Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Pan flute physics We are trying to create a custom pan flute. With some searching, we found a formula relating the length of a closed cylinder with the frequency at which it resonates, namely L = c / 4f, with c being the speed of sound. Based on this, we calculated that a cylinder to produce 880 Hz, or A5, would need t... | Your formula ignored the "end correction" to the length of the pipe. The standing wave in the air does not end exactly at the end of the pipe, but at a distance approximately 0.6D outside it, where D is the pipe diameter.
If your pipe diameter was about 7mm, that would explain the difference between 880Hz and 840Hz.
No... | {
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Calculating new velocities of $n$-dimensional particles after collision I am working on a particle simulation where there is no gravitational force exerted on particles, they simply travel through space and, upon collision, change trajectories accordingly. There isn't a set number of dimensions the simulation can be ru... | The exchange in momentum (impulse $J$) happens along a single direction. With the simple model of just spheres you can calculate the direction from the positions of the particles
$$ \boldsymbol{n} = \frac{ \boldsymbol{r}_j - \boldsymbol{r}_i }{ \| \boldsymbol{r}_j - \boldsymbol{r}_i \| } $$
where $\| \boldsymbol{r}_j-\... | {
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Loop-correction for non-commutative quartic theory
What is the meaning of the second, third and fourth graph? The image is from arXiv:hep-th/9912072.
| *
*The Feynman rules in non-commutative field theory are classified using 't Hooft double-line notation. In particular, the legs in a vertex has a cyclic order, cf. eq. (2.5) in Ref. 1.
*Interestingly, non-planar graphs are suppressed due to extra phase factors. (This is somewhat similar to the planar limit/large-$N... | {
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Why does blending hot food in the Nutribullet blender create a "pressure seal"? I have noticed that when blending cold foods in the Nutribullet, it is easy to unscrew the blender once the blending process is finished. When I blend something hot (i.e, boiled tomatoes, to create a tomato cream soup), I noticed it is very... | At the time that you fasten the lid, the vapor pressure of the hot liquid in the head space is equal to the equilibrium vapor pressure of the liquid at the high temperature of the liquid in the container. But, during the mixing, the liquid cools a little, and its vapor pressure decreases. So some of the vapor in the ... | {
"language": "en",
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Derivation of curl of magnetic field in Griffiths Can someone please derive how $$\frac{d}{dx} f(x-x') = -\frac{d}{dx'} f(x-x')~?$$
In Griffiths electrodynamics, this is directly mentioned. I'm really confused, can someone elaborate!
| This follows directly from the chain rule:
$$\frac{\partial}{\partial x}[f(x-x')] = f'(x-x')\frac{\partial}{\partial x}[x-x'] = f'(x-x')$$
whereas $$\frac{\partial}{\partial x'}[f(x-x')] = f'(x-x')\frac{\partial}{\partial x'}[x-x'] = -f'(x-x').$$ (Here I take $f'(x-x')$ to mean that (total) derivative of $f$ with respe... | {
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What is gravity's relationship with atmospheric pressure? I'm asking for clarification here. If Earth had the same atmospheric mass per square unit of ground but the Earth had suddenly gained mass so it had twice the gravity at the surface, would the Earth now have twice the atmospheric pressure just because of the dou... | The phenomenon that determines atmospheric pressure is very similar to Pascal's Law for incompressible liquids. But air isn't an incompressible liquid: as a gas its density is quite dependent on pressure and temperature, for instance.
A doubling of $g$ would nonetheless double also the atmospheric pressure.
I know pre... | {
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Why every system tends to be more stable? An entire topic of inorganic chemistry, i.e. chemical bonding, which is also one of the most important topics, is based on the idea of stability. But whenever I ask why every system tends to get stable, I never get a satisfactory answer. People say that's how nature "wants" to ... | 1- Because that's the definition of stability: you can't escape it
In the words of Peter above :
In this sense a system tends to become stable because stable states
are the only states a system can remain in.
2 - Not all systems are "stable" some are oscillatory (like our star system or a single atom). But you may ca... | {
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Why is stress defined in the way as it is? Stress is like pressure and it doesn't matter in which direction the force acts (given it is perpendicular to the surface).
I read in my book that if we have a rope which is being pulled on both sides by a force $F$ , then the stress at any cross section of the rope is define... | Firstly, by its definition, the restoration force developed per unit area inside the body when subjected to the deforming force is called stress.
Secondly, by Newton's third law of motion every action has an equal and opposite reaction and both act on two different bodies.
Now let's take your rope or whatever body it i... | {
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Nature of Work done by friction I have always been told that work done by friction can, at most, be zero, but never positive.
But consider two blocks placed one on top of the other, such that their surfaces in contact are rough. If we give the block on the top a certain horizontal velocity, then in crude words, we can ... | *
*Friction is a force that apposes the motion. It does negative work.
*The second block is subjected to reaction force due to friction and as such is not friction force.
*Just some terminology.
| {
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Why is it easier to handle a cup upside down on the finger tip? If I try to handle a tumbler or cup on my fingertip (as shown in fig), it is quite hard to do so (and the cup falls most often).
And when I did the same experiment but this time the cup is upside down (as shown in fig), it was quite stable and I could han... | Maybe because when the cup is the right way up, it’s centre-of-mass is above the point on your finger meaning that as your finger tries to balance the cup any small motion will generate a torque about this c.o.m making it harder to balance.
When the cup is upside down, you have your finger on or going through the c.o.m... | {
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How is flow velocity defined in Navier-Stokes equations? I know Navier-Stokes equations rely on the continuum assumption. In this context, how is the flow velocity mathematically defined? Is it merely a spatial average of the micrscopic particles velicities inside the Representative Volume Element? Or is it a mass-weig... | First of all, I would not necessarily call it the continuum approximation. I think that physically, "coarse grained" is a better word. Obviously, there is no system for which $\vec{v}(\vec{x})$ has meaning at arbitrarily short distances.
Also note that fluid dynamics is about the motion of conserved charges in a system... | {
"language": "en",
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Relativistic Jets in Black Holes It is understood till now that nothing is faster than speed of light and we also know that even light cannot come out of black hole(that’s why the name black). So does that mean that the Relativistic jets which (assuming I am true) come out of the black hole are faster than the speed of... | Relativistic jets do not come out of the black hole. They originate from near the black hole but not, of course, from inside the event horizon.
The relativistic jets consist of streams of charged particles that are accelerated close to the black hole and travel, often in both directions, along the presumed rotation axi... | {
"language": "en",
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Hamiltonian formalism of General Relativity Textbook I've been reading Wald's book on General Relativity and in appendix $E_{2}$ it discusses the Hamiltonian formalism of General Relativity.I would like to understand it more, can you recommend me a textbook about ADM formalism?
P.S.
I have already read Eric Poisson boo... | Besides the original literature DanielC enumerated,
*
*Bojowald's Canonical Gravity and Applications is specifically about the Hamiltonian formalism;
*D'Inverno's Introducing Einstein's Relativity has a fairly good introduction to the Hamiltonian formalism, as well, but simpler...more friendly for students (I'd imag... | {
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What quantum gates are needed to get the state $|01\rangle+|10\rangle$ from $|00\rangle$? I was wondering if I start with two qubits in the state
$$|00\rangle$$
If it's possible to apply gates to get it to the state
$$\frac{|01\rangle + |10\rangle}{\sqrt{2}}$$
I have tried applying the Hadamard Gate, Controlled X etc, ... | Let's consider a space of four states $\{|00\rangle, |01\rangle, |10\rangle, |11\rangle\}$. The question is whether exist any operator for which,
$$
\left(\begin{array}{cccc}
a_{11} & a_{12} & a_{13} & a_{14} \\
a_{21} & a_{22} & a_{23} & a_{24} \\
a_{31} & a_{32} & a_{33} & a_{34} \\
a_{41} & a_{42} & a_{43} & a_{44} ... | {
"language": "en",
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Is it possible for a wavefunction to partially collpase? What would happen in this situation: You have an ideal empty space with only two objects: a photon emitter, and a small observer. The emitter emits a photon in a random direction, with every direction being equally likely.
Given that the probability of observing ... |
The wavefunction only collapses if it collapses onto the observer. Otherwise, the wavefunction will be modified to exclude passing through that point
That's correct, except that what you called "modified" is also a collapse. The case where the photon is not detected, but the wavefunction nonetheless is modified/is up... | {
"language": "en",
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Will the velocity be constant in a vertically oriented tube?
The tube here is placed into a water stream moving with a velocity $v$
My query is will the velocity be constant throughout the pipe or only in some places?
I have conflicting opinions on this, the equation of continuity would say the velocity is constant th... | The equation of continuity and Bernoulli's equation should always be satisfied (at least in ideal condition i.e. no viscosity and ...)
What you are forgetting is the pressure in Bernoulli's equation. The pressures at the beginning of blue line and at the end of the blue line are not the same. That explains how the velo... | {
"language": "en",
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How can photons destructively interfere? This is a concept I don't fully understand. If I have two photons each with frequency $\nu$, then they each have an energy of $E = h\nu$. If they get matched with an inverted phase, then the summed wave will be null due to destructive interference. Then where does the energy go?... | In the present day physics standard model photons are elementary particles , on par with the other particles in the table. This means they are point particles, of fixed (in this case zero) mass with spin 1 and $E=hν$ . The $ν$ is the frequency that the classical light will have, as it is composed of zillions of photon... | {
"language": "en",
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General plane motion and freely floating rigid body
Consider a rigid rectangular plate of length $l$, width $w$ and thickness $t$ which is at rest and is floating freely in space (no gravity). The center of the plate is at $O_L$ with respect to global coordinate frame $O_G$. The initial pose (position and orientation)... | you have to solve those equations
\begin{align*}
&m\,\boldsymbol{\ddot{R}}=\boldsymbol{S}(\boldsymbol\varphi)\,\sum_i\,\boldsymbol{F}_i\\
&\boldsymbol\Theta\,\boldsymbol{\dot{\omega}}+\boldsymbol\omega\times\,\left(\boldsymbol\Theta\,\boldsymbol\omega\right)
=\sum_i \left(\boldsymbol{r}_i\times \boldsymbol{F}_i\right)\... | {
"language": "en",
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Entropy reducing power generator An 8.3 EER 1200 W air conditioner will move 10000 BTU of heat per hour. 1 BTU is 1055 J of heat. Per second this is moving 2930 W of heat energy. It is possible to get them even more efficient e.g. 12 EER.
This means 4130 W of heating on hot side, and 2930 W of cooling on cold side.
T... | No, such a machine cannot exist in reality. One critical thing that you neglected in your analysis is the temperature. Every heat engine or heat pump has a hot side and a cold side. The efficiency depends strongly on the temperature difference. The heat pump operates with a much lower heat difference than the steam eng... | {
"language": "en",
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Generalization of first law of thermodynamics What is the mathematical statement for the first law of thermodynamics, accounting for kinetic energy, potential energy, internal energy, work, heat and most importantly taking into consideration the work-energy theorem?
Also, is $∆U=∆Q-∆W$ only valid for systems whose cent... | The law of conservation of energy states that the total energy of an isolated system is constant; For a thermodynamic process (closed system) without transfer of matter, the first law is often formulated
$$dU=\delta Q+\delta W$$
or
$$dU=TdS-PdV$$
In the case of a closed system in which the particles of the system are o... | {
"language": "en",
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Why can't dark matter lose energy by gravitational waves and collapse into itself? Because of lack of electromagnetic induction, dark matter can't lose its gravitational potential energy. That is preventing it from collapsing like an ordinary matter cloud in space.
But why can't dark matter lose energy by gravitational... | Well, we do not know what it is. On top of that IF it is made of particles, the density is very very low. So, it needs a lot of time to collapses.
| {
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Why does air pressure decrease with altitude? I am looking to find the reason: why air pressure decreases with altitude? Has it to do with the fact that gravitational force is less at higher altitude due to the greater distance between the masses? Does earth’s spin cause a centrifugal force? Are the molecules at higher... |
Has it to do with the fact that gravitational force is less at higher
altitude due to the greater distance between the masses?
The gravitational force does decrease as you go higher up, but that's not the reason. The pressure would still be greater at the bottom even in some weird physics where gravity got stronger f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/602020",
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When did liquid first appear? When and where did matter in liquid state first appear in our universe?
Liquid has never been a global state of the universe, but it certainly appears nowadays locally in some places.
As far as I know, liquid currently only exists on planets, but I can well be mistaken.
I can imagine a cou... | Have a look at a paper 1312.0613 by A. Loeb. He considers possible existence of rocky planets with liquid water as early as $100<(1+z)<137$ (about 10-17 million years since Big Bang).
From the footnote 2:
After the first stars formed, the subsequent delay in producing heavy elements from the first supernovae could ha... | {
"language": "en",
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Dirac fields: Do particle and antiparticle creation operators act differently on the vacuum? Given a Dirac field $$\Psi(x):=\int\frac{d^4k}{(2\pi)^4}\delta\left(p_0-\omega(\mathbf{k})\right)\sum_s\left(a_s(k)u_s(k)e^{-ikx}+b^\dagger_s(k)v_s(k)e^{ikx}\right)$$
with the creation operators $a^\dagger_s(k),b^\dagger_s(k)$ ... | Ah I think I understand your question now and I think this is a simple notational issue. The single particle states for the particles and antiparticles should be denoted differently, i.e. trying to be as close to your notation would give something like
$$|k,s\rangle \equiv a^\dagger_s(k)|0\rangle \ \ \ \ , \ \ \ \ |\t... | {
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Why only reversible adiabatic processes are called isentropic and not irreversible ones? For both reversible and irreversible adiabatic processes, $dQ =0$,and by the definition of entropy $dS=dQ/T$, it should imply that entropy is constant for both. Why it is not so?
| In general, you can write that for all processes $\frac{\delta q}{T} \le dS$ (Clausius) but in the case of a reversible process you have equality $\frac{\delta q}{T}|_{rev} = dS$. If the process is adiabatic then by definition $\delta q =0$ hence for the reversible case you have the equality $dS=0$, i.e., an isentropic... | {
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Is it the gravitational field created by an object which exerts force on another object or the interactions between their fields that exerts force? We are taught that Gravitational force exerted by an object is a two-step process:
*
*The object creates a field around it.
*The field exerts a force on bodies present i... | Gravity is neither a force or a field. It is the effect of matter, or energy, on the curvature of spacetime, which affects the matter or energy imbedded in that spacetime. The single least understood component of physics as it is currently understood. Many paradoxical aspects of gravity exist.
Most notably, gravity ... | {
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"timestamp": "2023-03-29T00:00:00",
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Last step derivation of hamiltonian of particle in electromagnetic field My textbook quantum mechanics does an analogues derivation of the hamiltonian as given here, but I'm struggling to understand the last step: The final obtained hamiltonian is (in my textbook's case)
$$H = \frac{1}{2}m\dot{\vec{x}} + eV$$
with V th... | The mistake you're making is in assuming that $$p_x = m \dot{x}.$$ This is not true. $m \dot{x}$ is known as the kinetic momentum, while $p_x$ is known as the conjugate momentum (to the coordinate $x$). In most (all?) problems in Classical Mechanics these two concepts are equal, but they aren't the same in general.
The... | {
"language": "en",
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Did I make an electric circuit with my cat? This is definitely the dumbest question I've asked, but I'm curious. My cat was resting her head on my left hand while I pet her with my right. Suddenly, my left hand began receiving regular static electric shocks. Was I pulling electrons from her fur with my right hand, thus... | I think you did steal a bunch of electrons from your cat. Hair typically loses electrons very quickly. For more information look up triboelectric series.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/602710",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is this constraint equation written right here?
This is a constraint equation he has written here.
This is a trick to solve constraint equations faster.
Now he has made a equation that a2 ( acceleration of 2kg block) and a1(acceleration of 1kg block).
a2 = 2a1.
I have done earlier constant equation by other method.I t... | Your question will not be understood by people who don't know this trick you should provide a link or give a short derivation. That being said,
$\sum T.a$ Is the summation of the dot product of the tension force and acceleration you should know that the dot product is the product of their magnitudes and the angle betwe... | {
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"source": "stackexchange",
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Scalar product of fields in Schwarzschild space-time The scalar product of fields in curved space-time is defined by (Birrel, Davies)
$$\left(\phi_{1}, \phi_{2}\right)\equiv-\mathrm{i} \int_{\Sigma} \phi_{1}(x) \overset{\leftrightarrow} {\partial_\mu}\phi_{2}^{*}(x)\left[-g_{\Sigma}(x)\right]^{\frac{1}{2}} \mathrm{~d} ... | First of all that is not a scalar product but it is a symplectic form.
Yes you can use the lightlike infinity provided
(a) no information escapes through the timelike infinity,
(b) you have rewritten that integral in the language of differential forms ,
(c) the field is massless (otherwise it vanishes too fast before... | {
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Why does wind blowing across a bird bath cause the water to freeze even though the ambient air temp is 39 - 40 degrees F? Frequently, after cold frontal passage, a strong NW wind blows across the open marsh and through our back yard. With ambient temps still well above freezing, the surface of the water in our concrete... | Surely evaporative cooling is a significant factor. The wind carries away water molecules that have evaporated from the water, so not as many return to the water (through collisions with air molecules) than without the wind. Therefore the net evaporation rate is enhanced, and so is the evaporative cooling.
The cooling ... | {
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What happens to phase after wavefunction collapse? Suppose an initial quantum state $\psi = a_1\phi_1 + a_2\phi_2 + ... + a_n\phi_n$, where $\phi_i$ is the eigenfunction with eigenvalue $\lambda_i$ of some measurement operator. Post-measurement, we will find the system in state $\phi_i$ with probability $|a_i|^2$.
What... | In quantum mechanics, states are represented by rays in Hilbert space, or more accurately, the space of states is projective Hilbert space - for example, for a finite dimensional system, the space is $H_n / \sim \ \cong \mathbb{C}P^{n-1}$, where for $u, v \in H_n$, $u \sim v$ if $u = \alpha w$ for some non-zero complex... | {
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What would happen if a 10-kg cube of iron, at a temperature close to 0 kelvin, suddenly appeared in your living room? What would be the effect of placing an object that cold in an environment that warm? Would the room just get a little colder? Would it kill everyone in the room like some kind of cold bomb? What would h... | There are about 30 m3 of air in a room, and the density of air is about 1.2 kg/m3. So the mass of air in the room would be about 36 kg. The heat capacity of air is about 1 kJ/kg-K. So the mass times heat capacity of the air is about 36 kJ/K. The mass times heat capacity of the 10 kg of iron is about 4.5 kJ/K. So, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/603701",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "41",
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Understanding dependent/independent variables in physics How does one determine the independent and dependent variables?
What do the terms mean?
Can they be derived from a formula?
For example I saw in a textbook $F = k\Delta l$, Hooke's Law, that $F$ is the independent variable. Is this because $\mathbf {F} $ is the s... |
How does one determine the independent and dependent variables?
It's totally relative. In $F = k\Delta l$ all three variables can be considered dependent or independent, depending on your purpose.
E.g. in $\Delta l=\frac{F}{k}$, $\Delta l$ would now be considered the dependent variable.
Now suppose you studied a set ... | {
"language": "en",
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"source": "stackexchange",
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Does Work become state function in an Isothermal Process and what are other processes in which it happens? In a reversible isothermal process and for an ideal gas we know from the definition of Helmholtz free Energy
$dF= -SdT -PdV$.
And as temperature doesn't change for an isothermal process, $dT$ must be zero. So dF c... | Here is an additional analysis that is consistent with my previous answer:
For a process in a closed system, the first law of thermodynamics tells us that $$\Delta U=Q-W$$Now, if we define an isothermal process (either reversible or irreversible) as one in which the temperature of the system in its initial and final th... | {
"language": "en",
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How do we know it is the Centripetal Force we have to calculate? A helicopter rotor blade is 7.80 m long and has a mass of 110 kg. (a) What force is exerted on the bolt attaching the blade to the rotor axle when the rotor is turning at 320 rev/min? (Hint: For this calculation the blade can be considered to be a point m... | There are actually three important components of the bolt force: vertical, to keep the blade from falling, horizontal-tangential which pushes or pulls on the blade perpendicular to its length, and horizontal, to keep the blade from flying away from the rotor axle.
In order to calculate the vertical force you would need... | {
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How is a tensor operator defined in terms of commutators? If $J_i$ represent the angular momentum operators, then a scalar operator $S$ (rank-0 tensor) is defined as an operator which satisfies $$[S,J_i]=0$$ for $i=1,2,3$.
$A_i$ is a vector (rank-1 tensor) operator, if it satisfies $$[J_i,A_j]=i\hbar\epsilon_{ijk}A_k$$... | Given
\begin{align}
\hat L_\pm \vert \ell m\rangle &= \sqrt{(\ell\mp m)(\ell\pm m+1)}\vert \ell,m\pm 1\rangle\, ,\\
\hat L_0 \vert \ell m\rangle &= m \vert \ell m\rangle
\end{align}
then by definition $\hat T^{(\ell)}_m$ commutes as
\begin{align}
[\hat L_\pm, \hat T^{(\ell)}_m]&=\sqrt{(\ell\mp m)(\ell\pm m+1)}\,\hat ... | {
"language": "en",
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How impulse is fundamentally different than momentum? Are impulse and momentum really different quantities?
Is there a conservation law of Impulse too just like momentum conservation.
And lastly, will impulse be conserved for the cases where body (say a rod)is hinged. I know that momentum conservation can't be applied ... | Momentum is the base quantity. Impulse is the change in momentum from an initial value $\mathbf{p}_i$ to a final value $\mathbf{p}_f$:
$$\mathbf{I} = \Delta \mathbf{p} = \mathbf{p}_f - \mathbf{p}_i$$
However, and hence, they both have the same dimensions and units (force times time, e.g. newton-seconds and prefixed der... | {
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Do pseudovectors also transform differently to vectors under spatial dilation, not just reflections and parity? It is frequently expressed online that the only difference between vectors and pseudovectors is a change in sign with reflection/parity transformations etc.
For instance the pseudovector angular momentum $\ve... | Well, one possibility is that this is just a matter of where attention is focused. Since, excluding the weak force, all physical laws are invariant under parity, it's interesting to note that pseudovectors transform differently than vectors under that operation. However, real physics isn't, as far as we know, invariant... | {
"language": "en",
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Why do we need instantaneous speed? I am new to this topic and was just wondering about the use of instantaneous speed. I mean, we use to calculate the speed of car let us say at 5 sec. So we take the distance travelled in 4.9 to 5.0 seconds and divide it by time. We get instantaneous speed. We could simply as well hav... | Because instantaneous speed affects physics. Imagine a wall $10~\textrm m$ in front of you. You walk towards it smoothly over a timeframe of, say, $20~\textrm s$, and without getting slower, you walk into the wall. You'll feel a slight bonk, but nothing serious is going to happen. Now imagine the same 20 seconds going ... | {
"language": "en",
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"source": "stackexchange",
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Is displacement current the rate of change of induced polarization? I know that the displacement current is proportional to the rate of local polarization change. Yet, I'm not sure if it is technically correct to attribute the displacement current to the rate of change in the induced polarization, as polarization itsel... | No, you can have a displacement current in a vacuum, where there is no polarization possible.
| {
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Application of the Cartan Structure Equations seems to imply the Einstein-Palatini action is zero? The Einstein-Palatini action can be written as
$$ S = M_{pl}^2\int\varepsilon_{abcd}\left(e^a\wedge e^b\wedge R^{cd}\right), $$
where $e^a={e^a}_\mu\text{dx}^\mu$ is the basis one-form and $R^{ab}=\frac{1}{2}{R^{ab}}_{\mu... | This part of yours is incorrect:
$$
\begin{align}
S &\sim \int\varepsilon_{abcd}\left(e^a\wedge e^b\wedge D\omega^{cd}\right) \\
&= \int\varepsilon_{abcd}\left(-De^a\wedge e^b\wedge\omega^{cd} + e^a\wedge De^b\wedge\omega^{cd}\right)
\end{align}
$$
The correct derivation is:
$$
\begin{align}
S &\sim \int\varepsilon_... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is there a phase shift $\pi$ radians when a pressure wave is reflected upon a medium having less acoustic impedance? In my text book it is written that a sound wave modeled as pressure fluctuations does not undergo a phase shift of $\pi$ radians upon reflection as there will be a pressure antinode at the interface and ... | Short answer: Yes, for a pressure wave reflected from a surface with less acoustic impedance than the original medium the phase shift would be $\pi$ radians, neglecting absorptive processes.
Longer answer:
I have some equations, so let me provide the full context. Consider a plane pressure wave propagating in a homoge... | {
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Where does the law of conservation of momentum apply? Take the scenario of a snowball hitting a tree and stopping. Initially, the snowball had momentum but now neither the snowball nor tree have momentum, so momentum is lost (thus the law of conservation of momentum is violated?). Or since the tree has such a large mas... | The snowball will likely break apart and some of that momentum will be transferred to its subsequently far-flung constituent far flung parts. It will probably deform, transferring some of that momentum into the new shape. Also, some of that kinetic energy will be converted to heat, both into the tree and into the mater... | {
"language": "en",
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Angular Momentum of a rigid body w.r.t to an axis about which it is not rotating suppose we need to calculate $\overrightarrow{L}$ about an axis, but the rigid body is not rotating about this axis. Can we define the $\overrightarrow{L}_{axis}$ still? I think we should be able to since $\overrightarrow{L}$ (for an infin... | Yes. If the angular momentum of a body about the origin is $\vec{L}=\vec{r} \times \vec{p}$, the angular momentum about an axis in the direction $\hat{n}$ is given by-
$$L_{axis}=|\hat{n}.\vec{L}|$$ You can see that for yourself pretty easily. This is simply the projection of the angular momentum of the body about that... | {
"language": "en",
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When a microwave oven stops, why are unpopped kernels very hot and popped kernels not hot? A commonplace empirical observation is that when a microwave oven stops, unpopped kernels are very hot (it's physically painful to touch them) and popped kernels are not.
Is there an elementary (or not) exposition of the physics ... | Popcorn pops in a microwave oven due to the microwaves interacting with the moisture in the popcorn kernel raising its internal temperature and pressure. Once the pressure increases enough the kernel pops and the moisture escapes and cools. The moisture in the un popped kernel remains hot.
Hope this helps.
| {
"language": "en",
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"source": "stackexchange",
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Why isn't the magnetic field density zero here? In my lecture notes for magnetostatics, my professor has this explanation of why H is not necessarily $0$ that I dont understand.
$$\nabla \times \bf{H} = \bf{J} \\ \bf{J}=0 \Rightarrow \nabla \times \bf{H} = 0 \not\Rightarrow H = 0 \\ \nabla \cdot H \neq 0 $$
"H is only ... | The field $\vec{H}$ in a medium is defined as
$$\vec{H}(r,t) = \frac{1}{\mu_0}\vec{B}(r,t)- \vec{M}(r,t)$$
where $M(r,t)$ is the magnetization field which depends on the medium properties. Maxwell's law states that $\vec{\nabla}.\vec{B}=0$, i.e., magnetic monopole does not exist. But that does not imply that there is n... | {
"language": "en",
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Partial derivative of thermodynamics properties I know that in finding the partial derivative of certain thermodynamics property such as $H=H(P,V)$, we can hold the other variable as constant. But what will happen if the relation have more than two variables? For example, if a certain thermodynamics property of pure su... | When you evaluate that partial derivative, you do not need to consider other properties, U and S, as constant. You have $$d(T\ \Gamma)=TdS+SdT-dU+VdP+PdV$$But, $$dU=TdS-PdV$$Therefore, $$d(T\ \Gamma)=\Gamma dT + Td\Gamma=SdT-VdP$$So, $$\left(\frac{\partial \Gamma}{\partial P}\right)_T=-\frac{V}{T}$$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Does all EM radiation consist of photons? Since university I've always accepted without question, that electromagnetic radiation consists of photons; but is it true?
I believe it was Einstein who demonstrated that light comes in small packets, 'photons', and since light is EM radiation, it is tempting to conslude that ... | Photons are what light is and they can have frequencies anywhere from radio to gamma. Billions of coherent photons resemble a wave.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/606593",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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What does it mean that a neutron has a 'negative' magnetic moment? Most questions about this ask why, or how, a neutron has a magnetic moment at all, or why it is negative....
But I am curious as to what it means, physically or experimentally, for a magnetic moment to be 'negative'....
I am reading that a neutron's 'an... | Suppose that a spinning body has equal amounts of positive and negative charge --- so its total charge is zero --- and the positive charge is near the rotation axis, while the negative charge is further away from the axis. Then the magnetic moment will point in the opposite direction to the spin. Presumably this is a ... | {
"language": "en",
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Which force exerted a torque? Suppose a horizontal disc fixed in the center with a vertical shaft passing perpendicular to the plane, is rotating at some angular speed and there is an insect sitting initially at center. The insect then starts moving radially outwards. From conservation of angular momentum of insect+dis... |
Therefore, there must be a force along the y axis, what can be such a force?
Friction is that force. It speeds the bug as it moves to tangentially faster moving parts of the ring. Resulting in an equivalent and opposite force slowing the ring down. In the disc's frame friction opposes the fictitious Coriolis force.
T... | {
"language": "en",
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How can we discern so many different simultaneous sounds, when we can only hear one frequency at a time? As I understand it, the eardrum works like any other kind of speaker in that it has a diaphragm which vibrates to encode incoming motion into something the inner ear translate to sound. It's just a drum that moves b... | As you mentioned, all the different waves get added together in a Fourier series.
The hair cells in the inner ear are essentially performing a Fourier analysis of this combined wave, splitting it back into its component frequencies. The amplitudes of each frequency are then sent to the brain, which performs higher leve... | {
"language": "en",
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Calculating the direction of friction on an inclined plane/Determining the fate of a round body on an inclined plane
Question:
If a round object (say ring or a sphere) is kept on a rough inclined plane of inclination $\theta$ and coefficient of friction $\mu$ is such that it exactly balances the component of weight of... | This is the mistake you are making:
$mg \sin \theta=\mu mg \cos \theta$
Friction will never be equal to $\mu mg \cos \theta$. Why?
Friction will be static and will only try to prevent the slipping between the point of contact and the ground. The net acceleration of point of contact of ground $\ne g\sin\theta$ due to... | {
"language": "en",
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Wavelength of reflected light vs transmitted light In the basic setup of the experiment below, the transmitted light is used to infer the absorbed wavelengths. The explanation of the experiment states that a high transmittance reading for a specific wavelength means that wavelenght is not absorbed.Does this mean that t... | Why are you asking about reflected light levels? Are you worried that the flask and/or the solution have spectrally-varying reflectances? If so, then the standard way to deal with that is to run a reference calibration with the flask and whatever solution you intend to use, but none of the test material itself. Tr... | {
"language": "en",
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Can sound be used for propulsion? I'm no physicist so this might seem absurd.
I Remember watching a cartoon as a kid where the character uses a powerful speaker to propel his cart and I was wondering if this was actually possible.
Being a highschooler I am aware to propel forward you shoot something backward.
So maybe ... | Sure! Sound waves carry energy and momentum. So you could use a speaker like a very weak rocket. Totally impractical, though.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/607611",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Rotation matrices in Schwinger's oscillator model of angular momentum I am Section 3.9 in Sakurai's Modern QM, 3rd ed (which is Section 3.8 in 2nd ed.) I am trying to obtain the given form for $\hat D(R)|jm\rangle$:
I employ $\hat D^{-1}\hat D=1$ and ignore the denominator to write
\begin{align}
\hat D(R)|jm\rangle&... | You may use the following formula:
$$(ABA^{-1})^{m} (ACA^{-1})^{n}=(ABA^{-1})(ABA^{-1})...(ABA^{-1})(ACA^{-1})(ACA^{-1})...(ACA^{-1})=AB^{m}C^{n}A^{-1}$$
where $A,B,C$ are operators and $m,n$ are some positive integers.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Physical meaning of the inner product of quantum states I would like to ask a simple question about quantum mechanics. Let $|a\rangle$ and $|b\rangle$ two states in which a quantum system can be. Then, I can consider the following inner product:
$$
\langle a|b \rangle
$$
Does this quantity have any physical meaning?
I ... | Physically, the quantity $\langle a | b\rangle$ is the probability amplitude that a measurement will find the system in state $|a\rangle$, given that it was originally prepared in state $|b\rangle$.
To get from this to the probability, you need to take the mod-square, i.e. $|\langle a | b\rangle|^2$.
| {
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Does alpha decay have anything to do with weak interaction? In alpha decay, an atomic nucleus emits an alpha particle (identical to a helium-4 nucleus). This happens in large nuclei because the nuclear force keeping the nucleus together is outweighed by the electromagnetic force.
Makes sense to me, but isn't the weak i... | The basic radioactive decay modes are alpha decay (the emission of a helium nucleus), beta decay (the emission of electrons/positrons and neutrinos), and gamma decay (emission of photons). These decays are governed by the strong, weak, and electromagnetic force, respectively.
Obviously, there are many details. There ar... | {
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Would we need Alternating Current if superconducting wires existed? The major advantage of Alternating Current is that it can be transmitted to large distances without significant losses, which is not possible in Direct Current.
Had economical superconducting wires existed, DC could be transmitted to any distance witho... | Ohmic power line losses occur in both DC and AC systems and are always proportional to the RMS value of the current, so your assertion that AC transmission has insignificant losses compared to DC is not correct.
The major advantage of AC power transmission is that the transmitting voltage can be transformed down as nee... | {
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Finding an exact value for energy in perturbation theory
Supose a particle of mass $m$ and electric charge $q$, subject to harmonic potential in 1D, is placed in an area with electric field $\vec E = E \hat u_x$. Determine the exact change in its energy spectrum caused by interacting with this field.
I started by wri... | If you want an exact solution, you can't use perturbation theory.
Try a change of variables $x\rightarrow y$ so that:
$$ \frac 1 2 m \omega x^2 + qE x = \frac 1 2 m\omega (y-a)^2 - b^2 $$
where $a$ is an offset to the (classical) ground state, and $-b^2$ is a global energy shift.
Classically, that energy shift is store... | {
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Reason of saturation region in MOSFET I can't wrap my head around the circumstance that, somewhen when I increase $ V_{DS} $ the current $ I_{DS} $ will remain constantly. Why is that?
https://www.electronics-tutorials.ws/amplifier/mosfet-amplifier.html
| For concreteness, consider an n-channel enhancement mode MOSFET whose source terminal is connected to the body. If $V_{DS}=0$ and $V_{GS}>V_{th}$, a conducting channel is opened between the drain and source. When $V_{DS}$ is increased, current flows across the channel.
However, increasing $V_{DS}$ has another effect ... | {
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Stability analysis basics I would like to see a rigorous treatment of stability analysis.
For example, a lot of high-school level texts give examples like this: https://courses.lumenlearning.com/physics/chapter/9-3-stability/
But they describe stability in very qualitative terms like "Hence, the chicken is in very sta... | Today I'm in the mood of trying to be an artist :
Chicken is stable only partially, otherwise why it needs nails ? Humans uses somatosensory system in brains to control stability and balance in a stationary or moving positions. Chicken has small nervous system, thus nails for compensation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/609262",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the meaning of $F=ma$? Does it mean that an object with mass $m$ will have an acceleration $a$ if an external force $F$ is applied to it? I know this is a very simple question, but I am just learning physics. I am seeing the basics of how a block on a horizontal frictionless surface gets accelerated by a force ... | The answers here are already great, but here's a small suggestion I can add: when learning Newton's laws, I think it's easier to start off by thinking of Newton's second law as
$$
a = \frac{F}{m}
$$
This is mathematically the same as $F = ma$, of course, but I've noticed that students tend to think that an equation $X ... | {
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Hypothetically, why can't we wrap copper wires around car axles and turn them into electromagnets to help charge the batteries? We already have a magnetic core, why can't we use it to recharge the batteries? The only problems I see with it are potentially wiping magnetic data, but doesn't the electromagnet have to be r... | Not stated in your question is the type of vehicle we are discussing - I am assuming this is about vehicles powered by internal combustion engines.
Attaching some sort of electricity generating device to the car's final drive to recover kinetic energy during braking comes down to cost/benefit.
Every piece of equipment ... | {
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Particle Physics: Decomposition of a Helicity Spinor I would have a general question: If we consider the decay of the $W^{-}$ boson into $l^{-}\nu_{\bar{l}}$, how can we calculate the polarization of the $l^{-}$?For example, Mark Thomson has on page 299, Eq. (11.17), the following decomposition of a right-handed helici... | Consider a particle moving in the $\hat z$ direction, for simplicity. Define $\kappa= p/(E+m)$ and note it collapses to 1 for m =0. In this frame,
$$
u_ \uparrow =\sqrt{E+m} \begin{pmatrix} 1\\ 0\\ \kappa\\ 0\end{pmatrix}, \qquad u_ \downarrow =\sqrt{E+m} \begin{pmatrix} 0\\ 1\\ 0\\ -\kappa \end{pmatrix}.\tag{4.... | {
"language": "en",
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Centrifugal Force Dilemma While learning Classical Mechanics, I am confused on nature and application of centrifugal force.
In my textbook, it is written that centrifugal force is a pseudo force that, depends on reference frame, but I can't understand that if it is pseudo force then why we feel something pushing us out... | It is also called fiticious force, or d'Alembert force, or inertial force. I prefer the term inertial force, because we do feel it, not an imagination.
We apply centrifugal force only when we are in a rotational frame, for example we stand on earth, there is a centrifugal force due to the spinning of the earth. The cen... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/609898",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does soap clean grease because it lowers surface tension? Or are these things independent?
Have you noticed how much easier it is to clean dirty, greasy hands or plates once you add soap to the water? By reducing the surface tension of water, soaps and detergents allow it to mix with oil and grease more easily. Warm w... | Soap has one end of its molecule which is soluble in water, while the other end is soluble in oily substances. This makes soap act like a glue that sticks oil molecules to water molecules, allowing the water to carry away the oil. In this way, soapy water will remove oily stains from fabric.
In addition, soap reduces t... | {
"language": "en",
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Why do we need to introduce thermodynamic potentials? Each thermodynamic potential (Enthalpy, Helmholtz free energy, Gibbs free energy) is the same as the 1st law of thermodynamics. Then, why do we need them? Why did people introduce them in the first place?
| Two central questions in thermodynamics are
*
*What are the conditions for spontaneous reaction?
*What are the conditions for equilibrium?
Constrained by First law of thermodynamics (Conservation of Energy), and hinted by second law of thermodynamics (Increasing entropy), under different conditions, these questions... | {
"language": "en",
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Quantum Harmonic Oscillator Virial theorem is not holding I'm asked to calculate the average Kinetic and Potential Energies for a given state of a quantum harmonic oscillator. The state is:
$$
\psi(x,0) = \left(\dfrac{4m\omega}{\pi\hbar}\right)^\frac{1}{4}e^{\frac{-2m\omega}{\hbar}x^2}
$$
The thing is, calculating
$\la... | You can have Gaussian fields that are not eigenstates, but then they are not time independent -- and time independence is the essential element of the virial theorem. For example, the harmonic oscillator time-dependent Schrödinger equation
$$
i\frac{\partial \psi}{\partial t} = -\frac 12 \frac {\partial^2 \psi}{\pa... | {
"language": "en",
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Magnetization and Polarization in an electromagnetic field theory I am currently reading through a paper by Hughes and Ramamurthy (ref: https://arxiv.org/abs/1508.01205), which describes the electromagnetic response of a line-node semimetal by the action
$$S[A,B] = \frac{e}{16 \pi^2}\int d^4x \; \epsilon^{\mu \nu \rho ... | See here. For a more detailed source on the Lagrangian formulation of electrodynamics in matter, there is a wonderful book "Classical Field Theory" by David Soper.
| {
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Why does a wooden spoon creates bubbles when put in hot oil? This question might be a bit weird, but I just asked myself why a wooden spoon creates bubbles when put in oil at about 170°C. My idea is, that the water in the spoon reacts with the Oil, but why does this just starts to happen when the Oil reaches approx 170... | I doubt whether this has to do with the content of the spoon, as old and new spoons behave in the same way. I suspect the reason is that oil is a mixture of different oils, and that oils with smaller molecules have a lower boiling temperature. The oil may contain a small proportion with a boiling temp of about 170°C. T... | {
"language": "en",
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How warm are radioactive metals? I read that radium is warm to the touch -- is that because of actual heat or is that because, for example, the radiation it emits creates the sensation of warmth? How high of a temperature can a radioactive element or isotope actually have?
| Subcritical chunks of enriched uranium and plutonium are naturally warm to the touch, because of the thermal energy released as they spontaneously fission. Plutonium has a higher spontaneous fission rate and this effect is stronger for Pu.
If you place two such subcritical chunks near one another and slide them togethe... | {
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What does particles with asterisk superscript * mean, such as $Z^*$ or $W^*$, in decay production? I can always find that in some articles the production of higgs decay written as "$\rm H\to {ZZ}^*\to 4l$", "$\rm H\to ZZ\to 4l$", "$\rm H\to Z\gamma^*\to\ldots$” What dose it mean when some particles with a superscript *... | In this context, the asterisk refers to a virtual particle, one that is off shell.
A $\rm Z$ boson, for instance, has a mass of $\sim 91~\rm GeV$, while a Higgs boson has a mass of $\sim 125~\rm GeV$. A Higgs boson is less massive than two $\rm Z$ bosons, and so the decay $\rm H\to ZZ$ is not possible unless one of the... | {
"language": "en",
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Why is energy lost here? Let's say a $1 \ \text{kg}$ block is moving.
With a speed of $1 \ \text{m/s}$ so its kinetic energy is $\frac{1}{2} \ \text{J}$. Now let's gently place a block of mass $3 \ \text{kg}$. Now as linear momentum is conserved due to lack of external forces on the system the blocks move together with... | Let the initial body be $A$ and let it move along $X$ axis. Let the other one be $B$
The reason why we get loss of energy is because we are looking at half the picture. Ideally if body $B$ was to fall on to body $A$, then it should bounce back from conservation of momentum (no matter how small the speed of placement wa... | {
"language": "en",
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Non-Analytic Equations and Chaos Could anyone please tell me an example of an equation with no analytic solution(s) that is not a chaotic one? And what is the physical meaning of having analytic solution? For instance, the three body problem does not have in general analytic solution and it leads to chaos. But I don't ... | Like the following?
$$ \sin (x) = \lambda x \tag{1} $$
for $\lambda < 1$
Or do you want an ODE? You did not specify in the question.
| {
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How to calculate the heat that leaves the furnace through one opening? I recently read in the newspapers that one man died through the flame that left the iron furnace. I wasn't sure about this. Iron is melting at 1500 °C. The furnace they used is 8 cubic meters, he was standing one meter from the furnace. The opening ... | I think there was a sudden burst of flame out of an opening in the furnace that impinged on his body, not from radiative heat transfer from the furnace. This can happen very quickly allowing no time to move away. This can occur due to a combination of extra oxygen combined with a localized higher fuel source, and/or ... | {
"language": "en",
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Is projectile motion an approximation? Doesn't the acceleration vector points towards the center of the Earth and not just downwards along an axis vector. I know that the acceleration vector's essentially acting downwards for small vertical and horizontal displacements but if the parametrization of projectile motion do... | Assume Galilean relativity and Newtonian gravity. Neglect the drag due to the atmosphere. The gravitational field of the Earth is the same as the one produced by a point particle in its center (with the same mass, the usual $1/r^2$ gravitational force field). Now, you may know that a test particle in this $1/r^2$ force... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/611916",
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Is it even theoretically possible for a perfect clock to exist? I have heard that even atomic clocks lose a second every billion years or so. That raises the question, is it even theoretically possible for a perfect clock to exist, one that never gains or loses time?
| To say that something is perfect, accurate or absolute, is in itself a lie if we consider the realm of our cosmos being governed by the laws of physics - be it classical, modern, or others.
The most convenient way to say is that nothing is absolute in this real world ( ha! I know that the speed of light is constant in ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Branching ratio of two particles decaying to the same channel When looking at the numbers for the $WW$ decay's branching ratios, I have the impression that a factor $2$ is taken into account only when the $W$s decay to different channels.
For example:
$Br(WW \to qql\nu) = 2* Br(W \to qq) \cdot Br(W \to l\nu)$
$= 2 * 0.... | You have two $W$.
For the final state $qql\nu$, one $W$ decays to $qq$, the other to $l\nu$. But the decay to $qq$ could come either from the first W or the second W, thus you have the following possibilities :
First possibility
-first $W$ decays to $qq$, thus the second $W$ decays to $l\nu$.
-second $W$ decays to $l\n... | {
"language": "en",
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Why do we need Newtonian gravitational field (vector)? Let's ignore GR(scalar) and I am wondering why do we need to model Newtonian gravitational field using vectors? I can understand electromagnetism because of Lorentz force (right hand rule) but what about gravitational field it just the difference in strength at eac... | The way gravity comes into the framework of Newtonian mechanics is as a force, i.e., it has a direction from the get-go. So, it has to be a vector. More directly, as mentioned elsewhere, the gravitational field at the North pole and the South pole are roughly of the same magnitude but they are still different vis-à-vis... | {
"language": "en",
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Least count of cesium clock and maximum possible significant figures for time We know that a second is defined as being equal to the time duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 ato... | The number $N=9\, 192\, 631\, 770$ is used to define a second. Do not mistake this as an accuracy or precision. These are completely different concepts from the definition. Thus it is of course possible to measure things with an accuracy lower than $1/N$.
| {
"language": "en",
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Can beats be produced by two waves moving in opposite direction? I've always seen beats to be produced when two waves are said to be moving in the same direction with different frequency.
Can beats be produced by addition of waves moving in opposite direction ?
| Two waves moving in opposite directions that have the same amplitude and frequency produce a standing wave. If one of those waves has a slightly different frequency than the other, it should produce a "standing wave" that slowly moves. As the anti-nodes and nodes move past an observer's ear, they would hear an increa... | {
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Rotation matrices and reference frames Lets say I have 2 3x3 rotation matrices, we will call them A and B. I am told to find frame B relative to A. how would I go about doing this basic operation? would I do it similar to position (with taking B's coordinates and subtracting A's points from them) or is it different? (o... | If you have a vector with co-ordinates $v_A$ relative to frame $A$, how do you find its co-ordinates relative to frame $B$ ?
First you multiply $v_A$ by $\mathbb A$ to rotate it back to the original frame, then you multiply by $\mathbb B^{-1}$ to rotate to frame $B$. Now you just need to find one matrix that combines ... | {
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Why does mist on glasses disappear when you go back outside in freezing weather? This evening after a walk in the cold weather, about -5 degree Celsius, my glasses were misting up when I got back into the warm house, about +20 degree Celsius.
However, shortly after I went outside in the cold again, and the mist on my g... | The $absolute$ humidity is much lower outside. The lenses of your glasses have some thermal inertia, and while you were outside they got pretty cold. When you step inside, where the absolute humidity is higher, a thin layer of air near the lenses cools to below the dew point, and condensation occurs.
Then when you go b... | {
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Superposition of eigenstates in statistical mechanics Consider the simplest case in quantum statistical mechanics, where we find the density of states in the case of a cuboidal 3 dimensional box. In the derivation we take only those states which are product seperable into wavefunctions along the three directions i.e. c... | The question that we are concerned with is the following, given a point in the $k$ space $(k_{1},k_{2},k_{3})$ and an infinitesimal volume centred at this point, how many states can be found within this volume? The superposed state $$\frac{1}{\sqrt{2}}\left(|1,0,0 \rangle + |0,1,0\rangle\right)$$ is found in two differ... | {
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Is a wave function a ket? I just started with Dirac notation, and I am a bit clueless to say the least. I can see Schrödinger's equation is given in terms of kets. Would I be correct to assume if I were given a wavefunction, say $\Psi(x)=A\exp(-ikx)$, would I be able to just use the notation $\lvert \Psi\rangle =A\exp(... | It depends on the equation, that is: $V(x)$. If it's free particle ($V(x)=0$), with $\hbar=1$, then:
$$ \psi(x) = Ae^{-ikx}$$
is proportional to the momentum eigenstate:
$$ |k\rangle$$
Then:
$$ \hat p |k\rangle = \hbar k|k\rangle = k|k\rangle$$
is easier to deal with then:
$$ i\frac{d}{dx}\psi(x)=i\frac{d}{dx}Ae^{-ikx}... | {
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What distinguished physical and pseudo-forces? Why are some forces are considered pseudo-forces while some are considered real or physical forces?
The definition of pseudo-forces that I know of is that they exist in noninertial reference frames but don't exist in inertial reference frames. Among other arguments is that... | Because it is different in different reference frames. You would expect a universal force to be the same regardless of how you look at it.
Also, it is not easy to figure out the source of the force.* You feel like being pushed by something you can't identify, which appears to break with Newton's 3rd law. That is an ind... | {
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Infinite acceleration without loss of energy in a vacuum, gravity-less void? Suppose we have a void that is free of any other objects or forces, even gravity (impossible I know but hypothetically). If one were to propel an object forward, would that object be able to accelerate infinitely without requiring further addi... | First of all, energy is conserved. An object could not, without external forces, propel itself faster and faster as this would mean an ever-increasing kinetic energy. The only way to achieve this would be to apply, non-stop, a force that accelerates it. If you do work on a ball and accelerate it, the ball would travel ... | {
"language": "en",
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In electromagnetic theory, do photons obey the inverse-square law? The energy ($E$) of a photon depends on its frequency ($f$):
$$E = hf = hc/\lambda$$
Notes:
*
*$E$ = energy of the photon (in joules)
*$h$ = the Plank constant ($6.63 \times 10^{-34}$ joules)
*$f$ = frequency in hertz, Hz
*$c$ = speed of light
*$\l... | The confusion comes from mixing the classical and QM theories of light. In reality, the classical theory is beautifully built up by the herd of photons as described in QM.
https://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html
In your example, as you move away from the source, the same number of ... | {
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Why is the magnetic field $B$ a pseudo-vector? Physically speaking, "pseudo-vectors" are vectors $v\in \mathbb{R}^3$ which transform as $ v'= (\det {R})v$ if the "system were to transform as $R\in O(3)$". However, what does this mean mathematically? And in particular, why is the magnetic field $B$ a pseudo-vector?
I wo... | I thought about this a little further, and I think I can explain that $B$ is a pseudo-vector (without using too much math jargon).
Let $R\in O(3)$ and let $\omega:\mathbb{R^3} \to \mathbb{R^3}$ be a smooth vector function such that $A$ or $B$. Let me define transforming the vector as $R$ as group action on $\omega$ de... | {
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D'Alembertian of a delta-function of a space-time interval (i.e. on the light-cone) How one differentiates a delta-function of a space-time interval? Namely,
$$[\partial_t^2 - \partial_x^2 - \partial_y^2 - \partial_z^2] \, \delta(t^2-x^2-y^2-z^2) \, .$$
Somewhere I saw that the result was $$4\pi\delta^{4}(x).$$ However... | The action of any distributional "function" such as a delta function is really only determined when you integrate it with a test function; and two distributions are equal if and only if their actions agree on all test functions. So let's see what this distribution does when we integrate it with a smooth test function... | {
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Why do fans spin backwards slightly after they (should) stop? Today, I've decided to observe my PC fan as I shut the computer down. The fan slowly lost angular momentum over time. What I've found really interesting is the fact that the momentum vector change did not stop at the zero vector, but instead flipped its orie... | The overshoot behavior you noticed is called cogging and occurs when the magnet arrangement in the motor "catches" the rotating magnetic core of the motor during shutdown and jerks it back to one of the local strong spots in the field.
You can demonstrate this yourself by carefully rotating the fan blade around with yo... | {
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Will a changing $E$ field induce a current in a loop similar to a changing $B$ field? An induced current in a wire loop that is caused by a changing B field is a common EM question. However, I couldn't find examples online where the B field was substituted for a changing E Field.
The following question was given on a t... | I think that the idea of the question is to note not only that there is a changing field, but also that the time derivative is constant.
So, your conclusion is OK in the first part. In the second part $B$ is constant around the loop, so the charges are not affected and there is no current.
The electric field acts insid... | {
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How do you make more precise instruments while only using less precise instruments? I'm not sure where this question should go, but I think this site is as good as any.
When humankind started out, all we had was sticks and stones. Today we have electron microscopes, gigapixel cameras and atomic clocks. These instrument... | In error analysis, the errors multiply/add up (basically effect) only if all these sources of error are independent. That need not be the case always. And further using different instruments like moving form Cloud Chamber detector to Semiconductor detectors have increased the resolution my 100s of magnitudes, the reaso... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Amplitude spectral density vs power spectral density I'm reading the Wikipedia article on spectral density. It is said:
Sometimes one encounters an amplitude spectral density (ASD), which is the square root of the PSD; the ASD of a voltage signal has units of V Hz−1/2.[6] This is useful when the shape of the spectrum ... | The units are the key, so let's consider an example. Suppose we are measuring a voltage. Thus, the unit of the $PSD$ is $V^2/ Hz$, and the integral over the frequency range
$$
\int_{f_1}^{f_2}PSD\; df
$$
has the unit $V^2$. Hence, the result of the integration has the unit $[signal]^2$. In signal processing the square ... | {
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Is galactic gravitational lensing self-magnification big enough to contribute noticeably to the galaxy rotation curve problem? Gravitational lenses magnifies the appearance of themselves, so in the case of a galaxy it looks bigger than it is. Thus the outer stars in a galaxy seems to have a higher tangential velocity.
... | For a spherically symmetric potential, the apparent radius of an object seen from far away is
$$R_{\infty} = R \left(1 - \frac{2GM}{Rc^2}\right)^{-1/2}\, $$
where $M$ is the total mass-energy and $R$ is the radius in Schwarzschild coordinates.
For a big spiral galaxy (like the Milky Way), and ignoring any contribution ... | {
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"answer_id": 0
} |
Hamiltonian Mechanics without a Lagrangian Let's say I want to develop Hamiltonian mechanics from scratch without going through Lagrangian mechanics and Legendre transformations. How would I go about doing that? What I am struggling with is a definition of conjugate momentum. It is usually defined as a derivative of La... | You can just define some Hamiltonian $H(\vec{q},\vec{p})$ and the equations of motion are Hamilton's equations
\begin{eqnarray}
\frac{{\rm d} q_i}{{\rm d} t} &=& \frac{\partial H}{\partial p^i} \\
\frac{{\rm d} p^i}{{\rm d} t} &=& - \frac{\partial H}{\partial q_i}
\end{eqnarray}
If you integrate the equations you'll ge... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/615621",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 0
} |
Why does changing $X\to iX$ in the definition of the CNOT make an important difference? How to find a ket $|\psi \rangle$ that illustrates how changing X to iX in the definition of the CNOT gate makes an important difference because of what happens when CNOT is applied to $|\psi \rangle$?
The definition of the CNOT gat... | Assuming your question is "What $| \psi_i \rangle $ would have different resulting $| \psi_f \rangle $ having undergone a $C-X$ gate vs. a $C-iX$ gate?"
Consider $| \psi_i \rangle = \frac{1}{\sqrt2} \Big( |00 \rangle + |11 \rangle \Big)$
$$C-X | \psi_i \rangle = \frac{1}{\sqrt2} \Big( |00 \rangle + |10 \rangle \Big)$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/615725",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Pseudo-forces in revolving frame in contrast with rotating ones A person in a rotating coordinate system, to do Newtonian mechanics has to use pseudo forces such as Coriolis and centrifugal.
We use such forces for rotating coordinate systems,ones that rotate about a fixed axis.
A person on the surface of earth is not... | The method I'm familiar with is a little strange. It uses the tools of general relativity. I did this awhile ago, but I don't have that notebook anymore. I tried to find it computed somewhere online. (I found it. but ignore the t->t' transformation)
$F^i =\frac{d^{2}{x^i}}{dt^2}+ {\Gamma^i}_{rs} \frac{dx^r}{dt} \frac{d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/615890",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 2
} |
Reflection on moving mirrors Say I have an endless mirror, in a x y plane, at y=1.
Situation 1: the mirror is stationary and when we send light vertically from the origin, the light reflects back and returns to the origin.
Situation 2: let the mirror move horizontally at a constant velocity. Would the light reflected ... | A nice way to answer this question is to do the calculation in the rest frame of the mirror. Light propagating in the $y$ direction in the lab frame will propagate in some other direction in the rest frame of the mirror. It will then reflect off in the ordinary way in that frame (angle of reflection equals angle of inc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/615978",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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