Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why doesn't planet Earth expand if I accelerate upwards when standing on its surface? According to General Relativity I am being accelerated upwards by planet earth while writing this question. But a curious person on the the other side of the planet relative to me would have the same experience. That means we are acce... | Because of Earth's gravity (and rotations, but we will focus on gravity since that seems to be the point of your question) you are in an accelerated frame of reference, not an inertial one. Near the surface of Earth g is about 9.8 meters per second squared. This will make your weight be about the same on Earth as it w... | {
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "10",
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"answer_id": 4
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Why is Schrodinger equation taught while it does not describe an electron? Strictly speaking, it is "wrong" because it does not describe spin-1/2 particle like an electrons. Why in every QM textbook is it taught, not as a historical equation, but as a current equation?
|
Why is Schrodinger equation taught while it does not describe an electron?
This question is of the same order as asking:
"Why is Newtonian gravity still taught everywhere since it has been seen that General Relativity is the underlying theory of gravity" and thus should explain everything?
There are even observatio... | {
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How to calculate Water Vapor Pressure? So, we know that
$$\text{Relative Humidity(%)}=\frac{\text{Actual Water Vapor Pressure}}{\text{Saturation Vapor Pressure}}$$
Now, we can find saturation vapor pressure only from the ambient temperature [1]:
$$e_S=0.6113\text{ exp}\left(5423\left(\frac{1}{273.15-T}\right)\right)$$
... | The equation is transcribed incorrectly, it should be:
$$
e_S=0.6113 exp\left(5423\left(\frac{1}{273.15}−\frac{1}{T}\right)\right)
$$
For the record, $e_S$ in kPa, T in Kelvin.
From day to day, even at the same temperature, the relative humidity varies because the amount of water in the air varies. Therefore, as the pr... | {
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What will happen if I multiply a ket vector by a complex number? I was reading Zettili’s Quantum Mechanics book. There I have seen
when a ket (or bra) multiplied by complex number, we also get a ket (or bra)
But how do we infer this by mathematics?
| Think about this like that,- when you multiply a vector by a scalar, you just re-scale original vector. Same idea applies here to vectors in Hilbert space, aka. ket. You just re-scale Hilbert vector by a complex number, an hence get another ket in same Hilbert space.
| {
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Bernoulli Pipe Flow Equation Physical Meaning I have just been introduced to the Bernoulli Equation for fluid flow. However, I am unable to understand why the pressure and velocity are inversely proportional.
Because, as the fluid goes through a smaller cross-sectional area, the flow velocity increases, but due to the ... | As Chet Miller alluded in the comment, since a liquid element is accelerating as it approaches the bottleneck, there has to be force that is causing this acceleration. The only forces present are pressure forces from surrounding liquid, so pressure upstream has to be higher than downstream, to cause this acceleration.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/587122",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
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Is $U^\dagger(R)\hat{H}U(R)=\hat{H}$ always true? Consider a Rotation transformation on momentum state,
$$U^\dagger(R)\hat{\mathbf{p}}U(R)=R\hat{\mathbf{p}}$$
Now the question is whether,
$$U^\dagger(R)\hat{H}U(R)=\hat{H}\,?$$
Here, $\hat{H}$ is the Hamiltonian of a free particle. Is it always true? Is there any counte... | It is true in this specific case that, if $\hat H=\frac{1}{2m}\mathbf{p}^2$ is the Hamiltonian for the free particle, then $U^\dagger\hat{\mathbf{p}}^2 U=\hat{\mathbf{p}}^2$ for $U$ a rotation.
Maybe the 2d case is sufficient to illustrate the point. We have
\begin{align}
R^\dagger_z(\theta)\hat{p}_xR(\theta)&=\hat{p}... | {
"language": "en",
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Force as a function of velocity as $t$ goes to infinity, strange result Here is the question:
"A particle with mass m is given an initial velocity $v_0$ so that it moves in a straight line (you can consider it positive). It is subject only to a force that is inversely proportional to the square of
its speed, as $F = −... |
But as t goes to infinity, v approaches 0, suggesting the distance is finite, and x goes to infinity which is contradictory.
The position goes to infinity before the velocity starts decaying to zero fast.
| {
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How angles transform under Lorentz transforms - a thought experiment Lets say I have two frames, $S$ and $S'$; they are in standard configuration and $S'$ is moving with speed $v$ away from $S$. I have a pipe in $S'$, which is at angle $\theta'$ from its $x$ axis. I can calculate the angle which would be measured betwe... | The speed of light, not the velocity of light, is Lorentz-invariant.
Wikipedia discusses the relativistic aberration of light.
| {
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"source": "stackexchange",
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Why can we set $c$ and $\hbar$ to 1 when it changes the result? So in my QFT course, my professor said that you can set $c$ and $\hbar$ to 1. And he gave us an example:
$$E = mc^{2}$$
And then set $c = 1$:
$$E = m$$
This seems completely ludicrous to me to do. Doesn't it change the result? Why can this be done and why ... | It's easiest to think about this as a matter of units. What is the value of $c$? $3 \times 10^8 \mathrm{m/s}$? $6.7 \times 10^8$ miles/hour? Suppose I invented two new units, the florp (for space) and the zoob (for time). It just so happens that the speed of light in my system is exactly one florp per zoob, so you don'... | {
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Charge conjugation of fields This page on Wikipedia says, "In the language of quantum field theory, charge conjugation transforms as -
*
*$\psi \Rightarrow -i\big(\bar{\psi} \gamma ^0 \gamma ^2 \big)^T $
*$\bar{\psi} \Rightarrow -i\big(\gamma ^0 \gamma ^2 \psi \big)^T $
Could someone explain the reason behind choos... | You want to implement the symmetries as transformations on the fields (and also corresponding operators on the Hilbert-space in the QFT), i.e. transformations of the dynamical variables in your Lagrangian $\mathcal{L}(\psi, \bar{\psi},...)$. The reason is that these symmetries of the Lagrangian have important consequen... | {
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Why Mandelstam variables in Minkowski do not cover the whole allowed space? It was mentioned by N.Arkani-Hamed https://www.youtube.com/watch?v=uPrlD0vorzk that Mandelstam variables in Minkowski signature $(+---)$ do not cover that whole allowed space of $s$, $t$, whereas in some other signature, namely, $(++--)$ they d... | The Mandelstam variables $s, t,$ and $u$ are mostly used in $2 \to 2$ scattering and $1 \to 3$ decays. As for $2 \to 2$ scattering with initial momenta $p_1$ and $p_2$ and final momenta $p_3$ and $p_4$, they are defined as
$s = (p_1 + p_2)^2 = (p_3 + p_4)^2$
$t = (p_1 - p_3)^2 = (p_2 - p_4)^2$
$u = (p_1 - p_4)^2 = (p_2... | {
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How do wavelengths add-up? If I have 3 LED lights of following colors and wavengths:
Red 650 nm
Blue 450 nm
Green 550 nm
All three are placed side by side and turned ON.. then what will be the wavelength of the combined light that my eye will see? Most probably the combined color will be 'whitish' because the mixing of... | White light does not have a single wavelength but instead is described by a spectral distribution, which is not uniquely determined. There are many light compositions that can pass as white. The spectrum of the white light from the three LEDs combined is just the sum of the individual LED spectra, weighed with the prop... | {
"language": "en",
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Perturbative non-renormalizability of brane action In the second chapter of string theory book by Green-Schwarz-Witten, the advantages of string theory over others is discussed. It is stated that the higher-dimensional analogs, with the action proportional to the world-volume of a "brane" object, are not perturbatively... | The curvature has dimensions (length)^−2
, and therefore the D-dimensional
Newton constant G_D must have dimension (length)^D−2
. This is proportional
to the square of the gravitational coupling constant, which therefore has
negative mass dimension for D > 2. Ordinarily, barring some miracle, this
is an indication of n... | {
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Is the Green function of electromagnetism a scalar or a tensor? When I check classical electromagnetism books Maxwell equations
\begin{equation}
\Box A^\nu (x)=\frac{4\pi}{c}j^\nu (x)
\end{equation}
can be solved using a scalar Green function $G(x,x')$
\begin{equation}
A^\nu (x)=\int G(x,x')j^\nu (x')d^4x'
\end{equatio... | Its a tensor
$$G_{\mu\nu}(x-y)=\langle \Omega|TA_\mu(x)A_\nu(y)|\Omega\rangle=\int \frac{d^4k}{(2\pi)^4}\frac{ie^{-ik(x-y)}}{k^2+i0_+}\bigg(g^{\mu\nu}+\xi\frac{k^\mu k^\nu}{k^2+i0_+}\bigg)$$
here $\xi$ is some parameter that depends on your gauge choice, and $g^{\mu\nu}$ is metric of space-time.
What does it mean is fo... | {
"language": "en",
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Why can’t gravitons distinguish gravity and inertial acceleration? If gravitons mediate the gravitational force, couldn’t the detection of gravitons by an observer be used to distinguish whether they are experiencing gravitational acceleration vs. inertial acceleration, contradictory to general relativity? If this is n... | This second entry in answer to:
Why can’t gravitons distinguish gravity and inertial acceleration?
I have found this article "Gravitational Waves: Sources, Detectors and Searches"
which gives data (from a reference) for gravitational waves from a man made dumbbell, , given a rotation.
imagine a dumbbell consist... | {
"language": "en",
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Why don't we use the concept of axis of mass in place of center of mass? Being a high school student, I read the concept of center of mass and it was written in my book that
When a spinning ball is projected with some velocity , then all the points on the ball have complicated paths except the center of that ball whic... | Your 'axis of mass' depends on how the ball is spun, which depends on the whim of the person throwing it. So it is not a property of the ball on its own. But the centre of mass follows a parabola however the spin is aligned.
| {
"language": "en",
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"question_score": "6",
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Effect of coloured filters on white light I am concerned about the accuracy of some information in a science textbook which I would like to clarify please. When white light is shone through a blue filter, only blue light will pass through. When the emergent blue light is passed through a red filter, no light gets thro... | The results will depend on the filter transmission bandwidth. For near-ideal filters with short bandwidth (transmitting only one color and absorbing/reflecting others), virtually no light will be transmitted in any of these cases. The order of the two filters doesn't matter.
When using wide band filters, some light bet... | {
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Landau-Lifshitz Equation of Motion for Triangular Heisenberg Antiferromagnet There is a paper (PhysRevB.95.014435) in which the dispersion relation for some Heisenberg model on the honeycomb lattice is derived from the Landau-Lifshitz equation:
\begin{align}
\frac{d S_i}{dt} = - S_i \times \mathcal H_{\rm eff}
\end{al... | I see two possible problems in your consideration.
*
*You've investigated perturbations of ferromagnetic ground state. When spin variations $\delta m$ are zeros, spins on three sublattices are the same:
$$
S_i = (0, 0, 1),\quad \forall i.
$$
*The Landau-Lifshitz equation is a nonlinear one. Effective field ${\cal H... | {
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Why don't photons interfere/interact with one another, as common mechanical waves would? After all, they are a (self-sustaining) perturbation of the same field, like sound waves or water waves are "energy flow" (except these ones experience dissipation).
And how can our eyes be so clever to perfectly sort and recognize... | Photons are particles and not to be confused with electromagnetic waves or wave packages. They do not interfere. EM waves do interfere. The EM interference pattern, more precisely$^*$ the value of $E^2$ at a position, gives the probability to detect a photon at that position.
$^*$ This assumes the photon is detected by... | {
"language": "en",
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Confused about SM neutrinos I am a bit confused about neutrinos in the standard model. The vertex of the weak interaction charged current, implies that any neutrino interacting through the charged current must be left handed. However the neutral current allows coupling to the right handed particles, too (and we see tha... | *
*Short answer: vanishing weak hypercharge.
Unlike the charged leptons, neutrinos are electrically neutral, so for the weak isospin singlet neutrinos, $Y_W= 2 ( Q-T_3)=0$.
This means that right-handed neutrinos don't couple to the $W_3$, nor the $B$ gauge fields, hence neither to γ nor the Ζ, the physical Weinberg ... | {
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What does it mean by exchange of matter?
What does it mean by exchange of matter and energy means here?
| Consider a simple example of the Human body. You, like all living things, are an open system, meaning that you exchange both matter and energy with your environment. For instance, you take in chemical energy in the form of food, and do work on your surroundings in the form of moving, talking, walking, and breathing.
In... | {
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Why does a capacitor act as a frequency filter? What is it about a capacitor which allows it to filter frequencies?
I understand the construction of a high-pass RC filter, and the mathematics behind it, but I'm struggling to find an explanation of the physics behind the phenomenon.
In my mind I can picture the broad sp... | Picture a parallel plate capacitor made of perfect electrical conductor, separated by a perfect insulator. Clearly if you hook up a DC voltage source to either side of this no current will flow, because it's an open circuit. There will, however, be a voltage across the plates, which is exactly the voltage of the source... | {
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Why is the electrostatic force felt in straight lines? When two positive charges are kept close, they get repelled in the direction of a line joining both the charges. Why is it so?
Also, why is the repulsion in a straight path?
In both the cases, the potential energy of the charge which gets repelled decreases. What... | Maxwell's equations (along with the Lorentz force law) tell us that the force between two charges is radial (along the line connecting the charges).
You can also appeal to symmetry, which is related to R.W. Bird's point about conservation of angular momentum. Unless the charges have an inherent "orientation" associated... | {
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Proof that the Einstein Tensor is the Contraction of the Double Dual of Riemann How can one prove that the Einstein tensor (as it is usually defined in the field equations) is the contraction of the double of the Riemann curvature tensor?
Specifically, I want to show
$$
R^\mu_\nu-G^\mu_\nu = \dfrac{1}{2}R\delta^{\mu}_{... | I may as well convert my comment to an answer. The $\mu=\nu$ calculation is actually a contraction over all cases, not just the case not satisfying $\mu\ne\nu$. Since the latter obtains $0$, $R^\mu_\nu-G^\mu_\nu=A\delta^\mu_\nu$ in general iff $R^\mu_\mu-G^\mu_\mu=4A$.
| {
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Does mass really exist? In elementary physics, I have learned mass as the amount of matter (naively) and energy as the ability to do work. Now we know that they interchangeable by famous Einstein's equation:
$$E=mc^2$$
It seems from here that they are interchangeable, but then I watched this video, which says, in a nut... | The $m$ in the equation $E=mc^2$ is the rest mass and should be written as $m_0$.
$E$ is also equal to $h\nu$ where $\nu$ is the frequency. So $m_0c^2 = h\nu$.
This implies that the rest mass $m_0 = \frac{h}{c^2}\nu$.
The mass of an object at rest is proportional to frequency. We can think of mass as a vibration, even... | {
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Properties of the dot product Suppose we have three vectors $\textbf{A}$, $\textbf{B}$ and $\textbf{C}$. If $\textbf{A}\cdot\textbf{C}=\textbf{B}\cdot\textbf{C}$, does that mean that $\textbf{A}$ must be equal to $\textbf{B}$? If so, can this property be proven?
Though the question is mainly mathematical, it has occurr... | Here is a proof. If $\mathbf{A}\cdot\mathbf{C} =\mathbf{B}\cdot\mathbf{C}$ for all $\mathbf{C}$, then $(\mathbf{A}-\mathbf{B})\cdot\mathbf{C} = 0$ for all $\mathbf{C}$. In particular we can choose $\mathbf{C} = \mathbf{A}-\mathbf{B}$ so that $(\mathbf{A}-\mathbf{B})\cdot(\mathbf{A}-\mathbf{B})=0$. Since the dot product... | {
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On measuring velocity of light in Vacuum While watching YouTube, I came across the following popular video:
Why no one has measured the speed of light
It appears to say that speed of light could depend on direction it is traveling and we would never know.
I was under the impression that the Michelson-Morley experiment ... | The objection raised in the video is that fundamental measurements of the speed of light are based on a round trip and assume that the speed of light is the same in both directions. This would be a reasonable objection if the speed of light had only been measured on one occasion in one direction at one location.
But, a... | {
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Can someone explain the measurement problem with little bit of mathematics? Can someone mathematize the statement of the quantum measurement problem? I am only interested in the statement of the problem (and not its solutions). Thanks.
Still confused. Stated in this way (as in the current answers), the measurement pro... | When you measure observable $O$, which has eigenfunctions $\psi_i$, how does a wavefunction, say $\sum_ic_i\psi_i$, which is a superposition of multiple eigenfunctions before the measurement, become a single eigenfunction, say $\psi_n$, after the measurement?
| {
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Why does power increase as a constant force accelerates a body? If a constant force is being applied to a body, without any other external forces, F = ma says that that body will accelerate at a constant rate. This acceleration will continuously increase the body's velocity.
According to P = Fv, since the force is cons... | Suppose you are pushing a box on a surface and want to apply a constant force, F. As you point out, the box will accelerate. But as its speed increases, you have to run faster in order to continue supplying the same force F. You must use more energy per unit time (power) in order to keep the force at F. So the answer t... | {
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Can there be waves in different fields? I am a physics fan, but I am not a physicist. I don't even know that the question I have asked make sense or not.
There can be waves in the gravitational field. So I would like to know if there can be waves in other types of fields, such as electromagnetic field, Higgs field etc.... | In the electromagnetic field there are photons or light which is a wave. In the Higgs field a Higgs boson can be considered to be an oscillation of the Higgs field (a wave hovering above the ground state of this field). All quantum fields (electron, quark etc) have particles associated with this field and as such these... | {
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Superconductivity resistance I'm confused about the resistance of superconductors. It is known that the resistance at the the critical temperature goes exactly to zero (the resistance is not very small, its really zero, right?). But in a superconducting state, not all electrons form Cooper pairs right? so why then is t... | It is absolutely true that the resistance of a superconductor goes to zero at at absolute zero, but just below the critical temperature, most of the conduction electrons are still in the normal state. The current density has two parts: J=...A+...E, the coefficients being proportional to the numbers of electrons in th... | {
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They say the universe is expanding. Is that the same as saying that time is contracting? Apparently the distance between galaxies used to be smaller in the distant past. That means it used to take fewer units of time to get from one galaxy to the next. So either the distance really was smaller in the past or the unit... | 1-3 are all true.
*
*If you use the most common cosmological coordinates, in which position is scaled by a factor $a(t)$ that increases with time, then the coordinate distance between galaxies is constant but the measured distance increases because of the scaling.
*If you use conformal coordinates, in which both po... | {
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Solving expectation value of product of position and momentum I have already worked out the expectation value of the the product in the opposite order $\langle x\,p_x\rangle$. I'm now trying to work out the expectation value $\langle p_x \, x\rangle$. I've been trying to work it out from
$$
\int \psi^* \left( -i\hbar\,... | Is that * by the expectaion value meant to be an equals sign? If so I think you are trying to obtain the commutator of the position and momentum operator, not the expectation value. That given answer definitely isn't correct but the commutator given by the square brackets:
$[A,B] = AB-BA$
$[x,p_x]\psi = -[p_x, x]\psi =... | {
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How is the non-local nature of quantum entanglement explained? From what I understand, Einstein tried to introduce real but hidden variables to remove the apparent non-local nature of quantum entanglement, but Bell's inequality showed local realism isn't possible.
I have read physicists believe in locality than hidden ... | Quantum mechanics is local, in the sense that it doesn't allow for superluminal interactions. This does not contradict results such as Bell inequalities or anything allowed by entanglement.
The point is that quantum mechanics allows for correlations that cannot be explained by any local classical theory. But at the sam... | {
"language": "en",
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Can the universe be considered a thermodynamic system? With matter a type of energy, can/should the universe be considered a thermodynamic system? At what scale would it be relevant?
| It is the nature of understanding the cosmology of the observable universe that we assume as an axiom, regarding a cosmological model, that at a large scale it is homogeneous. It is impossible to know what is actually going on in that part of the universe which is not part of our observable universe. However, this fact... | {
"language": "en",
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"source": "stackexchange",
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Conserved quantities quantum field theory In classical field theory, due to Noether's theorem, corresponding to every continuous symmetry there is a conserved current/charge. However, to arrive at this conclusion one has to assume that the Euler-Lagrange EoM holds,
$$\partial_\mu\frac{\partial\mathcal{L}}{\partial \lef... | The simplest possible Lorentz-invariant equation of motion for a field is $\Box \phi = 0$. The classical solutions are plane waves. For example a solution is $\phi(x) = a_p(t) e^{i \vec p \cdot \vec x}$, which is the equation of motion of a harmonic oscillator.
A general solution is
$\phi(x, t) = \int \frac{d^3 p}{(2 \... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Query in inner product axioms in QM In inner product spaces in $\mathbb R$ we have an axiom stating that:
$$ \langle x, x\rangle \geq 0\ \ \text{and} \ \ \langle x, x\rangle = 0 \iff x = 0$$
In Griffiths' textbook for Quantum Mechanics, they have stated that,
$$ \langle\alpha|\alpha\rangle \geq 0\ \ \text{and} \ \ ... | $|\alpha\rangle$ is a state, not a number. The rules of inner product state that
$$
\langle \beta |\alpha \rangle \in {\mathbb C} , \qquad \langle \beta |\alpha \rangle^* = \langle \alpha |\beta \rangle.
$$
It follows that
$$
\langle \alpha |\alpha \rangle^* = \langle \alpha | \alpha \rangle \quad \implies \quad \langl... | {
"language": "en",
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Destructive interference Take the most simple academic example for interference. Since it is not any real experiment, one can have shocking contradictions.
For example: 2 monochromatic plane waves with (parallel) amplitudes propagating in the same direction. The Poynting vectors of the 2 waves without superposition are... | I do not think "energy flow" is a well defined variable for electromagnetic waves.
The single photon at a time double slit experiment, shows that the energy from the dark lines has gone to the bright ones
*
*Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to... | {
"language": "en",
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Is the Hamiltonian an Observable? From the book Quantum Mechanics by Cohen-Tannoudji it seems that the only requirement for an Operator to be an Observable is to form an orthonormal basis in the state space (finite or infinite dimensional)
"By definition, the Hermitian operator $A$ is an observable if this orthonormal... | Eigenvalues of $H$ are the energy states of the system, so in order to have a real value for the energy $H$ has to be hermitian and so an observable. Also the hamiltonian operator is based on the momentum operator that is hermitian too. You can try to write the integral form of $\langle \psi|H|\psi\rangle $ and $\langl... | {
"language": "en",
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Problem with the proof that for every timelike vector there exists an inertial coordinate system in which its spatial coordinates are zero I am reading lecture notes on special relativity and I have a problem with the proof of the following proposition.
Proposition. If $X$ is timelike, then there exists an inertial coo... | Actually, your matrix can be greatly simplified as
$$
M =
\begin{bmatrix}
\frac{1}{\sqrt{a^2 - p^2}} a & \frac{p}{\sqrt{a^2 - p^2}} & 0 & 0 \\
\frac{p}{\sqrt{a^2 - p^2}} & \frac{a}{\sqrt{a^2 - p^2}} & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{bmatrix}
$$
since $(\mathbf{e}, \mathbf{q}, \mathbf{r})$ forms an ortho... | {
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"source": "stackexchange",
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Why thin metal foil does not break like a metal stick? Consider a metal stick, say iron or aluminum. From the experience, even if it's resilient, bend it forward and backward a couple of times, it would be broken.
However, consider a thin iron foil or thin aluminum foil. From the experience, we know that it could be be... | Let me use just a simple geometrical reason.
You can in principle bend a monodimensional row of bound particles to a wide angle affecting only the angle of the bond at about the pivotal point.
Conversely, if you bent a 2-D ensemble of particles (variously bound, it can be multiple rows as above slightly interacting or ... | {
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"source": "stackexchange",
"question_score": "18",
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Planck distribution integration Does anyone know how to compute analytically or numerically the following integral (for $T=10^4$K)?:
$$n_\gamma=\frac{1}{\hbar^3\pi^2c^3}\int\limits_{2.1789\cdot 10^{-18}}^{+\infty}\dfrac{E^2\mathrm{d}E}{e^{\frac{E}{kT}}-1}$$
I tried with R, MATLAB, Maxima, Maple and Wolfram but I failed... | Sometimes, one just need to do a little work before the analytic software can handle the integration. Here is a suggestion. First write it in the form:
$$ \frac{A}{\exp(Bx)-1}=\frac{A\exp(-Bx)}{1-\exp(-Bx)} . $$
Then expand the denominator
$$ \frac{A\exp(-Bx)}{1-\exp(-Bx)} = A\exp(-Bx)\sum_n \exp(-nBx) . $$
Now you (or... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/593174",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is $E=0$ included in the energy spectrum of the free particle in 1d? In finding the eigenfunctions, $\psi_E$'s, of the free-particle Hamiltonian in 1d,
$$
H = -\frac{\hbar^2}{2m}\frac{d^2}{dx^2},
$$
with eigenvalues $E$'s, subject to the conditions that they are bounded, one finds that corresponding to each energy $E>0... | This question has an immediate answer - yes, because the spectrum of any operator is always closed. This follows from the fact that the resolvent set $\rho_A$ of an operator $A$ is always open, and that the spectrum $\sigma_A=\mathbb C \setminus \rho_A$ by definition.
Note that the delta function can be expressed as
$... | {
"language": "en",
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Can we use Heisenberg Uncertainty Principle to prove that time travel to past is impossible? Suppose the case that someone in future makes a time machine which can be used to time travel in past. Now s/he can accurately measure momentum of a particle without caring about the particle's position at that time and then s/... | That is a beautiful idea. And I believe it is true. If time travel were possible, you could measure (for each) particle observable A and remember which ones lead to what result. Then travel back and do the same for observable B. Then travel back again and you remove the particles from the ensemble based on your knowled... | {
"language": "en",
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"source": "stackexchange",
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Maximum horizontal distance of a freefalling ball with one allowed bounce anywhere along its initial path? I was washing a spoon in the sink and this question popped into my mind:
If a ball is dropped from height H and is allowed a single deflection of any angle $0 < \theta < 180$ at any height $ 0 \leq H' \leq H$, wha... | This document gives an equation for finding the maximum range $R$ of a simple projectile given an initial height from the ground $h$ and velocity $v$:
R = sqrt((2v^2)/g * (h + v^2/(2g)))))
From conservation of energy, we know the velocity $v$ for $H$ and $h$:
v = sqrt(2 * H' * g).
The bigger H', the higher its velocity... | {
"language": "en",
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Two Cylinders on Ramp Suppose I have two cylinders: a light one and a heavy one. Now, I let the cylinders roll down a ramp without slipping. My question is, which one will get to the bottom of the ramp first, and why?
| Let's take a look at the net force for a cylinder on an inclined plane:
$$ \Sigma F_{\parallel} = mg\sin{\theta} - f\tag{1}$$ where $f$ is force of friction.
Now the torque about the COM (which is the point about which there is rotation) is:
$$\Sigma \tau = Rf \tag{2}$$
where $R$ is the radius of the cylinder. By Newto... | {
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What is Mach number = 0? If you look at a paper on fluid dynamics, you will see a paper that is performing CFD simulation with a mach number of 0. This means that the flow velocity is 0, so I thought that no flow would occur, but when I looked at the results, the flow existed and emitted vortices. What does mach number... | Often when fluid mechanicians refer to zero-Mach flows, the implication is not that the flow velocity is zero but that the speed of sound is infinitely large.
This usually implies that acoustic disturbances and other transient physical phenomena related to compressibility propagate away from their sources infinitely fa... | {
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Are we gaining or losing time as our planet revolves around the Sun? I understand that the Earth (or someone standing on our planet) will undergo time dilation due to a number of reasons compared with someone hovering in interstellar space. I would like to focus on two of those causes. One the time dilation due to the ... | Yes, this is a fairly routine calculation, e.g. using the open source Black Hole Perturbation Toolkit. (Using a nuke to shoot a mosquito here.)
Taking into account the the orbital parameters for the Earth-Sun system, we loose about $0.47$ seconds each orbit due to time dilation, due to the gravitational potential of th... | {
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Energy bond and number of photons If I am given the energy bond of a specific bond in a molecule, is that the energy of one photon? and if I have, for example 2 bonds like this, there will be needed 2 photons, etc...? (In other words- does each photon required to break one bond)?
Thank you very much
| Good question, but no, it is not like that. One should not regard the chemical notation literally. In the nitrogen molecule N$_2$, there is a covalent bond between the atoms. One should not regard the three sticks in the diagram as sticks that could be broken seperately. Without going into details, the molecular orbita... | {
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Why is the tension on both sides of an Atwood machine identical?
The field forces $F_{g1}$ and $F_{g2}$ push down on Block 1 and Block 2, respectivley, where
$$F_{g1}=m_1g$$$$F_{g2}=m_2g$$
Since the pully system reverses the direction of each force, wouldn't the following be true?
$$T_1 = F_{g2} = m_2g$$$$T_2 = F_{g1}... |
how could the same force T accelerate both of them an equal amount?
This part of your question holds the key - specifically the word acceleration.
Lets start with your second question first: Why are the accelerations the same?
This is a result of the constraint that the string is a fixed length. As long as this is t... | {
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Will a rods edge rotate if a small force acts for a small ammount of time in the one edge and the information have not reached the other edge yet? So assume we have a rod capable of rotating at its center of mass. Now we apply a force at its right edge for a very short time. Let's assume also that by the time we stop a... | The information is actually a slight bending of the rod that travels in a wave from one end to the other. Imagine the rod is made out of soft rubber and you give one end a whack and watch the slow motion replay. At first only the end you hit will compress and bounce away, and the rod will start to bend, while the end... | {
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What do photons look like? We have many theories that advocate the particle nature of light. But have we ever observed photons physically?
If so: what do they look like? How big are they?
If not: why not? Is it because they move at the speed of light?
| Frame challenge:
Everything we see looks like photons... because photons are what our eyes are sensitive to. Our eyes are impressively good not only at detecting photons, but at sorting the photons by energy and direction as well. This is how we get colors and shapes.
Outside of this, "photon" is just a model for a pre... | {
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Does local mean infinitesimally small? I have studied General Relativity and there is one thing that I have trouble comprehending.
What does local really mean? I will give some examples:
The Hessian
The Hessian is a way to compute the local curvature of a function. What does local mean in this case? At a small area tha... | If you want a more sort of geometrical way of figuring out what "local" means, you can always compute the fermi normal coordinates for a point:
https://en.wikipedia.org/wiki/Fermi_coordinates
The key point here is that this coordinate system, for a given point, makes the metric tensor at that point equal to the minkow... | {
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We know a human cannot run on water, but could a much stronger and faster animal? We know a human cannot run on water, but could a much stronger and faster animal?
This viral video shows a moose running across a body of water:
https://www.youtube.com/watch?v=K5-0d00hV1c
Some say the video is fake. Others think the wat... | Yes, some human sized animals can run for a few seconds over water - but not humans nor moose.
As other answers pointed out, the animal would need fins and a large power output - that is, large muscles arranged in a way that a large part of its power can be directed to efficiently move the fins.
Dolphins have both, and... | {
"language": "en",
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Filling order in the Shell Model of the nucleus I have read that, in the nuclear shell model, nucleons are distributed filling energy levels following the Pauli exclusion principle. These energy levels can be designed with the $nl_j$ notation: $1s_{1/2},1p_{3/2},1p_{1/2}, 1d_{5/2},...$
I have two questions in relation ... | Protons and neutrons fill different levels. On the one hand they are distinct fermions and on the other they evolve in a slightly different average potential because of the residual electromagnetic interaction.
There is no obvious mnemonic device. In fact it depends a bit on how one models the nuclear potential. Ph... | {
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Lift on Airplane wing Why commercial airplanes use long, slender wings? Isn't it to maximize lift, we make the plane's wings as wide as possible?
| They need a particular amount of wing area, in order to get the desired amount of wing loading (weight per unit of area) at the speed they want to fly.
Then, drag is minimized if the aspect ratio (ratio of wing length to wing width) is maximized. So at a given area, they want long narrow wings.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/595540",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Redshift time relation I was reading that the relation
$dt=\frac{dz}{H(z)(1+z)} $
between time and redshift (H is the Hubble constant) holds.
I don't understand this. I thought the relation between time and redshift is
$z=H(t-t_0)\Rightarrow dz=H dt$
What am I doing wrong?
| $$dt = \frac{dt}{da}da \frac{a}{a}$$
and we know that $1/a = 1+z$ and $da = -(1+z)^{-2}dz$ and $\frac{da/dt}{a} = H_0E(z)$
so we obtain
$$dt = \frac{1}{H_0E(z)} \times \frac{-dz}{(1+z)^2}\times(1+z)$$
$$dt = -\frac{dz}{(1+z)H_0E(z)} \equiv -\frac{dz}{(1+z)H(z)} $$
| {
"language": "en",
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Why does lightning strike lightning rods sometimes? I watched some videos and read a lot of posts mentioned that pointy shaped objects create denser electric field than other objects (especially spherical ones), that's why people use pointy and conductive metals to make lightning rods. As the clouds started to gather c... | A positive cloud overhead will attract electrons and cause a significant build up of negative charge in the ground (or water) below it. A high, sharp, well grounded rod can bleed this induced charge into the air, reducing the field between cloud and ground, and reducing the probability of a strike. I'm not sure that t... | {
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"To come back to Earth...it can be five times the force of gravity" - video editor's mistake? I've watched The Truth About Gravity With Professor Jim Al-Khalili | Gravity And Me | Spark where astronaut Chris Hadfield says at 3:55:
To come back to Earth is violent
Then after several seconds of music and video of desce... | This is the "braking acceleration" from atmospheric resistance that slows down the descent. The capsule is specifically shaped to provide sufficient but not too great deceleration. See the article Returning from Space: Re-Entry on the web.
| {
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"source": "stackexchange",
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What are matter waves made of and what is their speed? We know electromagnetic waves are made of oscillating electric and magnetic fields that can travel at the speed of light without a need for a medium. But, how about matter waves proposed by de Broglie? What are they made of? What is their speed? Do they need a med... | E-M waves are not "made" of anything other than the current state of various fields. Matter waves are similarly not "made" of anything; they simply represent the wavelike behavior of things we treat as solid mass, e.g. electrons. The whole point of wave-particle duality is that you cannot separate one from the other.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/596185",
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Mössbauer effect to verify the gravitational redshift
"The tower used by Pound and Rebka in 1960 to exploit the Mossbauer effect is only about h = 20 meters high, and so the effect (gravitational redshift) is only $(GM/(Rc^2))(h/R) ∼ 10−15$! How would one of do the experiment?”
This question was asked in the middle o... | In an experiment like the one you're wondering about, typically the crystal would be moved back and forth in a sinusoidal fashion. When the crystal moves at a speed that Doppler shifts the incoming radiation to the resonant frequency, the crystal will absorb the incoming radiation. Timing of the detected signal relat... | {
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Why is a wave packet normalizable? I'm doing some reading in Zettili's quantum mechanics book and came across this passage:
Now the thing I'm left dumbfounded on is why it can be considered normalizable? I tried finding some explanation in the book but that didn't yield anything other than some vague verbal argument f... | Non-normalizable wave functions probably have no physical significance. The reason is that the square of amplitude of the wave function should give you the probability of the existence of that particle (scaled to a factor $c$ ). The sum of all these probabilities should go to $c$. So if there is no constant factor ($c=... | {
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"timestamp": "2023-03-29T00:00:00",
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Writing a simple sum with einstein notation Is there any shorthand using the Einstein notation to write a simple sum?
$X = X_1 + X_2 + X_3 ....$
Can I write: $X = X_i$ ?
I don't think so because the definition states that only indices that appear twice is summed over. What is the correct way to write a simple sum like ... | Such a sum is, as far as I know, not easily expressible in Einstein notation - you could probably write it in a convoluted way, but that would not really be simpler or easier to understand than $X = \sum_i X_i$.
The summation convention is not a shorthand for any sum, but only for certain kinds of sums which arise in l... | {
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Are Van Der Waals Forces related to the Van der Waals Equation? In a physics class, I learned about Van Der Waals forces that allow geckos to stick.
*
*Do they have any relation to the Van Der Waals Equation relating gas pressure to temperature and volume?
| The connection is simply this... Van der Waals postulated that there were attractive forces between gas molecules even when these weren't in contact. The $a/V^2$ term in his gas equation is a simple way to take account of such forces, without knowing how they vary with separation between molecules, beyond their being s... | {
"language": "en",
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"source": "stackexchange",
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Transforming a Left-Handed Spinor into a Right-Handed Spinor In pg. 125-126 of Symmetry and the Standard Model book, it was stated that for a spinor $\psi_L$ in the left-handed representation and a spinor $\psi_R$ in the right-handed representation, we can define
$$\overline\psi_L=i\sigma_2{\psi_L}^*\tag{3.253}$$
$$\ov... | OP has a point: What Ref. 1 meant to say is that one can go between the left & right Weyl spinor representations (i.e. complex conjugate representations) by using$^1$
$$\psi_R~=~f i\sigma_2\psi_L^{\ast}\qquad\Leftrightarrow\qquad\psi_L~=~f (-i\sigma_2)\psi_R^{\ast}, $$
where $f$ is a phase factor that Ref. 1 chooses to... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Proof 4-current is indeed a 4-vector for a system of particles Suppose we have a system of particles with positions $\textbf{x}_k(t)$ and charges $e_k$.
We define its charge density as
\begin{equation}
\rho(\textbf{x},t) = \sum_k e_k \delta^3(\textbf{x}-\textbf{x}_k(t))
\end{equation}
And current density as
\begin{equa... | $\rho dV = dq$
$dq dx^{i} = \rho dV dx^{i} = \rho d^{4}x \frac{dx^{i}}{dt}$
In L.H.S. $dq$ is invariant and $dx^{i}$ is a 4- vector hence R.H.S. should be a 4-vector too but we know $d^{4}x$ is invariant. Hence $\rho \frac{dx^{i}}{dt}$ is a 4-vector which is a 4-current.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Hubble expansion rate and reaction rates In terms of early universe cosmology I often stumble over sentences like:
We assume that, at sufficiently early times, reaction rates for
particle interactions are much faster than the expansion rate, so
that the cosmic fluid is in thermal equilibrium.
The quote is from the ... | This is a question that puzzled me once. This is simply a misleading statement. For now, a more satisfying one would be:
Once the interaction rate drop to $\Gamma\approx H$, the neutrino, for instance, is expected to have less than one scattering until the end of time($t\rightarrow\infty$). Namely, calculate this:
$$N=... | {
"language": "en",
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"source": "stackexchange",
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Gravity inside a massive sphere with varying density There are 2 spheres. 1 is massive and the density linearly decreases, with each shell of the sphere of equal thickness having the same mass.
Density at any Radius*Volume of Layer with constant width=Constant Mass
Additionally, there is a second sphere, this time holl... | An equivalent of Gauss's law applies to spheres of mass. The acceleration of gravity at any radius inside of your first sphere depends only on the mass which is inside of that radius. All of that included mass can be treated like a point mass located at the center of the sphere.
| {
"language": "en",
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Why do we bend little forward for rising from Chair? How does torque arises when not bending forward and how does it gets cancelled while bending little forward? Please give me a video explanation or figurative explaination if possible.
| When you are sitting in a chair, any movement left or right will generate a torque which will cause the chair to spin. But if you tilt your body forward, you move your centre of mass away from the chair’s axis of rotation. Because of conservation of angular momentum, this will cause the chair to stop spinning rather qu... | {
"language": "en",
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What is the meaning of size in celestial bodies? I read about a star collapsed to a size of 12 km. Does the size mean that the new radius is 12 km or the diameter of the star
| It really depends on the context. In this case, it's probably the radius, since that's what we tend to use in equations. Eg, in Newtonian physics, the gravitational force between 2 bodies depends on the centre to centre distance:
$$F=\frac{Gm_1m_2}{r^2}$$
and so the gravitational acceleration on the surface of a planet... | {
"language": "en",
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Is the present (total) pressure in the universe negative? I read from cosmological books that the pressure associated with the dark energy component, which is responsible for the accelerating expansion of the universe, is negative. Is the total pressure of the universe negative as well? If yes, is there any mathematica... |
Is the present pressure in the universe negative?
Yes. In the current standard model of cosmology, known as Lambda-Cold Dark Matter, there are three contributions to the energy-momentum tensor $T^{\mu\nu}$ on the right side of Einstein's field equations: radiation, matter, and dark energy.
Radiation has pressure, but... | {
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Why $\psi(x)$ needs to be square integrable? The question might be due to some incompleteness. A state vector ket, $|\psi\rangle$ can be expanded in terms of position basis as,
$$|\psi\rangle = \int |x\rangle \langle x|\psi\rangle dx$$
Now if I multiplied a bra $\langle \psi|$ and say that the inner product is one I.e.... | The modulus squared of a wave function has the interpretation of probability density, which is why it should integrate to unity. There are however situations where one chooses different normalization: integrating it to the total number of particles (in the context of superconductivity/superfluidity/quantum Hall effect)... | {
"language": "en",
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Formula for centripetal acceleration: simple proof that does not use calculus? I teach physics to 16-year-old students who do not know calculus and the derivates. When I explain the formula for centripetal acceleration in circular uniform motion, I use this picture:
Here,
$$\vec{a}_{\text{av}}=\frac{\Delta \vec{v}}{\D... | Here's an attempt.
First for the magnitude $|\vec{a}|$: use dimensional analysis. For uniform circular motion the only independent quantities are $|\vec{v}|,m,r$. Therefore we must have $|\vec{a}|=C |\vec{v}|^2/r$ for some constant $C$.
For the direction of the acceleration vector: you can take $\vec{a}$ and project to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/599701",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Confusion about Joule expansion for ideal gases We concern the Joule expansion for ideal gases, where the gas is initially kept in one side of the container and the other side is evacuated. Then the partition between the two side is released, letting the gas fill the whole container.
This Wikipedia article argues that ... | The ideal gas is the whole system. The void on the initial state contains no energy, since it's void.
I think of the Joule expansion as a "proof" that the internal energy of an ideal gas is a function of its temperature. Internal energy $U$ does not vary since there is no heat $Q$ coming out or into the system and ther... | {
"language": "en",
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Why is it impossible to measure position and momentum at the same time with arbitrary precision? I'm aware of the uncertainty principle that doesn't allow $\Delta x$ and $\Delta p$ to be both arbitrarily close to zero. I understand this by looking at the wave function and seeing that if one is sharply peeked its fourie... | The correct form of the uncertainty principle is that the product of delta x and delta p is always greater than or equal to (hbar)/2. Among other things, this means that the more precisely we know x, the less precisely we can know p.
This has nothing to do with the so-called observer effect; it has to do with the wave-... | {
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Can I apply first law of thermodynamics on atoms? I am sorry if this question is dumb but can we apply the first law of thermodynamics directly on atoms?
I've say an ion and I'm adding an electron to it, can I write anything like
$$d U=d Q-d W$$
to this process,which is related to the first law of thermodynamics?
| I agree with @anna v answer.
To illustrate that thermodynamics applies to "statistical ensembles" consider the property of temperature, $T$.
The kinetic temperature of a substance is a measure of the average translational kinetic energy molecules of that substance. The speed, and thus kinetic energy, of individual mole... | {
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Please explain the meaning of below statement Newtons second law is a local law.
(In the book,it says that it means that it applies to a particle at a particular instant without taking into consideration any history of the particle or its motion.)
Um, I couldn't understand what do they mean by " taking into considerati... | it means that "it" does not care what the particle was doing before the incident. For example, it does not matter if the particle was part of another object, it was moving freely or was large or smaller before the incident.
| {
"language": "en",
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Intuition for energy I was wondering how one might intuitively think of energy, especially in a 'compare and contrast' relationship with force. I tried to think of force as the rate of change of momentum, but was unable to think of a solid intuition for energy in particular. I'm just in high school so I will probably n... | When I was in high school and I asked this question to my professor, he answered me something like "energy is just a quantity which has the nice property to be conserved", that's it. Maybe it is a little abstract, but I think it is a good way to think about it. And when you will go a little further in physics and learn... | {
"language": "en",
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Is there an accepted Lagrangian for the transport equation? Perhaps because it is so simple, I have not seen a lagrangian form of the transport equation
$$(\partial_t + a \partial_x)q = 0.$$
This equation is first order, which makes obtaining it from the Euler-Lagrange equation a bit tricky.
It would appear that the la... | OP considers the equation of motion (EOM)$^1$
$$(\partial_t + a \partial_x)\psi(x,t)~\approx~0\tag{1}$$
*
*By a linear coordinate transformation in spacetime we may assume$^2$ w.l.o.g. that $\partial_t + a \partial_x$ is $\partial_t$. This is a reminiscence of Aristotelian mechanics (AM), cf. this Phys.SE post.
OP i... | {
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Question about total energy of ejected electrons? We know total energy of a body is the sum of total kinetic energy + potential energy.
What I learned from atomic electromagnetic theory of light is that kinetic energy of ejected electrons = Hf - W(Work function ).
My question is , then what about the electrostatic pote... |
what about the electrostatic potential energy which happened when the electron got separated from the atom?
That's what the work function is.
If you consider a single atom then to eject an electron you have to supply an energy equal to the energy of the highest energy electron. For example in a hydrogen atom the high... | {
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Equilibrium of rotating bodies - non-balancing vertical forces? I am slightly confused about this problem.
We have a $6$ kg non-uniform rod $MN$ which is pivoted about $M$. There is a force of $40$ N applied at $N$ at an angle to the rod.
The rod is said to be in equilibrium as a result of the $40$N force.
However, my ... | The hinge at M provides a force of constraint. For equilibrium, the net torque about point M is zero (the force of constraint at M provides no torque about M); so you can calculate the center of mass distance along MN for equilibrium (the rod MN is not uniform). The force at M is as required to counter the net force f... | {
"language": "en",
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PN junction basics: why is there diffusion to create depletion initially? I consider two doping N and P materials.
N and P are neutral, but N is composed of impurities that increase the number of free electron. P is composed of impurities that increase the number of holes.
When we put N and P together, what is said is ... | If your junction is at a temperature $T>0 K$ how certainly it will be because of the third principle of tdm, then the free electrons in the N doped region are moving randomly inside the semiconductor; the same is true for the holes in the P doped region. When you join the two regions, there will be some free electrons... | {
"language": "en",
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Net Coulomb Force on a charge in a system Suppose that there are $n$ charges each at rest and positioned at the vertices of an $n$-sided regular polygon with side length $l$. Each charge has a magnitude of $q$ $C$.
Can a general formula be derived which gives the net Coulomb force on any charge $q$ in an $n$-sided reg... | You can achieve it by a few steps:
*
*let's try to find the force on one of the charges $q_o$
*assume the n-sided regular polygon is positioned such that the force on it has only x component.
*find the side and angles of a n-sided regular polygon (see here https://en.wikipedia.org/wiki/Regular_polygon)
*sum all th... | {
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Is this a new derivation of Lorentz transformations? Let L be a Lorentz transformation in one dimension of space and one of time. Let V and W be the two world lines of light traveling in the positive and negative directions. Then V and W are eigenspaces of L (constancy of speed of light). If F is the linear map ta... | Sorry for reading too quickly. That derivation looks fine, but it's not what I would really call particularly new. Your derivation centers on several assumptions:
*
*Lorentz transformations are linear, so they can be represented by matrices
*The speed of light is the same in both directions, and the inverse of a b... | {
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On what things can two observers agree or disagree? This question was inspired from the fact whether a moving body can become a blackhole in a frame of reference. On looking it up here, I found the answer was that its not possible since it violates priciple of relativity as you can be in a frame where the black hole wa... | (i)Why does that violate the principle of relativity? Which law is violated?
(2) On what can observers actually agree and what decides that (i.e what quantities are invariant and what decides that)?
I try to answer both of the questions at once. The observers will always agree on $ds^2$ both in special and general rela... | {
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Why some alpha particle tracks shows curvature *without* applied magnetic field? For the past few months I have been observing alpha tracks with my homemade expansion cloud chamber assembly, trying to replicate early achievements in particle physics using modern, low-cost materials. I've seen some interesting stuffs bu... | The straight lines are visible because of continuous small angle scatters of the alpha particle with the electrons of the medium .
The original forked scatter is on a nucleus, the apparent curve comes from the scattering of the low energy proton on another nucleus. If the consecutive scatter at the end of a low ener... | {
"language": "en",
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Radiative Heat Transfer In Nuclear Fusion Given the extremely high plasma temperatures that are required to sustain a nuclear fusion reaction in a device such as a tokamak reactor, how can such high temperatures be maintained in the presence of radiative heat transfer from the plasma to the walls of the reactor vessel?... | This is a really big problem, for at least two reasons.
First, when trying to get the plasma energetic enough to support fusion, the plasma in response tries very strongly to radiate its heat away. That radiated heat has to be continuously replentished in order to hold the desired temperature.
Second, the plasma temper... | {
"language": "en",
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Inverted pendulum on a cart - Lagrangian without moment of inertia? I am modeling the inverted pendulum on a moving cart using Lagrangian methods. I see most examples model the pendulum's kinetic energy as a sum of translational and rotational components (using a $I\dot\theta^2$ term), but I also encounter examples tha... | Your approach has some overlap in the translational and rotational terms for the mass $m$.
To completely separate translation and rotation, you have to break down kinetic energy as:
$$KE = \text{translation of the center of mass} + \text{rotation around the center of mass}.$$
If you model your entire rigid body as a ma... | {
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Problem in derivation of propagator of vector meson I have been reading A. Zee's book on QFT. In chapter I.5, equation (2) is given as,
$$\left[(\partial^2 + m^2) g^{\mu\nu} - \partial^\mu \partial^\nu\right] D_{\nu\lambda}(x) = \delta^\mu_\lambda \delta^4(x).$$
In order to go to momentum space, we find,
$$D_{\nu\lambd... | I think you went wrong in the second to last line since you're not talking about
an on-shell particle
$$
g_{\mu\nu}k^{\mu}k^{\nu}=k^2\neq m^2
$$
The most straight forward way to solve such equations is using Nihars's 'trick'.
| {
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"source": "stackexchange",
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Lorentz Transformations for Polar coordinates or Inertial Frame in Polar Coordinates Do polar coordinates define an inertial frame or not?
Everywhere in GR, the authors of all the books talk about bring the metric to diag(-1, 1,1,1) which would show that a Local Inertial Frame exists at each point on the manifold. And ... |
Can't we construct inertial frame using polar coordinates.
Yes, polar coordinates can be used as coordinates for an inertial frame. For example, when we solve the gravitational two-body problem in Newtonian mechanics we typically use polar coordinates to write $\mathbf F=m\mathbf a$. The equations then take a nicer f... | {
"language": "en",
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Why does a car moving in a circular track experience static friction if it is already in motion? Our physics teacher told us that a car moving in a circular track experiences static friction whose perpendicular component to the tangential velocity acts as centripetal force. But how can static friction act on a moving b... | Unless the car is drifting, then the friction will be static.
Consider the point of the wheel that touches the ground. That is the point of contact. The force of friction acts through this point of contact.
What's important to grasp is that the velocity of the point of contact with respect to the ground is zero.
The re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/603126",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does a non-rotating satellite always show the same side towards the main body? If an initially non-rotating (zero angular momentum) satellite starts moving around a main body, such as the earth,
*
*will then the satellite continue to have zero rotation or
*will it show the same face towards the main body, thereby h... | Initially it would still have no rotation, but as it is in a non uniform gravity field the center of gravity would be slightly below the center of mass. This can create a torque on it.
"A body's center of gravity is the point around which the resultant torque due to gravity forces vanishes. Where a gravity field can ... | {
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Implications of massless pulleys in Atwood machines Consider the double Atwood machine below:
I understand the classic approach to a solution for the acceleration of each mass involves setting the tension in the upper string equal to twice that of the lower string to achieve equilibrium in the lower pulley. The common... | The lower pulley is holding to two masses, which account for the acceleration.
| {
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Measuring Weight with Multiple Scales If I am weighting a long tube of (nearly) uniform weight with multiple hang-scales (really a 10-ft long Helical Antenna), how do I calculate the total weight from the multiple scales?
*
*Can I just add the measured weights at each point regardless of the spacing?
*If the spacing... | Assuming that
*
*antenna is in static equilibrium (i.e. not moving)
*the only forces holding it up are forces exerted by the scales,
*the forces applied by the scale are applied directly upwards (this one is important!)
then the weight will in fact equal the sum of the forces exerted by each scale. So you can sum ... | {
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$\phi^4$-theory, S-matrix Feynman diagram to first order from Peskin and Schroeder This relates to page 111 in Peskin and Schroeder.
We have the $\phi^4$ S-matrix for a 2-particle to 2-particle scattering reaction:
$$-i\frac{\lambda}{4!}\int d^4x \langle p_1p_2|\mathcal T\left(\phi(x)\phi(x)\phi(x)\phi(x)\right)|p_Ap_B... | Suppose we have a general term of the form
$$\langle 0 | a_{p_1} a_{p_2} \cdots a_{p_{n-1}}a_{p_n} a_{p_1}^\dagger a_{p_2}^\dagger \cdots a^\dagger_{p_{m-1}}a_{p_m}^\dagger | 0 \rangle$$
We can eliminate $a_{p_1}^\dagger$ by commuting it past all the $a_{p_i}$ factors until it anhilitates the vacuum state. Along the wa... | {
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Will this spaceship collide with the star? (time dilation) I thought of the above thought experiment and arrive on 2 conflicting conclusions. I can't seem to identify the flaw in my reasoning.
Suppose there is a star 4 light years from earth that has will explode and turn into a white dwarf in 3 years (as measured in t... | *
*In the earth frame, there is a star 4 light years from earth,
due to turn into a white dwarf in 3 years. A spaceship travels to the start at speed $v=\sqrt3/2\approx .866$. (All speeds are stated as multiples of the speed of light.)
*When the spaceship leaves earth, let's say the earth observer and the spaceshi... | {
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"answer_id": 0
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Difference in equations from four-vector conservation This is a question, kind of related to my previous question but is here as a stand-alone. I've been reading the book 'essential relativity' by Rindler and have a question similar to 5.20 which is bothering me. It is the problem that when a photon hits a stationary p... | The threshold condition applied at the end ($\gamma=1$, $\vec{v}=0$) is wrong. If the photon has the minimum energy required to produce the $\pi^0$, the pion will be produced with zero momentum in the COM frame. Since OP is writing $P_\gamma$ and $P_p$ in the LAB frame, $P_\pi$ must also be written in the LAB frame.
Wh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/604147",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
When we push a box, the box applies an opposite force on my hand, but why does my hand move with the box as I push the box if the net force of is 0? When we push a box, the box applies an opposite force on my hand, but why does my hand move with the box as I push the box if the net force of my hand is 0? What is happen... | This ambiguity is completely cleared if you try looking with free body diagrams(FBD).
Your hand is a continuous mass distribution if you try looking at FBD of any section you would see that the section experiences two forces on sides ---
*
*Force from third law as a contact or normal force by the part of hand pushi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/604251",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
An application of Conservation of Angular Momentum One of the applications of the law of conservation of angular momentum involves a helicopter with a single propeller. A/c the book, a helicopter with one propeller would rotate itself in the opposite direction. However, I am not able to visualise this phenomenon. Can y... | Conservation of angular momentum. Since no external torques are applied to the helicopter (the forces causing the torques that spin the rotor are internal), the total angular momentum must stay constant, and equal to zero (since initially there is no angular speed). In other words, the following must be true $$I_\mathr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/604320",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 3
} |
Reversible Or Irreversibile If we know the path on P-V diagram, are we definitely sure that the process, in general, is reversible ? For example, we consider that the engine cycles are reversible, is it because we know the path?
| In an irreversible deformation of a fluid (gas or liquid), the force per unit area exerted by the fluid on different parts of the system interface with the surroundings (which you would probably refer to as the pressure, and more advanced students would refer to as the normal compressive stress, with includes viscous s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/604641",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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