Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Temperature on the surface of the sun calculated with the Stefan-Boltzmann-rule In a German Wikipedia page, the following calculation for the temperature on the surface of the Sun is made:
$\sigma=5.67*10^{-8}\frac{W}{m^2K^4}$ (Stefan-Boltzmann constant)
$S = 1367\frac{W}{m^2}$ (solar constant)
$D = 1.496*10^{11} m$ (E... | A rough estimate of a body's temperature in the solar system is
$$T=\frac{280K}{\sqrt{D_{AU}}}$$
if we calculate the AU fraction from the Sun's "edge" to its center, R over D = $4.65x10^-3$, and substitute this into the formula, the Sun's temperature would be about 4100K.
Not very close to your 5776 K, but utilizes t... | {
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"timestamp": "2023-03-29T00:00:00",
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Oscillations in forces other than the Weak As I understand it neutrino oscillations arise due to the neutrino mass eigenstates being distinct from the neutrino flavour eigenstates.
Flavour eigenstates are the states in which neutrinos interact via the weak force, and so are the eigenstates in which they are created and... | Think that there is some confusion. I assume that you associate particle oscillations with the weak interaction because you consider the specific example of the neutrinos (that indeed can only weakly interact)
See also the wikipedia article about neutral particle mixing:
You need a particle $A$, that is different from ... | {
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Is it more efficient to stack two Peltier modules or to set them side by side? Is it more efficient to stack two Peltier modules or to set them side by side?
And why?
I have a small box that I want to cool down about 20 K below ambient -- cold, but not below freezing.
(I want to keep my camera cool, so I'm putting in t... | You'll want a much bigger heatsink!!
(and maybe just one TEC)
If it's being cooled only by convection then maybe a heat sink area* that is 10 times that of the TEC. (maybe bigger)
The classic mistake with a TEC is to make the heat sink too small. With too small a heatsink the hot side of the TEC gets hotter, more t... | {
"language": "en",
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"source": "stackexchange",
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Quick question on sketching wavefunction in well
Usually for an infinite well, the sketch for n=3 level is this:
Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than the right side, so the wavefunction should have higher amplitudes on the lef... | Just so this doesn't slip past:
Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than the right side, so the wavefunction should have higher amplitudes on the left (skewed to the left):
This is incorrect. Between A and B the well is deeper, so... | {
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Speed distribution in 1 dimension In 3D, the maxwell velocity distribution is:
$$f = \left(\frac{\alpha}{\pi} \right)^{\frac{3}{2}} e^{-\alpha v^2} d^3 \vec v$$
To get the speed distribution in 3D, we simply expand $d^3\vec v = 4\pi v^2 dv$
Thus in 3D, the maxwell speed distribution is:
$$w = 4\pi^2 \left(\frac{\alpha}... | You should simply multiply by two, to get
$$f =2 \left(\frac{\alpha}{\pi} \right)^{\frac{1}{2}} e^{-\alpha v^2} \text d v.$$
This is because your integral over speed will now be from zero to infinity, and you need to 'fold over' the integral from minus infinity to zero. Otherwise, there are no further geometrical fact... | {
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Where does the term "boost" come from for rotation-free transformations? I had never seen rotation free transformations called "boosts" (I think I have it right) before reading some questions here. I'm too old perhaps. I have not found the etymology after some searching, though it sounds like something V.I. Arnold woul... | Not necessarily the original source of the term, but the earliest use I can find, occurs in Brandeis University Summer Institute in Theoretical Physics, 1964 Vol. 1: Lectures on General Relativity, where on p. 208:
If we use the term boost for a Lorentz transformation from one frame to another parallel to it but with ... | {
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Dielectric boundary I am trying to determine why electric field may be confined to a certain region if there is a large difference in the permitivity for example if electric field flows through water and then reaches a water air boundary.
I have also been reading about EM waves, is it possible to model electric field ... | One way to understand what append at the boundary of two dielectrics is to use the Fresnel formula when you know about the indices of your media.
Then, you have to solve the wave equation (d'Alembert equation) with the boundaries condition given by thoses Fresnel coefficient.
The confinement is due to the boundaries co... | {
"language": "en",
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Is there any operator behind probability, in quantum mechanics? In Quantum mechanics, the probability of finding a particle at position $x$ is given by $|\psi(x)|^2$, where $\psi$ is the wave function. Wonder what is the operator which gives this probability? Is probability the result of any operator acting on $\psi$?
| No. These cancerous probabilities come in because of the probabilistic interpretation, which also brings in all kinds of famous paradoxes that infect QM. By itself, the formalism of the theory requires just the solution of a second order differential equation to calculate $\psi(x,t)$ - a process which is completely det... | {
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Why are the 'color-neutral' gluons confined? What makes the two 'color-neutral' gluons
$(r\bar r−b\bar b)/\sqrt2$ and
$(r\bar r+b\bar b −2g\bar g )/\sqrt6$ different from the pure $r\bar r +b\bar b +g\bar g $ ?
Why don't they result in long range (photon-like) interactions?
| There is no fundamental difference between the gluons $(r\bar{r}-b\bar{b})/\sqrt{2}$ and $(r\bar{b} + b\bar{r})/\sqrt{2}$. The first one is represented by the matrix
$$
Z = \frac{1}{\sqrt{2}}\left(\begin{array}{rrr} 1&0&0 \\ 0& -1 & 0 \\ 0 & 0 & 0\end{array}\right)$$
and the second by the matrix
$$
X = \frac{1}{\sqrt{2... | {
"language": "en",
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Does the temperature of water determine how much heat will be removed from air used to evaporate it? This is a question about evaporative cooling as used in residential evaporative cooling appliances. This type of cooling uses the heat in the ambient outside air to evaporate water and remove the heat from the air, then... | After evaporating the water is at the same temperature as the ambient air. The heat removed from the air is whatever it takes from the starting condition of the water to get to water vapor at that temperature. In particular, cooling the water will require the air to heat it, so each degree C the water is colder will ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/116897",
"timestamp": "2023-03-29T00:00:00",
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Calculating probability current for scattering problem I'm trying to calculate the probability current for a scattering problem. The potential is $V = V_0 > 0$ in $x>0$, with $E>V_0$
So I have in the region $x \le 0$:
$$\psi = \exp(ikx) + R \exp(-ikx)$$
And in $x>0$
$$\psi = T \exp(i \kappa x)$$
I am trying to calculat... | You say
$$j = \frac{hk}{2m} (1 + R \exp(-2ikx) - \bar{R} \exp(2ikx) - R\bar{R})$$
But instead as
$$j=\frac{-i\hbar}{2m}(\bar\Psi\Psi'-\bar\Psi'\Psi)=\frac{-ih}{4\pi m}(\bar\Psi\Psi'-\bar\Psi'\Psi)$$
In $x<0$,
$$\bar{\psi} \psi' = ik -ikR\exp(-2ikx) + \bar{R}ik\exp(2ikx) - ikR\bar{R}$$
$$\bar{\psi}' \psi = -ik -ikR\e... | {
"language": "en",
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Interpretation of the WIMP annihilation cross section graph I have some trouble in the interpretation of the WIMP cross-section annihilation versus their mass.
I understand that the lines represent a upper bound on the cross section from the observation. But what do the contours from, e.g., DAMA mean?
| The DAMA collaboration have claimed to have actually detected dark matter, but this is in conflict with the results of other searches. But here one is assuming some model that describes the way dark matter interacts with nuclei and the properties of the dark matter halo. (e.g. spin independent WIMP-nucleus interactions... | {
"language": "en",
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"source": "stackexchange",
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Moment of inertia of a cylinder When I tried to calculate the moment of inertia ($I_C$) of a cylinder (mass M, height H, radius R) around the rotating axis going symmetrically through its middle, I came up with a different result than expected ($\frac{1}{2}MR^2$), but I do not spot my mistake, since my calculation make... | Lets start from the general definition for the moment of inertia
$$I=\int_{0}^{M}r^{2}dm$$
The mass element is $dm=\rho dV$ with $dV=L2\pi rdr$ ($L$ being the length of the cylinder). Substituting you'll get
$$I=2\pi\rho L\int_{0}^{R}r^{3}dr$$
.Taking into account that $\rho=\frac{M}{\pi R^{2}L}$ can you spot you're m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/117151",
"timestamp": "2023-03-29T00:00:00",
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What is intrinsic gravitational entropy? What is intrinsic gravitational entropy? Does it have to do with dark matter or coarse graining in the universe? Is it unique to general relativity, or there are predictions from quantum mechanics as well? Please explain in detail.
| The statement is by Hawking. Assuming I understand him correctly he means that there is an entropy associated with gravitational fields that is quite separate from any any entropy associated with matter or radiation. In other words this entropy is intrinsic to the gravitational field and will always be present regardle... | {
"language": "en",
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When a planet has a high gravity, is it impossible to build and launch a successful chemical rocket to space? Just recently a a large rocky planet has been discovered. "Astronomers have discovered a new type of rocky planet beyond the solar system that weighs more than 17 times as much as Earth while being just over tw... | It would be possible, though much more complicated than on earth.
Chemical rockets on earth deliver ~3% of it's launch weight to low earth orbit.
On this superheavy planet some 0.1-0.01% of launch weight might be delivered to low orbit.
While human exploration would be extremely hard in such conditions, it would be p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/117347",
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Physical Interpretation of four velocity in GR I'm confused about the physical interpretation of the four-velocity $U^\mu=\frac{dx^\mu}{d\tau}$ in General Relativity. I know that it is a tangent vector to a particle's "worldline", but what does this mean more physically?
For example, I am comfortable with what $U^\mu$ ... | The 4-velocity is defined to be normalized, i.e.:
$g_{\mu\nu}u^{\mu}u^{\nu}=-1 \; ,$
so if you choose comoving observers, for which $u_i=0$, then $u_{0} = \frac{1}{\sqrt{|g_{00}|}}$.
From the above formula you can read the difference between the time felt by the comoving observer and the proper time, indeed $\frac{dx^... | {
"language": "en",
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Moon's pull causes tides on far side of Earth: why? I have always wondered and once I even got it, but then completely forgot. I understand that gravity causes high and low tides in oceans, but why does it occur on the other side of Earth?
| First we must understand a little what is meant by "tide." A tide is the difference of gravitational force an object feels across its volume from another object. In the Earth's case the side closest to the moon feels a stronger force pulling it towards the moon than the center of the Earth does, while the side opposi... | {
"language": "en",
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"source": "stackexchange",
"question_score": "80",
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Placing two similarly charged particles in space Now, I will make a hypothetical situation. Assume that we place two similarly charged particles (lets take electrons) in space. Imagine that there is no other force acting on the particles except the repulsive force and the gravitational force of the particles. In other ... | as they move farther apart,, the magnitude of potential energy of the system reduces(which is 0 at infinity and infinity at 0 seperation in terms of magnitude),,, and the kinetic energy increases(which in this case tends to a specific value at infinity given by (2q1q2/4.pi.e)rm)^(1/2) where r is initial seperation
),, ... | {
"language": "en",
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Is the scalar curvature of the Schwarzschild solution 0? The Schwarzschild solution is meant to be a solution of the vacuum Einstein equations. That is
$$R_{\mu\nu}=0.$$
So, the Ricci tensor must be null for $r>0$.
Now, if the scalar curvature is nothing but the Ricci tensor contracted, and the Ricci tensor is null, th... | You're correct that $R=0$. $R_{abcd} R^{abcd} = \frac{12 r_s^2}{r^6}$ is the Kretschmann scalar for the Schwarzschild metric, an invariant used to find the true singularities of a spacetime. In this case, only the singularity at $r=0$ is a spacetime singularity, not a coordinate-system one.
| {
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The Helium mass fraction from the Big Bang Nucleosynthesis In Perkin's book Particle Astrophysics (page 144): I do not understand how one comes to the following expression (the second equality with $r$) for the Helium mass fraction due to the Big Bang Nucleosynthesis:
$$Y= \frac{4N_\text{He}}{4N_\text{He}+N_\text{H}}= ... | The problem is you have the wrong relations between $\{N_\mathrm{H}, N_\mathrm{He}\}$ and $\{N_\mathrm{p}, N_\mathrm{n}\}$. Every hydrogen contains 1 proton, and every helium contains 2, so $N_\mathrm{p} = N_\mathrm{H} + 2 N_\mathrm{He}$. The neutrons are only contributed to by helium in the accounting: $N_\mathrm{n} =... | {
"language": "en",
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the energy relations in oceanography description I'm reading the following paper and do not entirely understand a point that the author is trying to make. In page 99 (2 of article) the author refers to the following equation:
$$ Q^{*} = \beta S^{*}e^{-\beta z} + 2B^{*} \delta \left(z\right) $$
and in the following para... | The first term on the right is $\beta S^{*}e^{-\beta z}$
This means that the amount of light penertrating into the ocean decreases exponentially with depth $z$.
The second term on the right is $2B^{*} \delta \left(z\right)$
This takes into account heat transfer processes taking place only at the surface, such as evapo... | {
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How can $J_1^2, J_2^2, J_{1z}, J_{2z}$ commute mutually? I'm reading through J. J. Sakurai's Modern Quantum Mechanics book and currently looking at the "Angular-momentum addition" part.
Here, it says you have two options and that one option is to construct simultaneous eigenket $\vert j_1j_2;m_1m_2\rangle$ of $J_1^2, ... | Technically when two operators $A$ and $B$ commute it means that $AB = BA$, but from a physical standpoint yes it means that both observables can be measured simultaneously, and in that respect you kinda answered your own question. They're independent so they commute. For an analogy think of the spin of the electron in... | {
"language": "en",
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Heat equation: boundary conditions? Say we have a bar centered at $x=0$, that is heated. We have the 1D Heat equation which we can solve to find a parabolic temperature profile :
$$\kappa \frac{d^2 T}{d x^2}=-\frac{Q}{L S}$$
with
$$T(L/2)=T(-L/2)=T_{\infty}$$
$T_{\infty}$ is the ambient temperature at the end of the ba... | I think the problem is that while in the first case your differential equation applies to all your domain of interest and you can just use it, in the second situation the DE doesn't apply at x=0. This means you need to solve the DE at the domains $0<x<L/2$ and $-L/2<x<0$ separately, where it does still apply.
When appl... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does my house seem to warm faster in summer than it cools in winter? In summers when we switch off the air conditioner, the room seems to instantly get hot again.
But in winter, when we switch off the heater the room seems to remain hot for some time. Why this difference?
| This question can be answered with a nice visual comparison.
Let's take a pan of water, and put it on the stove at full power. You periodically throw in an ice cube to keep it at room temperature. Obviously, the moment you stop doing this, your pan is going to heat up very quickly. Now, take that same pan and put it in... | {
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Why $SU(3)$ and not $U(3)$? Is there a good reason not to pick $U(3)$ as the colour group? Is there any experiment or intrinsic reason that would ruled out $U(3)$ as colour group instead?
| It would be double counting, since total phase rotations of the quark wave function are already part of the model and the photon that makes them into a gauge symmetry already exists.
The total gauge group is SU(3) × SU(2) × U(1), so the question "where has the U(1) gone" has as its answer that it already was included. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119190",
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Energy of an EM Wave and its temperature and amplitude I'm trying to understand why classical physics fails to explain black body radiation.
I'm confused.
According to Boltzmann, energy calculation for em wave is based on temperature.
According to Maxwell, energy calculation for em wave is based on amplitude.
Are thos... | Maxwell is talking about a single wave. Boltzmann is talking about an ensemble of many many many many many such waves. Boltzmann finds that the average energy of an ensemble of waves depends on the temperature of whatever the waves contact, assuming that we've let enough time go by that the measurable properties of t... | {
"language": "en",
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Why can the entropy of an isolated system increase? From the second law of thermodynamics:
The second law of thermodynamics states that the entropy of an
isolated system never decreases, because isolated systems always
evolve toward thermodynamic equilibrium, a state with maximum entropy.
Now I understand why t... | Take a room and an ice cube as an example. Let's say that the room is the isolated system. The ice will melt and the total entropy inside the room will increase.
This may seem like a special case, but it's not. All what I'm really saying is that the room as whole is not at equilibrium meaning that the system is exchang... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119387",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
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Blackbody and standing waves I'm reading articles about black body radiation and why classical mechanics fails to explain it. My question is:
Why do EM waves have to be standing wave in a cavity?
|
I'm reading articles about black body radiation and why classical mechanics fails to explain it.
More correctly, people could not explain it with classical physics (pre 20-th century physics). Nobody seriously thought that classical mechanics was sufficient even then - radiation is described by electromagnetic theor... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/119444",
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Has string theory been able to produce masses of elementary particles? Masses of elementary particles in standard model are strange numbers. Is it possible to obtain these masses in string theory (presumably by using very few number of input parameters)?
| If you know which string theory vacuum you have (which compactification, which fluxes etc) and you know how the symmetries are broken, then you could in principle compute the masses.
Alas, nobody knows which is the right vacuum and how the symmetries are broken. Thus, the answer is in principle yes, in practice no.
T... | {
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"timestamp": "2023-03-29T00:00:00",
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Efficiency of a thermal reactor I was told that the efficiency of any thermal reactor increases if it is operated at higher temperature- in this case, nuclear reactor was referred to. But I cannot seem to understand why...
| Presumably this is in the context of using reactors to generate electricity. Any power generator works by transferring heat from a hot source to a cold sink, and using the heat flow to do work. This work then generates electricity.
The archetypal heat engine is the Carnot engine, and its efficiency at converting heat t... | {
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Why is the constant velocity model used in a projectile motion derivation? I was re-studying university physics last week, I'm now in the chapter about kinematics in 2 dimensions and specifically the one treating projectile motion. In page 86 of his book (Serway - Physics for scientists and engineers) he derives the eq... | I don't understand question 1: where does he equate a speed to a position?
As far as question 2 is concerned, it is basically what DavePhD said, but maybe I can extend it a bit more saying something about the conservation of linear momentum:
Along the x-direction, there is no external force (because gravity points down... | {
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Maximum helicopter height Helicopters or dual/quadcopters stop rising after reaching some height from the ground. What causes that? And what one should do if he want to prevent this, if he want the helicopter to keep rising up?
| In the most simplified view, a helicopter is basically a really powerful fan, which is something that pushes air (and therefore feels a force in the opposite direction). When you get high enough, the air starts thinnning, so there is less to push, so that force becomes too low to hold it up. Imagine the limiting case o... | {
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Why is the speed of light arbitrarily the limit? I know Einstein was great and all. Why is it that exactly at the speed of light is where infinite energy is required to accelerate any object with mass? Is it simply because the math of relativity checks out and explains most of everything? Are there any physicists who d... | Let's assume, for argument's sake, that the Galilean transformation holds rather than the Lorentz transformation.
Then your questions would become
Why is infinite speed arbitrarily the limit? Why is it that exactly
at infinite speed is where infinite energy is required to accelerate
any object with mass?
I suspe... | {
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Bragg diffraction and lattice planes Crystalline substances show, for certain sharply defined wavelength and incident directions, very sharp peaks of scattered X-ray radiation.
From the illustration below we see that we get constructive interference when the path-length difference is a multiple of the wavelength $\lamb... | $d$ is constrained to be integer multiples of any ($hkl$) planar separation. The use of Miller Indices really helps realise how many planes there can be to reflect off, especially when it comes to more complex crystal structures. An alternate representation of Braggs law is $n \lambda = 2d_{hkl}\sin\theta$ to explicitl... | {
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Difference in decay for muon and anti muon In a couple weeks, I will conduct a lab experiment where I measure the lifetime of the muons from the secondary cosmic radiation. For that, we have two detectors above each other, one will give a start signal, the other will give a stop signal, assuming the muon came to rest i... | The flux of negative muons at the surface of the earth can be smaller, than the flux of positive muons, because of muon capture by proton (which typically follows after the formation of an hydrogen-like atom with the $\mu^-$ in place of the electron). Such a reduction of the flux, if not taken into account properly, co... | {
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Why doesn't time change in the non-relativistic limit of Lorentz transformations? A simple boost in the $x$ direction is given by:
$$ \Lambda = \begin{pmatrix}
\cosh(\rho) & \sinh(\rho) & 0 & 0 \\
\sinh(\rho) & \cosh(\rho) & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
\end{pmatrix} $$
Which get linearized to the followi... | The Lorentz transformations : \begin{pmatrix}
\cosh(\rho) & \sinh(\rho) \\
\sinh(\rho) & \cosh(\rho) \\
\end{pmatrix}
form a group.
The galilean transformations :
\begin{pmatrix}
1 & 0 \\
v/c & 1 \\
\end{pmatrix}
form a group
But the transformations :
\begin{pmatrix}
1 & v/c \\
v/c & 1 \\
\end{pmatrix}
do not... | {
"language": "en",
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Where does the steam pressure go? Lets say you build a steam boiler and then you connect several turbines to the boiler in series. What limits the number of turbines that you can connect to the boiler in this way? In my mind, it seems that the steam still has to escape, so no matter how many turbines are in the way, ... | Yes, the same mass flow of water coming out of the boiler must ultimately pass thru all the turbines. However, the part you appear to be missing is that with multiple turbines in series, the pressure drop accross each one is reduced. There is no free lunch here.
The total pressure drop from boiler to ambient (or a co... | {
"language": "en",
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Sign of gravitational force I'm reading Lanczos's The variational principles of mechanics, and on pp. 80-81 there is an example involving a system made up of $n$ rigid bars, freely jointed at their end points, and the two free ends of the chain being suspended.
The coordinates are chosen so that the $x$ axis is horizon... | I) Yes, it appears that the sentence
[...] the $y$-axis vertically downwards [...]
in Ref. 1 p. 81 should have been
[...] the $y$-axis vertically upwards [...]
II) Let us also mention that Ref. 1 p. 29 eq. (17.9) introduces a function $U$ to be minus the potential energy, however, this $U$ seems unrelated to above.... | {
"language": "en",
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Why $e$ in the formula for air density? I am reading a book that says that the density of air is approximately $D = 1.25 e^{(-0.0001h)}$, where h is the height in meters. Why is Euler's number $e$ used here? Was a differential equation used in deriving this formula?
| Euler's constant appears naturally in phenomena where the spatial gradient of a quantity (or rate of change with time) is proportional to the quantity itself: $$\frac{\mathrm{d}X}{\mathrm{d}x} = X/x_0$$ ($x_0$ determines the strength of the proportionality, and keeps units straight.)
The solution of this differential ... | {
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Why does angular momentum shorten the Schwarzschild Radius of a black hole? Angular momentum causes the event horizon of a black hole to recede. At maximum angular momentum, $J=GM^2/c$, the Schwarzschild radius is half of what it would be if the black hole wasn't spinning.
Can someone explain why angular momentum redu... | Maybe a qualitative answer motivated from thermodynamics: If you let your black hole rotate, you reduce the number of symmetries of your system, this will decrease your entropy $S$ which is proportional to the surface area. The surface area however is for sure monotonic increasing with your Schwarzschild radius, theref... | {
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Integrating the generator of the infinitesimal special conformal transformation (c.f Di Francesco, Conformal Field Theory chapters 2 and 4).
The expression for the full generator, $G_a$, of a transformation is $$iG_a \Phi = \frac{\delta x^{\mu}}{\delta \omega_{a}} \partial_{\mu} \Phi - \frac{\delta F}{\delta \omega_a}$... |
However, I don't really see how to exponentiate the infinitesimal form
to actually get to the finite form
In addition to the detailed answer of @LubošMotl, you may notice that conformal transformations transform light cones in light cones.
This means the following. Starting from a light cone :
$$(x'-a')^2 = x'^2-2... | {
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Is it ok to have two events $A$ and $B$ so that for one person $A$ occurs before $B$ but for another $B$ preceds $A$ Imagine two laser beams A and B are released at the same moment to bounce between two mirrors, A was moving and B was at rest, doing the calculations I found that for a person at rest B would reach the u... | Yes, that's ok! You've stumbled upon one of the basic strange phenomena of relativity.
| {
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How stellar aberration is measured? A simple calculation shows that stellar aberration due orbital motion of earth is roughly 20 arcseconds. My questions are:
*
*Practically how this small value is measured?
*Does this value is in the range of accuracy of a 11 inch reflective telescope with a camera?
*And how t... | The Wikipedia article on angular resolution
https://en.wikipedia.org/wiki/Angular_resolution
is a source of many useful facts relevant for the question. For example, it was empirically established already by the English 19th century astronomer W.R. Dawes that the angular resolution $\theta$ in arcseconds is about
$$ ... | {
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Help explain how direction change relates to acceleration I was doing some simple harmonic motion problems and I came across this picture describing the position, velocity and acceleration of a linear oscillator. At the moment in time when v is 0 the linear oscillator should not be moving, only changing directions. ... | The expression "change in direction" implies some sort of discontinuity in motion, where in the referenced graphs, there is none. One could easily choose a different frame of reference such that the oscillating object appears never to change direction, only periodically speed up and slow down. The fact that the velocit... | {
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Can an LC oscillator be used to generate visible light? The LC oscillator is most commonly used to generate radio waves for practical use and the frequency $\omega$ of the LC oscillator equals that of the electromagnetic wave so produced. So, can they in principle be used to emit visible light?
The frequency of visible... | An electric oscillator for light exists indeed. They are called LASER diodes. Due to the works of a number of Nobel prizewinners (e.g. Einstein predicted the working in 1911), you can buy then in a store and simple powers then with a DC power source. It's a sort of oscillator, not with electric current, but with light.... | {
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Invariance of a tensor under coordinate transformation I know, that a tensor is a mathematically entity that is represented using a basis and tensor products, in the form of a matrix, and changing a representation doesn't change a tensor, is kind of obvious.
So does the invariance of a tensor under coordinate transform... | I guess there is two different notions of invariance of tensors. First notion is that if you look at a tensor as a mapping then the first notion of invariance is what you mentioned above. The other notion of invarance is that you do transformation but the " component" of metric does not change. For instance, if we do L... | {
"language": "en",
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How much does the sound definition vary during an LP (Vinyl)? This question came to me when I realized how the linear speed varies while listening to a Vinyl LP.
The linear speed variation has to be compensated with a variation in the resolution of the grooves, that is, since the linear speed decreases, the groove reso... | Your question is a little misstated, since it's not so much the "groove resolution" as the high linear frequency limit to which the groove can be cut. The stylus (and piezo or magnetic components which convert motion to electrical signal) doesn't really care about linear speed in the along-track direction, just the tr... | {
"language": "en",
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Renormalizability of standard model I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities:
*
*The renormalizability of all of the interaction described by the Lagrangian before spontaneous symmetry breaking (SSB) by the nonzero vacuum expectation value (VE... | The Standard Model Lagrangian before and after spontaneous symmetry breaking (SSB) is renormalizable. To see that recall that the rule is (though it may not be immediately obvious as to why this rule holds) that a theory is renormalizable if all the terms in the Lagrangian are of dimension 4 or less. This is true by de... | {
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Uniformity in a solenoid I know the magnetic field strength increases as the number of turns in the solenoid increases.
However, I've learnt the field inside the solenoid is usually nearly uniform.
So, does the number of turns in the solenoid effect the uniformity of the field inside the solenoid? Does the field gets c... | If the windings in a solenoid are not closely spaced, there will be some inhomogeneity in the field - so more turns per unit length helps. Usually for "ideal" calculations one assumes a continuous sheet of current.
The second thing is the length. For a finite length magnet the field quickly drops off as you move away f... | {
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Why must a singularity form inside a black hole? What is the exact reason that normal matter can not exist within an event horizon?
I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less than its Schwarzschild radius and an event horizon forms around it.
But ... | We do not know that "normal matter can not exist within an event horizon".
For all we know, aliens may be sitting around and drinking coffee watching us.*
We have theories on what could happen. different theories have different views.
Nothing has been tested, scientifically proven as yet.
Some calculations (the status... | {
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Cooling induction current generation We know that conducting materials can be heated by electromagnetic induction. Is it possible to generate current using a cooling process?
| Short answer is: If you heat up the whole material, then no.
If you heat up the material in on end (an iron bar e.g.), then yes. The thermoelectric effect will cause a small current to flow between the two ends of different temperature.
It looks like you are mistakenly assuming that electromagnetic induction causes he... | {
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Why ONLY Maxwell's equations are the basic equations of electromagnetism? In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know: is this(to assume that there is no requirement of any other rule)only an assumption, a practical observation, ... |
In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of Maxwell. But I want to know that is this only an assumption
It is not an assumption, it is an elegant way of joining the diverse laws of electrictity and magnetism into one mathematical framework.
or a practic... | {
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Analytical problems with Green's function I have a question about the right definition of the Green's function in physics. Why do we introduce (or not) an infinitesimal, positive number $\eta$ to the following definition:
$$\left[ i\hbar\frac{\partial}{\partial t} - \hat{H}(\mathbf{r}) \pm i\eta\right]G(\mathbf{r},t;\m... | This type of problem can be conveniently treated using the complex
Laplace transform. For a function $f(t)$ with $t\geqslant 0$ it is defined as
\begin{equation*}
\hat{f}(z)=\int_{0}^{\infty }dt\exp [izt]f(t),\;Imz>0.
\end{equation*}
Setting $z=\omega +i\eta $ ($\eta >0$ but arbitrary otherwise) we have, with
$\theta (... | {
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Electrostatics - Inserting a brass plate between two charges The question is: if I were to insert a brass plate between two charges, what will happen to the force between the charges? Would it increase, decrease or stay the same?
Does the brass plate increase the value of permittivity of the medium and therefore the f... | The brass plate is a conductor, so the potential will be the same on both sides. The thickness of the brass plate therefore subtracts from the effective distance between the two charges, making the electric field strength higher in the remaining open space between the charges. This stronger field will cause more forc... | {
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Is entropy in quantum mechanics emergent or fundamental? Since a quantum mechanical system, even an isolated system containing one particle, can be described by a density matrix, with entropy for the system given by $\langle S\rangle=-k \rho\ln(\rho)$, is not entropy therefore a property of the system like mass or ener... | You have provided the von Neumann entropy definition which is derived from its density matrix. I would consider it an intrinsic rather than fundamental property, but this is just semantics.
Some recent work by John Baez has investigated the dynamics of quantum entropy called quantropy.
| {
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Why does wavelength affect diffraction? I have seen many questions of this type but I could nowhere find the answer to "why". I know this is a phenomenon which has been seen and discovered and we know it happens and how it happens. But my question is why would wavelength affect the amount of diffraction? I am looking f... | The question "why does the wavelength affect diffraction", I think, could be best answered by looking at the two extreme cases. Assuming a narrow opening is illuminated:
*
*If the wavelength is much smaller than the width of a slit, wave effects can be completely ignored, because interference effects won't play a ro... | {
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Natural entanglement system I'm a beginner and amateur interested in quantum physics.
I would like to know if entangled systems of natural states exist or whether such systems require human intervention?
Is it possible? Either no or yes, Why?
| In short, entanglement is perfectly normal. I am sure that entanglement is ubiquitous in, say, atoms with more than one incomplete subshell, as well as in some kind of organic molecules, but I am not a quantum chemistry expert and can’t provide an easy-to-realize example.
Generally, any decay process produce particle ... | {
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How could the multiverse theory be disproven? Theorists (physicists) suggest that there is the term/entity, the Multiverse that contains a huge number of universes not necessarily like our own.
I personally find this theory very elegant because its explains the probabilistic outcomes of the experiments with fixed condi... | Any particular theory of (astro)physics that predicts a multiverse will be disproven the moment experimental results or observations are found to be in conflict with the theory. In physics all theories are falsifiable, so this is not a problem in principle. However, you can then postulate that there may still exist a m... | {
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How can a gas support tensile stresses? In working through a rigorous derivation of the compressible Navier-Stokes equations, I find that the momentum flux in the X-direction should be driven not only by the normal pressure gradient $\frac{\partial p}{\partial x}$ and shear stress terms $\frac{\partial(\tau_{yx})}{\par... | It looks like the question boils down (at least in part) to the following: can a fluid have negative ABSOLUTE pressure? This question has been discussed here several times. My take is: it can (although such state is probably metastable in the best case), because the force between two molecules can be attractive. See, e... | {
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Difference between weight of water and pressure of water (I didn't even have a basic formal education in physics. I'm learning through the internet out of my own interest, so if there are any silly mistakes, kindly bear with and guide me through.)
Everywhere, everyone is saying that pressure will same be for a given he... | Consider this diagram showing the three columns you describe all connected to the same body of water:
Your question asks whether the three pressures $P_1$, $P_2$ and $P_3$ will be the same. The answer is obviously yes, because the columns are all connected to the same body of water. For example if $P_1 > P_2$ then wat... | {
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Why does the Walecka model not include pions? The Walecka or $\sigma$/$\omega$-model is an effective theory describing nucleon-nucleon interaction by an exchange of $\sigma$/$\omega$-mesons. Why does it not include interactions by pions?
| The answer given in Walecka's 1974 paper is mostly correct. The one pion exchange contribution to the Hartree energy vanishes in balanced nuclear matter. The same point was made in the 1972 paper of Miller and Green (Phys Rev C5 241) where the same type model was used for doubly magic (finite) nuclei. If exchange is i... | {
"language": "en",
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Magnetic field and Newton's third law If a magnet exerts force on a iron block (opposite and EQUAL), does a iron block also exerts force on magnet (via Newton's third law)? If yes then what magnetic property does it has to produce equal and opposite force on magnet considering that its not a ideal environment? If no th... | Its a violation of Newton third law..because Newton third law only valid when
1)same kind of force ie when there is force of same nature
So electromagnetic and block forces are not of same nature so Newton third will not hold
| {
"language": "en",
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Singularity in Newton's gravitational law If $r=0$ in the well know equation $F= G\dfrac{m_1\cdot m_2}{r^2}$, it will not follow that the force will be infinite?
May someone please clarify it to me?
| True point masses and other singularities can wreak all kinds of havoc in Newtonian physics. A couple of examples:
*
*Particles can attain infinite velocity in finite time: Saari, D., and Zhihong J. (1995), "Off to infinity in finite time." Notices of the AMS 42:5.
*Particles can exhibit non-deterministic behavior.... | {
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Gradient is covariant or contravariant? I read somewhere people write gradient in covariant form because of their proposes.
I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of gradient must be in contravariant form. However we know by transformation properties an... | Gradient is covariant! Why?
The components of a vector contravariant because they transform in the inverse (i.e. contra) way of the vector basis. It is customary to denote these components with an upper index. So, if your coordinates are called $q$'s, they are denoted $q^i$.
Therefore, the gradient (or a derivative if ... | {
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Is a "shift in the meaning" of Accuracy and Precision occurring? Accuracy and precision are among the most fundamental concepts in experimental physics, and, I always believed, completely unambiguous.
Recently I found that the Wikipedia article on Accuracy and Precision claims that a "shift in the meaning of these term... | (Currently editing answer.. previous version at https://physics.stackexchange.com/revisions/135002/7)
| {
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Is there a difference between "average acceleration" and centripetal acceleration? Question adapted from Examkrackers MCAT prep book:
A particle moves along a half circle (diameter=$10\text{ m}$) at a constant speed of $1\text{ m/s}$. What is the average acceleration of the particle as it moves from one side of the ha... | Here the average acceleration can be understood as follows:
The particle going from A to B along a half circle with speed 1m/s can be here viewed as the particle going from A to C and again to A with an initial velocity 1m/s as shown in the figure:
The particle in the half circle, will move under a centripetal acceler... | {
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Wrong calculation of work done on a spring, how is it wrong? So I would have thought that this would be how you derive the work on a spring: basically the same way you do with gravity and other contexts, use $$W=\vec{F}\cdot \vec{x}.$$ If you displace a spring by $x$, then it exerts a force $-k x$, so $F=-kx$, since th... | in w=F.X, x is displacement of center of mass of the body not the displacement of system.
here also force is 'kx' and displacement of c.o.m. is 0.5*x,so work done will be 0.5kx^2.
| {
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Ampere's law and Biot-Savart law gives different terms for magnetic field in middle of a current running in a loop
I would like if someone could clarify this issue for me:
When dealing with a current $I$ running in a loop with radius $R$ and looking for the magnetic field in the middle of the loop.
By using Ampere's l... | The Biot Savart law is
$${\bf B} = \frac{\mu_0}{4\pi} \oint \frac{ I\, d{\bf l} \times {\bf r}}{|{\bf r}|^3}$$
In this case $d{\bf l} \times {\bf r} = dl\,|r|$ directed along the loop axis and integrating around the closed loop leads to a B-field magnitude $ B = \mu_0\, I/2R$ as you suggest.
However, I think there is ... | {
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What will be the effect of placing a light source very close to a photodiode? What will be the effect of placing a photodiode really close to a laser source and what should be the appropriate distance between a light source and photodiode to get maximum output current?
| Looks like the photodiode's ball lens is arranged to focus a collimated beam onto the diode so ideally you would want to create such a beam with a diameter less than the diameter of the lens to avoid large reflections and poor focus as the rays move off the optical axis. As long as the beam is arranged like that the di... | {
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Why do some hand dryers blow hot air? I am not sure why some hand dryers are blowing hot air and not just air at room temperature.
To me, hair dryers are just a way to dry one's hands using the same principle as when we shake our hands in the air, or when we blow some air over a hot drink.
Given that the blown air temp... | Fact:
By increasing the air's temperature, one also increases the amount of water vapor it can hold before saturating.
Speculation:
Therefore, the osmotic pressure on water molecules in your hair increases and the water vaporizes more quickly than with room temperature air.
| {
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Radiation emission and absorption Any object can emit and absorb radiation and the power of emission can be represented by the Stefan-Boltzmann law:
$$P=A\epsilon\sigma T^4$$
In many texts the net power radiated is the difference between the power emitted and the power absorbed:
$$P_{net}=A\epsilon\sigma (T^4-T_s^4)$$... | The Stefan-Boltzmann law for net power radiated pertains to the object. That is, we're simply asking, how much radiation leaves this object (this depends on the object's emissivity), and how much radiation is absorbed by this object (this depends on the objects absorptivity). The emissivity and absorptivity in the eq... | {
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Is the Baum Framptom a valid alternative to Big Bang? In the Baum Frampton model, proposed in 2007, because $\epsilon\lt-1$, after the Big Rip the universe starts again empty. The problem of this model is that inverting the arrow of the time, after a certain number of Big Rips it should have been a single universe from... | I have no idea if it is compatible with observations of 2013. However, I do remember that in one of Frampton's papers, he stated (back in mid 2000s) that the phantom energy density that he was considering was almost ruled out. It is unlikely that any of these models will be confirmed in our lifetime, and it is also unl... | {
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Why is the pressure inside a soap bubble higher than outside? Apparently, the air inside a soap bubble is under higher pressure than the surrounding air. This is for instance apparent in the sound bubbles make when they burst. Why is the pressure inside the bubble higher in the first place?
| I drew an image to illustrate the forces at play.
For any curved surface of the bubble, the tension pulls parallel to the surface. These forces mostly cancel out, but create a net force inward. This compresses the gas inside the bubble, until the pressure inside is large enough to counteract both the outside pressure,... | {
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Pool in a submarine A common theme in aquatic science fiction is the submarine pool/access to the ocean. That terrible TV show Seaquest had it, The Deep & Deep Blue Sea (Samuel L Jackson is standing in front of it when the shark chomps him). My question is how this could possibly work? From what little knowledge I have... | Is there a particular way that you think this scheme will fail?
Rather than have an airlock with that particular portion of ship, you can simply pressurize the entire vessel. There are practical reasons why you would not want to do this at great depths (related to how much gas you use and toxicity), but the problems a... | {
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Which ball touches the ground first? This is a very well known problem, but I can't find an answer in the specific case I'm looking for.
Let's consider two balls :
*
*Ball 1 weighs 10 kg
*Ball 2 weighs 1 kg
*Balls have identical volumes (so Ball 1 is much more dense)
*Balls have identical shapes (perfect spheres)... | Other answers & comments cover the difference in acceleration due to drag, which will be the largest effect, but don't forget that if you are in an atmosphere there will also be buoyancy to consider.
The buoyancy provides an additional upward force on the balls that is equal to the weight of the displaced air. As it i... | {
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Length contraction and simultaneous length measurements I am just working through an argument from Halliday Resnick to derive the Lorentz contraction (see quote below).
Some paragraphs before this, the authors note that:
If the rod is moving, however, you must note the positions of the end
points simultaneously (in... | It's interesting. It is implicit in Sams relation that what Sally calls length is indeed the coordinate difference taken simultaneously in her frame. Sams relation for length actually corresponds to simultaneity in Sally's frame.
| {
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Calculate water flow rate through orifice I'm not very good with fluid physics, and need some help. Imagine the following setup with water contained in-front of a wall with an opening on the bottom:
How do I calculate the water flow $Q$?. I have made some re-search and found I need to (partially) calculate the pressur... | I have used the Darcy Formula together with the following formulas for a quick numeric solution (only a few iterations needed)
*
*$$h_f = \frac{\Delta P}{\rho g}$$
*$$ f = {\rm Darcy}(Re)$$
*$$ h_f = f\,\frac{L}{D}\,\left( \frac{v^2}{2 g} \right) $$
*Solve above for $v$
*$$ Re = \frac{\rho D\,v}{\mu} $$
*Go to ... | {
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Why infrared absorption is a nonlinear technique? I am looking for a good explanation explaining why infrared absorption technique is essentially nonlinear (eg. for carbon monoxide quantification).
When using UV/visible/near-IR absorption technique, Beer-Lambert Law often is valid and then you have quite straight way t... | Edit: putting the summary of discussion in comments into my answer.
Beer-Lambert law assumes that every photon has equal probability to be absorbed by every molecule. It is only valid for sufficiently monochromatic light
– that is, the bandwidth of light source should be smaller than the width of the absorption line. ... | {
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How would an X-ray mirror work? I was wondering if light can be reflected how can someone reflect X-ray of what material does it need to be made of and is its design completely different to that of our original mirrors? Does this mean during long-space voyages in which radiation is an problem why can scientists not dev... | Unfortunately X-ray and gamma mirrors are impossible to build the way you think - mainly because there is much less interaction with the matter comparing to UV - it will go through all materials commonly used for making mirrors. Even for EUV light (wavelength of 13.5nm) building effective mirrors is a royal pain.
As w... | {
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Boundary Element Method or Boundary Integral Method Computational Aspects I have to solve a Helmholtz equation inside a simply connected domain. I know that in general the boundary integral can be written as,
$$\phi(x)=\int_V G(x,x') \rho(x')\ d^3x'+\int_S \left[\phi(x')\nabla' G(x,x')-G(x,x')\nabla'\phi(x')\right] \cd... | May I understand that, since the domain is 2D, the surface integral is actually the following: $\vec{E}\cdot d\vec{\sigma}' = \vec{E}\cdot\hat{n}dl$, where $\vec{E}$ is an arbitrary 2D vector, $\hat{n}$ denotes the normal of the domain boundary and $dl$ is the line element ? Suppose I understand you correctly and then ... | {
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Is there a substance that doesn't reflect OR absorb light from the visible light spectrum? Is there a substance that doesn't reflect or absorb visible light but may reflect light from another spectrum? Is there a theoretical substance that would have these properties?
EDIT:
Sorry I wasn't quite clear with my original q... | Lol it's all around you. We call it air. It doesn't absorb or reflect light so it's usually invisible but it does reflect intense light as found in a laser beam.
| {
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Why are magnetic fields so much weaker than electric? In EM radiation, the magnetic field is $ 3*10^8$ times smaller than the electric field, but is it valid to say it's "weaker". These fields have different units, so I don't think you can compare them, but even so it seems like we only interact with the electric field... | It's a quirk of units: notice that the conversion between them is dimensionful, and has the value $3\times 10^8\,\mathrm{m/s}$, which is the speed of light.
In the CGS system both fields have the same units, and field-squared is an energy density.
In SI units, the energy density for a configuration of fields is given b... | {
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Where does wave frequency come from? I am trying to wrap my head around where do oscillations in electromagnetic waves come from. As an example if I would take a string of guitar and ring it, it would produce a certain sound based on the amount of vibrations per second. That amount of vibrations would be the sum of mov... | The thing which is "vibrating" is the electromagnetic field, namely its $\vec E$ and $\vec B$ vectors. The animations here show precisely this.
Of course, it's not that some particles vibrate in this case. The electromagnetic wave can exist without any matter at all — all it needs is the field, which is present everywh... | {
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The Alcubierre drive and closed timelike curves Under what conditions would it be possible to create closed timelike curves, assuming an Alcubierre drive could exist? Would it be possible to have the latter without the former?
See here for information on the chronology protection conjecture.
| If somehow, it is only possible to create one alcubierre drive, and it can never turn around, then you won't get closed timelike curves. Otherwise, any construction is going to have them.
The reason is that you can "zoom out" far enough that the distortions to spacetime caused by the drive are no longer present, and t... | {
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Kinetic energy and potential energy variation over distance in SHM When you compute the average potential energy of a horizontal spring mass system from the mean position to the positive amplitude A, the value comes out to be $\frac{1}{6}kA^2$. For the average kinetic energy over the same range and direction, it is $\f... | One can't discuss the difference between factors of $1/3$ and $1/6$ without mathematics. The difference between these two numbers – and generally, any fact about any numbers – is all about mathematics.
If all values of $x$ between $0$ and $A$ were equally likely, the average value of $kx^2/2$ would be $kA^2/6$ as you s... | {
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Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?
*
*Does Free Will Theorem imply that quantum mechanics plays crucial role in our brain’s functioning (consciousness)?
*Is opposite statement of Free Will Theorem right: If elementary particles have a ce... | I am under the impression that the uncertainty principle is simply an epistemic principle in that our uncertainty is only a function of our inability to make a measurement weak enough to not destroy the prior information we had about the system. This is the reason we have a wave function in the first place. To the fr... | {
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Airplane on a treadmill I've heard conflicting answers, and would like to see the record set straight:
An jet/propeller airplane is traveling on a giant treadmill at takeoff speed. Will the plane takeoff, or will it remain on the runway, and why?
| An airplane's propulsion does not depend on friction between its wheels and the runway so the relative motion of the runway to the body of the airplane has no effect on the plane's motion$^1$. For example an airplane can take off from ice, where the friction between the wheels and the runway surface is effectively zero... | {
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How to measure trajectory regularity? I have two animal running trajectories. A regular one with repeated back and forth running between point A and B, like the one on top in the figure. The other one is very irregular, animal paused and turned around a lot in the middle. Is there any algorithm to measure the regulari... | If it were me, I would take the velocity as a function of time, and split into constant segments. For real data you will likely have to determine a threshold for what constant means, but in either case, split the trajectory up into "constant" velocity segments. Then compute distance traveled in each of these segments... | {
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Can a neutrino act as a virtual particle between two electrons to mediate an electron-electron fermonic interaction? Can a neutrino act as a virtual particle between two electrons to mediate electron-electron fermonic interaction analogous to how a photon acts as a virtual particle between two electrons to mediate a bo... | I'm a bit rusty on my qed, but I'll give this a shot. The simplest case would be described by a diagram similar to:
But the $e^--e^--\nu_e$ vertex doesn't exist (also note that I can't draw the required arrow on the neutrino) - the vertices of the standard model (with the exception of vertices involving the Higgs and ... | {
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Diffusion and Drift currents in a PN junction In a forward-biased PN junction, the potential barrier decreases, allowing more majority carriers from one side to diffuse to the other side where they are minority carriers. After they cross the potential barrier, they form a diffusion current, the drift current of minorit... |
Why do minority carriers form a diffusion current not a drift current after they cross the potential barrier?
Because the electric field is zero outside the depletion region, so a drift current cannot be driven.
| {
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Calculating Hubble's constant at earlier times I want to calculate Hubble's constant at some redshift $z$. I have found the following formula:
$$H^2=H_0^2\left(\Omega_m\left(1+z\right)^3+\Omega_{\Lambda}\right)$$
Now it's obvious that at higher redshift $z>0$ (earlier times) the Hubble's constant $H$ increases, which s... |
so, it's actually only numerically solvable? and is there no analytic expression for $H(z)$?
In my answer I'll be using the scale factor $a$ instead of the less wieldy redshift $z$. The two are simply related by $a = 1/(1+z)$.
In general the first Friedmann equation can be written as :
$$
H^2 = \left( \frac{\dot{a}}{... | {
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Is there inductance to a DC circuit? When a DC circuit is carrying current, large amounts or small, is there induced-emf due to the inductance? Or is it only applied to AC circuits?
| If the change is withing the time constant of the circuit, DC will in fact produce on going back emf that opposes the original current flow thus control current. inductive reactance then comes into play initiated by the inductance change thus when the current flow changes a frequency is applied to the DC thus inductive... | {
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Why do liquids boil when their vapor pressure equals the ambient pressure? Given that the boiling point of a liquid is the temperature at which the vapor pressure is equal to the ambient (surrounding) pressure, what significance does a liquid's vapor pressure have in the formation of bubbles that happens at and above t... | When you heat water on the stove top, you see bubbles forming on the bottom of the pot. The bubbles are created where the heat applied (if you move the pot, you see the bubbles forming in a different spot) and is sufficient to convert the liquid into a vapor (less heat would just heat the water). These bubbles form eve... | {
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Average Velocity of a body moving in a circle with constant speed $v$
A Body is moving with constant speed $v$ along a circle of radius $R$. Find the average velocity of the body from time $t = 0 $ to $t= \frac{R}{3V}$.
My attempt at the question:
Let distance traveled along the circle be $d$.
$$ d= \left(\frac{R}{... | Just off the top of my head, $T=\frac{2\pi R}{v}$ so the time $t=3R/v$ is a fraction $3/2\pi<1/2$ of the total period. Just less than one half, which means that the angle sub tended is not $\theta=1/3$ actually $\theta = 3rad\sim\pi$ so that most of the one direction of motion along the semi circle will have canceled o... | {
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What is $c + (-c)$? If object A is moving at velocity $v$ (normalized so that $c=1$) relative to a ground observer emits object B at velocity $w$ relative to A, the velocity of B relative to the ground observer is
$$ v \oplus w = \frac{v+w}{1+vw} $$
As expected, $v \oplus 1 = 1$, as "nothing can go faster than light"... |
I'm getting the sense that my fears were correct, it's physically a
nonsensical situation.
Applying a formula outside of the context in which it was derived will likely produce nonsensical results.
In the derivation of the relativistic velocity addition formula, and using your notation, there is an object B with un... | {
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How to approximate acceleration from a trajectory's coordinates? If I only know $x$- and $y$- coordinates of every point on a trajectory without knowledge of time information, is there any way to approximate Cartesian acceleration angle at each point? Time interval between every two points is very small, ~0.03 second. ... | Yes. Provided you are only interested in the direction of the acceleration, and not it's magnitude. And further assuming your time samples are equally spaced, you can take the second derivative of the path and this will be proportional to the acceleration.
A decent method in practice would be to use a second order ce... | {
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Potential Energy Concept Imagine a book that we lift it with a force that is exactly equal to the force of gravity so the forces cancel out and the book moves with a constant velocity.
Consider the situation after the book has been lifted, and it has come to rest once again. According to the work and kinetic energy la... | If you lift the book with a force that is exactly equal (but opposite) to the force of gravity acting upon it the book won't go anywhere. After all, that's exactly what a table does when you leave the book on it.
To get to book going you need to lift with a force greater in magnitude than that of gravity, resulting i... | {
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Proving the equivalency of the potential energy of a system of charges and the work required to assemble a system of charges This is a very cool, and highly beneficial problem in my opinion. I feel as though truly understanding this proof would broaden anyone's conceptual understanding of electric potential.
My textboo... | Hint:
The divergence theorem tells us that the divergence of a vector field integrated over a region $R$ with boundary $\partial R$ equals the integral of that vector field dotted with the outward-pointing normal along the boundary;
\begin{align}
\int_R dV\, \nabla\cdot \mathbf v=\int_{\partial R} dS\, \mathbf v\cdot... | {
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Seesaw type-1 and integrating out heavy fields Let's assume seesaw 1 type of generation of left neutrino Majorana mass:
$$
L_{m} = -G_{ij}\begin{pmatrix} \bar{\nu}_{L}& \bar{l}_{L}\end{pmatrix}^{i}i\sigma_{2}\begin{pmatrix}\varphi_{1}^{*} \\ \varphi^{*}_{2} \end{pmatrix}\nu_{R}^{j} - M_{ij}(\nu_{R}^{T})^{i}\hat{C}\nu_{... | The interaction term disappears because when you integrate out the right handed neutrinos you insert in a linear combination of the other fields in their place. For example I expect that we would have something of the form,
\begin{equation}
G _{ ij} \sigma \bar{\nu} _L ^i \nu _R ^j \rightarrow G _{ij} G _{jk}\sigma ... | {
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"answer_id": 0
} |
Quantum Entanglement and BB84 protocol Can Quantum entanglement can be used to strengthen the security or increase the efficiency of communication via the BB84 protocol? If so, how?
| All different QKD protocols are well covered in most Quantum Information textbooks, e.g. Quantum Information by Jaeger. Trying to give a complete, understandable coverage of the matter is impossible in a post like this, so I'll just give you an overview:
In the E91 scheme, entangled photon pairs are used between Alice ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/130213",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
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