Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Sum of all forces Let us glue up these two images, where we get closed loop thrust of water. Force $F_3$ has direction $-x$ and force $F_2$ has $x$ direction. What is the sum of all forces? Can it be more than zero? Speed of water is constant.Angles are the same.Half circle is not exactly circled at the ends due to the... | If I understand the question, you are basically talking about a stream of water flowing in a closed loop. Assuming the density is constant, and the speed of the water at each point is constant, then the total momentum of the water (which is the sum of the momentum of each little piece of water in the stream) is constan... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66639",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Function for heating of a planet by its star I'm looking for an algorithmic model which will gives rough estimate of the average temperature of a planet's atmosphere (good enough to say whether there will be liquid water anywhere, or if metals and plastics will melt/ignite) based on the luminosity of its star, the radi... | I recently wrote a tutorial for my astronomy club which seems to address your question. It includes numerical examples that specifically covers planetary temperatures and greenhouse effects.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66715",
"timestamp": "2023-03-29T00:00:00",
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Maximum angular velocity to stop in one rotation with a known torque I have an object I can rotate with a given torque. I would like to stop applying torque once I've reached a defined maximum rotational speed. The maximum rotational speed should be defined so that applying maximum torque will stop the rotation of the ... | To stop the object you must do work. For a constant torque perpendicular to the moment arm, the work it does is equal to $\tau\cdot\Delta\theta$, and you want $\Delta\theta\leq2\pi$.
It should be obvious that the greatest angular velocity that a torque $\tau$ can stop will take it the full $2\pi$ radians to stop. In a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/66866",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Where can I find the full derivation of Helfrich's shape equation for closed membranes? I have approximately 10 papers that claim that, from the equation for shape energy:
$$ F = \frac{1}{2}k_c \int (c_1+c_2-c_0)^2 dA + \Delta p \int dV + \lambda \int dA$$
one can use "methods of variational calculus" to derive the fol... | The paper you're looking for is probably:
"Bending energy of vesicle membranes: General expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders"
Ou-Yang Zhong-can and Wolfgang Helfrich
Phys. Rev. A 39, 5280–5288 (1989)
http://pra.aps.org/abstract/PRA/v39/i1... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
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When are the OPE relevant? I've seen OPEs commonly used in 2d CFT, it's quite apparent to me that, in that case, it dresses a bridge between the algebraic and the operator formalism especially when combined with radial ordering and the use of contour integral. Even more powerful in the minimal models where it leads to ... | My memory of Peskin & Schroder is a little hazy, but they're probably discussing the Shifman-Vainshtein-Zakharov sum rules. The idea is that you can use the OPEs for composite operators representing mesons/hadrons to derive formulae that express meson/hadron n-point functions in terms of the VEVs of various QCD conden... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67298",
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"source": "stackexchange",
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Graphene as optical and UV mirrors One usually hears about graphene as a good thermal conductor, and good light absorber due to its tunable bandgap properties. But i haven't heard about its aplicability as an optical mirror. In fact, mostly the opposite is true: the optical transmissivity of monolayer graphene is very ... | There has been some research in the use of graphene in optics, such as from Berkeley's Ultrafast Nano Optics Group and this article about the use of graphene in digitl communications.
In terms of graphene's UV and visual reflective properties, according to the University of Manchester and "High optical absorbance of gr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/67376",
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What could magnetic monopoles do that electrically charged particles can't? I understand the significance to physics, but what can a magnetic monopole be used for assuming we could free them from spin ice and put them to work? What would be a magnetic version of electricity?
EDIT
Sorry this wasn't clear. The questio... | Partly related to your question, Artificial Magnetic Monopoles Discovered, from an article in ScienceDaily just late last month. The monopoles apparently act the same as the ends of a dipole magnet, as has been suggested by Dilaton in the comment above. A more comprehensive article is from Particle Data Group.
| {
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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... | Norton's Dome is an example of nondeterminism in Newtonian Mechanics. There is a potential $V(r)=mgCr^{3/2}$ (say from a dome shaped like $h=Cr^{3/2}$) that gives multiple solutions with no way to pick when, if, or in which direction the particle moves.
However, this is not a serious blow against determinism because f... | {
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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)
| Hmm, interesting question at least. Visible as in see two balls crash into each other; no, visible as in see the light emitted from the collision; probably not.
The emitted photons are of the order of $\rm{}MeV$, around $10^{-13}\rm{}$ joules. The human eye works at around $10^{-5}$. So individual collisions no.
| {
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"source": "stackexchange",
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How to cut a stone on a White Dwarf? I've heard that white dwarf stars are extremely dense and hard. So, if I had a piece of white dwarf matter, would it be possible to cut it (or otherwise) into a custom shape? How could one do that?
| We know that matter in White Dwarfs and Neutron stars become hugely dense, ten or fifteen orders of magnitude more dense than ordinary matter. What we don't know is, if such matter stays stable away from the deep gravity well of the star corpses where they form.
We certainly haven't found a single grain of such matter ... | {
"language": "en",
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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 ... | Most likely is its always hotter than the outside. the frames absorb heat up into the 160 plus mark depends on where you live. 100 degrees usually about 150 degrees gained we call it solar gain.
| {
"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?
| The basic idea is that microwaves are a form of electromagnetic radiation-- light. That light consists of an oscillating magnetic and electric field component. By Faraday's Law of Induction, a magnetic field in flux induces a current in a conductor... so it is the non-conservative, induced electric field in the conduct... | {
"language": "en",
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How general relativity gets to an inverse-square law I understand that a general interpretation of the $1/r^2$ interactions is that virtual particles are exchanged, and to conserve their flux through spheres of different radii, one must assume the inverse-square law. This fundamentally relies on the 3D nature of space.... |
I understand that a general interpretation of the $1/r^2$ interactions is that virtual particles are exchanged [...] General relativity does not suppose that zero-mass particles exchanged.
You don't need quantum field theory for this. In a purely classical field theory, we have field lines, and the field lines from a... | {
"language": "en",
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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... | Nuclear physics is in the realm of quantum mechanics. To first order one can think of "one nucleon" in the collective left over strong interaction field of all the rest, as a potential. As for strong interactions nuclei are indistinguishable to first order the binding energy per nucleon makes sense. The larger this en... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68145",
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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 ... | Here is a nice answer, taken from http://www.enchantedlearning.com/subjects/astronomy/stars/twinkle.shtml
The scientific name for the twinkling of stars is stellar scintillation (or astronomical scintillation). Stars twinkle when we see them from the Earth's surface because we are viewing them through thick layers of ... | {
"language": "en",
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Have general relativistic effects of all of the components of the stress-energy tensor been measured? The stress-energy tensor is:
Have general relativisic effects of all of the components of the stress-energy tensor been measured? I've heard that the accelerating expansion of the universe is due to negative pressure,... | Nice question. The gravitational effects of the pressure components have been directly verified in at least two ways that I know of. The early universe was radiation-dominated, so I don't think you can reproduce any of the relevant cosmological data (e.g., big bang nucleosynthesis) if you leave out the pressure terms. ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Mathematics for Statistical Mechanics I am studying Statistical Mechanics and Thermodynamics from a book that i am not sure who has written it, because of its cover is not present.
There is a section that i can not understand:
${Fj|j=1,..,N}$
$S= \sum_{j=1}^{N} F_{j}$
$<S>=< \sum_{j=1}^{N} F_{j}> = \sum_{j=1}^{N} <F_{j... | The average/expected value of a product is in general not the same as the product of expected values. (The "mean value" function is linear though: a sum of mean values is equal to the mean value of the sum.)
The product of the sum and sum of product are related by the covariance:
$cov(X,Y) = <XY> - <X><Y>$, as you stat... | {
"language": "en",
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Method of images tutorial I'm having an exam in Electrodynamics soon. I think I have most of it under control, but the method of images I'm not quite sure about.
There is not much in my book about this, so I was thinking some of you might know a website, article or something like that, maybe even with examples, that co... | πFor better understanding I had added an image which shows,
*
*An infinitesimally thin grounded sheet AB (I know the diagram is quite different but just assume it)
*A charge $q$ present at right side at distance $l$ from the sheet
"Let me tell you that our purpose of grounding is just to develop zero potential ov... | {
"language": "en",
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"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... | *
*according to de Broglie, the wave packet is moving with the group velocity vg and the phase wave is moving with vp=f*lamda. the de Broglie relation lamda=h/p where p=m*vg but lamda=vp/f. this equation involve both wave-particle duality.(p=m*vg for matter and vp=f*lamda). therefore, in this relation, the frequency ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can we write the electromagnetic potential covariantly in terms of the four-current? In the Lorenz gauge, we have a beautiful relation between the four-current and the four-potential:
$$\Box A^{\alpha} = \mu_0 J^{\alpha}$$
To get $A$ in terms of $J$, however, we have to use a considerably uglier formula; or, at least, ... | The integral expression is Lorentz-covariant, too, and it may be made manifestly Lorentz-covariant, too.
The integral measure $\int d^3 r' / ||\vec r - \vec r'||$ is equal to and may be rewritten as the four-dimensional integral with a delta-function (and step function) added:
$$2\int {d^4 x'} \cdot \delta[(x-x')^2]\cd... | {
"language": "en",
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Uncertainty in path integral formulation In Feynman's path integral formulation, in order to calculate the probability amplitude, we sum up all the possible trajectories of the particle between the points $A$ and $B$.
Since we know precisely that the particle will be at $A$ and $B$, does it mean that the uncertainty of... | Position/momentum Uncertainty, and path integral formulation are exactly the same thing.
Suppose you cut the time interval in time $t_0= t_A, t_1,....,t_n=t_B$.
At time $t_0$, the particle is at the position $x_0=x_A$. Because we know the position, uncertainty about momentum is infinite, but this simply means, that, at... | {
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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 ... | You are right. The simple way to understand mechanical advantage with pulleys is to count the number of ropes that "come out" of a particular block. With the same tension on each of the ropes, the total force is just the tension in each rope times the number of ropes.
Example (advantage of 1, 2, 3):
Whether the weight... | {
"language": "en",
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Elastic vs Inelastic vs isospin violating scattering particle physics models I'm looking for a nice paper that explains the difference between three particle physics models for spin-independent dark matter interaction with nuclei: elastic, inelastic and isospin violating scattering. I've found a nice paper that is givi... | "Elastic" and "inelastic" mean the same things they do in an introductory mechanics class. In elastic collisions the total mechanical energy is the same after the interaction as before (in a dark matter interaction this means effective the total kinetic energy), while in inelastic interaction that equality can not be c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68919",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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 u mind the MWI interpretation of QM, then the answer is: there are no universes where 1st law ofb thermodynamics does not work, but there are universes where the 2nd law of thermodynamics does not work. So some laws work everywhere while others do not.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/68987",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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$? ... | What you wrote is a variable change in the frame of the same Lagrangian. It remains a Lagrangian.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69133",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can isotropic states have bound entanglement? Let us consider the maximally entangled state
\begin{equation}
|\psi\rangle=\frac{1}{\sqrt{n}}(|0,0\rangle+\cdots+|n-1,n-1\rangle)
\end{equation}
and construct the pseudo-pure state
\begin{equation}
\rho_\lambda=(1-\lambda)|\psi\rangle\langle\psi|+\lambda\frac{I_{n^2}}{n^2}... | First of all, note that you can extend this class a little bit:
$$
\rho_\mu^\prime=(1-\mu)|\psi\rangle\langle\psi|+\mu\frac{I_{n^2} - |\psi\rangle\langle\psi|}{n^2-1},
$$
where $0 \le \mu \le 1$. You can check that $\rho_\lambda = \rho_\mu^\prime$, with $\lambda = \frac{n^2}{n^2-1}\mu$.
So $\rho_\lambda$ for $1 < \lamb... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69442",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do some air-conditioned stores blast you with jets of air as you enter? I went to a grocery store on a hot day that was very well air-conditioned, and I noticed as I went through the open entrance that there seemed to be a very powerful downward air current right at the doorway. After crossing the invisible thresh... | Most shopping malls have this kind of air door that blast you with high velocity air flow when you enter. As you might have noticed, shopping malls are always the cleanest places of them all. And I am not just talking about cleanliness of the floor area but the entire atmosphere in a mall. The reason they keep it clean... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69510",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Chemical Potential of Ideal Fermi Gas In Wikipedia's article on Fermi Gases, they have the following equation for the chemical potential:
$$\mu = E_0 + E_F \left[ 1- \frac{\pi ^2}{12} \left(\frac{kT}{E_F}\right) ^2 - \frac{\pi^4}{80} \left(\frac{kT}{E_F}\right)^4 + \cdots \right]$$
where $E_0$ is the potential energ... | I not sure how you obtained the last expression. The standard Sommerfeld expansion (for details, see e.g. Ashcroft & Mermin) gives a slightly different result, which is
$$
E_{F} \approx \mu\left[1+\frac{\pi^{2}}{8}\left(\frac{k_{B}T}{\mu}\right)^{2}\,\right]^{2/3} \approx \mu\left[1+\frac{\pi^{2}}{12}\left(\frac{k_{B}T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69664",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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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?
| No, the water would not be sucked up.
Even if you take a pipe with vacuum, closed the top and dipped the open end of that pipe in water then the water would only rise 10 meters. After that the 'pull' from your vacuum is in balance with the force of gravity acting on a 10 meter water column.
Maybe needless to say: T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69806",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
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Is there a name for a quantity that represents (volumetric) flow per unit of mass? In a lot of medical literature about blood flow in the brain, researchers denote the amount of volumetric blood flow that passes through a certain amount of brain tissue as "cerebral blood flow". However, its associated unit is volumetri... | The word "specific" (as in specific gravity or specific heat capacity) means per unit mass, so you could call it "specific flow" or "specific volumetric flow".
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69877",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why don't planets have Circular orbits? This might be a completely wrong question, but this is bothering me since many days ago. Given the mass (Sun) curves the space around it, gravitation is the result of such curved space (Correct me if I am wrong, source: A Documentary film). Given any point on a circle with center... | Comets are coming from almost infinite distance towards Sun. Due to Sun's Gravitational force they should be pulled into Sun rather than forming Elliptical or Hyperbolic trajectory.
If object is starting travel from closer distance at considerable speed, we can visualize formation of Elliptical orbit. For object com... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/69997",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "39",
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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?
| I'm a electrical engineer, and have never used either one in over 30 years of designing circuits. I vaguely remember that we went over them briefly in school, but since I haven't used them (knowingly) since, I can't tell you what the physical meaning of either is, which of course perpetuates the fact that I'm not goin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/70062",
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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?
| The basic idea in all three cases is that the energy becomes heat, and is extracted using turbines, just like in a fossil fuel burning power station. On a microscopic level the energy is released in the form of kinetic energy of the helium nucleus and the neutrons that are given off. These then collide with other parti... | {
"language": "en",
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What is meant by Vacuum? What is the exact meaning of the word vacuum? Is it just a state of very low pressure or is it nothingness (as in there is nothing)? Also, when we say space is vacuum - it must be referring to pressure as space has light travelling (which means photons) besides the big masses of comets, planets... | In Newtonian mechanics this term is pretty easy to define - vacuum is a region of space free of matter. In quantum mechanics, things get a little bit complex, for more details I recommend you to read the corresponding section of the Wikipedia article you've put the link to, it explains the term well enough for a beginn... | {
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Quantization for particle in a box problem Consider the particle in a box problem in QM. The crux of the reason why QM is able to explain the physical phenomenon is not just the theory but also able to impose boundary conditions which eventually result in quantization. Now in the particle in a 1-d box problem, the wave... | Differentiability of the wave function is only required for finite changes in the potential. If the your potential is infinite (as it is outside the inifinitely deep potential well which you describe) the Hamiltonial is ill-defined anyways.
An other case where you can have an infinite potential is if you have a $\delt... | {
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How does one define "Nuclear Harmonicity"? How does one define Nuclear Harmonicity?
Although the title is pretty much the entire case, the main question is, what exactly is "harmonicity" in terms of nuclear physics? What does it mean for a nucleus to be quasi-harmonic or nearly-harmonic? Is it perhaps in the sense that... | Without more input on your part I will refer you to the shell model of nuclear physics:
In order to get these numbers, the nuclear shell model starts from an average potential with a shape something between the square well and the harmonic oscillator. To this potential a spin orbit term is added. Even so, the total pe... | {
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Calculating the torque at a point when a motor is stopped? So, I'm trying to solve for the torque $\tau_A$ of a motor. I have attached a strong stick to the motor, like so:
I apply a force $F$ on the stick which stops the motor. The distance from the outside edge of the cylinder to the end of the stick is $L$. The tor... | Well, nothing is starting to move, right? So there's no net torque at all. Neither around point $A$, not around point $B$.
Let me clarify:
Around point $A$, there is the torque of the motor, $\tau_A$, and the torque due to the force at the end of the stick, $-(r+L)F$. So, the net torque is indeed zero (as is should). T... | {
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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... |
What is negative mass in this context
Consider a single bubble in the middle of a glass of water on your desk.
Normally, gravity pulls air above the desk downwards towards the desk surface.
However, in this case the air in the bubble does not move downwards under the influence of gravity. It moves in the opposite dir... | {
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How can you weigh your own head in an accurate way? I read some methods but they're not accurate. They use the Archimedes principle and they assume uniform body density which of course is far from true. Others are silly like this one:
Take a knife then remove your head.
Place it on some scale
Take the reading
re-attach... | A more accurate solution than the "relax your neck muscles" and similar ones:
Go to the morgue. Cut off the head of a recently deceased person with a similar body type. Measure the ratio of the weights of the head and body. Measure your weight.
Even more accurate: measure the density of the head you just cut off. Now... | {
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Vectors with more than 3 components
*
*I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 dimensions?
*Also, how can a Vector have a fourth dimension? How can we graphically... | In general, a vector in $D$ dimensions will indeed have $D$ components. A vector with $d<D$ components may, however, always be viewed as one in $D$-dimensional space but with $D-d$ of its components equal to zero.
Visualizing higher dimensions is always tough, because it's not something we have any experience with. We ... | {
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How do ice spikes form? I recently saw this picture posted on Twitter which shows a so-called ice spike rising from an ice cube tray.
I have read the Wikipedia page, but it doesn't mean much to me. My instinct was that it is caused by vibrations from the freezer setting up a resonant frequency on the surface of the wa... | I think what is happening in rough qualitative terms is that the water freezes around the sides and the top first leaving a hole in the centre. Ice expands by 4%-9% when freezing so as the water below freezes it forces the remaining water up through the hole where is freezes around the edge. The hole shrinks as the wat... | {
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Where does $p^i/p^+$ come from in the EOM of an open string? I have a stupid question about Eq. (1.3.22) in Polchinski's string theory volume 1.
In the equation of motion for an open string, Eq. (1.3.22),
$$X^i (\tau, \sigma) = x^i + \frac{ p^i}{p^+} \tau + i \bigl(2 \alpha'\bigr)^{1/2} \sum_{\substack{n= -\infty,\\... | From $(1.3.18$), we have :
$$\Pi^i = \frac{p^+}{l} \partial_\tau X^i$$
The definition of the total momentum is $(1.3.23 b)$ :
$$p^i = \int_0^ld\sigma ~\Pi^i(\tau, \sigma)$$
So, by definition :
$$p^i = \frac{p^+}{l} \int_0^ld\sigma ~\partial_\tau X^i(\tau, \sigma))~~~~~~~~~~~~~~~~(1)$$
Now, considering equation $(1.3.... | {
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What is physics behind of explosion under Atmospheric pressure? An explosion is a rapid increase in volume and release of energy in an extreme manner.
A blast wave in fluid dynamics is the pressure and flow resulting from the deposition of a large amount of energy in a small very localised volume.
The equation for a F... | If you start with a finite amount of gas in the inner sphere and then deposit a massive amount of energy, the molecules of the gas begin moving rapidly outwards and piling up, creating the blast wave. However, the rate at which the gas is moving outwards may not be balanced by the amount of gas molecules being created ... | {
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Is there an EMF in a conductor moving at constant speed across the uniform magnetic field If a conductor - a long rod - moves at constant speed across the "lines" of a uniform magnetic field, is there an EMF within this conductor? Or, if a conducting rod rotates at uniform rate, pivoted in the middle or at one of its ... | An EMF is generated whenever a conductor moves relative to a magnetic field so that the conductor is cutting across the magnetic field lines. The EMF generated is the cross product of the magnetic field and the motion of the conductor (I may have the sign flipped, don't remember off the top of my head).
To answer your... | {
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Can I call additional conditions on potentials a Gauge choice? Let's say I have an electromagnetics problem in a spatially varying medium. After I impose Maxwell's equations, the Lorenz gauge choice, boundary conditions, and the Sommerfeld radiation condition, I still have more unknowns than equations and the solution... | Per your comment to user1504, you are correct: the Lorenz gauge contains considerable arbitrariness.
To wit, suppose potentials $\Phi, \boldsymbol{A}$ satisfy:
$$ \nabla^2 \Phi - \frac{1}{c^2} \frac{\partial^2 \Phi}{\partial t^2} = - 4 \pi \rho $$
$$ \nabla^2 \boldsymbol{A} - \frac{1}{c^2} \frac{\partial^2 \boldsymbo... | {
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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... | This is the second time in only a few days that I've cited Luboš Motl's excellent answer to What are the various physical mechanisms for energy transfer to the photon during blackbody emission?. As Luboš points out, the precise microscopic mechanisms of the radiation are unimportant because the statistical properties e... | {
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Understanding the different kinds of mass in gravity On this site, the Phys.SE question Is there a fundamental reason why gravitational mass is the same as inertial mass? has been asked. See also this Phys.SE question. The 'answer' provided on this forum has been that the curvature of spacetime explains both. The answe... | What you're probably looking for is something like the famous Eötvös experiment which used a kind of torsion balance to test the equivalence of gravitational and inertial mass.
| {
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Can this ratio be written any better? This topic is closely related to previous topic where we were to calculate ratio $\lambda_e/\lambda_p$ for proton and electron with same velocities.
This time we I want to know if it is possible to derive a ratio $\lambda_e/\lambda_p$ for proton and electron who have same kinetic ... | It's difficult to simplify much more your last expression, but:
\begin{align}
\frac{\lambda_e}{\lambda_p} = \frac{\tfrac{h}{p_e}}{\tfrac{h}{p_p}} = \frac{p_p}{p_e} = \frac{\sqrt{1 + 2\frac{E_{0p}}{E_{kp}}}}{\sqrt{1 + 2\frac{E_{0e}}{E_{ke}} }} =\sqrt{\frac{1 + 2\frac{E_{0p}}{E_{kp}}}{1 + 2\frac{E_{0e}}{E_{ke}}}}
\end{al... | {
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SL(2,R) to SL(2,Z) in Type IIB String Theory I heard from Prof. Katrin Becker (in her "SUSY for Strings and Branes - Part 1" lecture) that the classical $SL(2,\mathbb{R})$ symmetry in type IIB String theory becomes $SL(2,\mathbb{Z})$ in Quantum because of charge quantization. However, I cannot see how does it work. Is ... | It's simple. The dilaton-axion (complexified) field in supergravity (and similar classical theories with a noncompact symmetry) is invariant under $SL(2,R)$ transformations
$$\tau \to \frac{a\tau+b}{c\tau+d}, \quad ad-bc=1$$
However, the same transformation must also transform the charges of objects. For example, one-d... | {
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What is canonical momentum? What does the canonical momentum $\textbf{p}=m\textbf{v}+e\textbf{A}$ mean? Is it just momentum accounting for electromagnetic effects?
| Imagine this situation:
at time t=0, we have a infinite long straight wire with current zero, and a charged particle q with zero velocity.
at time t=T, we make the current to be I, thus we have a $ \mathbf{B}$ field, and $ \mathbf{A}$ field.
during this process, $ \mathbf{A}$ is build up from zero to some value, there... | {
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Hooke's law doesn't work well with my spring? I'm trying to make an application for Hooke's law using a spring, but the law doesn't give any correct result with my spring, because when I hang a $100\,\mathrm{g}$ object on the spring it's elongates about $0.3\,\mathrm{cm}$ and when I hang a $200\,\mathrm{g}$ object the ... | Let me guess: you take the spring as it is and hang your objects, right? Then measure the displacement.
Try to do the following: hang any arbitrary object so that the string will stretch a bit from its initial state. Then add you 100g and 200g objects to the initial mass and measure the difference in spring's length. I... | {
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Lorentz homogeneous group and observables For generators of the Lorentz group we have the following algebra:
$$
[\hat {R}_{i}, \hat {R}_{j} ] = -\varepsilon_{ijk}\hat {R}_{k}, \quad [\hat {R}_{i}, \hat {L}_{j} ] = -\varepsilon_{ijk}\hat {L}_{k}, \quad [\hat {L}_{i}, \hat {L}_{j} ] = \varepsilon_{ijk}\hat {R}_{k}.
$$
F... | Yes, a representation labeled by $(j_1,j_2)$ corresponds to the total spin $j_1+j_2$, (rigourously speaking of spin needs that one of $j_1$ or $j_2$ is zero) and if $j_1=j_2$, this is a real representation, but you may have a representation which is a sum or irreductible representations , some examples:
$(\frac{1}{2},... | {
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Can visible light be emitted from a non-thermal source? I was reading about thermal and non-thermal radiation and I was wondering if visible light can be emitted from a non-thermal source?
| Super-continuum sources are well known non-thermal white light sources. The gist is a laser beam interacts with a specially tailored nonlinear material to generate ultra-broadband coherent light. A few references:
Supercontinuum light
Demonstration of Stimulated Supercontinuum Generation – An Optical Tipping Point
Gene... | {
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Does magnetism affect corrosion? Supposing there is an iron nail that is left to rust, if we compare the time it takes to rust with that of a magnetized iron nail, will there be any difference in the time of corrosion (assuming other environmental factors are constant)?
| Looks like magnetization can accelerate corrosion (http://www.ifw-dresden.de/de/institute/institut-fuer-komplexe-materialien/abteilungen/chemie-funktioneller-materialien/corrosion/corrosion-of-permanent-magnet-materials/impact-of-the-magnetization-state-on-the-corrosion-of-ndfeb-permanent-magnets/ ) (I did not look at ... | {
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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... | It's just a convention in physics we are more interested in getting some work output say a mechanical device , engine etc while in chemistry we are more concerned with the internal energy things so we do so in both the cases the result is same
physics case : du = dq - dw , doing work on system increases internal energ... | {
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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~... | The car accelerates from 0 to 20 m/s in 12 s. It has an average speed of 10 m/s over that time, and so covers 120 m in that time. In that same time, the RC car goes 14 m/s * 12 s = 168 m. So the car didn't catch up while accelerating. At 12 s, the car is 168 m - 120 m = 48 m behind the RC car.
The car is now going ... | {
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Steering forces on a bicycle I always notice this weird thing and try to overcome it but cant.
As shown in the image when I ride the bike by just one hand and pull the handle back say from the right side so as commonly the handle should rotate towards right and the bike should turn to right. But that doesn't happen. No... | Pulling the right handlebar towards you causes the front wheel to turn to the right, which causes the entire bicycle to bank to the left, because the support points are moved to the right.
Then, unless you simply let the bike fall over to the left, you unconsciously balance the bike by turning into the bank.
| {
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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... | In your equation
$$\frac{1}{4 \pi \epsilon_0} \frac{q^2}{x^2} - \frac{mgx}{2l} = m \ddot{x}$$
$ \ddot{x}$ can be written as $$\frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt}= v\frac{dv}{dx}$$
so the first equation can be written in terms of $x$ for all the terms (as you are given $v$ in terms of $x$ in the question).
After ... | {
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How are low energy effective actions derived in string theory? For example the eq 2.1 here with regards to Type IIB.
Unless I am terribly missing/misreading something Polchinski doesn't ever seem to derive these low energy supergravity actions.
I would like to see a beginner's explanation (maybe together with review p... | I think that the quickest route to the effective action actually isn't through string amplitudes, but through the beta functions. The conditions for worldsheet conformal invariance are equivalent to the spacetime equations of motion, and from these you can infer an on-shell effective action. This is all you can hope fo... | {
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Does the termination point(level) influence water flow from a pipe I get water to my home from a nearby Tank A at a certain height above ground level.
I have a 1" pipe through which I get this water to my home.. I leave this water into my well by connecting a 1" tube to this pipe.
Reason for question: I have seen wate... | A longer (and deeper emerged pipe) will yield a slightly lower flow rate. This is because the longer pipe will yield a higher drop in the loss of pressure, due to friction. A longer and deeper pipe will never increase the flowrate, since what is causing the water to flow is the height difference between the two water s... | {
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Opening the fridge door to cool a room I'm well aware that the default answer to this textbook default question is "it doesn't work", but still, I believe it does.
To cool the insides of the fridge, the compressor must do work, and since the efficiency isn't 100% you are constantly warming the whole room to cool it's i... | No, you are making the fridge do extra work, so more energy is coming in (through the plug) as the pump continues to run since it's not reaching it's cold point. A normal operating fridge does not manifest cold air; it just pumps all the heat out of the inside of the fridge.
The action of pumping the heat out also h... | {
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Why does the guy moving on spaceship look younger in twin paradox? If there is no particular absolute choice of frame of reference, the guy who sits on Earth is also moving away from the guy on spaceship perspective and hence time on Earth should also dilate when viewed from the guy on spaceship perspective. But why do... | Here's how I think about it.
First of all, twins A and B have identical clocks consisting of two mirrors, where a photon bounces back and forth between them. That's what you call a "tick" and "toc", and it's a nice way to build a clock because the speed of light is always constant no matter who measures it.
What's more... | {
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What do you call the period after sunrise when the sky is bright? At sunrise, the sky isn't actually up in the sky yet. Twilight occurs before sunrise, then at sunrise the leading part of the sun crosses the horizon. But, the sky isn't bright yet. It takes some time for the sky to be blue again.
Then, at the closing of... | There is daylight, civil twilight, nautical twilight and astronomical twighlight. Each defined by the position of the sun relative to the horizon.
The wikipedia article seems unusually helpful. With diagrams as well.
| {
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Torque on a Box I think I'm missing something with torques. I seem to have gotten myself confused.
I have a box that's centered at ( 0 , 0 , 0 ) with length ( $x$ dimension ) = 1 , width ( $y$ dimension ) = 0.25, and height ( $z$ dimension ) = 0.5. The edges are parallel to the axes. The $x$ axis is left(-) and right(+... | Firstly, if the $x$-axis is positive to the right, and the $y$-axis is positive upwards, then the positive $z$-axis should point out of the page in order for your coordinate system to be right-handed (recall that $\hat{\mathbf x}\times\hat{\mathbf y} = \hat{\mathbf z}$ and use the right-hand rule), so let's assume that... | {
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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?
| Depending on the velocity of the neutron one can combine different materials to shield neutron radiation.
Diagrams for common materials can be found in The ILL Neutron Data Booklet, 4-2.1 (Download PDF 9 MB)
The strategy is to use
dense material => collisions
hydrogen as moderator => makes neutrons slower
absorbers li... | {
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Is the symmetrisation postulate unnecessary according to Landau Lifshitz? The symmetrisation postulate is known for stating that, in nature, particles have either completely symmetric or completely antisymmetric wave functions. According to these postulate, these states are thought to be sufficient do describe all poss... | The way Shankar addresses the problem (pg. 278) is by introducing an "Exchange Operator" $P_{1,2}$, which would swap your two particles as follows:
$P_{1,2} |\xi_1, \xi_2 \rangle = |\xi_2, \xi_1 \rangle$
I like the operator notation because it makes it clear (to me, at least) that applying the operator twice is just th... | {
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Can inertia be explained by Bremsstrahlung? Considering that on the atomic level objects consists of densely spaced positively and negatively charged particles, does not the acceleration of those objects lead to Bremsstrahlung of those particles? And although the monopole field is zero, couldn't higher order multipole ... | No, Bremsstrahlung does not cause inertia.
The power radiated by Bremsstrahlung scales as charge but not mass. Also, it scales as acceleration squared.
This does not reduce to the classical inertia $m\vec a$.
| {
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Why do ice cubes stick together or to the edges of a drinking glass? I was drinking iced-water from a drinking glass (made of glass) at a restaurant yesterday when I was taking a drink, I noticed that there is very little ice water coming out and then suddenly, the ice water mixture comes crashing down. With my open mo... | *
*OK as much I think when two ice cube come together and their sides stick to each other the water on the surface between the two cube starts freezing because on both the sides there is only ice which brings down the temperature of the water between the cube to freezing point which causing the water between then to f... | {
"language": "en",
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How do we know photons have spin 1? Electrons have spin 1/2, and as they are charged, they also have an associated magnetic moment, which can be measured by an electron beam splitting up in an inhomogeneous magnetic field or through the interaction of the electrons's magnetic moment with an external magnetic field in s... | One method is based on the conservation of angular momentum.
The electronic transition must follow the selection rule $\Delta l=\pm 1$. So the first thing to do is to choose an atom with zero total angular momentum, then let the atom absorb a photon and make a transition to $l=1$ state.
Secondly, we use the Stern-Gerla... | {
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Why does electricity need wires to flow? If you drop a really heavy ball the ball's gravitational potential energy will turn into kinetic energy.
If you place the same ball in the pool, the ball will still fall. A lot of kinetic energy will turn into thermal energy because of friction, but the gravitational potential e... | When you ask: "why don't the electrons just "move" like the ball? Why don't the electrons just "move" through the air to the positive terminal." I think you need to keep in mind that the ball is made up of neutral atoms which are themselves made up of negatively charged electrons and positively charged protons. The el... | {
"language": "en",
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How mirror equation can explain farsightedness correction? I have a friend who has just show me his medical prescription for hyperopia (farsightedness) correction and he needs glasses with 4,25 diopters for that, which seemed to be weird for me because I had learned, from the mirror equation, that the maximum correctio... | Extreme hyperopia would correspond to your eye lens in relaxed conditions being close to an optical flat. In such a case you would need a contact lens with a focal length of about 25 mm (typical human eyeball diameter). This corresponds to a lens of 1000/25 = 40 diopters.
In other words: a farsighted eyeless requiring ... | {
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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?
| Some people (myself included) would regard field equations like Gauss' Law as more "fundamental" than force equations. The most obvious reason for this is that Coulomb's Force Law only works when the charges in question are held static - it has to be modified once they are allowed to move.
As the others have stated, th... | {
"language": "en",
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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... | You can think of diff as bianchi id. The additional 4 dof is killed by the fact that 4 of the 4 of the EFE are constraints.
| {
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What are correlated magnetic moments? My book has the following sentence and I don't understand what correlation or lack of correlation means:
At high temperature the magnetic moments of adjacent
atoms are uncorrelated (to maximize the entropy) so the crystal has no net magnetic moment.
The book is touching on sec... | Correlation between two variables (or objects) is, very simply put, how much a change in one variable affects or determines a change in the other. Replacing variables with spins, highly correlated spins would mean that, due to some interactions between them, a change in the direction of one spin will cause a change in ... | {
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How far can you scatter light using a prism? If I were to scatter light how far do you think it would disperse? What prism most effectively scatters light?
| Prisms don't scatter light, they refract it. The amount of refraction depends on the material's index of refraction, or the change in the speed of light in that substance (assuming that the prism is surrounded by normal air). The highest index of refraction, as far as I am aware, belongs to diamond, so a diamond prism ... | {
"language": "en",
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Weak interaction and the Chirality of anti-particles Consider a weak current of the form
$
J^{\mu} = \bar{u}_{\nu}\gamma^{\mu}(1-\gamma^5)u_{e}
$
This describes the part of a weak process where a left-handed electron converts into a left-handed neutrino by emitting/absorbing a W boson. Equivalently, it should also desc... | Yes, antiparticle is still involved in left-handed chirality. The right-handed antiparticle that some books mention is actually helicity. I know many textbooks are WRONG by claiming that antiparticle is right-handed chirality. You can read the book Quantum Field Theory for Gifted to clear this common misconception
*** ... | {
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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... | What do you mean by "to work"? If you mean that you can transfer energy, then to where?
If you continuously alternate the potential at one end of a wire, then this creates a wave that propagates to the other end. Say that other end is earth. If the potential is 0 on earth like and ideal ground, this means it cannot sus... | {
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Study of Black-body Radiation Why did scientists study black body radiations from something as complicated as a hollow container rather than the radiation from something simple like a thin solid cylinder?
| A black body is a perfect absorber, and in practice it's difficult to make a material that is a perfect absorber. So to make a black body we choose a material that is as good an absorber as we can find, and form it into a hollow sphere with a small hole in it. The black body is then the hole, not the sphere. It's a nea... | {
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Weather forecasting with coffee bubbles The other day I saw this life-hack:
And I was wondering how true it is. First of all, I always thought(listening to weather forecasts) that low-pressure atmosphere is what correlates with rain; although I never learned the argument behind it.
Anyway, even if low atmospheric pre... | This is quite humorous.
In an 1883 offical US military publication, "Weather Proverbs" by 1st Lt. Dunwoody, at page 107 it is stated "When coffee bubbles collect in the centre of the cup expect fair weather. When they adhere to the cup, forming a ring, expect rain." This is the opposite of the lifehack proverb!
I... | {
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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... | The expression your wrote down for the energy is the expression for the ensemble average kinetic energy of a monatomic ideal gas. Therefore, we see that for this system, the average energy of the system is simply proportional to the temperature.
For a general statistical mechanical system, however, it might not even m... | {
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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... | The picture you have about unpolarized light is correct, I think, but I would try to avoid the idea of "rotating fast", because it gives an idea of continuity, that I think is what you try to avoid in the concept of unpolarized light.
So, in essence unpolarized light is modelled by short wave trains of some arbitrary p... | {
"language": "en",
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Intuitive understanding of the irreps like Wigner-$D$ matrix? Wikipedia defines Wigner $D$-matrix as an irreducible representation of groups $SU(2)$ and $SO(3)$. What is a good way to visualize this representation? Is there any physical system which can be kept in mind as a simple example of the same?
A general explana... |
Is there any physical system which can be kept in mind as a simple example of the same?
Yes. Consider a single spin $1/2$ particle, like an electron. In this case, the matrix will be $2$-by-$2$ since its a representation of $\mathrm{SU}(2)$ acting on the two-dimensional spin-$1/2$ Hilbert space. The idea here is t... | {
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Strings and their masses How do strings present in particles give mass to them? Is it only by vibrating? I have been trying to find the answer but could not find it anywhere, can this question be answered?
| While it is true that an excited string (hence one with a vibration mode above the ground state) looks like a massive particle from far away, this is not the effect that is supposed to explain the mass of any particle ever seen. This is because the mass of the first excited mode of the string is already huge as far as ... | {
"language": "en",
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How is momentum conserved when a magnet attracts a metal? Suppose your have any magnetic object and no external force acts upon it, and the object comes near a metal which causes an impulse (think that will happen). However, the magnetic force is internal to the object, and momentum should be conserved, so where have ... | There is a corresponding reaction force on the metal object, which is attracted to the magnet. If the metal object is large (say, a fridge) then this is hard to notice and you observe the magnet going to the metal, but for smaller objects like paper clips it's the opposite.
| {
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Where does gravity get its energy from? I would like to know where gravity gets its energy to attract physical bodies?
I know that the law of conservation states that total energy of an isolated system cannot change. So gravity has to be getting its energy from somewhere, or else things like hydropower plants wouldn't ... | As per Newtonts law each thing have energy to attract another thing, beacause in every thing there is potential energy. Due to friction that potential enrgy can convert in another form. for eg. our sirt colour get more dirty, because of friction between neck and colour, in anciant period for generating th fire people u... | {
"language": "en",
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Connection between particles and fields and spinor representation of the Poincare group Let's have a definition of massive particle as an irreucible representation of the Poincare group. Then, let's have a spinor field $\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot {\beta}_{1}...\dot {\beta}_{m - 1}}$, whic... | The definition is that a particle in Minkowski space is a unitary irreducible representation of the Poincare group. So one needs to see how various P.D.E.s are related to the classification of unitary irreducible representations of $iso(3,1)$ or $iso(d-1,1)$ in the case of $d$-dimensions instead of $4$.
Note that these... | {
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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(... | The motion in such a curve is quite hard to calculate, and even more so if you do not want to get into the messy details of Jacobi elliptic functions like $\text{sn}(u|k)$. However, for the case of small oscillations there is a simple scaling argument that lets you calculate the dependence of the period on the amplitud... | {
"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... | I doubt that it's superheating, as I understand superheating is a rather violent phenomenon. The most likely explanation is dissolved gases; gas solubility in water decreases with temperature. The kettle boiling process is very turbulent and so can release all the dissolved gases, resulting in pure hot water. The micro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/75465",
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Why can't we destroy energy? From a wikipedia article:
In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form; for instance, chemical energy can be converted to ... | The point of defining energy is to obtain a conserved scalar quantity -- as an example of how this works out, have a look at the derivation of the Newtonian formula for kinetic energy, where energy conservation is disguised as "kinetic energy is equal to the heating produced when it's destroyed".
There are plenty of co... | {
"language": "en",
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View from a helicopter rotor: why is the horizon distorted? This video ("rotor panorama") was captured by a camera attached to the rotor head of a radio-controlled helicopter, with the frame rate set to the rotor's frequency. During a long segment of the video, the horizon looks distorted:
What causes this distortion?... | This is most likely caused by wobble in the motion of the rotor, compounded with the fact that pixels are captured linearly, probably from left to right (this is what the description refers to as "scanning shutter"). Thus there is a time delay between the capture of the pixels on the left and those on the right; if the... | {
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What does E/M field look like when I close a circuit? Suppose that we have a charged capacitor with two pins: $ C_+ $ and $C_-$.
Suppose that we have a long wire with fixed geometry, that is already connected to the pin C+.
Let the distance along the wire be called $s$.
I closed a circuit by conne... | Recall $$I = n q v_d A \tag{1}$$
Note that the electrical current depends only on the cross sectional area of the wire and not on its length...
However if we manipulate eq.1 we find that
$$I = \frac{nqsA}{t}$$
Since $v_d = s/t$ if we continue further we see that
$$I = \frac{nqV}{t }$$
Where $V$ is the ... | {
"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?
| The optical path difference is the length difference $d$ (dimensions of length: $[L]$) in the paths travelled by two different rays from one plane, at which they are typically assumed to have the same phase, to a second location (typically another plane, surface or point).
Light is a wave with a wavelength of $\lambda$... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why do meteors explode? A report on the Chelyabinsk meteor event earlier this year states
Russian meteor blast injures at least 1,000 people, authorities say
My question is
*
*Why do meteors explode?
*Do all meteors explode?
| Remember that meteoroids are celestial objects. At these scales, it is quite common for relative velocities to be extremely large.
When such a fast-moving object enters the atmosphere of the Earth, the air slows it down due to its viscosity. However, the meteor is moving very, very fast. Unlike most falling objects, i... | {
"language": "en",
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"source": "stackexchange",
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Double Slit Experiment: How do scientists ensure that there's only one photon? Many documentaries regarding the double slit experiment state that they only send a single photon through the slit. How is that achieved and can it really be ensured that it is a single photon?
| Quantum dots. nanoscale semiconductor materials that can confine photons in 3 dimensions and release them a measurable time after. Based on material used the decay time is known empirically. frequency is also known. the latter is sufficient to calculate the energy of one photon. The former is then sufficient to calcula... | {
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CMBR temperature over time? How has CMBR temperature dropped as function of time? A graph would be nice, but I'd be happy with times (age of universe) when it cooled enough to not be visible to human eye, became room temperature equivalent, or reached some interesting temperatures regarding matter in the universe.
If t... | In terms of the redshift, the background temperature is
$$
T(z) = T_0\left(1+z\right)
$$
where $T_0\sim2.725$ K is today's CMB temperature. For simplicity, one can invoke a uniformly-expanding universe to get the relation between $z$ and $t$ as
$$
1+z\propto\frac{1}{t^{2/3}}
$$
So as $t\to0$, $T(t)\to\infty$ and as $t\... | {
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Superconformal approach to supergravity In the book (Supergravity - Daniel Z.Freedman & Antoine Van Proeyen - Cambridge), there is (Chapters 16-17) a presentation of pure supergravity or supergravity with matter, from a superconformal approach.
The "simplest" link, is to begin with a superconformal gauge multiplet coup... | *
*The "simplest" link, is NOT to begin with a Superconformal gauge multiplet coupled to a chiral multiplet, but to couple the Weyl multiplet to a superconformal chiral multiplet.
*It is just a mathematical tool to make your life easier. As a matter of fact, you can take the superconformal action and make a field re... | {
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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, ... | Both sides of a complex number are each real numbers. Either the real part or the imaginary part can be used for computing the value of a measurable quantity. And the results are always the same. Then we are left with only 'i', to determine it's Mathematical and then physical meaning. The allegory of 'i' harbors a real... | {
"language": "en",
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Intuition behind defining divergence as flux divided by volume? For a continuously differentiable vector field $F$ the divergence theorem can be used to give
$$(\nabla\cdot F)(a) = \lim_{r\to 0} \frac{3}{4\pi r^3}\int_{|x-a|=r} F \cdot n dA$$
This should mean that for $c<3 $
$$\lim_{r\to 0} \frac{3}{4\pi r^c}\int_{|x-a... | The basic reason for this is that we want the limit to be finite. As $r$ approaches zero, there are two reasons why the flux shrinks.
One is that the flux is proportional to the surface area, which goes like $r^2$. The other is that flux tends to cancel on opposite sides of the volume. If the field is constant, this ca... | {
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What are the equations of motion of a hole in a soap bubble? Imagine the following situation: I have a thin stationary water film, like a soap bubble, suspended inside a large ring. I throw a small loop of string onto the film and punch a hole inside it. How can I describe the motion of the hole in the water film bound... | Let the large ring be placed vertically. For simplicity, consider a weightless string, which thickness is equal to the film thickness. Also, assume that the hole is quite far away from the edge of the ring so that we can ignore the surface phenomena of the film. Then the speed of the rising hole can be estimated as fol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/76861",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 1,
"answer_id": 0
} |
Quantum states as rays as opposed to vectors I recently read that a quantum state is actually defined by a ray and not a vector. That is it is possible to multiply a state $\psi$ by any complex number $c\in \mathbb{C}$ and you won't be changing the physics in any way. I understand this mathematically, but I don't under... | There is no particularly interesting new physical significance to such a state vector. As you already stated, it represents exactly the same physical state. The only difference is that, on taking the modulus squared, the new state gives an unnormalised probability distribution over possible measurement outcomes. You ca... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/76939",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 2,
"answer_id": 1
} |
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