?
| To the best of my knowledge, it would not. Perhaps pedalling would become more awkward due to the incline but in terms of the mechanics/physics of the bike it would be the same.
Most stationary trainers have a resistance setting to deal with the difficulty of the incline. But this is not really your question.
I can’t i... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Coefficient of an 1-form in position-representation of momentum operator where configuration space is NOT $\mathbb{R}^m$
I found this in the book Geometric Phase in Quantum Systems by A. Bohm et al.
Where the position space representation of the momentum operator carries a (Where exactly my doubt is) coefficient of 1-... | *
*For $M=\mathbb{R}^m$, starting from the canonical commutation relations (CCRs), we have the Stone-von Neumann theorem, which proves the existence of the standard Schrödinger position representation (i.e. without the 1-form $\omega$) up to unitary equivalence, cf. e.g. this Phys.SE post.
*However conjugating with ... | {
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Is electron-positron annihilation time reversible? Consider that a low energy electron and positron annihilate creating two 511keV photons with no other particles around. To time reverse this process, we send two 511eV photons to collide hoping that they would produce an electron/positron pair.
However photons don’t in... |
However photons don’t interact with each other, at least not at such low energies.
Half an Mev photon is a gamma ray, and you are asking about the crossection of gamma gamma scattering.
In this paper the reverse reaction is considered to use in astrophysics obsvervations.
Instead of colliding, they just ignore each... | {
"language": "en",
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Proof of form of 4D rotation matrices I am considering rotations in 4D space. We use $x, y, z, w$ as coordinates in a Cartesian basis. I have found sources that give a parameterization of the rotation matrices as
\begin{align}
&R_{yz}(\theta) =
\begin{pmatrix}
1&0&0&0\\0&\cos\theta&-\sin\theta&0\\0&\sin\th... | For each of your 4D rotation matrix $~\mathbf R~$ if this equation
$$\mathbf Z^T\, \mathbf Z= \left(\mathbf R\,\mathbf Z\right)^T\,\left(\mathbf R\,\mathbf Z\right)$$
is fulfilled the rotation matrix $~\mathbf R~$ is orthonormal .$~\mathbf R^T\,\mathbf R=\mathbf I_4$
where
$$\mathbf Z= \begin{bmatrix}
x \\
y \\
... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does gravity get stronger the higher up you are on a mountain? So I saw this article stating that gravity is stronger on the top on the mountain due to there being more mass under you however I have read some questions other people have asked and most of the responses state that the mass is concentrated at the middle o... | You are getting different answers from NASA and from other sources, as they are talking about slightly different things.
NASA is talking about the acceleration of the GRACE satellite towards the earth, as it orbited over different regions. When it went over the Himalayas, for example, the acceleration (gravity) was hi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/652752",
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"source": "stackexchange",
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Why does $dG < 0$ imply that processes involving chemical reactions are spontaneous? Here is a short proof/derivation of why $dG < 0$ implies that a process is spontaneous (for constant temperature and pressure):
But this derivation assumes that only mechanical work is done on the system. If the process involves chemi... | Indeed the derivation assumes that only mechanical work can be done on the system, and no transfer of particles and associated energy can happen; it is in the first sentence, "no matter can come in or out".
This does not mean chemical changes inside the system are forbidden; instead, they can happen but they don't affe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Law of conservation of energy using work done vs maxwell theory of electromagnetic radiation Consider the motion of a charged particle in a uniform magnetic field. $\vec{B} = B_0(-\hat{k})$. Let the initial velocity with which it enters the field be $\vec{v_i} = v_0(-\hat{i})$. It is well known that it follows a circul... | Yes, your second reasoning is correct. Accelerating charges do emit electromagnetic radiation, and what you described is known as synchrotron radiation. This energy loss increases sharply as the particle approaches the speed of light. In fact, this is a limiting factor of the maximum speed that particle accelerators ca... | {
"language": "en",
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How would I determine the charge density of an active lava flow? It is my understanding that in molten silicates, such as a basaltic lava flow, electrons are decoupled from solid state structures. If this is the case, as lava is flowing through a tube, how would I estimate the charge density and current of the flow for... | Perhaps through the use of some sort of semiconductor material. I am watching a documentary right now and it is talking about the sun being misunderstood as just a ball of burning gas . On the contrary it is an electrically charged sphere of what they believe is a liquid material. Could be very possible that lava could... | {
"language": "en",
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What's the difference between a perfect fluid and an ideal gas? This is how I understand it at the moment:
*
*A perfect fluid is a collection of non-interacting particles, which are as a whole characterised by energy and pressure.
*An ideal gas is also a collection of non-interacting particles, but here the ideal ga... |
An ideal fluid is a fluid that is incompressible and no internal resistance to flow (zero viscosity). In addition ideal fluid particles undergo no rotation about their center of mass (irrotational). An ideal fluid can flow in a circular pattern, but the individual fluid particles are irrotational. Real fluids exhibit ... | {
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Can incompatible observables share an eigenvector? I was recently introduced to the concept of compatible and incompatible observables and specifically the generalized uncertainty principle, which is written in my textbook as:
$$ \sigma_A^2\sigma_B^2 \geq \left(\frac{1}{2i} \langle [A, B] \rangle \right)^2 $$
where $A$... | It is possible for two non commuting operators to have an eigenvector in common.
Consider two operators $A$ and $B$, that in some basis can be written as
$$ A =
\begin{pmatrix}
1 & 0 & 0\\
0 & 2 & 0\\
0 & 0 & 3
\end{pmatrix}$$
$$ B =
\begin{pmatrix}
1 & 0 & 0\\
0 & 0 & 1\\
0 & 1 & 0
\end{pmatrix}$$
$$ AB-BA =
\begin{pm... | {
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Could wavefunction values be quantized? According to standard quantum mechanics, Hilbert space is defined over the complex numbers, and amplitudes in a superposition can take on values with arbitrarily small magnitude. This probably does not trouble non-realist interpretations of the wavefunction, or explicit wave func... | One problem with this idea is normalization:
$$\int_{\mathbb R} \psi^* (x) \psi(x)~ dx = 1$$
You are integrating over infinite space. If $\psi$ has a minimum non-zero value, $\psi$ must be $0$ everywhere except a finite volume.
Now switch to the momentum basis. Because $\psi$ has bounded support, the Fourier Transform ... | {
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Brachistochrone to a vertical line Just for fun, I am working through some problems in Mathematics of Classical and Quantum Physics by Byron and Fuller. Problem 2.13 reads:
Prove that a particle moving under gravity in a plane from a fixed point $P$ to a vertical line $L$ will reach the line in minimum time by follow... | Hint :
You must start from the time to travel between $\theta_1$ and $\theta_2$ on a cycloid :
\begin{equation}
t_{2}-t_{1}=\sqrt{\dfrac{\,R\,}{g}}\, \int\limits_{\theta_{1}}^{\theta_{2}}\mathrm{d}\theta=\sqrt{\dfrac{\,R\,}{g}}\, \left(\theta_{2}-\theta_{1}\right)
\tag{01}\label{01}
\end{equation}
If the motion of the ... | {
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Units of a scalar field Consider the Lagrangian density
$$\mathscr{L} = \frac{1}{2} \partial_\mu a \partial^\mu a + \frac{m^2}{2} a^2.$$
I understand why $[a]=m$, i.e. $a$ has mass dimension one. What and why are the units of $a$ in the SI system?
If I were to know the units of $a$ in the SI, then knowing where and how... | There is no standardization of units for fields in particle physics. The fields themselves are not physical observables, so there is no need to specify precise units for them. As a consequence, they are normally given (like everything else) in units of power of energy, $[a]=$ GeV. If you wanted to convert that to SI... | {
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Understanding two algebra steps in Altland & Simons I would like to understand two summations on page 184-185, where we are told that assuming $x > 0$:
$$ G_{\pm} (x, \tau) = - \frac{T}{L} \sum_{p, \omega_{\, n}} \frac{1}{- i \omega_n \mp p} e^{- i p x - i \omega_{\, n} \; \tau} \; $$
$$= \mp i T \sum_n \Theta(\pm n) e... | I think Altland&Simons have in mind approximating both momentum and Matsubara frequency sums by integrals, which is permissible in the limits $L\to \infty$ and $T\to 0$ respectively. Introducing the spacings of momentum and frequency grids $\delta p=2\pi/L$ and $\delta\omega=2\pi T$ $$ G_{+} (x, \tau) = - \frac{T}{L} \... | {
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Why the amplitude in the third region is decreasing as compare to that of first region? Please explain its physical significance
Consider a finite potential barrier and the case where the energy of the particle is lower than that of finite potential. The figure is shown and we have three regions. As I solved the Schrö... | If it's about a particle moving from left to right, classically it wouldn't go past the barrier.
However in quantum mechanics it's possible that it can do 'tunnelling' and there is a small probability that it can get to the other side.
The amplitudes of the waves squared are proportional to the probability that the par... | {
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Bremsstrahlung Radiation A thought experiment.
Consider an electron falling into a black hole. From an external observer to the electron and the black hole, the electron accelerates, and should give off Bremsstrahlung radiation
From the electron's frame of reference, it is travelling along a geodesic in free fall, and ... | You don't need a black hole for this thought experiment: just drop an electron from a height on the surface of the Earth, and you have exactly the same problem.
The Equivalence Principle of General Relativity claims that such a system should be indistinguishable from an accelerated electron.
However, Maxwell's Equation... | {
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Water drainage from AC to a bucket kept on floor I have a split AC at home, the water outlet pipe from that was extended and kept into a bucket so that the water doesn't make puddles on the floor . The AC mechanic told when the bucket fills with water and the pipe gets submerged the water would stop flowing and it wou... | Basically, when the bottom pipe is submerged in the bucket, the pressure of the water surrounding the mouth of this pipe will be $$\tag 1 P=P_0+\rho gh$$ where $h$ is the depth of the pipe, $P_0$ is atmospheric pressure, $\rho$ is the density of water and $g$ is the acceleration due to gravity.
Even though at the top ... | {
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Gravitational wave of two interacting masses Consider two masses $m_1$ and $m_2$ that are connected by a spring. Mass 1 follows the worldline $x_1(\tau)$ while mass 2 follows $x_2(\tau)$. Note that the argument $\tau$ is the proper time in the rest frame of mass 1 and in the rest frame of mass 2 respectively but we do ... |
What is the freely falling system? Weber writes in his paper that it is the center of mass between the two masses. Why should the center of mass be freely falling in the presence of a GW?
In an old-fashioned Newtonian picture, you could say a "freely-falling" system has no forces acting on it besides gravity. As resp... | {
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Pressure exerted by an ideal gas according to kinetic theory of gases In my textbook and Wikipedia, I have observed that force exerted on a wall of the container by one molecule is taken into account. Such that $F=\frac{mu} {\Delta t}$ where ${\Delta t}=\frac{2l}{u}$. But this change in time is the time required for a ... | Your answer to the first question is correct.
We assume individual atoms travel the whole way across. This is not true. They collide some (although much less often than you’d think; try creating two jets of air from fans and notice they seem to have no effect on each other. Like point one at your face, and then bring i... | {
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What is the relation between the frequency vector and the Nyquist frequency? When trying to comprehend the concept of Nyquist frequency in FFT, I came across the following definition for half of the frequency range:
$$f = -f_{n}/2:df:f_{n}/2-1;$$
where $f$ represents the frequency vector and $f_n$ represents the Nyquis... |
Why only take half of the frequency range into consideration?
This is actually the full frequency range. Any other frequency you can think of outside this range is an alias of some frequency in this range.
And why specifically this half and not start at the 0 point?
It's an arbitrary choice.
One reason to do it thi... | {
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How do geodesics explain two identical balls thrown up at the different speeds? As stated in the title, two identical balls, both thrown directly upward, but at different speeds. The slower ball will reverse direction at a lower height than the faster ball. But the curvature of spacetime that they are passing through... | You must take into account the time dimension. You are assuming that since both balls where thrown upward from the same location on the same gravitating mass that they will follow the same geodesic. This is not true. You must take into account the time dimension (in addition to space). When you do this, you see tha... | {
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Is there a relationship between quantum physics and chaos theory on a classical scale? Im a complete physics lay person and I read somewhere that chaotic systems are subject to tiny differences in initial conditions and that the brain is a chaotic system.
Does that mean our thoughts are subject to quantum randomness?
| We don’t know to what extent (if at all) our thoughts are influenced by quantum phenomena.
Some scientists, including Nobel laureate Roger Penrose, are convinced that quantum phenomena are a fundamental component of consciousness. Others, including Max Tegmark, argue that neurons are too large and too slow to be signif... | {
"language": "en",
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What happens within an extended object passing the event horizon of a black hole? I hope this question is not too infantile: Falling into a Black Hole (intentionally or by accident) and thereby passing the Schwarzschild radius is very often said to be "nothing special" in the view of the falling observer. Tidal forces ... | I'm inclined to say that that your "funny" view is correct. It is impossible to transmit information out of a black hole if the information originates inside the event horizon. You can't turn on a light on the tail by sending a signal from the head, because what will carry the signal? Light cannot escape the event hori... | {
"language": "en",
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Can we feel heat in outer space? Is there air outside of earth atmosphere? If not, could we feel heat coming from sun?
| The pressure in space is very low as there are very few atoms per unit volume (compared to the atmosphere).
As a result, convection and conduction do not work for heat transfer, but radiation still works. Without sunlight, there is only 2.7 K background microwave radiation from big bang, so very cold (-270 deg Celsius)... | {
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Perturbative expansion of $\varphi^4$ theory and Green's functions I'm working in the $\varphi^4$ QFT where
$$S(\varphi)=\frac{1}{2} \mu \varphi^{2}+\frac{1}{4 !} \lambda_{4} \varphi^{4}$$
and the text says that we can expand (assuming small $\lambda_4$) as
$$\exp (-S(\varphi))=\exp \left(-\frac{1}{2} \mu \varphi^{2}\r... | Here are some tips (to do in order):
*
*Swap the order of integration and summation (truncate the series first since we cannot do this with an infinite series and we are just forming an asymptotic expansion anyway).
*Change the integration variable to $x=\frac{\mu^2 \phi^2}{2}$.
*Use the definition of the gamma fun... | {
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About the "worst prediction in all of physics": the cosmological problem Physicist Sabine Hossenfelder on YouTube just recently posted a video about vacuum energy, the cosmological constant and the "worst prediction" in physics. The worst prediction in physics refers in this case to the enormous discrepancy of a factor... | The 120 orders of discreapancy between predicted QED enormous value and actual tiny value measured by cosmolgical constant is due to the fact that Dark energy of free space is hidden from our time-like spacetime.
We see only the tip of the ice-berg in the form of Dark Energy's noise thus the ZPF energy. Beyond, ZPF vac... | {
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Stress developed in a Hoop due to rotation
In the given question with constant angular velocity. It asks us to find longitudinal stress at each of the positions. Now I'm not even sure what longitudinal stress is but here is what I tried as A is the farthest it will have the highest Radius and hence highest centripetal... | I would think that the tensions at points B and C should combine to produce the centripetal acceleration of the center of mass for the right side of the hoop. I currently have no idea how you would find the tensions at O and A.
| {
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Magnetic moment and angular momentum of electron I recently got to know about something really interesting.
These are as follows:
1: The magnetic moment of an electron is, $\cfrac{ev}{2πr}$, where $e$ is the charge of the electron, $v$ is its velocity, and $r$ is the radius of the orbit it revolves.
2: The direction of... | What you described is called the gyromagnetic ratio
between magnetic moment ($M$) and orbital angular momentum ($L$)
of the electron
$$\gamma_l=\frac{M}{L}=\frac{e}{2m}$$
where $e$ and $m$ are charge and mass of the electron.
However this relation holds only for the orbital angular momentum.
The corresponding relation ... | {
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Is the Heisenberg equation invariant under unitary transformation of momentum and position operators? Let $P$ be the momentum operator, $Q$ the position operator and $H\left(Q,P\right)$ the Hamiltonian operator. The Heisenberg equation of motion is
$$\dot{P}=-i\left[P,H\left(Q,P\right)\right] \tag 1$$
Suppose we have $... | Every unitary operator $U$ that depends on time can be written in the form
$U=e^{if(t)A}$ where $A$ is hermitian and $f:\mathbb{R}\rightarrow\mathbb{R}$ is a sufficiently regular function of time. We then have $U^{\dagger}=e^{-if(t)A}$.
Thus we have $\dot{U}=i\dot{f}Ae^{if(t)A}=iAU$ and $\dot{U^{\dagger}}=-i\dot{f}Ae^... | {
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A lattice of synchronized clocks Over the years I have seen this image which always confused me:
(from Wikipedia Spacetime)
"In special relativity, the observer measures events against an infinite latticework of synchronized clocks." This sounds needlessly artificial and abstract.
Let me take a stab at what they are t... | All it means is that in your stationary frame you have a plane of simultaneity, so if it is 2:37pm where you are it is 2:37pm everywhere in your frame of reference.
For example, if it is 2:37pm where you are 'now' it is also 2:37pm 'now' on Jupiter, which is about 33 light minutes away. If a light from Jupiter arrives ... | {
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How to treat pointlike objects in General Relativity? In general relativity we usually treat falling bodies and most small objects as pointlike. It is then enough to solve the geodesic equation in order to predict their motion.
However, it appears to me that a pointlike object in General Relativity should always give r... | Even an extended body has a metric that appears to be that of a black hole far enough from the body. For example, the Schwarzschild interior solution is an exact solution for the interior of on incompressible fluid, which can be matched exactly to the exterior Schwarzschild solution (i.e. the Schwarzschild black hole ... | {
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Deriving the equivalent capacitance in a series circuit formula When we derive the formula for the effective capacitance in series, we say:
$$Q/C_{eqv} = Q/C_1 + Q/C_2 + Q/C_3$$ (if there were 3 capacitors in this case). We would then cancel $Q$ to obtain the formula.
I understand why each capacitor has the same charge... | Just think of one c with the plattes some distance. Now put a conducting plate in the middle without touching the two outer plates. This plate will have one one side positiv charges, on the other side negativ charges. and it is now the same as two C in line. but you cannot get any of the charges on the inner plate. If ... | {
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Virtual displacement for a block sliding down a wedge
A block slides on a frictionless wedge which rests on a smooth horizontal plane. There are two constraints in this system. One that the wedge can only move horizontally and another that the block must remain in contact with the wedge.
We want to find the virtual di... | If the block is accelerated down the ramp, it gains momentum, but momentum is conserved, so the ramp must move in the other direction.
This can be calculated using Lagrangian mechanics as follows:
*
*The kinetic energies of the block ($b$) and the wedge ($w$) are
$$
T_b = \frac 12 m_b (({\underbrace{\dot d \cos(\alph... | {
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Does transformer with load drain more power from source than just load? Let's consider AC source of $\rm 12\ V$ and load of $\rm 12 \ Ohm$. Current is $1\ A$ and power is $\rm 12\ W$.
Now, we have the same source and the same load, but now is an ideal transformer in path with ratio of turns $p=1/100$.
Then current thr... | A load is normally given in units of power. A resistance becomes a load when you apply a particular voltage.
So, no, the load (power) doesn't change across an ideal transformer. But the power across a resistance does vary as you change the voltage.
It is definitely possible for a transformer to make an ideal voltage ... | {
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A bowling ball on an infinitely long track We knew that a after a bowling ball is threw out with a certain velocity to a non smooth track, it first rolls and skids as the translational velocity (decelerates due to friction) of the center of mass is greater than tangential velocity of the point of contact of ball with t... |
My question here is after rolling without slipping is achieve how does the translational kinetic energy and rotational kinetic energy change? How does translational kinetic energy decrease while rotational kinetic energy is increase by torque due to friction?
Once the ball is rolling without slip, it will roll foreve... | {
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Is a westward flying plane heavier than an eastward one? I understand that you weigh less at the equator due to the increased centrifugal force. From my understanding, the faster you circle the Earth, the less your effective normal force you would feel, up to the point where you are orbiting the planet and the force be... | The airplanes experience identical centrifugal forces at the equator, regardless of their flight direction.
The equation of motion in a frame fixed to the surface of the Earth is:
$$\vec F -2m\vec{\Omega}\times\vec{v}-m\vec{\Omega}\times(\vec{\Omega}\times\vec{r})=m\vec a$$
If we put that on the equator in standard Nor... | {
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It more efficient to generate heat burning electrolyzed hydrogen, or through an electric resistance? It's convenient and simple to use electricity to generate heat, doubtlessly, say in en electric kettle or boiler or heater, but is it more efficient to generate heat burning electrolyzed hydrogen, or through the resista... | According to this wikipedia article, electrolysis has an efficiency between 70-80%, so not all of the electric energy used for electrolysis would go into dissociating water molecules, but some would be lost as heat.
Therefore, the energy that can be obtained from burning the hydrogen obtained from electrolysis would be... | {
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Quantum properties of long wavelength electromagnetic radiation How could we have known that Electromagnetic radiation is quantized if we only knew about long wavelength radiation? What are the 'quantum' properties shown by long wavelength electromagnetic radiation?
| I will assume here that by "long wavelength" you mean longer than ~150 meters (i.e., in the AM radio band).
It is true that all EM radiation exists in quanta, each photon with energy E = (planck's constant x frequency). But in the AM radio regime, the energy per photon is so small that there is no experimental evidence... | {
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$\rm kph/MeV$ for Light yield? I was reading an article on Scintillation and I came across a peculiar unit $\rm kph/MeV$ for Light yield. It stated for Organic Scintillators, it has a Lower light yield (1-10 kph/MeV). Here do kph mean kilometers per hour or am I missing something? I am technically used to Photons per M... | As nobody else seems to have a better idea, I'll convert my comment into an answer.
Without seeing the "article on Scintillation" I can't really say what the writer was talking about, but one possibility is that they meant "thousands (k) of photons (ph) per MeV".
| {
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Can an ideal dipole experience an electric force? It is known that electric force a charged body is given as $\vec{F} = q \vec{E}$ given that $\vec{E}$ is uniform. Now, for an ideal dipole, what would we take as the charge for calculating the force exerted on it by an external electric field?
| You can simply use the formula you stated to compute the force on each component of the dipole separately and then you add them up to get the net force. Note that this will be zero unless the electric field varies in space.
To give more details, consider a dipole of positive charge $q$ with separation $d\,$ lying along... | {
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Rigorous proof that a net force of zero guarantees zero linear acceleration in rigid bodies I've never found a rigorous proof of this fact.
The center of mass' acceleration is not necessarily the linear acceleration, specially if the body is attached to a pin or another geometric constrain, then the center of mass spin... | I may be misinterpreting this question. But if not, then the statement is true by definition. If there is some other constraint which redirects the center-of-mass motion, such as a pin at the corner or whatever, then that constraint has by definition imparted a force. For any acceleration of the center of mass, the cor... | {
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Is a 6-quark particle viable? It is my understanding (which may be flawed) that protons and neutrons are stable because the 3 (R, G, and B) quarks form a "white" color singlet. Wouldn't 6 quarks or even 9 quarks create a white singlet? What about RGBGR?
| The deuteron (or $^{2}$H nucleus) is a color-neutral bound state of three $u$ quarks and three $d$ quarks. Because six quarks can combine to make a color-neutral state, this six-quark state is possible. However, the quarks inside are not arranged in anything like a symmetric state. They are tightly bound into two sub... | {
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"answer_id": 0
} |
Is superconductor just a perfect conductor or anything more than that? If I had a hypothetical perfect conductor having infinite conductivity and I cool it below a certain temperature, will it be a superconductor? If not, then how can we distinguish between the two using the experimental and theoretical methods?
I only... | The main difference between superconductor (SC) and perfect conductor:
In a SC the kinetic energy of every charge carrier is quantized, so a supercurrent, once established, can be dissipated only by external energy excitations stronger than the kinetic energy quantum. In a perfect conductor the kinetic energy of every ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/661726",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 3
} |
Do we have an upper bound to the size of the six hypothetical curled up dimensions in string theory? String theory requires ten (or eleven for M-theory) extra dimensions. These dimensions are not observed at large scales and so it has been hypothesised that they are curled up and invisible at larger scales. Often times... | Roughly $10^{-19}$ meters.
http://arxiv.org/abs/1012.3375 , Search for Microscopic Black Hole Signatures at the Large Hadron Collider
Mureika et al, http://arxiv.org/abs/1111.5830 , Any black holes at the LHC?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/661868",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What would have caused the Gravitational Waves in the Gravitational Wave Background? We have discovered the CMB, Cosmic Microwave Background, in 1965. It's the oldest light that we can see and it came from 3,80,000 years after the Big Bang. It has been proposed that there must be a Gravitational Wave Background (GWB) t... | It's actually the same mechanism that's ultimately responsible for the temperature fluctuations in the CMB.
Quantum fluctuations during inflation get stretched outside the horizon, and "freeze" into a classical state which we later observe as background radiation.
The CMB temperature fluctuations are thought to be fluc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/662080",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
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