Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Introductory texts for functionals and calculus of variation I am going to learn some math about functionALs (like functional derivative, functional integration, functional Fourier transform) and calculus of variation. Just looking forward to any good introductory text for this topic. Any idea will be appreciated.
| Have a look first at several chapters in Stone and Goldbart, "Mathematics for Physics" (the free preprint is here) before entering into more specific books. I think you may want to see chapters 1, and parts of 2 and 9.
You may find some parts of what you want in classic books of the "Comprehensive Mathematical Methods ... | {
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Why is a classical formalism necessary for quantum mechanics? This is not a question pertaining to interpretations, after the last one I realized I should not open Pandora's Box ;)
For theories to be consistent, they must reduced to known laws in the classical domains. The classical domain can be summed up as:
$$\hba... | This is an excellent question and the answer is it follows from the crucial postulates of quantum mechanics. Namely, the operator corresponding to a dynamical variable is obtained by replacing the classical canonical variables by corresponding quantum mechanical operators and any pair of canonically conjugate operators... | {
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Why does Venus spin in the opposite direction? Given: Law of Conservation of Angular Momentum.
*
*Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based).
*Surface same degree of aging all over.
*Hypothetical large impact is not a sufficient answer.
Assuming any object large enough... | IMO there is no solid explanation, as anna said. Only clues (WP).
In this simulation (2002) Long term evolution of the spin of Venus- II, Numerical simulations we find a mix of: 'chaotic zone', instability, large impact, close encounter, tidal effects, planetary perturbations,...
There is room for speculation:
I think... | {
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Massless charged particles Are there any massless (zero invariant mass) particles carrying electric charge?
If not, why not? Do we expect to see any or are they a theoretical impossibility?
| Since a particle only can be said to exist if it can express its existence, its properties in interactions if it has energy and localized energy is a source of gravity and we define mass as something which exerts and feels gravity, then there cannot exist massless particles.
(That is, if we define a particle as an enti... | {
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How do electrons "know" to share their voltage between two resistors? My physics teacher explained the difference between voltage and current using sandwiches. Each person gets a bag full of sandwiches when they pass through the battery. Current = the number of people passing through a particular point per unit time. ... | Continuing Marek's reply, I will add that in electrical circuits the value of the current depends on the elements of the circuit: the voltage , the resistors summed when in series, summed inversely if in parallel. The whole defines the value of the current, and currents in the parallel parts, according to the electri... | {
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Are these two quantum systems distinguishable? Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two level atom. Half the time the atom is produced in the ground state, and half the time the atom is produced in the excited state, but other ... | This is such a nice philosophical question with such a neat resolution that I can't resist dropping a comment. The reduced density matrices of the atom are the same for Stanford and National, but quantum mechanics is irreducibly holistic. The wave function describes the entire universe. If the atom was prepared by Stan... | {
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Mathematical justification of Hartle-Hawking "no boundary" proposal In Hartle-Hawking "no boundary" proposal it is proposed that Riemannian spacetimes rather than Lorentzian dominated the path integral near the big bang.
Moments after the big bang however spacetimes with Lorentzian metrics started to dominate over the... | What is bothering you here is not Hartle-Hawking per-se, but the process of analytic continuation inside a path integral. This can be mystifying, because the actual functions which dominate the integral are never analytic, they are hardly ever continuous or even bounded. Usually they are distributional, so that they fl... | {
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What are the conditions to be satisfied by a theory in order to be a quantum theory? This is in continuation to my previous question. It is not a duplicate of the previous one. This question arises because of the answers and discussions in that question.
Can we call a theory, quantum theory, if it is consistent with HU... | In mathematical reasoning, and not only, there are what are defined as necessary conditions, and others that are defined as sufficient conditions.
Necessary means that without this condition the theory cannot be proven/ be consistent. Sufficient means that just from this condition the theory is consistent.
The QM post... | {
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Are there examples in classical mechanics where D'Alembert's principle fails? D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero.
This is obviously true for the constraint of a rigid body where all the parti... | You can have instances where there is no local extremum of the action--for instance, take the lagrangian $L=m\left(\dot x ^{2}+\dot y^{2}\right)$ over the space defined by a crescent embedded in $\mathbb{R}^2$--then, even though the tips of the crescent are both perfectly good starting and ending points in your domain,... | {
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Why do all the planets of the solar system orbit in roughly the same 2D plane?
*
*Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the orbits distributed all around the s... | *
*The orbital planes of different planets has small inclinations to the ecliptic plane. The corresponding wikipedia diagram should give a better view than the 2D images you've seen.
*Both Voyager 1 and 2 are beyond the Solar System
| {
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Chern-Simons Theory in 3D For the CS theory on a three manifold $M$ with a gauge group $G$, it is said that the gauge field $A$ is a connection on the trivial bundle over $M$. Why the bundle should be trivial? I know that space of classical solutions is made of flat connections but why should we assume the bundle is tr... | Answering the first question. The Chern-Simons functional expressed in terms of the vector potential $A$:
$$S(A) = \frac{k}{8 \pi^2} \int_M tr(A \wedge dA + \frac{2}{3} A \wedge A \wedge A )$$
is well defined only for a trivial principal bundle, because in this case the gauge connection is
a Lie algebra one form over ... | {
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Can a disk like object (like UFO's) really fly? UFOs as shown in movies are shown as disk like objects with raised centers that emit some sort of light from bottom. Can such a thing fly?
My very limited knowledge in physics tell me that a disk like object may not be able to maneuver unless it has thrusters on sides and... | Have a look at the flying car
There is even a video.
| {
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Voltage drop along an idealized resistance-free wire in a circuit? If you connected the positive terminal of a battery to the negative terminal to a battery with a wire with (hypothetically) no resistance, and are asked to give the voltage drop of a segment of wire in the circuit, how would you determine this?
| Let $V$ be the e.m.f of the battery/ voltage source
Let $i$ be the current through the wire of resistance $R$.
Actually $i= \frac{V}{R}$, as per the question, $R$ tends to ZERO, hence $i$ tends to a very very large number.
Let the drop across the wire be $V_1$ then $V_1=$(current through the wire)*(resistance of the wi... | {
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Have CMB photons "cooled" or been "stretched"? Introductory texts and popular accounts of why we see the "once hot" CMB as microwaves nearly always say something about the photons "cooling" since the Big Bang. But isn't that misleading? Don't those photons have long ("cool") wavelengths because space expanded since the... | Cooling and stretching essentially mean the same thing here. The temperature of any blackbody radiation is related to the peak wavelength by Wien's Law $$\lambda_{\mathrm{max}} = \frac{b}{T} $$ Therefore as the universe expands, all of the photon wavelengths get stretched out and so does the peak wavelength. $$\lambda ... | {
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Is it possible to know the exact values of momentum and velocity of a particle simultaneously? I know that by Heisenberg's Uncertainty Principle that it is not possible to know the exact values of position and momentum of a particle simultaneously, but can we know the exact values of momentum and velocity of a particle... | If in your theory the momentum operator and velocity operator are proportional to each other, then yes. Knowing one's eigenvalue means knowing the other's. It is always the case with any function of a "known" operator.
| {
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Supergravity calculation using computer algebra system in early days I was having a look at the original paper on supergravity by Ferrara, Freedman and van Nieuwenhuizen available here. The abstract has an interesting line saying that
Added note: This term has now been shown to vanish by a computer calculation, so tha... | It sounds like it may have been an early version of SHEEP, or some extension thereof. SHEEP was 'officially' released in 1977, but its predecessor, ALAM, was developed by d'Inverno in 1969. It was used to automate some of the complicated algebra in early calculations of the Bondi mass. You can read a bit about the hist... | {
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Is there a direct physical interpretation for the complex wavefunction? The Schrödinger equation in non-relativistic quantum mechanics yields the time-evolution of the so-called wavefunction corresponding to the system concerned under the action of the associated Hamiltonian. And this wavefunction is, in general, compl... | I'll leave an answer for your last question on whether complex numbers are necessary for QM.
Scott Aaronson has a nice lecture here http://www.scottaaronson.com/democritus/lec9.html , scroll down to the section on Real vs. Complex numbers.
My favorite argument there is the first one -- that if you have a linear operato... | {
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More on matter and anti-matter
*
*Does every particle that has rest mass also have an anti-particle with which it would annihilate?
*Does annihilation only occur between like particles? For example what happens if a antineutron (anti u, anti d, anti d) collides with a proton (uud)? What happens if a positron colli... |
1.) Does every particle that has rest mass also have an anti-particle with which it would annihilate?
For fermions in the standard model scheme , yes.
The three columns on the left are fermions. Bosons are their own antiparticle and the term "annihilation" has no meaning other than "interaction" and whether it is ... | {
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What is the Physical Meaning of Commutation of Two Operators? I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics?
E.g. an operato... | You may consider commutativity of different variables as physical independence, something like separated independent variables:
$\frac{\partial}{\partial x} \frac{\partial}{\partial y} = \frac{\partial}{\partial y} \frac{\partial}{\partial x}$.
| {
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Has quantum entanglement been demonstrated to be able to take place over infinite distances? In my poor understanding of quantum physics, quantum entanglement means that certain properties of one of two 'entangled' quantum particles can lead to change over infinitely large distances when the other particles' properties... | Since my Alma Mater was involved I can point to this:
A team of European scientists has
proved within an ESA study that the
weird quantum effect called
'entanglement' remains intact over a
distance of 144 kilometres.
(Source)
In September 2005, the European team
aimed ESA's one-metre telescope on the
Ca... | {
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Why is it hard to solve the Ising-model in 3D? The Ising model is a well-known and well-studied model of magnetism. Ising solved the model in one dimension in 1925. In 1944, Onsager obtained the exact free energy of the two-dimensional (2D) model in zero field and, in 1952, Yang presented a computation of the spontaneo... | Exaxt solvability has nothing to do with NP-completeness.
For equations on a lattice or a continuum, exact solvability happens to be equivalent with having enough symmetries to allow the solution to be determined by exploiting these. (To a large extent, this even holds for ordinary differential equations in more than a... | {
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When water is about to boil Have ever noticed? When water is about to boil, no matters the kettle, there is some sound I have no idea where it comes from, sometimes long before it boils.
Is there any explanation for this phenomena?
| The water near the heating element turns into water vapor. This vapor then rises up to the surface but as it meets colder water upwards it turns back into water.
As the water/steam transition is not smooth (e.g. the volume changes rather rapidly during phase change), the constant transition between vapor and liquid sta... | {
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Anti-matter repelled by gravity - is it a serious hypothesis?
Possible Duplicate:
Why would Antimatter behave differently via Gravity?
Regarding the following statement in this article:
Most important of these is whether ordinary gravity attracts or repels antimatter. In other words, does antihydrogen fall up or do... | EDIT: fixed thought experiment.
If antimatter anti-gravitates, it would be possible to build a perpetual motion machine:
1) Start with a zero-net momentum pair of photons. Have them collide, and make a particle/antiparticle pair. These can be moved around arbitrarily with zero net work, since any gravitational force ... | {
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Glycerol: refractive index & absorption spectra in 0.2-0.4um range Could anyone suggest where can I find absorption spectra & refractive index of Glycerol?
I am specifically interested in UV range, 200-400nm, everything I was able to find out was for standard conditions only...
Is there any software which can get these... | 1st, UV-spectrum.
There is none! To have some absorption above 200 nm You need some
conjugated double bonds. The standard solvent for UV-spectroscopy is
ethanol for that reasons, if one needed a much more polar solvent
one would use water or in extreme cases (of polarity) glycerol.
2nd, Refractive index.
This is a... | {
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$cm^3/g$ as a unit of adsorption I recently saw $cm^3/g$ as a unit for amount adsorbed. Usually, you see either $\mathrm{kg_{adsorbate}/kg_{adsorbent}}$ or $\mathrm{mole_{adsorbate}/kg_{adsorbent}}$. Does anyone know the meaning of this unit?
| Indeed, when you just want to measure how much material has been adsorbed, it's more natural to use the same units for both materials.
I think that 1 cubic centimeter per gram is not a unit of "adsorption" per se - adsorption is a process, not a quantity, after all - but it's a unit of "specific pore volume". You take ... | {
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What is "pure energy" in matter-antimatter annihilation made of? I used to read the term "pure energy" in the context of matter-antimatter annihilation. Is the "pure energy" spoken of photons? Is it some form of heat? Some kind of particles with mass?
Basically, what does "pure energy" in the context of matter-antim... | In particle antiparticle annihilation the end products come from the table of elementary particles created so that quantum numbers are conserved.
photons, two to conserve momentum in the cmsystem, pions and other mesons etc.
| {
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Phase Accumulation of Hankel-waves upon propagation Hankel functions are solutions to the scalar Helmholtz-equation $$\Delta\psi + k_e^2\psi = 0$$ in cylindrical and spherical geometry (with respect to a separated angular dependence). Thus, they are very important describing spherical and cylindrical waves. Here is an ... | I am not sure how you get outwardly travelling waves from Hanken functions alone without also using Bessel functions. My understanding is that by analogy with plane waves, you have the stading wave solutions eg.
sin(kx)*cos(wt) and
cos(kx)*sin(wt)
and the travelling wave comes from the sum of these two. Similarly in c... | {
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Assuming everything else is equal, which will stop first: a heavier car or a lighter car? If the friction from brakes, wind resistance and all such factors remain constant, which will stop first? A heavier car or a lighter car? How will the momentum of the car and gravitational pull on a heavier object influence the st... | dmckee has answered what I believe to be the intent of the question; but Joe has correctly answered the absolute letter of the question.
Level ground seems to be implicitly assumed.
If all other things are EQUAL (e.g. coefficients of friction), except where they need to be PROPORTIONAL to be equal (e.g. wind resistanc... | {
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Are all superalgebras Clifford algebras? I believe the answer to be yes, but I realize that sometimes physicists place additional constraints that might not be obvious. If superalgebras are Clifford algebras, why make a literary distinction?
| The answer is No, as Lubos Motl has already pointed out. Here I would like to make a couple of general remarks.
*
*On one hand, the notion of superalgebras is a huge topic, which includes, e.g., associative superalgebras and Lie superalgebras. Important examples of Lie superalgebras are super-Poincaré algebras.
*On... | {
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Online QFT video lectures I'm aware of Sidney Coleman's 1975/76 sequence of 54 lectures on Quantum Field Theory. Are there any other high-quality QFT lecture series available online?
| CERN Lectures
--
Lecturer: Herman Nicolai
Title: Quantum field theory
Year: 1997
Abstract: The lectures are intended to provide an introduction to Quantum Field Theory at an elementary level. In particular, the following topics will be treated: 1, Basic principle of QFT; 2, Representation theory of the Poincaré group; ... | {
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Simple Quantum Mechanics question about the Free particle, (part2) Continuing from my first question titled, Simple Quantum Mechanics question about the Free particle, (part1)
Griffiths goes on and says,
"A fixed point on the waveform corresponds to a fixed value of the argument and hence to x and t such that,"
x $... | Quantum mechanics states that the wave function must be square integrable. So, even although the plane wave is a solution of the stationnary Schrödinger equation, its not a physically accepted wave function. Now the wave packets or linear combinations of wave planes are physically acceptable solution but are NOT a solu... | {
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Gravitational time dilation at the earth's center I would like to know what happens with time dilation (relative to surface) at earth's center .
There is a way to calculate it?
Is time going faster at center of earth?
I've made other questions about this matter and the answers refers to:
$\Delta\Phi$ (difference in Ne... | Dear HDE, it's not hard to estimate the gravitational potential at the Earth's center. Of course, it's smooth. Let me assume that the Earth's mass density is uniform which is an OK estimate - up to factors of two or so.
The gravitational acceleration at distance $R$ from the center is $GM/R^2$ if $R$ is greater than th... | {
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A question on a system of particles governed by laws of gravity and electromagnetic field Consider a system of many point particles each having a certain mass and electric charge and certain initial velocity. This system is completely governed by the laws of gravitation and electromagnetic field. If this system is left... | You can always create discontinuous waves (which are solutions that exists even in the total absence of sources (be them gravitational or electromagnetic)
You can always write a discontinuous function and use it to define, say, the electric field at some time $t_1$, and ask what do the fields look at time $t_0 < t_1$. ... | {
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Is the wave function objective or subjective? Here is a question I am curious about.
Is the wave function objective or subjective, or is such a question meaningless?
Conventionally, subjectivity is as follows: if a quantity is subjective then it is possible for two different people to legitimately give it different val... | The wave function is not an observable, so you can characterize it however you want.
However, any alternative explanation you want to put forth must agree with experimental reality, which in the end will mean it must be mathematically equivalent to the usual approach and will accordingly have some object that is isomor... | {
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Is there a "Size" Cutoff to Quantum Behaviour? We all know that subatomic particles exhibit quantum behavior. I was wondering if there's a cutoff in size where we stop exhibiting such behavior.
From what I have read, it seems to me that we still see quantum effects up to the nanometer level.
| The classic experiment demonstrating quantum effects, the 2 slit experiment, has been preformed with subsequently larger and larger particles as our technology available to do it advanced. Originally, it was performed with electrons, which are just as much matter as any other matter, but are extremely small. The larg... | {
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Graduate Physics Problems Books Need to brush up on my late-undergrad and early-grad physics and was wondering if anyone can recommend books or lecture notes (hard copy, or on-line) that also have solutions.
Two that I have come across are:
Princeton Problems in Physics with Solutions - Nathan Newbury
University of Ch... | (I have a suggestion to make this question a CW.)
General Physics: (Early undergrad and advanced high school)
*
*Problems in Physics I.E Irodov - (Highly recommended)
*Problems in Physics S S Krotov - (Once again, highly recommended but out of print)
*Physics Olympiad Books - (Haven't read but saw some olympiad pr... | {
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Understanding the cause of sidebands in Amplitude Modulation I've read it many places that Amplitude Modulation produces sidebands in the frequency domain. But as best as I can imagine it, modulating the amplitude of a fixed-frequency carrier wave just makes that "louder" or "quieter", not higher-frequency or lower-fr... | Let your carrier signal be $A_0 \cdot \cos(\omega_c t)$ with amplitude $A_0$ and carrier frequency $\omega_c$.
Let your signal be a simple wave, $\phi(t) = A_s \cdot \cos(\omega_s t)$.
Then the modulated signal becomes
$$A_0 A_s \cdot \cos(\omega_c t) \cdot \cos(\omega_s t)$$.
In addition, as pointed out by George in... | {
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What are the forces of constraint if there are multiple equivalent constraints? Suppose a large (rigid) block is sitting on top of two smaller blocks of equal height $1$, both of which rest on the ground. We wish to find the position of the block (easy) and the forces of constraint on the block coming from the two smal... | You can still do this with Lagrangians, even if it's the hard way around. I define $z_1$ and $z_2$ as the height of the boxes above the table, and the constraints are $f_1 = z_1-\frac{h}{2}=0$ and $f_2 = z_2-z_1-\frac{h}{2}=0$, or "the bottom box sits on the table and the top box sits on the bottom box." I assumed that... | {
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How do laser rangefinders work when the object surface is not perpendicular to the laser beam? I find the functioning of a laser rangefinder confusing.
The explanation usually goes like this: "you shine a laser beam onto the object, the laser beam gets reflected and gets back to the device and time required for that is... |
so only a tiny fraction of beam energy
is reflected back to the device.
This tiny fraction is enough. With respect to ambient light:
One can modulate the laser beam, and filter the the voltage
of the receiving photodiode for this modulation frequency and phase.
Another precaution is to have a light filter in fro... | {
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Can heat be transfered via magnetic field in a vacuum? Say you want to store hot coffee in a container surrounded by a vacuum. To remove all sources of conductive energy loss the container is suspended in the vacuum by a magnetic field and does not have a physical connection to the sides of the vacuum chamber,
My quest... | Heat consists of random vibrations in a material. If a magnetic field connects two objects, then it creates a mechanical coupling between the two objects. Such a coupling will couple vibrations, therefore heat will be conducted by the magnetic field.
In practice, the effect will be very small, but given enough time, he... | {
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Why are smaller animals stronger than larger ones, when considered relative to their body weight? I am interested in why many small animals such as ants can lift many times their own weight, yet we don't see any large animals capable of such a feat.
It has been suggested to me that this is due to physics, but I am not ... | To answer this question you just need to know that the force scale like the transection surface of a muscle. In other words the bigger the muscles the stronger. Therefore you have
$F ∝ σ_s S$,
where $σ_s$ is the maximum developed muscle stress. It so happens that on earth the muscles work pretty much the same in all t... | {
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Experimental evidence showing the kinetic energy of an electron changes in a static non-uniform magnetic field? In a previous question, Does a magnetic field do work on an intrinsic magnetic dipole?, one highly rated answer suggested that static magnetic fields do work on intrinsic magnetic dipoles in a non-uniform mag... | The Stern Gerlach experiment is such an example (although we have an extra complication because the wave function splits)
1) There is a change in the EM Field energy $\tfrac12 B$ because the total magnetic field (static field + electron's own magnetic field) becomes less. A static field in isolation doesn't change per ... | {
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What causes the Pauli exclusion principle (and why does spin 1/2 = fermion)? It seems to be related to exchange interaction, but I can't penetrate the Wikipedia article. What has the Pauli exclusion principle to do with indistinguishability?
| Indistinguishableness of particles is formulated in QM in terms of the total wave function symmetry. Then the wave functions can be symmetric or antisymmetric on their arguments. In case of antisymmetry ($\psi(x_1,x_2) = -\psi(x_2,x_1))$ the particles are called fermions and $\psi(x_1,x_2=x_1) = 0$. They say "the parti... | {
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Calculating diffraction-limited resolution for a lens setup Supposed a lens arrangement is prepared where light from an object is collimated, focused and recollimated etc. before entering a CCD array. Given that we can calculate the diffraction-limited resolution for each lens in the system, how do we measure the diffr... | (Edited based on your comments)
I want to briefly clarify what exactly is meant when we talk about being "diffraction limited." As light is focused, it will reach some minimum spot size before it begins to expand again. The size of this spot depends on how much the light beam is distorted.
A perfectly collimated beam (... | {
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Thought experiment that seems to involve something growing at twice the speed of light. Is anything wrong? Let foo be some unit of distance and bar be some unit of time which have been chosen so that the speed of light c = 1 foo/bar. Position several observers along a line each separated by one foo, and place light so... | Lagerbaer gives an excellent detailed explanation, but to put it more simply: there is no contradiction, no logical fallacy, the distance $r(t)$ as you have defined it does indeed grow at a rate of $2c$ as measured by any of the observers A, B, C, etc. But $r$ does not correspond to a real thing. It does not measure th... | {
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What do we consider "Perpetual Motion" I know this is a bad question to most serious Physics but I have a question about what is considered “Perpetual motion.” The Foucault pendulum in the UN consists of sphere that passes directly over a raised metal ring at the centre that contains an electromagnet, which induces a c... | From the webster.com dictionary , perpetual:
a : continuing forever : everlasting
In our universe as far as we have learned, nothing continues forever. So the definition of perpetual motion is a relative definition in time.
For a human lifetime the earth will be continuously turning on its axis,
as well as with th... | {
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Why are WW gg ττ branching ratios so similar for a 115 GeV SM Higgs? In a previous question on Higgs branching ratios, I find this image
(originally from page 15 here).
I am VERY intrigued by the fact that decays to WW, gg, and ττ are almost equally probable, for a standard model Higgs with a mass in the vicinity of ... | In this graph, you have clearly found the triangle composed of three curves which is the smallest one. The triangle made of $gg$, $ZZ$, $\tau\tau$ near $m_H=130$ GeV is comparably small but larger.
Still, none of the triangles is infinitesimal. Even though your triangle is the winner among the small ones, it doesn't sh... | {
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Length of a curve in D dimensional euclidean space In a book I am reading on special relativity, the infinitesimal line element is defined as $dl^2=\delta_{ij}dx^idx^j$ (Einstein summation convention) where $\delta_{ij}$ is the euclidean metric. Next, if we have some curve C between two points $P_1$ and $P_2$ in this s... | I think you should take that as the definition of the word "length". I wouldn't try to derive it at all.
It is basically saying that if, for example, you want to know the length of the unit circle in the first quadrant, set
$$x^1 = \cos t$$
$$x^2 = \sin t$$
$$\dot{x}^1 = -\sin t$$
$$\dot{x}^2 = \cos t$$
and do
$$\int_... | {
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Simple Harmonic Motion - What are the units for $\omega_0$? I'm trying to understand the units in:
$$mx''+kx=0$$
And the general solution is $$x(t)=A \cos(\omega_0 t)+B \sin(\omega_0 t).$$
Let $\omega_0 =\sqrt{\frac{k}{m}}$ - the unit for the spring constant $k$ is $kgms^{-2}$
or $Nm^{-1}$, where $m$ is in $kg$, so tha... | I find it helpful to use rad in units to understand these mechanical properties:
The unit for spring constant k for a torque spring (clockwork spring) is N.m, but call it (N.m)/rad and it is easier to understand: "Torque per angle".
Also N.m is "formally" the same as J, and this can make it hard to distinguish from tor... | {
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Why is the gravitational force always attractive? Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time?
PS: If the simple answer to this question is that mass makes space-time curve in a concave fashion, I can rephrase the question as why does mass ... | When I was a schoolboy, our teacher of physics asked once one of our brilliant students (a girl), something like: "What is the nature of gravity?". She thought for a moment and answered: "I do not know. And what is it? Our teacher replied: "If I had known..."
As long as gravity is not derived from other nature features... | {
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How is thermodynamic entropy defined? What is its relationship to information entropy? I read that thermodynamic entropy is a measure of the number of microenergy states. What is the derivation for $S=k\log N$, where $k$ is Boltzmann constant, $N$ number of microenergy states.
How is the logarithmic measure justified?
... | The reason for the logarithm in the statistical definition of entropy is that it makes the entropy additive and the number of microstates multiplicative. This means that if you have subsystems A & B, total number of microstates is the product of the subsystem’s number of microstates, and the entropy is additive over su... | {
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What are the properties of two bodies for their collision to be elastic? For example, must the shock wave in each body be of a particular form which influences the shape and material properties of the bodies?
I suspect part of the the answer is that the objects must be spherical, and the round-trip of the shock wave in... | Extended reply to Anonymous Coward:
Perfect, I'll argue that gaining rotation in a collision doesn't make it inelastic. The kinetic energy is still there, it's just in the form of rotational kinetic energy. But yes, that is strictly semantics. You pretty much covered the question.
Generally I would claim that no mac... | {
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On a bicycle, why does my back tyre wear so much more quickly than the front? This question is cross-posted from Bicycles.SE, but it is really one for those that know a bit about physics.
Why does the back tyre of a bicycle wear out quicker than the front tyre?
I have my uneducated suspicions but I would appreciate an ... | Unless the cyclist is leaning forward most of the weight is on the back tire. Therefore it has more contact with the road and when you turn there is more lateral force on the back. You do more braking whith the back so you don’t go head first. And finally you are applying your entire forward force on it so that contrib... | {
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how does a helicopter get forward thrust? Just passed a helicopter on my way to work. We have read in some detail how an airplane gets forward thrust and lift by deflecting air. How does a helicopter with horizontal fans achieve that ?
| In general, the forward thruswt is achieved by tilting the entire helicopter forward. This converts some of the lift produced by the main rotor into a forward component of force. The same is true for turns.
Yes, the swashplate may be used to create a thrust imbalance; but this imbalance does not provide any horizon... | {
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Batman spotlight in the sky I have noticed that obstructing a spotlight typically results in a blurred shadow unlike the crisp batman symbol in the comics of batman. Is there a way to create a spotlight with a crisp batman symbol?
| You can use a Laser. Just track it whit moving mirrors like the beam of a TV tube. There are computers that do an outline but its totally possible to track horizontal lines that appear and disrepair at the proper moments and the smoke from fire woks can make a perfect screen. O ya and a BIG laser.
| {
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Non-Linear Density Shell Problem I'm trying to understand Newton's Shell Theorem (Third)
http://en.wikipedia.org/wiki/Shell_theorem
However this applies to a sphere of constant density. How is this formulated for sphere of varying density, e.g., a ball of gas bound together by gravity?
Actually, this requires another ... | A really simple way of thinking about the shell theorem is that it applies to an infinitesimally thin spherical shell of constant surface density. Then, any spherically symmetric ball of stuff (even if it varies in density with distance from the center) can be built of these shells (with different densities for each sh... | {
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How does stuff glow in the dark? Many things have glow in the dark properties (glow sticks, paint, toys ..), and I am wondering what is the physics behind them. How do these materials store light energy and emit it later when dark?
What dictates the wavelength(s) of the glow? Is there a limit on how much energy can be ... | When one excites fluorescence with light (e.g. blue light), the incoming photon pushes an electron into a higher state. Generally one always excites vibrational states (movement of the molecules' atoms) as well. Therefore the emitted photon has lower energy (e.g. green light). The lost energy (internal conversion) heat... | {
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Detection of the Electric Charge of a Black Hole By the "No Hair Theorem", three quantities "define" a black hole; Mass, Angular Momentum, and Charge. The first is easy enough to determine, look at the radius of the event horizon and you can use the Schwarzschild formula to compute the mass. Angular Momentum can be fou... | I will say that this question has a bit of a misconception--you don't need to interact with the horizon or extreme-limit GR effects like the ergosphere in order to measure the parameters of the black hole. The metric tensor is different for black holes with different masses and charges, and have different $\frac{1}{r^... | {
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How come an anti-reflective coating makes glass *more* transparent? The book I'm reading about optics says that an anti-reflective film applied on glass* makes the glass more transparent, because the air→film and film→glass reflected waves (originated from a paraxial incoming wave) interfere destructively with each oth... | The thickness of the AR coating is chosen such that the reflections from the two interfaces cancel out (at the wavelength for which the AR coating was designed):
See Anti-reflective coating in Wikipedia.
As endolith points out in the comments, to explain how the transmission is enhanced, you have to draw a few more ra... | {
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Why is it that when driving in a car, and a lightning bolt strikes, my AM radio gets cut off for a while, but FM stays on? I noticed this one day, a lightning/thunder occurred and my Fabulosa Spanish music died for a second. But not FM?
| For a more complete answer, one should also consider the basic difference between the two transmission schemes. AM - i.e Amplitude Modulation - encodes a signal by varying the amplitude of a radio wave of a single frequency. FM - i.e. Frequency Modulation - encodes a signal by varying the frequency itself within a na... | {
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What happens to light in a perfect reflective sphere? Let's say you have the ability to shine some light into a perfectly round sphere and the sphere's interior surface was perfectly smooth and reflective and there was no way for the light to escape.
If you could observe the inside of the sphere, what would you observe... | If you are observing the inside of the sphere, you are absorbing light to make the observation. The light would get dimmer and dimmer very quickly until you could see nothing at all.
| {
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Do eyeballs exhibit chromatic aberration? Fairly straightforward question. If not, why not?
I suspect that if they do, it is not perceived due to the regions of highest dispersion being in one's region of lowest visual acuity.
| Because refractive index is a function of wavelenght, every lens experiences chromatic aberration, and so does a human eye.
This could have severe effect on human vision. However, eye has tuned spectral bandwidth - it is well known eye is most sensible to visible light which has wavelenght of 550 nm. Relative luminosit... | {
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What are the mathematical problems in introducing Spin 3/2 fermions? Can the physics complications of introducing spin 3/2 Rarita-Schwinger matter be put in geometric (or other) terms readily accessible to a mathematician?
| Free spin 3/2 fields cause no problems; see Weinberg's QFT book, Volume 1.
The problem with elementary spin 3/2 fields is the difficulty of accounting for the interaction with the electromagnetic field. The Rarita-Schwinger field equations with the standard minimal coupling via the covariant derivative violate causalit... | {
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'Getting in' to research physics? I'm going to be choosing a university course soon, and I want to go into a branch of physics. A dream job for me would be to work in research, however, I do realise that this isn't for everyone and is difficult to reach. So what is the best way to go about achieving this aim? What thin... | Make sure that you have some sort of life skill when you're done that isn't research, too. Teach yourself to program, or work on an experiment where you build things. It will enhance your research, and make you more employable should reasearch not work out.
| {
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Does a slide in a projector act as a diffuser? I was wondering whether or not a slide in a slide projector acts as light diffuser? So when I have a light source that does not have a parallel beam on the slide can I expect that the other side of the slide is illuminated with a Lambertian of similar reflectance?
I am won... | The slide will not act as a diffuser, but there will often be a diffusing element upstream near or adjacent to the slide, so treating it as a diffuse source is probably a good approximation.
| {
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Roughly how many atoms thick is the layer of graphite left by a pencil writing on paper? Actually I can't expand much as the question pretty much explains the query. I would be interested in the method of estimating an answer as well as a potential way to measure it experimentally. Thanks.
P.s. I'm not sure what tags t... | We run an experiment on my A Level Physics course to answer this question.
*
*Expose the graphite in the pencil you wish to use at either end. Measure the length of the graphite, its diameter (then calculate its cross-sectional area) and the electrical resistance along its length (either by direct measurement using ... | {
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Trying to understand the EPR paradox So I keep reading all these articles on the EPR paradox, and I follow them pretty easily right up until it gets to the most important matter.
Assuming you are trying to measure x and y spin,
Wikipedia and others say that when you measure x-spin on the first particle, it suddenly bec... | As reading the wikipedia article, we can clearly see a way to transfer information faster than the speed of light, therefore we know there is an error in the article.
Let's say entangled particle pair has identical x-spins. We measure y-spin of one particle. The x-spin of the measured particle becomes random, the x-spi... | {
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Physical Interpretation of a Scalar Quantity Related to Currents/Conservation Laws Let $Q_{ab} = (\psi_{;a})(\psi_{;b}) - (1/2)g_{ab}|\nabla \psi|^2$ be the energy-momentum tensor of the wave equation in some space time. I will use semicolons to refer to covariant differentiation and $\partial$s to refer to coordinate ... | Here we will not give a physical interpretation per se, but just derive an alternative covariant expression for the sought-for scalar.
There are given a scalar field $\psi$ and a metric
$$ds^2~=~g_{ab} ~dx^a dx^b.$$
Let $\nabla$ be the corresponding Levi-Civita connection. The Lagrangian scalar function is:
$$ \Lambd... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Books that every layman should read To add to Books that every physicist should read:
A list of popular physics books for people who aren't necessarily interested in technical physics.
(see also Book recommendations)
| *
*'One Two Three ... Infinity' - By George Gamow
*'Mr. Tompkins in paperback' - By George Gamow ( combines Mr. Tompkins in Wonderland with Mr. Tompkins Explores the Atom )
*'Mathematics for the Million: How to Master the Magic of Numbers' - Lancelot Hogben
*'Relativity Simply Explained' - By Martin Gardner
| {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is the earth expanding? I recently saw this video on youtube:
http://www.youtube.com/watch?v=oJfBSc6e7QQ
and I don't know what to make of it. It seems as if the theory has enough evidence to be correct but where would all the water have appeared from? Would that much water have appeared over 60 million years? Also what... | It's not that the earth is expanding; instead the primary effect is that the earth's surface is shrinking. The effect occurs because the earth's surface doesn't remain flat. Instead, it gets tilted and folded. Some parts of the crust get subducted; once they disappear, what's left appears smaller.
Over any appreciable ... | {
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"source": "stackexchange",
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Which Friedmann equation is redundant? For flat FLRW cosmology, we can write down two Friedman equations and one matter equation. Namely,
\begin{align}
H^2 & =\frac{8 \pi G}{3} \rho, \tag{1} \\
\frac{\ddot{a}}{a} &= -\frac{4 \pi G}{3} (\rho +3p), \tag{2} \\
\dot{\rho} &= -3 H (\rho + p). \tag{3}
\end{align}
It is well ... | I suppose a lot of what constitutes the "Friedmann Equation(s)" is just up to definitions. However, with the 3 equations you listed, there will be redundancy.
Here is the normal derivation I usually see (feel free to skip the first two paragraphs if you aren't familiar with tensors/GR):
Given einstien's equation in the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/13187",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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In dimensional analysis, why the dimensionless constant is usually of order 1? Usually in all discussions and arguments of scaling or solving problems using dimensional analysis, the dimensionless constant is indeterminate but it is usually assumed that it is of order 1.
*
*What does "of order 1" mean? 0.1-10?
*Is... | Well, of course you have to pick the quantities in your dimensional analysis right.
Example: Use dimensional analysis to estimate the potential energy of a star, hold together only by gravitation.
Solution: Newtons gravitational constant $G$ better show up somewhere. This requires us to include something with units $k... | {
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"source": "stackexchange",
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Photons in expanding space: how is energy conserved? If a photon (wave package) redshifts (stretches) travelling in our expanding universe, is its energy reduced?
If so, where does that energy go?
| Since you say you're talking about what happens locally (in a small volume), I'll answer from that point of view. The usual formulation of energy conservation in such a volume is that energy is conserved in an inertial reference frame. In general relativity, there are no truly inertial frames, but in a sufficiently sma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/13577",
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"source": "stackexchange",
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Does the wavelength always decrease in a medium? I was studying a GRE Physics Test problem where optical light with a wavelength of 500 nm travels through a gas with refractive index $n$.
If we look at the equations for wave motion and index of refraction
$$c=\lambda_0\nu\quad\text{(in vacuum)}$$
$$v = \lambda\nu\quad\... | As for your second question, dielectrics which change the frequency, any medium which changes the frequency must be a nonlinear medium. There are many of them. They do not change the frequency continuously, but rather they generate higher order harmonics, an integral number times the original frequency.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What are the details around the origin of the string theory? It is well-known even among the lay public (thanks to popular books) that string theory first arose in the field of strong interactions where certain scattering amplitudes had properties that could be explained by assuming there were strings lurking around. U... | Well I believe the original clue was Regge trajectories. It was observed that if you plotted mass squared vs. angular momentum for strongly interacting resonances, they tended to follow straight lines. This could be explained as the spectrum of rotating strings connecting massless particles.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/13728",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "23",
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With potential $V(x)= ax^6$ the quantized energy level $E$ depends on which power of $n$? A particle in one dimension moves under the influence of a potential $V(x)= ax^6$, where $a$ is a real constant. For large $n$, what is the form of the dependence of the energy $E$ on $n$?
| For large $n$, the semiclassical approximation is valid and for bound states we may use the Bohr-Sommerfeld quantization condition:
$n = \frac{1}{h}\oint p dq$, where $n$ is the principal quantum number, $h$, the Planck constant,
$q$, the position and $p$, the momentum on the classical trajectory.
In our case due to th... | {
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"source": "stackexchange",
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Positive Mass Theorem and Geodesic Deviation This is a thought I had a while ago, and I was wondering if it was satisfactory as a physicist's proof of the positive mass theorem.
The positive mass theorem was proven by Schoen and Yau using complicated methods that don't work in 8 dimensions or more, and by Witten using ... | Given that your argument requires moving in an accelerating frame and considering its Rindler horizon, I wonder if what you stated is more similar to statements about asymptotically hyperbolic hypersurfaces in a space-time. In which case, that the analogue of the positive mass theorem can be derived using only the weak... | {
"language": "en",
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Solid objects inside the event horizon - can they remain "solid"? So, once something is inside a black hole's event horizon, it can only move towards the center. This is fine for a point-object. But 3D solid objects rely on molecular forces to stay in one piece. These forces act in all directions inside the solid. But ... | No solid can be placed inside an event horizon because any solid matter under the horizon means information about it is lost.
Also a solid object inside the BH would allow to transfer information from inside, say, by changing its gravitational field by rotating it.
The both things are impossible thus no body containin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/13957",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 4,
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How can it be that the beginning universe had a high temperature and a low entropy at the same time? The Big Bang theory assumes that our universe started from a very/infinitely dense and extremely/infinitely hot state. But on the other side, it is often claimed that our universe must have been started in a state with ... | I had puzzled about that as well. But while the temperature is high the mass/energy density is extremely uniform (as ilustrated by the uniformity of the cosmic microwave background radiation 380,000 years later in the evolution of the universe). And gravity changes everything. Uniform density is very low for systems... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14004",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "34",
"answer_count": 10,
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Plotting a wave function that represents a particle The problem is this:
A particle is represented by the wave function $\psi = e^{-(x-x_{0})^2/2\alpha}\sin kx$. Plot the wave function $\psi$ and the probability distribution $|\psi(x)|^2$.
This the problem 2.1 in the book Fundamental University Physics Volume III by ... | Then plot first with $x_0=0$, $\alpha=1$, and $k=1$.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors? I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean?
More specifically,
*
*Why is it that dot product of vectors $\vec{A}$ and $\vec{B... |
I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean?
Perhaps you would find the geometric interpretations of the dot and cross products more intuitive:
The dot product of A and B is the length of the projection of A onto B multiplied by the length... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14082",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "83",
"answer_count": 9,
"answer_id": 0
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How can area be a vector? My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector:
Noun: A quantity having direction as well as magnitude, esp. as
determining the position of one point in space relative to another.
My question is - what is the direction of ar... | There is an especially picturesque example of the Law of Pythagors in three dimensions applied to the areas of a simplex. (Where by "simplex" I believe I mean a section of space bounded by three orthogonal planes and one arbitrary plane.) The sum of the squares (of the areas) of the three small faces are equal to the s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14165",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "34",
"answer_count": 4,
"answer_id": 3
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Collision of Phobos Mars has two moons: Phobos and Deimos. Both are irregular and are believed to have been captured from the nearby asteroid belt.
Phobos always shows the same face to Mars because of tidal forces exerted by the planet on its satellite. These same forces causes Phobos to drift increasingly closer to Ma... | First, you state a few things that aren't quite right in your question. While the view that's generally talked about is that Phobos and Deimos are likely captured asteroids, dynamically it's a pretty difficult problem (you generally need a third (in this case fourth?) body to take away the extra energy, and it's hard ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14212",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 4,
"answer_id": 1
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Rainbow around Sun From the perspective of a person, a rainbow is formed when the Sun is behind the person, and there is a critical angle made by the rainbow.
However, on several occasions, usually at noon when the Sun is higher, I saw a ring around the Sun made of the colors of the rainbow. Is that a rainbow? Is wit... | The other answers describe a rainbow-like phenomenon involving ice crystals, which may very well be what you saw. However, there is another possibility.
A normal rainbow occurs when light enters a spherical drop, refracts at the curved surface (dispersing the colors), reflects off the back of the drop, and then leaves ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14254",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does the proton have an equatorial bulge around its spin axis? And if so, can we observe a difference in the electron scattering cross section with transversely polarized VS longitudinally polarized protons?
P.S. Let me make my question more precise. Consider the charge shape of the proton. In the rest frame of a proto... | At the level of individual Proton interactions I reckon it is far more common to use the parton model, ie it is a collection of three quarks, $uud$, and associated gluons.
Also the 'spin' axis is a quantum physical term and is best not converted to classical terms.
nb. This answer was given to a previous, simpler ves... | {
"language": "en",
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"source": "stackexchange",
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Surface tension of solutions and mixtures The inspiration for this question is over on cooking.stackexchange, asking more about actual measurements for commonly consumed liquids, but I'm interested more generally as well.
What determines the behavior of surface tension for solutions and mixtures with respect to concent... | The wikipedia section on the influence of temperature and solutes on surface tension is actually pretty decent with some good reference to basic text on this topic.
That said, there is no straightforward answer to your question because it all depends a lot on the liquid(s) that you are looking at. If for example you ha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14399",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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How do you prove $S=-\sum p\ln p$? How does one prove the formula for entropy $S=-\sum p\ln p$?
Obviously systems on the microscopic level are fully determined by the microscopic equations of motion. So if you want to introduce a law on top of that, you have to prove consistency, i.e. entropy cannot be a postulate.
I c... | The functional form of the entropy $S = - \sum p \ln p$ can be understood if one requires that entropy is extensive, and depends on the microscopic state probabilities $p$.
Consider a system $S_{AB}$ composed of two independent subsystems A and B. Then $S_{AB} = S_A +S_B$ and $p_{AB} = p_A p_B$ since A and B are decoup... | {
"language": "en",
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"source": "stackexchange",
"question_score": "28",
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Why is the string theory graviton spin-2? In string theory, the first excited level of the bosonic string can be decomposed into irreducible representations of the transverse rotation group, $SO(D-2)$. We then claim that the symmetric traceless part (i.e. the 35 rep) is the spin-2 graviton - but isn't the label "spin-2... | It is traditional to label massless (and some massive) states in higher dimension by their 3-d "spin" counterparts, even thought he label is completely inaccurate, as you say. All antisymmetric forms are "spin-1", the symmetric two-index object is "spin-2", a fundamental spinor is "spin 1/2" and a vector of spinors is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14484",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Reference area of a parachute I am trying to do an aerodynamic drag equation on a descending parachute (the round variety) and have no idea what the reference area on one would be. I know for a sphere, you can use radius*radius*PI to get the reference area. Is that the same for a parachute?
| Poking around on Google with various search terms that included "parachute shape" i came upon "The Parachute Manual" by Dan Poynter. Table 8.1.7 from that book catalogs empirical data on a host of parachute shapes. Assuming that the parachute is round, as you say, and does not have any holes (apparently, many designs p... | {
"language": "en",
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Is visible light and radio waves made of the same thing? I understand that there is such a thing as the electro magnetic spectrum, and that light and RF are both on it, so dose that mean that they are made of the same thing? Just at different frequencies.
| you see, the point here is waves are just oscillating energy vectors.
Do you consider a male voice and a female voice as same? Then yes, visible light and RF waves are same!
Its only a matter of how much energy each of them is carrying.
While, RF is having lower photon energy than visible light attributed because of th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why are the even and odd Regge trajectories degenerate? This is an old classic which I don't think ever got a clear answer. The Gribov-Froissart projection that gives the relativistic version of Regge trajectories treats even angular momentum differently from odd angular momentum. The trajectory functions in general ar... | Once upon a time, I asked an experienced phenomenologist who worked on particle physics in the 60s why even and odd signatured trajectories lie on top of each other.
He said the phenomenon was called 'exchange degeneracy' and that so far no one has an explanation.
I'm looking back at my notes on Dual Resonance Models, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14791",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Nonextensive statistical mechanics I know that the Tsallis($S_q$) entropy is called nonextensive information measure in the sense that if $P$ and $Q$ are two probability distributions then $S_q(P\times Q)=S_q(P)+S_q(Q)+(1-q)S_q(P)S_q(Q)$. My question is what is meant by nonextensive statistical physics? What is its con... | Normally entropy is seen as an extensive thermodynamic coordinate, i.e. proportional to the mass of particles: Volume increases by considering a larger amount of gas in the "same state", while pressure will stay the same. So for simple systems entropy of a system that is a combination of 2 systems will be sum of indivi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14845",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Would a generator in vacuum/space provide electricity endlessly? At it's simplest, electricity generation is achieved by induced voltage due to a changing magnetic field. In a vacuum in the absence of friction, would the initial spin imparted to the rotor of a generator ever come to a halt?
i.e. Would a traditional ge... | No, because the process of transferring the voltage into a useable form or device will reduce it. In other words, under perfectly idealized conditions (which are impossible), yes it might spin forever, but as soon as you try to use your generator to power a device, you'll slow it down.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14900",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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How would you store heat? Um .. naive question perhaps but if somebody wanted to store heat, how would they go about it? Can heat be stored?
I'm told that decomposing kitchen waste in a closed vessel results in a rise in temperature on the body of the vessel. I'm just wondering whether it could be stored for later use... | Building off of the comments to the question.
It might be instructive to think carefully about what is being stored when you store "electricity" in a capacitor or battery.
Note that it is not electrons as I can charge a capacitor either positive or negative relative to a floating ground. The "what" in that case is en... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/14961",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 0
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Graphene space elevator possible? I just read this story on MIT working on industrial scale, km^2 sheet production of graphene.
A quick check of Wikipedia on graphene and Wikipedia on space elevator tells me
Measurements have shown that graphene has a breaking strength 200 times greater than steel, with a tensile stre... | Most proposed designs of the space elevator are such that the whole structure is under tensile stress from the ground anchor point. In these designs, there are stress limits that constraint the material properties of the ribbon. The calculations (based on geosynchronous height of earth) point to that 130 GPa figure.
Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15052",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 6,
"answer_id": 2
} |
Indirect band gap semiconductor for LEDs? Can someone please explain why Indirect band gap semiconductor can not be used for LED creation. Can you also please give me some reference link for details.
| Indirect bandgap semiconductors do not emit as well as do not absorb light for photon energies close to band gap due to reasons described above. Namely, the main reason is the momentum conservation law. However, it is possible to make photodetectors (absorbers) on such semiconductors utilizing interband electron transi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15089",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
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Why is it important that Hamilton's equations have the four symplectic properties and what do they mean? The symplectic properties are:
*
*time invariance
*conservation of energy
*the element of phase space volume is invariant to coordinate transformations
*the volume the phase space element is invariant with res... | Coordinate invariance guarantees that the phase space $M$ can be endowed with a symplectic 2-form $\omega$ which locally is given by $\omega = dq^i \wedge dp_i$. This form is closed ($d\omega = 0$) and nondegenerate, i.e. $\omega^n$ is a volume form, where $2n$ is the dimension of $M$. The other conditions say that fo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15195",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Is an electron/proton gun possible? In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to also fire the same number of protons in the other direction, dissipating the mass of t... | Both electron gun and proton can be made but they don't work the way you want. Electrons or cathode rays flow from high potential region to a low potential region. To accelerate electrons you need high voltage. I agree with dmckee regarding protons. Protons are made by ionizing the Hydrogen gas because that's the easy ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15290",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 2
} |
Apple falls for which of these 2 reasons? Needles to say I am a visitor here. I do not belong to the science world;)
But I have read both of these things before:
*
*Apple falls to the ground because curved spacetime pushes it there (same force as keeps moon in orbit)
*Apple 'falls' to ground because the ground is r... | Number 1 is correct. Number 2 is incorrect. The apple has the same velocity as the Earth since it grew on earth. Also, if the earth were moving into the apple you wouldn't see the apple accelerating unless the Earth is constantly linearly accelerating at 9.8m/s^2, which is impossible.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15349",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 3
} |
How does a change in temperature affect relative humidity Assume that the air pressure and the amount of water in the air stay constant. How can I figure out how much a change in temperature affects the relative humidity?
| Relative humidity is just the percentage of what the air at a given temperature can hold. This is given by the Clausius–Clapeyron equation, which rises roughly exponentially with temperature doubling approx every 10degrees C. So if your relative humidity is X, and the saturation vapor pressure at the new temperature is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15395",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 0
} |
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