Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Is there a nice physical interpretation of this formula? As a trivial example in our vector analysis class, we did the following computation.
Let $\overrightarrow{\omega} = (\omega_1, \omega_2, \omega_3)$ be the angular velocity and $\overrightarrow{r} =(x,y,z)$ be the position. Then we have a vector field $\overrighta... | I think the comments of @J.G. and @Cleonis add up to a complete answer. In particular see the answer of Ian to that maths stack exchange question: the factor of 2 is geometric in origin. The geometric definition of the curl, or rot, at a point P is the limit of the loop integral around an arbitrary loop enclosing P div... | {
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"Earth spinning faster will break GPS and atomic clocks".. Umm, how? Since it's just come out that Earth is apparently spinning about a milliscecond and a half faster.. I see a bunch of "articles" claiming this will.. somehow.. break atomic clocks and make GPS useless.. (Google "earth spinning faster break atomic c... | None of the articles (e.g. this one) I came across say anything about breaking atomic clocks. The problem is simply a logistical one - if we have to implement a negative leap-second, then we will be doing something which most of the software which implements ordinary leap-seconds has not been explicitly designed to do... | {
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Why does the graviton polarization satisfy $\epsilon_{ij}(\mathbf{k},\lambda)\epsilon^{ij}(\mathbf{k},\lambda') = 2 \delta_{\lambda\lambda'}$? I am reading the paper ``Graviton Mode Function in Inflationary Cosmology'' by Ng (link here). The graviton $h_{ij}$ is here expanded (in the TT gauge) where
$$
h_{ij}(x) \sim \... | I can't comment with certainty on $\epsilon_{ij}(\mathbf{k},\lambda)\epsilon^{ij}(\mathbf{k},\lambda') = 2 \delta_{\lambda\lambda'}$, but I suspect that it's because gravitons actually have only two independent polarizations, so this is a way to go from polarization labels ($\lambda$) to real space ones ($i,j$).
I can,... | {
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Why flapping rudder produce net thrust if one half-stroke produce thrust and second half-stroke drag? In small sailing boat like optimist is well know technique when there is no wind, rudder pupming which push boat forward.You just need push-pull rudder stick left to right with fast movement.
Rudder works complety unde... | I suspect it has nothing to do with regions of higher or lower pressure (if those even exist). When you pump the rudder you are pushing water backward and by Newton's Third Law that water exerts an equal and opposite force on the boat, pushing it forward.
| {
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What is the average recessional velocity of an object in the universe? I’m trying to get a better grasp on cosmological horizons and have a question regarding recessional velocity. In particular:
What is the average recessional velocity of a cosmological object (irrespective of distance) an observer would expect to obs... | If I understand your assumption that all of the matter objects are similar, and all on a large scale have similar densities, then what determines one's velocity from us is determined by the equation:
$$V = D * H_0.
$$
$V$ is velocity from us, $D$ is distance from us, and $H_0$ is the Hubble constant with the reciprocal... | {
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What is virtual photon concept in classical electrodynamics? If we observe a charged particle like an electron passing us at some high speed $u$, then as $u \to c$ the field we observe looks like a superposition of plane waves normal to the trajectory of the electron. The field can be Fourier transformed, and the modes... | It's the same photon but, in this context, it's part of a "back of the envelope" type calculation based on energy quantization ($E=hf=\hbar \omega$) and the assumption that each sufficiently small interval of the energy spectrum $U_\omega\mathrm d\omega$ consists of a number of "equivalent photons" $N_\omega$. It's pr... | {
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Measured Data Question regarding Galaxies with or without Dark Matter and Supermassive black holes My understanding is that all Ultra Diffuse Galaxies (UDGs) have no Dark Matter nor do they have Supermassive Black Holes. It is also my understanding that all other galaxies have both Dark Matter and Supermassive Black H... | *
*Ultra-Diffuse Galaxies actually have a wide range of dark matter content. Some indeed seem to have little or no dark matter, but others are quite dominated by dark matter. For example, Dragonfly 44 in the Coma Cluster has an estimated dark-matter halo mass similar to that of the Milky Way, even though the total mas... | {
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Computing the maximum force a rod can bear Suppose I had a rod of diameter $d$ composed of some material with tensile strength $T$. If I then exterted a pulling force $F$ on the ends of the bar, how do I compute the force $F$ for which the rod will break apart? Is there some general equation that I can use to compute... | Breaking stress is the maximum force that can be applied on a cross sectional area of a material in such a way that the material is unable to withstand any additional amount of stress before breaking.
Breaking stress is calculated with the formula:
Breaking Stress = Force / Area (in your case Area= pi*d^2/4)
Breaking s... | {
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What's a good simple model for wind attacking drone? I'm trying to simulate a drone on https://rapier.rs/. My idea is to do an X shaped object, with a force $P$ on each end of the X, always perpendicular to the drone plane.
I want to simulate wind, which I think would be good if it were a $W$ vector force acting on eac... | Assuming all of the propellers rotate the same direction, when the wind hits them it will create more lift and drag on the side of the propeller that is moving toward the wind. The right propellers will have more lift on the outside blade, and the left propellers will have more lift on the inside blade (for example)
Lo... | {
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Besides traveling at the speed of light, how can we be sure that it is possible to have energy and momentum without mass? How can we be sure that it is possible to have energy and momentum without mass? If something were to continually lose energy, would it not also lose a corresponding amount of mass? I understand tha... | How about this: even in classical electrodynamics (no quantum, no relativity) electromagnetic waves carry momentum. Waves can't have mass because they are not objects. And electromagnetic waves are disturbances in a medium that isn't made of stuff with mass.
And it has to be that way for conservation of momentum to be ... | {
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Acceleration of wedge and mass locked on axes Consider this diagram:
Mass m1 can only move in the x direction and mass m2 in the y direction. Find the acceleration of both m1 and m2, and the reaction of the wedge. Negligible Friction.
I tried attempting to solve this problem by finding the normal force on m1 from m2, ... | Using this algorithm you can solve almost all of high school mechanics(except rotational mechanics):
*
*I will ignore the wheel at the end of the rod since friction is negligible and therefore no rolling.
*Draw the free body diagram for the experiment.
*Find the constraint equation(In this case, the wedge and the... | {
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Is the equal sign in "$0 ^\circ \mathrm{C} = 273.15\, \mathrm{K}$" fair? I'm in doubt whether the equal sign in an expression like "$0 ^\circ \mathrm{C} = 273.15 \,\mathrm{K}$" is fair because, normally, if $A=B$, then, say, $2A=2B$, which is hardly applicable to "$0 ^\circ \mathrm{C} = 273.15 \,\mathrm{K}$".
So is it ... |
I'm in doubt whether the equal sign in an expression like "$0 {\ ^\circ\mathrm{C}} = 273.15 {\ \mathrm{K}}$" is fair because, normally, if $A = B$, then, say, $2 A = 2 B$, which is hardly applicable to "$0 {\ ^\circ\mathrm{C}} = 273.15 {\ \mathrm{K}}$".
I think that the equals sign is totally appropriate, and the rul... | {
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Wave Function Collapse and the Dirac Delta Function When the wave function of a quantum system collapses, the probability of finding it at some specific point is given depends on $||\Psi||^2$:
$$
\int_{\mathbb{R}^3}{d^3 \mathbf x \; ||\Psi||^2} = 1
$$
Could this modulus square, the instant you measure, be thought as t... | I suppose that you think that when a measurement is done then probability of a finding particle at a given point is certain, thus it can be equated with delta function which has value of one at a point and zero otherwise. Also this is after measurement, so wavefunction is collapsed.
In the case been asked, once a measu... | {
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What causes light passing through a hole to change direction? On diagrams showing light passing through a hole, the wave of light appears to change direction when it emerges from the hole.
What causes that change of direction? Is it maybe the walls of the hole imparting a pulling force or the sudden absence of light ne... | Light is a wave , at the edge of the hole the oscillation spreads in all directions but the highest intensity is forward.
| {
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Why electron do not eject out even when there is photon of less threshold energy with increasing in time When photon having certain energy less than threshold energy strikes on the electron of metallic plate. Electron do not eject out. But my question is when photon are falling continuously then electron must gain the... | It's not that simple. Electron can only absorb such photons which exactly hits electron quantum jump levels, for example check Lyman, Balmer series, etc. Otherwise non-compatible photons "are ignored" by electrons. Unless incident light is very strong, i.e. you shine with an intensive laser light on metal, even laser w... | {
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Why does the opposing force differ in when falling on concrete vs on water in spite of Newton's third law? If a person jumps from the first floor of a building and lands on a concrete surface, they will suffer serious injury because of Newton's third law.
If the same person jumps the same distance and lands in swimming... |
But the person in both case lands with same amount of force. Then why
doesn't water offer the same amount of force in return as concrete
does?
The person does not land with the same amount of impact force. The average impact force that the concrete exerts on the person is greater than the average impact force the wat... | {
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If Aristoteles was right and heavier objects falled faster towards the ground how would be Newton's Laws of Motion described? It seems like it would be like:
a(m)=km
and may be a(m1,m2)=K(m1-m2)
Am I doing any sense?
Btw I'm no negationist, nor I'm trying to create a negationist movement here, I just wonder how physics... | When solving Newtons equation for a free falling object the mass cancels out on both sides, which implies that two objects of the different mass fall with the same acceleration
$$
m a = F = - m g \quad \Rightarrow \quad a = -g
$$
For the acceleration to be mass dependent you would need to change either side of the equa... | {
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Why is it easier to raise AC current to high voltage than DC? In my country (and maybe all around the world I don't know) once electricity has been generated, it is then raised to 200k Volts for transportation.
I know this is to reduce the loss. Given $P=U.I$ and $P=I^2.R$, raising U will lower I and so limit the loss ... | As with most engineering decisions, it all boils down to "what's the best trade off between conflicting constraints and requirements".
*
*AC allows very simple conversion between different voltages using passive transformers
*AC conversion scales nicely across a large range of voltages and powers
*AC is the histori... | {
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Computation of $\nabla_a\nabla_b X^d$ All my notation follows Chrusciel's book "Elements of General Relativity". For a vector field $Y$ and connection $\nabla$, we define
$$\nabla_a Y^b:=dx^b(\nabla_a Y)$$
where $\nabla_a:=\nabla_{\partial_a}$. So in English, this would be taking the b-th component of the vector field ... | Your mistake is a subtle one, and is related to the notational ambiguity you mention at the beginning of your question. In abstract index notation, the expression $X^b$ is to be understood to mean the vector field $X$, with the superscript $b$ not being a numerical label (i.e. the $b^{th}$ component) but rather as a f... | {
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Negative energy solutions in Dirac equation for hydrogen atom Solving Dirac's equation for the hydrogen atom $^1$,
$$(\boldsymbol{\alpha}\cdot\boldsymbol{p}+\beta\cdot m)\Psi=E\Psi$$
after some mathematical machinery we find the condition for energy eigenvalues
$$\varepsilon^2=\frac{1}{1+\left(\frac{\alpha}{1+\gamma+n'... | It is easy to see that the negative energy solutions would be unphysical.
First of all, the proton is positively charged and the negative energy solutions would be a positron rather than an electron, and there should not be a positron bound to a proton.
If you are more mathematically minded, you could try to solve the ... | {
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Why spontaneous emission? From what I have understood Einstein somehow deduced the A and B coefficient for spontaneous respectively stimulated emission to match the observed blackbody radiation/Planck spectrum. How did he come to this conclusion that there should be emissions that are spontaneous? What causes that all ... | If stimulated emission was the only radiative emission process then objects in thermal equilibrium would be transparent.
Any absorption of a light beam would be exactly balanced by stimulated emission that is in phase and in the same direction as the incident radiation. The absorption coefficient, which is the true abs... | {
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Spectral theorem in QFT I know that the spectral theorem holds for unbounded normal linear operators on infinite dimensional Hilbert-spaces. We usually employ it in Quantum mechanics to explain the role of self-adjoint operators.
However, I'm not sure wether the theorem also applies to the observables of QFT, the reaso... | I am not sure to understand the nature of the problem.
The spectral theorem, as it is a mathematical fact, holds also in QFT. It does not matter if we do not know how the Hilbert space is made, it is sufficient to know that it is a Hilbert space and that the used operator is selfadjoint. Regarding operator valued distr... | {
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Delta v of a trans-Mars injection (TMI) Why does it only take about 600 m/s more than Earth's escape velocity to have an encounter with Mars while it takes much more Delta v (about 3 km/s) from a solar orbit (same as Earth orbit) to have an encounter with Mars?
What explains this difference?
Is it the Oberth effect or ... | Yes, it seems related to the Oberth effect. Starting from the solar orbit, we need $\Delta v$ to enter an orbit to Mars. By energy conservation the velocity of the spaceship at launch from Earth has to be
$$v_0 = \sqrt{v_{\text{esc}}^2+\Delta v^2} \ ,$$
where $v_{\text{esc}}$ is the escape velocity. For $v_{\text{esc}}... | {
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Why are sunspots cooler than the other regions? The Sunspots appear darker than the other regions because they are cooler; and I know that according the Babcock model, the Sunspots are places where the tangled magnetic fields burst out through the Sun's surface. How does these bursting magnetic field lower the Sun's su... | As I discuss in https://physics.stackexchange.com/a/415248/59023 and https://physics.stackexchange.com/a/708183/59023, a sunspot is a pressure-balance structure. The total pressure in a collisionally mediated plasma includes the thermal and magnetic pressures. Since the regions involved in generating sunspots arise f... | {
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Is the non-simply connected version of AdS space a maximally symmetric spacetime? A common construction of anti-de Sitter space is the following:
*
*Start with the flat five-dimensional manifold with metric $ds_5^2 = -du^2 - dv^2 + dx^2 + dy^2 + dz^2$.
*Consider the hyperboloid submanifold given by $-u^2 - v^2 + x^2... | Related answers: this one by me and this one by Slereah, which has a classification of maximally symmetric spaces with one timelike dimension (citing Spaces of Constant Curvature: Sixth Edition by Joseph A. Wolf).
Your hyperboloid (which Wolf calls $\mathbb H^3_1$) is topologically $S^1\times\mathbb R^3$. The maximally... | {
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Displacement Vector and resultant vector I am struggling with the concept of displacement. From my understanding displacement can be found for 1D motion along the x-axis as $\Delta x= x_{f}-x_{i}$. For example someone walks $1\,\mathrm{m}$ to the left then $1\,\mathrm{m}$ to the right then $2\,\mathrm{m}$ to the left a... | Responding to your question and follow up comment, displacement is indeed final position minus initial position. But in your example, the numbers you are listing are in fact displacements, not positions.
Let us number your positions as follows:
\begin{array} {r|r} \hline x_0 & 0 \\ x_1 & -1 \\ x_2 & 0 \\ x_3 & -2 \\ ... | {
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What makes a photon a photon? As i understand photons are excitation of the electromagnetic field. Therefore charged particles are affected by this excitation. But what if we have (highly theoretically) a particle that has the exact same properties like a photon (spin 1, no electric charge, no color charge, no mass etc... | I think the existing answers are already excellent. I wish merely to add that this kind of question is one which is asked in theoretical physics all the time. Whenever we have some aspect of physics which seems to show something not accounted for in the Standard Model (dark matter is an example) then one thing to try i... | {
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What work does a microwave oven do? I learned that when energy is transfered it either produces work or it becomes thermal energy (heat).
Work implies a force that acts on an object producing changes in its position.
I'm learning these concepts from Khan Academy, and in this article they say:
A hot cup of coffee has a... | *
*Work in thermodynamics is usually associated with motion of the boundaries of the system. The standard example is a gas in a cylinder fitted with a piston. To move the piston to either compress or expand the gas involves work. But there are more ways to transfer work to a thermodynamic system and one example is #4 ... | {
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Deriving $\langle H\rangle$ from average momentum and position for a LHO Assume that we know the values of $\langle x\rangle$ and $\langle p\rangle$ for a LHO, that is in a random superposition of zeroth and first state. Derive $\langle H\rangle$.
So I tried solving this problem with writing $H=\hbar\omega (a^*a+1/2)$.... | generally you can't derive $\langle H \rangle$ only from $\langle x \rangle$ and $\langle p \rangle$, because you end up needing the expectation values of $\langle x^2 \rangle$ and $\langle p^2 \rangle$, as you wrote. However, here you are given another crucial piece of information: that the state is in a superposition... | {
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Work done by an eccentric force on a rigid body I am hoping someone can explain in simple terms where I might be going wrong in my logic below.
We have a thin rigid rod (see diagram A) where a couple is acting and rotates the rod about its COM by an angle θ .
I am assuming that the work done by the couple is F.r.θ
Now ... | The work applied is still Force times distance.
The angular travel of the body reduces the travel of the body’s COM. Additionally, the travel of the COM reduces the angular travel.
If we were using this work to accelerate the bar (give it kinetic energy) some would go to the rotational motion and some would go to the t... | {
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Does the earth’s rotational angular velocity change? This is what is written in The Feynman Lectures on Physics, Vol. 1 (ch.5)
We now believe that, for various reasons, some days are longer than others, some days are shorter, and on the average the period of the earth becomes a little longer as the centuries pass.
Wh... |
There is no “gravitational” source of external torque acting on the earth
Yes, there is. The tides are caused by the Moon's gravity. That energy has to come from somewhere. The drag caused by the tides is slowly changing the angular momentum of the Earth, and the tides from the Sun also doing so, albeit even more slo... | {
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Why Is Capacitance Not Measured in Coulombs? I understand that the simplest equation used to describe capacitance is $C = \frac{Q}{V}$. While I understand this doesn't provide a very intuitive explanation, and a more apt equation would be one that relates charge to area of the plates and distance between them, I'm havi... | Capacitance is not a measure of how much charge that is stored on the plates.
It is a measure of how much charge that is stored per volt of sustained voltage.
Just like how, say, pressure is not the amount of force exerted, but the amount of force per area exerted. You mustn't ignore the qualifier in such definitions.
... | {
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Assigning initial conditions for Schrodinger's equation I am self-teaching myself quantum mechanics, and my understanding so far is as follows. In the most general case, we would like to find a wave function $\varphi(x,t) \in \mathcal{H}$, where $\mathcal{H}$ is some appropriate Hilbert space. This wave function encode... | Given a state $\Phi(x,0)$ at $t=0$ you can always expand in in eigenstates of $H$:
$$
\Phi(x,0)=\sum_k c_k\varphi_k(x)
$$
where the coefficients $c_k$ (they are not $E_k$) are obtained from
\begin{align}
c_k=\int dx \varphi_k^*(x) \Phi(x,0)\, .
\end{align}
The time evolution of $\varphi_k(x)$ is known:
\begin{align}
\P... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What happens if I rewrite the acceleration in work formula this way? Work is known as
\begin{equation}
W=\vec{F}.\vec{q},
\end{equation}
thus for a gravitational force $\vec{F}_g=m\vec{g}$ we have
\begin{equation}
W=mgh.
\end{equation}
My derivation is as follows:
\begin{equation}
dW=\vec{F}_g\cdot d\vec{q}
\end{equati... | In the integral
$$
\int m \frac{v^2-v_0^2}{2q}dq
$$
$v$ is a function of $q$, since $v$ changes over the range of integration. So it cannot be treated like a constant and cannot be pulled out of the integral as you have done.
In fact, as you showed, $v^2 = v_0^2 + 2 q g$, and so the integrand simplifies to $mg$ and th... | {
"language": "en",
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Energy from spacetime expansion? Are there any processes or mechanisms in the universe involving spacetime expansion where energy is produced somehow out of this expansion?
I ask this in part due to this article by Sean Carroll 1 which it says at some point:
(...) In general relativity spacetime can give energy to mat... | General relativity, in an arbitrary spacetime, has local conservation of energy but not global conservation of energy. On practical scales, spacetime can be modeled as asymptotically flat. In an asymptotically flat spacetime, one can define a conserved measure of energy. So if you're going to extract energy from cosmol... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why does particle leave circular motion after string slacks? If a particle is attached to a string and made to move in a vertical circle with initial velocity of $\sqrt{4gl}$ $m/s$ where l is the length of string, at some angle (approx $131°$ with the initial position), the string slacks and the particle leaves the cir... | Answering the second part first: While the force of gravity provides exactly the required centripetal force at the highest point, the force of gravity does not change direction as required for the centripetal force. The centripetal force has a horizontal component everywhere except for the highest and lowest points, an... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Is the normal force the reaction force? There is a box on the surface of earth. The earth exerts a force to the box (black arrow). The box exerts a reaction force to the earth(brown arrow). But this reaction force is exerted to the earth not the box, so where is the normal force? If the reaction is the normal force the... | The best way to visualize and solve force problems like this is with a Free Body Diagram, in which you isolate each body and draw all forces acting upon it. That way it is easy to see what forces are acting where.
In this case, the block has two forces acting on it: gravity, and the normal upward force.
The ground also... | {
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"source": "stackexchange",
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Explain Heisenberg's uncertainty principle There was one homework question that asks what Heisenberg uncertainty tell us about the energy of an electron in an infinite square well when the length of the well decreases. The correct answer is that the energy decreases when length increases. I know that the energy should ... | The expected answer is direct. A particle in a stationary state in the box has zero averaged momentum, just because the particle stays there stationarily. Hence $(\Delta P)^2 = \langle P^2\rangle$ which is proportional to the averaged energy of the particle. However, this value is also the eigenvalue of the energy sinc... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Rule swing with spring experiment: how can I modify it?
Basically I want to replicate this experiment (https://youtu.be/GqPGbHq2fxU). It's a ruler oscillating with one fixed end and one end attached to a spring. In my previous experiment, I used a short spirng (didn't measure the spring constant which I regret a lot).... | Why not bore a hole or two in the ruler? Or use a cheap wooden strip, you don't need a ruler since you can measure the distances. If you don't use the hole, it may always swing in more directions. Use for the spring: attach first a weight comparable to the ruler or strip and measure the frequency, if it is slow enough... | {
"language": "en",
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"source": "stackexchange",
"question_score": "1",
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Work Integral and its derivation The work integral is something I saw long time ago and in completely understood it.
\begin{align}
W_{12} & =\int F(x)dx=m\int^{t_2}_{t_1}adx=m\int\left(\frac{dv}{dt}\right)dx=m\int\left(\frac{dv}{dx}\right)\left(\frac{dx}{dt}\right)dx\\
&=m\int\left(\frac{dx}{dt}\right)dv=\frac12\left(m... | Simple use of chain rule:
\begin{equation*}
\frac{d \dot{x}^2}{dt}=2\dot{x}\frac{d\dot{x}}{dt}
\end{equation*}
| {
"language": "en",
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"source": "stackexchange",
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How to teach yourself physics systematically？ I'm just a university student and I am not physics majors, but I am interested in physics. I plan to self-taught physics. However I don't know how to teach yourself physics systematically. I want to know what math I need to learn, what is the order of learning, which textbo... | At my university (MIPT) there are the subjects and plans for them:
1st semester:
-General physics: mechanics - https://pastebin.com/UgHnVtaY
-Introduction to Mathematical Analysis - https://pastebin.com/fkbPuC36
-Analytical geometry - https://pastebin.com/MKyniqtS
2nd semester:
-Multidimensional analysis, integrals and... | {
"language": "en",
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"source": "stackexchange",
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I'm having trouble understanding the intuition behind why $a(x) = v\frac{\mathrm{d}v}{\mathrm{d}x}$ I was shown
\begin{align}
a(x) &= \frac{\mathrm{d}v}{\mathrm{d}t}\\
&= \frac{\mathrm{d}v}{\mathrm{d}x}\underbrace{\frac{\mathrm{d}x}{\mathrm{d}t}}_{v}\\
&= v\frac{\mathrm{d}v}{\mathrm{d}x}
\end{align}
However, this feels... | For a simple function like $x=t^2$ you can show that the chain rule works.
$x=t^2 \to \dot x = v = 2t \to \ddot x = \dot v = a = 2$
$t=x^{1/2} \to v=2x^{1/2} \to \frac{dv}{dx} = x^{-1/2}= 1/t$
$\frac {dv}{dx} \cdot v = 1/t \cdot 2t = 2 = a$
Looking at the slopes of the graphs you can imagine that as time progresses t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Change of velocity without doing work Body of mass $1\rm\, kg$ is moving towards left side at velocity of $-2\rm\,m/s$ and is slowing down due to the constant external force until it stops. After that, it's speeding up towards the right side due to the same force until it reaches velocity of $2\rm\,m/s$. How much work ... | Suppose we apply a uniform force $F$, which is of course positive. Now let's say that the total work $W$ is the sum of the work when the body moves to the left side $W_-$ and when the body moves to the right side $W_+$:
$$W=W_-+W_+$$
By definition of work,
$$W=W_-+W_+= F\cdot \Delta x_-+ F\cdot \Delta x_+= F\cdot (\Del... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/731089",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the correct direction of turbulence energy cascade? I have learned from a fluid mechanics textbook [1] that the turbulence energy is cascaded from the largest eddy to the smallest eddy and is then dissipated by the molecular viscous effect. But recently I was reading Chapter 3 of a thermodynamics textbook [2],... | Depends on the flow! In homogeneous isotropic turbulence, energy may go in both directions, though there is a clear preference for it going to the smallest eddies (called forward cascade), in line with the theories of Kolmogorov and many others. When energy goes the other way, it is called backscatter.
In this paper (a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Does "non-interacting" (fermions) really mean "no interactions other than Pauli exclusion"? When one speaks of non-interacting elections (or other ferimons), doesn't one technically mean non-interacting but with the exception of Pauli exclusion? I wonder if it is appropriate to view Pauli exclusion as essentially an i... | Not really. The concept of 'non-interacting fermions' refers to the fact that a many-body Hamiltonian quadratic in fermion operators can be reduced to a single-particle Hamiltonian, where the wavefunction and energy of a single fermion is unaffected by the others. To see this, consider Hamiltonian
$$
H = \sum_{ab} H_... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Waves and linear dependence on space and time Any function that depends on space and time through the combination $\vec{k}\cdot\vec{r}-\omega t $, namely a function $$f(\vec{r},t)=g(\vec{k}\cdot\vec{r}-\omega t)$$ where g is an arbitrary function of a single real variable, represents a perturbation that propagates in t... |
But do all types of wave have such space-time dependence?
Certainly not. General form of wave equation is :
$$ \Box u=0, ~~~(1)$$
where,
$$ \Box ={\frac {1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}-\nabla ^{2} ~~~(2)$$ is
a d'Alembert operator
.
So any function $u(\vec r,t)$ which satisfies eq. 1, has wave prop... | {
"language": "en",
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Equivalence between small distance and high energy I see in a lot of particle physics literature statements along the lines of: 'This is valid for high energies (small distances)'. Exactly what do we mean by small distances in this case? From QFT, QM and other physics courses, the connection between small distance and ... | Connections between energy and distance tend to involve the factor
$$
\hbar c= \rm 197\ eV\ nm=197\ MeV\ fm
$$
and some additional factors from doing algebra. The algebraic factors tend to be values like $\frac13$ or $\sqrt 6$, but it is unusual to do a page of first-principles algebra and come up a purely numerical fa... | {
"language": "en",
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"source": "stackexchange",
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Electromagnetic radiation reflected normally causing interference to itself Is it possible to have a body reflect almost perfectly any radiation falling normally with the insident ray so that the reflected ray interferes with the incident and hopefully reduce or cancel it out ?
| "Interference" is the linear superposition of waves, i.e. it is really the absence of interaction of the wave with itself. As a result the energy in waves can not disappear and waves can not actually "cancel" out. They form minima and maxima that can be located in fixed positions in space ("standing waves") instead. We... | {
"language": "en",
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Is there a general version of Bell's inequality, like the general version of uncertainty principle? By the general version of uncertainty principle, I mean the result involving general operators $A$ and $B$, which says that the products of standard deviations is equal to the sum of the expected value of the commutator ... | Probably the most generic statement about correlation that is still useful in this context is Tsirelson's bound for the CHSH inequality:
The setup are four observables $A_0,A_1,B_0,B_1$ with possible outcomes $\pm 1$ and $[A_i,B_j] = 0$ (but not, crucially, $[A_0,A_1] = 0$ or $[B_0,B_1] = 0$). This isn't as restrictive... | {
"language": "en",
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Does a random number generator have real entropy? In thermodynamics, entropy is defined for gases. Of course, my laptop is not a gas. However, it contains a random number generator and I have seen the word ‘entropy’ being used in this context. Is this the same entropy? How can this entropy be linked to the definitions ... | Are you asking if running an algorithm on your laptop generates entropy? Yes, it does. It is an irreversible process. The electronics requires electrical energy and converts it into heat. Is that the minimal entropy generation of the algorithm? No. It's many orders of magnitude more than that with current technology. H... | {
"language": "en",
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Calculating heat removed by cooling system using output fluid temperature I am trying to calculate the amount of energy removed by a cooling system for some medical research. I'm a little out of my depth with the physics calculations.
I have fluid flowing through a variable temperature object (an organ being heated) at... | The following variables apply:
$Q$ = the amount of heat transferred out of the organ, BTU/s
$m$ = the mass flow rate of the water, lb/s
$C_p$ = the specific heat of water, BTU/lb-degF
$T_i$ = the temperature of the water entering the organ, deg F
$T_f$ = the temperature of the water leaving the organ, deg F
The heat tr... | {
"language": "en",
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Thermodynamics : an empty container surrounded by an atmospheric gas I have a small exercices of thermodynamics if anyone can help me :
We start with an empty container of volume $V$. The walls of this container are adiabatic and will not change over time surrounded by a gas of pressure $P_0$ and of temperature $T_0$.
... | There are two ways of doing this. One is using the closed system version of the 1st law, and the other is using the open system version. I'll show you how it is done using the open system version. Let n be the number of moles of gas which eventually enter the container. Applying the open system version to the situa... | {
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Associativity of covariant derivatives I'm having trouble proving that covariant differentiation is an associative operation.
Essentially I'll have to show
$$\nabla_\mu( \nabla_\nu \nabla_\sigma) = (\nabla_\mu\nabla_\nu) \nabla_\sigma. $$
But is it enough to show that both LHS and RHS yield the same result when acted... | If you see the covariant derivation as a bundle-map between the relevant vector bundles of tensors, associativity is automatically guaranteed by the usual associativity of composition of functions.
| {
"language": "en",
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Weight in Interplanetary Space How is weight zero in interplanetary
space? The Moon is orbiting the Earth because of the gravitational pull of earth. Then gravity must exist in interplanetary space too. So any body in space must also have an acceleration due to gravity ($g$) but $g$ must actually be 0 for weight to be ... | It's not that gravity doesn't exist in interplanetary space - gravity has no "maximum range", it exists everywhere - but that you don't feel it. Imagine a weighing machine attached to the floor of the spacecraft and you standing on it. If the reading is $0$, then you are weightless, although you are still being acted o... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Can we physically explain superconductor mean field order parameter (gap function) as Cooper pair wave function? We usually define mean field order parameter (gap function) in BCS theory
$$
\Delta(r_1,r_2)_{s,s'} = \langle GS | \hat{\psi}_s(r_1)\hat{\psi}_{s'}(r_2) |GS\rangle,
$$
where $\hat{\psi}_s(r_1)$ is field oper... | I don't know my answer make sense or not what i understand about that order parameters given by
wave function mod square it represents the copper pair forming probability density which is zero above some critical temperature and critical fields.
Now the formation copper pair is little bit tricker but this is how i i... | {
"language": "en",
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Experimentally Measuring the Velocity of Water coming out of an Orifice I plan on doing an investigation into Torricelli's Law, where I will be looking at one of the following:
*
*How the cross-sectional area of an orifice affects the velocity of water coming out of it (constant height).
*How the height of an orifi... | I did some work on this once and came across a range of references on this topic. I can't remember if they specifically cover what you ask for here, but might be in one of these:
Paulo Murilo Castro de Oliveira, Antonio Delfino, Eden Viera Costa and Carlos Alberto Faria Leite,“Pin-hole water flow from cylindrical bott... | {
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What is the definition of the phase of a particles (points) on a travelling wave? If we have a travelling wave of equation $y=5\sin(\omega t-\pi x +0.5)\:\rm m$. I know that the phase is 0.5 but how can I visualize this and what is the definition of phase difference between 2 points along the same wave that are $n$ met... | The phase of an oscillation is the 'position' (usually expressed as an angle) that it has reached in its cycle. For example the phase of your wave at time $t$ and distance $x$ from some fixed point is $(\omega t -\pi[\text m^{-1}] x+0.5)$. It needs also to be stated whether the function is sine or cosine.
In your examp... | {
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Why does a sensitive thermometer absorb little heat? In an experiment to measure the specific heat capacity of water I'm trying to make it as accurate as possible. And somewhere I read that a sensitive thermometer absorbs little heat. By "sensitive" I am referring to the amount of change in thermometric property for a ... | A thermometer is "sensitive" when it absorbs as little heat as possible from the item it is trying to measure. Any heat absorbed by the thermometer will lower the temperature of the item, and hence cause a false reading.
This problem occurs whenever you are trying to measure anything. Your measuring device should alway... | {
"language": "en",
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Why is an equilateral triangle not a 2d unit cell? An equilateral triangle obeys the crystallographic restriction theorem, but it is not a part of 2d crystal structure. What symmetry does it lack? Why can't it be a Bravais lattice?
| It is a possible 2d lattice structure, it just so happens that in the case of equilateral triangles we can observe them to tile together into hexagons. A hexagonal lattice is sometimes called a triangular lattice. https://en.wikipedia.org/wiki/Hexagonal_lattice
We can see clearly how the lattice vectors of a hexagon ca... | {
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"timestamp": "2023-03-29T00:00:00",
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Local $SU(2)$ symmetry breaking and unitary gauge In a $SU(2)$ gauge field theory with scalar field $\phi$ in the fundamental representation of the $SU(2)$ group with lagrangian $$\mathcal{L} = -\frac{1}{2}TrF_{\mu\nu}F^{\mu\nu} + (D_{\mu}\phi)^\dagger(D^{\mu}\phi) + \mu^2\phi^\dagger\phi - \frac{1}{2}\lambda(\phi^\dag... | Your text should be illustrating the H-E-Brout phenomenon by parameterizing the Higgs doublet in the chiral parameterization, as opposed to the linear σ-model one you are using. They are, of course, equivalent, and it behooves you to catch your mistake in translating back to yours. (Observe $( \varphi_1^* \varphi_1+\va... | {
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"source": "stackexchange",
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Should a system be “uniform” to qualify for it to be in steady state? I am wondering about whether a system need to be “uniform” to qualify for it to be in steady state or can not uniform systems also act as a steady system.
Can someone please clarify this.
Thanks in advance!
Any help would be appreciated.
| Steady state just means whichever state is in question doesn't change. If you pick uniformity as the state in question then it's a tautology that uniformity is required for a steady state.
If you pick virtually any other state then uniformity is not required for steady state. Suppose you pick the number of elements as ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Given a system, how to decide whether a closed orbit is homoclinic, not periodic, solely based on its phase portrait? Background and definitions:
*
*A system is conservative if it has at least one conserved quantity.
*In a phase portrait of a nonlinear conservative system, trajectories that start and end at the sam... | One misconception here is to assume that
If we knew the system were conservative, closed orbits in its phase portrait were homoclinic.
Actually a typical conservative system's closed orbits are almost always quasiperiodic or periodic. For instance, the only homoclinic point in the phase portrait below is the x-shaped... | {
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Cleaning silt off magnets I gone done a foolish thing; I got my set of spherical (⌀ 5 mm) neodymium magnets covered in of (what is presumably iron based) ferromagnetic silt/sand particles.
With some difficulty, I've been able to remove most of the sand sized particles (by grabbing them with some needle-nose pliers). ... | I have found that using an adhesive can work well to remove small pieces of dust like this. I have used packing tape to pull the particles off of small neodymium magnets.
I found this method on the K&J magnetics FAQ page, link here.
| {
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"timestamp": "2023-03-29T00:00:00",
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"question_score": "2",
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Surface tension per unit length Can shear stress be expressed as surface tension per unit length? How do I interpret it physically?
| Surface tension has the dimension of a force per unit length, stress has the dimension of a force per unit surface.
You can imagine the surface tension as the integral of stress over a surface with one infinitely small dimension,
$\Delta \mathbf{F} = \displaystyle \int_{\Delta S} \mathbf{t_n} dS = \displaystyle \int_{\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/736248",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How can acceleration in special relativity be uniform? Acceleration is defied as the rate of change in velocity, implying that $v(t) = at + v_0$. Say that an object is accelerating at $5 m/s^2$ with respect to an inertial frame in special relativity. Using the definition of acceleration alone, we now have $v(t) = 5t + ... | I’ll just formalize my previous comments. Let me restrict to 2D flat spacetime with a certain inertial frame $t,x$ ($c=1$ and the metric signature is $(+,—)$ like in particle physics). Then hyperbolic motion of proper acceleration $a$ can be parametrized by its proper time $\tau$ given (up to a space-time translation):... | {
"language": "en",
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Collapse of wavefunction in hydrogen atom under measurement of $L^2$ If a hydrogen atom is in the state $\Psi = \frac{1}{\sqrt{3}}(\psi_{100} + \psi_{211}+\psi_{21-1})$
and the square of the angular momenta was measured to be $2\hbar^2$. After the measurement will the state be
$\Psi' = \frac{1}{\sqrt{2}}[\psi_{211}+\ps... | After the measurement the state of your Hydrogen atom will be $\frac{1}{\sqrt{2}}[\psi_{211}+\psi_{21-1}]$. With the measurement you are projecting onto the states with angular momentum quantum number $l=1$ as the eigenvalues of $L^2$ are $l(l+1)\hbar$.
The state of your Hydrogen atom remains of course in a "state of t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Number of free parameters in $SU(5)$ GUT model Lately, I have been studying the potential of scalar fields in this theory. In general, what is the point of this GUT if, there, more free parameters have been added?
The standard Higgs potential in the Standard Model with only 2 free parameters (Higgs mass and self-coupli... | This is simply the most arbitrary renormalizable, gauge invariant potential for SU(5) with the given field content. The minimization conditions of the potential eliminate some of those arbitrary coefficients in terms of the vacuum expectation values and masses of the Higgses in the 5, and 24 rep.
While you do end up wi... | {
"language": "en",
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In firing a single photon at the center divider of a double slit, does it ALWAYS go through the slits? If we think of a single photon approaching the slits as a wave function, and we fire the photons at the midpoint of the two slits, one at a time, then I would think the probability function is highest at this midpoint... | You are correct. To the left of the "wall with slits" we typically approximate that we are illuminating the wall/slits with a plane wave. If the wall is much bigger than the diameter of the beam then what matters is the fraction $\eta$ of the slit area compared to the total beam area. It is only this fraction $\eta$ of... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does high frequency have high energy? The electromagnetic spectrum's wavelengths all travel at the same speed, $c$. Also, the wavelength $\lambda$ and frequency $\nu$ are related by $c = \lambda \cdot \nu$. Since all moving particles here would have the same speed, why would higher frequencies have more energy?
| Planck's constant is a conversion factor which changes the units of energy from a classical basis (as joules, for example) to a quantum basis which has wavelength (and therefore frequency) in it: E = hc/(lambda).
Note that if we write the laws of physics in natural units then energy has units of 1/(seconds) or "per sec... | {
"language": "en",
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When are my fluid approximations wrong? I did some classical approximations of the Navier Stokes equations, fluid is:
*
*non-viscous
*incompressible
*irrotational
When are these approximations wrong? and particularly is there a "general method" to evaluate in a theoretical way "the error" of an approximation?
For ... | I want to focus on the part of the question that deals with viscous effects: The dimensionless version of the conservation of linear momentum is largely equal to its dimensional version, except the term that deals with the stress tensor: In the dimensionless version, the divergence of the stress tensor is divided by th... | {
"language": "en",
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How can both of these equations for pressure be correct? Consider the Gibbs equation:
$$du=Tds-pdv$$
Identifying partial derivatives, one obtains:
$$-p=\left( \frac{\partial u}{\partial v} \right)_T$$
But you can also show that:
$$p=T\left( \frac{\partial s}{\partial v}\right)_T -\left( \frac{\partial u}{\partial v} \r... |
Consider the Gibbs equation:
$$du=Tds-pdv$$
Identifying partial derivatives, one obtains:
$$-p=\left( \frac{\partial u}{\partial v} \right)_T$$
No.
$$-p=\left( \frac{\partial u}{\partial v} \right)_s$$
But you can also show that:
$$p=T\left( \frac{\partial s}{\partial v}\right)_T -\left( \frac{\partial u}{\partial v... | {
"language": "en",
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Avoiding heat death in an accelerated expanding universe? Would there be any way to avoid heat death in an accelerated expanding universe?
https://en.m.wikipedia.org/wiki/Heat_death_of_the_universe
Is the heat death of the universe completely unavoidable in an universe with an accelerated expansion dominated by dark en... | We don't know exactly how the universe will face its fate, whether through big rip or heat death, although heat death seems more plausible.
Note that heat death exactly isn't caused by accelerated expansion by dark energy but is a manifestation of thermodynamic's second law. It states that all systems will eventually r... | {
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Why can the coriolis force potential be written as $ E_\text{cor}=m\dot{\theta}\begin{vmatrix} X & Y \\ \dot{X} & \dot{Y} \end{vmatrix}$? I found the following formula for the Coriolis force written here:
$$ E_\text{cor}=m\dot{\theta}\begin{vmatrix}
X & Y \\
\dot{X} & \dot{Y}
\end{vmatrix}=m\dot{\theta}\ (\dot{Y}X-\do... | This can be seen as a consequence of the fact that we can write the triple product $\vec{v} \cdot (\vec{\Omega} \times \vec{r})$ as a determinant, rearrange it, and then do an expansion by subminors:
\begin{align*}
\vec{v} \cdot (\vec{\Omega} \times \vec{r}) &= \begin{vmatrix} v_x & v_y & v_z \\ \Omega_x & \Omega_y & \... | {
"language": "en",
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"source": "stackexchange",
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How one can use Wick's theorem for the product $A:\mathrel{B^{n}}:$? I try to use Wick's theorem in the case that some products we deal with are already normal ordered.
My guess is that it could be something like
\begin{equation}
A:\mathrel{B^{n}}:~=~:\mathrel{AB^{n}}:+nA^{\bullet}B^{\bullet}:\mathrel{B^{n-1}}:\tag{1}
... | *
*There is usually a second implicitly written operator ordering besides the normal order. [This plays a role in e.g. eq. (2).] E.g. in the context of 2D conformal field theory, there is typically an implicitly written radial ordering ${\cal R}$.
*Then eqs. (1) and (2) become examples of a nested Wick's theorem dis... | {
"language": "en",
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Question about adjoint representation and Lie algebra My question is: In Polchinski II, section 11.4, page 62, said that
"the adjoint representation is the antisymmetric tensor, which is contained in the product of two vector representations".
May I ask why is this?
| *
*More generally, Ref. 1 is considering an orthogonal group
$$G~=~O(V)~=~\{g~\in{\rm End}(V) \mid \forall v,w\in V: \beta(gv,gw)=\beta(v,w)\}$$
over an $\mathbb{F}$-vector space $V$ with a non-degenerate $\mathbb{F}$-bilinear symmetric form $\beta:V\times V\to\mathbb{F}$.
*The adjoint representation $${\rm Ad}: G\t... | {
"language": "en",
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Does horizontal acceleration affect gravity? If we apply 1G horizontally in some object, will this constant force equal to G affect the time of falling? If the force does not affect gravity, why gravity is prioritized over this force if both are equal?
Edited: For the ones who didn't understand what i mean well, i mean... | We have Newton's second law F = ma which is a vector equation. If we look at the horizontal and vertical components, gravity acts vertically and your 1g force acts horizontally. So the vertical acceleration is determined by gravity. The 1g force has no vertical component so does not affect the vertical motion.
In your ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Interesting relationship between the 2D Harmonic Oscillator and Pauli Spin matrices I have an isotropic 2D Harmonic Oscillator in cartesian coordinates
\begin{equation}
H = \frac{p_x^2}{2m} + \frac{p_y^2}{2m} + \frac{1}{2} m\omega^2 (x^2 + y^2)
\end{equation}
In terms of the usual creation and annihilation operators fo... | It is well known the operators
$$
\hat C_{ij}=a_i^\dagger a_j\, ,i, j=1,\ldots, n
$$
span the Lie algebra $\mathfrak{u}(n)$. If you choose $\hat C_{ij}, i\ne j$ and use $h_i= \hat C_{ii}-\hat C_{i+1,i+1}$, you get instead the Lie algebra $\mathfrak{su}(n)$. Yours is just the special case with $n=2$.
The $n=3$ case is... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What gives rise to mass gap for gluons, even if they are massless? It is known that QED does not have a mass gap.
On the other hand, at the heuristic level, QCD has a mass gap.
But photons and gluons are both "massless". Could anyone explain (at least at the conceptual level) what the fundamental difference between glu... | The difference is gluons carry their own charge and thus are bound in glueballs, and while gluons are massless, glueballs are not. It is glueballs, not gluons, which give a mass gap.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/739196",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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When a football/rugby ball (prolate spheriod) is dropped vertically, at an oblique angle, why does it bounce at an angle? A prolate spheroid like a rugby ball or American football, dropped vertically with no rotation, will bounce vertically if it is oriented along one of it's axes of symmetry (in other words, if its ce... | If the football is at an angle, the pointed end is not below the center of gravity. The point strikes the ground first. The ground pushes up on the point. This creates a torque that starts the ball rotating.
Since the point is on the ground, it may stick or dig in. Or there may be friction. The rotation may direct the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/739318",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the state of an entangled photon after its twin is absorbed? Let's two photons are entangled in polarization after a laser beam passes through a Betha Barium Borate crystal. They take different paths and one of them (1) is absorbed in a black sheet. What is the state of the leftover photon (2)? Is it in superpo... | When two photons are entangled in polarization, the state of each photon is dependent on the state of the other. In the scenario you describe, if one of the entangled photons (photon 1) is absorbed by a black sheet, the state of the remaining photon (photon 2) will change instantaneously. However, the exact state of ph... | {
"language": "en",
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"source": "stackexchange",
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Conservative Force: Translational Invariance I have a question about the following.
Why if there are two masses, $m_1$ and $m_2$ respectively, and the only force acting on them is from their mutual interaction which is conservative and central, the following is true?
$U(\vec{r_1},\vec{r_2})=U(\vec{r_1}-\vec{r_2})$
(It ... | Imagine the situation you have described. Let the potential be denoted as $U(\vec{r_1},\vec{r_2})$. Note that this picture shouldn't change if I decide to observe what they do in one place or the other. Therefore, the potential should be invariant if I decide to displace the particles in the same direction by the same ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Is there a "fundamental problem of thermodynamics"? The "fundamental problem of mechanics" can be boiled down to finding and solving the equation of motion of a system. Similar statements can be said for quantum mechanics for the Schrödinger equation and for electrodynamics and Maxwell's equations, etc. But is there su... | I think the best description of what is the "fundamental problem" in Thermodynamics remains the one by H.B. Callen in his textbook (Thermodynamics and an Introduction to Thermostatistics. John Wiley & Sons):
The single, all-encompassing problem of thermodynamics is the determination of the equilibrium state that event... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What's the smallest signal to noise ratio for which a signal has been extracted? Suppose we have some physical variable $y$ that is changing in some way and we want to detect this change in the presence of noise (e.g. white noise) in that same physical quantity. For example $y$ is an electric field amplitude and there ... | WSPR, a "ham radio" digital radio transmission protocol with redundancy and error-correction, can be routinely decoded at a level 29dB below the noise floor. This is good enough to permit error-free radio communication between any two points on earth on much less than one watt of radiated power, as long as ionospheric ... | {
"language": "en",
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Do we need a quantum gravity theory to model an hydrogen atom on earth? The hydrogen atom is a quantum mechanical system. However, it is also attracted by the gravitational pull of the earth. Therefore, do we need quantum gravity to model its behavior correctly? Conversely, can we study hydrogen atoms on earth to obtai... | We don't need a quantum theory of gravity to model a hydrogen atom in the gravitational field of the Earth. In general, it's understood how to model quantum fields on a fixed gravitational background (see, e.g., the book by Birrell and Davies) — at least at a mathematical level; experimentally it's very hard to probe t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/741366",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Why the double slit pattern is a blurred image instead of two strips? I am complete dilettante in physics, when i was first introduced to quantum mechanics by a You tuber named Arvin ash, he explained about the double slit experiment with quantum particles, there in his video when the which way path of the particles is... | Without interference, the energy intensity at a point on the screen is proportional to $A^2+B^2$, where $A$ and $B$ are the amplitudes of the waves coming through each slit individually. With interference, it's proportional to $A^2+B^2+2AB\cos θ$, where $θ$ is the phase angle between the waves from the two slits.
If $A... | {
"language": "en",
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How to go from Lagrange equations to d'Alembert's principle? All sources I know show how to use d'Alembert's principle and/or Hamilton's principles to derive Lagrange equations. It is also common to use d'Alembert's principle to derive Hamilton's principle (see Lanczos "the variational principles of mechanics", p.112) ... | Lets look at this example
Pendulum 2D space
the kinetic energy is
$$T=\frac m2 (\dot x^2+\dot y^2)$$
the potential energy is:
$$U=m\,g\,y+\lambda\,\underbrace{(x^2+y^2-l^2)}_{\text {holonomic constraint eq.}}$$
thus the equations of motion
$$\ddot x=-\lambda\,\frac{2\,x}{m}$$
$$\ddot y=-g-\lambda\,\frac{2\,y}{m}$$
how ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/741701",
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Why is the degeneracy factor for Bose Einstein distribution set to 1 automatically? In https://scholar.harvard.edu/files/schwartz/files/12-bec.pdf, the article says
"With Bose-Einstein statistics, we determined that using the grand canonical ensemble the expected number of particles in a state i is"
$$\langle{n}_{i}\ra... | The expected number of particles in a given state $i$ is given by $$\langle n_i\rangle = \frac{1}{e^{\beta(\epsilon_i-\mu)}-1}$$
If there are $g(\epsilon)$ states which all have energy $\epsilon$, then the expected number of particles with energy $\epsilon$ is given by
$$\langle n(\epsilon)\rangle = \frac{g(\epsilon)}{... | {
"language": "en",
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What would a standing wave of light look like? I want to know what a standing wave of light would like and what properties it might have that are interesting.
| It arguably doesn't "look" like anything. The standing wave in an optical resonator (e.g., a laser cavity) is trapped in the cavity. It isn't entering your eye. If we're talking about a laser, then the part that escapes the cavity and ultimately enters your eye† arguably is no longer a standing wave.
A diagram that rep... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
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Is the operator identity $[X,F(P)]=[X,P]F'(P)$ always true? I came up with the operator identity in my QM textbook
$$
[X,F(P)]=[X,P]F'(P)
$$
where $X,P$ are Hermitian operators whose commutator commutes with them: $$[X,[X,P]]=[P,[X,P]]=0.$$ $F(x)$ is some well-behaved function.
In the book, the identity is proved by ve... | As it finally emerges from your graduated comments, you certainly ought to have indicated that your Hilbert space goes beyond the image of all functions of X and P! In the language of the field, this center Y is a "constant", to the extent X and P commutations don't affect it. You need not fuss with weird operators:... | {
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Why does a chimney sometimes create a "draft"? Sometimes, while lighting a fire in a wood stove in a basement, the smoke does not exit through the chimney like it normally does. Rather, a large amount of the smoke seems to get "pushed back" into the room instead of exiting through the chimney.
Why does this occur?
| Airflow around buildings and over walls can compress air at the top of the roof at higher pressure and bring low pressure at the sides of the house and the shielded zones.
If the chimney has very cold conditions at the top, and compressed air on the roof, the chimney can draft backwards, especially if the house has lea... | {
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"url": "https://physics.stackexchange.com/questions/742910",
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About a battery's positive terminal Does the positive terminal of the battery mean that the concentration of electrons is more there. In some places people say that current moves from positive to negative and they call it a convention what does this really mean and others say it flows from negative to positive it's rea... | The names 'positive' and 'negative' were assigned to charges long before protons and electrons were discovered and even before batteries were invented. The type of charge that glass acquired when rubbed with silk was called 'positive', and the type that amber acquired when rubbed with fur was called 'negative'.
In the ... | {
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Maximum Range for Projectile Motion This is a question concerning a trick I observed while solving for the angle responsible for maximum range of a projectile.
What I have observed is :
If you draw two lines, one opposite to the acceleration faced by the body(i) , another in the direction we want to find the projectile... | The proof of this is a straightforward generalization of the one for maximizing horizontal distance given downward acceleration. You mention differentiating with respect to the angle so I'm not sure which part you got stuck on.
Nevertheless, orient your axes WLOG so that the distance you want to maximize is $x$. Let th... | {
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Timescale for unstable stratification to resolve itself The ocean is typically vertically stratified, that is the deeper you go the higher the density should be. This can be because of increased salinity or decreased temperature.
If that is not the case then we have an unstable stratification and this instability is ca... | In real oceans this is complicated by currents, eddies, wind driven surface flows, thermohaline gradients, …, but in an idealized two-layer system with a sharp boundary and a density difference of about 0.1%, convective mixing over a 1 m distance should take less than a minute.
For an upper and lower layer with densiti... | {
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"timestamp": "2023-03-29T00:00:00",
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Does fractional freezing always happen in mixtures that are prone to it? Let's assume that we have a mixture that is prone to fractional freezing, such as water with table salt, or water with alcohol.
If we place the mixture in a sufficiently cold environment, will we always have fractional freezing, with ice forming f... | Not sure if this answers your question, but if the temperature is below the freezing point for both components of the solution, and the solution cools down fast enough, there will not be fractional freezing.
Also, some mixtures can form an "eutectic system", which has a freezing point that is lower than that of both it... | {
"language": "en",
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How do we maintain polytropic processes? In polytropic processes for an ideal gas,
$$PV^{\alpha}=constant$$ where $\alpha \neq 0,1,\gamma$
And $\gamma$ is adiabatic exponent of gas
So, how these processes are maintained?
What things are done to initiate this process?
| You add or remove heat to change the temperature along the polytropic path in such a way that the exponent $\alpha$ remains constant. You have $$d\ln{P}+\alpha d\ln{V}=0$$and $$d\ln{P}+d\ln{V}=d\ln{T}$$So $$dln{T}=(1-\alpha)d\ln{V}$$or$$TV^{\alpha-1}=const$$
| {
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Is momentum conserved in a traversable wormhole? Wikipedia says:
A wormhole (Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.
If a traversable wormhole existed, could its ends move relatively to each other ... | General relativity with one test particle (i.e you) can be described by an action principle. The action only depends on the metric and your position, so it's translationally invariant. Hence by Noether's theorem, it has four symmetries, corresponding to translation in space and time. The conserved quantities associated... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744144",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Third principle of thermodynamics and the unattainability of absolute zero Consider a $S-T$ diagram (entropy-temperature) and consider cooling a substance by doing a series of succesive isothermal and reversible adiabatic processes between two volumes $V_{1}$ and $V_{2}$.
Now when cooling the substance from $T_{1}$ to ... | Another perspective: The equation is simply not defined for $T_2=0$, since this would result in dividing by 0. You could at most let $T_2$ go against 0 for both sides, but then you have to prove that you can commute the limit with the integral. (In general e.g. by using Lebesgue's convergence theorem).
tl;dr: Correct m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744237",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is there any intuition for why bisecting an angle gives the optimal angle to throw a ball? Let's say that I am holding a ball and have zero height, and there is a wall with a height of $h$ that is a distance $d$ away. At what angle should I throw the ball such that getting it over the wall requires minimal speed?
We ca... | starting with
$$x=v\,\cos(\theta)\,t\\
y=v\,\sin(\theta)\,t-g\frac{t^2}{2}$$
solve those equations for $~t~,y~$ you obtain
$$y(x,v,\theta)={\frac {x{v}^{2}\sin \left( 2\,\theta \right) -g{x}^{2}}{{v}^{2}\cos
\left( 2\,\theta \right) +{v}^{2}}}
$$
$$t={\frac {x}{v\cos \left( \theta \right) }}=t_l$$
from here with
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744320",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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Feynman's QED 36000 revolutions per inch In Feynman's book, QED, on page 27 he says "As long as the photon moves, the stopwatch hand turns (about 36,000 times per inch for red light); when the photon ends up at the photomultiplier, we stop the watch.
There are about 36,000 wavelengths of red light in one inch. So is ... | Feynman's stopwatch is the phase of a complex number, $e^{i k x}$, where $k=2\pi/\lambda$ is the wavenumber and $\lambda$ is the wavelength of the wave. One rotation of the complex number occurs when $k x = 2\pi$; $N$ rotations occur when $kx = 2\pi N$.
Therefore, given $\lambda=36000^{-1}\ {\rm inch}$ (or in other wor... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744539",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How do atoms emit an electromagnetic wave (infrared radiation)? From what I understand, when an object has a certain temperature, its atoms vibrate and this atomic vibration accelerates the electrically charged particles and this generates infrared radiation.
To generate infrared radiation, it is therefore necessary to... | It is not the atoms composing an object that emit radiation, called black body radiation, it is changes in the quantized energy levels within a solid or a liquid that will be emitted as photons.
From what I understand, when an object has a certain temperature, its atoms vibrate
Its atoms change energy levels in the l... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/744698",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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