Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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How can a photon collide with an electron? Whenever I study the photoelectric effect and the Compton effect, I have always had a question about how a photon can possibly collide with an electron given their unmeasureably small size. Every textbook I've read says that the photo-electrons are emitted because the photons ... | Both photons and electrons may be considered point-like particles, but the interaction/force that they feel has a range: the electromagnetic interaction has a pretty long range. Actually it is infinite in the absence of screening effects (ideal cases).
You could ask yourself, what does it even mean colliding? For examp... | {
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Wavefunction of a particle on a ring ($E > V$) using WKB method For a particle on a ring (with radius $R$ and changing angle $\theta$) with only kinetic energy ($V=0$) we get the expressions for the wavefunction (normalized) and eigenvalues $$\Psi_n (\theta) = \frac{1}{\sqrt{2 \pi}} e^{in \theta}$$ $$E_n= \frac{\hbar ^... | *
*For the case $V=0$, note that the semiclassical WKB approximation cannot be trusted for the ground state $n=0$ corresponding to zero momentum $p=0$, or equivalently, infinite de Broglie wavelength $\lambda=h/p=\infty$.
*More generally, the semiclassical WKB approximation typically estimates the ground state poorly... | {
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Electric field in a sliding bar along frictionless conducting rails When discussing a conducting bar sliding frictionless over two parallel conducting rails in the context of motional emf as in the picture below, Chabay and Sherwood write in their book Matter and Interactions (4th edition, page 821)
The electron curre... | Let's call the $+x$ direction to the left, the direction the bar is moving. The current through the bar is up. A current up in a field out of the page gives a force to the right:
$$
F_x = ma = -ILB \Rightarrow\\
m \frac{dv}{dt} = -ILB.
$$
The current is given by Ohm's Law, where the emf is the motional emf:
$$
I = \fra... | {
"language": "en",
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Is a photon reflected, transmitted or in a superposition? When a photon hits a half-silvered, mirror quantum mechanics says that rather than being reflected OR transmitted it enters into a superposition of transmitted AND reflected (until a measurement takes place). Is there an experiment that demonstrates that this is... | When the photon is detected, it always ends up with a single outcome. The superposition is simply an expression of the fact that until it is detected there are non-zero probabilities for different outcomes.
Confusion arises because there is a fundamental difference between probabilities given in quantum mechanics and ... | {
"language": "en",
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Variance of an Overlap Between States: Bra-Ket Notation? Imagine two eigenstates of a system $|0\rangle$ and $|1\rangle$, and suppose you manage to prepare your system in the superposition $|\psi_{in}\rangle = (|0\rangle + |1\rangle)/\sqrt{2}$. After some time, the system evolves naturally to the state $|\psi_{out}\ran... | The variance of an operator $\hat A$ is
$$\langle \psi| \hat A ^2 |\psi\rangle - \langle \psi | \hat A |\psi\rangle^2 ,
$$
as in statistics, $\overline{A^2}-\bar {A}^2$. You have used this in the uncertainty principle.
Your operator $\hat A$ here, however, is a projector, $P=|\psi_{in}\rangle \langle \psi_{in}|=P^2$, ... | {
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Why does a rubber band become a lighter color when stretched? I was stretching a pink colored rubber band, and I noticed that the longer I stretch it, the lighter the pink becomes. I haven't found answers to this question anywhere else. Is there a reason for this phenomenon?
Why does this happen?
| Rubber bands are made of polymers (more specifically elastomers). A given polymer in the band can either be aligned with other polymers around it, or it can be misaligned. Therefore, you can end up with regions of order and regions of disorder in the band. In an unstretched band you have much more disorder, but when yo... | {
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"A spinning top spins much longer because it experiences less frictional torque" is wrong? The above quote was found in my physics textbook, but it struck me as strange because my understanding of friction is that the surface area doesn't matter in calculating the amount of frictional force.
Another question that asked... | The surface area doesn't matter because $F_a = \mu N$. If the contact area is very small as in a top, the normal is the same, and $F_a$ doesn't change.
But the average distance ($d$) between the center of spin in the ground and the other points of contact (because the "point" of contact indeed has some area) is very sm... | {
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Are antileptons and antibaryons linked? The recent news about the T2K experiment got me thinking: is there any linkage in the Standard Model between the matter and antimatter categories across the families of Standard Model particles? Are antileptons necessarily linked to antibaryons?
As a specific example: In our uni... |
What I am trying to ask: is there any reason that p and e− must be grouped together as matter (other than their current abundance in the universe).
The basic and only reason is that the grouping is consistent and unique within the standard model of particle physics, which emerged from a great number of data validatin... | {
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Why does a hollow conductor does not have a electric field inside it when it is enclosing a charge? When a positive charge is enclosed in a thick hollow sphere which is a conductor, the inner surface gains a negative charge distribution and due to that the outer gains a positive charge distribution. So there should be ... |
Why does a hollow conductor does not have a electric field inside it when it is enclosing a charge?
You can take this as a given in electrostatics.
You can also take this fact as derivable from your statement that "the potential difference in a conductor must be zero." The potential difference divided by the distanc... | {
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Inverse of a metric tensor on a Hermitian manifold Let $(M, g)$ be a Hermitian manifold. We have a metric tensor $g^{i \bar j} dz_i \otimes d\bar{z_j}$, where $(g_{i \bar j})$ is a hermitian positive definite matrix. Now we naturally get the inverse of the metric $(g^{i \bar j})$. I have been told being inverse to each... | The inverse property implies $$\sum_k(g^{-1})^{pk} g_{kq}+\sum_{\bar{k}}(g^{-1})^{p\bar{k}} g_{\bar{k}q} ~=~ \delta^p_q.$$
It is standard convention to not write the power "$-1$" explicitly for the inverse metric. Next use symmetry $g_{\bar{k}q}=g_{q\bar{k}}$ and that for a Hermitian metric $g_{kq}=0$ to obtain the so... | {
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Under which conditions do two moving bodies start orbiting each other around their center of mass? If two bodies are close, both will get attracted to each other and collide. Under what conditions will the two bodies start revolving around their common center of mass? I understand that such bodies represent the graviti... | Unless other objects are "near enough" to complicate the motion, the bodies can always be described by a two-body solution whenever both are in freefall (nothing is pushing one of them). The only difference that being close makes is that forces from other objects become less significant.
You could then describe their ... | {
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What is the meaning of vertical bars in paths of high symmetry points? I am a new to the study of high symmetry paths. After looking at the Silicon path that is $Γ—X—U|K—Γ—L—W—X$, I am not able to understand the meaning of $U|K$ in this path?
| Silicon's crystal structure is the diamond crystal structure and the Bravais lattice is the fcc lattice. The first Brillouin-Zone (a truncated octahedron) looks like this:
(Image source and further information)
As you can see, the path includes every one of the red lines, always connecting neighboring symmetry points,... | {
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Baryons in flavor $SU(N)$ (in ChPT) For flavor $SU(2)$ (Isospin) we have two $\frac{1}{2}^+$ baryons, the nucleons. For flavor $SU(3)$ we have the eight baryons in the octet. In a world with $N$ light quarks we would see a baryon multiplet of dimension $\frac{N}{3}(N^2-1)$.
Such a theory would see the chiral symmetry b... | Baryons in ChPT are an advanced subject, so I won't presume to do your Googling for you. But you recall baryons are fermions, so you don't need gimmicks: $SU(N)\times SU(N)$ is realized linearly on vectors of an m-dimensional representation.
Recall the nucleon isodoublet
$$\begin{pmatrix} p\\n\end{pmatrix}$$ is acted... | {
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Where is the wiggle room in current gravity theories? As far as I know, General Relativity has long since been proved experimentally to every qualified person's entire satisfaction, and modern technology such as GPS relies on its accurate predictions.
So although there may be debatable aspects, such as local conservati... | To understand where the "wiggle room" in general relativity is it is useful to look at one of the main theorems that constrains GR, Lovelock's theorem. This says that if we start from an action that
*
*is local
*depends only the spacetime metric
*is at most second order in derivatives of the metric
and
*is in 4 s... | {
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Which should be the correct option? Question--
A person standing on the floor of an elevator drops a coin. The coin reaches the floor of the elevator in time t1 if the elevator is stationary and in time t2 if it is moving uniformly. Then
(a) t1 = t2
(b) t1 < t2
(c) t1 > t2
(d) t1 < t2
or
t1 > t2 depending on whet... | The thing you're missing is that if the elevator is travelling uniformly at some velocity $v$, the coin starts with that same velocity.
So taking our SUVAT equation - in the case where the elevator isn't moving, you have:
$$\tfrac12 g t_1^2 = h$$
and when it is, $H$ is clearly equal to $v t_2$ so:
$$v t_2 + \tfrac12 g... | {
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Confusion regarding Ampère's law and non-planar loops To show that $\int_{C} \vec{B}\cdot \vec{dl}=4\pi I/c$ for this loop
Purcell uses this other path ($C'$)
He argues that since $C'$ doesn't enclose the wire
$$\begin{align*}\int_{C'}\vec{B}\cdot \vec{dl'}&=0\\
\int_{C_1}\vec{B}\cdot \vec{dl_1}+\int_{C}\vec{B}\cdot... | Imagine that you pulled and reshaped the part of the loop you called $C1$ as shown below.
In doing this you have not cut through the current carrying conductor.
You can now see that within your Amperian loop you have the current carrying conductor.
| {
"language": "en",
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Contradiction in canonical transformation
The problem I'm supposed to solve is finding $Q$, such that $(p,q)\rightarrow(P,Q)$ is a canonical transformation. In this case $\mathcal{H}=\frac{p^{2}+q^{2}}{2}$ and the new hamiltonian $\mathcal{K}$ is $\mathcal{K}=P$.
This means $\dot{q}=p$ and $\dot{p}=-q$
Since $\mathca... | I am not that much familiar with Hamiltonian mechanics, but are you not supposed to write $F_1$ as a function of $q$ and $Q$ only? You need to replace $p$ in $F_1$ by a combination of $q$ and $Q$, which will obviously have a non-zero partial derivative with respect to $q$, thus changing your calculation.
I will be "che... | {
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Classic Man on a Boat problem To be clear I have indeed reviewed the question asked by helios321 (Classic man on boat problem). But i have something else to ask related to man on a boat problem.
The man on a boat problem goes like this:
A man is standing on one side of a boat and the boat is stationary. We ignore fr... | There is no external force on the system right? So shouldn't the centre of mass remain stationary?
Let me give you an example too.
A man is standing on the boat and jumps onto the pier. As a result, the boat moves backward and centre of mass of system is still at rest
So back to this problem, the boat also acquires a ... | {
"language": "en",
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Schumann resonance frequency I keep hearing that Schumann resonances have been increasing rapidly in recent years. And that it was relatively stable before. I failed to find any scientific data proving or disproving this. I would really appreciate a chart depicting what has been happening over the years in that concern... | Of course, the Schumann resonance frequency can't constantly rise. We can see continuous fluctuation (with seasonality). As for "human brain resonance", I'd not call it "pseudo-science" (I'm referring to one of the comments above, unfortunately, I don't have enough reputation yet to write a comment).
There is nothing m... | {
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Is the force of gravity always directed towards the center of mass? This is a pretty basic question, but I haven't had to think about orbital mechanics since high school. So just to check - suppose a [classical] system of two massive objects in a vacuum.
If the density of either object is the same at a given distance f... | Perhaps I am wrong, given the other answers, but it was my understanding that gravity would indeed always be directed towards the centre of an object's mass. I would argue this by proposing a 2D plane rather than a 3D space. in this example, we would like to see the direction of gravity between a point and, say, a rect... | {
"language": "en",
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What is aperture of a lens? I read that aperture of a lens is the surface from which refraction takes place and it is represented by the diameter of the lens.
So, by saying that the aperture refers to the surface from which refraction occurs, do we mean that the surface area of the curvature would be the numerical valu... | The aperture of a lens is the working area of a lens: practically diameter of a beam which is refracted. If you place a pinhole with a variable diameter (sometimes called an aperture) before the lens, you can decrease the working area of the lens up to 0. Opening the pinhole fully, you obtain the full working area whic... | {
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What is wrong with this calculation of work done by an agent bringing a unit mass from infinity into a gravitational field? Let us assume that a gravitational field is created by a mass $M$. An agent is bringing a unit mass from $\infty$ to distance $r < \infty$, both measured from mass $M$.
The agent is always forcing... | You made a mathematical error in trying to prove the result. It arises in many scenarios.
To give you an insight into your mistake I would like to tell you the correct method of integration in physics.
Remember that we always consider an element $dx$ at a distance $x$ from origin in the direction of $x$.
What you di... | {
"language": "en",
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Approximation of the total number of accessible microstates So, here is a system having two subsystems $\alpha$ and $\beta$ where the two subsystems can exchange energy between them, then the total number of accessible microstates of the whole system is given by, $$\Omega(E)=\sum_{E_{\alpha}}\Omega_{\alpha}(E_{\alpha})... | I'll put the conclusions first. Take ideal gas as an example, if you define the function $f(E_{\alpha}) = \Omega_{\alpha}(E_{\alpha}) \Omega_{\beta}(E-E_{\alpha})$. This function f(E) will look like:
$$
f(E)=E^{N}e^{-E}
$$
where N is a very large number (same order as the number of particles, around $10^{23}$), $E$ her... | {
"language": "en",
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Why is the acceleration of the string connected to the cylinder different from which the cylinder is moving forward with?
The following Object 'B' is a cylinder. It is kept mounted horizontally on a massless block, when a tension T is applied by a string passing over the lower end of cylinder, the acceleration of the ... | First of all $$\vec{F_{ext}}=m\vec{a_{cm}}$$
This equation conveys us the messge that the net external force is the only force which is responsible for the acceleration of center of mass of the system.
It doesn't means that $\vec{a_{cm}}=\vec{a_{i}}$, where $\vec{a_{i}}$ represents the acceleration of $i^{th}$ particle... | {
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What exactly happens when $\rm NaCl$ water conducts electricity? Assume a DC power source with $2$ electrodes made of Fe. We dip those $2$ electrodes into table salt water. What happens exactly?
*
*Will $H^+$ and $Na^+$ migrate to the negative electrode by electrical field
or diffusion or a combination of both?
*... |
...I believe there is one general principle that can explain all. Something that can explain the priority of all possible reactions.
Under normal conditions sodium chloride has a crystalline structure. Each ion from $Na^+$ and so from $Cl^-$ is surrounded by six ions of the opposite charge. From this we learn that on... | {
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Mathematically prove that a round wheel roll faster than a square wheel Let's say I have these equal size objects (for now thinking in 2D) on a flat surface.
At the center of those objects I add equal positive angular torque (just enough to make the square tire to move forward).
Of course the round tire will move fast... |
At the center of those objects I add equal positive angular torque (just enough to make the square tire to move forward).
You do not apply torque at the center, a single point. It requires at least two points. This is an important detail. Because the second force applied to the object is a friction force. This fricti... | {
"language": "en",
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What would cause an infrared thermometer to malfunction in a specific room? The situation is as follow:
When used to measure body temperature, my infrared thermometer will always measure an abnormal high temperature in ONE certain room (40/41 degree celcius), but it will always measure a normal temperature outside of t... |
Is there any wave or radiation that would affect the accuracy of an infrared thermometer?
To potentially state the obvious, infrared radiation would do that. Have you checked your lights in that room? LEDs and incandescent bulbs give off an enormous amount of IR radiation, which could cause your thermometer to read... | {
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If heat is merely molecular motion, what is the difference between a hot, stationary baseball and a cool, rapidly moving one? This is from the Exercises for the Feynman Lectures on Physics, exercise Exercise 1.1. I believe that a hot stationary ball has more thermal energy due to the inter-molecular motion of the base... | Definition of temperature in statistical mechanics terms:
$$T_{\text{kinetic}}=\frac{2}{3k}\left[\overline{\frac 1 2 m v^2}\right]=\frac{2}{3k}\text{KE}_{\text{average}}$$
Please read the linkfor the constants, what is important to note is that temperature is analogous to average kinetic energy
Also 3. applies
When k... | {
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About magnetization in ferromagnetic material I am studying about ferromagnetism and have wondered whether the magnetization can be aligned independently of external magnetic field direction.
As far as I know, the ferromagnetic material has no linear relationship between magnetization M and external magnetic field H, t... | Above the critical temperature such a material exhibits paramagnetic properties, i.e. the spins align along the magnetic field. However, below the critical temperature it is in a ferromagnetic phase, which a specific value of the magnetization. Changing the direction of this magnetization than requires applying a suffi... | {
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Eddington-Finkelstein coordinates not well-defined? Consider the Schwarschild solution $$d s^{2}=-\left(1-\frac{2 m}{r}\right) d t^{2}+\frac{d r^{2}}{1-\frac{2 m}{r}}+r^{2}\left(d \theta^{2}+\sin ^{2} \theta d \varphi^{2}\right) $$
and the radial null geodesics (in Schwarschild coordinates): $$t=\pm(2 m \ln |r-2 m|+r)+... | When you choose $(\bar{t}, r \ldots)$ instead of $(t, r \ldots)$ and notice that inside $r<2m$ the EF metric is a valid and regular solution, what you find is an extension (like an analytical extension) of the solution in the region $r>2m$ into a region below the event horizon. It was not there before because of the co... | {
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Why is a pump's head usable for any fluid? As far as I investigated, a pump has a specific head in a determined flow rate (relating to its power and rotating speed). Then considering the formula ($\Delta P=\rho g H$), $\Delta P$ is adjusted for any fluid (with a different density) to obtain the same head.
But my questi... | I am assuming you are referring to a centrifugal pump. If that is the case, the term head is used in place of pressure. To understand where the pump will operate you must plot the system head curve onto the pump characteristic performance curve. The pump curve starts on the left side of the chart and normally arcs down... | {
"language": "en",
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Horn equation (wave propagation in an object with a circular cross-section) I have a problem with finding eigenfrequencies for wave which propagate in an object with a circular cross-section. I don't know how to start. I'll be very grateful for solution and comment or solution of very similar problem.
$G(x)\frac{∂^2u(x... | Webster's Horn equation at frequency $\omega$ is just an engineer's name for a special case of the Sturm-Liouville equation. Your case is a particularly simple example. Firstly change your independent variable to $\xi = x+1$ so your equation becomes
$$
\xi^2 \frac{d^2u}{d\xi^2}+2\xi \frac{d u}{d\xi}+ \frac{\omega^2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/549772",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Force, Newtons second law In the book "An Introduction to Mechanics - Second edition" by Kleppner D., Kolenkow R, I came across a paragraph:
pg. 54 , sec 2.5.2(force)
It is worth emphasizing that force is not merely a matter of definition. For instance, if we observe that an air track rider of mass $m$ starts to accel... | The author is trying to convey the message that it was not the acceleration which made us observe a force, the force was already there. In other words, force is not the consequence of acceleration, rather it's the other way around, acceleration is the consequence of force, which implies forces are more fundamental.
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there an authoritative data source for EM spectrum assignments? I'm working on some software to coalesce various standard constants (eg SI, CODATA, AME) into an easy-access library. However, trying to find an authoritative source I can find for EM spectrum assignments is a little less clear, which I suppose makes se... | ISO 21348 seems to be a good set of definitions, with major and minor categorisation (eg Radio and UHF).
| {
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On-shell SUSY-transformations for interacting Wess-Zumino model I'm learning SUSY with Quevedo, Cambridge Lectures on Supersymmetry and Extra Dimensions.
Setup:
The SUSY transformations of the component fields of a chiral field $\Phi$ are given by (p.41)
\begin{align*}
\delta_{\epsilon,\overline{\epsilon}}\varphi &= \s... | *
*When we eliminate/integrate out the auxiliary field $F$, the SUSY transformation for $F$ is rendered moot, and the appearance of $F$ on the RHSs of the other SUSY transformations is replaced with its algebraic EOM.
*It's not true that we do not know anything about the model -- we assume that the action $S$ is SUSY... | {
"language": "en",
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Why is the Force of Gravitational Attraction between two “Extended” bodies proportional to the product of their masses? Newton’s Law of gravitation states that force of attraction between two point masses is proportional to the product of the masses and inversely proportional to the square of the distance between them.... | The simple explanation is that any finite body (i.e. occupying a bounded region of space) looks like a point from sufficiently far away. This observation also tells you what is the range of validity of this "law". The distance between the bodies needs to be much larger than the linear size of each body.
Using math and... | {
"language": "en",
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What is causality? I was looking a few videos on youtube and I came across a video named the speed of light is nothing related to light. In the video, it was said that speed of light is actually speed of causality so what actually is causality?
| In the broadest sense, a world which exhibits causality is one in which 1) things have causes (i.e., magic does not operate) and 2) those causes precede their effects. As pointed out by PM 2Ring, a strict definition of this can be furnished in a space-time diagram, in terms of the past and future light-cones and their ... | {
"language": "en",
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Can we use quantities other than temperature to describe thermal equilibrium? From the 0th law, Thermal equilibrium is when there is no heat transfer between two objects. So I want to ask is temperature the only "potential"-esque quantity which should be equalized for stop of heat flow? If temperature is the only one t... | First, the 0th law is not what you think it is...
From the 0th law, Thermal equilibrium is when there is no heat transfer between two objects.
This is not the 0th law, this is just the definition of thermal equilibrium.
The 0th law is just something needed to make thermal equilibrium a well-defined "equality" between... | {
"language": "en",
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Should the thermos flask better be half full or half empty? Every evening I am preparing hot water for my two year old son wakes up in the night to get his milk. We use a rather bad isolation can for this. It is a typical metal cylinder shaped can holding half a liter. If I put cooking hot water into it, I know that ab... | Actually the heat of liquid you have poured in flask is half of the volume of Thermos so the heat of liquid will get conventionally transfer to air which is another half of Thermos so better to fill it to full to get long time to put water hot.
| {
"language": "en",
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If the integral of $\frac{dQ}{T}$ over an engine cycle is less than 0 , then why is entropy of the universe always increasing? For a reversible process, we define $ dS= \frac{dQ}{T}$ , so, the integral being negative would suggest that the entropy of universe decreases with each cycle of the engine because the clasius ... | The value of $\Delta S_{\text{sys}}$
You are confusing the entropy change of the system with the total entropy change. Now since the process is cyclic, the total entropy change for the system will be zero ($\Delta S_{\text{sys}}=0$). It does not matter whether the process is reversible or irreversible because entropy i... | {
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Why does light behave like a wave? When discussing a single or double slit experiment, where light is shined through a very small slit, it is often compared to a water wave going through a similar, if larger, slit. It's my understanding that when a ripple hits a wall with a hole in it the reason the ripple "bends" and ... | Yes water and sound waves are share similarities but are also very different to light waves which travel in a vacuum. Diffraction of light is caused by an interaction of the EM field of the photon with the EM field of the material at/in the slit edges. Any size aperture will effect the light path to some degree. The li... | {
"language": "en",
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Amount of electrons in a material? Is there a way to calculate the amount of electrons in a plate of a certain material and certain dimensions?
What I want to know is how many electrons are available to remove from a plate when light of appropriate wavelength hits the plate(photoelectric effect).
| As an addition to the answer by @SuperfastJellyfish, consider this.
Your charge of $18.1\times10^{28}$ electrons is approximately equal to $3\times10^{10}$ Coulomb. If we have that charge removed to a distance of $1 m$ (and the opposite positive charge is left on the aluminium), the force on the removed electrons is gi... | {
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Optimize crossbow I'm currently building a crossbow
and was wondering how I might improve the performance of it? I was suggested to fine-tune the rubber band more and maybe change the projectile maybe to a zinc alloy one instead of the plastic ones I use. I do understand this is sort of engineering feat but I think i... | A better crossbow design than a fixed wooden rod and an elastic band is a tough piece of string connecting to "sprung" arms that are pivoted at the join. They can be sprung by winding up elastic as the string is pulled back.
This makes for a better crossbow as it is much more effective at storing elastic potential ener... | {
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What does CERN do with its electrons? So to get a proton beam for the LHC, CERN prob has to make a plasma and siphon off the moving protons with a magnet. Are the electrons stored somewhere? How? I don’t mean to sound stupid but when they turn off the LHC, all those protons are going to be looking for their electrons. ... | The beam has a positive charge, so there's an electric field that surrounds it. But the beam pipe is metal, conductive. At the surface where the field intersects the metal, electrons flow to cancel the field. There is thus a layer of electrons on the metal surface, with equal but opposite charge to the beam.
The beam p... | {
"language": "en",
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Does solar cells absorb sub-bandgap photons? My understanding is that although we are taught that solar cells only absorb photons of energy higher than the bandgap of the material, some of the sub-bandgap photons still gets absorbed, which is evident when looking at the absorption coefficient spectra (it is not zero wh... | At 300K there are intrinsic free holes and electrons due to thermal excitation across the bandgap. These give rise to absorption. Note the text under the logarithmic graph: " The drop in absorption at the band gap (around 1100 nm) is sharper than might first appear".
Note that there also may be charge carriers due to s... | {
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Angular momentum of the earth We know the tidal waves are decreasing the spin rate of the earth which causes the days to longer, so as the angular momentum of the earth decreases it means it rotational kinetic energy also decreases since energy is always conserved the translational kinetic energy of earth must increase... | Note that energy can be radiated into space as heat, while angular momentum is harder to get rid of. The total angular momentum of the Earth-Moon-Sun system is approximately constant, even as Earth's daily spin rate slows slightly.
| {
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What happens to an inductor if the stored energy does not find a path to discharge? Suppose an inductor is connected to a source and then the source is disconnected. The inductor will have energy stored in the form of magnetic field. But there is no way/path to ground to discharge this energy? What will happen to the s... | A fine example of the stored energy of an inductor used to generate a useful voltage, is the ignition coil in petrol engines. When the points open the current in the primary cct. of the ignition coil, the magnetic flux rapidly collapses as the magnetic energy is converted to electric field energy in the intrinsic capa... | {
"language": "en",
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"source": "stackexchange",
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Regarding total rotational kinetic energy The rotational kinetic energy for a body that is rolling is is $\boldsymbol{\frac{1}{2}Iω^2}$ (where $I$ is moment of inertia about its centre of mass) and the translational kinetic energy is $\boldsymbol{\frac{1}{2}mv^2}$ for a rolling body..where $v$ is speed of its centre o... | Here, though it is a rigid body, you cannot use $KE_{TOT} = \frac{1}{2}M{v^2}_{cm}+\frac{1}{2}I\omega ^2$ because the particles closer to the larger axis (Radius $R$) are moving slower than those far away.
So we must find KE_TOT as :
$KE_{TOT} = \frac{1}{2}I_o{\omega_o}^2 + \frac{1}{2}I_p{\omega_p}^2$........(1)
The m... | {
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Fermi energy, occupation factor and number of particles Using the grand canonical ensemble, we can show that the occupation factor of an energy level (when the temperature $T$ and chemical potential $\mu$ are fixed) is given by $$ f_E(T,\mu) = \frac{1}{\exp \frac{E-\mu}{kT} \pm 1} \quad (1)$$. The total number of par... | Solved it.
The grand potential is
$$
A =kT\int dE\,D(E)\log\left(1-\frac{1}{\exp\left(\frac{E-\mu}{kT}\right)+1}\right)
=-kT\int dE\,D(E)\log\left(1+\exp\left(\frac{\mu-E}{kT}\right)\right)$$
from where we calculate
$$ S=-\left.\frac{\partial A}{\partial T}\right|_{\mu,V}=-\frac{A}{T}-\frac{1}{T}\int dE\,D(E)\frac{(\m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/553124",
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Is it necessary that a capacitor stores energy but not charge? Is it necessary that a capacitor stores charge? The definition of capacitor given in books is that it store electric energy. So is it possible that the capacitor does not store charge but stores energy only?
| It depends on what the capacitor is used for:
*
*In some cases it is indeed a way of storing energy, similar to the battery. It however allows for higher transfer of this energy, although a rather short storage time.
*Capacitors may be used as a way of creating high electric fields. In this case the potential dif... | {
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When creating term symbols, how do you know if the angular momentum $L$ is antisymmetric of symmetric? For example I'm trying to get the term symbol of $(1s)^{2}(2s)^{2}(2p)^2$ .
In the answers they state the following:
The combination of angular momenta $L_1 = L_2 = 1$ gives $L = 2$
(symmetric), $L = 1$ (antisymme... | For two particles with the same angular momentum $\ell_1=\ell_2=\ell$, the permutation symmetry follows immediately from the symmetries of the Clebsch-Gordan coefficients:
$$
C^{LM}_{\ell m_1;\ell m_2}=(-1)^{2\ell+L} C^{LM}_{\ell m_2;\ell m_1}
$$
so that (in accordance with the answer of @Superciocia), the symmetric st... | {
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Infinite Square well: Abrupt change in well's length So, one of my homework problems reads
A particle is trapped in an infinitely deep square well of width $a$, suddenly the walls are separated by infinite distance so that the particle becomes free. What is the probability that the particle has momentum between $p$ an... |
How does the wavefunction change with this abrupt change in the well's dimensions?
It doesn't. The term 'abrupt' implies that the change in the potential is so fast that the state of the system does not have time to react to the change before it is complete, so the state when the new situation becomes operative is id... | {
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Interpretation of rolling without slipping Here is an interpretation I came up with,
The friction, for a rolling body, converts the kinetic energy into rotational energy. Instead of dissipating it.
Questions:
1. Is my interpretation correct?
*what happens to the motion once all the k.e is converted to rotational en... | Rolling without slipping occurs when the static friction force between the rolling body and surface (e.g, tire and road) does not exceed the maximum possible static friction force of $f_{max}=u_{s}N$ where $N$ is the force normal (perpendicular) to the surface. For a level surface, $f_{max}=u_{s}mg$.
There is no dissip... | {
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How does a water jet hitting a wall move parallel to the wall if momentum is conserved? Classical mechanics says that if I throw a ball with velocity perpendicular to the wall and it collides elastically with the wall with a velocity $v_0$, then it bounces back with the same velocity $v_0$.
However, if I shoot a beam ... | Conservation of momentum is valid only for systems with no external forces.
In the case of water, the molecules are polar so they get attracted by the surface you are throwing it on. Hence the external forces on the system is not zero.
Also since water molecules are ejected as a stream of particles, Even if some m... | {
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In the equation: $a = dv/dt$ , is $dt$ the time taken to achieve that instantaneous acceleration? If you solve for $dt$ from $a = \frac{dv}{dt}$ , is it the time taken to to achieved that instantaneous acceleration?
$a$ : acceleration
$v$ : velocity
$t$ : time
| In the equation $a= \frac{dv}{dt}$, $dt$ is actually the time in which that small change in the velocity of the body is brought.
So you can say that it is the time to achieve that very acceleration.
But actually acceleration is defined as the change in velocity in a certain amount of time. Mathematically you can get ti... | {
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Does the action remain dimensionless after the renormalization? After the renormalization procedure, fields will gain an anomalous dimension, $\gamma$, which means that their scaling dimension will be different from what we would guess from the dimensional analysis. My question is whether this means that the action wil... | Yes, the action remains dimensionless. The "failure" of dimensional analysis is due to the fact that dimensional quantities that could be neglected under certain conditions (e.g., at a Gaussian fixed point in the renormalization group flow) cannot be neglected at other non-trivial fixed points in the renormalization gr... | {
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In physics, are all functions fields? I really confused if there is a function (mostly in physics, functions represents physical quantities) which is not a field? I feel all functions in physics are fields. Is there any functions which are not fields?
I see a lot of questions in stackexchange about functions and fields... | Functions are a mathematical construct, they have nothing to do with physics other than the fact that we use them as for their mathematical relevance. They become meaningful whenever physicists give them a physical meaning. Fields are, mathematically, functions but they have a deeper meaning in the physical sense. In p... | {
"language": "en",
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"source": "stackexchange",
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How and why does an electron add up (enters) in the valance shell of an atom? How does an electron add up (enters) in the valance shell of an atom? Why is energy released when an electron adds up in the valance shell of an isolated atom.
| Energy isn't always released when an electron is added to an atom. It depends on the kind of atom you are adding the electron to.
Energy is released if the electronegative atom attains a more stable state by accepting the electron (by say attaining a octet configuration in the valence shell). Stable states have less en... | {
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How is it physically possible that the electric field of some charge distributions does not attenuate with the distance? Let's consider for instance an infinite plane sheet of charge: you know that its E-field is vertical and its Absolute value is $\sigma / 2 \epsilon _0$, which is not dependent on the observer positio... | I believe that it is your intuition that is failing here, and since mathematical arguments have already been provided, I'll offer a simpler and more intuitive approach.
Take a more or less similar example which is more familiar to you, the sky. The sky, from where we are, looks like an infinite plane, this is not entir... | {
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How should I interpret the 'Location area (deg^2)' table on Wiki's 'List of gravitational wave observations' page? Is it in 'square degrees'? Wikipedia's page for 'List of gravitational wave observations' has a location table called 'Location area (deg^2)'. Just to be sure, if you click on 'deg^2' it takes you to the ... | It is quite hard to determine precisely the direction from which the GW signal is coming from, so instead of a single point in the sky we give a confidence region: check out figure 8 in https://arxiv.org/abs/1811.12907, there they show what kind of shape and size these regions have.
Note that we are not 100% certain t... | {
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Is my friend right about omitting $c^2$ in world famous tiny equation? I know $E = mc^2$ says that inertial mass of a system is equal to the total energy content of a system in its rest frame. My friend told me the $c^2$ can be omitted from this equation because that's just an `artifact' when measuring inertia and ener... | Your friend is right. If you adopt the length unit l = 299 792 458 metres then c=1 l/s. This can be convenient because in these units $E^2=m^2+p^2$ instead of $E^2=m^2c^4+p^2c^2$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/554935",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Miss understanding related with the energy density of radiation in the context of cosmology The usual definition of radiation energy density in the context of statistical physics is given by
$$U=a_{B}T^{4}$$
With $a_{B}=7.5657\times 10^{-16} J m^{-3} K^{-4}$. So $U$ has units of $J m^{-3}$
On the other hand I read in ... | In astrophysics and cosmology it is common to omit factors of $c$, where $c$ is the speed of light. This means that in these units an energy density will look like a mass density. To fix this, you have to put in a factor $c^2$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/555326",
"timestamp": "2023-03-29T00:00:00",
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What is really meant by the area of black hole? The area of a black hole is an important parameter in the thermodynamic description of a black hole. In particular, reading popular literature, everyone knows that the entropy of a black hole is proportional to its area as discovered by Stephen Hawking. Can someone explai... | You can calculate the area of the event horizon by taking the limit of the area of a sphere surrounding the event horizon as the radial coordinate tends to the Schwarzschild radius. This gives a coordinate independent result. E.g. you could calculate the area after defining a radial coordinate $$R=r-r_s,$$ and take the... | {
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Properties of timelike congruences in flat spacetime I'd like to learn about (or confirm) certain properties of congruences, concerning some presumably rather simple cases, namely of timelike congruences in the setting of flat spacetimes $\mathcal S$. Therefore I have here three closely related questions:
1.
Are there ... | *
*Yes. Consider a 1+1 spacetime with metric $ds^2=dt^2-dx^2$. In congruence A, the curves are $(t,x)=(t,x_0)$, with one curve for each value of $x_0$. In congruence B, the curves are $(t,x)=(t,x_0+v|t|)$ with $v=x_0/(1+|x_0|)$. If a smooth congruence is desired, we can smooth out the kinks at $t=0$ without changing t... | {
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How do I tensor differentiate a factor without tensors? How do I tensor differentiate a factor without tensor, such as:
$$\partial_\mu e^{i\Lambda(x)}\tag{1}$$
Should it be zero or should I differentiate it twice changing the order of the tensors follows:
$$\partial_\mu e^{i_\mu \Lambda^\mu}+ \partial_\mu e^{i^\mu \Lam... | This is a standard application of the chain rule. If $\Lambda$ is a scalar function of $\mathbf x = (x^0,x^1,x^2,x^3)$, then
$$\partial_\mu e^{i\Lambda (\mathbf x)} = \frac{\partial}{\partial x^\mu} e^{i\Lambda(x^0,x^1,x^2,x^3)} = i\frac{\partial \Lambda}{\partial x^\mu} e^{i\Lambda(\mathbf x)} = i(\partial_\mu\Lambd... | {
"language": "en",
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Is orbital and wave function are same thing? As we know that wave functions are the solution of schrodinger wave equation which contains all the information about an electron. We also tought that these wave functions are the atomic orbitals of that electron. But my question is as orbitals are the region where the probe... | I'm not a historian, so my interpretation/usage of these terms is subjective.
When I use the term orbit I refer to Bohr's atom model ("invented" around the year 1913). In Bohr's atom model the electrons circle around the nucleus on fixed orbits.
The term wave function came later (around 1925).
Schrödinger used a pr... | {
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Velocity of undamped pendulum On this page, under the heading "Orbit Calculations": http://underactuated.mit.edu/pend.html or here.
The author says,
"This equation has a real solution when $\cos{\theta} > \cos{\theta_{\rm max}}$"
and then they give a piecewise function for $\theta_{\rm max}$.
I have no idea how th... | As mentioned above by @bRost03, the condition to be obtained, is when the the angular displacement, is maximum $\theta=\theta_{\text{max}}$ and thus $\dot{\theta}_{\text{ma}x}=0$.
Then, the condition becomes
$$\pm \sqrt{ \frac{2}{I} \big[E+ mgl \,\cos[\theta_{\text{max}}(t)]\big]}=0$$
or
$$\cos[\theta_{\text{max}}(t)]... | {
"language": "en",
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Does putting a thin metal plate beneath a heavy object reduce the pressure it would have applied without it My dad bought an earthen pot and he kept it on our glass table. Worried that the glass could break on filling the pot with water. I kept a metal plate beneath it. At first, it seemed like a good idea , but on fur... | Yes, definitely by putting a plate you are reducing the pressure the pot exerts on the table because $$p= f/a$$ where p is pressure, f is force and area is a . That basically is not a description but a definition of the word pressure itself. Though I'm not sure about this, I think the plate is better than the three coi... | {
"language": "en",
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Diffraction of sound - long versus short wavelengths I am having some problems finding an explanation why long sound wavelengths travel around objects easier than short ones, hence making lower frequencies audible across longer distances. Most online sources use a slit/opening for the explanation of diffraction but som... | Sound is really not about air molecules hitting obstacles. It's about the collective motion of the air molecules, which translates to pressure waves in the air. When the wave hits an obstacle, it reflects or is absorbed, but does not continue on its original path. Portions of the wave that bypass the obstacle do con... | {
"language": "en",
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Gauge fixing conditions in general relativity Is there a limit to gauge fixing conditions we can impose in gravity ? I have seen two gauge fixing conditions. The DeDonder gauge $\partial_\mu g^{\mu\nu}$ and then in 3+1 formalism the gauge fixing condition $\nabla^2 t = 0$ is imposed where $t$ is the time coordinate. Wh... | In the case of linearised GR, one of the main reasons for choosing our gauge fixing condition is just sheer convenience. If we're doing a metric perturbation of $g_{\mu \nu} = \eta_{\mu \nu} + h _{\mu \nu} $, then our corresponding action that we get from perturbing our Ricci scalar is the Fierz-Pauli action which is ... | {
"language": "en",
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Applying the principle of Occam's Razor to Quantum Mechanics Wolfgang Demtröder writes this in his book on Experimental Physics,
The future destiny of a microparticle is no longer completely determined by its past. First of all, we only know its initial state (location and momentum) within limits set by the uncertain... | No. If the classical path was assumed to be the only path, there would be no quantum theory. It would just be classical. And clearly from the need for and success of a quantum theory that explains things outside the domain of the classical one, we know the world to be following quantum rules.
In Feynman’s highly reada... | {
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What's the debate about Newton's bucket argument? I visited some other QA threads about this topic, and I don't understand why people think it's mysterious that the bucket knows about its rotation.
If a non-rotating bucket is all there is in the universe, then, initially, all the parts of the bucket are at rest wrt to ... | Newton thought that there could only be a meniscus on the bucket if the bucket was rotating relative to something. He took it to be a demonstration of the existence of Absolute Space, because his equations were formulated in terms of Absolute Space. Mach may or may not have discussed whether absolute space can be repla... | {
"language": "en",
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How are the constants in the inflationary hypothesis derived? The inflationary hypothesis as I understand it is a correction to GR to account for the observed flatness of the universe in a model in which the universe is expanding.
How are the constants behind this inflationary hypothesis derived?
I am looking to establ... | The age of the observable universe is determined from the end of the inflationary expansion, which is effectively the hot Big Bang. The end of inflation is associated with the hot Big Bang because, during inflation, matter and energy are exponentially diluted and the universe “reheats” after inflation ends, as the infl... | {
"language": "en",
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One third of Lyapunov exponents are zero? What does it mean? This may be quite a straightforward question, but I have a dynamical system with a high dimensional phase-space. I calculated the Lyapunov spectrum for it and saw that one third of my Lyapunov exponents are approximately zero (which is a lot and was quite une... | What first comes to my mind is that you're probably sampling invariant quasiperiodic tori, which are typically neutrally stable.
The associated motion is regular, but not periodic, in that the phase space trajectory comes arbitrarily close to previous states, but never exactly repeats itself (hence quasiperiodic).
Espe... | {
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Cooling behaviour of beverage I offer my colleague some milk in her coffee. The milk has just come out of the fridge.
"Not now," she says. "Not till after I've finished my sandwich, and I don't want it to go cold."
So: identical mugs and quantities of hot coffee and milk at same temperature; only difference is that the... | The question is an old conundrum and can be found in various guises on the Internet and in handbooks. One can summarise it as follows:
If I add milk to my coffee and wait 5 minutes before drinking it and another person waits 5 minutes and then adds the milk to his/her coffee, who is drinking the hottest coffee?
A the... | {
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Does the frame in which the CMB is isotropic violate the Copernican Principle? The Copernican Principle states that Earth is not at a special place in the Universe, and by extension, that there are no "special places" in the Universe (per homogeneity of the universe, aka the cosmological principle). However, the frame ... | CMB frame provides a privileged foliation of spacetime by spacelike hypersurfaces, essentially by defining universal cosmic time via some function $t_c=f(T_\text{CMB})$. A given “slice” $t_c=\mathrm{const}$ could be then interpreted as a space part of a spacetime.
Copernican Principle as stated by OP means that “there ... | {
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RG fixed points and $T_{\mu\nu}$ It is common to refer to fixed points of the renormalization group as scale invariant theories. This statement can be formulated as $$ \beta(\mu) \Big |_{\mu^*} = 0 \; \; \Longrightarrow \; \; T^{\mu}_{\mu} = 0 .$$
However, I never saw a proof of this fact and I do not think it is trivi... | This is a hard problem, it is about the conditions which ensure that scale invariance implies conformal invariance. In two dimensions any unitary local scale invariant theory is conformally invariant. In four dimensions it is not yet known a set of necessary and sufficient conditions. Here are some references.
[1] J. P... | {
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Explanation for an unexpected rainbow Yesterday, I observed an unexpected rainbow in the sky. There was no forecast for rain, neither was it raining anywhere nearby. I have been trying to find an explanation but don't seem to find any. Can someone please explain what this rainbow is?
Note:the colours were way more vivi... | These are tropospheric Iridescent Clouds
According to AtmosphericOptics:
When parts of clouds are thin and have similar size droplets, diffraction can make them shine with colours like a corona. In fact, the colours are essentially corona fragments. The effect is called cloud iridescence or irisation...
The usually de... | {
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"source": "stackexchange",
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Hydrogen atom and scale transformation for radial variable While solving Schrödinger equation for Hydrogen atom we make a scale transformation for radial variable ($r=\frac{ax}{Z}$; where $a=$ Bohr radius, $x=$ dimensionless variable and $Z=$ atomic number), this turns out to be a very good scale transformation. But my... | Usually when transforming into dimensionless variables one looks at the relevant constants in the problem. For hydrogen atom we have the electron charge $e$, electron mass $m_e$, Plank constant $\hbar$, permittivity of free space $\epsilon_0$
Then one does dimensional analysis to make scales based on the above constan... | {
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Finite potential well with quantised energy In a finite potential well like that in figure, is the potential constant between $-L/2$ and $L/2$? Since that energy is quantised, if I'm in the second excited state, would the potential still be constant and equal to $0$, so that energy is only kinetic?
| The potential is constant by definition. It's independent on your energy state, and it is in fact one of the elements that dictates the behaviour of your system.
| {
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"Boiling is to evaporation as melting is to... ?" Or, why aren't 31 degree ice cubes wet? Well before a liquid reaches boiling point, it gradually looses molecules with exceptionally high kinetic energies to its surroundings, which is called evaporation. Does this phenomenon occur to some solids as well, where before ... | If you look at the phase diagram of water you will see that below the temperature of the triple point, ice turns directly into vapour rather than into liquid. In other words it sublimates
| {
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Doubt on Tetrads, Energy-momentum tensors and Einstein's equations Given, for instance, the perfect fluid energy-momentum tensor:
$$T_{\mu\nu} = (\rho+p)u_{\mu}u_{\nu} - pg_{\mu\nu}\tag{1}$$
We can put (due to diagonalization procedure) into the diagonal for as:
$$T_{\hat{\mu}\hat{\nu}} = Diag[\rho, \tau,p_{2},p_{3}] ... | The Einstein field equations read $G_{\mu\nu}=8\pi T_{\mu\nu}$, so if we contract one side with $e^\mu_{\hat\mu}$ we have to do so to the other side as well. Hence, yes, both need to be in the orthonormal basis.
This is just a special case of the more general principle that indices should match on both sides of an equa... | {
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How can we transform energy conservation laws on inclined plane? Suppose a inclined plane
Now in normal projectile problem we can normally apply energy conservation laws but in this case since this is a inclined plane we have to transform the conservation laws now this sounds confusing but i am saying that suppose a b... | The change in potential along the incline will be equal to the work done by the component along the incline.
| {
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Does it make sense to say that something is almost infinite? If yes, then why? I remember hearing someone say "almost infinite" in this YouTube video. At 1:23, he says that "almost infinite" pieces of vertical lines are placed along $X$ length.
As someone who hasn't studied very much math, "almost infinite" sounds like... | Even (and especially) someone who has studied math a great deal would concur with your second paragraph
As someone who hasn't studied very much math, "almost infinite" sounds like nonsense. Either something ends or it doesn't, there really isn't a spectrum of unending-ness.
The intended meaning of the offending phrase ... | {
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Canonical transformation to diagonalize Bosonic Hamiltonian The Hamiltonian of the system of bosons ($a$, $a^{\dagger}$, $b^{\dagger}$ & $b$ are Bose operators) is:
\begin{equation}
H=\epsilon_{1} a^{\dagger}a+\epsilon_{2}b^{\dagger}b+\frac{\Delta}{2}\left(a^{\dagger}b^{\dagger}+ba \right)
\end{equation}
where $\eps... | You need to make sure the bosonic commutation realtions hold for any basis you choose. For that you need the equivalent of a $z$-Pauli matrix
$$\sigma_3 = \begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & -1 & 0\\
0 & 0 & 0 & -1
\end{pmatrix},$$
where this is just an example for two bosonic operators, the size o... | {
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Does this motor move? Say we have a motor coil like this:
We hang a mass (red ball) on the motor to prevent it's rotation. We make the mass heavy enough such that it's Weight Force directly opposes the motor force produced by that wire.
$$mg = BIL$$
Does this motor turn? I feel like the answer is no, because that wire... | Answer: Yes, motor's coil will turn.
Notice, the magnetic field $B$ exerts a force $=BIL$ to the right hand wire in vertically downward direction (given by Fleming left hand rule). Similarly, it exerts an equal force $=BIL$ on left hand wire in vertically upward direction. These two equal and opposite forces for a coup... | {
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Significance of Diagonalization in Degenerate perturbation Theory I am studying Degenerate perturbation Theory from Quantum Mechanics by Zettili and i'm trying to understand the significance of diagonalizing the perturbed Hamiltonian. He uses the stark effect on the hydrogen atom as an example. Im gonna skip the calcul... | Yes and yes. For this particular problem, it is true that any method of finding eigenvalues will yield the answer you're looking for–though finding the eigenvalues is virtually synonymous with diagonalizing the matrix (the diagonalized matrix is simply the eigenvalues down the diagonal).
There is tremendous physical si... | {
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Is the Lagrangian density of electromagnetism half-blind? The Lagrangian density of electromagnetism is
$$
\mathcal{L}_{EM}=\frac{1}{4\mu_0}F^{ab}F_{ab}
$$
This represents one of two fundamental Lorentz invariants of electromagnetism. The second one is:
$$
\frac{1}{2}\epsilon_{abcd}F^{ab}F^{cd}
$$
Since $\mathcal{L}_{E... | The quantity you propose is a total derivative; specifically,
$$
\frac{1}{2} \epsilon_{abcd} F^{ab} F^{cd} = \partial^a \left( \epsilon_{abcd} A^b F^{cd} \right).
$$
Since adding a total derivative to any Lagrangian doesn't change the classical equations of motion, it doesn't matter if this invariant is in the Lagrang... | {
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Describing forces in rolling Consider a wheel on a frictionless horizontal surface. If we apply a horizontal force (parallel to the surface and above the level of the center of mass), what happens to the wheel? Does it roll or slide forward or rotate only or does any other phenomenon happen? Please guide me. Also draw ... | Look neglecting friction makes it simple. We have to think only about the applied force for rotational motion as well as translational motion.
So since there is an external force , the body will have some translational motion in the forward direction. This will happen for sure and we can find the acceleration using
F=m... | {
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Why can't many models be solved exactly? I have been told that few models in statistical mechanics can be solved exactly. In general, is this because the solutions are too difficult to obtain, or is our mathematics not sufficiently advanced and we don't know how to solve many of those models yet, or because an exact so... | Try finding an analytical solution of the particle position $(x,y,z)$ at time $t$ when the movement is described by the Lorenz attractor equation system:
$$
{\begin{aligned}{\frac {\mathrm {d} x}{\mathrm {d} t}}&=\sigma (y-x),\\[6pt]{\frac {\mathrm {d} y}{\mathrm {d} t}}&=x(\rho -z)-y,\\[6pt]{\frac {\mathrm {d} z}{\ma... | {
"language": "en",
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What is the probability of measuring $p$ in the momentum space? I have a wave function $\Psi (x,t)$. According to the Max Born postulate, $\lvert\Psi (x,t)\rvert ^2$ is the probability density. This quantity specifies the probability, per length of the $x$ axis, of finding the particle near the coordinate $x$ at time $... | You’re exactly right: $|\phi(p)|^2$ gives the probability of measuring momentum $p$ at time $t=0$. An analogous relation holds for the time-dependent case:
$$\Phi(p,t)=\frac{1}{\sqrt{2\pi\hbar}}\int_{-\infty}^{\infty}dx e^{-i px/\hbar}\Psi(x,t)$$
This is simply due to the fact that one independently transforms between ... | {
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Is the question asking for the primitive translation vector of simple cubic or reciprocal lattice?
Can anyone please give me a clue on what the question wants? Based on the question, I am clueless if it asks for primitive translation vector of simple cubic or reciprocal lattice?
Because the form of the given $\mathbf ... | We assume that the cubic lattice has side length $a$. Then the first Brillouin zone will look like BZ $=(-\frac{\pi}{a},\frac{\pi}{a}]^3$ (why?) with periodic boundary conditions along all three directions. Because of the periodic boundary conditions, we know that k-vectors are only physical modulo any reciprocal latti... | {
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Equivalence of Hermitian operator and Hermitian matrix in Quantum Mechanics I learned that a Hermitian matrix $A$ is defined as a matrix that satisfies
$$A^\dagger=(A^*)^\intercal=A,$$
i.e. its Hermitian conjugate $A^\dagger$ is the same as the original matrix $A$.
I also learned that in QM, a Hermitian operator $H$ is... | $\langle f|Ag\rangle=\langle f|A|g\rangle$.
$\langle Af|g\rangle$:
*
*$(\langle Af|) = (|Af\rangle)^\dagger =(A|f\rangle)^\dagger = \langle f |A^\dagger$,
*so $\langle Af|g\rangle = \langle f |A^\dagger|g\rangle$
If $A = A^\dagger$, then $\langle f|Ag\rangle =\langle Af|g\rangle$.
| {
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What would happen to the Sun if you reflect all its emitted e.m. radiation back? What would happen to the Sun if you would reflect, in whatever way, all the outgoing electromagnetic radiation (Solar winds can be neglected)?
| This is the same as asking what would happen if the sun couldn't get rid of the heat it generates. In that case, the heat builds up, the sun's temperature goes up, and in response the sun expands a bit. This expansion causes the fusion reactions in the sun's core to slow down, which slows down the rate of heat generati... | {
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Boltzmann distribution in Ising model I've written in Matlab a code for a Ising model in 1 dimension with 40 spins at $k_{B}T=1$.
I record the energy of every step in a Metropolis Monte Carlo algorithm, and then I made an histogram like this.
I want to show the theoretical Boltzmann distribution. What is the exact for... | I have to make a number of assumptions, as you did not state all the necessary information. So, I am going to assume that you are using periodic boundary conditions, that is, your Hamiltonian is
$$
\mathcal{H}(\sigma) = -\sum_{i=1}^N \sigma_i\sigma_{i+1},
$$
where I have denoted by $N$ the number of spins (that is, $N=... | {
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Recommend books for learning lattice QCD I want to learn lattice QCD by myself, but I don't know how to start. Can you recommend some books for lattice QCD?
| In my opinion, one of the best modern references is a book by Gattringer and Lang https://www.springer.com/gp/book/9783642018497. This book contains rather a broad introduction of the subject, from the elementary details, such as path integral on lattice and different discretizations. And then there is discussion on m... | {
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How to show that $[L_i, v_j]=i\hbar\sum_k \epsilon_{ijk}v_k$ for any vector $\textbf{v}$ constructed from $\textbf{x}$ and/or $\nabla$? In Weinberg's Lectures on Quantum Mechanics (pg 31), he said that the commutator relation
$$[L_i, v_j]=i\hbar\sum_k \epsilon_{ijk}v_k$$
is true for any vector $\textbf{v}$ constructed... |
Theorem: Let $\mathbf{A},\mathbf{B}$ be vector operators. then
$\mathbf{A}\times\mathbf{B}$ is a vector operator. But e.g.
$\mathbf{A}\mathbf{B}$ is a scalar. That is $[L_j,\mathbf{A}\mathbf{B}]=0$
The proof is done by straight forward algebra, using the definition of a vector operator $[L_j,A_i]=i\hbar\epsilon_{jik... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561372",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 2
} |
Is $b$ in the drag force formula $F=-bv$ constant for a certain medium and object? I heard that $F=-bv$, where $F$ is the drag force, $b$ is the damping coefficient, and $v$ is the velocity of an object, can be used to calculate the drag force exerted on an object moving at a moderate velocity.
*
*What range is this ... | *
*It is not referring to some absolute range of velocities, rather it means the flow of fluid around the object is laminar flow.
We can establish whether or not the flow is laminar by computing the so-called dimensionless number $\mathbf{Re}$, i.e. Reynolds number:
$$\mathbf{Re}=\frac{vD}{\nu}$$
where:
*
*$v$ is t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/561615",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does an up quark decay into products more massive than itself? According to https://en.wikipedia.org/wiki/Up_quark the up quark can decay into a down quark plus a positron plus an electron neutrino. The problem is that the mass of the by-products is greater than the original particle. This would violate conservat... | Quarks can never be observed isolated, since they only exist in confinement. What you are asking about is basically the conversion of a proton into a neutron. Even then, the proton cannot decay in isolation (except if there is a incident antineutrino with sufficient energy), and there are basically two main types of ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562006",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
In metals, the conductivity decreases with increasing temperature? I am currently studying Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edition, by Max Born and Emil Wolf. Chapter 1.1.2 Material equations says the following:
Metals are very good conductors, bu... | The key point is that thermal motion disrupts the periodicity of the potential. As stated in ch. 26 of Ashcroft and Mermin: "Bloch electrons in a perfect periodic potential can sustain an electric current even in the absence of any driving electric field; i.e., their conductivity is infinite. The finite conductivity of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/562392",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 3
} |
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