Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What would happen if charged plates are placed horizontally? My idea is placing charged conducting plates in such a way that they won't see each others' surfaces unlikely to the typical design of parallel plates. If they are placed like this, would be the force that one plate exerting to other same as in the typical de... | If the two plates are made of conducting material, there is nothing preventing charges from flowing as close as possible to each other, which, in this case, means toward the edge of each plate closest to the other, right next to the insulating layer.
If we now suppose the layer to be thin (dimension $d$) with respect ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/130961",
"timestamp": "2023-03-29T00:00:00",
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"question_score": "2",
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Wouldn't the presence of dark matter slow the expansion of the universe? If there is a huge element of dark matter in the universe, wouldn't this extra gravity prevent the accelerated expansion of the universe?
| The short answer is yes, the presence of dark matter would act to counter the expansion of the universe. And in fact it does--but not enough to stop the expansion. Dark matter has gravity just like normal matter. In fact, that's pretty much the only reason we know dark mater exists at all: we can observe dark matter... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/131014",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Hilbert space for Density Operators (instead of Banach spaces) Is it possible to construct a well defined inner-product (and therefore orthonormality) within the set of self-adjoint trace-class linear operators? In the affirmative case, dynamics could be analyzed in Hilbert space, which seem way more simple that Banach... | It is possible indeed !! It is called Hilbert Schmidt scalar product, it is defined in a Hilbert space of bounded compact operators including trace class operators.
$$\langle A|B\rangle := tr(A^\dagger B)\:.$$
The space of Hilbert Schmidt operators is made of all bounded operators $A$ in the considered Hilbert space,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/131104",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is entropy really? On this site, change in entropy is defined as the amount of energy dispersed divided by the absolute temperature. But I want to know: What is the definition of entropy? Here, entropy is defined as average heat capacity averaged over the specific temperature. But I couldn't understand that defini... | Here's an intentionally more conceptual answer: Entropy is the smoothness of the energy distribution over some given region of space. To make that more precise, you must define the region, the type of energy (or mass-energy) considered sufficiently fluid within that region to be relevant, and the Fourier spectrum and p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/131170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "46",
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Definition of derivative operator on a manifold I'm hoping to understand the motivation for certain parts of the definition of a derivative operator $\nabla$ on a manifold $M$. In Wald's General Relativity, two clauses of the definition are:
*
*Commutativity with contraction: For all tensors $\mathit{A} \in \mathscr... | For $1.$, you have, by applying the Leibnitz rule for covariant derivatives :
$\nabla_{d}(\mathcal{A}^{a_1...c...a_k}_{b_1...c...b_l})
\\= \nabla_{d}(\mathcal{A}^{a_1...c'...a_k}_{b_1...c...b_l} \delta_{c'}^{c})
\\= \nabla_{d}(\mathcal{A}^{a_1...c'...a_k}_{b_1...c...b_l} g^{ca}g_{ac'})
\\=(\nabla_{d}\mathcal{A}^{a_1... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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2-slit experiment In the 2-slit experiment, is it possible to "account" for all of the energy in the incoming beam - i.e. does all of the incoming energy show up in the bright spots or is some of it "destroyed" when destructive interference takes place?
If it is destroyed, what form is it converted into?
If it's NOT de... | This question is really classical. If you model two-slit interference in Maxwell's electrodynamics, the same thing happens: opening the second slit causes the intensity at some points on the screen to decrease. It happens with water surface waves too, and any other kind of wave. Destructive interference at one point is... | {
"language": "en",
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Physical applications of matrices and determinants Other than notation devices, I don't see any direct application of matrices/determinants in physics. For example, they are just a different way to write a partial derivative and determinants find if they can be explicitly solved if written down as simultaneous equatio... | Applications of matrices:
*
*Matrix (aka quantum) Mechanics, obviously
*Mechanics of deformable solids (where matrices describe stresses)
*Statics (most in engineering contexts), where matrices describe stresses.
*Symmetries (where matrices describe rotations/scaling/translations etc..)
*Coordinate transformatio... | {
"language": "en",
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Capacitor-like-thing for controlling temperature of fluid? I want to minimise the Gibbs' phenomenon like thing i.e. sudden peaks (temperature peaks here) in a container.
Assume you have a cone where you want to block the transmittance of the temperature into the cone like current by capacitors.
The ideal situation wou... | The usual hydraulic analogy for a capacitor is an elastic membrane:
A capacitor doesn't allow current to flow across it, but you can push charge onto it by applying a potential. In the hydraulic analogy an elastic membrane across the pipe doesn't allow water to flow through it, but you can push some water through the ... | {
"language": "en",
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Why is density an intensive property? I am still trying to understand what are intensive and extensive
properties. Possibly someone can give a pointer to a decent text (preferably on the web), as I
am not too happy (to say the least) with what I found so far on the web.
I already asked here one question on this, which ... | Consider $10~\mathrm{ kg}$ of a substance. Take a few $\mathrm{kg}$ of the substance and measure the mass density. The density is same as before.
So we can say that from the above explanation, density is an intensive property.
| {
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Skin depth of current density in magnetic conductor at boundary between two different materials Imagine a magnetic conductor with a cylindrical cross section, surrounded by a coil with a time varying current of
$$I = I_0\cdot \cos (2\pi f t)$$
The conductor is split into two parts, the first with a conductivity and a r... | Well, I hope I didn't go too much off track. I'm open for discussion.(possible solution path is on the bottom)
Looking at the formula for $\delta$ I see that it is actually related to the speed of EM waves in the medium. The speed of propagation for a medium with the properties $\kappa_1$ and $\mu_1$ is:
$$c_1=\frac{1... | {
"language": "en",
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How much voltage should be applied to an object to create a certain amount of charge? I am curious as to how much voltage should be applied to create a specific charge. Is there a formula to calculate it, and what are the parameters that can affect the relation between voltage and charge created in that object?
P.S: I ... | Voltage has absolutely nothing to do with charge. I can "move" an infinite amount of charge trough a superconductor with zero voltage. Are you asking about the relationship of charge to voltage on a capacitor? That's a linear relationship: Q=C*U. The charges, in that case, are not "created" but merely separated. If you... | {
"language": "en",
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Photons to Represent a Wave I fear that I have a fundamental misconception about the "wave particle duality" of light, but in a related question, the answerer said, in some sense, that a light wave propagates until it hits something, at which point in time it (can) act(s) like a photon. Which is fine to me, but there a... | "Running out" of photons simply means that your wavefront is absorbed or scattered in a different direction or something like that. Either way, the original wave is "consumed", so you loose intensity or photons, depending on which picture you like better.
For the case of a single photon source: One photon can only inte... | {
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"source": "stackexchange",
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How can I calculate the force that is applied on a tube by another tube? Let's say there is two tubes(cylinders with no tops or bottoms) with charges $q_1$ and $q_2$, radii $b_1$ and $b_2$, lengths $l_1$ and $l_2$. These tubes are located along the axis of each other's surfaces like in this figure:
If the electric fie... | Are you talking about the forces two parallel current-carrying wires exert on one another?
Given two current-carrying wires, $a$, and $b$, we can determine the force exerted on wire $b$ by wire $a$ with $$F=(µ_oI_a/2πr) I_bL$$
Where F is the force exerted, $µ_o$ is the magnetic permeability of a vacuum, $I_a$ is the c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Sound difference between musical instruments I know that the difference between two musical notes is given by the sound frequency, and the difference in volume is given by the amplitude.
What I am wondering is why does the same note sound different on different musical instruments?
What in the wave makes the differenc... | It's not just a pure single frequency of sound that is being transmitted by an instrument. Just like with light, if you ask the frequency of the sun's emission, the answer would be that it's a whole broad spectrum (hence its ability to produce a rainbow, or allow objects to reflect colours other than yellow) but its pe... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Can a third type of electrical charge exist? Upon reading my book on physics, it mentions that there are only two discovered types of electric charges. I wonder if there could be a third type of elusive charge, and what type of effects could it have upon matter or similarly?
| Mathematically, electric charge current 4-vector conservation refers to the invariance of theory under U(1) transformations, so there aren't different types of electric charge (like in SU(n) theories) excepting the usual plus-minus.
Moreover, the fact of conservation of physical quantity means that corresponding operat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/132654",
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"question_score": "22",
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How can metal objects become electrically charged, if current flow means that an equal number of electrons enter/leave the object? I am trying to answer to the question in the title. I am restricting my question to metal objects only.
Here is my logical reasoning:
*
*Current is the flow of charge over time.
*In a ... | There's a problem in that you are assuming that all current takes place in a circuit. But in some circumstances, like in a lightning strike or other form of electrostatic discharge for example, a current exists for a while, but it does not take place in a circuit.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Which of these two textbook equations of geodesic deviation is correct? My previous question Textbook disagreement on geodesic deviation on a 2-sphere got shot down as “off topic”, so I'm having a second stab at it.
Misner et al's Gravitation (p34) gives the geodesic deviation equation as$$\frac{D^{2}\xi^{\alpha}}{D\t... | Despite my comment, on second look your second equation, attributed to Lambourne, is always identically zero. This is because you multiply the symmetric tensor
$$\frac{dx^{\beta}}{d\lambda}\frac{dx^{\gamma}}{d\lambda}$$
against $R^{\mu}{}_{\nu\beta\gamma}$, and the riemann tensor is antisymmetric on those last two in... | {
"language": "en",
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If a photon has no mass, how can it be attracted by the Sun? I read that the photon doesn't have mass, but my teacher says that the photon has mass because the sun can attract it (like in the experiments to prove the theory of relativity).
I think that there is another reason to explain that. How can I explain that th... | To properly understand what is going on you need to understand general relativity. Massless particles, like photons, travel on null geodesics and mass bends spacetime so the null geodesics are not straight lines. The problem is that neither you nor your teacher understand general relativity so this isn't a very convinc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133056",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Scientists observe the laws of the physics but, Where do they come from? Has anyone ever considered how the laws of physics that we study came into being.
| Actually...
There is a branch of physics that attempts to answer that question. It's called Physical Cosmology. Among many other things, cosmologists want to know why the physical laws are as they are. The trouble is, there just are not that many other universes ready for us to compare. We also don't know what is going... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133151",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A step in zeta function regularization I'm just wondering about the mathematical step
$$\sum_{n=1}^\infty n\exp[-\epsilon n\sqrt x]=\frac1{\epsilon^2 x}-\frac1{12}+\mathcal O(\epsilon).$$
Why is this equality so? I see that
$$\sum_{n=1}^\infty n\exp[-\epsilon n\sqrt x]=-\frac1{\sqrt x}\frac{\partial}{\partial\epsilon}\... | \begin{align*}
\sum_{n=1}^\infty n\exp[-\epsilon n\sqrt x]
&=-\frac1{\sqrt x}\frac{\partial}{\partial \epsilon}\frac{1}{1-\exp[-\epsilon\sqrt x]}\\
&=\frac{\exp[-\epsilon\sqrt x]}{(1-\exp[-\epsilon\sqrt x])^2}\\
&=\frac{1}{\exp[\epsilon\sqrt x]-2+\exp[-\epsilon\sqrt x]}\\
&\simeq\frac{1}{\frac2{2!}(\epsilon\sqrt x)^2+\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133237",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Potential difference between point on surface and point on axis of uniformly charged cylinder Question:
Charge is uniformly distributed with charge density $ρ$ inside a very long cylinder of radius $R$.
Find the potential difference between the surface and the axis of the cylinder.
Express your answer in terms of the v... | By Gauss' Law,
$E\cdot A=\frac {q}{\epsilon_0}$ (assuming that the Electric Field is constant at every $dA$ and that it is always parallel to $dA$, which it is in this case)
Let us define the charge contained in the original problem cylinder as being $Q$ whereas the charge in the smaller Guassian cylinder as being $q... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133322",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
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Dark matter a medium for light propagation Is dark matter a candidate to fill void left by luminiferous ether as a medium for light travel?
| No.
There is no void left by the lack of an aether. The very notion of aether should serve as a warning as to how catastrophically analogical reasoning can fail. "Water waves are in water, sound waves are in air, therefore there must be something in which light propagates." This is flawed logic, and decades of physics ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133463",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does Dirac show that $\langle B|\bar{\bar{\alpha}}|P\rangle\;=\; \overline{\langle P|{\bar{\alpha}}|B\rangle}\;=\; \langle B|{\alpha}|P\rangle$? Dirac shows that the conjugate imaginary of $\langle \!P|\alpha$ is $\bar{\alpha} |P\!\rangle$ and then starts with the identity on page 27 in his book:
$$\langle B|\bar{{... | The relation (4) literally switches the states, adds an overall complex conjugate, and removes a hermitian bar over the operator.
(Actually, no one uses bars anymore to denote hermitian conjugates, they use daggers instead. And because stacked bars get ugly, I'll use stars for complex conjugation of plain complex numbe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133648",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Derivation of formula of potential energy by a conservative force the formula for potential energy by a conservative force is given by:
$$ F = -\nabla U(r), $$
which in one dimension may be simplified to:
$$ F = -\frac{dU}{dx} .$$
My question is how is it derived and why do we use a negative sign in the formula?. Is th... | If the particle moves from the point $x$ to $x+dx$, and assume $dx\gt 0$ for simplicity, then its potential energy increases by
$$ dU = \frac{dU}{dx}dx $$
Well, it increases if $dU$ is positive and decreases if $dU$ is negative. So far I have only used the definition of the derivative – pure mathematics.
However, the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133714",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Advantages/Disadvantages of "hanging off" a motorcycle when leaning The closest question I could find with regards to this subject was this one:
Countersteering a motorcycle
However, it does not address the specific physics of what I would like to know.
There are 3 ways to lean when turning a motorcycle:
*
*Upper bo... | The important thing about leaning in is that it puts you closer to the road so you don't have so far to fall when you exceed the stickiness of your tires.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/133766",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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A light so strong it has a shadow I have recently taken an interest in shadows. I know that in order for a shadow to exist that you must have a solid in the way of the light. My hypothesis is that there can be a light so strong, like a laser beam, that it acts like a solid in the sense where it doesn't let light pass t... | Yes and no.
Photons don't interact in free space. So a beam of light can't block another beam of light in vacuum.
Photons can interact due to the nonlinearity of the medium. So it's plausible to block another beam of light if you have the right mediators.
It's however not the light itself becoming a solid. See, for exa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/134000",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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If everything is relative to each other in this universe, why do we keep the Sun to be the reference point? and study the solar system and universe relative to it and why not relative to the Earth?
| When you're trying to understand the mechanics of a system it's usually convenient to choose coordinates that reflect the symmetry of the system. The solar system is roughly centrally symmetric because the Sun is by far the largest mass in it, and the coordinates that reflect this symmetry are polar coordinates with th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 2
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How to prove the Levi-Civita contraction? I want to prove the following relation
\begin{align}
\epsilon_{ijk}\epsilon^{pqk}
=
\delta_{i}^{p}\delta_{j}^{q}-\delta_{i}^{q}\delta_{j}^{p}
\end{align}
I tried expanding the sum
\begin{align}
\epsilon_{ijk}\epsilon^{pqk}
&=&
\epsilon_{ij1}\epsilon^{pq1}
+
\epsilon_{ij2}\eps... | The product $\epsilon_{ijk}\epsilon^{pqr}$ has certain symmetry properties. They are the same properties as the determinant
$$\begin{vmatrix} \delta_i^p & \delta_i^q & \delta_i^r\\ \delta_j^p & \delta_j^q & \delta_j^r \\ \delta_k^p & \delta_k^q & \delta_k^r \end{vmatrix} $$
It's a rank 6 tensor, it changes sign under e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/134156",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
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Is real voltage always the real part of complex voltage? If I have a complex voltage $V_z$, is real voltage $V$ (i.e. the voltage used in the normal ohms law and the voltage
we normally talk about) always given by $V=Re(V_z)$? And if it is not the case, how do we find $V$ from $V_z$?
Does the same apply to current?
| A voltage or current given as a complex constant is a phasor. A voltage given as the complex constant $V_z$ represents the real voltage
$$V(t) = \operatorname{Re} \left( V_z e^{i\omega t} \right)\ \ ,$$
where $\omega$ is the voltage's angular frequency and $t$ is time.
Currents represented as phasors work the same way... | {
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Why uncharged particles do not feel the Lorentz force? Why uncharged particles do not feel the Lorentz force? Please do not answer with the formula $ \vec F = q\left( \vec E + \vec v \times \vec B \right) $.
Edit after an answer which is an circular reasoning.
Let me explain this question with an example. Imagine, you ... | The Lorentz force is by definition the force acting on a charged particle due to electric and magnetic fields. Therefore, if the particle has no charge, then any forces on it, by definition, cannot be Lorentz forces. Thus, it is easy to say that uncharged particles do not feel the Lorentz force because it is only defin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/134440",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Difference between heat capacity and entropy? Heat capacity $C$ of an object is the proportionality constant between the heat $Q$ that the object absorbs or loses & the resulting temperature change $\delta T$ of the object. Entropy change is the amount of energy dispersed reversibly at a specific temperature. But they ... | If you consider a constant volume transformation, the corresponding specific heat will be defined as:
$C_v(T) \equiv \left( \frac{\partial U}{\partial T}\right)_{N,V}$
Now, it is not forbidden to use Leibniz rule for the decomposition of partial derivatives and for instance:
$\left( \frac{\partial U}{\partial T}\right)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/134496",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 6,
"answer_id": 4
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How would the universe change? How would the universe be modified if protons (as we know them) have negative charge and electrons (as de know them) have positive charge.
| As the comments say, it would do nothing if you change all negative charges to positive and viceversa for all know particles. You actually have a real physical example: antimatter (which in most theories behaves just as standard matter but there might be some non-symmetries when you include all particles (it depend on... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/134585",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is there any evidence that matter and antimatter continuously appear and disappear on the edge of a black hole? I heard Stephen Hawking got a Nobel prize for this, someone said there was no evidence for it which I find quite strange since he got an award for it.
| According to the Hawking radiation Wikipedia article, there was one experiment in 2010 which the experimenters claimed showed evidence of Hawking radiation, but that claim is in doubt, and there hasn't been any other experimental evidence of Hawking radiation. Stephen Hawking has received a number of awards and honors... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/134655",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Moduli spaces in string theory vs. soliton theory In both string theory and soliton theory, moduli spaces are frequently used.
As far as I known, for soliton theory, moduli spaces are something like collective coordinates for solitons, and for string theory, moduli spaces is the spaces of all metrices divided by all c... | This is a situation where knowing the history of the terminology can be helpful.
The QFT/string theory terminology comes from algebraic geometry, where the term moduli space is used for any space whose points correspond to some kind of geometric object. The projective space $\mathbb{P}(V)$, for example, is the moduli ... | {
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Projectiles Launched at an Angle with unspecified Initial Velocity I'm attempting to do my Physics homework, and I did the first one right, but that problem gave me initial velocity. This problem gives me only the angle relative to horizontal and the distance it covers. Can anyone help me figure out where to start? I'v... | In projectile motion the horizontal velocity is always same through the journey, only vertical component of velocity changes.
After resolving the given velocity vector U (say) into X and Y components as Ux and Uy respectively.
You can write
R=Ux.T ( R is horizontal range, T is time of flight)
Therefore, R=u^2 sin(2... | {
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What is going on in front of and behind a fan? Why is it that when you drop paper behind a fan, it drops, and is not blown/sucked into the fan, whereas if you drop paper in front of a fan, it is blown away?
| Here's a standard fan with some (hard to see) arrows indicating air flow.
The fan works by pulling air in and then making it move faster. The air flow behind the fan is slow moving and wide (you can see the arrows behind the fan coming from above and below the fan blades) whereas the air flow in front of the fan is fa... | {
"language": "en",
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Is there a classical analog to quantum mechanical tunneling? In comments to a Phys.SE question, it has been written:
'Tunneling' is perfectly real, even in classical physics. [...] For sufficiently large temperatures this can put the system above a hump in its potential energy.
and
the only difference between the ... | Evanescent waves are the mechanism beind both quantum tunneling and frustrated total internal reflection in @SteveB's answer. Evanescent waves and frustrated total internal reflection are not limited to light, but can occur in any phenomena governed by the wave equation, including sound and water waves.
| {
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"source": "stackexchange",
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What is the current in a circuit with two voltage sources in series?
What happens? We have 2 voltage sources and 2 currents. When I2 and I3 come together (they have opposite sides), what happens?
I tried writing down the voltage relations but I'm stuck because I don't know what current should I work with (to determine... | Well, a net current results.
I will write the general equation for the current, and determine all possible scenarios, keeping in mind that in writing this equation I assume the current is going clockwise (I assume the left voltage source is at a higher potential, and if this wasn't the case, my current will simply be ... | {
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What happens to ice cream when you stir it? I hope this is the appropriate forum for my question. I also considered posting it in the chemistry forum.
When I eat ice cream I often stir it into a texture similar to that of soft serve. During the process, the bowl in which the ice cream is kept, tends to become quite col... | This is a bit of a soft question (get it?).
Intuitively, the ice cream and bowl (and your hand) will move towards a state of equal temperature (second law of thermodynamics). When you stir the ice cream you are doing at least four things:
*
*you are 'encouraging' the heat to become more uniformly distributed (as you... | {
"language": "en",
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Is there any physical quantity that does not have uncertainty? I saw this video and I got a thought: Is there any physical quantity that does not have uncertainty?
Basic models are:
for lenght
for time end energy (so for mass too) and I realized that (based on the video) photons near to each other have uncertain amo... | I'm convinced that nothing in this world can be measured without uncertainty. Take the measurement of a current. One have to use in this case an ammeter which has to be a low as possible resistor. But it has to have an ohmic resistor. Take the measurement of electric potential. One have to take a voltmeter which has to... | {
"language": "en",
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How to get the relation for dependence of anomalous dimension on regularization? Here is the anomalous dimension:
$$
\gamma_{\Gamma}(t, g) = \left[\frac{\partial }{\partial t}\ln \left(Z_{\Gamma}(t , g) \right)\right]_{t = 1},
$$
where $Z_{\Gamma}$ is renormalization factor which arises in n-point functions $\Gamma $, ... | I'm not quite sure where the details of the last equations come from, but I think that the step that you are missing is to identify,
$$q(g) = \frac{1}{Z_\Gamma(g)} \, .$$
| {
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Blowing your own sail?
How it this possible? Even if the gif is fake, the Mythbusters did it and with a large sail it really moves forward. What is the explanation?
| As others have said, the skater would move faster if he simply pointed the leafblower behind him, rather than bouncing it off the umbrella.
However, there is a real use for this technique. Jet engines normally suck in air from all directions and blow it out of the back in order to move forward. However they are also c... | {
"language": "en",
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"source": "stackexchange",
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$\rm Lux$ and $W/m^2$ relationship? I am reading a bit about solar energy, and for my own curiosity, I would really like to know the insolation on my balcony. That could tell me how much a solar panel could produce.
Now, I don't have any equipment, but I do have a smartphone, and an app called Light Meter, which tells... | Lux is a unit that depends on the sensitivity of the "standard" (e.g. more or less average) human eye, as well as on the power distribution of light within the visible part of the spectrum. Your previous answers deal with that well enough.
The conversion from irradiance, or flux, in Watts per meter squared, to apparent... | {
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Tensor product notation convention? For two particle state, the Dirac ket is writren as
$$\lvert\textbf{r}_1\rangle \otimes \lvert\textbf{r}_2 \rangle. $$
Then how do we write its bra vector,
$$\langle\textbf{r}_1\rvert \otimes \langle\textbf{r}_2\rvert ~~\text{or}~~\langle\textbf{r}_2\rvert \otimes \langle\textbf{r}_1... | Remember that by definition of the tensor $$(a_1\otimes b_1)(a_2\otimes b_2)=(a_1a_2)\otimes(b_1b_2),$$
and that $\mathbb C\otimes\mathbb C=\mathbb C$.
| {
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"source": "stackexchange",
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Difference between high-level and low-levels of electromagnetic radiation can someone please explain me what we mean by 'high-level' or 'low-level' in electromagnetic radiation? for example, it is believed that high-level microwave radiation is harmful to human but not the low-level one.
what is this level here we are... |
It is believed that high-level microwave radiation is harmful to human ...
It is not just believed but well known that extremely intense microwave radiation will cook people. We use microwaves to cook meat, after all, and a good portion of our bodies is in the form of meat. Lesser intensities can cause survivable bur... | {
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Rabi oscillations with quantized light: which is the "quantum" effect, collapse, revival or both? In wikipedia http://en.wikipedia.org/wiki/Jaynes%E2%80%93Cummings_model#History it is stated that
It was later discovered that the revival of the atomic population inversion after its collapse is a direct consequence of ... | Both Rabi oscillations and the revivals are quantum mechanical effects. However, they consequences of the quantization of two different systems. Rabi oscillations can be explained and derived with a semi-classical theory in which the atomic system has quantized energy levels but the incident light fields are classical.... | {
"language": "en",
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Why does Energy-Momentum have a special case? I was reading Energy-momentum, and I came across this simplified equation:
$$E^2 = (mc^2)^2 + (pc)^2$$
where $m$ is the mass and $p$ is momentum of the object. That said, the equation is pretty fundamental and nothing is wrong when looked upon, I similarly also believed thi... | I didn't see anyone mention the practical reason to use an approximation for energy. It is that in most problems you will be computing differences in energy. In that case, for small velocities, you can not only go the approximation ${m v^2\over 2}+m c^2$, but if you are also not converting mass to energy or vice-vers... | {
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What is zero impedance in AC circuit? If a capacitor is connected with an inductor, then because $$Z=\frac{1}{j\omega C}+j\omega L,$$ the Z may be zero. Does that mean when I apply a voltage, the current will be infinite large?
What's more, in transmission line theory, the characteristic impedance could be $\sqrt{L/C}$... | Essentially, the answer to your question is yes but your equation is not quite in the general form. Typically, impedance is $$Z=R + jX$$ with $R$ being the resistance, and $X$ being the reactance which is almost the equation you show, but without the imaginary component. Specifically, $$X = \omega L - \frac{1}{\omega... | {
"language": "en",
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How do photons "decide"? I was reading that when horizontally polarized light hits a vertical Polaroid all the light is blocked out. But when the Polaroid is off the vertical, some but not all photons "decide" to jump into the new plane of polarization. Could this be a "road less traveled" kind of effect?
If a run of t... | If that happened, we would be able to detect it by looking at correlations between successive photons' "decisions."
That is, suppose you represent each pair of consecutive photons (1 and 2, 2 and 3, 3 and 4, etc.) with $+1$ if they both made the same "decision" or $-1$ if one went through the polarizer and the other di... | {
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Does gravity affect magnetism, vice-versa, or do they "ignore" each other? I am suddenly struck by the question of whether gravitation affects magnetism in some way. On the other hand, gravity is a weak force, but magnetism seems to be a strong force, so would magnetism affect gravity?
Or do they "ignore" each other, ... | The electromagnetic field tensor $F_{\mu\nu}$ which encodes all the information about the electric and magnetic field, certainly contributes to the energy-stress tensor $T_{\mu\nu}$, which appears in the Einstein Field Equations: $$G_{\mu\nu}= 8\pi G T_{\mu\nu}$$
The left hand side of this equation encodes the geometry... | {
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Special relativity; rocket moving towards a mirror
An observer in a rocket moves toward a mirror at speed $v$ relative to the reference frame in which the mirror is stationary - call this frame $S$. A light pulse emitted by the rocket travels toward the mirror and is reflected back to the rocket. As measured by an obs... | Be careful on (a), the rocket is moving too and will have moved a distance of $v \Delta t$ by the time the light comes back. So we have:
$$2d-v \Delta t=c \Delta t$$
Solving for $\Delta t$:
$$\Delta t = \frac{2d}{c+v}$$
For (b), your answer certainly cannot be correct because it is independent of velocity. The easiest ... | {
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Is the ground state closest to the uncertainty relation? For simplicity, suppose we are only talking about discrete energy levels, i.e., bound state case. The energy levels are $E_1, E_2\cdots$, and the corresponding wave functions are $\psi_1, \psi_2 \cdots$.
My question is, is it true that $\sigma_x \sigma_p$ is mini... | The ground state of a system is by definition the state of minimal energy, i.e. the system is located at the minimum point of the potential.
Now, if we were in classical mechanics, this would mean that the system is at a stable fixed point.
Of course in QM that is not possible since we have to satisfy the Heisenberg un... | {
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Alternative liquid for Galileo thermometer So a friend of mine broke my Galileo thermometer recently. The glass tube and the liquid inside were lost, but the bulbs survived. I've cleaned out an old tall glass candle, and tried filling it with water. Even when the water is steaming hot the bulbs still float, so the liqu... | You should be able to start with methylated spirits - ethanol with a bit of methanol mixed in to make it toxic and cheap (or ethanol if you can get your hands on it - but it will be expensive because of excise taxes unless you can prove "scientific exemption".) It is much lighter than water and highly miscible with it.... | {
"language": "en",
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Will 5 pizzas in the same Hot Bag stay warmer than 5 pizzas in 5 separate Hot Bags? For example, say I am delivering 5 pepperoni pizzas to 5 different addresses. In one scenario, I Keep all 5 in the same insulated Hot Bag, I carry that bag to the door, and I quickly remove one of the pizzas from the bag to give to the ... | If they were ideal insulators, the 5 separate bags would be better because you wouldn't have repeated heat loss from opening the same bag 5 times. Primarily this heat loss would be in the escape of hot air, exchanged for colder outside air. If the hot bags were extremely poor insulators - effectively as if you weren't ... | {
"language": "en",
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How do we estimate $10^{23}$ stars in the observable universe? Now, I read somewhere, that there are $10^{23}$ stars in the observable universe. How did scientists estimate this?
| Have a look at this article. It gives the number as $10^{24}$ rather than $10^{23}$, but it's such a vague estimate that a factor of ten is within the expected error.
The number is the number of stars in the observable universe i.e. within 13.7 billion light years of Earth at the time the light we see today was emitted... | {
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What causes the random movement of particles inside a conductor? I'm reading about currents in electricity right now, and it was mentioned that even if there's no electric field inside a conductor, charged particles inside are still undergoing random movement.
I wanted to know what forces cause this random movement to ... | Does your conductor have any resistivity? In that case the fluctuation-dissipation theorem applies. In the case that your conductor is a perfect superconductor, it would still couple inductively to the electromagnetic field around it, which, per 3rd law of thermodynamics must have a non-zero temperature. To remove thos... | {
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Where does the $\partial \vec{E}/\partial t$ term from Maxwell's equation go in Ampere's Law? One of Maxwell's Equations (ME) is:
$$\nabla\times\vec B = \mu_0\vec J+\epsilon_0\mu_0 \frac{\partial \vec E}{\partial t}.$$
While Ampere's Law (AL) is:
$$\nabla\times\vec B = \mu_0\vec J.$$
Griffiths E&M book derives that for... | It is mentioned in the book Introduction to electrodynamics that Ampere could not find the second term because such a thing is hard to detect in laboratory. But now as we all know (because of Maxwell) that changing electric field produces magnetic field.
If you take laplace transform of the second term in M.E. you will... | {
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Estimating the force needed to increase height of a mountain? How would you estimate the force required by a tectonic plate to make the height of a mountain increase when it pushes against another?
I've used a method to try and do it for Mt Everest and have ended up with 8x10^(-7)N required to increase its height which... | When tectonic plates collide, the crust can become thicker at the edge of collision by the folding and faulting of crustal rocks. Because crust has a lower density than the asthenosphere and mantle, the region of thicker crust can rise due to buoyancy forces until it reaches isostatic equilibrium. This model of orogeny... | {
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Is there only radial motion in the Hydrogen ground state? The ground state of the Hydrogen atom is spherically symmetric. In other words, the wave function Psi depends only on the distance r of the electron from the nucleus.
As a consequence all derivatives of Psi with respect to angles theta and phi yield zero.
Does ... | On average there is no motion at all, i.e., there is no systematic displacements. But there are "fluctuations" with non zero squares averaged. Classically speaking, it is like a Brownian motion in a limited space. But let us set aside a classical picture. Apart from momentum representation of the wave function, there i... | {
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What is the difference between diffraction and interference of light? I know these two phenomena but I want to know a little deep explanation. What type of fringes are obtained in these phenomena?
| Diffraction is spreading of the beam of light as it goes through aperture or is emitted from a finite area source. It is due to the fact that the beam of light has some k-vector spectrum that has some finite width.
You can think of it like a bunch of photons having a spread of momenta. It is related to uncertainty prin... | {
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Superpositioning of fire I once recognized that when you light two candles and you move one of the candles towards the other, you will see that the total fire height (let's call it $f_3$) is higher than the sum of the single fires.
Candle 1: fire height $f_1$
Candle 2: fire height $f_2$
Candle 1+2 (the two fires touche... | When placing the candles next to each other you effectively create a single "fire". We know, from work by Thomas et al (1961) that the flame length is:
$$l/D=f\left(\frac{\dot m^2}{\rho^2gD^5\beta\Delta T}\right)$$
Where $l$ is flame length, $D$ is diameter of fuel, $\dot m$ is fuel mass lose/flow rate, $\rho$ is fuel ... | {
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What would happen if an accelerated particle collided with a person? What would happen if an accelerated particle (like they create in the LHC) hit a person standing in its path?
Would the person die? Would the particle rip a hole? Would the particle leave such a tiny wound that it would heal right away? Something else... | Amazingly this actually happened to a Russian scientist called Anatoli Bugorski (WARNING: this is pretty gruesome).
The beam basically just killed all the tissue it passed through. The symptoms were the relatively mundane ones expected from tissue death.
The LHC has a much, much greater energy than the one that struck ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/138151",
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Finding 3-Sphere Christoffel connection coefficients using variational calculus, Sean Carrol problem I have A 3-Sphere with coordinates $x^{\mu} = (\psi,\theta,\phi)$ and the following metric:
\begin{equation}
ds^2 = d\psi^2 + \text{sin}^2\psi(d\theta^2 + \text{sin}^2\theta d\phi^2)
\end{equation}
I know how to get the... | I'll show you how to do this for the 2-plane in polar coordinates. Once you work this out, it should be doable to work it out in your case.
You start with the metric
$$ds^{2} = dr^{2} + r^{2}d\theta^{2}$$
Since the geodesics of this metric (i.e., straight lines) minimizes distance, we know that the geodesics are an ex... | {
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Evaluating Feynman diagram for coupling between scalar field and dirac particle and anti particle If I have a scalar field $\alpha$ and a Dirac particle $\beta$ and its anti particle $\overline{\beta}$, such that the three couple to give a vertex factor of $-ik$ when evaluating the Feynman diagram (where $k$ is a dimen... | Basically this is a tree-level diagram of an $\alpha$ particle decaying into a pair of
$\beta \overline{\beta}$ pair.
You need to draw the Feynman diagram.
And now, single "internal" lines are propagators, and external lines are currents.
But you need to direct the external lines so as to have a current.
For referenc... | {
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Why rubber is incompressible material? Why rubber is incompressible material? I know its Poisson's ratio is nearing to 0.5. So I don't understand physically, what it means by 0.5 Poisson's ratio and incompressibility. When I tried searching it, I found that rubber (or similar polymers) conserve volume after deformation... | Conserved volume means volume before and after any deformation must be equal (like in a rolling operation, forging operation, etc). In this situation the Poisson ratio becomes 0.5. Rubber behaves like incompressible deformation; that is, if we stretch rubber its length increases and width decreases proportionally, so i... | {
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"source": "stackexchange",
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How do mirrors look & behave atomically? I was observing mirrors recently and I was thinking about how an mirror would look atomically. I was always used to looking at atoms as being colored that said, I was always concerned at how they looked. I looked at previous questions and found silver atoms could play a part in ... | Reflection,refraction and transmission of light are macroscopic manifestation of a phenomenon called scattering.In this incoming photons are absorbed and either the quantum energy level of an atom is raised (as in case of resonance absorption) or the outer electron cloud is set into motion(this is responsible for light... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/138707",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Gibbs free energy and maximum work I'm getting confused between two important results.
The Gibbs free energy is $G = H-TS$
where $H$ is the enthalpy and $S$ is the entropy.
When the temperature and pressure are constant the change in the Gibbs energy represents maximum net work available from the given change in system... | The math derivation can be made below
$$G=H-TS$$
$$dG = dH -d(TS)$$
$$dG = d(U+PV) -d(TS)$$
$$dG = dU + PdV +VdP -TdS - SdT$$
at constant pressure and temperature, $dP=0$, $dT=0$,
$$dG = dU + PdV -TdS$$
From above, we know dG decreases when internal energy is transferred out, system does work and system entropy incre... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Apparent Contradiction with Faraday's Law Say we have a non-uniform magnetic field that is static in time. Specifically, let's make it:
$\overrightarrow{B}(x,y,z) = x \hat{z} $
Now say we have a metal loop in the xy plane which has a non-zero velocity in the +x direction. Say we pick a random point in time, and then ... | I'm pretty sure that the answer to this is that we're cheating by saying that there's an E-field in the loop in the first case.
Well, we're "cheating" in a very narrow sense of the word. What we're doing is implicitly Lorentz transforming to a reference frame where the loop is stationary. If we do this, then the ma... | {
"language": "en",
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"source": "stackexchange",
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Can we deviate a bullet from its target? Did anybody try this? Can we deviate a bullet from its target? Means by applying any strong field at the target? Is there any technique so far like this!
| Here is another completely different answer with a different technology. It is the use of spaced charged armour to disrupt the jet of molten metal from a shaped charge. The idea is that as the metal jet bridges the two sheets of armour is completes a short circuit as the armour is connected to a high energy capacitor. ... | {
"language": "en",
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A hypothetical question on mechanics Being located in a tropical region, I am quite acquainted with the Ceiling fan. I have a question about it.
If the top, that is, the axle (I'm not sure of the terminology: I mean the part which is thin, rodlike, attached to ceiling)...is rigidly fixed, then when the fan is turned on... | If your fan is not connected to anything, and the blades do not encounter any air drag (outer space) then conservation of momentum means that
the blades will turn in one direction, and the motor assembly in the other direction
If you know the moment of inertia of the blades, call it $I_b$, and of the motor, $I_m$, th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/139279",
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"source": "stackexchange",
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Why does the sea horizon line always seems to be at the same height as one's eyes? I wonder why, when I look at a sea/ocean, the horizon line always seems to be at the same height as my eyes, no matter how many meters I am above the sea level.
This is something I noticed when I trek, and it happened in many places. It... | The construction and calculations below show that if the altitude is very small compared to Earth's radius, the line of sight as measured from local vertical is very near 90 degrees. The Earth's radius is about 6371 km. For the line of sight to fall 1 degree you would have to elevate your point of view by about 370000 ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/139348",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Is it possible for larger antimatter atoms to decay to matter and visa versa? Following on from previous questions:
If you have antimatter-matter interactions where there is a larger antimatter particle (say carbon or Silicon), is there any reason to believe that the antimatter particle could decay to matter particles ... | In some normal matter there is the phenomenon of positron decay. That is, an unstable atom decays by the emission of an anti-electron. Presumably there is a mirror form of this where antimatter decays by electron emission.
| {
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How detectors in particle colliders can differentiate neutrons from antineutrons? Their mass is the same. None of them interacts with EM fields. And their decay (around 1000s) is far too slow to see their decay products yet in the detector.
How is it then possible to differentiate them?
| Detectors at particle colliders are layered like onions around the collision vertex.
The CMS detector at CERN
First there are charged particle sensitive detectors where charged particles leave tracks because of ionisation, but mass density is low so strong interactions do not happen often; their momentum can be m... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Moment of inertia of rods Ok so I'm extremely comfortable with calculating moment of inertia of continuous bodies but how do we do it for a system not continuous.
For example if 3 rods of mass $m$ and length $l$ are joined together to form an equilateral triangle what will be the moment of inertia about an axis passing... | The moment of inertia is defined relative to the point of rotation, which in this case is the centre of the equilateral triangle. Then you can multiply this result by 3.
| {
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"source": "stackexchange",
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What does the $c$ in $eV/c^2$ stand for? I have been wondering(also searching) for what does the $c$ in eV/$c^2$ stand for?
(For example, mass of the electron is $0.511 \, \text{MeV}/c^2$.)
I have read that this unit has been derived from Einstein's equation, $E=mc^2$, but how it is possible, We use the symbol $c$ for ... | A sample unit conversion for the second half of your question:
\begin{alignat}{2}
0.511\,\mathrm{MeV}/c^2 &=
0.511\,\mathrm{MeV}/c^2
\times \frac{10^6\,\mathrm{eV}}{1\,\mathrm{MeV}}
\times \frac{1.60\times10^{-19}\,\mathrm{joule}}{1\,\mathrm{eV}} \\
&\quad\qquad \times \frac{1\,\mathrm{kg\cdot m^2/s^2}}{1\,\mathrm{joul... | {
"language": "en",
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Do transmitters create magnetic fields and radiation? In the company I work for (I am a software engineer) we develop a system which uses a transmitter (antenna) that creates a magnetic field. I also know that radio station transmitters create radio waves, so I am somewhat confused.
Do the coils built into the transmi... | The coil controls the fluctuation of the current and thus the fluctuation of the magnetic field around the transmitter. The antenna in that arrangement, I assume an electric dipole or monopole, is a kind of a capacitor and its role is to change the ratio of the electric to magnetic field before it is to hit free space,... | {
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Is there a difference between the speed of light and that of a photon? As in the title I am curious whether there is a difference between the speed of photon and the speed of light, and if there is what is the cause of such a difference?
| In quantum mechanics a particle can be treated as a wave and a wave can be treated as a particle. This is the notorious wave particle duality. I won't go into this any further here because it's been discussed to death in lots of previous questions. Search this site for wave particle duality if you're interested in find... | {
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What happen to a spoon which is detached from the satellite? Suppose a spoon is a part of satellite but after detachment from the satellite Does it fall to the ground straight or does is take a parabolic path or any other path before coming to the surface of Earth
| A few assumptions before we get started:
1) The satellite that you refer to is traveling in an orbital path around the Earth, as opposed to some other type of motion (You did not specify whether the satellite was in orbital or sub-orbital flight. If assumed incorrectly, please let me know with a comment.)
2) Relative ... | {
"language": "en",
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Transformation to a uniformly rotating frame I'm midway through a problem at the beginning of a GR course, my question is simply this:
If
$$
x=x'\cos\Omega t-y'\sin\Omega t
$$
where $x'$ and $y'$ indicate the rotated frame of reference. What does that make $dx^2$?
I need this so I can make substitutions into the equati... | $$ dx = \cos (\Omega t) dx' -x' \Omega \sin (\Omega t) dt - \sin (\Omega t) dy' -y' \Omega \cos (\Omega t) dt$$
It's basically just the product rule and the chain rule.
| {
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Rewriting the Hydrogen Schrodinger Equation as a system of differential equations I have only ever seen the Schrodinger equation for the hydrogen atom written out in a form like this:
$$
-\frac{\hbar^2}{2\mu}\left[\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2\frac{\partial \psi}{\partial r}\right) + \frac{1}{r^2\si... | If you assume separability of the wave function, i.e., $\psi(\mathbf x)=u(x)v(y)w(z)$, you can solve the individual components separately:
\begin{align}
-\frac{\hbar^2}{2\mu}\frac{d^2u(x)}{dx^2}+V_1(x)u(x)&=E_1u(x)\\
-\frac{\hbar^2}{2\mu}\frac{d^2v(y)}{dy^2}+V_2(y)v(y)&=E_2v(y)\tag{1}\\
-\frac{\hbar^2}{2\mu}\frac{d^2w(... | {
"language": "en",
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How did Newton establish his famous third law of motion? For every action,there is equal and opposite reaction . This is the famous Newton's third law of motion. But how did he come to this conclusion? We can prove 2nd law using calculus. But how did Newton prove this law? Or did he just used practical examples?
[Acc... | This page has a helpful summary of the history--it seems he initially accepted the Aristotelian idea that objects could only continue to move if some "force" inside them was moving them (keep in mind this is before his technical definition of 'force'), and it took him a while to switch to the idea that bodies naturally... | {
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OPE of fermionic field bosonization in string theory, in Polchinski 10.3.12 In Polchinski's String Theory Vol. 2, equations 10.3.12 are
$$e^{iH(z)}e^{-iH(-z)}~=~\frac{1}{2z}+i\partial H(0)+2zT_B^H(0)+O(z^2)\tag{10.3.12a}$$
$$\psi(z)\bar\psi(-z)~=~\frac{1}{2z}+\psi\bar\psi(0)+2zT_B^\psi(0)+O(z^2)\tag{10.3.12b}$$
How are... | I've got the answer by myself.
Simply do Taylor expansion of the left hand side. Expand both the exponential, and the field around $H(0)$ or $\psi(0)$, then the right hand follows naturally after plugging in definitions of $T_B$.
| {
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"source": "stackexchange",
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Magnetic field of a static disk magnet I have a magnetic disk (Radius R, height h) that creates magnetic field lines (axisymmetrical). I simulated the field lines, exported the data and am now trying to fit a function into the data to have a analytical solution for the magnetic flux density of my specific magnet. For s... | My answer will probably be a little off topic, but why do you need this kind of analytical function ? Since you have the magnetic flux density (FEM simulation I guess), you can use any interpolation to get the B value anywhere...
Unless you have a very specific need, if you only want to get the value of B anywhere, tha... | {
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"source": "stackexchange",
"question_score": "3",
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Kinetic energy vs. momentum? As simple as this question might seem, I failed to intuitively answer it.
Let's assume there is a $10,000$ $kg$ truck moving at $1$ $m/s$, so its momentum and KE are: $p=10,000$ $kg.m/s$ and $KE=5,000$ $J$.
Now if we want to stop this truck, we can simply send another truck with the same ma... | A momentum-based analysis is the way to go for the motorcycle-rope-truck scenario.
In your kinetic energy argument, you are assuming that kinetic energies add like vectors. This is not the case.
If you want to properly apply a kinetic-energy-work argument, you need to think about the force $F$ that the rope exerts on t... | {
"language": "en",
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"source": "stackexchange",
"question_score": "8",
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Reality of "electrical explosion" I have often heard people who have been electrocuted refer to the "explosion" and how they were "thrown back" by the "blast". Sometimes the force of the blast is reported to throw people many metres.
There is no explosive involved - how can there be a repulsive force from a discharge o... | CuriousOne's comments basically answered your question. I will add that if enough current is allowed to suddenly flow it can vaporize materials very rapidly, including metal. This sudden vaporization can create a rapid expansion and if that expansion is restricted by something then it can explode in the same fashion ... | {
"language": "en",
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Why do electrons orbit protons? I was wondering why electrons orbited protons rather than protons orbiting electrons.
My first thought was that it was due to the small amount of gravitational attraction between them that would cause the orbit to be very close to the proton (or nucleus). The only other idea that I would... | The short answer is: protons are much more (1800 times) massive than electrons. That makes them (approximately) the center of mass of the system, that's why electrons are the ones orbiting protons and not vice versa.
The term 'orbiting', however, means something essentially quantum. It is the reason of the stability of... | {
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Would using Cherenkov radiation for lighting be feasible? Could Cherenkov radiation be used for general illumination, for example, to replace LEDs, light bulbs etc? I.e. are there, or could there be, methods to produce substantial amount visible light with Cherenkov radiation:
*
*using devices compact and cheap enou... | Quite aside from the issue of ionizing radiation, Cerenkov generating particles also lose energy by other processes and that ends up as heat.
Moreover, all the kinetic energy of the particles once they drop below the Cerenkov threshold is lost in non-optical channels (i.e. more heat).
So no, they could never be anywhe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/142132",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do tachyons violate causality? Something moving faster than light should have imaginary mass, like photons have zero mass and thus travel at $c$.
I have read this article of physicist E. C. George Sudarshan.
He said taking mass to be imaginary we get real energy and momentum. (I think I have understood that.) Howev... | In the context of bosonic string theory, the ground state with no oscillator excited, has a mass,
$$M^2 = -\frac{1}{\alpha'}\frac{D-2}{6}$$
where $\alpha'$ is the Regge slope, satisfying $\alpha' = 1/2\pi T$, where $T$ is the tension of the spring, and $D$ are the spacetime dimensions. It seems it has an imaginary mass... | {
"language": "en",
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What does it mean by $t=-1$? if the position vector of a particle is $\hat{r}=\left(4+3t\right)\hat{\imath}+\left(t^3\right)\hat{\jmath}+\left(-5t\right)\hat{k}$, i want to find at what time this particle passes through the point $\left(1,\:-1,\:5\right)$. I found that $t=-1$ for this particle to pass through that poin... | Yes, you defined the zero of time as when the particle is at $(4,0,0)$. It passed through $(1,-1,5)$ one second before that.
| {
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"source": "stackexchange",
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Inconsistency in the delta potential I encountered an inconsistency in the one-dimensional delta potential. Suppose we have a one-dimensional infinitely deep square well from $-L$ to $+L$. We know the eigenstates are sine and cosine functions. They are either even or odd.
Now let us add one delta potential $g \, \del... | The main point that although a pointwise convergent Fourier series of cosine modes is an even function $\psi(-x)=\psi(x)$, it does not have to be differentiable at $x=0$. A pointwise convergent infinite sum of differentiable functions is not necessarily a
differentiable function.
More generally, as OP already mentions... | {
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Explanation for negative specific heat capacities in stars? I've just found out that a negative specific heat capacity is possible. But I have been trying to find an explanation for this with no success.
Negative heat capacity would mean that when a system loses energy, its temperature increases. How is that possible i... | Although John's answer is quite comprehensive, I would like to add this answer in order to reinforce my qualitative understanding of the matter and to try to provide the OP a more intuitive and qualitative explanation for the negative specific heat capacity as the OP seems to be looking for a more qualitative (and intu... | {
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Why aren't classical phase space distribution functions always delta functions? The phase space distribution function (or phase space density) is supposed to be the probability density of finding a particle around a given phase space point. But, classically, through Hamilton's equations, the system's time evolution is ... | You are right that if you know exactly the initial conditions of your system that is the exact location of your system's state in phase space then its evolution is entirely determined.
But that's where lies the issue; we don't know exactly the state of the system as described by a point in phase space.
Instead we may k... | {
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"timestamp": "2023-03-29T00:00:00",
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Say, a liquid is made to flow in a tube. Why does the layers of the liquid in contact with walls of the pipe have zero velocity? Say, a liquid like water is made to flow in a pipe. Why does the layer of water near the walls of the pipe have zero velocity? Does that mean that the layer of water near the pipe is stationa... | The article you cited explains it pretty well, unless there was something not explained to me about it in chemistry too. This property is a generalization for viscous fluids.
For your purposes we will take fluid to mean liquid
Basically a molecule in a fluid forms weak bonds (See Van Der Waals Force) with the other mo... | {
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Why is $\pi$ used when calculating the value of $g$ in pendulum motion? I am trying to intuitively understand why $\pi$ is used when calculating the value of $g$ using the harmonic motion of a pendulum:
$$g ~=~\frac{4\pi^2L}{T^2}.$$
Does it have something to do with the curvature? I am thinking something along the line... |
Does it have something to do with the curvature of the Earth which is
assumed to be spherical
You'll probably groan when you read this answer since it isn't nearly as complicated as you might think.
Essentially, there is factor of $\pi$ since the angular frequency $\omega = 2\pi f = \frac{2\pi}{T}$
A well know resu... | {
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How do the flow equations relate to the actual situation? This question might seem silly but I'll try to make it clear. It's a question (I think) about partial differential equations systems in general, but since currently I'm studying fluid mechanics I'll ask on that context.
The equations for an incompressible flow a... | Both boundary conditions and initial conditions matter equally when connecting the model to the real world.
Consider the flow around a cylinder that you mention. We know that the Reynolds number,
$$
{\rm Re}=\frac{u L}{\nu}\tag{1}
$$
can characterize laminar or turbulent flows, depending on the values in (1). Below are... | {
"language": "en",
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Is a suit that hides a soldier's heat signature fundamentally possible? I recently played "Crysis", a game where the protagonist wears a suit that allows the player to hide both himself and his heat signature. Then I watched Iron Man 3, where a kid suggests that Tony Stark should have implemented retro reflection panel... | I guess this is possible: for example, thermal radiation can be emitted within a very small solid angle, e.g., upwards.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/142971",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "28",
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How can I estimate the density of fog? I'm working on investigating the effect fog has on drag. I have assumed an air density of $1.225 \frac{\text{kg}}{\text{m}^3}$ for dry air, but I don't know what value for density I could assume that would be typical of fog.
I can't even reason out whether or not fog is more dense... | This is an instrument that measures fog density and has an experimental plot, figure 9 .
Once you have the relative humidity at the fog appearance at a temperature and pressure , one can use known equations to get the density. This link gives a calculator.
| {
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Unification of the electroweak theory Can the electroweak theory be described by the spontaneous symmetry breaking of $SU(3)$ to $SU(2)\times U(1)$?
| It is indeed possible to break $ SU(3) $ to $ SU(2) \times U(1) $. To see that we need to check that $ SU(2) $ and $ U(1) $ are subgroups of $ SU(3) $. Its easy to see that $ SU(2) $ is a subgroup since the first three Gell-mann matrices are given by,
\begin{equation}
\lambda _i = \left( \begin{array}{cc}
\sigma _i ... | {
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Electric and Magnetic field's phase difference shift in linearly polarized electromagnetic waves I am a high school student and we currently studying the electromagnetic theory. In my textbook i read that the oscillating electric the magnetic fields have phase difference equal to π/2 rad near the source (for example an... | Let me explain the nearfield phase shift of π/2 by how an antenna work. The antenna is an open electrical "circuit" where a electrical generator push and pull electrons inside the antenna rod. And the antenna rod one can imagine as a capacitor with its electrical field.
How the electrical and the magnetic fields are pr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/143361",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
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Switching from sum to integral I'm specifically asking about an equation in An Introduction to Quantum Field Theory, by Peskin and Schroeder. Example from page 374:
$$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$
$$= (VT)\cdot\int\frac{\mathrm{d}^4k}{(2\pi)^4}\log(-k^2+m^2),\tag{11.71}$$
The factor ... | One may only talk about a discrete sum over $k^\mu$ vectors if all the spacetime directions are compact. In that case, $k^\mu$ is quantized.
If the spacetime is a periodic box with periodicities $L_x,L_y,L_z,L_t$, then $V=L_x L_y L_z$ and $T=L_t$. The component $k^\mu$ in such a spacetime is a multiple of $2\pi \hbar /... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/143467",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
} |
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