Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
functional determinant and WKB approximation let be a Hamiltonian in one dimension, i would like to evaluate the functional determinant $ det(E-H) $ in onde dimension
i believe that $ det(E-H)= Cexp(iN(E)) $ here $ N(E)$ is the number of energy levels less than a given number 'E'
my steps
*
*i use the identity $ lo... | The formula doesn't work. Most of the manipulations are formally ok, although it is probably best to start right at step 3--- the derivative of the logarithm of the determinant is the (trace of the) Green's function, which is better behaved than the determinant itself.
Step 5 is incorrect--- there is no reduction using... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Can a photon passing by an open space barycenter of a system of masses be modeled as if all the system's mass is at the barycenter? To be clear, this example can't apply to the Solar System, since the barycenter is within the Sun, similarly the Earth/Moon system's barycenter is within the Earth.
But, given a system o... | The barycenter has no mass and therefore no forces emanating. This is evident by your example of the moon earth barycenter which continually moves in the mantle 1700 km down or so. If it had any effect it would be working as a whip in cream, generating from quakes to volcanoes!
It is just a geometrical point whose us... | {
"language": "en",
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"source": "stackexchange",
"question_score": "1",
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About the Ether Theory acceptance Why was the Ether Theory refused by Modern Physics? If you please explain me, I just wanted to understand it more.
| It's because the luminiferous aether was, by definition, composed out of some particles or elementary building blocks with a well-defined location in space. Consequently, it picks a privileged reference frame, the rest frame of the aether. In this rest frame, the speed of light – vibrations of the aether – could be con... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 5,
"answer_id": 4
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Why is beta negative decay more common than beta positive? In simple terms, why is beta negative decay more common than beta positive?
I know it's something to do with occuring inside/outside the nucleus - but I can't find a simple, easy to understand explanation!
| (The following extends Georg's remarks earlier, where K-capture refers to K-electron capture.)
Beta-plus decay competes with electron capture, but there are few positrons around for beta-minus decay to compete with, so even when beta-plus decay is possible, its branching ratio may be small or overwhelmed by EC.
Moreove... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Quality factor for a quantum oscillator? I've been reading papers about nanomechanical oscillators, and the concept of quality factor often pops up. I understand to some extent about Q factor in classical sense, but since nanomechanic oscillators are often treated quantumly, what does Q factor mean then?
| This is just a quick answer that I'm hoping will be superseded, because I'd like to see a good answer to this question. In the context of microwave resonators etched on superconducting chips, I know from experience that the Q factor seems to be basically the $T_1$ time. Sorry I can't be more help -- this is a point of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16724",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Planetary model of atom still valid? When I was in school, I learned (from Democritus) that an atom was
similar to a solar system, with the nucleus being the sun, and the
electrons being the planets. Of course, there are some differences:
*
*The "sun" isn't a single entity, but a collection of protons and nuetron... | Yes, in some cases.
Nearly a century after Danish physicist Niels Bohr offered his planet-like model of the hydrogen atom, a Rice University-led team of physicists has created giant, millimeter-sized atoms that resemble it more closely than any other experimental realization yet achieved.
Using lasers, the researchers... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16831",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Additional accelerating force during take off of a rocket? During the take off of a rocket, the exhaust produces some pressure below the rocket, which gives an additional force. How large is this force in comparison to the force produced directly by the exhausted gases because of conservation of momentum?
When the rock... | Any pressure difference along the rocket will result in air motion. Normally the rocket jet entrains some air down and makes a negative pressure difference. However, if you enclose the rocket in a container, you can get a positive pressure difference. Watch videos of rocket launching, especially those vapor clouds alon... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The time component is $\gamma m c$, so shouldn't $E=mc$? Basically, the book is Brian Cox's Why Does $E=mc^2$?: (And Why Should We Care?).
I just finished Chapter 5, where we derived the spacetime momentum vector (energy-momentum four vector, as he establishes the physics jargon).
Let $\gamma=\frac{1}{\sqrt{1-\frac{v^2... | Uh, because $mc$ is not energy? And what do you mean "time component"? Your $\gamma mc$ is momentum.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Relativistic transformation of the wave packet length Let us suppose we have an excited atom at rest. It has a certain mean lifetime $\tau_0$. If we wait sufficiently long time $t>>\tau_0$, we will find a deactivated atom and a (spherical) electromagnetic wave function of photon with about $\tau_0\cdot c$ long layer wi... | First, just as a note, I would want to say that the problem will be somewhat ill defined because in QM it may be simple to define transition probabilities for going from one state from another, but, the actual process over time which should give you the Dirac transition current from charge and spin, the current which i... | {
"language": "en",
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"source": "stackexchange",
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Decoherence inside black holes I have a question about decoherence. Assume there is a macroscopic black hole floating around and you have some macroscopic object with you with a huge number of internal degrees of freedom. Conventional decoherence theory predicts decoherence. If this macroscopic object is dumped into th... | The question by the OP is misguided as it stands. Both choices of partial traces end up with decoherence. That is easy to see when the partial trace is over the internal degrees of freedom. It is also the case when it is over exterior of the black hole precisely because Hawking radiation is thermal and decoherent. Corr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17136",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Can Plasma Ignite? This question on Scifi.se: Why does warp plasma burn green? mentions a fictional type of plasma called 'Warp Plasma' that is capable of igniting and when it does it sprays plasma flames/gas out of pipes as if it were oil or some other form of fuel.
Wikipedia says that the sun consists of hot plasma i... | Plasma is a kind of matter very similar to gas in which atoms have been ionized. It is very hot and lets off radiation (also in the visible spectrum) due to recombination so it might already be considered flame. Thus it isn't clear what "igniting plasma" really means.
In cold plasma where only a small fraction (few per... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17191",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What is the force between two magnetic dipoles?
*
*What is the force between two magnetic dipoles?
*If I have two current loops parallel to each other with currents $I_1$ and $I_2$ and radii $R_1$ and $R_2$ a distance $z$ from each other, what is the force between them?
*What would change if they were two solenoids... | The field of a magnetic dipole is, at long distances (in some naturalized unit convention), equal to
$$ B_i = \partial_i ({\mu \cdot r \over 4\pi r^2})$$
where $\mu$ is the magnetic moment vector (the current times area of the loop, in the direction perpendicular to the area of the loop, times N for a solenoid with N w... | {
"language": "en",
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"source": "stackexchange",
"question_score": "3",
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Hamiltonian with position-spin coupling I am solving a Hamiltonian including a term $(x\cdot S)^2$.
The Hamiltonian is like this form:
\begin{equation}
H=L\cdot S+(x\cdot S)^2
\end{equation}
where $x$ is the position operator, $L$ is angular momentum operator, and $S$ is spin operator. The eigenvalue for $L^2$ and $S^2... | This problem appears interesting for the following reason. Let us write it down in Cartesian coordnates:
$$-\frac{1}{2}\left(\frac{\partial^2\psi}{\partial x^2}+\frac{\partial^2\psi}{\partial y^2}+\frac{\partial^2\psi}{\partial z^2}\right)+\frac{1}{2}(x\cdot S)^2\psi+L\cdot S\psi=E\psi$$
where I have introduced a 1/2 f... | {
"language": "en",
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"source": "stackexchange",
"question_score": "5",
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Renormalization Group: Different fixed points Extending the Gaussian model by introducing a second field and coupling it to the other field, I consider the Hamiltonian
$$\beta H = \frac{1}{(2\pi)^d} \int_0^\Lambda d^d q \frac{t + Kq^2}{2} |m(q)|^2 +
\frac{L}{2} q^4 |\phi|^2 + v q^2 m(q) \phi^*(q)$$
Doing a Renormaliz... | The short answer is that if you have coefficients for all the terms, you have two independent exact fake scale invariance for the field $\phi$ and $m$ which just rescales the fields and the coefficients appropriately to keep the Hamiltonian exactly the same. This is not a real invariance of the action, since it changes... | {
"language": "en",
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"source": "stackexchange",
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Why can't $ i\hbar\frac{\partial}{\partial t}$ be considered the Hamiltonian operator? In the time-dependent Schrodinger equation, $ H\Psi = i\hbar\frac{\partial}{\partial t}\Psi,$ the Hamiltonian operator is given by
$$\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V.$$
Why can't we consider $\displaystyle i\hbar\frac... | Asking why
$$i \hbar \frac{\partial}{\partial t}$$
isn't the hamiltonian operator in QM is the same as asking why the time derivative isn't the hamiltonian in Hamilton's equations:
$$
\frac{d p_i}{dt} = -\, \frac{\partial H}{\partial q_i}, \qquad \dots
$$
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "105",
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"answer_id": 9
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Radar Frequency Bandwidth I've come across an interesting question in the course of doing some exam review in a quantum mechanics book and thought I'd share it here.
"What must be the frequency bandwidth of the detecting and amplifying stages of a radar system operating at pulse widths of 0.1usec? If the radar is used... | The first part of the question deals with the so called "Transform Limited" pulses. A transform limited pulse is one where the time-bandwidth product is a minimum (unity). This can be loosely thought of as a manifestation of the energy time uncertainty relationship.
So:
$\Delta t\times B=1$. From this you can find the ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What are some interesting calculus of variation problems? That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)
| Here is one I just made up, but it has a nice flavor--- suppose you have a 2-d bullet going very fast through a 2-d gas. The gas molecules reflects specularly off the bullet, making glancing collisions. What shape of bullet of a fixed area has the least drag?
This problem gives
$$\int {1\over 1+y'^2} + \lambda y dx $$
... | {
"language": "en",
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What is the physical sense of the transition dipole moment? So if the states are the same we achieve the expectation value of the dipole moment for a given state. I mean
$ \langle \mathbf{\mu} \rangle = \langle \psi \vert \hat{\mathbf{\mu}} \vert \psi \rangle$
But I don't feel the physical sense in the case of transiti... | Actually the name transition dipole moment pretty much contains its definition. It describes the possibility of a transition between states $\psi_1$ and $\psi_2$.
Physically this can be understood as well. An atom in a particular state may, by absorbing say an electromagnetic wave, change its state. The probability for... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17594",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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This Expansion-of-the-Universe-Diagram Confuses Me The following blue-cone Wikipedia diagram confuses me.
At any point of cosmological time the encircling horizontal lines in the diagram are of finite circumference. That is indicative of a closed model of the universe.
Queries:
1. Why does the author use a closed mod... | The author of the diagram explains very well how and why he drew the diagram this way:
http://en.wikipedia.org/wiki/File:Embedded_LambdaCDM_geometry.png#Mathematical_details
In particular it states:"I deliberately cut off the embedding short of a full circle to emphasize that space does not loop back on itself (or, if... | {
"language": "en",
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"source": "stackexchange",
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Why do 3d spheres and gravity tend to rotating discs on one plane? Whether is it our solar system or a whole galaxy, there is usually a massive object (star or black hole) at the centre with gas and objects rotating around it.
The gravitational effect of the star/black hole extends uniformly (more or less) in every di... | It's not true that everything tends towards a single plane.
A counterexample are the dark matter halos of galaxies : See for instance http://news.bbc.co.uk/2/hi/8444038.stm .
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18004",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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"answer_id": 1
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What is escape velocity? In reality, how can something no longer be under the gravitational influence of something else? Isn't G a continuous function and although you leave the immediate vicinity of the earth with an escape velocity won't it always exert a force, however small it may be. Won't that force eventually pu... | Yes the Earth will always exert a force, but that force will get smaller and smaller as the object get further and further. Even if we assume Earth and the object are the only 2 masses in the universe, the gravity from earth will always slow down the object, forever (ie until its distance is infinite), but the velocity... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18070",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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"answer_id": 3
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Physics Paradox about Newtons Second Law $F=ma$
*
*If force equals mass times acceleration, wouldn't a basketball dropped from the top of the Eiffel tower exert the same force on the ground as a basketball dropped a foot off the ground? They both have the same mass, and they both are accelerating towards the ground a... | Force does equal mass times acceleration. However $9.8~\text{m/s^2}$ is the acceleration of the ball imposed by gravity. The acceleration that the ball experiences upon impact with the ground is instead proportional to its current velocity.
Upon impact, $a=-\frac{v}{t}$, where v is current velocity and t is the time im... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18387",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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"answer_id": 8
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How does gravity work underground? Would the effect of gravity on me change if I were to dig a very deep hole and stand in it? If so, how would it change? Am I more likely to be pulled downwards, or pulled towards the edges of the hole? If there would be no change, why not?
| Acceleration due to gravity at depth d below the earth's surface is given by:
$g(d) = G M_e \dfrac{R_e - d}{R_e^3}$
Where,
G = Universal gravitational constant
Me = Mass of the earth
Re = Radius of the earth
d = depth below the earth's surface
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18446",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "56",
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Difference between coordinate and proper distance in Schwarzschild geometry I'm trying to understand the difference between proper distance $d\sigma$ and coordinate distance $dr$ in Schwarzschild geometry. The bottom bit of the diagram represents flat space, the upper bit curved space. The inner circles represent Eucli... | In the Schwartzchild coordinates the r co-ordinate is the value you get by dividing the circumference of the circle by 2$\pi$. That is, it's the radius of the circles you've projected onto the base of your diagram.
As others have mentioned in the comments, deciding what you mean by the "real" distance from the circle t... | {
"language": "en",
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What does a unitary transformation mean in the context of an evolution equation? Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$.
Then what is the meaning of the equation
$$\det\bigl(I-U(t)e^{itE}\bigr)=0$$
where $E$ is a real variable?
| Just a mathematical note in response to the previous answer:
$e^{i \hat{H} t /\hbar}$ is not defined as the exp-series, although it is common to define it so in physics textbooks. But it is not possible to do this as the series is generally not converging (in the operator norm).
One has to use the spectral calculus, in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18539",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 3
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Effects of a Coiled Cable Okay, I've got a little bit of a layman's question here.
We're doing a bit of spring cleaning in our office and we've found a cabinet with boxes upon boxes of stored wires, so naturally, this discussion arose...
Picture a normal, bog-standard wire, with a plastic outer coating. Now, quite ofte... | Sorry for necromancing but someone on the internet is wrong.
Nothing major happens with regard to magnetic fields since the cable hold a wire pair carrying equal and opposite current, thus creating two magnetic fields that almost completely cancel each other out.
The most notorious feature of loaded coiled cables is th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18623",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why are the quarks so named? Quarks have a variety of names (or flavours):
*
*Up
*Down
*Strange
*Charm
*Bottom or Beauty
*Top or Truth
Why do they have such odd names?
| The up/down top/bottom should be self evident: in a matrix representation the vector is written that way
+1/2>
-1/2>
So in the isotopic spin space (the SU(2) of the SU(2)xSU(3)xU(1) of the Standard Model) according to the charge the one on top was called the up and the one on bottom, the down.
The strange got its nam... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Spin angular momentum of a system of particles : Is there any energy associated with it? Consider a system of point particles , where the mass of particle $i$ is $μ_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the system. Considering the system from ... | Similar to the derivation of separation of angular momentum into $L_{CM}$ and $L_{internal}$, one can derive similar expression for Energy as
$E = \frac{1}{2}M_{total}v_{CM}^{2} + \frac{1}{2}\sum \mu_{i} v_{i}^{'2}$.
Proof:
$$E = \frac{1}{2}\sum \mu_{i} v_{i}^{2}$$
$$v_{i} = v_{CM} + v_{i}^{'}$$
$$E = \frac{1}{2}\sum ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18715",
"timestamp": "2023-03-29T00:00:00",
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Elasticity of Space; How does the expansion of Space affect gravity? Does space have an elastic quality?
What I was thinking about was if space is expanding, is it being 'stretched', like a balloon being blown up, and if so, is this causing gravity to weaken? Imagine space as a 2 dimensional sheet (got this from one of... | I remember that Prof. Susskind said in the cosmology course of his "Stanford ongoing studies series" (it must have been somewhere in the first part of this 8 Lecture course)
http://www.newpackettech.com/Resources/Susskind/PHY28/Cosmology_Overview.htm
that space is continuously created in the course of the expansion suc... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18768",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Simple applications of group theory which can be understood by a senior undergrad I am looking for references (books or web links) which have "simple" examples on the use of group theory in physics or science in general.
I have looked at many books on the subject unfortunately they usually require extensive technical ... | My two favorites for group theory in physics are:
*
*Lie Groups for Pedestrians
for a general introduction to Lie groups, mostly in a particle physics context.
*Levine's Quantum Chemistry, for an introduction to group theory in molecules.
| {
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"source": "stackexchange",
"question_score": "9",
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What frequency photons are involved in mediating physical force? If the force felt when pushing an object is mediated by the electromagnetic interaction and hence photons, what is their frequency?
| Their frequency is determined with the velocities. For example, if you have a heavy, moving with $\vec{v}= const$ source charge that creates a time-dependent potentials $\phi(\vec{x},t)$ and $\vec{A}(\vec{x},t)$, then the Fourier expansions of those potentials will contain the following time-dependent exponentials: $\p... | {
"language": "en",
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What fundamental principles or theories are required by modern physics? We have been taught that speed of light is insurmountable but as we know an experiment recently tried to show otherwise.
If the experiment did turn out to be correct and confirmed by others, would it make physics to be rethought of? What other con... | Most progress in physics is incremental to start with, as far as data and experiments go. Theories change following new data but on the whole they change by incorporating the old theories as limiting cases for certain parameters of the new theories, or convolutions over the variables of the new theories.
@Ronmaimon's l... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why can't echoes be heard inside a room? If I go camping and shout anywhere, in the forest or on a cliff, I usually hear the echo of my voice.
Why when I shout in my room I do not hear any echoes?
| Sound does echo inside a room but you might not notice it much for two reasons.
Firstly the time for the echo to return is very small so you will not hear a long sound repeated as an echo, instead you will get a resonance type echo, like when you sing in the bathroom.
Secondly most rooms are full of soft furnishings th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19195",
"timestamp": "2023-03-29T00:00:00",
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Why doesn’t gravity break down in a large black hole? By popular theory gravity didn’t exist at the start of the Big Bang, but came into existence some moments later. I think the other forces came into existence a little latter.
When a black hole crushes matter to a singularity (infinite density), at some point should... | You are right. Both the Big Bang and a black hole are what is called a space-time singularity and the physics of these object is, to put it simply, poorly understood. We know a lot about a black hole seen from outside, or about what happened some ridiculously small after the Big Bang, but it is unknown if the laws of p... | {
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Physics related Podcasts
Possible Duplicate:
Are there any good audio recordings of educational physics material?
In the same way that was already asked about good books of Physics in this StackExchange, I would like to know good physics podcasts! What are the most informative and enjoyable to hear?
| I don't know of any regular podcasts, but there are lots of Physics lectures on Youtube. Just search for something obvious like "physics".
If you follow any of the Physics blogs you'll often see links to Youtube videos posted.
JR
| {
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Could gravity hold electron charge together? Could the gravitational force be what holds the charge of the electron together? It seems to be the only obvious possibility; what other ideas have been proposed besides side-stepping the issue and assuming a "point charge"? How would this affect the electron "self-energy" p... | The short answer... we do not know. (Were 'we' is humanity or physicists - take your pick.)
A more interesting answer is...
The electron size is known to be 10^-18 meters or smaller. If gravity was holding it together then it might be at the Schwarzschild radius.
Rs = 2GM/c^2
so with values substituted it would be
2 ... | {
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Why is Mendel Sachs's work not taken seriously? Or is it? Back in college I remember coming across a few books in the physics library by Mendel Sachs. Examples are:
General Relativity and Matter
Quantum Mechanics and Gravity
Quantum Mechanics from General Relativity
Here is something on the arXiv involving some of his ... | Mendel Sachs may have been blacklisted, which would certainly be wrong. But his theory has a fatal error. His derivation depends on the assumption that certain 2x2 complex matrices, standing for quaternions, approach the Pauli spin matrices in the limit of zero curvature. This is impossible; the Pauli matrices are not ... | {
"language": "en",
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how to represent the effect of linking rigid-bodies together? I have 2 rigid-bodies (b1,b2) if i linked one to the other (as if they are conjoined together) , how to represent b1 effect on b2 and b2 effect on b1
Is there any LAW that affect the position/orientation of the other body ?
notes :
*
*i am using Quater... | The open-source physics engine ODE allows you to connect two bodies using any of a number of different joints. One of those joints is the "Fixed" joint. It's much more stable, in the physics engine, to represent the two bodies as a single body but maintain two separate geometries for collision purposes. However, ODE... | {
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What is the connection between Poisson brackets and commutators? The Poisson bracket is defined as:
$$\{f,g\} ~:=~ \sum_{i=1}^{N} \left[
\frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} -
\frac{\partial f}{\partial p_{i}} \frac{\partial g}{\partial q_{i}}
\right]. $$
The anticommutator is defined as... | I don't know any link between Poisson bracket and anti-commutator, but I do know the link between Poisson bracket and commutator.
$$[\hat a,\hat b]=i\hbar\{a,b\}_\text{Poisson}$$
Subtleties
As the operator $\hat a$ and $\hat b$ are counterparts to classical dynamical variable, they must be ①functions of canonical coord... | {
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What is the meaning of speed of light $c$ in $E=mc^2$? $E=mc^2$ is the famous mass-energy equation of Albert Einstein. I know that it tells that mass can be converted to energy and vice versa. I know that $E$ is energy, $m$ is mass of a matter and $c$ is speed of light in vacuum.
What I didn't understood is how we wil... | c: “Light Velocity” (c: celeritas, Latin: “swift”),
is the speed of photons in a straight, flat vacuum:
299, 792, 458 meters per second ( 3e^8 mps).
This reference is a constant that never varies.
(Does NOT mean mass is moving at light speed!)
c^2 = 89, 875, 517, 873, 681, 764 ( 9e^16 ), where
“9e^16” becomes the “... | {
"language": "en",
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Where to find cross section data for $e^{-}$ + $p$ $\longrightarrow$ $p$ + $e^{-}$? Where to find cross section data for $e^{-}$ + $p$ $\longrightarrow$ $p$ + $e^{-}$ ?
PDG's cross-section data listing does not include it.
| The answer is highly dependent on the scale of the momentum transfer.
The figure of merit is $Q^2$ is the squared momentum transfer, and in some regimes the missing energy $\omega = \epsilon' - \epsilon$. The formalism is usually developed in the lab frame with a stationary proton target and a energetic electron beam. ... | {
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Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?
I have never seen dissipation explained, although what I have seen a lot is descriptions of dissipation (i.e. more det... | *
*The Second Law has nothing to do with time, and it isn't formulated in terms of S. Instead, it is used to define entropy. See Caratheodory and Born.
*Loschmidt's objection concerns the trivial fact: irreversible macroscopic behaviour cannot be derived using reversible equations of motion. Boltzmann obviously hail... | {
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Can the charge of particles spontaneously flip from positive to negative or vice versa? I'm thinking of matter antimatter annihilation, are there reactions where normal matter converts to antimatter?
| There are reactions where normal matter converts to antimatter. For example, in neutral kaon oscillations, a beam of kaons (or rather, what are created as kaons) will appear to convert to antikaons after some distance, then back to kaons, and so on.
However, a key property that allows this to happen is that the kaons a... | {
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How Does Dark Matter Form Lumps? As far as we know, the particles of dark matter can interact with each other only by gravitation. No electromagnetics, no weak force, no strong force. So, let's suppose a local slight concentration of dark matter comes about by chance motions and begins to gravitate. The particles wo... | My problem is with the time scale of the phenomenon. It has been proposed that the universal network of filaments and concentrated lumps of dark matter is the framework upon which ordinary matter condensed to form our present day clusters of galaxies. If this is so, it would seem reasonable that there be some rapid m... | {
"language": "en",
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Why does electron-positron annihilation prefer to emit photons? If gravitons are also massless, and neutrinos nearly so, why aren't pairs of either of them normally expected outcomes of electron-positron annihilations? Are they possible but simply unlikely, or is there actually some conserved quantity prohibiting their... | It is my understanding that electron-positron annihilation with neutrino-antineutrino production is possible at any energy, but the cross-section of such reaction is extremely low at low energy. While electron-positron annihilation with two photon production requires a virtual electron, electron-positron annihilation w... | {
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How are the Pauli matrices for the electron spin derived? Could you explain how to derive the Pauli matrices?
$$\sigma_1 = \sigma_x =
\begin{pmatrix}
0&1 \\ 1&0
\end{pmatrix}\,, \qquad
\sigma_2 = \sigma_y =
\begin{pmatrix}
0&-i\\ i&0
\end{pmatrix}\,, \qquad
\sigma_3 = \sigma_z =
\begin{pmatrix}
1&0\\0... | This link seems to be along the required path of thought.
Please note the "axiomatic" facts: experimental inputs in value of $S^2$, raising and lowering operators, desirability of hermitian operators... that go inside the derivation.
Also, once having chosen them, note that the 3 Pauli matrices along with the 2d identi... | {
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Calculating lagrangian density from first principle In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.
| Seek for 'Klein-Gordon equation' and 'Dirac equation' - they can be found in any textbook concerning basic relativistic quantum mechanics (such as, e.g. Landau ). Klein-Gordon (spin=0 and any natural spin after modifications) comes directly from the energy-momentum conservation of special relativity $p_\mu p^{\mu} = -m... | {
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What are the practical applications of decoherence? Let me clarify this question somewhat. I know decoherence is ubiquitous in nature and explains the emergence of a classical world from quantum physics. My question is really about how a knowledge of how decoherence actually works can be put to use in a practical appli... | Quantum key distribution comes to mind. It is used to ensure that there are no eavesdroppers on the key distribution channel because they would decohere it measurably.
| {
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Energy in an EM wave should depend on frequency I just finished reading Feynman's Lectures on Physics vol.I, §34-9: "The momentum of light". The author explains that there is a relation between the wave 4-vector $k^{\mu}$ and the energy-momentum 4-vector $p^{\mu}$ of an EM wave, namely
$$p^{\mu}=\hbar k^{\mu}, $$
or e... | The section you are referring to clearly states that those equations do not apply to the wave, but to the "particles" of light, the photons. The resolution is that two waves of the same amplitude but different frequencies contain different numbers of photons. This has interesting consequences, for instance it means it ... | {
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Physically what happens during Avalanche breakdown to the pn junction? What does breakdown mean physically?
I saw this in wikipedia:
The avalanche process occurs when the carriers in the transition
region are accelerated by the electric field to energies sufficient to
free electron-hole pairs via collisions with b... | The avalanche breakdown itself doesn't cause destruction, it just moves charge carriers around within the material.
But the breakdown results in extremely high currents through the semiconductor, which results in high temperatures. In particular with avalanche breakdown the higher the temperature gets, the higher the c... | {
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How is gradient the maximum rate of change of a function? Recently I read a book which described about gradient. It says
$${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r},$$
and suddenly they concluded that $\nabla T$ is the maximum rate of change of $f(T)$ where $T$ stands for Temperature. I did not understand. How gradi... | The equation
${\rm d}T~=~ \nabla T \cdot {\rm d}{\bf r}$,
says that the change in T, namely ${\rm d}T$, is the scalar product of 2 vectors, $\nabla T$ and ${\rm d}{\bf r}$, which can also be written as the magnitude of the 1st vector times the magnitude of the 2nd vector times cosine the angle between them.
${\rm d}T~=... | {
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How can a human eye focus on a screen directly in front of it? I am asking this question here because I think the answer has something to do with the way light is bent as it's captured through the eye.
I saw a show a while ago about tiny screens on contact lenses to pull up data on objects you see in the real world, I ... | In theory, an ultra ultra high resolution display could act as an holographic filter and produce an image that seems to originate from far away.
Or you can project an image from a single point straight into the eye. That does not require focus to be sharp. But it will be very challenging to align the virtual image wit... | {
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Why can't we think of free fall as upside down rocket? /\
/ \
| |
| m |
| |
------ <--- floor (Rocket A)
This rocket is accelerated (g) upwards then mass(m) falls on the floor.
------ <--- floor
| |
| m |
| |
\ /
\ /
\/ (Rocket B)
This rocket is accelerated (g) downwards then mass(m) ... | You can't.Cause the rocket is in a gravity free zone.When it accelerate downwards the mass inside the rocket feels a force proportional to it's acceleration in opposite direction.Which causes the mass inside the rocket moves towards the floor.
But for a free falling elevator in gravity field,the mass inside it feels no... | {
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What is the physical meaning of a "complete" Hilbert space in QM? What does the word "complete" means from the physical point of view?
I do not understand what it physically means to say that a Hilbert space is a complete vector space.
| I think your question is "why wasn't quantum mechanics formulated on normed vector spaces?" i.e "why was the completeness criterion required?"
I don't know a rigorous answer, but it seems reasonable for the following reason:
Completeness means that every Cauchy sequence of elements of H converges to an element of H. T... | {
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Finding distance when the force is a function of time I'm having trouble with this homework question
A mysterious rocket-propelled object of mass 49.0 kg is initially at rest in the middle of the horizontal, frictionless surface of an ice-covered lake. Then a force directed east and with magnitude $F(t) = (16.3\text{ ... | If the force is constant with time, then the distance is a polynomial with time of order 2. If force varies linearly with time, then the distance is a polynomial of order 3.
$$ x(t) = C_0 + C_1\, t + C_2\, t^2 + C_3\, t^3 $$
So there are four (4) unknown coefficients to the expression for distance. Two of them are giv... | {
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Calculating Impact Velocity Given Displacement and Acceleration
Assume a car has hit a wall in a right angled collision and the front bumper has been displaced 9 cm. The resulting impact is 25g. Also, it is evident by skid marks that the car braked for 5m with an acceleration of 1.5m/s^2. What is the impact velocity i... | Why is $a=196 m/s^2$? It's 20g, not 25g. And it looks like you did not take into account the deceleration before impact.
| {
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What determines color -- wavelength or frequency? What determines the color of light -- is it the wavelength of the light or the frequency?
(i.e. If you put light through a medium other than air, in order to keep its color the same, which one would you need to keep constant: the wavelength or the frequency?)
| Actually, there is something important all these answers are missing. Color is determined by the response of the human eye, not by energy or frequency. In order to get the full range ('gamut') of colors, I need a mix of red, green and blue light (hence the RGB displays) and the primaries can themselves all be different... | {
"language": "en",
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Does sending data down a fiber optic cable take longer if the cable is bent? Ok, so, my simplified understanding of fiber optics is that light is sent down the cable and it rebounds off the sides to end up at its destination. Which got me thinking, if it has to bounce more times (and having a shorter travel between eac... | That picture is only really true for lightguide type large plastic fibres. For single mode fibre used in communication the wave is essentially directly down the centre
| {
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The force of a phase transition At standard temperature and pressure, I fill a bottle to capacity with $N$ liters of water, then place a weight of mass $M$ kg on its opening to serve as a lid. What values of $N$ and $T$, where $T$ is the temperature of the bottle, are sufficient to raise the lid?
| Easy! Any value of $T$ will suffice. (unless it's ice in a certain temperature range)
Since it's probably a reasonable expectation that you're talking about liquid, subcooled, water for the duration of the problem this is nothing more than multiplication. The mass of the water is invariant from state $1$ to state $2... | {
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What happens when a supersonic airplane flies through a cloud? What happens when a supersonic airplane flies through a cloud? Will it punch a hole or is it more like a bullet through water (= hole closes immediately after the aircraft has passed)?
Is there some special effect because of the supersonic speed? Or maybe t... | It creates shock waves, which under the right conditions like a supersonic rocket did in this picture, causes concentric cloud rings. Clouds are essentially just volumes where the humidity, temperature, and pressure are such that the air is locally supersatured with water. The craft passing through the cloud will send ... | {
"language": "en",
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In a Sterling Engine, does heat from the hot side transfer to the cold side? A Sterling Engine is a closed system. The "hot" side oscillates between higher temperature with higher pressure and lower temperature with lower pressure. Does Nature switch back and forth between one temperature/pressure combination and ano... | A Stirling engine moves a fluid from a hot end to a cold end - extracting mechanical work as it does so. The power input comes from maintaining the temperature of the hot end - usually by burning some fuel externally.
The 'clever' part of a Stirling engine, and the thing that gives it it's high efficiency, is that the ... | {
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Newton's corpuscular theory Where did Newton get the idea that light had a particle nature and not a wave nature? At those times, AFAICT there were no phenomena that showed particle nature. But wave nature is much easier to detect. So, why didn't Newton change his theory to a wave theory? I recall something about "moti... | Newton gives two main arguments for a corpuscular view of light in his Opticks:
(1) Light consists of rays of inherent and inalterable dispositions (as regards colour, refrangibility, etc.). This is argued for throughout, but see esp. the classic prism experiments in props. I and II. Wave theorists, on the contrary, ba... | {
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Expected Energy Production From High Efficiency Solar Cells First, a bit about my thoughts. I believe we have the capability today to provide energy, water, food, education, and transportation to every man woman and child on the planet. To that end, I would like to become a force that brings about this change.
In try... | A fantastic, free, book for calculations of this kind is provided by David McKay in Renewable energy without the hot air.
| {
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Prove that negative absolute temperatures are actually hotter than positive absolute temperatures Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in the sense that if a ne... | Negative temperature - yes I encountered that once: I seem to recall that it's the state that arises when, say, you have a system of magnetic dipoles in a magnetic field, and they have arrived at an equilibrium distribution of orientations ... and then the magnetic field is suddenly reversed and the distribution is mom... | {
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What do the dimensions of circulation mean, and how is circulation related to action? The dimensions of circulation $\int_C \vec{v}\cdot d\vec{r}$ seem strange, but if you include
(even a constant) density $\rho$, then $\int_C \rho\vec{v}\cdot d\vec{r}$ has dimensions
the same as action/volume. Is there any significan... | The question is "What is the unit of circulation?"
Ans: $(m^2/s)$
Explanation: $\text{circulation} = \text{vorticity}\times\text{area} = (1/s)\times(m^2) =(m^2/s)$
| {
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Can someone explain the science behind MIT's 230% efficient LEDs? I was reading Gizmodo the other day and I didn't quite understand the Physics behind this. Could anybody shed some light on how this effect actually works?
| As others have said, a heat pump with an efficiency greater than unity doesn't have any problem with the laws of thermodynamics. There are still a few problems with this which mean that it isn't as good as it seems.
The efficiency of a heat pump depends on the temperature difference - you can get higher efficiencies w... | {
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Why are there 4 Dimensions and 4 Fundamental Forces? Is it a coincidence that there are four fundamental forces and four spacetime dimensions ? Does a universe with three spacetime dimension contain four fundamental forces? Can magnetism be realized in three dimensional spacetime?
Edit 1:
Thanks alot for the answer. I... | Well, I will not join the chorus in agreeing there are four fundamental forces.
Our everyday world depends on two forces, gravity and electromagnetism, and in this sense they would be fundamental to our everyday world.
When we started the scattering experiments we discovered another two forces, strong and weak. The hig... | {
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"answer_id": 0
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Why does optical pumping of Rubidium require presence of magnetic field? The optical pumping experiment of Rubidium requires the presence of magnetic field, but I don't understand why.
The basic principle of pumping is that the selection rule forbids transition from $m_F=2$ of the ground state of ${}^{87} \mathrm{Rb}$... | In a hyperfine pumping you pump atoms to the other hyperfine level, let's say you apply your laser to the $F_g = 2 \rightarrow F_e = 2$ transition of the $^{87}$Rb D$_1$, then the atoms from the $F_e = 2$ level will decay to both ground state hyperfine levels $F_g=1,2$ and eventually will be pumped into the $F_g = 1$ l... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 4,
"answer_id": 1
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Piston movements in four stroke cycle? I was reading about a four stroke cycle. Here's what I understood:
*
*In the first stroke, the piston starts at the top and moves down.
*In the second stroke, the piston moves upwards.
*In the third stroke, the piston moves down due to the combustion by spark plug.
*In the... | As Manishearth says, for engines with more than one cylinder the firing of the other cylinders rotates the crankshaft. However, as any fan of vintage motorcycles will know, you can have four stroke engines with a single cylinder. In this case the engine has a heavy flywheel attached to the crankshaft and the momentum o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22305",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
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Does it take significantly more fuel to fly a heavier airplane? I was reading in the papers how some-airline-or-the-other increased their prices for extra luggage, citing increased fuel costs.
Now I'm a bit skeptical. Using the (wrong) Bernoulli-effect explanation of lift, I get this:
More luggage$\implies$more lift ne... | One thing in your argument is that more lift, means a higher speed. This may not be what airliners do. Airplanes (at long flights) choosse their cruising altitude based on their weight. Higher weight means lower altitude. I think this should be included in the incremental cost calculation of additional piece of luggage... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22357",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Faster-than-$c$ photons As far as I know, according to quantum field theory, there are some photons that go faster than c, which is the speed of light in vacuum.
However, there seems to be a paper and a corresponding experiment that show every photon obeys the speed limit of $c$. (http://physics.aps.org/synopsis-for/1... | Special Relativity only requires that light travel at c in vacuum. In any normal dielectric the speed of light will be less than c. This is what gives rise to Cherenkov radiation. https://en.wikipedia.org/wiki/Cherenkov_radiation
If you consider phase and group velocity, the issue is really only straightforward in h... | {
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Magnetic force and work If the magnetic force does no work on a particle with electric charge, then:
How can you influence the motion of the particle? Is there perhaps another example of the work force but do not have a significant effect on the motion of the particle?
| The energy of a freely moving particle is its kinetic energy $E=\dfrac{m v^2}{2}$. If the energy of the particle remains unchanged after someone acts on it, it means that no work has been done. However, the direction of ${\bf v}$ could have changed, provided that $v^2$ and hence $E$ is kept the same.
This means that on... | {
"language": "en",
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A question about definition of Fermi energy Wikipedia states the definition of Fermi energy as for "a system of non-interacting fermions". If we have to assume free electrons in a solid behave this way before we are able to calculate Fermi energy, how can Pauli exclusion be justified (because electrons are non-interact... | You might say, of course, that in some sense the fermions do interact (and it is even called exchange interaction). However, it is physical forces, like Coulomb ones, that are understood to be absent. A relevant discussion has taken place here: Degeneracy Pressure, What is it?
Concerning the second question about singl... | {
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Difference in timbre between 'quiet' and 'far away' I'd like to know what are the differences in timbre - or the acoustic properties of a sound - that allow us to differentiate between a sound which is quiet (but close-by) and one which is far away.
For example, you can tell when someone near to you is playing an instr... | There are different cues to the perception of distance:
*
*intensity,
*direct-to-reverberant energy (D/R) ratio (decreases with distance),
*spectral balance (reverberations have more low frequencies than the source signal, so when D/R ratio decreases, basses increase. Sound going through walls and windows also los... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22665",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Slit screen and wave-particle duality In a double-slit experiment, interference patterns are shown when light passes through the slits and illuminate the screen. So the question is, if one shoots a single photon, does the screen show interference pattern? Or does the screen show only one location that the single photon... | Let me try a slightly different way to answer this (well worn) question.
The photon doesn't have a location, or at least not a well defined location, until you interact with it and cause it to localise.
When the photon hits the photomultiplier, or photographic plate, or whatever you're using as the screen the interacti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22923",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Flow rate of a syringe Suppose a syringe (placed horizontally) contains a liquid with the density of water, composed of a barrel and a needle component. The barrel of the syringe has a cross-sectional area of $\alpha~m^2$, and the pressure everywhere is $\beta$ atm, when no force is applied.
The needle has a pressure ... | The appropriate equation for laminar flow (i.e., not turbulent) of a
liquid through a straight length $l$ of pipe or tubing is:
$$Flowrate = \frac{\pi r^4 (P - P_0)}{8 \eta l}$$
where $r$ is the radius of the pipe or tube, $P_0$ is the fluid
pressure at one end of the pipe, $P$ is the fluid pressure at the other end ... | {
"language": "en",
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Why don’t photons interact with the Higgs field? Why don’t photons interact with the Higgs field and hence remain massless?
| There is an aspect to this question that nobody seems to have addressed and that is, although the higgs (the 'radial' component of the field) is neutral, and therefore doesn't interact with the photon at 'tree level' we still see the decay $h \rightarrow \gamma \gamma$. This is because, roughly, by quantum effects a hi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23161",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "28",
"answer_count": 5,
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Where is the flaw in deriving Gauss's law in its differential form? From the divergence theorem for any vector field E,
$\displaystyle\oint E\cdot da=\int (\nabla\cdot E) ~d\tau$
and from Gauss's law
$\displaystyle\oint E\cdot da=\frac{Q_{enclosed}}{\epsilon_0}=\int \frac{\rho}{\epsilon_0}~d\tau$
Hence,
$\displaystyle... | Your counterexample is obviously correct: it is not at all true that, if the integral of a function is the same as that of another function, then the two function coincide.
To mathematically prove the differential form of Gauss' law, if you choose the domain of integration as a paralellepiped $P$ whose sides are $[x_0,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Is the change in kinetic energy of a particle frame independent? Intuitively, I would expect the change in kinetic energy of a particle to be frame independent. It just doesn't "feel" right that between two points in time-space, one frame should measure a change in kinetic energy of a particle different to another fram... | The answer is No, the change in kinetic energy depends on the frame of reference. Consider e.g. a single non-relativistic particle measured relative to two different initial frames.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23323",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
} |
Neutrino beam energy Neutrino is one of the most mysterious particles in todays physics. Even when values of some parameters like for example mass associated with it are not known (or there is great range of possible values), its existence is not questioned. There is a field of research named neutrino astronomy. Becaus... | http://www.ncbi.nlm.nih.gov/pmc/articles/PMC33947/table/T1/ gives a table of neutrino number density for various sources and energies. The flux of solar neutrinos is 5 x 10$^{10}$cm$^{-2}$s$^{-1}$, i.e. 5 x 10$^{14}$m$^{-2}$s$^{-1}$, and the energy per neutrino is 10$^7$eV. 1eV is about 1.6 x 10$^{-19}$J, so I make tha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23429",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why do books have dog ears? I googled the question and found no explanation. It seems that dog ears are inevitable (for paperbacks, notably) even if you've always been careful. From my experience, they are about equally likely to appear on the top corners as on the bottom corners (for both the beginning pages and the e... | Paper is made out of cellulose fibers which are bound together by small amounts of glue under significant heat and pressure in the paper mill. Under a scanning electron microscope the surface of a sheet of paper looks like a haystack that has been smashed flat by great pressure.
As long as the glue (called binder) reta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
"answer_count": 5,
"answer_id": 1
} |
Why does a glass rod when rubbed with silk cloth aquire positive charge and not negative charge? I have read many times in the topic of induction that a glass rod when rubbed against a silk cloth acquires a positive charge. Why does it acquire positive charge only, and not negative charge?
It is also said that glass ... | You might know that all matter is made up out of atoms. Now, atoms themselves have a core, or nucleus, and electrons orbiting around the nucleus. The core has positive charge, the electrons have negative charge.
When you are rubbing the glass rod with the silk cloth, electrons are stripped away from the atoms in the g... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23515",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 5,
"answer_id": 2
} |
What would happen to electronic circuits when traveling near the speed of light? Imagine a space ship, loaded with all sorts of computer systems, traveling near the speed of light.
Electricity itself is very fast, and can reach speeds close the speed of light. (up to 99% according to wikipedia). So, what would happen t... | You're dealing with an incomplete form of relativity.
In the frame of the spaceship, nobody will notice anything different, since all inertial frames are equivalent
In the "ground" frame, electricity would be moving at a different speed, by the relation $$\rm v_{e,ground}=\frac{v_{ship}+v_{electricity}}{1+\frac{v_{ship... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23576",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to combine the error of two independent measurements of the same quantity? I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$.
$k$ is just the mean of $k_1$ and $k_2$. I thought that I would need to square-sum the error... | The formula you've specified
$$ \Delta k = \sqrt{(\Delta k_1)^2 + (\Delta k_2)^2} $$
is the formula to obtain error of quantity $k$, as being dependent on $k_1$ and $k_2$ according to the following expression
$$ k = k_1 + k_2.$$
Generally, to calculate experimental error of a dependent quantity (and the expression stat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23643",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there a general physics simulator for learning purposes? Is there a complete physics simulator that I can use to do general simulations for learning purposes? For example:
*
*Create a sandbox.
*Fill with a gas.
*Load a 3d solid model like this (but 3d).
*Fill it with a dense liquid.
*Load gravity.
*Watch, me... | The closest program to the description is Phun:
http://phun.en.softonic.com/
Download it, it's a lot of fun.
Oh, I see, you want 3D immediately. Ambitious enough so that I won't erase my answer.
Update, May 2012. You may try to download trial of Wolfram System Modeler,
http://www.wolfram.com/system-modeler/
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23676",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 6,
"answer_id": 0
} |
How to derive the Manley-Rowe relation for the process of the second harmonics generation? Derive the Manley-Rowe relation for the process of the second harmonics generation.
Manley-Rowe relation: ~ The Manley-Rowe relations are mathematical expressions developed originally for electrical engineers to predict the amou... | The Manley-Rowe relation arises from conservation of energy and momentum. For the case of SHG, the presence of the nonlinear optical (NLO) material eliminates the conservation of momentum (any momentum difference between the initial and final photons can be provided by the bulk material). So what's left is conservation... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why would it be true that people with longer legs walk faster than ones with shorter legs? When a person walks, the only force acting on him is the force of friction between him and the ground (neglecting air resistance and all). The magnitude of acceleration due to this force is independent of the mass of the object (... | Think about the limiting cases. An ant-sized marching band would take a long time to march the length of a football field. The reason they take so long has nothing to with friction - it's just that their legs are smaller and so each stride moves them a shorter distance.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23921",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 5,
"answer_id": 1
} |
The equivalent electric field of a magnetic field I know that Lorentz force for a charge $q$, with velocity $\vec{v}$ in magnetic field $\vec{B}$ is given by
$$\vec{F} =q \vec{v} \times \vec{B}$$
but there will exist a frame of reference where observer move at same velocity with that of charge $q$, so according to him ... | We can write the Lorentz transform of the fields in a very clean and easy to understand way.
To simplify the expression we use a short hand notation for the various components of the fields parallel and orthogonal to the boost $\vec{\beta}$, further simplified by setting $c$ to $1.$
Lorentz transform of the electromagn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24010",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 2,
"answer_id": 1
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A charged particle moves in a plane subject to the oscillatory potential A charged particle moves in a plane subject to the oscillatory potential:
$U(r)=\frac{m\omega^2 r^2}{2}$
There is also a constant EM-field described by:
$\vec{A}=\frac{1}{2}[\vec{B}\times\vec{r}]$
where B is normal to the plane.
This produces the ... | In polar coordinates $d\vec{r}=\hat{e}_r dr+\hat{e}_{\phi}rd\phi$. Devide it by $dt$ and you will have the particle velocity $\dot{\vec{r}}$. Square the latter and you will get the kinetic energy.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
In the known universe, would an atom not present in our periodic table exist? I have watched this movie Battleship. In it the researchers say this piece of metal is alien because we cant find this metal on earth.
So that would mean somewhere else in the universe any of the following should be true?
*
*Atoms' composi... | Metallic hydrogen is a metal that's not found on earth (but may be present in Jupiter): http://en.wikipedia.org/wiki/Metallic_hydrogen
Wether it does anything but evaporating or burning at ambient temperatures and pressures (or whatever conditions those aliens encountered in this movie), I don't know.
Since metals a ge... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24313",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why do objects follow geodesics in spacetime? Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation $$\frac{d^{2}x^{\alpha}}{d\tau^{2}}+\Gamma_{\gamma\beta}^{\alpha}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau}=0.$$ which describes "how" objects move through spacet... | It is related to what Einstein called "the happiest thought of my life", that for an observer falling freely from the roof of a house, the gravitational field does not exist.
If we could choose a system of coordinates and a suitable definition of derivative, so that the acceleration (the derivative of velocity) were ze... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24359",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 10,
"answer_id": 2
} |
Relative Change of Volume Simple question, in materials publications I often see the relative change of volume in a system reported as
$$ \Delta \left (V \right )/V $$
is the denominator volume supposed to be initial or the final volume? I would assume it is the final volume as it likely parallels the relative error ... | Usually, as for example in the formula that estimates volumetric thermal expansion
$$\frac{\Delta V}{V} = \beta \Delta T$$
$V$ represents initial volume.
Actually, the real definition of volumetric thermal expansion coefficient $\beta$ is stated in the differential form
$$\frac{\text{d} V}{V} = \beta \text{d} T,$$
whic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24405",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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How does the process of freezing water remove salt? How does freezing water to make ice remove whatever salts were in the water to begin with?
| In simple terms, there isn't any space in the ice crystal lattice for the extra atoms and there is no way to plug either of the ions (or the whole salt molecule) into the growing pattern.
So more and more water joins the frozen mass, leaving a more and more concentrated brine until essentially all the water is frozen a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24463",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 1
} |
noise level (units confusion) i had a question in one of my classes regarding SNR in underwater acoustic channels. There are a couple of terms with the unit dB re uPa. I know it stands for dB with reference to uPa but I am not exactly sure what it means. Can I convert it to dB. If yes, how?
Thanks in advance!!
| dB$\mu$Pa would mean "dB's with respect to 1 $\mu$Pa".
If I have a pressure of X Pascals, then to express it in dB$\mu$Pa, I would compute
$$20log_{10}(\frac{X}{1\mu Pa})$$
i.e
$$20log_{10}(10^6X)$$
since there are $10^6$ $\mu$Pa per Pa.
So the rule is: compute how many micropascals you have and take $20log_{10}$ of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24534",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is the converse of Noether's first theorem true: Every conservation law has a symmetry? Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.
Is the converse true: Any conservation law of a physical system has a differentiable symmetry... | I do not know how to prove the following but it should answer your question factually at least. The following I quote from the book 'Classical Mechanics' by Goldstein-
"It should be remarked that while Noether's theorem proves that a continuous symmetry property o a Lagrangian density leads to a conservation condition,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24596",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "73",
"answer_count": 5,
"answer_id": 0
} |
Worlds branching or diverging in Many-Worlds Interpretation? In recent years there seems to have been a growing discussion surrounding MWI's ontology.
In the 2010 volume "Many Worlds?", Simon Saunders has a chapter dedicated to discussing whether the worlds in MWI branch or diverge.
The branching view states that befor... | The two interpretations only differ in ontology. Neither is bullshit, rather both are standard MWI. When you have an observer, this is a computational entity, and to map it to a wavefunction is a nontrivial task. Whether you decide to say there were "really" two observers that were exactly the same before the measureme... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24729",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Will a stone thrown in space move forever? If I throw a stone in space, in a place where gravity is equal zero, and the space had no end, and no objects to collide with, will the stone move forward forever, because no air, so no friction?
| According to Newton's first law, yes. The velocity of any object will remain constant if no forces affect it. That holds in any Inertial frame of reference (if you are accelerating by yourself, then the stone will be accelerating relative to you, even if no forces act upon it).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24794",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 0
} |
How to create unusual sundial? I am considering small "artsy" project. I would like to create sundial by placing gnomon on the window and painting hour lines on the window facing wall.
Since this is to be placed in bedroom I am constrained by my geographic location, wall, window placement and orientation. The esthetic... | Look at this web page, it makes something similar to what you are looking for, http://sundial.damia.net
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24901",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
} |
What causes millisecond pulsars to speed up? Millisecond pulsars are supposed to be old neutron stars. However, they are spinning even more rapidly than newly formed pulsars. Since pulsars slow down as they age, something must have caused these older pulsars to "spin up" and be rotating as fast as they are. What is ... | They accrete gas from a disk, fed by either a wind or Roche lobe overflow from their companion. Almost all known millisecond pulsars are in binary systems, but I think some in globular clusters may have been disrupted by three-body encounters, so appear to be isolated.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24990",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 0
} |
Optimal Angular Field of View (AFOV) Given the rather huge price differences between eye pieces at the same focal length. How exactly does the AFOV affect the view seen through the eyepiece?
Are higher / lower AFOV better for certain situations? or is higher always better?
| Simply, a larger FOV provides a wider hunk of sky in the eyepiece. This is useful for capturing entire objects at higher magnifications than could be obtained with cheaper eye-pieces. It doesn't provide more light, just a wider view. As for better, if you've gone to the expense of buying one for a given focal length, i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25120",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 0
} |
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