Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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What makes Bell's original inequality unsuitable for experiments? Bell derives the inequality $$|E(\vec{a},\vec{b})-E(\vec{a},\vec{c})|\leq 1+E(\vec{b},\vec{c})$$ in his book Speakable and unspeakable in quantum mechanics. In this derivation he uses the assumption that when the axes $\vec{a}$, $\vec{b}$ are aligned, th... | The original derivation assumed that every measurement would give a result, such as for example "particle with up-spin detected," or "particle with down-spin detected" But in real experiments some particles never affected the detectors; presumably they "leaked out" or somehow vanished, and no measurements occurred. H... | {
"language": "en",
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Lagrange equation and a force derivable from a generalized potential I was reading the solution of this exercise and I have a doubt:
A point particle moves in space under the influence of a force derivable from a generalized potential of the form $$U(r,v) = V(r)+\sigma\cdot L $$
where $r$ is the radius vector from a f... |
What happened with $V\left(\sqrt{x^2+y^2+z^2}\right)$?
You mean, why does V(r) disappear from the $\frac{\partial }{\partial \dot q_j}$ term, right? It's because V(r) is a function only of $q_j$ not $\dot q_j$. Those variables are treated as independent and so $\frac{\partial V}{\partial \dot q_j}=0$.
and why
$\p... | {
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Could I break the sound barrier using circular motion? (And potentially create a sonic boom?) Ok, Lets say I get out my household vaccum cleaner, the typical RPM for a dyson vaccum cleaner reachers 104K RPM, Or 1.733K RPS. In theory, this disc would be travelling with a time period of 0.00057692307 seconds, If we take ... | I'm surprised to see no mention of turbofan jet engines in the answers so far. In fact, the blade tips of most modern turbofan engines do reach supersonic speeds. As predicted by a comment above by tpg, this does produce shockwaves from each blade tip and what you hear is a 'buzzing' sound, which is commonly described ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172451",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Solitons and its infinite extension A soliton, for example the KdV equation solution, has the profile proportional to a hyperbolic secant squared ${\text{sech}}^{2}(x-ct)$. And since it is hyperbolic it has an exponential dependence, so it has an infinite span, it has tails that extend to infinite.
However the solitons... | An exponentially decaying tail is almost like having no tail for all practical reasons. For example consider the yukawa potential for interaction through exchange of a massive particle, it is $\propto e^{-\mu r}/r$ which is even a stronger tail than the asymptotic behavior of the hyperbolic secant. There we say that th... | {
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Why temperature of liquid drops after spraying through a nozzle? We have tested in our lab as mentioned in the picture.
We connected hot water at $130^\circ F$ at $40 Psig$ to a nozzle (bottle sprayer). We measured the temperature differences inside tank and after spraying and found that there is a temperature drop of... | I think that the answer is more complicated than that. What holds liquid together when it is siphoned? People don't quite know however it would seem that there is some energy that holds it together. It is related to the vibration of each molecule in the system. When you force water through a nozzle you are in fact ... | {
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Understanding the Quantum Vacuum State In terms of the creation and annihilation operators $a_{j}$ and $a_{j}^{\dagger}$ (fermionic or bosonic, doesn't matter):
Is the vacuum state $\mid\mathrm{vacuum}\rangle$ exactly the zero vector on the Hilbert space $\mathcal{H}$ in question?
For a while I thought that the answer ... | Don't be fooled by the zero inside the ket. That is just a label. For example in Scalar QFT, the vacuum state of interacting theories is usually denoted as $|\Omega\rangle$ rather than $|0\rangle$. So no, the vacuum state does not represent the null vector of the Hilbert space.
Rather, the vacuum state is defined to be... | {
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Acceleration due to Gravity: Free Fall If we are in a free fall which implies we are accelerating at 9.8 m/sec every sec. And let's say that we are falling into a pit that has enormous depth. So isn't this be possible that we may accelerate and surpass the magnitude of speed of light?
| You make two wrong assumptions in your question, namely that if an object is accelerating the velocity would keep increasing ad infinitum without limit, and that the acceleration due to gravity on earth is always $9.8 m/s^2$ these are both not the case.
First of. The theory of relativity doesn't allow for objects that... | {
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Why is $F=ma$? Is there a straightforward reason? Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplicat... | The acceleration is the effect on the objects motion due to the cause(s), which is the vector sum/total of the forces acting on the object, i.e. the total force (composed of many forces) is responsible for the acceleration (which is just one vector).
The mass is just the constant of proportionality that links total for... | {
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If the Earth is a good conductor of electricity, why don't people get electrocuted every time they touch the Earth? Since the Earth is a good conductor of electricity, is it safe to assume that any charge that flows down to the Earth must be redistributed into the Earth in and along all directions?
Does this also mean ... | There is a concept of "voltage of a step"* in energy industry - if a high voltage power line is leaking into the ground and isn't shut down, then near that point the ground voltage difference over a single human step (when one feet is closer than the other) can be enough to kill a person; that's why it may be dangerous... | {
"language": "en",
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In $1$-dimensional space, how would the gravity generated by an electron affect a photon moving away from the electron if the photon can’t slow down? Suppose we had a universe obeying the same physical laws as our own. But it had only one spatial dimension (represented by the $x$ axis) and it was totally empty. There a... | The energy of a photon is given by the equation E = hf where h is Planck's constant and f is frequency. The energy would decrease, making the frequency decrease (since h is constant). So, if the photon was blue light, then it would get redder and redder as time when on. There is a point, however, when your system event... | {
"language": "en",
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Is it possible that every single isotope is radioactive, and isotopes which we call stable are actually unstable but have an extremely long half-life? I've read that tellurium-128 has an half-life of $2.2 \times 10^{24}$ years, much bigger than the age of the universe.
So I've thought that maybe every single isotope of... | We are never 100% certain of anything. The scientific method falsifies wrong theories, but it does not verify those we colloquially call "correct" or "true"
If we tomorrow detect a normal oxygen atom decaying, we'll have to devise new theories to explain it.
But we don't expect the things we call stable to ever decay (... | {
"language": "en",
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Does the microgravity environment in highly elliptical orbits differ from circular orbits? I think everyone understands the microgravity environment broadcast from the ISS. But the ISS stays in a fairly circular orbit, the acceleration of gravity should be fairly uniform, the altitude and velocity changing very little.... | When you are in a synchronous circular orbit, the gravitational force equals the radial force, at all times. If the orbit is elliptical, the variations in the orbit will translate into force variations. Whether these variations would be perceived by humans, depends on how "elliptical" the orbit is, and how close to o... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Black hole singularity in loop quantum gravity How is the singularity of a Black Hole treated in Loop Quantum gravity ? Does it go away ? And if it does, what's after the event horizon ?
| The theory of loop gravity would suggest that it would only become more dense in a singularity event. So It would not go away but become very very dense. So if anything the possibility arises That after the event horizon it would either become so dense it would simply just not be detected aside from its push of gravity... | {
"language": "en",
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Proton creation My question is simple: if proton antiproton pairs can be created in the laboratory (given certain energies) then they should also be able to be created in the universe at any time, not only during the Big Bang.
So, for example, a quasar could be a giant proton factory, or an accretion disc at the cente... | Yes this is how proton cosmic rays are produced... quasars, supernovae, gamma rays bursts... also anti proton cosmic rays originate from proton anti proton creation in proton cosmic ray collision with nuclei in interstellar medium (otherwise anti protons cannot leave the vicinity of a matter dominated (as opposed to an... | {
"language": "en",
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What exactly is the mass of a body? What determines it? The term "mass" is very common. But what does it depend on? How is it known?
| Since your tags are "newtonian-gravity" and "mass" I will attempt to answer this question in a classical framework. In classical mechanics, mass is essentially defined as a measure of an object's inertia.
Let me explain further. We have Newton's second law
$$F_\text{net}=ma$$
which is assumed to hold for all objects ... | {
"language": "en",
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Negative pressure How is negative pressure created in a fluid system?Isn't it counter intuitive that we are reducing the pressure of a system containing no molecules(zero pressure) to a lower value?
| 'Negative ' pressure is strictly a relative state; relative to what one may wish to define as zero pressure, and here on earth we chose to define that as one standard atmosphere of pressure which is about 760 mm Hg absolute pressure. If you are capable of removing all gas particles from a space, then you will achieve -... | {
"language": "en",
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Magnetic field and electric field induce one another forever A changing electric field produces magnetic field and vice versa. Does that mean that this process will carry on forever? Think of a circuit with a capacitor. The magnetic field due to the current at a point on the wire (by the Ampere-Maxwell law). But the cu... | The idea in the comments above is a good one. The reason you don't need to worry about the order is that you're looking for an equilibrium solution. In terms of going on forever, it's broadly true. I mean electro magnetic radiation is exactly the kind of effect you're talking about. In a circuit there is normally a dis... | {
"language": "en",
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Scalar and vector defined by transformation properties In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix $ \lambda $ .
Why is this important? I get that it leads to other... | Draw an arrow to represent a vector, with its length representing the vector magnitude. Draw a coordinate system and get the components of the vector. Now draw another coordinate basis, rotated with respect to the first, and get the components with respect to the new basis. The length of the arrow is the same in ... | {
"language": "en",
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Explanation for: A monopole antenna must contain a resistor (or equivalent) and therefore must have 2 terminals? Could someone explain why this sentence makes sense:
A monopole antenna transfers energy from electrical domain to the electromagnetic domain, hence must contain (equivalently) a resistor, hence must have ... |
Why must it contain a resistor
The author is most likely referring to the radiation resistance. A circuit delivers electrical energy to a resistor where it is converted to heat, i.e., the energy is not stored but is lost to the environment.
Analogously, a circuit delivers electrical energy to an antenna where it is ... | {
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Electron propagation
How can electrons travel in these beams if they repel?
|
How can electrons travel in these beams if they repel?
First of all, the picture you posted looks like lightning which is basically arcing, i.e., ionization of gas to create a conductive path. This is not what I would typically consider an "electron beam".
To answer you question: Creating and maintaining the integrit... | {
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Will the electrostatic force between two charges change if we place a metal plate between them? If a thin metal plate is placed between two charges $+q$ and $+q$, will this cause a change in the electrostatic force acting on one charge due to another? What is the concept behind this? What will happen if the metal plate... | According to the formula of electric force, the electric force will be zero if a metal plate is inserted between the two charges. The charges will not experience any force because it uses the same concept as that of the hollow charged sphere.
| {
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Coriolis force: why is pole-to-equator air flow eastly? I have little knowledge in fluid dynamics, so this may be naive. But I have a question while reading a textbook about the Coriolis force, by which the rotation of the earth from west to east changes the air circulation pattern.
The text states that
As a ring of ... | $R = r(\cos A\cos B,\,\cos A\sin B,\,\sin A)$ where $A$=latitude, $B$=longitude and $r$=Earth radius
Let
\begin{align}\frac{dB}{dt}&=\frac{2\pi}{24\,{\rm hours}} \\
\frac{dA}{dt}&=v/r\end{align}
mass $m$ moving due N with speed $v$.
Differentiate the vector $R$ twice with respect to time to find the acceleration that... | {
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How can the Schwarzschild radius of the universe be 13.7 billion light years? So i was reading about Schwarzschild radius on Wiki and I found a interesting thing written there link.
*
*It says that the S. radius of the universe is as big as the size of the universe?
*How is this possible?
*Since most the unive... | Firstly we should note that the universe as a whole is not described by the Schwarzschild metric, so the Schwarzschild radius of the universe is a meaningless concept. However if you take the mass of the observable universe you could ask what the Schwarzschild radius of a black hole of this mass is.
For a mass $M$ the ... | {
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Can gyroscope work in zero gravity? Most ships have two or more gyroscopes to balance on water, man made satellites uses gyroscope for orientation as they fall around earth. All these applications seems to be associated with gravity, therefore how can a gyroscope works in zero gravity?
|
man made satellites uses gyroscope for orientation as they fall around
earth. All these applications seem to be associated with gravity,
therefore how can a gyroscope work in zero gravity?
You are probably confusing or identifying the property of a gyroscope with the phenomenon of precession
The bicycle wheel (gy... | {
"language": "en",
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Beginners Textbooks in physics Hello I am fifteen and I already know everything that my school has been teaching me so I have been going ahead. I have already been studying mathematics far past where I am at school, but I am very interested in physics. I want to learn everything up to advanced topics such as super-st... | The textbook my school uses for my AP Physics 2 course is the fifth revised edition Giancoli textbook. Like you, I am reading ahead and trying to absorb as much information as possible. I am sure many high school physics books are a great starting place to go further in studying physics at your level, but do not forget... | {
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How do solar panels generate infinite electricity? We know that solar cells generate electricity utilizing the energy of the photon, but how can they generate electricity forever?
In a n-type terminal we have the bond of silicon and phosphorous so we have a free electron and when photons hit the panel they let the fr... | When photons from the Sun hit the crystallized silicon wafers in a solar panel, they energize electrons to become loose and make a complete trip around the closed circuit that include the solar collectors. So the solar panels do not lose electrons because they go out from one end and come back in from the other end
| {
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Spectral line formula Two years back my friend told me a simple formula for calculating the number of spectral lines. But, now I'm a bit confused about it
number of lines is =$ \frac{2(n-1)}{2}$ is this right or is there any error in it?
| You can derive it simply by noting that each level can have $n-1$ transitions,so we have
$n-1+n-2+...+1=n(n-1)/2$
| {
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Are there any scales other than temperature that have different zero points? For most physical measurements, zero is the same regardless of the units used for the measure:
$0 \mathrm{mi} = 0 \mathrm{km}$
$0 \mathrm{s} = 0 \mathrm{hr}$
but for absolute temperatures, different systems have different zeros:
$0 ^\circ\math... | Sound can be measured in deciBels ($\mathrm{dB}$) but also as an intensity measured in $\mathrm{W/m^2}$.
$0\,\mathrm{dB}$ on this scale is equal to $1\times10^{-12}\,\mathrm{W/m^2}$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/175153",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Prove Christoffel Symbol Identity In a book I am reading, the following identity is claimed and then "left to the reader to prove." $g_{ij}$ is the metric tensor, and $\Gamma$ is the Christoffel symbol of the second kind with the appropriate indices.
$$\partial_k g_{ij} = g_{jl}\Gamma^{l}_{ki}+g_{il}\Gamma^{l}_{kj}$$
I... | At the most basic level, you can just use the definition of the Christoffel symbols in terms of the metric:
$\Gamma^i_{jk} = \frac{1}{2}g^{is} (\partial_j g_{sk} + \partial_k g_{sj} - \partial_s g_{jk})$.
Plugging this into the right-hand side of your expression will yield the left-hand side.
However, one can obtain yo... | {
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Sun and planets orbit each other Do not the planets and the Sun revolve in orbits around each other and the shape of the orbit depends on where the center of gravity of the system is? The greater the mass of the Sun, the closer the orbit approximates a perfect circle.
| Yes, objects with mass all attract to each other and move each other of course, except that the star doesnt change it's theoretical orbital shape depending on it's mass, it probably just experiences small tidal forces that aren't much bigger than it's own centrifugal forces. The oscillation of the star position is a co... | {
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Path integral in quantum mechanics I am confused by the derivation in Srednicki QFT's chapter 6 from (6.8) to (6.9). In (6.8), we have
$$<q'',t''|q',t'>~=~\int DqDp \exp[i\int_{t'}^{t''}dt(p\dot{q}-H(p,q))],\tag{6.8}$$
and (6.9) we have
$$<q'',t''|q',t'>=\int Dq \exp[i\int_{t'}^{t''}dt L(\dot{q},q)].\tag{6.9}$$
It is... | I did not get my copy of Srednicki out but from what you have written...
Srednicki is referencing the method of steepest descent. Although these notes look to be better than wikipedia. Another page that is directly applicable to the quantum field theory case is here.
In short, exponential integrals may be estimated b... | {
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Neutral $K$ and $B$ mesons decay to 2 photons? The neutral pion $\pi^0$ decays almost exclusively to 2 photons, $\pi^0 \rightarrow \gamma \gamma$,
which got me thinking:
Can we have $K^0 \rightarrow \gamma \gamma$ and $B^0 \rightarrow \gamma \gamma$ or are they forbidden for some reason?
| They are both allowed, but they are flavor-changing neutral currents that are loop-supressed. The $B^0\to\gamma\gamma$ decay occurs by the Feynman diagrams from arXiv:1010.2229 and I imagine that kaon decay proceeds similarly.
They are so suppressed that the $B^0$ decay hasn't been measured, but PDG report an upper b... | {
"language": "en",
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What does it mean that a magnetic field's flux vanishes through any closed surface? I'm reading the Britannica guide to Electricity and Magnetism, and I came across the following quote:
A fundamental property of a magnetic field is that its flux through
any closed surface vanishes.
Can someone explain this in simpl... | There are no magnetic monopoles. i.e. Unlike electric field flux, there are no sources or sinks of magnetic flux.
Therefore the amount of flux entering any closed volume must equal the amount exiting.
| {
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Ways for undergrad to understand physics research? I am a college freshman who is looking to research in a experimental physics lab this year. I am an engineering student and have taken basic Physics classes, but I lack the background knowledge to fully understand what is going on with the topics this lab is researchin... | Wikipedia does a pretty good job at explaining the basics of this, in my opinion. Looking at review papers are very good for this and so are the papers(you can find the papers on sites like Pubmed and APS Journals). Just because the review papers are from the 80s, does not mean they are bad. Even if a tiny fraction of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/175779",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the capacitance and inductance of an ideal wire? I am reading a magazine for acoustics, one article is about the choice of speaker wire. The article said the ideal speaker wire should has no resistance, capacitance and inductance. I understand that for the low resistance in ideal case but doubts on the capacita... | This would actually be easier to answer over at the EE stackexchange site since there is a handy schematic editor built in.
First, note that, by speaker wire, we're actually referring to a speaker cable; in this case, a pair of wires.
For each wire, we can assign a series resistance and inductance (per foot), i.e., the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/175876",
"timestamp": "2023-03-29T00:00:00",
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Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip? I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance.
Am I correct?
Veritasium/Minutephysics video on... | No. The weight of the pencil is roughly 1 Newton, and the area is about 500 square picometer (5 * 10-22) which means the pressure on the tip is around 2 ZettaPascal. That's quite a bit more than what graphite (or diamond) can withstand (that's measured in GigaPascal)
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "96",
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Why do we use capacitors when batteries can very well store charges? Can batteries be used instead of capacitors? I am trying to figure out a basic, superficial and any obvious difference between the two.
| batteries are a much more efficient at storing electricity but in circuits, it makes much more sense to use capacitors in circuits as they are much more efficient for the short term storage of electricity. batteries are a lot more bulky and to work as a capacitor they would need to be rechargeable. it would not make se... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/176050",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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General Relativity visualization software As I am approaching the study GR, I was wondering if there are softwares that allow a quick visualization of custom metrics, curvature, and particle motion even in the limited context of 2D space.
Playing with equations is fun, but it would be more fun if I could play with var... | For particle/light motion in 2D space, my nomination would be GROrbits
It's free and requires a JVM to run, there is also a web start version for the brave ;)
Sorry but I've never found anything aimed at visualizing metrics or curvature (apart from plotting programs of course).
| {
"language": "en",
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Is there any physical meaning for the inverse metric? I've been wondering if we can attribute any physical meaning to the inverse metric. I mean when we talk about the metric itself, there are lots of insights we can have towards its role in spacetime, yet I cannot see any physical meaning for the inverse metric. For n... | The tensor algebra is symmetric between one-forms and vectors. One could start with defining any of them first and then obtain the rest of the things.
The inverse metric tensor is a linear map that takes two one forms on a manifold and maps into $\mathbb{R}.$
$g^{\mu \nu}: A_\mu,B_\nu \rightarrow \mathbb{R}$
It of cou... | {
"language": "en",
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Why stars are white? According to Rayleigh Scattering According to Rayleigh Scattering, the red waves are capable of travelling a long distance, so that only we are seeing the Sun as reddish during Sunset and Sunrise. If this was true then all other stars must also appear red in colour, as the distance through the atm... | The colour of stars as observed by an observer on Earth varies just like the colour of our own Sun, depending on where in the sky the source is relative to the observer.
However, the light of stars is generally too faint to notice this as clearly with the naked eye, because we cannot perceive colour for weak light sour... | {
"language": "en",
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Considering this hypothesis...is charge really quantized? [If anything goes against any mathematical or physical rules please let me know. I am a first year undergraduate student perusing a joint major in mathematics and physics so I do not have a complete background in those fields. I am just using my imagination and ... | The electron is an elementary particle in the underlying building blocks of matter organized in the elementary particles table of the standard model of particle physics. Elementary particles are point particles.
The standard model is a precis of a very large number of measurements (data) fitted by mathematical models ... | {
"language": "en",
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Why is the singularity of the Big Bang not considered to be the center of the Universe? If the universe is expanding, then at some time in the past, it must have started from a single point but why this point is not the center of the Universe. Just like the singularity of black holes is its center?
| I'll answer your question with an analogy. Imagine a really small balloon, so small that it occupies a point. Now, imagine that the balloon is expanding uniformly outward from that point. Note that that central point is not part of the balloon. It's the same idea as to what happened with the BB. In this analogy, the un... | {
"language": "en",
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How does temperature relate to the kinetic energy of molecules? In ideal gas model, temperature is the measure of average kinetic energy of the gas molecules. If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becomes hotter? Do we need t... |
In ideal gas model, temperature is the measure of average kinetic energy of the gas molecules.
In the kinetic theory of gases random motion is assumed before deriving anything.
If by some means the gas particles are accelerated to a very high speed in one direction, KE certainly increased, can we say the gas becom... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/177038",
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How do we know that the cesium-beam frequency used in atomic clocks is always the same? Atomic clocks use cesium-beam frequency to determine the length of a second. This has shown that the period of orbit of the earth is decreasing.
But what experiment showed that cesium-beam's period was so terribly consistent?
Did th... | The frequency is determined by the energy spacing between two configurations of the caesium atom. Caesium has a single electron in the outermost $6s$ orbital, and this electron can be aligned with or against the nuclear spin. These two configurations differ in energy by about 0.000038 eV, and transitions between them p... | {
"language": "en",
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Entropy - Gas Inside A Closed System Reaches Maximum Entropy Filling a box with a certain amount of gas with a specific total energy and allowing the gas to reach a maximum entropy state, what happens next?
Would the gas remain in a maximum entropy state indefinitely?
What would prevent the gas atoms/molecules to end u... | The second law of thermodynamics says that the entropy of an isolated system can increase, but that entropy can not decrease without the addition of energy to the system, or the transfer of entropy to another system.
Increasing entropy has been associated with the arrow of time, as entropy seems to be the only quantity... | {
"language": "en",
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Why doesn't a magnet on a refrigerator slide down? Obviously gravity pulls objects towards the earth's surface. Now suppose I have a refrigerator and a magnet. The magnetic force is perpendicular to the gravitational force. So it is not counteracting it. So why does the magnet not get pulled to the ground since no othe... | As you may know, the friction is proportional to the normal force of an object or in this case the force of attraction between magnet and refrigerator.
If your force is strong enough then the friction will be sufficient and the magnet will not slip (on earth the force of friction must exceed the mass of your magnet mu... | {
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Since electron clouds of different atoms repel each other, does that mean that touch is the feeling of electromagnetic repulsion? Also when we rest our hand on an object does that mean we are effectively levitating because of the repulsion of the electron clouds?
| Yes ... but let's be careful to understand that the sensation of touch is a psychophysical phenomenon. The electrons at the surface of an object "push" against the electrons at the surface of your fingers. The electrons never touch each other. Your skin deforms a bit, and the nerves in your fingers detect this defor... | {
"language": "en",
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What is the position as a function of time for a mass falling down a cycloid curve? In the brachistochrone problem and in the tautochrone problem it is easy to see that a cycloid is the curve that satisfies both problems.
If we consider $x$ the horizontal axis and $y$ the vertical axis, then the parametric equations fo... |
1. Brachistochrone
\begin{equation}
\boxed{\:
\begin{matrix}
x\left(\theta\right) = R\left(\theta-\sin \theta\right)\\
y\left(\theta\right) = R\left( 1-\cos \theta\right)
\end{matrix}\:}
\tag{b-01}
\end{equation}
\begin{equation}
\omega= \dfrac{\,\theta \,}{t}=\dfrac{\mathrm{d}\theta }{\mathrm{d} t}=\sqrt{\dfrac{\,g\... | {
"language": "en",
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Why performing axial symmetry, results in the same masses for pion and sigma mesons? Under axial transformations, $\sigma$ and $\pi$ are rotated into each other:
$\vec{\pi} \rightarrow \vec{\pi}+ \vec{\theta} \sigma $,
$\sigma \rightarrow \sigma+ \vec{\theta}.\vec{\pi} $.
In arXiv:nucl-th/9706075, page 12, it is the ... | The mass terms for the $ \sigma $ and $ \vec{ \pi } $ fields are,
\begin{equation}
m _\sigma \sigma \sigma + m _\pi \vec{ \pi } \cdot \vec{ \pi }
\end{equation}
You have two terms that are going to turn into each other under a symmetry transformation. Thus they need to have the same coefficient in order to remain i... | {
"language": "en",
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How can the speed of sound increase with an increase in temperature? I was reading a textbook. I found that it was mentioned the speed of sound increases with increase in temperature. But sound is a mechanical wave, and it travels faster when molecules are closer.
But an increase in temperature will draw molecules awa... | Sound waves propagate through a medium as the result of collisions between molecules. At higher temperatures, molecules have greater kinetic energy, and as they move faster their collisions occur at greater frequency and they carry sound waves faster. Greater kinetic energy = less inertia = increased speed.
However, ... | {
"language": "en",
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Why can't we use a pair of polarizers (whose pass axis are oriented at 90 degrees) to protect from entry of harmful radiation? If a pair of polarizers can block EM waves passing through it, then can we use them for
*
*protecting against harmful radiation (in nuclear reactors and also in spaceships)
*in thermo fla... | A polariser is quite good at blocking EM radiation, but not perfect.
No polariser is perfect, and does not block 100% of the radiation. This is typically specifed in terms of the extinction ratio. The best laboratory grade polarisers have extincition ratios of the order 100000:1 [1].
Such good polarisers are only possi... | {
"language": "en",
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Units of eigenvectors Consider for example a mass matrix $M$, $\lambda$ one eigenvalue and $X$ a corresponding eigenvector. Then $[M]=\text{mass}$ (the brackets indicate the "unit operator"), and $MX=\lambda X$ so $[M][X]=[\lambda][X]$, so $[\lambda]=\text{mass}$. That's why for example in oscillators, the pulsations ... | Not just with eigenvectors, but with any vector.
I always wondered when you decompose any vector into magnitude and direction who gets the units. Is it $(1,0.1,0)\cdot3\mathrm{m}$ or $3\cdot(1\,\mathrm{m}, 10\,\mathrm{cm},0)$ ?
I think it is up to the user to interpret a decomposition any way they see fit.
With eigen v... | {
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How come the length of a wire does not affects on the circuit current? Today we started learning about the electromagnetic induction. Out teacher gave us the following explanation:
Suppose we have a conduction frame inside a magnetic field $\vec{B}$ going towards the page. That frame has a stationary edge (also a condu... | Right, but you are not getting something for nothing. What about the energy losses? These scale as $I^2 R$ and so does depend on the length (and area) of the wire.
$$ W = I^2 R = \frac{v^2 B^2 A^2}{\rho^2} \frac{\rho d}{A} = \frac{v^2 B^2 A d}{\rho}$$
| {
"language": "en",
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How does electromagnetic radiation affect the velocity of a charged particle? I've heard that the acceleration of a charged particle releases electromagnetic waves. So let's say there is a charged electron moving forwards in a region with a downwards magnetic field. If the magnetic field is a certain strength, it shoul... | It will decelerate causing its speed to decrease, and because of $r=mv/qB$ the radius will decrease as well and you will get a spiral motion.
This deceleration due to radiation is known as the Abraham-Lorentz force of radiation backreation. Using these equations you can more precisely derive the spiral motion. This eff... | {
"language": "en",
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Can electricity flow through vacuum? People say yes, and give a wonderful example of vacuum tubes, CRTs. But can we really say that vacuum (..as in space) is a good conductor of electricity in a very basic sense?
| Summary: (?) A vacuum is the absence of atmosphere and is a neutral force--offering neither resistance nor conduciveness to proton/electron flow. The state of "vacuum" does not compare with the state of "space". Any/all space is a physical measure of distance and can be overcome by the optimal difference of potential.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Making sense out of covariance and contravariance I just read about co- and contravariant vectors and I am not sure that I got it right:
If we imagine that we have a n-dimensional manifold $M$ then a tangent space is spanned by the vectors $\partial_1,...,\partial_n.$ These guys transform from one coordinate system to ... | Basically, vectors are called contravariant because their components transform oppositely to the basis vectors: if our change of coordinates is such that
$$ \frac{\partial}{\partial x^i} = \frac{\partial y^j}{\partial x^i} \frac{\partial}{\partial y^j}$$
then if we have a vector $\mathbf{V}$, its components $V^i_x$ in ... | {
"language": "en",
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Why do spatial filters use microscope objectives, and not other types of lenses? A spatial filter is a device to 'clean up' a laser beam with an irregular intensity profile, and create a smooth Gaussian profile at the output.
It is usually said (e.g. here) that you need a microscope objective and a pinhole for this. Th... | Yes, that is a good answer. Microscope objectives are relatively cheap and well corrected on axis to provide a nice Airy pattern at the image. The pinhole usually sized so its diameter is the same as the first dark ring of the Airy pattern will provide a very clean beam when aligned properly. Also microscope objectives... | {
"language": "en",
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Paramagnetic/ferromagnetic transition under a magnetic field The paramagnetic/ferromagnetic phase transition is an archetypal example of a continuous (or second-order) phase transition. When the temperature $T$ approaches the Curie temperature $T_c$, the magnetization $M(T)$, which is the order parameter of the transit... | The Landau model for ferromagnetism has the following expression for the free energy density, as a function of temperature $T$ and magnetization $M$:
$$F(T,M)=F_0(T)+\dfrac{a}{2}(T-T_C)M^2+\dfrac{b}{4}M^4+\dfrac{c}{6}M^6+\mathcal{O}(M^6)$$
First order phase transition occurs when the first derivative of $F$ (namely, th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/179144",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Rotation in the x-t plane I am currently studying special relativity using tensors. My lecture notes (which happen to be publicly accessible, see top of page 99) say that the standard configuration can be viewed as a rotation in the x-t plane. Can anyone explain this a bit? Is there a good way to visualize it?
The Stan... | Bernhard Schutz discusses this reasonably well in his book A First Course in General Relativity.
Consider sending a light beam horizontally along an $x$ axis and then receiving it back again. A space time plot of this would look like
Here's an example of the rotation you are describing
And this is how everything be... | {
"language": "en",
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Do the same equations of motion imply the same Lagrangians? If two Lagrangian (densities) $\mathcal{L}$ give the same equations of motion, are they equivalent?
| If by 'equivalent' you mean equal, then no. They can clearly differ by a constant, but they moreover can differ by a total time derivative. So if two lagrangians $L_{1}$ and $L_{2}$ are such that $L_{1} - L_{2} = \frac{\mathrm{d} \Phi}{\mathrm{d}t}$ for some function $\Phi$, then they lead to the same equations of moti... | {
"language": "en",
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"Hollow Earth" like Theories for pedagogical porpuses I recently encountered the Hollow Earth theory, and I realize that This kind of theories can be used to give a really interesting discussion of a physical law.
For example, If we take the hypothesis that the earth is hollow and if we ignore the border effects of th... | Due to the rotation of the Earth, "inner-Earth-dwellers" would feel a fictitious centrifugal force pointing away from the axis of rotation. Ask your students how strong that force would appear to be.
Once they realize it's a very weak force indeed, ask them to determine how fast the Earth would be spinning to give inn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/180719",
"timestamp": "2023-03-29T00:00:00",
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Angular Momentum Expectation Values in Spherical Coordinates I have a homework problem that asks:
Using the spherical harmonics calculate $\langle J_x \rangle$, $\langle J_y \rangle$, $\langle J_z \rangle$ in the state $|l,m\rangle$. Use the derivative forms of the $J_{i}$ in spherical coordinates.
I'm not looking fo... | You have to compute $\int d\Omega\ Y_{lm}^*(\theta,\phi)\hat{J}_iY_{lm}(\theta,\phi)$ where $d\Omega=\sin\theta d\theta d\phi$, $J_i$ are the angular momenta operators represented in position space and $Y_{lm}$ are the wavefunctions for the state $|lm\rangle$, i.e. spherical harmonics.
| {
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"source": "stackexchange",
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Derivation of the energy-momentum tensor for an imperfect fluid In chapter 7 of the "Physical Foundations of Cosmology" Mukhanov uses this energy-momentum tensor for an imperfect fluid:
$$T^\mu_\nu = (\rho + p)u^\mu u_\nu - p\delta^\mu_\nu - \eta(P^\mu_\gamma u^{;\gamma}_\nu+P^\gamma_\nu u^\mu_{;\gamma}-\frac{2}{3}P^\m... | Here is a sketch of where it comes from. First just consider the perfect fluid terms and note the thermodynamic relation
$$
\rho + p = \mu n + T s,
$$
where $T$ and $s$ are temperature and entropy, $\mu$ and $n$ are a chemical potential and number density.
We also have a relation for derivatives of $p$
$$
dp = n d\mu +... | {
"language": "en",
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Normalizing a wave function in a mixed well So I got this potential and want to solve for the even wavefunctions
Since it's symmetric around the origin I need only to look at the interval $[0,b]$ and solve for the wavefunction there. The energy is lower than $V_0$ so I will get exponentials in $[a,b]$ and sine and cos... | Assuming you've done the algebra correctly, these equations can be solved for a relationship between $k$ and $K$, which should lead to the quantization of energy levels in terms of $a$, $b$, and $V_o$. Then you solve for $C$ in terms of $A$ from either equation (you MUST get the same result with either) and then normal... | {
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Conceptual explanation of the Single particle partition function The Single particle partition function is defined mathematically as
$$\text{Z=$\sum $}g_ie^{\left(\frac{-E_i}{K_BT}\right)}$$
But what is the physical interpretation of the partition function and it's significance to Thermodynamics? I'm seeking a simple y... |
But what is the physical interpretation of the partition function and
it's significance to Thermodynamics? I'm seeking a simple yet
understandable intuition.
The partition function has one simple physical interpretation in terms of Thermodynamic functions: Its natural log is proportional to the Free Energy (the p... | {
"language": "en",
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What's the differences between time in Physics and time in everyday use? OK. This question might sound as not a good question, but the word 'time' is so confusing to me. I mean thermodynamics says time is the product of entropy. Relativity says time is relative. Quantum Mechanics says time doesn't exist, and that we ca... | In everyday (or casual) use "time" is often (mis-)taken to mean
*
*duration, or
*a coordinate assignment to indications or entire events ("coordinate time").
In contrast, the current, correct and careful meaning of "time" in Physics is based on Einstein's definition of "time" as "the position of the little hand of ... | {
"language": "en",
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Is there a rotational equivalent to newtons laws? Newtons three laws of motion appears to apply only for linear motion:
*
*An object remains at rest or moves in a straight line at uniform velocity unless a force is applied.
*Force is mass times acceleration.
*Every action causes an equal and opposite reaction.
... | There is a rotational equivalence, but it is not what you stated. The problem, as pointed out by @curiousOne, is that conservation of angular momentum does NOT imply rotation about the same (fixed) axis. But I think a simple restatement like this could work:
*
*if no torque acts on a body, its angular momentum will ... | {
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Correct vector space of eigenkets of angular momentum When we say an particle is in the state:
\begin{equation}
|l,m\rangle,
\end{equation}
what is the underlying state space, as a vector space? Is it a tensor product vector space, of dimension:
\begin{equation}
l\times(2l+1)\ ?
\end{equation}
How can I find the matri... | My understanding of this limited, but this might help (too long for a comment):
The state space is spanned by the set of simultaneous eigenstates of the Hamiltonian, $ \hat L^2$, and $ L_z $. In fact, they form an orthonormal basis of a Hilbert space $ H $ which is the state space.
Out of convenience, we denote the eig... | {
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How to measure temperature of a laser cooled sample at picoKelvin temperatures? I'm reading about laser cooling.. my question is: how can the temperature of the sample be measured? (using laser cooling we can reach $10^{-12}K...)$
| I hope someone with more knowledge will pop into thread, but here is my education. There might be number of ways to measure such low temperatures. One I find fascinating is starting with material, namely Bose-Einstein condensate. Reference is this one: Cooling Bose-Einstein Condensates Below 500 Picokelvin, Leanhardt e... | {
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Feynman rules for gauge bosons and Goldstone bosons Does anyone know where I can find:
*
*gauge boson propagators (in an unfixed gauge) for the unphysical
Electroweak gauge bosons $A^1_\mu$, $A^2_\mu$, $A^3_\mu$ and
$A^4_\mu$ whose combinations give the physical $W^+_\mu$, $W^-_\mu$,
$A_\mu$ and $Z_\mu$? (With the f... | For anyone interested, I found a good document with all Feynman rules and different notations:
http://arxiv.org/abs/1209.6213
| {
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Does friction act on a wheel rolling at a constant speed One of the things I've seemed to have taken for granted is that its the friction the floor exerts on a rolling wheel that prevents slip from occurring.
However, I ran into something that challenges that assumption: the contact point of the wheel on the floor has ... | There might be normal friction acting on the rolling wheel, namely static friction. The static friction force, $F_f$, is often written as,
$$
F_f \leq \mu_s F_n,
$$
where $\mu_s$ is the coefficient of static friction and $F_n$ the normal force, in this case the weight of the wheel.
Note the less-than-or-equal-to sign. ... | {
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Sub-structure of hyperfine levels In studying introductory atomic physics I have come across fine structure splittings in energy levels due to spin-orbit coupling. Which has a sub-structure called hyperfine structure which comes from a coupling of the nuclear spin and the total angular momentum.
My question is, is ther... | As a matter of fact the list of the corrections to the hydrogen atom goes on and on. This is a list of corrections to the hydrogen atom and their order of magnitude for comparison.
*
*Bohr energy, which is very rough version of the hydrogen atom $\sim\alpha^2m_ec^2$
*Spin orbit coupling (AKA Fine structure of hydro... | {
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If the electrostatic potential is zero, why doesn't the electric field have to be zero? I thought the relation between the electrostatic field $\vec E$ and the electrostatic potential $V$ is as follows:
$$\vec E = - \nabla V$$
Thus, when $V$ is zero, $\vec E$ is also zero.
| It depends on what you mean when you say $V=0$. In the context of the equation:
$$\vec{E}=-\nabla V$$
which holds specifically in electrostatics $V$ is a scalar field, meaning that it is actually a function which assigns every point in space a scalar value. $\vec{E}$ is a vector field, which assigns a vector to every p... | {
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Weight distributions If a man is standing on two weighing machines (scales), with one foot on each, Will both machines show equal weight or his weight will be distributed in two machines?
|
$N_1$ the reading of force on the first weighing machine
$N_2$ the reading of force on the second weighing machine
$X_1$ the horizontal displacement of first leg from COM
$X_2$ the horizontal displacement of second leg from COM
we know that the man is in equilibrium. so
the weights shown on both meters will have thei... | {
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Is Interpretation of state vectors and density matrices according to Frequentist or Bayesian interpretation of probability? I asked a question on math stack exchange what does probability mean. I did not know about Frequentist and Bayesian interpretation of probability previously. So according to which interpretation a... | It's pretty hard to be Bayesian about quantum mechanics without believing in some sort of underlying hidden-variable theory. Such theories are highly unpopular in modern culture (not to mention experimentally falsified in the majority of cases) and so the overwhelming interpretation amongst physicists is an operational... | {
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Took a picture of my laptop screen with my iPhone. The yellowish pattern in the image look like magnetic lines. How is this possible? The pattern seems consistent with the magnetic force lines of a bar magnet.
| That looks like a Moire pattern to me. You have a camera with a grid of pixels on the imaging element and a screen with a grid of (colored) pixels. These elements don't line up exactly, so you get the odd patterns.
Try taking another image with the camera slightly twisted along the lens axis or slightly angle the l... | {
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4 dimensional interpretation Has it ever been hypothetized that, in a 4 dimensional space, being time the 4th D, one body could travel through the dimensions at the combined speed of $c$?
If a body is at rest in the classical 3 dimension, it would travel through time at $c$, but if traveling at $c$ in space, it would b... | As it happens, you are absolutely correct.
The velocities we encounter in everyday life are 3D velocities that are vectors defined as:
$$ \vec{v} = \left(\frac{dx}{dt}, \frac{dy}{dt}, \frac{dz}{dt}\right) $$
In special relativity we use a 4D velocity called the four-velocity, and this is a four-vector defined as:
$$ \v... | {
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Question about ohmic conductors I'm having some trouble understanding Ohm's law. My trouble is with the different ways it is described when referring to ohmic and non-ohmic conductors. If someone can answer this question I think it will clear up my doubts. (I made up this question myself -- it's not homework!)
Which on... | Ohm's law assumes the temperature remains constant.
An Ohmic conductor is one in which the current flowing through it is proportional to the voltage applied across it.
A non-ohmic conductor is one in which the voltage and current are not linear.
A) The resistance of most conductors increases as the temperature increas... | {
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What is the magnetic flux density "outside" the solenoid when AC current is passing through it? I know that there are well defined equations explaining the magnetic flux density in the solenoid.
However what about magnetic field outside the solenoid?
How is the magnetic flux density related with the current?
UPDATE : S... | Approximately zero for a solenoid of infinite length. As far as the magnetic field goes, nothing changes from the situation of a direct current passing through the solenoid. The magnetic flux is homogenous inside, and the magnetic flux outside is approximately zero (it's the same magnetic field as inside the solenoid b... | {
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Two objects with mass m with charge q connected to spring I am taking Physics 201 on Yale Open Courses. I having trouble with the 5th problem in the problem set 1, which says as follows:
Two sphere of mass m and negligible size are connected to two identical springs of force constant k as shown in Figure 1. The separa... | For part (i), the separation doubles when the charges are +q each.
The force at that moment is
$$F = \frac{q^2}{4\pi \epsilon_0 (2a)^2}$$
Now they are connected to two identical springs (not shown, I imagine these go to "opposite walls") meaning that each spring will be compressed by $\frac{a}{2}$.
It follows that
$$k\... | {
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Feasible way to cool water (ice) to temperatures around -20 degree celsius Is there an easy way to cool water to temperatures around -20 or -30 degree celsius that is economically and technologically feasible for a high school student. Can it be done using typical household equipments? Thanks :)
| Some domestic, commercially marketed deep freezers are able to reach that range of temperature. Here is one for example that advertises -20deg F, so almost -30 deg C.
It really depends also on the amount of mass you want to lower the temperature to. Whatever device to be considered must provide outward heat flow to co... | {
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Bending moment of a cantilever beam The following procedure is here.
Consider a cantilever fixed at one end and loaded at the other one. In cartesian coordinates (if $y$ is horizontal and $x$ vertical, meaning that the load acts parallel to the $x$ axis) the equation of the curvature is:
$$\frac{\frac{d^2x}{dy^2}}{\lef... | Generally speaking, Young's modulus is measured in terms of Gigapascals, or $10^9$ Pascals, or at least Megapascals, or $10^6$ Pascals. Hence, your answer should be fine. Here is a table with Young's modulus values for day to day materials. Notice how $E$ is measured in Gigapascals.
| {
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Is it possible to write the fermionic quantum harmonic oscillator using $P$ and $X$? The Hamiltonian of the quantum harmonic oscillator is
$$\mathcal{H}=\frac{P^2}{2m}+\frac{1}{2}m\omega^2X^2$$
and we can define creation and annihilation operators
$$b=\sqrt{\frac{m\omega}{2\hbar}}(X+\frac{i}{\omega}P)\qquad{}b^{\dagger... | Fermions are strange beasts in many ways. The first problem you will encounter, and which will make it impossible to write an harmonic oscillator for fermions is the following:
The fermion ladder operators $f$ and $f^\dagger$ require that $\{f,f^\dagger\}=1$. Translated to $X$ and $P$ this means that $\{X,P\}=i\hbar$. ... | {
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A general relativity question about the Einstein equations? Assuming a Robertson-Walker metric to describe homogeneous and isotropic cosmological models, Einstein equations with cosmological constant reduce to these 3 non-linear ordinary differential equations for a perfect fluid:
\begin{align}
\dot{\rho} &= -3H(\rho +... | If what you want a gut-feeling of what these equations mean, I can share mine.
Equation (2) is a consequence of the two others. Take the time-derivative of (3), remembering that K and $\lambda$ are constants and $H=\dot a/a$, combine this derivative with (1) and (3) and you get (2). So no gut-feeling for that one, jus... | {
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Does Time change over temperature? I am not a physicist, I am just an engineer.
But I dared to ask whether the temperature changes the perception of time.
Let's consider a particle that "stops" at absolute zero. I was thinking as a hypothesis, that our perception of time changes and the particle actually does not stop... | If everything were at zero temperature you probably* would not be able to distinguish between the past and future. Mathematically time would still exist, in the same way that spatial directions still exist on a completely featureless plane, but since it would not be measurable (even if there were something around that ... | {
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Phase added on reflection at a beam splitter? If we have light of a particular phase that is incident on a beam splitter, I assume the transmitted beam undergoes no phase change. But I thought that the reflected beam would undergo a phase change of $\pi$. I have, however, read that it undergoes a phase change of $\pi/2... | https://arxiv.org/abs/1509.00393
The answer is $\pi/2$. Interestingly, it doesn't matter if it is plus or minus $\pi/2$ or if the phase change is in transmission or reflection in analysis of quantum or classical interferometry.
From the above referenced article:
"Quantum optics essentially provides black-box models o... | {
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How can tangential acceleration from a radial force be explained? A mass is attached to a rope, and put into a circular motion. If I pull the string from the center, the tangential speed of the mass will increase (by conservation of angular momentum).
I am applying a force only in the radial direction, so how can the ... | No. The easiest way to see this without invoking rotating reference frames is to write out Newton's Law's in polar coordinates, which work out to be:
\begin{align*}
F_r &= m \ddot{r} - m r \dot{\phi}^2 \\
F_\phi &= m r \ddot{\phi} + 2 m \dot{r} \dot{\phi}
\end{align*}
From these, it's pretty easy to see that if we ha... | {
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What is the curve described by the water of a wet spinning tennis ball? I'm looking at this picture
from this site and I'm curious about what is the curve described by the water. The involutes
$$x=r\left[\cos(\theta+n)+\theta\sin(\theta+n)\right]\\
y=r\left[\sin(\theta+n)-\theta\cos(\theta+n)\right]$$ for different $... | I think you are right. (Involute spiral: Wikipedia)
If you take a string wound around a stationary ball and unwind it, its end traces an involute spiral.
Similarly, if the ball is rotating and the string runs out in one direction, it is the same curve with respect to the ball.
A drop of water leaving the surface of the... | {
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Density of states of 3D harmonic oscillator Consider the following passage, via this image:
5.3.1 Density of states
Almost all of the spin-polarized fermionic atoms that have been cooled to ultralow temperatures have been trapped by magnetic fields or focused laser beams. The confining potentials are generally 3D harm... | we only need to separate the energies
$$\epsilon_i = \hbar \omega_i n_i$$
then
$$\epsilon^2 =\epsilon_x^2 + \epsilon_y^2 + \epsilon_z^2 = \left(\hbar \omega_x n_x\right)^2 + \left(\hbar \omega_y n_y\right)^2 + \left(\hbar \omega_z n_z\right)^2$$.
we can make it better into
$$\epsilon^2 = \hbar^2 \left(\omega_x^2 n_x^2 ... | {
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Why does the water bottle not rotate when it is half full? Consider this water bottle:
When it is full and thrown up in the air, it rotates at a constant velocity.
When it is less than 1/8th full, the water bottle rotates even faster than when it was full.
When it is half full, however, the water bottle rotates for o... | i dont know if anyone cares yet, but i had this topic more or less at a physicist tournament:
The thing is: once u start rotating the bottle (for the somersault) the center of mass lays a few cm (depending on the bottle) under the waterlevel...therefore the water above (we know it cuz rotations happen aroung the center... | {
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Electron-Positron Annihilation: How is charge conserved at the verticies? How is reaction possible? The verticies do not conserve charge. Also, why is the arrow for the positron pointing downwards when as time increases, the positron should move towards its vertex?
Sorry, I just a bit all confused about this diagram a... | It is the way one reads/writes Feynman diagrams, a particle going backwards in time is the antiparticle. The electron radiates a gamma, and continues to meet the positron , annihilating charge with another photon. Two real particles are needed for momentum conservation in the center of mass, and two photon vertices are... | {
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The central density of a nucleus remains roughly constant? Let A be the atomic number
The density of a nucleus is computed using the ratio of the number of protons and neutrons, A, to the volume of the nucleus (which at my current level, is assumed to be a sphere)
The math is trivial.
Conceptually, the argument for the... | If you were to imagine each nucleon as a hard sphere, then the packed volume of such a sphere will be proportional to the number of nucleons and the sphere will have the same mean density, regardless of the number of nucleons.
Think about the forces experienced by one of these "hard spheres". It feels a strong force fr... | {
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Physical reason behind having greater amplitude when driving frequency$ < $ natural frequency than that when driving frequency $>$ natural frequency This is quoted from A.P.French's Vibrations & Waves:
If the driving force is of low frequency relative to the natural frequency, we would expect the particle to move ess... | This is just a footnote to Name's answer (which you should accept because it's correct) to give a slightly more intuition based argument.
If the driving force changes slowly compared to the natural frequency of the system then the system can move fast enough to stay in phase with the driving force. So most of the time ... | {
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Why do electric sparks appear blue/purple? Electric sparks tend to appear blue or purple or white in color. Why?
| The answer is that electrical excitation of air molecules is able to produce lots of excited singly ionised nitrogen ions.
The electronic structure of singly ionised nitrogen has a number of allowed radiative transitions, where the outer excited valence electrons can rearrange themselves into lower energy configuration... | {
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How much is if my internet provider says "we have increased your WiFi connection by 2 decibels"? I understand the definition of decibel as a logarithmic unit for intensity of anything. I just cannot imagine its "actual size" when comes to the wireless connection.
Can you provide something illustrative which would help ... | Let me assume your internet speed is the power of the router, divided by the square of the distance from the router (as the signal is spread over the surface of a sphere with area $4\pi r^2$).
$$
\text{speed} \propto \frac{P}{r^2}
$$
Your power increased by $2\,\text{db}$ - this means a fractional increase of $(10^{1/1... | {
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Quality Factor in a Parallel LC Circuit I was wondering if there is a notion of a quality factor in a parallel LC circuit, since there is no resistance.
One can show that this circuit has a resonance frequency as follows:
Impedance:
\begin{equation}
\frac{1}{Z_{parallel}}=\frac{1}{Z_{C}}+\frac{1}{Z_{L}}=\frac{1}{\frac{... |
since there is no resistance.
That's not quite correct; in fact, there is infinite parallel resistance or, better, zero parallel conductance.
Recall that, for a parallel RLC circuit, the circuit elements are parallel connected. If the parallel resistance were zero, the Q would be zero since the resistance is effecti... | {
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Bifurcate Killing Horizon of the Ads-Schwarzschild solution I need your help.
I'm considering the AdS-Schwarzschild solution:
$ds^2=V(r)dt^2 + \frac{1}{V(r)}dr^2+r^2dΩ^2$
where $V(r)=1-\frac{2m}{r}+\frac{r^2}{l^2}$ with $m$ the mass of the black hole and $l$ the radius of the AdS spacetime.
Now, given $r=r_+$ one of th... | A bifurcate Killing horizon is a killing horizon in which the past and future horizons intersect at a point in the Penrose diagram, which is the bifurcation two-sphere. At this point, the generator of the horizon vanishes, which is to say $\xi = 0$ as opposed to being simply null.
In order to show that this is the cas... | {
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Two people are holding either end of a couch, is one person exerting more force than the other? I was carrying a couch with my flatmate yesterday, and I started thinking about this.
Often when carrying objects like this, one person will be taller and has thus lifted his end of the couch higher than the other person's. ... | I believe the following diagram tells you everything you need to know: when the center of mass is above the support point, then the lower point will carry more of the weight since it is acting closer to the center of mass ($x_1 < x_2$) and torque balance requires that $F_1 x_1 = F_2 x_2$. Conversely, if the center of m... | {
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What is the physical interpretation of second quantization? One way that second quantization is motivated in an introductory text (QFT, Schwartz) is:
*
*The general solution to a Lorentz-invariant field equation is an integral over plane waves (Fourier decomposition of the field).
*Each term of the plane wave satis... | The term is practical, but in reality, there is only one quantization.
This was to stretch it a little, as I then consider the Klein-Gordon equation as classical. That is motivated by that I consider Maxwell's equations as classical. Both equations are on the same level and so I consider Klein-Gordon to be classical. T... | {
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"answer_id": 2
} |
Heating suprecritical water in a closed water tank How does the pressure of water in a closed tank evolve in the following setting:
- closed tank of 2 liters (filled up with water)
- water initially at 25°C and pressurized to 3 bars
The water is now heated up to 130°C, thus remaining a fluid (based on water property ta... | Fluid reserved in a fixed volume and with no inlet and outlet of mass variations are represented well by a parameter called internal energy, although, it does not variates expressive by the pressure, but it does from the temperature. It is an important parameter to systems like yours.
I usualy use a software that does ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/187201",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
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