Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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How is it that the Earth's atmosphere is not “blown away”? The Earth moves at a high rate of speed around the Sun, and the solar system is moving quickly around the Milky Way. How is it that the Earth's atmosphere is not “blown away”?
| Your intuition about objects facing a head-wind when traveling quickly only works near the surface of the Earth in Earth's atmosphere. In the atmosphere air molecules must be pushed out of the way.
In space though, there isn't anything to do the blowing. There is no interstellar medium / fluid that could drag / push ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66053",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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A Musical Pathway Using a small number of sound emitters, could you create a room where certain nodes emitted particular tones, but no meaningful sound was heard anywhere else.
So, for example, by walking down a certain path, you could hear the tones for "Mary Had a Little Lamb." Is there a generalized algorithm to ma... | Lower frequencies tend to dissipate in all directions, while higher frequencies tend to be "directed". (For example, you can place your subwoofer anywhere in the room, as the sound waves will propagate in all directions, while your other speakers are more "directed" because they reproduce higher frequencies).
See this... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66129",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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"answer_id": 2
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Quantum Mechanics, Uncertainty Principle-- help understanding notes There is a section of my notes which I do not understand, hopefully someone here will be able to explain this to me. The notes read (after introducing the uncertainty operator):
If the state $\chi_A$ is an eigenstate of $\hat O_A$ then the uncertaint... | Assuming we have already proved the uncertainty principle(which can be found here), we know:
$$\sigma_A \sigma_B \geq \sqrt{\Big(\frac{1}{2}\langle\{\hat{O}_A,\hat{O}_B\}\rangle - \langle \hat{O}_A \rangle\langle \hat{O}_B\rangle\Big)^{2}+ \Big(\frac{1}{2i}\langle[\hat{O}_A,\hat{O}_B]\rangle\Big)^{2}}=C$$
Where C is a ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Can open, unsafe nuclear fusion reaction burn the atmosphere? I happened to hear people saying that the nuclear fusion bomb tests could set the atmosphere on fire. I have some serious doubts about that - but I have no facts.
Nuclear fusion reaction requires $15*10^{6}$ kelvins to start. If we produce such temperature i... | Around the 60s, a treaty was signed to ban development of nuclear fusion devices with yield greater than about 50 MT (don't remember exact number), in order to prevent fusion of atmospheric hydrogen, thus the uncontrolled multiplication of the device explosive yield. That was before the Threshold Test Ban Treaty was si... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66276",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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Momentum of particle in a box Take a unit box, the energy eigenfunctions are $\sin(n\pi x)$ (ignoring normalization constant) inside the box and 0 outside. I have read that there is no momentum operator for a particle in a box, since $\frac{\hbar}{i}\frac{d}{dx}\sin(n\pi x)=\frac{\hbar}{i}n\pi\cos(n\pi x)$ and this isn... | I think this is a great question. http://arxiv.org/abs/quant-ph/0103153 This article explains why we shouldn't enforce the boundary conditions that we do (the wavefunction goes to 0 at the boundaries) and instead should use the condition that the wavefunction is equal at both end points. The justification is partly for... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66429",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What happens when a photon hits a beamsplitter? Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact (Wheeler's delayed choice experiment). Part of what is puzzling me is the beam-splitter. Are the individual photons actually being split into two new photons of less... | The crucial word is "beam", in "beam splitter". Beam means an ensemble, in contrast to "photon" which is an individual particle.
A light beam is an ensemble of photons and if it is of a single frequency $\nu$, all photons have energy $E= h*\nu$. A light beam can be split in a beam spliter, i.e. the ensemble of photons ... | {
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Discovery of $E=hf$? How was the equation $E=hf$ discovered?
Was the proportional expression between energy and frequency of light $E\propto f$ discovered only by experiment? Or is there some logical(theoretical) senses affected?
| Discrete spectral lines (frequencies) of atoms were known since long ago. So an emitted wave has a quite certain frequency. If an absorber has many "resonators", it is the resonance resonator who likely will absorb the wave entirely. But this exchange says nothing about the relationship of the wave energy and the wave ... | {
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Human power on treadmill On an elliptical treadmill a regular person can easily burn 1000 calories in one hour (treadmill reports calories burnt). This translates into:
$$(1\times 10^3\mathrm{cal/hr}\times 4.2\times10^3\mathrm{J/cal})/3.6\times 10^3\mathrm{s/hr} \approx 1.2 \; \mathrm{kW} \approx 1.5 \; \mathrm{hp}$$
O... | The trainers in the gym measure total energy used, based on an estimate of how much oxygen you use for certain levels of workout.
They also notoriously over estimate - if you are at the gym to lose weight you will use the machine that promises 1000cal/hour rather than the one that claims 500. And so the gym will buy th... | {
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SUSY (Supersymmetric) Quantum Mechanics I have seen some books, e.g. by Fred Cooper (Supersymmetry in Quantum Mechanics), define:
$A = \frac{\hbar}{\sqrt{2m}} \frac{d}{dx} + W(x)$,
$A^\dagger = \frac{-\hbar}{\sqrt{2m}} \frac{d}{dx} + W(x)$,
$V_1(x) = W^2(x) - \frac{\hbar}{\sqrt{2m}} W'(x)$,
$V_2(x) = W^2(x) + \frac{\h... | The second convention only differs from the first one by using the symbol $W'$ for what is called $W$ in the first convention. There is a one-to-one correspondence between (reasonable enough) functions and their derivatives so the translation between the two conventions is completely trivial.
| {
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Particle density operator in second quantization form The particle-density operator is given by
$n(\mathbf{x})=\sum_{\alpha}\delta^{(3)}(\mathbf{x}-\mathbf{x}_{\alpha})$, then how to derive its representation in terms of creation and annihilation operators $n(\mathbf{x})=\psi^{\dagger}(\mathbf{x})\psi(\mathbf{x})$?
| $\newcommand{\bx}{\mathbf{x}}
\newcommand{\psih}{\hat{\psi}}
$This is worked out on p. 20 of Fetter and Walecka. I'll add just a little extra detail here.
Your particle density operator $n(\bx)=\sum_\alpha\delta(\bx-\bx_\alpha)$ is in first-quantized form and $\hat{n}(\bx)=\psih^\dagger(\bx)\psih(\bx)$ is second-quanti... | {
"language": "en",
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On Einstein notation with multiple indices On Einstein notation with multiple indices: For example, consider the expression:
$$a^{ij} b_{ij}.$$
Does the notation signify,
$$a^{00} b_{00} + a^{01} b_{01} + a^{02} b_{02} + ... $$
i.e. you sum over every combination of the indices? Or do you sum over the indices at the sa... | Well, you do it one at a time:
$$a^{ij}b_{ij} = \sum_{j}a^{ij}b_{ij} = a^{i0}b_{i0}+a^{i1}b_{i1}+(\dots). $$
Then you expand on the other index
$$a^{ij}b_{ij} = a^{i0}b_{i0}+a^{i1}b_{i1}+\dots = (a^{00}b_{00}+b^{10}b_{10}+\dots)+(a^{01}b_{01}+a^{11}b_{11}+\dots)+(\dots).$$
If you write $a^{jj}b_{jj}$, then you will obt... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67295",
"timestamp": "2023-03-29T00:00:00",
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Is length/distance a vector? I have heard that area is a vector quantity in 3 dimensions, e.g. this Phys.SE post, what about the length/distance? Since area is the product of two lengths, does this mean that length is also a vector quantity, and why?
| Length and distance are not vector quantities (they are scalar quantities), but position and displacement are vector quantities (at least according to common terminological conventions). Here is how all of these are defined. Note that I am restricting the discussion here to vectors in three-dimensional Euclidean spac... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67375",
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Can deterministic world view be denied by anything other than quantum mechanics If we ignored quantum mechanics and looked at the world with a deterministic Newtonian view. Does not that mean that there is no randomness and that if all the information of the state of the universe during the big bang is accessible one c... | Determinism is not denied by anything (QM included). The so-called no-go theorems against deterministic hidden-variable theories are logically fallacious. They start with the assumption that determinism is false (using fancy names like "free-will assumption" or "no-conspiracy assumption") and conclude, guess-what, that... | {
"language": "en",
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Is a proton collision (collisions like in the LHC) visible to the human eye? I was curious if a proton collision is visible to the human eye.
(This might sound like a really basic question and forgive me if it is. I am very inexperienced in Physics and just wanted an answer to my curiosity)
| These collisions don't produce significant amount of light in the visible range, so the easy answer is "no".
They also take place in a vacuum, inside a beampipe which is itself buried in a detector apparatus that is ten meters plus on a side and packed full of stuff with no room for a human.
That said, there are sever... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67592",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do current-carrying wires heat up? Obviously wires heat up too, but why do they heat up? And for the same reason, why do we get electrical burns?
| All wires which have electric current flowing through them have electrons moving through the wire. The reason for why wires heat up when a current flows through them is that a battery converts chemical energy into electric potential energy. This electric potential energy is given to the electrons, and since the elect... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67639",
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"source": "stackexchange",
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Dissolving oxygen into water I was wondering how one would actually calculate how much oxygen would dissolve into water given the necessary initial conditions, and what those initial conditions would need to be. I assume they would be pressure, and initial concentration, but I really don't know where I would go from th... | Well you wouldn't "calculate" it so much as measure it. You'd have some water, change the O2 partial pressure above it and measure how much dissolves. Then you'd have a chart where you can calculate the chemical potential of O2 in water vs. partial pressure, Henry's law coefficient, ect.
You could try to do a simulati... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the Sun feel hotter through a window? I have this big window in my room that the Sun shines through every morning. When I wake up I usually notice that the Sunlight coming through my window feels hot. Much hotter than it normally does when you're standing in it outside. I know if the window were a magnifying ... | This is due to the greenhouse effect (that how a normal greenhouse works).
Glass has a low thermal conductivity, but is also transparent. So the sun light enters though the transparent window, turns in to heat, and then cannot leave outside. Trapped, the heat accumulates at the air close to the windows, and that is wha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67815",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Why do metal objects in microwaves spark? I heard that electrons accumulate at points on metals, and this clearly explains the arcing phenomenon, but how does a microwave make an electron imbalance on the fork?
|
Why do metal objects in microwaves spark
Those sparks are due to dielectric breakdown of air.
Microwaves are absorbed by metal and majority of it is reflected off with same phase, just like a mirror.
However, because of this, there can be a large concentration of electric fields in some parts, it causes the massive ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67880",
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"source": "stackexchange",
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Radiation: Inverse square law Gamma radiation follows the inverse square law, I understand this as "double the distance, quarter the intensity"
So if you have a gamma source, at the source (distance = 0), the Intensity is $I_0$, and say at distance = 1, the Intensity is $\frac{I_0}{2}$ (You can't work this out just fro... | This isn't the intensity as a function of distance from a point source in open space. It's intensity as a function of penetration through shielding. They're defining $x$ as the amount of material that a gamma ray has a probability of 1/2 of penetrating. Independent probabilities multiply, so the probability of penetrat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67965",
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"source": "stackexchange",
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Ball jumping from water Few days ago I played with ball(filled with air) in swimming pool. I observed interesting phenomenon.
When I released a ball from 3 meters depth the ball barely jumped above the water surface but when I released it from 50 cm depth it shoot out of the water like nothing.
I observed when released... | At 50cm 'depth' the ball was not actually submerged, because the water did not have sufficient time to refill the 'crater' created by the ball entering the water. The ball can be said to be 'floating' on the base of the crater. As the water returns at very high speed to refill the crater the bottom of the crater with t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68055",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Nuclear Binding energy The nuclear binding energy, is the energy that is needed to seperate the nucleons in a nucleus. And binding energy is also defined as the energy given out when a nucleus forms from nucleons.
Also the larger the nucleus is, the more energy is required to break it apart, so why doesn't that mean t... | Your basic nuclear reaction conserves the number of nucleons present.1
That is important, because at a bit less than 1 GeV each the mass of the nucleons dominates the total energy of all these states.
So the only place available to get or lose energy in a reaction is by
*
*Changing the flavor of nucleons. Every neut... | {
"language": "en",
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Why do stars flicker? Why do stars flicker and planets don't? At least this is what I've read online and seen on the night sky. I've heard that it has to do something with the fact that stars emit light and planets reflect it. But I don't get it, isn't this light, just "light"? What happens to the reflected light that ... | This is just a sidenote to Nijankowski's nice answer: This twinkling of stars caused by atmospheric turbulence was a major problem for the earlier reflecting telescopes when astronomers tried to look deep into the sky.
Placing the telescope over mountains solved only a part of the problem. A good solution was brought u... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68200",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is this a correct description of bonding in a metal? I am reading the paper "Twenty five years of Finnis-Sinclair potentials" by Graeme Ackland, Adrian Sutton, and Vasek Vitek, Philosophical Magazine 2009, 89, 3111-3116. It is a review-type article describing the notion that pair potentials are inadequate for describi... | I'm not sure if it's correct. However assuming that it is, keep in mind atoms in a metal are positively charged relative to the "electron sea". That being the case, intuition says if you have more atoms near eachother in a metal, you have larger positive charge density, which diminishes the electrostatic attraction (po... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68265",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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No well-defined frequency for a wave packet? There are similar questions to mine on this site, but not quite what I am asking (I think). The de Broglie relations for energy and momentum
$$ \lambda = \frac{h}{p},
\\
\nu = E/h .$$
equate a specific frequency and wavelength to a particle, yet we know that a wave packet
i... | This is a very good question.
As Ben Crowell says, the photon life-time is finite and so its energy is spread by a range of frequencies, i.e. it's not a delta-function over a specific frequency.
The photon's energy can be obtained integrating over all the spectrum and might be the one corresponding to the peak, E= h•f... | {
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Frame of reference of the photon? In the frame of photon does time stop in the meaning that past future and present all happen together?
If we have something with multiple outcomes which is realized viewed from such frame? Are all happening together or just one is possible?
How the communication between two such frame ... | I think you are asking about how a photon experiences the passage of time? There is no right time. Photons are not ordinary things moving through space. So from the point of view of the photon this time is not moving at all but the point of view of the photon is that it's place in space is changing but no time is pass... | {
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Is my boss wrong about our mechanical advantage from our pulley system? I work on a drilling rig as a roughneck and we had a lecture today (at the office) about mechanical advantage in pulley systems. Now, I know that my boss is well educated in oil drilling, but my instincts tell me that he may have this one wrong.
A ... | As a crane operator since 1972 I work a lot with pulleys blocks and you are a 100% right, looks like you are rig with 6 parts lines which multiplies by six the line pull of the winch.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68841",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Neutrinos: how can they carry information about universe? I know that neutrinos are particles with a very small mass and no electric charge. They infrequently interact with matter and so they can give us information about the "old" universe. But how can they do it?
| In the "old" universe there is interaction of matter by the the 4 fundamental forces. Neutrinos occur in the weak nuclear interactions. By studying the neutrinos one can study these weak interactions. They might not interact much, but they sure do carry energy.
So by a application of the conservation of energy one cou... | {
"language": "en",
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If the multiverse theory is true, can there be a Universe where there are different laws of physics? This is probably a very difficult question. But my question is essentially this, if there are other Universes can different laws of physics exist in those Universes and if so, can't there be a Universe where the laws of... |
If the multiverse theory is true, can there be a universe with different laws of physics.
Yes, of course. This follows trivially from the way that you phrased the question ie as a syllogism.
However, the 'if' is a very big if. The multiverse hypothesis is highly speculative, not very well understood, and has absolu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68987",
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Why can't we obtain a Hamiltonian by substituting? This question may sound a bit dumb. Why can't we obtain the Hamiltonian of a system simply by finding $\dot{q}$ in terms of $p$ and then evaluating the Lagrangian with $\dot{q} = \dot{q}(p)$? Wouldn't we obtain then a Lagrangian expressed in terms of $t$, $q$ and $p$? ... | While I appreciate that Wouter's response shows that you can not indeed just perform the aforementioned substitution, it really doesn't answer the question (i.e. why doesn't the substitution work) in my opinion.
The underlying confusion probably comes from the fact that in mathematics if substitution $\dot{q}(p)$ is in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69133",
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Is it possible to accelerate a mass indefinitely using gravitational field? As a particle's velocity increases, its mass increases(gamma times). Therefore, if a particle is in a gravitational field, the gravitational force it experiences must also increase(gamma times). The net acceleration of the particle, i.e.(gamma*... | (The below answer from five years ago is wrong, I will write a corrected answer soon.)
No. It is not possible. The misconception you have is because you are thinking of the gravitational field as being constant. However, this is not true. Ignoring air resistance for the time being, consider a projectile launched off t... | {
"language": "en",
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Doubt over Kelvin-Planck statement of thermodynamics' second law I have a doubt over the Kelvin and Planck's statement of thermodynamics' second law, in particular applied to a cycle. Let's take a Carnot cycle as an example, and let's call the first two transformations (the isotherm and the adiabatic) done. Now, isn't ... | in simple words we can expain kp statement as it is impossible to completely convert heat into work in a cycle(*).
while in case of a single process say a isothermal expansion as dt=0 therfore ineternal energy which is a function of temp so dE = 0 neglecting k.e and p.e so from 1st law we get dq = dw .
in isothermal ... | {
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Why do some air-conditioned stores blast you with jets of air as you enter? I went to a grocery store on a hot day that was very well air-conditioned, and I noticed as I went through the open entrance that there seemed to be a very powerful downward air current right at the doorway. After crossing the invisible thresh... | This is called an air curtain or air door and it actually keeps flying insects from being able to enter the store. It also helps trap the colder air inside.
Edit: see the link for how it works.
| {
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"url": "https://physics.stackexchange.com/questions/69510",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Operator on Function of Momentum (QM) I have exactly 0 clue on how to start this problem, but I would be forever grateful for a hint in the right direction.
Given the operators $\hat x=x$ and $\hat p=-i\hbar \frac{d}{dx}$, prove the following relation:
$$
[\hat x, g(\hat p)]=i\hbar\frac{dg}{d\hat p}.
$$
| Like Prahar had said, the problem reduces fairly simply in momentum-space.
We note that, in such space: $\hat x = i\hbar\frac{\partial}{\partial p}$ and $\hat p=p$, thus, using some auxiliary function $f$:
$$
[\hat x,\hat g(\hat p)]f=i\hbar\frac{\partial (\hat gf)}{\partial p}-i\hbar\, \hat g\frac{\partial f}{\partial ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69577",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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A water pipe from sea level to beyond the atmosphere If a pipe extended from just above the ocean floor to outside the atmosphere, would water be sucked up it by the vacuum beyond the atmosphere? If a hole was made in the pipe, above sea level, how would that affect the flow of water? Would it stop it completely?
| From what I understand, vacuums such as space don't actually "suck" or "pull" at all.
When a box of compressed air is introduced to a vacuum, the air molecules are actually being pushed by the other, higher-pressure air molecules into the low-pressure region of space. This means that, with regards to your question, the... | {
"language": "en",
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Are Lagrangians and Hamiltonians used by Engineers? Analytical Mechanics (Lagrangian and Hamiltonian) are useful in Physics (e.g. in Quantum Mechanics) but are they also used in application, by engineers? For example, are they used in designing bridges or buildings?
| In civil engineering they use it for structures, and strength of materials in the elastic realm. It goes by the name of the enegy method. Google books might give an indication.
Some authors are Beer and the mechanical engineer Stephen Timoshenko.
This is for some what "static" indeterminant structures. So, there is... | {
"language": "en",
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A rope attaches the Moon to the Earth. What happens? Consider the Earth (mass $M$, radius $R$, rotating about its own axis at $\Omega$) and the moon (mass $m$, radius $r$, with axial rotation equal to $\omega_m$), whose centre of masses are $d$ apart. They rotate around their barycentre at $\omega_e$ and $\omega_m$ rad... | The string breaks. Though on an elementary level, it appears as though the orbit of the moon about its barycentre is circular, its actually elliptical. So the distance between the centres of the earth and the moon is not constant, so the string breaks under the tremendous tension developed in it.
| {
"language": "en",
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"source": "stackexchange",
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How is energy extracted from fusion? I understand that combining deuterium and tritium will form helium and a neutron. There are three methods to do this (1) tokamak (2) lasers and (3) cold fusion. I would like to know after helium is formed. How is that energy extracted from tokamak and stored?
| Another, non mainstream thought is the use of Helium-3 instead Helium-2 of as a fuel:
3He + 3He → 2 1H + 4He + 12.9MeV
or:
2H + 3He → 1H + 4He + 18.4MeV
Here the reaction products are all charged, which means that they could work directly on an electrostatic field, thus transferring their kinetic energy directly to a c... | {
"language": "en",
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Thermal radiation in the Unruh Effect The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator):
$$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} \langle n | O | n \rangle e^{-2 \pi n \omega}(1-e^{-2 \pi \omega})=Tr(O \rho_{\Omega... | First, let's see the density matrix of thermal mixture (in some cases is the Planck's law):
$$
\rho_{Thermal}=\frac{1}{Z}\sum_{n=0}^{N}e^{-\beta E_n}|n\rangle \langle n|
$$
Now we note that the expectation value $\langle \Omega|O|\Omega \rangle$ is equal to
$$
\frac{1}{Z}\sum_{n=0}^{N}e^{-\beta E_n}\langle n|O|n \rangl... | {
"language": "en",
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How is time measured inside the bubble created by an Alcubierre drive? I am a layman. I am aware that the Alcubierre Drive has not yet been proven to be possible, but there is something about the concept itself that I am confused about. If there is no movement within the bubble, how is time measured inside the bubble? ... | The passage of time inside the bubble will be the same as outside the bubble; the passengers inside the bubble will be able to transfer between points separated by vast distances as if they were effectively moving faster than the speed of light but locally this is not the case since it is impossible to move faster than... | {
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Rate of twinkling of stars According to "Why do stars flicker?", the twinkling of stars (stellar scintillation) is caused by the thick layers of turbulent air in the Earth's atmosphere. While the explanation is convincing, it would be better to have some quantitative justification.
Since the twinkling of stars is easi... | The underlying theory would be atmospheric turbulence with the size of turbulent elements ranging from several hundred meters to millimeters. Therefore, the twinkling rate will not be a single frequency but a continuous spectrum of frequencies ranging from 0.001 Hz to 1000 Hz. Of course, the amplitude of the lower freq... | {
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Is sound relative? Is sound relative?
For example, if I and my friend are having a ride at 1000 mph and I shout towards him (speed of sound 700 mph). What would happen? Will the speed of the sound relative to the ground be 1700 mph? Or will it be something else? Why?
| The speed of sound is a property of the medium(air). So speed of sound is fixed with respect to the medium. As the medium is at rest with respect to the ground(assuming no wind), the speed of sound w.r.t ground will stay 700 mph.
If there is wind, you vectorialy add velocity of the wind and velocity of sound relative t... | {
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How does rolling resistance of rail wheel depend on diameter? Freight train is more efficient than truck due to lower rolling resistance. And I wonder which one has lower rolling resistance<>, small diameter or larger one or it doesn't not depend on diameter at all? Both are steel wheel on steel rail.
| If you look at the Wikipeda article on rolling resistance that @fibonatic pointed out, you can find an equation for the coefficient of rolling friction:
$C_{rr}=\sqrt {\frac z d}$
There is another equation after it that is for steel on steel, but that also shows that C is proportional to $d^{-\frac 1 2}$. So from this... | {
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What are the forces acting between two air bubbles in water? The exact question is
Two air bubbles in water
*
*attract each other
*repel each other
*do not exert any force on each other
*may attract or repel depending upon the distance between them.
The chapter is about gravitation.
The given answer is
A light... | I think I see the argument:
One should go to the line joining A and B. And draw two vertical tangent on the right for A and on the left for B. There is more water volume to attract the water in the region on the left of A, so there will be a force towards B, and vice versa.
Anyway bubbles in liquids are not a simple ma... | {
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Buoyancy in muddy water Consider the buoyancy force in water with very small but macroscopic particles in it. Such particles (suspension) will very slowly drift downwards and will eventually settle on the bottom. If one did not know that the particles are present there then for calculating the buoyancy force, $F = \rho... | I would think the tension force will increase, as the average liquid density has increased. Note, for example, that the water pressure on the bottom will increase more than it would be if the same volume of water is added. The particles move downwards with a constant speed, so their full weight acts on the water (until... | {
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Is there an EMF in a conductor moving at constant speed across the uniform magnetic field If a conductor - a long rod - moves at constant speed across the "lines" of a uniform magnetic field, is there an EMF within this conductor? Or, if a conducting rod rotates at uniform rate, pivoted in the middle or at one of its ... | If the setup you have in mind is like the image below, there will be a voltage across the conductor.
This is due to the fact that there no closed path for a current.
The mobile electrons in the conductor "feel" a magnetic force towards the b end of the rod.
The electrons "bunch" up at that end resulting in an electri... | {
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What causes a black-body radiation curve to be continuous? The ideal black-body radiation curve (unlike the quantized emission seen from atomic spectra), is continuous over all frequencies. Many objects approximate ideal blackbodies and have radiation curves very similar in shape and continuity to that of an ideal bla... |
perhaps the degree of quantization is so small the radiation curves look continuous
Yes, this is the reason. The correspondence principle says that quantum mechanics has to become classical in the appropriate limit. One way to obtain an appropriate limit is with large numbers of particles. As you increase the number ... | {
"language": "en",
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What is the invariant associated with the symmetry of boosts? Noether's Theorem states that if a Lagrangian is symmetric for a certain transformation, this leads to an invariant: Symmetry of translation gives momentum conservation, Symmetry of time gives Energy conservation etc.
The Galilean principle stating that all... | The conserved quantity corresponding to boost symmetry is
$$
\int d^3 x (P_0 x_i - P_i t)
$$
which is the relativistic analogue of $x_{CM} - v_{CM} t$, the position of the center of mass at $t=0$. It is quite a useless conserved quantity, and that is why people don't talk about it.
| {
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"source": "stackexchange",
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Why does positronium decay into 2 photons more often than into 3 photons? I cannot find the answer to the above question.
I know that para-positronium is created with a probability of $25\%$ and decays into 2 photons, while ortho-positronium is created with a probability of $75\%$ and decays into 3 photons.
I also kn... | Jezstarski is mostly correct,
The para-positronium (p-PS) state ends up being the main mode of annihilation of positronium (PS). Positrons can annihilate in at least eight different ways but once ortho-positronium (o-PS) forms in a void/vacuum, it has additional time to undergo another mode of annihilation.
P-PS annih... | {
"language": "en",
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Difference between a quantum process and a thermal process? I was reading an article online pertaining to quantum mechanics and I stumbled across these few sentences.
A look at the corresponding energy regimes shows (Beck and Eccles 1992) that quantum processes are distinguishable from thermal processes for energies ... | The quantum uncertainty in position of particles (micro sites) of mass $m$ moving or vibrating at thermal speeds characteristic for a temperature $T$, is given by the thermal De Broglie wavelength $\sqrt{\frac{2 \pi \hbar^2}{m \ kT}}$. If this uncertainty in particle (micro site) position is larger than or comparable ... | {
"language": "en",
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Any physical example of an "explosive" differential equation $ y' = ky^2$? I was told that in physics (and in chemistry as well) there are processes that may be described by a differential equation of the form $$ y' = ky^2. $$ That is, the variation of a variable depends from the number of pairs of the elements.
I und... | This is perhaps stretching the definition of "physical" but Metcalfe's law says that the value of a telecommunications network is proportional to the square of the number of users. A growing network might reasonably have a rate of growth proportional to its "value", which would lead the the differential equation you de... | {
"language": "en",
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"source": "stackexchange",
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Are orbits reversible in general relativity? It seems if I reverse velocities then things begin orbiting backwards, at least in classical mechanics.
From here:
Every orbit and trajectory outside atmospheres is in principle reversible, i.e., in the space-time function the time is reversed. The velocities are reversed a... | For the simple case of a black hole in a locally flat spacetime(so that it does not accelerate) you don't have to worry about losing precision due to relativistic effects, because Schwarzschild and Kerr black holes emit exactly zero gravitational radiation(because they are both cylindrically symmetric), that is: the me... | {
"language": "en",
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What are the advantages in using 2 identical capacitors? What advantage might there be in using two identical capacitors in parallel connected in series with another identical parallel pair, rather than using a single capacitor?
| The resultant capacitance of capacitors in parallel is the summation of the capacitances:
$$C_{eq} = \Sigma C$$
While, the inverse of the resultant capacitance of capacitors in series is the summation of their inverses:
$$\frac{1}{C_{eq}} = \Sigma\frac{1}{C}$$
Connecting capacitors in parallel will therefore help in in... | {
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What is the sign of the work done on the system and by the system? What is the sign of the work done on the system and by the system?
My chemistry book says when work is done on the system, it is positive. When work is done by the system, it is negative.
My physics book says the opposite. It says that when work is done... | Taking it in a different sense: chemistry is taken the approach that you want to create a new configuration inside the reaction vessel (and input energy like heat or such) and the physics course book is taking about letting the system doing work (eg. burning what is in the reaction vessel).
In both ways entropy will b... | {
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Overtaking with non-constant acceleration I have tried to solve this problem by adding the sum of the displacements during acceleration, constant velocity and deceleration, but it does not work out.
Question:
A car accelerates from rest to $20~\text{m/s}$ in $12$ seconds ($a =5/3~\text{ms}^{-2}$), it travels at $20~... | Plotting the displacement time graph helps a lot in these kind of problems.
From this graph we can say the RC is ahead of the car initially. The car catches up and overtakes the RC at t=20 seconds.
Note:
You do not need graph plotting tools to plot these graphs. Basically, you don't need to plot these graphs to accura... | {
"language": "en",
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A Rolling Quarter A U.S quarter is rolling on the floor without slipping in such a way that it describes a circular path of radius $R=4 \text{cm}$. The plane of the coin is tilted at an angle of $\theta=45^{∘}$ with respect to the horizontal plane. Find the coin's period $T$ in seconds, that is, the time it takes for t... | This is a well known problem. So, I will try to solve it in the general case. For a somewhat more detailed answer, please look at Chapter 9 of David Morin's Introduction to Classical Mechanics book. Also, since this looks like a homework, whenever you think you can do the rest of the problem yourself, stop reading and... | {
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Can spheres leaking charge be assumed to be in equilibrium? I am struggling with the following problem (Irodov 3.3):
Two small equally charged spheres, each of mass $m$, are suspended from the same point by silk threads of length $l$. The distance between the spheres $x \ll l$. Find the rate $\frac{dq}{dt}$ with which... | I think the answer is sonething that you have overlooked, a (. ) AKA FULL STOP.
You state that the web results say the answe is dt/dq a this is a constant because (a) is A constant.
The question you ask is
"
Does the problem tacitly imply we should assume equilibrium and hence dt/dq is constant, or am I missing someth... | {
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"source": "stackexchange",
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Statistical analysis of data in Physics Analysis of data is integral in bridging the gap between theory and experiment. How much do the results of the analysis depend upon the choice between Bayesian and frequentist methods?
For instance, consider experiments in particle physics. This paper by Louis Lyons states that p... | If there are enough data and the prior is not completely unreasonable, the frequentist and the Bayesian approach give essentially the same answer. This is related to the central limit theorem.
If data are fairly scarce, the two approaches may differ a lot. In this case the Bayesian approach is far preferable but only ... | {
"language": "en",
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Sliding force less or equal? Why is the force required to slide a magnet off a steel plate A LOT less than the force required to directly pull it off?
The force required to pull the magnet can be: 20lb
While the force required to slide the magnet can be: 1lb more/less.
Why is that?
| After much studying, and experimentation.
I conclude that indeed, the force required to "slide" the magnet's is less than the force required to "pull" them directly off.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/72900",
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How to prove that we are living in a 3+1D world? Is there any scientific experiment that can lead us to conclude we live in 3 spatial dimensions without the premise of the conception of limited dimensions?
Thank you all who helped in the improvement of this question (which was not clear at first).
EDIT:
I know that th... | Verify any inverse-square law process, like gas diffusion or classical forces.
| {
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The relation between Gauss's law and Coulomb law and why is it important that the electric field decrease proportionally to $\frac{1}{r^{2}}$? My question relates to the third MIT's video lecture about Electricity
and Magnetism, specifically from $21:18-22:00$ : http://youtu.be/XaaP1bWFjDA?t=21m18s
I have watched the d... | Gauss's law states that the ratio of charge and the dielectric constant is given by a (two-dimensional) surface integral over the electric field:
$$\int E\cdot dA=\frac{Q}{\epsilon_0},$$
where I have omitted vector notation for simplicity.
It can be linked to Coulomb's law by assuming spherical symmetry of the electr... | {
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Projectile Motion Question involving a ball and a ramp inclined at an angle The question is to finde the initial horizontal velocity of the ball at end of the ramp, where it is released.
I know how to do this using gravitational potential energy and kinetic energy ($v=\sqrt{2gh}$), assuming all potential energy is conv... | There is an 'error' in your reasoning. The velocity of the ball at the end of the ramp is not given by $v=\sqrt{2gh}$. This assumes that the ball slides down the ramp. Presumably it rolls and gains rotational as well as translational kinetic energy. If the ball has uniform density and rolls without slipping then the ve... | {
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How to block neutrons What is a good way to block neutrons and what is the mechanism that allows this? It's my understanding that polyethylene is somewhat effective. Why?
| Being bulk neutral neutrons participate only weakly in electromagnetic interactions which is the dominate interaction for charged particles.
Instead neutron scattering can be thought of as primarily a contact interaction with the nuclei of atoms in the way. Light atoms (and hydrogen in particular)
*
*have a larger ... | {
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How to derive the metric for a 2-sphere I have a question in Polchinski's string theory vol I p 167. It is said
For example,
$$ds^2= \frac{ 4 r^2 dz d \bar{z} }{(1+ z \bar{z})^2} = \frac{ 4 r^2 du d\bar{u}}{ (1+ z \bar{z})^2} \tag{6.1.3}$$
describes a sphere of radius $r$ and curvature $R=2/r^2$.
Why Eq. (6.1.3) ... | Writing :
$x_1 = \sin \theta \cos \phi$,
$x_2 = \sin \theta \sin \phi$,
$x_3 = \cos \theta $
The unit radius $2$-sphere metrics is $ds^2=(d\theta^2 + \sin^2 \theta ~d\phi^2)$
We are going to use the stereographic projection : $ \large z = \frac {x_1+ix_2}{1-x_3}$
This gives : $z = cotg(\theta/2) ~e^{i \phi}$
So, $$ d... | {
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What happens when the black hole at a galactic core eats the galaxy? I'm making several assumptions, not sure if any are correct:
*
*there is a black hole at the center of a galaxy
*the black hole is eating the galaxy
Eventually the galaxy will be gone, right?
Has this been observed? Do we know what happens after... | A black hole is "just" a massive object. Interesting things happen when close to the black hole, because the high gravity makes all the Einsteinian effects more apparent, including the "horizon" and the trapping of light, and so on. But from afar, this is "just" a massive object, which other objects handle like any oth... | {
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What is the percentage of useful energy do we get from matter-antimatter annihilation? This is a theoretical question since we haven't made enough antimatter to try it in reality of course. But I am asking about the physics part in this.
Also, by "useful energy" I mean the energy we are able to use either as a heating... | I found a interesting paper on the use of antimatter for rocket propulsion from NASA that addresses this subject. Your question has a pretty complicated answer.
I think you will find more formation than you wanted reading that article. In the report it says about an electron-positron collision:
His results indicate ... | {
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Why does light diffract only through slits? We can see diffraction of light if we allow light to pass through a slit, but why doesn't diffraction occur if we obstruct light using some other object, say a block? Why are shadows formed? Why doesn't light diffract around the obstruction as it does around the slit?
| Diffraction can also occurr around abstruction . Suppose u put ur finger infront of light w.front such that ur fingers shadow will appear on the screen placed behind ur finger . When light w.front strikes ur finger then the light ray at the upper and lower extremes of obstruction will bend and enter in to shadow region... | {
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"url": "https://physics.stackexchange.com/questions/74051",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Localization of wave or particles
Nonlinear field theories contain a large number of localized solutions.
I have found this text in a article. What I don't understand is "what is localized?". Is it refer defining position of a particle or a wave?
Can someone give me an elaboration with example?
| I would guess that the article is referring to solitons. I'm not sure if every non-linear system gives soliton solutions, but many do. The Wikipedia article I've linked gives lots of examples of classical solitons, but I'm not sure to what extent (if at all) they're important in the Standard Model. Perhaps one of the Q... | {
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Why is there a factor of $4\pi$ in certain force equations? I mean to ask why there is $4\pi$ present in force equations governing electricity? Though all objects in universe are not spherical and circular, the constant of proportionality in both equations contain $4\pi$. Why?
| The main reason is that it makes the calculation easier and the results look nicer. For example, suppose the field (or force) is given by
$$ E = \frac{1}{4\pi} f(\mathbf{r})$$
for some function $f(\mathbf{r})$.
If the system process rotational symmetry, after sum over the density, you will get a factor of $2\pi$. If th... | {
"language": "en",
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"source": "stackexchange",
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Degrees of freedom of the graviton versus classical degrees of freedom I have a puzzle I can not even understand.
A graviton is generally understood in $D$ dimensions as a field with some independent components or degrees of freedom (DOF), from a traceless symmetric tensor minus constraints, we get:
*
*A massless g... | I used to count dofs in terms of spinor representation. There are two spinor representation of SO(3,1) (1/2,0) and (0,1/2) denoted by dot and no-dot indices.
Vector (spin 1) representation in spinor indices is (1/2,0) X (0,1/2) = (1/2,1/2) which has 4 dofs. If the theory is massless, the theory is gauge invariant, the... | {
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Path of least resistance vs. short circuit Some sources on the web claim that "electricity follows the path of least resistance" is not true, e.g. this physics SE question. However, in every explanation of "short circuits", the author says that current flows through the short because it's following the path of least re... | The statement electricity flows through the path of least resistance means that electricity flows more into the path with less resistance, because it is proportional to the inverse of resistance, obeying:
$$I_1=I\frac{R_2}{R_1+R_2}$$
$$I_2=I\frac{R_1}{R_1+R_2}$$
From these relations you can find out that in two cases ... | {
"language": "en",
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Melting and freezing point Why is the melting and freezing point of a substance are always the same? This was quoted in my textbook but they didn't give a reason for this being so.
| It's the same temperature because it's the only temperature at which the liquid phase and the solid phase may co-exist – which is a symmetric description of the temperature.
When we add heat to this mixture of "ice" and liquid, it will keep the temperature at the same point but the percentage of "ice" will be decreasi... | {
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Does alternating current (AC) require a complete circuit? This popular question about "whether an AC circuit with one end grounded to Earth and the other end grounded to Mars would work (ignoring resistance/inductance of the wire)" was recently asked on the Electronics SE.
(Picture edited from the one in the above lin... |
Does AC current require a complete circuit?
Can AC circuits really function without a complete loop?
I think that neither AC nor DC theoretically needs a complete loop. (ie, without reusing the electrons/charge carriers that flow in the circuit)
And you don't even need to think about capacitors for that. A capacitor ... | {
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Red Giant branch and Asymptotic Giant branch What's the difference between the RGB and the AGB? I can't seem to find an clear distinction anywhere.
Thanks.
| Red giants and asymptotic giants have some close similarities, and one actually evolves into the other. Both have an extended envelope of relatively cool, non-burning material (mostly $\rm{H}$, $\rm{He}$). They also each have a core of dense, non-burning material; in the case of the red giant this is mostly $\rm{He}$, ... | {
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When is temperature not a measure of the average kinetic energy of the particles in a substance? I had always thought that temperature of a substance was a measure of the average kinetic energy of the particles in that substance:
$E_k = (3/2) k_bT $
where $E_k$ is the average kinetic energy of a molecule, $k_b$ Boltzm... | There are a number of ways of defining temperature, for example using:
$$ {\partial S \over \partial E} = {1\over T} $$
This definition is the basis of negative temperatures. This is a case where the temperature is not a measure of average kinetic energy.
| {
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Unpolarized light vs. randomly rotating polarized light? I am confused with physical picture about unpolarized light.
Is unpolarized light very fast rotating polarized light? or co-existing state of two orthogonal polarization? (or something else?)
If there is a linear polarizer which rotates very very fast and randoml... | Unpolarized light can be thought of as a superposition of wave trains of a finite duration of order $0<\tau<\infty$, each of which has a certain pure polarization, which may be elliptical, with a random direction. The phases of the pulses and their start and end times are also random.
What this means in practice is tha... | {
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What are magnetic field lines? Does a magnetic field have concentrations of magnetic force lines as seen when putting iron filings over top a bar magnet or are these imaginary? I.e. are they just an artifact of the iron being a 'conductor' of the magnetic field lines making them look like they are concentrated along t... | Field lines are a visualization tool for the magnetic field (and for other fields, too). They are a way of representing the field (which is a physical---if intangible---thing) in a drawing. They are not unique in this: there are other ways of representing vector fields, but they have a long history.
Now, magnetic field... | {
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Frequency of small oscillation of particle under gravity constrained to move in curve $y=ax^4$ How to find the frequency of small oscillation of a particle under gravity that moves along curve $y = a x^4$ where $y$ is vertical height and $(a>0)$ is constant?
I tried comparing $V(x) = \frac 1 2 V''(0) x^2 + \mathscr O(... | You got the correct answer on your own, but I'd like to point out a useful treatment for this type of questions, from Landau and Lifschitz, Course of theoretical physics.
It will get you only the result up to a numerical constant, but it's
beautiful and absolutely general.
I quickly recall the definition of an Euler ho... | {
"language": "en",
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Why does boiling water in the microwave make a cup of tea go weird? When I boil water in the kettle, it makes a nice cup of tea. Sometimes I need to use a microwave because a kettle isn't available. I boil the water in the mug and it looks pretty normal, but when I drop in the teabag the water froths up and looks foa... | A common problem with microwave is that you lack control of the
temperature of the water.
Second problem is that the water is heated from the top and the sides of the mug mostly.
Result is, that the content of the mug is not really boiling hot everywhere,
altogether (after mixing) it is well below 100 °C
A side eff... | {
"language": "en",
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Could we see a lower dimension within our universe? My question refers to the fact, that, say if our universe were to be sitting on a 4 (spatial) dimensional plane, that we cannot see, then within our universe could there be a point mass in which 1 or 2 (spatial) dimensions could exist. We may not be able to see them, ... | Based on the string theory tag in your question, you're probably asking for something like a brane world. In such a scenario, standard model interactions, which are mediated by open strings, and are thus bound to the branes. According to some research (e.g.), it is possible to ensure general relativity also behaves nor... | {
"language": "en",
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What is the difference between phase difference and path difference? The path difference is the difference between the distances travelled by two waves meeting at a point. Given the path difference, how does one calculate the phase difference?
| Path difference and Phase difference are very similar things.
Let me show this in a bit more intuitive way!
In our world, we have "good" waves and "bad" waves (atleast for calculations)
For example :
*
*A good wave is y=sinx plotted on a graph having crests and troughs at $\frac{n\pi}{2}$ alternatively.
*
*A ba... | {
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Does light loses its energy when it passes through denser medium? I know it does not because it emerges out of denser medium at 300,000 KM per second, but according to $E=mc^2$ and given that speed of light decreases inside denser medium with refractive index greater than 1, does not it suggest that energy of light ins... | A light wave consists of many photons that give its amplitude. While the frequency of the light stays the same the number of photons or waves amplitude may change if there’s absorption.
Every real substance absorbs and scatters even the transparent. But statistically the frequency is same.
The way you asked the questi... | {
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Are dark energy and zero-point energy the same thing? According to Quantum Mechanics is it possible that the famous "dark energy" and "zero-point energy" are the same thing that drives the accelerated expansion of the universe or maybe related to each other?
| Nobody knows. There are multiple explanations for dark energy that haven't been eliminated. One of the explanations that hasn't been eliminated is zero point energy:
http://arxiv.org/abs/1205.3365.
Another possible explanation is that the alleged expansion is actually a result of neglecting the effects of inhomogeneiti... | {
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Controlling Neutrinos for Communication Neutrinos travel straight through earth at the speed of light. Therefore, it seems that they could be great for intercontinental communication. Of course, I assume a lot still needs to be learned about detecting, producing and controlling neutrinos before they can be used for the... | Radio waves normally transmit information by amplitude or frequency modulation. This assumes there is a carrier wave that can be modulated, and as twistor59 says in his comment, creating a carrier wave using neutrinos would be very difficult.
However many radio and TV stations are already streamed digitally, and in pri... | {
"language": "en",
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What does imaginary number maps to physically? I am taking undergraduate quantum mechanics currently, and the concept of an imaginary number had always troubled me. I always feel that complex numbers are more of a mathematical convenience, but apparently this is not true, it has occurred in way too many of my classes, ... | @Prathyush's answer is completely correct and provides nice reference, but I just wanted to add that behind his discussion about phases and path integrals is the concept of unitary and conservation of probability, which is a physical concept, and the OP asked about what imaginary numbers "map to physically". Thinking ... | {
"language": "en",
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Expansion of the universe and strain From cosmological models that involve expansion of the universe, can we not say that there are ever increasing tidal forces felt by solid bodies?
If so, the material in solid bodies like metal blocks, glass rods, skeletal systems will tend to separate causing a strain on the body wh... | This is really just a footnote to Luboš's answer, but for completeness (and because it's fun :-) we should note that the equation of state of dark energy has not been determined and it remains possible that the ratio between the dark energy pressure and its energy density is less than or equal to -1. If so, this is kno... | {
"language": "en",
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Which way do black hole jets spin? The centers of black holes and quasars often have jets coming out the two poles of an accretion disk, say north and south. Is it known if the two jets spin in the same direction or opposite directions to each other?
| Looking at Earth's spin down upon the north pole, it is counter-clockwise. Looking at Earth's spin down upon the south pole, it is clockwise. The sense of helicity depends upon the observer's position. (If the spin is relativistically propagating, the observer only has one POV. Beta-rays are chiral left-handed until... | {
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Background radiation: radon vs potassium 40 In doing a little research into natural background radiation, I came upon a table from the National Council on Radiation Protection and Measurement (NCRP). It shows that inhaled radon gas is by far the largest contributor to average annual dose equivalent from background radi... | In addition to the deposition location when EnergyNumbers mentions in the comment the types of radiation and the length of the decay chain are an issue.
Radon sits at the top of a long sequence of decays many of which are alpha emitting (quality factor $\approx 10$--$20$) including Po-210 (5.34 MeV alpha, yikes!). Also... | {
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Feynman's subscript notation Consider this vector calculus identity:
$$
\mathbf{A} \times \left( \nabla \times \mathbf{B} \right) = \nabla_\mathbf{B} \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A} \cdot \nabla \right) \mathbf{B}
$$
According to Wikipedia, the notation $\nabla_\mathbf{B}$ means that the subscrip... | The notation $\vec \nabla_B$ means simply that the derivative are applying only on the vector $\vec B$.
That is :
$$(\vec \nabla_B)_i (\vec A\cdot \vec B) = \vec A\cdot\frac{\partial \vec B}{\partial x^i}\tag{1}$$
| {
"language": "en",
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Proof of conservation of energy? How is it proved to be always true? It's a fundamental principle in Physics based on all of our currents observations of multiple systems in the universe. Is it always true to all systems? Because we haven't tested or observed them all.
Would it be possible to discover/create a system t... | A simple solution can be like this-
Firstly, we find the rate of change of kinetic energy.
The process is as follows.
$$\frac d{dt}\left(\frac 12 mv^2\right)=\textbf{F}\cdot\textbf{v}$$
Now imagine this case of a constant force acts on the body which is equal to $-mg$ (minus indicates downward direction). So, the RHS o... | {
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What is the Momentum Operator? I know the equation for the momentum operator, but what exactly is the momentum operator? It's bizarre to me that taking the derivative of the wave function, which is an operator, should return something that isn't just a function. Specifically, my confusion is that first momentum is writ... | The momentum operator, like other operators in quantum mechanics, acts on a given wave function (state). Multiplication of operators in linear algebra is the same as them "acting on" a mathematical object. Originally quantum mechanics was called 'matrix mechanics'; so when you study linear algebra you're really studyin... | {
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If gravity doesn't exist,what are the implications? I just heard about new theories proposed by Erik Verlinde about the fact that Gravity doesn't exist..or at least it's not a foundamental force. My question is : if this is true what are the implications on current models like string theory , eternal inflation ecc ecc ... | I take the question being asked to be:-
"If gravity doesn't exist, what are the implications ?"
Ergo, anything to do with Erik Verlinde is irrelevant to the question.
Gravity is one of the two infinite range forces; the other being the Coulomb force between electric charges.
Unlike electric charges, eg proton and elect... | {
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Are there two types of D-term and two types of F-term in SUSY? I've noticed that one can obtain D-terms either by integrating a vector superfield (the vector multiplet) over superspace or by integrating a Kahler potential over superspace. In both cases we get functions of the D-auxiliary field (albeit different functio... | The D-term is the last term in the Taylor expansion of a vector superfield over fermionic coordinates, $D \theta^1\theta^2\bar\theta^1\bar\theta^2$. Similarly, the F-term is the "middle" term $F\theta^1\theta^2$ which only contains the unbarred fermionic variables. Chiral superfields only depend on these coordinates (... | {
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Why should nature of light(or any quantum object) depend on observation? We know that, in the double slit experiment, observation changes the behavior of a quantum object, that it behaves like a particle when observed and a wave when not observed. But why should its nature depend on observation? What if we didn't exist... | This question is still an open question in science. We know that a particle when it is not observed is described by a wave function, that wave function evolves in time. The wave function is described as a superposition of possible states of the particle (called eigen states)
If a measurement was made, the wave function... | {
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Does the black hole only increase? I don't understand this:
The more mass a Black Hole has, the more gravity it create! The more gravity it has, the more mass it can get!
With this lines, someday, all the universe will be a black hole.
Is this correct?
| That conclusion does not (logically) follow from those two premises.
It's true that if a block hole gains mass, then it's gravitational pull on matter will be stronger. If the gravitational pull is stronger, then matter doesn't have to come as close to the black hole in order to be pulled in. It does not mean, however,... | {
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Surface gravity of Kerr black hole I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand.
Firstly, the metric is given by
$$\mathrm{d}s^2=\left(\frac{\Sigma}{\rho^2}\sin^2\theta\omega^2-\frac{\rho^2\Delta}{\Sigma}\right)\ma... | You are right that the $(\Omega_H-\omega)^2$ term doesn't contribute. This is because it is the square of something that vanishes at the horizon: when you take the derivative, there remains a vanishing factor. As for the other term, since $\Delta$ vanishes at the horizon, this term vanishes except when the derivative h... | {
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Why is the receiver of this solar tower cream-colored? I wonder, why the receiver of this solar tower is not black? Wouldn't a black receiver be more efficient? If not, why is it not white then, but is an intermediate color?
It seems that the receiver of other solar towers, such as Solar One is indeed black:
Does it ... | In the picture you posted the collector is on the other side of the tower so you can't see it. Have a look at this PDF for detailed pictures of the tower - the collector is shown on page 40, and it is indeed black.
| {
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Why doesn't Bernoulli's Principle apply to Current and Resistors in a circuit? Bernoulli's principle makes sense when you apply it to fluids. If you decrease the diameter of a pipe then the velocity of the fluid increases because it needs to keep the same rate of fluid moving through the pipe.
So my question is:
If Vo... | True but in my experience traffic is usually jammed up before going through a tunnel but when you get to the other side the traffic magically disappears....same amount of cars same amount of roads space.
| {
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Is there an easy way to get water at roughly 70°C in our kitchen? Some green tea requires to pour water at 70°C. I have no thermal sensor or kettle with adjustable temperature with me.
Do you know a way to get water at roughly 70°C like “boil water and wait for x minutes” or “mix x part of boiling water with 1-x part ... | "Wait for $x$ minutes" is difficult because the cooling rate will depend on a lot of non-universal details (room temperature, the surface of the water, the material the pan is made of and its thickness).
However, there are two temperatures which are easy to attain in your kitchen. $100\,^\circ\mathrm C$ (don't need to ... | {
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Adiabatic filling of a container Suppose a thermally insulated container is filled with atmospheric air until the pressure reaches 5000 psi. This could represent the filling of a diving cylinder, before thermal dissipation becomes significant.
Initially, then, some mass of air has atmospheric temperature $T_1$ and $p_... | The practical thing that you are missing here is that the air compressor is cooled constantly so that it doesn't melt during operation (can't be adiabatic). So the upper limit on the temperature is driven by the operating temperature of the compressor. Then the other posters comments about heat transfer out of the tank... | {
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Period $T$ of oscillation with cubic force function How would I find the period of an oscillator with the following force equation?
$$F(x)=-cx^3$$
I've already found the potential energy equation by integrating over distance:
$$U(x)={cx^4 \over 4}.$$
Now I have to find a function for the period (in terms of $A$, the am... | Since
$$\frac1 2mv^2+U(x)=U(A)$$
We have
$$dt=\frac{dx}v=\frac{dx}{\sqrt{2(U(A)-U(x))/m}}=\frac{dx}{\sqrt{c(A^4-x^4)/(2m)}}$$
Then
$$\frac T4=\int_0^{\frac T4}dt=\int_0^A\frac{dx}{\sqrt{\frac{c}{2m}(A^4-x^4)}}$$
Thus
$$T=4\int_0^A\frac{dx}{\sqrt{\frac{c}{2m}(A^4-x^4)}}$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/78415",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
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