Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How do the unit vectors in spherical coordinates combine to result in a generic vector? I might be missing the obvious, but I can't figure out how the unit vectors in spherical coordinates combine to result in a generic vector. In cartesian coordinates, we would have for example $ \mathbf{r} = x \mathbf{\hat{i}} + y \m... | In spherical coordinates, the $\theta$ and $\phi$ are like latitude and longitude on the surface of the Earth. At a given point, if we want to express a "south pointing direction" tangent to the surface, we'd use the $\theta$ basis vector. Likewise, an "east pointing direction" would be expressed using the $\phi$ basis... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529113",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 7,
"answer_id": 6
} |
How does the current remain the same in a circuit? I understand when we say current, we mean charge (protons/electrons) passing past a point per second. And the charges have energy due to the e.m.f. of the power supply.
Now tell me, if a lamp has resistance and you hook it in the circuit, how will the current stay the ... | Here is why the current stays the same going through the bulb:
Think of current as water flowing downstream in a river. The water comes to a dam, and flows over the top, and then falls all the way down to the bottom of the dam, then resumes flowing downstream. Every gallon of water that was flowing in the river will go... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529224",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 9,
"answer_id": 4
} |
Normal modes of vibration of a plate vs a membrane I have been studying Chladni patterns but recently I have stumbled on some conceptual questions that I seem to not have an answer. At first I thought that the theory would be the same of a vibrating membrane, with very well defined solutions for given geometries like a... | The difference depends on the physical structures: the tension of the membrane must be imposed by means of external forces whereas that of a plate naturally exists in its interior. In other words the relation between deformations and stress is different.
The small deformations of the structure, in the first case, are ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529343",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
Normalization of the action in Special Relativity The action for a massive point particle in Special Relativity is given as
$$A =-mc^2\int d\tau,$$
Where $\tau$ represents the proper time, and $m$ represents the (rest) mass. From what I could understand, the Action must not change with respect to the reference frame, a... | The equation you mention is the action of a single point particle.
$$S =-mc^2\int d\tau$$
The unit of action is energy multiplied by time, in the present case the rest energy which corresponds to the mass of the particle multiplied by the proper time of the particle.
This equation refers to the action from the point o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 4,
"answer_id": 2
} |
Can a Black Hole become a normal mass again? It is well known how Black hole forms. But once it is formed are there any circumstances which can lead a black hole to becoming a normal mass again?
| Hawking radiation leads to a complete evaporation of black holes, whether there are remnants and the problems this creates is a matter of ongoing discussion.For example see here for a review.
Forty years after the discovery of Hawking radiation, its exact nature remains elusive. If Hawking radiation does not carry any... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529841",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 2,
"answer_id": 0
} |
The Calculation of work in different frames Say there is a man running on a road. Friction is applying a force hence he is accelerating, but the friction is static hence does no work. We know that the change in kinetic energy is due to internal work done by his muscles.
Now say that the same man is running on a wooden... | From the ground reference frame, there is no net work done. Friction did displace you by a distance of say $d$. However, the same friction also displaced the wooden board by a distance $d'$. These two perfectly cancel and this can be realised by noticing that the center of mass remains fixed throughout this process.
H... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529918",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
If magnetic field lines don't exist, what are these iron filings doing around a magnet? Obviously the iron filings can be seen aligning themselves along the virtual magnetic field lines produced by the permanent magnet, the virtual magnetic field line is made of electromagnetic field due to the alignment of electrons i... | Magnetic field lines show the direction of force a magnetic mono-pole would experience if it were free to move under the influence of a magnet, but unfortunately, we all know that mono-poles are just a thing of imagination and don't exist in reality. This is given by Gauss' law for magnetism which states
$$\oint \math... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530030",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "56",
"answer_count": 7,
"answer_id": 5
} |
Boyle's Law and hot air balloon A bit dumb question because it is really difficult to imagine it. :-
Pressure is force per area. Talking about gases, the pressure is said to be the force molecules exert on walls of let's say a balloon.
Usually in examples of Boyle's law, our teachers mention hot air balloon, that the s... | For the system to be in equilibrium, the pressure outside must be equal to the pressure inside, otherwise the inside will contract (if the pressure outside is higher) or expand (if lower). There is a minor contribution given by the elasticity of the balloon capable of handling some extra pressure but we can neglect tha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530129",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Gravitational Wave - What is waving? Two kinds of wave transmission are:
*
*Light waves, where a substance (photon) travels as a wave.
*An attached rope, like at the gym, that is "waved" up and down. Here, no substance travels to a new spot, but adjacent parts transmit the energy to others.
QUESTION: Which method d... | Let us clear at first that photons are elementary quantum mechanical particles. That classical electromagnetic waves emerge from a confluence of photons can be shown, but classical electromagnetic theory works with the self propagation of the light energy, carried by electric and magnetic fields.
Two kinds of wave tra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530362",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
If sound passes through material, vibration is produced. So are electromagnetic waves produced too? Sound means vibration of molecules and vibration produces electromagnetic waves. So, this means that sound produces electromagnetic waves directly.
Is this possible?
| If the vibrating material is charged, then electromagnetic radiation will be produced.
There is a type of microphone called the capacitor or condenser microphone, in which the microphone is a capacitor whose capacitance varies with the acoustic vibrations.
https://en.wikipedia.org/wiki/Microphone#Condenser_microphone
T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/530863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 7,
"answer_id": 3
} |
Dynamicity inside a stationary water drop I was doing some experiments with water drops on lampblack when I saw this.
You can see the full video here.
Inside a water drop which is perfectly still from the outside, you can see some moving things, which I suppose are some lampblack flakes from the surface. I am not both... | Those are flakes of lampblack. Their wettability in water is unequal around their periphery. This allows surface tension forces to apply a netforce in some random direction on the flake and force it to scoot around, until the wettability difference goes away as the water begins to wet out the previously poorly-wetting ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531124",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 2,
"answer_id": 0
} |
Direction of average acceleration in circular motion I know that the instantaneous acceleration is always directed towards the center of the circle.But what about average acceleration.
In the above figure my book says place change in velocity along the line that bisects angle $r$ and $r'$ and observe that it is directe... | The average acceleration over one or more complete revolutions is zero. This can be seen from the fact that when the object is on the opposite side its acceleration is opposite.
If the average acceleration were nonzero, the object would not keep returning to the same location.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531369",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
Why does the same proportion of a radioactive substance decay per time period? (half life) Just wondering, if decay is random, why does the activity half every half life, as in, why does it have to reduce by the same proportion in the same time period?
| It's a consequence of the fact that the nucleus doesn't know how many other nuclei are in your lump of material. A 3kg block of uranium has to decay at the same rate as three 1kg blocks of uranium. Which means a 1kg block has to decay at 1/3 of that rate. A 1kg block is the same as 3 1/3kg blocks, so a 1/3kg block has ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531441",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "65",
"answer_count": 5,
"answer_id": 3
} |
What is the general prescription for constructing the quantum mechanical momentum operator conjugate to a given coordinate? Obviously, if $x$ is a Cartesian coordinate, then the corresponding momentum operator is $-i \hbar \partial_x$. But what if $x$ is something more complicated, like some sort of curvilinear coordi... | If an $n$-dimensional configuration manifold $M$ of some physical system is orientable and endowed with a positive volume form
$$\Omega~=~\rho(x)\mathrm{d}x^1\wedge\ldots\wedge\mathrm{d}x^n, \qquad \rho(x)~>~0,$$
we can define a sesquilinear form
$$\langle \phi | \psi\rangle~:=~\int_M \! \Omega ~\phi^{\ast} \psi. $$
Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531774",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
If I use the Earth as my point of reference on a model, would it be valid if I said that the Sun orbits the Earth? (in my model) What the title says.
If I create a model, and I use the Earth as my point of reference, is it valid to say that the Sun orbits the Earth inside my model? Or is claiming that invalid?
| You are talking about the geocentric model and that model has very complicated orbits of planets around the earth. Here have a look at the orbits of planets around earth:
So why not just use the simpler one in which all planets revolve around the barycenter of the solar system.
Also a point to note is that a model wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/531869",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
How many $pep$-related electron-neutrinos $\nu_e$ does the Sun produce? In the sun neutrinos can be produced by the rare proton-electron-proton (pep) reaction:
$$ {}^1_1 H + e + {}^1_1 H \to {}^2_1 H + \nu_e $$
How many pep-related electron neutrinos does the Sun produce?
| The solar pep neutrinos were first detected in 2011 by Borexino collaboration (arXiv:1110.3230). The abstract reads:
We observed, for the first time, solar neutrinos in the 1.0-1.5 MeV energy range. We measured the rate of pep solar neutrino interactions in Borexino to be [3.1$\pm$0.6(stat)$\pm$0.3(syst)] counts/(day ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532202",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Due to incompressibility of water same volume of water should flow through pipe of different cross section . is that really true This seems true when I slightly compress the opening of pipe the speed of water flowing through pipe increases and same amount of water flows out but as I further decrease the opening of pipe... | From the law of mass conservation $$\partial_t \rho + \vec \nabla (\rho \vec v) = 0 $$ follows in the case of a static, incompressible fluid $$\vec \nabla \cdot \vec v = 0,$$ implies, when integrated over a volume $dV$ $$\int dV \; \vec \nabla \cdot \vec v = 0,$$ which, by using the Gaussian theorem we can transform f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532290",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Is there an approximation for the Lorentz factor for very large velocities? I am aware of the approximation generally used for low speeds to calculate the Lorentz factor, that being,
$$\gamma \approx 1 + \frac{1}{2} \left(\frac{v}{c} \right)^2$$
But I need the exact opposite thing -- is there any suitable approximatio... | This is roughly the simplest you can get it:
$$\gamma = \frac{1}{\sqrt{1-v^2/c^2}} = \frac{1}{\sqrt{1-v/c} \sqrt{1+v/c}} \approx \frac{1}{\sqrt{2}} \frac{1}{\sqrt{1-v/c}}.$$
In other words, if $\Delta v$ is how far the speed is below $c$, then
$$\gamma \approx \sqrt{\frac{c}{2 \Delta v}}.$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532562",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 0
} |
How is a 25-year-old can of soda now empty without having been opened or poked? I just discovered in my parents' basement a Sprite can from 1995* and also a Coca-Cola can probably from the same year.
Both cans are unopened and have no visible damage or holes. The Coca-Cola can feels "normal", but the Sprite can is emp... | This also happened to me with an unopened 7up can from 1993 which I had stored in my collection. When the can was about 6 years old I found it looking intact but feeling completely empty; underneath and around it was a small puddle of sticky clear goo, hinting that its contents had very slowly leaked through a tiny, in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532731",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 7,
"answer_id": 5
} |
Age of Universe from Friedmann Equation - How to actually solve the integral? The Friedmann equation for a flat universe can be written as
$$
H(t)=\frac{\dot{a}}{a}=H_0\sqrt{\Omega_{m,0}\cdot a^{-3}+\Omega_{\Lambda,0}}=H(a)
$$
To calculate the age of the universe, many books jump directly to the result. But there shoul... | for flat universe ($\Omega_m + \Omega_{\Lambda}=1)$
$$H^2 = H_0^2(\Omega_ma^{-3}+\Omega_{\Lambda})$$
or $$\frac{\dot{a}^2}{a^2} = H_0(\Omega_ma^{-3}+\Omega_{\Lambda})$$
which becomes
$$\dot{a}^2 = H_0(\Omega_ma^{-1}+\Omega_{\Lambda}a^2)$$
taking square root
$$\dot{a} = H_0\sqrt{\Omega_ma^{-1}+\Omega_{\Lambda}a^2}$$
le... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/532828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
"answer_id": 2
} |
Generator of translations in classical mechanics The generator of spatial translations is momentum. In quantum mechanics this makes a lot of sense to me and so we can write the translation operator like this:
$$\hat{T}(\Delta \textbf{r}) = e^{\frac{i}{\hbar}\Delta \textbf{r} \cdot \hat{p}}.$$ Is there an equivalent exp... | Considering a translated function:
$$f(x)\rightarrow f(x+\Delta x)$$
We can expand in Taylor series around $x$ and write
$$f(x+\Delta x)=\sum_{n=0}^\infty\frac1{n!}\left. \frac{\partial^n f}{\partial x^n}\right|_{x}\Delta x^n\equiv\sum_{n=0}^\infty\frac1{n!}\left(\Delta x\left. \frac{\partial}{\partial x}\right|_{x}\ri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533176",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 0
} |
Is there a thermodynamic process with constant internal energy but variable enthalpy? Lately I've been trying to wrap my head around those two concepts and the difference between them.
In an ideal gas, $PV$ is said to be an energy related to the kinetic energy of molecules boucing against the boundaries of the system. ... | $H=U+pV$, so a change in enthalpy will amount to: $dH=dU+VdP+P dV$.
If you want $dU=0$ you can impose $dT=0$. Using the equation of state for an ideal gas we get: $V dP+P dV=nRdT$, and because you want $dT=0$ in your process you have $VdP=-PdV$.
Replacing that in $dH$ you get:
$$dH=0$$ Thus you cannot have a process f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533444",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why doesn't Rayleigh scattering happen at low altitude in air? An answer I found online was: At high altitude where molecules are far apart, scattered photons can travel without interfering with each other, thus they fill the sky with blue light. But at low altitude, molecules are so close to each other that scattered ... | There is no problem with energy, and an explanation in terms of waves is more intuitive. How else could one easily understand a wavelength dependence?
First there is dispersion, the increase of the index of refraction at short wavelength, which can be understood with the model of Lorentz oscillators.
In a gas there are... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533553",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 0
} |
When the star formation begins? We can separate the history of the universe in different epochs.
Radiation dominated epoch, matter dominated epoch, and dark energy dominated epoch, and we can divide the epochs in different ways.
For example the radiation dominated epoch can be divided in the epoch before atoms could f... | This is the history according to the mainstream model, the Big Bang
After the decoupling of photons at 380.000 years, there is a period marked as "neutral hydrogen forms" that carefully is not given a time to the line of the next stage, which is modern universe. In other plots of timeline for the Big Bang the line i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533720",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Does Another Universe Where Time Runs Backwards Revive the Idea of a Cyclical Universe? https://www.pbs.org/wgbh/nova/article/big-bang-may-created-mirror-universe-time-runs-backwards/
This article talks about a new theory where the big bang happened in one direction for us and the other direction where time is going ba... | The problem with mirrors in this situation is the question of energy.
What one person might be doing in a situation might be the mirror image of what another is doing, but is the energy the same? In the situation of a mirror universe colliding with our universe, in theory if you put a mirror in the middle, it should b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533815",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 4
} |
Clarification of the concept "less resistance means less heating" in a wire So my textbook says that the reason cables that are suppose to carry high currents, are thicker that those that are meant to carry lesser current, is that "less resistance (of the wire) means less heating..."? Is this even true?
Isn't CURRENT ... | Not necessarily. This is because it is not always the current rather a coupling of both which causes the heating effect to occur. What this means is that for wires carrying high currents, lower resistance leads to less dissipated power, according to P=I^2*R, where I is the current in the wire, and R is the resistance. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/533927",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 8,
"answer_id": 5
} |
Post-measurement $\psi$ in quantum mechanics I have a question regarding the wave function after a measurement. Everything I found online says that this is the following formula:
$\psi = \frac{M_m\psi}{\sqrt{P(m)}}$
Where $P(m)$ is the probability of observing m, the $\psi$ on the left is the wavefunction AFTER the me... | You have to think about what a measurement is in QM. Generally speaking, you are going to measure an eigenvalue of an observable. Lets say that you measure $A$ that follows the eigenstate equation $A|a>=a|a>$. Then if you begin with a general state $|\psi>$, after the measurement you will get another state $|\psi'>$ fo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534024",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
What happens to oxygen during atmospheric absorption of radiation with a peak at 60 GHz This question discusses atmospheric absorption of radiation (specifically 5G radio waves) due to oxygen at 60 GHz.
I would like to know exactly what happens to oxygen in all its forms (be it air or ozone) when it absorbs radiation a... | The oxygen molecule is unusual in having a ground state that has unpaired electrons, and this means it has a net spin of one. Technically the ground state is a triplet. This is unusual because ground states normally have spin zero i.e. they are singlets. For example the $\mathrm{N}_2$ molecule has a singlet ground stat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534128",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Gravity, matter vs antimatter I have a simple question regarding matter-antimatter gravity interaction.
Consider the following though experiment:
If we imagine a mass $m$ and an antimass $m^-$, revolving around a large mass $M$
the potential energy of mass $m$ should be:
$$ U_1=-\frac{GmM}{R} $$
and the potential energ... | This is a perfectly good argument and one of the reasons that all the physicists I know believe that antimatter behaves just like matter in a gravitational field.
It is important to distinguish between antimatter, which is well understood from countless collider experiments, and negative matter (also known as exotic ma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534289",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 4,
"answer_id": 1
} |
The Enigma of Universal Gravitation Forces This is taken from a book called "Physical Paradoxes and Sophisms" by V. N. Lange.
1.22. The Enigma of Universal Gravitation Forces
The law of gravitation can be written $F=\gamma\frac{m_1m_2}{R^2}$.
By analyzing this relationship we can easily arrive at some interesting ... | Because in general gravitational attraction is much weaker than electromagnetic repulsion.
For example when you compare gravitational and electrostatic forces between two electrons, both forces are proportional to $R^{-2}$, but if you compare their actual values, you get that gravitation is around $10^{37}$ times weake... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534515",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 8,
"answer_id": 4
} |
What does this notation for spin mean? $\mathbf{\frac 1 2}\otimes\mathbf{\frac 1 2}=\mathbf{1}\oplus\mathbf 0$ In my quantum mechanics courses I have come across this notation many times:
$$\mathbf{\frac 1 2}\otimes\mathbf{\frac 1 2}=\mathbf{1}\oplus\mathbf 0$$
but I feel like I've never fully understood what this nota... | I should concur with the other answers that there is no substitue for reading up in good texts and WP.
You are right that, in a given basis, there is a similarity (equivalence) transformation implied in the equation of your title: it basically means that the tensor product on the l.h.s. is reducible, by an orthogonal ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/534887",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 4,
"answer_id": 1
} |
Quantization of complex scalar field I'm learning Peskin's qft now and I'm a little confused about problem 2.2 .
Suppose I write the field $\phi(x)$ as:
$\phi(x) =\int \frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_{p}}} (a_{p}e^{-ipx}+b_{p}e^{ipx})$
I know that $b_p$ should be written as $b_p^\dagger$ because it annihilate a... | To begin with, Peskin gives the following action:
$$
\mathcal{S} = \int d^4 \left[ \partial_{\mu} \phi^{\ast} \partial^{\mu} \phi - m^2 \phi^{\ast} \phi \right].
$$
Let's begin by considering the classical field theory. The equation of motion is
$$
\left( \partial^2 + m^2 \right) \phi = 0
$$
(and its complex conjugate)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535149",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Where does energy go in joining capacitors of different capacitance charged by different potential, hypothetically assuming no resistance in circuits? I don't understand why there is any change in initial and final energy since we have already assumed a perfectly conductive circuit. I mean, theoretically at least, ther... | Yes, even assuming a perfectly conductive circuit, there would be some inductance (you may not have studied this yet) which would create an oscillating LC circuit, which would radiate. Some early spark gap radio transmitters worked like this.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535367",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 2
} |
Geometry of Young's experiment for optical path length I am currently studying the textbook Modern Optical Engineering, fourth edition, by Warren Smith. When presenting the concept of optical path length, the author says the following:
With reference to Fig. 1.13, it can be seen that, to a first approximation, the pat... | The assumption is that AB is very small compared with D. Then the two triangles are similar and the sine of the small angle is OP/D = Δ/AB
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535549",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Is there work done on a mass from matter-antimatter pairs? Imagine I have a vaccuum at very low temperature and I put a single neutron in, then gamma rays interact to form matter-antimatter pairs within this vaccuum and assume that this happens extremely close to the aforementioned neutron. Since the matter-antimatter ... | It is not possible to have the topology you describe. In order for a gamma ray to create a particle antiparticle pair, it needs the electromagnetic field of a nucleus for energy and momentum conservation to work in the center of mass of the e+e- pair.
In this feynman diagram Z is the nucleus in whose electromagnetic ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535607",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How do we know not all photons are absorbed? Only those of specific energies? When a photon hits an electron in an atom, its energy has to be equal to the difference in energy between the current shell and a shell with a higher energy level, otherwise it is not absorbed at all.
How do we know not all photons are absor... |
How do we know not all photons are absorbed?
You can shine monochromatic light on a sample of a material and see whether it is absorbed or not.
For example if you shine different wavelengths of light through a chamber containing a pure gas, and you'll see that only wavelengths that match transitions of that gas mole... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/535851",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Conservation of crystal momentum I am trying to convince myself that crystal momentum is conserved in a periodic lattice modulo a reciprocal lattice vector.
Consider a Hamiltonian $H$ which is periodic under translations of a Bravais lattice vector. The canonical momentum operator $\mathbf{P} = (P_x,P_y,P_z)$ is the g... | There is no need to expand the exponential at all. Let the lattice have basis $\mathbf{a}_i$. The fact that
$$[e^{i \mathbf{a}_i \cdot \mathbf{P}}, H] = 0, \quad [e^{i \mathbf{a}_i \cdot \mathbf{P}}, e^{i \mathbf{a}_j \cdot \mathbf{P}}] = 0$$
indicates that we can simultaneously diagonalize the $e^{i \mathbf{a}_i \cdo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536039",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Outside temp of vessel of is 40 Deg C and Water inside it is 86 Deg C.. Why? I was boiling water in a steel utensil.
Used Fluke's IR Gun (59 Max) to measure the temperature of Water inside AND the surface temp of vessel outside.
The boiling water read 86 Deg C whereas the outside surface temp of vessel read just 40 D... | How these thermometers works is based on the principle of blackbody radiation and the Stefan-Boltzmann law. There is an IR sensor housed inside the thermometer that senses the total power radiated in a window of IR. And this power is related to the temperature of the emitter. But there is also a dependence on emissivit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536251",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Why is the speed of light in vacuum a universal constant? While getting familiar with relativity, the second postulate has me stuck. "The speed of light is constant for all observers". why can't light slow down for an observer travelling the same direction as the light?
| It is the speed of causality. If there was no limit in how fast information can travel all would happen at once. The universe is a causal place because information needs time to travel a distance. Your question is probably much deeper than you intended it to be.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536432",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 7,
"answer_id": 4
} |
Can the real-time Green's function be written in the form of path integral on the real axis? In every textbook, the path integral of the Green's function is written in imaginary-time. I wonder whether we could write real-time green function in the path integral form.
| PS: I notice that if we can distort the time integral line (to include imaginary part), then it is possible to establish the path integral formulation of real-time green function (at least for fermions). So I edited my question so that the time integral has to be defined on real axis.
—————
All right after discussing w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536561",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Do reflection and diffraction occur at the same time?
When waves pass through a gap as the above, diffraction occurs.
As the upper and lower part of the plane wave (indicated by yellow colour) are striking the barriers, does reflection occur at the same time? Is this the cause of the decrease in amplitude when diffra... | You can design the barriers such that wave hitting them is absorbed other than reflected (Key word: impedance matching). The reason why decrease in amplitude in the diffracted wave happens, is not because of reflection, but because of the portion of the wave that passed the opening now has to occupy wider wave front th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/536943",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Decay of electron? Have we detected any decays of electrons to an electron neutrino and $W$-boson in Fermilab or in CERN? Are neutrinos the only possible stable leptons inside an electroweak field?
|
Have we detected any decays of electrons to an electron neutrino and W- boson in Fermilab or in CERN?Are neutrinos the only possible stable leptons inside an electroweak field?
This cannot happen because energy and charge conservation are absolute laws. Particles can decay to other particles when the sum of the mass... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537293",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Why complex numbers are used in electronics? The impedance of a capacitor or an inductor is imaginary. How do we know these quantities are imaginary?
| An RLC circuit satisfies$$L\ddot{I}+R\dot{I}+C^{-1}I=\dot{V}.$$To solve this with AC voltage such as $V=V_0\cos\omega t,\,V_0\in\Bbb R$, it's convenient to take the real part of a complex choice of $I$ for the case $V=V_0\exp j\omega t$. Substituting $I=I_0\exp j\omega t,\,I_0\in\Bbb C$ gives$$I_0=\frac{j\omega V_0}{C^... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537446",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 1
} |
Why can vector components not be resolved by Laws of Vector Addition? A vector at any angle can be thought of as resultant of two vector components (namely sin and cos).
But a vector can also be thought of resultant or sum of two vectors following Triangle Law of Addition or Parallelogram Law of Addition, as a vector ... | This is mainly because the X and Y axes are also perpendicular to each other and therefore to measure quantities along these axes the vectors are resolved into X and Y components.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537550",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 7,
"answer_id": 4
} |
Does the effect of gravity get slower at high speeds? If a sentient object was vibrating at near light speed and was some distance off the ground. Compared to being relatively stationary to the ground, would it take a longer while for them to fall down onto the floor from their perspective?
| You are basically asking whether an oscillating clock would run slower then a stationary clock on the surface. The answer is yes, because the velocity of the oscillating clock causes time dilation.
However we can answer your question very easily because both effects 1 and 2 make the falling clock run more slowly, so o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Rotation in molecules I am a bit confused about the rotational motion in molecules. Assuming the bond length is constant, the motion can be described as a rigid rotor. In the center of mass frame the energies are given by BJ(J+1) and the wavefunctions are spherical harmonics. However when we measure the energies or the... | Like NewUser mentioned, the motion can always be broken down into motion of centre of mass and motion about centre of mass. In our case, we interact with the system using light. And this causes transitions in the energy levels.
The system factors into one continuous energy spectrum corresponding to the kinetic energy ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537773",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why is a Lorentz transformation of a Lorentz transformation also a Lorentz transformation? Why is a Lorentz transformation of a Lorentz transformation ($x''$,$y''$,$z''$,$t''$) also a Lorentz transformation?
| I would say that you want a mathematical proof. You can see in Reign's answer a particular case, but here I will post a more general one.
As you may know, a Lorentz transformation can be written as a 4-dimensional matrix, $\Lambda$, so that $x' = \Lambda x$. This matrix must fulfill this relation,
\begin{equation}
\Lam... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537873",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 4
} |
Can a wormhole be created if it has not always existed? I know there are solutions to Einstein's field equations that give a wormhole geometry. But they are time independent. They are static. Is there a process where empty flat spacetime can evolve into a wormhole by an appropriate flow of matter and energy and negativ... | The current state of knowledge is basically that we don't know.
The topology change is contentious - it is unclear if it is permitted, but there are also disagreements about why and how. The standard approach is to shout "quantum gravity!" and escape in the confusion.
One classical argument for why making a wormhole w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/537994",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "36",
"answer_count": 3,
"answer_id": 2
} |
Cup anemometre can measure 3D wind component? As part of my PhD thesis I am looking for information about anemometres.
I have heard that cup anemometre can only measure the x and y component of the wind, the z being left out because it measures the wind thanks to moving part.
I have been unable, so far, to find a sourc... | After some more searches I have found two online sources confirming my statement:
*
*https://www.omega.ca/en/resources/anemometers
*https://www.eas.ualberta.ca/jdwilson/EAS327/eas327wind.html
As well as a book "Wind Energy: theory and practise" p40. which says: "cup anemometers are the sensor type most commonly u... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538251",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is *physical meaning*? What do we mean when we talk about physical meaning of a quantity, an equation, theory, etc.? Should the physical meaning touch on the relation between the math and the real world? Or does it have more to do with how the equation/theory is used by physicists?
Background
For the immediate bac... | I understand physical meaning as setting the context.
We can learn a lot about the maths of 2-spin particles, operators, probabilities and expected values for example. But without learning about Zeeman effect and Stern-Gerlach experiment, all the stuff seems coming from nowhere.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538350",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 2
} |
Why do antiferromagnets occur at lower temperature than ferromagnets? The minimal model for describing magnets is the Heisenberg Hamiltonian
$$H = -\frac{1}{2}J\sum_{i,j} \mathbf{S}_i \cdot \mathbf{S}_j$$
Where $i,j$ are nearest neighbors and the factor of $1/2$ is for double counting.
If $J$ is positive, spins will w... | This is just speculation, but the excitation spectrum of a ferromagnet is (in general) quadratic, while the spectrum of an antiferromagnet is linear. Possibly this difference in the transition temperature arises from the greater ease of creating excitations in antiferromagnets.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/538480",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
} |
Is De Broglie's formula $\textbf{p}=\hbar \textbf{k}$ applicable to a discrete wave number system? I don't know if my question has sense at all but while doing my homework there appeared in my mind this question.
Say, for a particle in a box, the confinement makes that the wave number k is discrete, depending on integ... | Yes it is applicable. Note that the expectation value of momentum is zero for any stationary solution in a box, so $\langle \psi | \frac{\hbar}{i} \vec \nabla |\psi\rangle = 0$. Still $ \psi | \vec p |\psi = 0$, without the integration over space is the Noether momentum distribution belonging to the Schrödinger lagrang... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540099",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
How do we know that one particular solution for the velocities of a two-body elastic collision is the correct one over the other? Assuming there is a 1-D collision between two bodies, having masses $m_1$ and $m_2$, if we conserve energy and momentum, we get two solutions.
$$
v_{1,i} = v_{1,f} \\
v_{2,i} = v_{2,f}
$$
... | Conservation of Energy and Momentum alone does not give you a decision between the two options; it's the same with normal three-dimensional billiard balls.
Energy and momentum are conserved perfectly fine if the two billiard balls just pass 'magically' through each other and continue their movement unchanged. Still th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540239",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Explain how scaling of the inverse square law breaks down at a stars surface If the radiation pressure at distance $d>R$ from the center of an isotropic black body star is found to be $$P_{rad}=\large{\frac{4\sigma T^4}{3c}}\left[1-\left(1-\frac{R^2}{d^2}\right)^{\frac{3}{2}}\right],$$
a) How do I show that $P_{rad}$ o... | For the answer to the question a), just use a Taylor expansion in the parameter $x= R/d \ll 1$, so that
\begin{equation}
(1-x^2)^{3/2} \simeq 1- \frac{3}{2} x^2
\end{equation}
and then you obtain a inverse square law in $d$
\begin{equation}
P_{rad}= \frac{2\sigma T^4}{c} \frac{R^2}{d^2}
\end{equation}
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540337",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
How can a red light photon be different from a blue light photon? How can photons have different energies if they have the same rest mass (zero) and same speed (speed of light)?
| They differ in their energy. Special relativity states that $E=\sqrt{m^2c^4 + p^2c^2}$. For a massive particle, there is a one on one relation between its energy and speed. In the limit $m \rightarrow 0$ this is no longer the case. All massless particles move at light speed, but their energy/momentum can vary.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "29",
"answer_count": 6,
"answer_id": 3
} |
Why does frequency remain the same when waves travel from one medium to another? I was reading about reflection and refraction on BBC Bitesize and I can't understand why frequency is a constant in the wave speed equation. I can't visualise the idea of it. I know that wave speed and wavelength are proportional to each o... | Instead of thinking of a travelling wave, it is better to think of a field, where each point in space and instant of time is associated to an electric and a magnetic field. The EM fields are normal to the direction of propagation. Let's choose a field in the $z$ direction and propagating in the $x$ direction, and suppo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540685",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Why can't a wave travel in a non-elastic medium? Why a wave cannot propagate in a non-elastic medium
We know that wave is a distrubance and carries energy. In this sense let imagine fall of dominoes, which carries disturbance and energy. Here fall of dominoes is non-elastic and we can see that wave propagates.
Can I c... | I think it goes like this.
A mechanical wave is indeed a periodic perturbation the particles of the medium through which it travels, and if the medium is non-elastic, as most media are, then energy will be lost at each 'passing on' of the energy from one particle to the next. This is the cause of the attenuation of me... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540791",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Imaginary part of semiconductors index of refraction I understand that the index of refraction is complex and can be expressed as such: $ \widetilde{\eta} = \eta + i \kappa $. However I’ve been searching for a bit and I am unable to find the derivation of why the imaginary part of the refractive index in semiconductor... | If $\alpha$ is the attenuation coefficient, such that $|E|^2 \propto e^{-\alpha x}$ it is, by pure identification, the definition of
$\alpha$.
Let's write:
$$ E=E_0 \exp\big(i (n+ik)k_0 x\big) $$
where $k_0=\frac{2\pi}{\lambda}$ is the vacuum wave number.
You get then:
$$ E=E_0 e^{ink_0 x} e^{-k\,k_0\,x}$$
and
$$|E|^... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540865",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why do we need Gauss' laws for electricity and magnetism? The source of an electromagnetic field is a distribution of electric charge, $\rho$, and a current, with current density $\mathbf{J}$. Considering only Faraday's law and Ampere-Maxwell's law:
$$
\nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}\qquad... | There is a paper linked to the cited statement at wikipedia. In short the system is actually not overdetermined. The authors report that numerical methods, which ignore the divergence-free conditions lead to inaccurate solutions. They show that they are needed to guarantee the uniqueness of the solutions (you have to t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/540991",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 3,
"answer_id": 1
} |
Why does the dielectric field not cancel out the capacitor's field? When a conductor is in a region with electric field, free charges will move until they balance out the external electric field. However in dielectrics this does not happen. I know that charges are bounded to the atoms, and there is only a small portion... | Any volume element within the dielectric that's large enough to encompass many molecules, but smaller than any scale of interest, will be electrically neutral regardless of whether or not there is an induced polarization. So the molecules in the bulk do not contribute to the macroscopic electric field.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541061",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Is heat $\delta Q$ an exact differential for an isochoric process (ideal gases)? Generally speaking, heat and work are path-dependent, thus $\delta Q$ and $\delta W$ are not exact differentials. By first law of thermodynamics, we know that $dU=\delta Q - \delta W$
but $\delta W=0$ for an isochoric process, that yields... | The reason why heat and work are path dependent and therefore not exact differentials is that, unlike internal energy, they are not system properties. While there can be a change in internal energy of a system, there is no “change” in the work or heat of a system because a system does not “possess” work or heat.
Con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541220",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Entropy as a state function - Is it just a postulate of the second principle? I read quite a few questions on this website dealing with the idea of demonstrating that entropy is a state function. None of the answers I read seemed to be fully conclusive. So my question is : is there anything wrong in saying that the sec... | One complete description of the second law of thermodynamics is:
$\exists \quad S=S(U,V) \quad \textrm{with} \quad dS\geq0$
It indeed contains the existence of entropy as a state function. I for myself don't like the weird historical formulations.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541319",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why does the range of this integral work out this way? I have a bit of trouble in finding the same limits for the integral in Eq. (17.111) from Peskin & Schroeder. We have something like
$$ \int_0^1 dx' \int_0^1 dz f(x',z) \delta(x-zx').$$
Posing $y=zx'$, I find
$$\begin{align}
\int_0^1 dz \int_0^1 \frac{dy}{z} f\biggl... | P&S's equation implicitly assumes that $0\leq x\leq 1$:
$$\begin{align}\int_{[0,1]} \!dz &\int_{[0,1]} \!dx' ~f(x',z)~ \delta(x-zx')\cr
~=~&\int_{[0,1]} \!dz\int_{\mathbb{R}} \!dx' ~1_{[0,1]}(x')~f(x',z)~ \frac{1}{|z|}\delta(\frac{x}{z}-x')\cr~=~&\int_{[0,1]} \!\frac{dz}{|z|} 1_{[0,1]}(\frac{x}{z})~f(\frac{x}{z},z)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541381",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Term for radius and gradient of spacetime distortion? A black hole would distort spacetime time to a greater degree than planet Earth. That is, both the radius and the gradient of the distortion are greater.
Is there a term that combines "greater radius" and "greater gradient" into one?
In layman terms, a black hole d... | Spacetime distortion is measured by the Riemann curvature tensor $R_{\mu\nu\lambda\kappa}$. This tensor has 256 components, but various symmetries reduce the number of independent components to 20. So, in general, it takes 20 numbers at each point in spacetime to fully describe how spacetime is distorted.
The simplest ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/541651",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Can pressure inside system ,with small hole in them , build up when heated? Can one build up pressure in system for example kettle with hole sufficent of releasing water vapor ?
Kettle starts with 21c 1atm inside and outside and will be heated as fast as possible, can this system build up pressure inside The kettle eve... | If heating fast enough, one can build a pressure, since it takes finite time for the pressure to equilibrate through a small hole. Let us take, for example, a punched air baloon or a tire - initially the pressure inside is high and the extra air escapes through the hole; it happens quite fast, but not instantly.
An exa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542152",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Massless string vs massless spring in a mass-spring system
Two masses connected by a massless spring, on a frictionless surface , and a force of $60$N is applied to the 15kg mass such that it accelerates at 2 $\frac{m}{s^2}$. What is the acceleration of the $10kg$ mass?
I came across this question. I first thought ... | a string is rigid so cannot be extended or compressed, its both end would move with same acceleration
in spring, it can extend, if spring extends then it would apply equal forces on both
bodies i.e $kx$ ,towards left for $15 kg$ and towards right for $10 kg$.
the only force moving $10 kg$ is $kx$
now if you apply t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542333",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Can an electron transit within the same $n$-level? Under selection rules for multi-electron atoms in LS coupling, its generally written that there is no restriction on the total quantum number $n$. Does it mean that an electron transit within the same $n$ level, i.e., can $\Delta n =0$?
| As far as i know when you derive the transition rules for some interaction with some interaction hamiltonian $H_{int}$ you investigate the matrix element $\langle f | H_{int} |i\rangle$ between some initial $|i\rangle$ and final $|f\rangle$ state labeles by the appropriate quantum numbers. The allowed transitions are g... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542562",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
What was the mean distance photons travelled before colliding with electrons in the matter plasma before recombination? What was the mean distance photons travelled before colliding with electrons in the matter plasma before recombination?
I have checked other answers close to this but they only mention a mean distance... | Since the cat is out of the bag and I calculated this in another (non-duplicate) question, I'll repeat the calculation here.
The baryon density today is about $\rho_0 \sim 4\times 10^{-28}$ kg/m$^3$, then at a redshift of $z\sim 1200$ (just prior to recombination), the number density of free electrons (assuming a fully... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542789",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Physics of the trikke tricycle I love my trikke, but I still do not understand what propels it forwards.
It is very clear that the energy comes from my legs and not from my arms (I only have to touch the handle bar ever so lightly), but I do not see how my shifting weight from side to side can result in a forward point... | First off, you might as well ask, what makes any vehicle go forward? When you're riding a bike, you're just pushing pedals up and down, so how does that end up making the bike go forward? When you're driving a car, how does the engine make the car go forward? After all, the pistons in the engine just oscillate back and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542899",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 3,
"answer_id": 0
} |
Is information lost from black body radiation? If you heat water in a microwave all of the water is heated by a narrow wavelength of photons. As the water cools it emits different photons of radiation in the form of infrared light.
Can you tell how the water was heated from the cooling process? How many photons and th... | In a way the information is in the blackbody radiation: each photon carries $3.897\pm 2.522$ bits of information. It is just scrambled.
The important thing here is that water does not have a very good memory. Certainly there are hydrogen bonds producing a complicated microstructure, but the interactions mix up any info... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/542990",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Does Lorentz's force and magnetic dipole alignment torque explain same or different forces inside an electric motor? As depicted in the image below borrowed from this page the motion of the rotor in an electric motor can be explained by appealing to the Lorentz force on a current carrying wire (left side) or by the ori... | I had hoped to see answers to your question, but since this is not the case, I allow my own answer here.
The torque in your left image can be explained as follows:
*
*Electrons have a magnetic dipole moment. In a wire without an external magnetic field, the magnetic dipoles of the electrons are randomly oriented.
*... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/543342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How to calculate the width of the dark fringes? I am talking about the single slit diffraction experiment.
The width of the central bright fringe is twice as wide as that of the others bright fringes. It can be calculated easily as follows.
\begin{align}
\text{width of other bright fringes} = \frac{\text{wave length}\t... | This is actually somewhat more involved. You can compute the intensity/irradiance of the Fraunhofer diffraction pattern exactly and the result is the so-called Airy pattern:
$I(\theta)=I_0\cdot \left[ \frac{2 \cdot J_1(k \cdot a \cdot sin \theta)}{k \cdot a \cdot sin \theta} \right]^2$,
where $\theta$ is the observatio... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/543466",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Calculating work of an object moving up a slope If an object is being pushed across a horizontal surface, the equation for the work done is $W = F s$, where $s$ is the horizontal displacement.
If an object is being lifted to a height of $h$, the equation for the work done is $W = F h$, where $h$ is the vertical displac... | You should understand the fact that (Work)W = F.S
(Work Done)W = FS Cos(theta)
We will not consider Horizontal motion because Weight of the object makes 90 Degrees with Horizontal displacement which gives Work Done in Horizontal Displacement as Zero [Cos(90) = 0] .
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/543766",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
“Bananagrams” under black light? There is a game called “Bananagrams” which includes a bunch of pieces with a letter on each. It seems when I shine a black light flashlight on the letters, the “M” letters glow, but no other pieces do.
All the pieces appear the same under normal lights (except of course the letters on e... | Well, obviously either the 'M' pieces are made of some different material which flouresces, or they are painted / coated with some material that does while the other pieces are not.
I would be tempted to mail the makers and say, basically, 'I found this interesting thing' and ask them if they know: they look like they ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/543905",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
What is global Lorentz transformation and what is local Lorentz transformation? I will consider $\textbf{spacetime}$ as $(M,\eta)$ where $M$ is a four dimensional $\textbf{manifold}$ and $\eta$ the metric which in this coordinates
$$
\begin{align*}
x \colon M &\longrightarrow \mathbb{R}^4\\
p &\mapsto x(p)=(x_0,x... | The three definitions are the same. They are ways of saying the same thing. Since you have a manifold $(M,\eta)$ this is a flat, Minkowski, spacetime. The Lorentz transformation is global on Minkowski spacetime.
In a curved spacetime the metric is usually denoted $g$, rather than $\eta$. $g$ is, in general, a function ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/544193",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
How does one interpret thermodynamic differentials? When we study we usually refer to quantities in terms of differentials, why is this?
Secondly how do we get an intuitive idea of how to deal with the infinitesimal quantities involve? Like what is the right perspective to look at these things from? It is quite differe... | I guess most of the time you are interested in understanding how a system's, for example, internal energy change as you change the volume. On the other hand, some quantities such as internal energy or enthalpy are independent of the way you change the system so therefore like gravitational potential energy they only de... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/544678",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
} |
Are antileptons and antibaryons linked? The recent news about the T2K experiment got me thinking: is there any linkage in the Standard Model between the matter and antimatter categories across the families of Standard Model particles? Are antileptons necessarily linked to antibaryons?
As a specific example: In our uni... | This was the first thing Dirac thought of when he produced the Dirac equation which predicts the positron. He thought there might be some hidden loss of symmetry, and that the positron could be the proton. Within a couple of years of the hypothesis, it had been fairly conclusively rejected and Dirac predicted that the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545014",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 2
} |
Wavefunction of a photon Does anyone have an explicit closed-form expression for the wavefunction of a single photon from a multipolar source propagating through free space? Any basis is acceptable as long as it is a single photon state.
A reference would also be appreciated, but not essential.
————————
A possible du... | I posted an answer to a similar question here. Admittedly, many different things may be implied when talking about the wave function of a photon. However, one should keep in mind is that, unlike electrons, photons are classically waves. Quantization neither adds nor subtracts from their wave-like properties, but inject... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545184",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Does Loop Quantum Gravity predict general relativity in semi-classical Limit? Recently i read about Loop Quantum Gravity in Wikipedia and found this below statement here.
Presently, no semiclassical limit recovering general relativity has been shown to exist.
But i also came across a paper in arxiv whose abstract cl... | About a decade ago, Ashoke Sen did some calculations that show that you can use Euclidean methods compute the logarithmic corrections to the entropy of Schwarzchild black holes in terms of low-energy, classical data. He remarked that these entropies had also been calculated within loop quantum gravity, and that the re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545314",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 2,
"answer_id": 1
} |
Can Higgs potential provide a cosmological constant? Usually, in particle physics, people do not care about a constant term in scalar field potential. Rather, attentions are paid to the local profile at the minimum. But in the context of cosmology, the absolute value of the potential has a physical meaning; it is a cos... | There are two things to consider here: the late-time accelerated expansion, often discussed within the context of the cosmological constant, $\Lambda$, and primordial inflation. Let's take the latter first.
In primordial inflation, one has a field initially evolving in the false vacuum of some potential energy funct... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545509",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Escape velocity for electric field As we know gravitational force and electric forces are quite similar I was wondering if there is minimum velocity called escape velocity required to escape gravitational field of earth so is there a minimum velocity to escape electric field of earth since electromagnetic forces are st... | A problem is that the Earth is not just a conducting sphere with charge on its surface as this text Electricity in the Atmosphere illustrates.
However you also need to consider the charge on the object trying to escape which may well be under the influence of other charges which are surrounding it.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545740",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
When Is It Appropriate To Use The Ladder Operator Method in Quantum Mechanics? I'm trying to understand when it is intuitively obvious that the ladder method would be best used to tackle a problem in quantum mechanics.
| Two excellent examples of the use of ladder operators can be found in Introduction to Quantum Mechanics (3rd Ed, Griffiths):
1. The 1D harmonic oscillator, in chapter 2 (pg 43) and
2. The spherical harmonics for the total angular momentum operator (pg 159).
In both of these, there is a common theme. If there exists tw... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/545883",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Lorentz transformation of four potential In the following, $c=1$ (and so $\beta=v$) and the signature is $(-+++)$.
The four-potential is $A_\mu=(-\phi,\mathbf{A})$. It transforms as $A'_{\mu'}=\Lambda_{\mu'}^{\ \ \ \ \mu}A_{\mu}$ so that, under a boost in the $x^1=x$ direction, it becomes $$A'_{\mu'}=\begin{pmatrix}A'_... | It might help in this case to consider that the electric and magnetic fields are the "components" of the electromagnetic tensor. Then one can use the transformation properties of a rank-2 tensor to derive the expression of the transformed fields.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546064",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is tension needed to create a wave in a string? Suppose, a long straight string is present in vacuum. I oscillate one end of the string with a certain frequency. Shouldn't a wave be formed? If it is formed, what will be the velocity of the wave?
| Tension provides a restoring force, which is necessary to have oscillations (like a spring or gravity for pendulums). Otherwise any attempt to excite waves will only produce an inelastic deformation.
However, if the gravity is present, there will be tension created due to the non-zero mass of the string which might be ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546279",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Mach cone geometry from Mach number Given a Mach number, how would I go about determining the geometry of the associated Mach cone? Apologies, I'm not too well versed in physics.
| A wave in the shock front moves away from its point of origin at the speed of sound. The plane moves away from that point at the Mach number times the speed of sound. In a given time the distance traveled by the plane forms the hypotenuse of a triangle with the distance traveled by the sound forming the side opposite... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546413",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
What is the term to describe when pressure exerted between two obejcts is balanced? I'm searching for a term here.
All materials compress (some more than others).
Newton's Third law states:
...all forces between two objects exist in equal magnitude and opposite direction: if one object A exerts a force FA on a second... | This (when total force on an object or interface is zero, such that there is no net motion) is just called "mechanical equilibrium."
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546514",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why doesn't a backward wave exist? (Huygens principle) Since every point on a wavefront act as a source of secondary wave (wavelets) then why do we get only forward wavefront not backward.
Huygens principal says that amplitude of the backward wave is zero, but why and how it happens?
| Today the principle could be explained as follows.
Every medium has an elasticity and a viscosity. In simple words, the first describes how deeply a body can penetrate or shift the medium over time. The second describes how the medium around is displaced over time.
Imagine a hammer falling lightly on a metal block. The... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546665",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
What is the possibility for a gamma ray photon to pass through a composite particle like a proton? As I know, the photon can be either absorbed or reflected from a particle, but as baryons or other hadrons are composite particles is there a defined possibility of passing through the volume inside the particle, and if i... | At the level of gamma ray energies, it is more complicated. Once there is enough energy in the photon for production of particles , scattering of photons on nuclei becomes more complicated. See what a proton looks like here.
See this experiment how many channels with created particles there are .
elastic γp → V , V ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546767",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Is the net torque of an only translating rigid body zero, independent of the point chosen? I know that the Newton-Euler equations can be proven using the center of mass as reference, but I was wondering if this is a special case, or if you can provide a counter-example. We know that when a rigid body is only translatin... | The net torque on an object can be defined as
$$\boldsymbol{\tau}=\frac{\mathrm d {\mathbf p}}{\mathrm d t}\tag{1}$$
where $\mathbf p$ is the angular momentum. The angular momentum of any body about any general point is
$$\mathbf p=I_{\text{COM}} \boldsymbol{\omega} +m\mathbf r\times \mathbf v$$
where $I_{\text{COM}}$ ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/546847",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why don't we use rapidity instead of velocity? In school we learn that we can add velocities together, and then later on we learn that it's not correct and that there is a speed limit. Why create all this confusion when we could just use rapidity to begin with?
Rapidity is defined as $w = \mathrm{arctanh}(v / c)$, wher... | I think the main reason, as already captured in part by other answers (e.g. Davide Dal Bosco's), is the following: velocity is a physical quantity, it tells us how far something goes in a given time.
Rapidity may be mathematically convenient due to its relativistic addition properties, but what does it tell us?
As an e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/547371",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "35",
"answer_count": 13,
"answer_id": 9
} |
Is the force of gravity always directed towards the center of mass? This is a pretty basic question, but I haven't had to think about orbital mechanics since high school. So just to check - suppose a [classical] system of two massive objects in a vacuum.
If the density of either object is the same at a given distance f... | No. For example, the gravity of a cubical planet of uniform density, which can be computed analytically, is not directed towards its center (or any other single point).
You can also imagine a dumbbell-shaped mass distribution where the two heavy ends are very far apart. If you drop an apple near one end it is going to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/547505",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 6,
"answer_id": 1
} |
Can massless particle have effective mass? The effective potential was probably very familiar in many concepts.
However, what about effective mass?
Suppose a massless particle. For simplicity, suppose it's not some superficial particle, i.e. it has observable effect.
Is it possible for such massless particle to gain... | A photon, when propagating in a photonic crystal, will have a nonzero effective mass in all bands, except possibly the point $\vec k=0$ in the lowest band. This effective mass has all the weird properties of that of electron in crystal: anisotropy, varying value in the Brillouin zone, varying sign etc..
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/547610",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
Is the potential energy stored in a spring proportional to the displacement or the square of it? Suppose a mass of $M$ kg is hanging from a spring in earth. The mass will stretch the spring about $x$ m. So the change in the gravitational potential energy is $mgx$ J (supposing $x$ to be very small compared to the radius... | The elementary work $dW$ done on the spring in a elementary displacement $dx$ is:
$dW = Fdx$.
At this point the spring has already been stretched by $x$, so $F = kx$.
$dW = kxdx$.
Integrating from $x=0$ (the unstretched position) until the final $x$:
$W = \frac{kx^2}{2}$
$\frac{kx^2}{2} = mgx$, the loss of potential ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/548021",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 4
} |
Magnetic flux through circular loop Purcell says
if finite current flows
in a filament of zero diameter, the flux threading a loop made of such
a filament is infinite! The reason is that the field $B$, in the neighborhood
of a filamentary current, varies as $1/r$ where $r$ is the distance
from the filament, a... | $\dfrac{\mu _0 I}{2R}$ is the magnetic field at the centre of the loop, however, the magnetic field is not the uniform across the plane of the loop, getting stronger closer to the loop and exploding as Purcell notes if the filament radius is zero.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/548103",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does cutting a spring increase spring constant? I know that on cutting a spring into n equal pieces, spring constant becomes n times.
But I have no idea why this happens.
Please clarify the reasons
| This happens because spring constant is not really a constant. If you consider any normal elastic material, when a force F is applied, the strech is given by hooke's law :
$$\frac{{F}/{A}}{{\Delta L}/{L}}=Y$$
where $Y$ is the young's modulus of material, which is upto a limit, constant and depend only on the material.
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/548186",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 6,
"answer_id": 4
} |
Mathematically prove that a round wheel roll faster than a square wheel Let's say I have these equal size objects (for now thinking in 2D) on a flat surface.
At the center of those objects I add equal positive angular torque (just enough to make the square tire to move forward).
Of course the round tire will move fast... | If you allow an eccentric star gear hub like a Wankle engine then neither has a moving center of mass. The square would wear out faster due to uneven loading (same issue as Wankle engine seals).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/548519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "64",
"answer_count": 12,
"answer_id": 9
} |
What is the range of Pauli's exclusion principle？ In many introductions to the pauli's exclusion principle, it only said that two identical fermions cannot be in the same quantum state, but it seems that there is no explanation of the range of those two fermions. What is the scope of application of the principle of exc... | In quantum mechanics, particle interactions can be of two types, scattering interactions and bound states.
What is the scope of application of the principle of exclusion?
The Pauli exclusion principle applies to bound states of electrons in the solutions of potential equations for atoms/molecules/lattices. It will... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/548642",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 6,
"answer_id": 3
} |
Do things have colors because their electrons are getting excited when photons hit them? Atomic electron transitions can be caused by absorbing a photon with a certain wavelength. An electron jumps to an higher energy level, then it falls back and a photon is emitted. The perceived color of the photon depends on the en... | In addition to the other answers one should add color perception. White light contains all frequencies, if some are absorbed the scattered back light will have a different spectrum perceived differently by the receptors in our eyes.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/548900",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
In what sense is the equation of motion of a damped oscillator not time-symmetric? Consider the equation of motion of a damped oscillator
$$\frac{d^2 x}{dt^2} + \gamma \frac{dx}{dt} + \omega_0^2 x = 0 \,. $$
Why does the equation of motion not satisfy time-symmetry? Is it related to drag term?
I am new to this area..so... | Indeed, it is the drag term: it is easy to see that $y(t) = x(-t)$ satisfies equation
$$\frac{d^2y(t)}{dt^2} -\gamma\frac{dy(t)}{dt} + \omega_0^2y(t)=0.$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/549143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Does the $U(1)$ vector current flip under charge conjugation? The conserved $U(1)$ current of the Dirac Lagrangian is given by $j^\mu = \bar{\psi} \gamma^\mu \psi$, where $\bar{\psi} = \psi^\dagger \gamma^0$. As this is interpreted as electric current I would expect it to flip sign under charge conjugation. Charge conj... | For any fermion bilinear we have
$$
\psi^T_\alpha A_{\alpha\beta} \chi_\beta = - \chi^T_\beta A^T_{\beta\alpha}\psi_\alpha\,.
$$
So
$$
\begin{aligned}
(\bar\psi \gamma^\mu \psi)^* &= -\psi^* (\gamma^\mu)^\dagger(\gamma^0)^\dagger\psi
\\&= -\psi^* \gamma^0\gamma^0(\gamma^\mu)^\dagger\gamma^0\psi \\&=
-\bar\psi \gamma^\m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/549272",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.