Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
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Can a huge gravitational force cause visible distortions on an object In space, would it be possible to have an object generating such a huge gravitational force so it would be possible for an observer (not affected directly by gravitational force and the space time distortion) to see some visual distortions (bending) ... | Of course! This is exactly what we see in images of gravitational lensing, where enormous clusters of galaxies bend the light from other galaxies around themselves.
This bending of light was also one of the first lines of evidence that supports Einstein's General Relativity, where we observed our own Sun bending the li... | {
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What is the difference of the two stable states of a Flip-flop?
In electronics, a flip-flop or latch is a circuit that has two stable
states and can be used to store state information. [...] Flip-flops and latches are used as data storage elements. Such data storage can be used for storage of state, and such a circu... | If you imagine a small loop lying on a surface, how many different directions can an electric current go within it?
The answer is two of course. With some pretzel-like shape changes, that's also what happens in a flip-flop: "flip" is (for example) a counter-clockwise current, and "flop" is a clockwise current (again, t... | {
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Is GPS time measuring the proper time on the mean sea level or the GPS station itself? LeapSecond.com states:
Global Positioning System time is the atomic time scale implemented by the atomic clocks in the GPS ground control stations and the GPS satellites themselves.
Does GPS time measure the proper time on the mean... | GPS time is locked to TAI time, with a constant difference of 19 seconds as you say. In fact GPS is used as part of the TAI process. See for example http://tycho.usno.navy.mil/ptti/1993/Vol%2025_13.pdf and http://tycho.usno.navy.mil/ptti/ptti2000/paper12.pdf for details.
If you're interested in this area there's a lot ... | {
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What equations govern the formation of droplets on a surface? When some smooth surface (like that of a steel or glass plate) is brought in contact with steam (over e.g. boiling milk) then water is usually seen to condense on that surface not uniformly but as droplets. What are the equations which govern the formation ... | It is more about properties of the material and surface roughness/texture, than geometry of the surface on the large scale. There is a nice Wikipedia article on wetting, which you may find useful. In brief, that is the difference in surface tension at liquid-solid ($\gamma_{LS}$), liquid-air ($\gamma_{LA}$), and solid-... | {
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Sound frequency of dropping bomb Everyone has seen cartoons of bombs being dropped, accompanied by a whistling sound as they drop. This sound gets lower in frequency as the bomb nears the ground.
I've been lucky enough to not be near falling bombs, but I assume this sound is based on reality.
Why does the frequency dro... | If you're on the aircraft which is dropping a bomb that whistles, you'll hear the pitch drop as the bomb accelerates downward away from you. Perhaps the classic cartoon sound effect was inspired by the experience of someone who flew on a bomber rather than an observer on the ground.
| {
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Will adding heat to a material increase or decrease entropy? Does adding heat to a material, thereby increasing electrical resistance in the material increase or decrease entropy?
Follow up questions:
Is there a situation were Heat flux ie. thermal flux, will change entropy?
Does increasing resistance to em transfer ... | If by "heating" you mean "adding heat", then the answer is yes, except for the unusual situation where a material is at negative temperature. When you add heat to a system
$$ dS = {dQ\over T} $$
and this is always positive when T is positive. This is the definition of the thermodynamic temperature in the most fundament... | {
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Is my electric kettle collecting old water during the week? I have an electric kettle at work. On Monday, it's empty and I pour in about 1.5 liters of water. I usually end up drinking about 1 liter per day and refilling 1 liter each morning.
At the end of the week, I rinse it out because in my mind, there is .5 liters ... | Realistically, you're probably very close to having it fully mixed. There are at least three sources of mixing present. Diffusion is a very slow process, so you can ignore it. You will presumably be agitating the water a lot when you pour the new water in, and that might completely mix everything. If that doesn't fully... | {
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How does one quantize the phase-space semiclassically? Often, when people give talks about semiclassical theories they are very shady about how quantization actually works.
Usually they start with talking about a partition of $\hbar$-cells then end up with something like the WKB-wavefunction and shortly thereafter talk... | Many symplectic manifolds (phase spaces of mechanical systems) admit a coordinate system where the symplectic two form can be written locally as:
$\omega = \sum_i dp_i \wedge dq_i + \sum_j dI_j \wedge d\theta_j$
Where $ p_i, q_i$ are linear coordinates $ I_j$ are radial coordinates and $\theta_j$ are angular coordinate... | {
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How do I show that all Brillouin zones have the same volume? I have read in a few books that all Brillouin zones have the same volume, and I can vaguely see how it works, but have not been able to think up a formal proof.
Help?
| A Brillouin zone is defined as the range of k's which represent a unique one particle pseudomomentum state in the crystal. If you count the total number of states in the Brillouin zone, you do an integral over k:
$$ \int {d^dk\over (2\pi)^d} = {V\over (2\pi)^d} $$
Where V is equal to the total volume in momentum space.... | {
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What is a tensor? I have a pretty good knowledge of physics, but couldn't deeply understand what a tensor is and why it is so fundamental.
| Tensor is a multi dimensional vector in colloquial language.
Where the variations in one direction effects the other.
In Newtonian mechanics we assume all forces, velocities etc that are mutually orthogonal $\Rightarrow$ mutually independent.
$$F=F_x\vec i + F_y\vec j +F_z\vec k $$
$F_x\vec i . F_y\vec j =0$ since $\v... | {
"language": "en",
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Phase shift of 180 degrees of transversal wave on reflection from denser medium Can anyone please provide an intuitive explanation of why phase shift of 180 degrees occurs in the Electric Field of a EM wave, when reflected from an optically denser medium?
I tried searching for it but everywhere the result is just used.... | It is easy to see why there is a sign change in the case where the electric field reflects from a conducting surface. The electric field would excite a current in the conducting surface, which in turn would force the electric field to be zero at the interface. Therefore, the reflected field must be such that it cancels... | {
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Does gravity slow the expansion of the universe? Does gravity slow the expansion of the universe?
I read through the thread http://www.physicsforums.com/showthread.php?t=322633 and I have the same question. I know that the universe is not being stopped by gravity, but is the force of gravity slowing it down in any way?... | The answer is that yes gravity does slow the expansion of space (leaving aside dark energy for the moment), but to get a better grasp on what's going on you need to look into this a bit more deeply.
If we make a few simplifying assumptions about the universe, e.g. it's roughly uniform everywhere, we can solve the Einst... | {
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Partition function of an interacting gas By reading an article, I found a partition function that, according to the author, describes an interacting with random variables as coupling constant.
$$Z =\int \mathrm{d} \lambda_i e^{i(K^{ij}\lambda_i\lambda_j + V^{ijk}\lambda_i\lambda_j\lambda_k)}\mathrm{exp}(e^{iS_{eff}(\la... | This is a quantum partition function, not a statistical mechanical partition function. He is just talking about an idealized self-interacting field. If you have a scalar with cubic self interactions, you write the Lagrangian as
$$ \partial_\mu \phi \partial^\mu \phi - \lambda \phi^3 $$
If you fourier transform the fie... | {
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Apparent contradiction between quantum calculations and intuition for reflection at step potential? I am rather confused because it would seem that mathematical conclusions I have drawn here goes against my physical intuition, though both aren't too reliable to begin with.
We have a potential step described by $$V(x)=\... | Recall that if we have an incident wave
$$\frac{1}{\sqrt{k_1}}e^{ik_1 x}$$
from left (region 1, $x<0$, with constant potential $V_1$) that is partially transmitted
$$\frac{T}{\sqrt{k_2}}e^{ik_2 x} $$
to the right (region 2, $x>0$, with constant potential $V_2$), and partly reflected back to region 1,
$$\frac{R}{\sq... | {
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About an electrostatics integral and a delta-function kernel I'm having trouble with an integral and I would like some pointers on how to "take" it:
$$
\int \limits_{-\infty}^{\infty}\frac{3\gamma a^{2}d^{3}\mathbf r}{4 \pi \left( r^{2} + \frac{\gamma^{2}}{c^{2}}(\mathbf r \cdot \mathbf u)^{2} + a^{2}\right)^{\frac{5}{... | First choose a direction for u, along the z-axis. Then the integral is
$$ I = \int {1\over (x^2 + y^2 + A z^2 + B)^{5/2} } dx dy dz $$
Rescale z by $\sqrt{A}$ to get rid of A and restore rotational invariance.
$$ I = {1\over \sqrt{A}} \int {1\over (x^2 + y^2 + z^2 + B)^{2.5}} dx dy dz $$
Now you do find the B dependenc... | {
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Measurement and uncertainty principle in QM The Wikipedia says on the page for the uncertainty principle:
Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two corresponding bases are Fourier transforms of one another (i.e., position and m... | Can I provide a pedestrian answer? When you measure the position of a quantum, you project or force it to commit to a unique position, and from Fourier Analysis, this commitment requires all possible momenta. Think of focusing a quantum wave to single location (ala Dirac Delta), this would require a wave generator to ... | {
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Why does vibration loosen screws? I am trying to figure out why vibrations (say, from an engine) loosen screws. It seems to me that there is evident symmetry between loosening and tightening a screw. I am wondering what breaks this symmetry.
| Regardless of whether the "local" situation is symmetric or not with respect to loosening and tightening, what you essentially have is a random walk. At any point in time, the screw can stay where it is, get a little looser or get a little tighter. There is, in practical terms, a limit as to how tight the screw can get... | {
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Hamiltonian and the space-time structure I'm reading Arnold's "Mathematical Methods of Classical Mechanics" but I failed to find rigorous development for the allowed forms of Hamiltonian.
Space-time structure dictates the form of Hamiltonian. Indeed, we know how the free particle should move in inertial frame of refere... | From reading the comments to the question, I think that a partial answer could be to show the Hamiltonian character of the relativistic dynamics of a material particle in an electromagnetic field. If this interpretation of the question isn't correct then at least I hope to help in finding out its true interpretation.
... | {
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Has anyone else thought about gravity in this way? Picture yourself standing on a ball that is expanding at such a rate that it makes you stick to the ball.
Everything in the universe is expanding at this same rate.
To escape the earths gravitational pull we would need to jet upward faster than the expansion of the ear... | This view fails to account for free orbiting behavior. You know, the planets around the sun, the moons around the planets, artificial satellites around the Earth.
| {
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Can light exist in $2+1$ or $1+1$ spacetime dimensions? Spacetime of special relativity is frequently illustrated with its spatial part reduced to one or two spatial dimension (with light sector or cone, respectively). Taken literally, is it possible for $2+1$ or $1+1$ (flat) spacetime dimensions to accommodate Maxwell... | No, because the polarization of the electromagnetic field must be perpendicular to the direction of motion of the light, and there aren't enough directions to enforce this condition. So in 1d, a gauge theory becomes nonpropagating, there are no photons, you just get a long range Coulomb force that is constant with dist... | {
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What does symplecticity imply? Symplectic systems are a common object of studies in classical physics and nonlinearity sciences.
At first I assumed it was just another way of saying Hamiltonian, but I also heard it in the context of dissipative systems, so I am no longer confident in my assumption.
My question now is,... | Classical mechanics is the study of second-order systems. The obvious geometric formulation is via semi-sprays, ie second-order vectorfields on the tangent bundle. However, that's not particularly useful as there's no natural way to derive a semi-spray from a function (ie potential).
Lagrangian and Hamiltonian mechanic... | {
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Is it theoretically possible to reach $0$ Kelvin? I'm having a discussion with someone.
I said that it is -even theoretically- impossible to reach $0$ K, because that would imply that all molecules in the substance would stand perfectly still.
He said that this isn't true, because my theory violates energy-time uncerta... | from WP-negative temperature
In physics, certain systems can achieve negative temperature; that is,
their thermodynamic temperature can be expressed as a negative
quantity on the kelvin scale.
A substance with a negative temperature is not colder than absolute
zero, but rather it is hotter than infinite tempera... | {
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Can I study Quantum Computing or Quantum Mechanics with an Engineering background? I am currently studying Electrical & Electronic Engineering. I wish to pursue Quantum Mechanics or Quantum Computing as my research subject. Is it possible for me to do my M.Tech. and then pursue my research subject? What are the prerequ... | Mathematical prerequisites for studying introductory Quantum Mechanics are basics in complex numbers, fourier analysis, differential equations and linear algebra. I think it is also necessary to have a grounding in Classical Mechanics. It would also help if you are comfortable working with probabilities at a basic leve... | {
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Explanation for $E~$ not falling off at $1/r^2$ for infinite line and sheet charges? For an infinite line charge, $E$ falls off with $1/r$; for an infinite sheet of charge it's independent of r! The infinitesimal contributions to $E$ fall off with $1/r^2$, so why doesn't the total $E$ fall off the same way for the infi... | $E$ falls off at $1/r^2$ when there are 3 degrees of freedom for the field lines to spread. When you have an infinite line in three dimensional space, that's equivalent to having the field spread from a point in a cross section of this space, which goes as $1/r$. Similarly, field lines spreading from a flat sheet have ... | {
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Reflectance vs. Thin Metal film Thickness Graph Is there formula that gives reflectance of very thin film of given metal (tens of nanometers) to the visible light of given wavelength(808nm) ? Which properties of metals are needed for the formula ?
I would like to draw a plot of reflectance that is a function of titaniu... | You need to know the index of refrection of the metal AND the substrate. (You didn't mention the substrate, but I assume your 10nm-thick film is not floating in space!!)
This is a three-layer structure: Air, thin film, substrate. You need to know wavelength, the incident angle, the refractive index of all three layers,... | {
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Dual Resonance Model: Fermions I am going through Ramond's 1971 paper Dual Theory for Free Fermions Phys Rev D3 10, 2415 where he first attempts to introduce fermions into the conventional dual resonance model.
I get the 'gist' of what he's doing: he draws an analogy of the bosonic oscillators satisfying the Klein-Gord... | Ramond provides some explanation of his usage of averages in a recollection paper, "Early supersymmetry on the prairie".
| {
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Why does burning magnesium explode when sprinkled with water? Magnesium powder burns extremely well and reaches temperatures of 2500°C. However, attempts to extinguish such a magnesium fire with conventional water (e.g. from a garden hose) only make it worse: the flame grows astronomically and the whole thing gets even... | Magnesium is flammable due to the fact is has hydrogen. When the hydrogen and water combine including the magnesium that is not a good combination and the water spreads causing more issues than there already is.
| {
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What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra o... | Many recommendations have already been made. I would just like to recommend Principles of Quantum Mechanics by Ramamurti Shankar.
I like this book because it starts with all necessary algebra, then goes into operator formulation of classical needed in quantum, and then into quantum.
I would recommend it over Griffiths ... | {
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Must all symmetries have consequences? Must all symmetries have consequences?
We know that transnational invariance, for example, leads to momentum conservation, etc, cf. Noether's Theorem.
Is it possible for a theory or a model to have a symmetry of some kind with no physical consequences at all for that symmetry?
| What do you mean by "consequences"?
Classically, topological numbers might fit that bill. In quantum field theory, that depends upon whether it is sensible to consider superpositions of topological sectors. If there is an S-duality, it might possibly be.
| {
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Electrial Conductivity of Thin Metal Films What is the best way to find specific/electric conductivity which is dependent of very thin film thickness?
| One way to do this is either a two point or four point measurement - the four point will be more accurate if you have significant contact resistance. If not, a simpler two point setup will be sufficient.
One basic setup is to pass a known current between two probes which lie on the outside of two other probes, which yo... | {
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Hawking radiation from point of view of a falling observer This paper tells that Hawking claimed that the falling to a black hole observer will not detect any radiation. But only because the frequency of the Hawking radiation will be of the order $1/R_s$ so that the falling observer will not have a suitable detector.
T... | According to http://edoc.ub.uni-muenchen.de/6024/1/Deeg_Dorothea.pdf, section 5.3.2, the hawking radiation for the free falling observer vanishes at the event horizon, if the observer is at rest at the horizon, but is nonzero above the horizon.
| {
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Understanding Tensors I don't seem to be able to visualize tensors. I am reading The Morgan Kauffman Game Physics Engine Development and he uses tensors to represent aerodynamics but he doesn't explain them so I am not really able to visualize them. Please explain in very simple ways. I just want to understand the basi... | You could probably do a lot worse than taking a look at the video "What's a Tensor?" by Daniel Fleische on YouTube: http://www.youtube.com/watch?v=f5liqUk0ZTw
He gives a nicely visual, but maths-lite answer to that question by using children's blocks, small arrows, a couple of pieces of cardboard and a pointed stick. ... | {
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Bound states in QCD: Why only bound states of 2 or 3 quarks and not more? Why when people/textbooks talk about strong interaction, they talk only about bound states of 2 or 3 quarks to form baryons and mesons?
Does the strong interaction allow bound states of more than 3 quarks?
If so, how is the stability of a bound s... | There is no known reason that you can't have bound states like $qq\bar{q}\bar{q}$ or $qqqq\bar{q}$ or higher number excitations, but none have been observed to date.
You do have to make a color-neutral state, of course.
In the mid-2000 some folks thought that they had of pentaquark states (that the $qqqq\bar{q}$) for a... | {
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Height of the atmosphere - conflicting answers Okay. I have two ways of working out the height of the atmosphere from pressure, and they give different answers. Could someone please explain which one is wrong and why? (assuming the density is constant throughout the atmosphere)
1) $P=h \rho g$, $\frac{P}{\rho g} = h = ... | The first formula is just a first order expansion in $1/r$ of the second formula which is thus the exact one.
The expansion is:
$$h = \frac{P}{\rho g} - \left( \frac{P}{\rho g} \right)^2 \frac{1}{r} + \frac{5}{3} \left( \frac{P}{\rho g} \right)^3 \frac{1}{r^2} + \ldots$$
| {
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"url": "https://physics.stackexchange.com/questions/33627",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to charge an object with electricity I know this is a rather basic question, but how do you charge an object? Not a battery, an object. I'm guessing it involves static electricity, but I'm not sure. Some resources I've been reading talk about charging two objects with opposing voltages, and I am trying to figure ou... | To charge an object, you first need to make sure that it is insulated, so the charge cannot leak away. That is easy if you are charging an insulator, but if you want to charge a metal object you need to mount it on an insulator as metals conduct electricity.
Then you can charge the object. To do this you need to add o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33758",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Is dimensional analysis used outside fluid mechanics and transport phenomena? Most dimensionless numbers (at least the ones easily found) used for dimensional analysis are about fluid dynamics, or transport phenomena, convection and heat transfer - arguably also sort of fluid mechanics.
My understanding of dimensional... | Particle physics uses dimensional analysis quite often, not only to derive and verify equations, but also to understand the physics behind many quantities that are not classical.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How does nature prevent transient toroidal event horizons? How does nature prevent transient toroidal event horizons?.. and does it really need to?
Steps to construct a (transient) toroidal event horizon in a asymptotically flat Minkowski spacetime:
*
*take a circle of radius $R$
*take $N$ equidistant points in the... | The problem with this argument is that in 4d, the horizon of a black hole scales linearly with the mass. If you divide a circle into N segments, and have black holes whose radius is order R/N, where R is the radius of the big circle, their total mass is order R, so that the light rays passing through the center can be ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/33963",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Special Relativity Second Postulate That the speed of light is constant for all inertial frames is the second postulate of special relativity but this does not means that nothing can travel faster than light.
*
*so is it possible the point that nothing can travel faster than light was wrong?
|
So is it possible the point that nothing can travel faster than light was wrong?
No. The "nothing can travel faster than light" restriction logically follows from the two postulates of special relativity.
I'll try to briefly show you how to get to the conclusion.
*
*First you have to convince yourself that the t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34024",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it wrong to talk about wave functions of macroscopic bodies? Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not?
For example in the "Statistical Physics, Part I" by Landau & Lifshitz it is argued that such systems must be described via th... | Those degrees of freedom of a quantum system that are described by a pure partial state must be very well shielded from unwanted interactions with the environment, otherwise they will be decoherered to a mixed state in a moment. This shielding can be done for a few degrees of freedom (like a superconducting current) bu... | {
"language": "en",
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Is there a non-perturbative remormalization? If so, how does it work? Is there a method to renormalize a theory without using perturbative expansions for the divergences? For example, is there a method to get masses and other renormalized quantities without using expansions and counterterms?
O have heard about Lattice ... | The problem with renormalizations in QFT is that, while the conter-terms are known, they cannot be joined with the bare Lagrangian, but are supposed to be treated perturbatively. A quote of Lagrangian from A. Zee (Edition of 2003, page 175):$$L= \left [ \frac{1}{2}[(\partial \phi)^2 -m_P ^2\phi^2]-\frac{\lambda_P}{4!}\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34147",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What criteria distinguishes causality from retrocausality? The brilliant philosopher David Hume remarked that if two events are always found to be correlated to each other with one event happening prior to the other, we call the earlier event the cause and the latter event the effect. However, it has been pointed out t... | I don't see any problem at all with your definition of retrocausality. After all, it's just a definition... So your first question is moot.
The difference between causality and retrocausality is the parameter time. On the quantum scale we do use equations such that time moves backward to describe certain interaction... | {
"language": "en",
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Hawking radiation and black hole entropy Is black hole entropy, computed by means of quantum field theory on curved spacetime, the entropy of matter degrees of freedom i.e. non-gravitational dofs? What is one actually counting?
| No it isn't. This is a mysterious thing in quantum field theory on curved space, as first noted by 't Hooft. If you assume there is a certain amount of entropy in the quantum fields surrounding the black hole, due to their thermal nature, you might estimate that there is a local contribution to the entropy from each ap... | {
"language": "en",
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Shor's algorithm and Bohmian Mechanics Do quantum computer's tell us anything about the foundations of quantum theory? In particular Shor argued in the famous thread by 't Hooft
Why do people categorically dismiss some simple quantum models?
that quantum computation was at odds with 't Hooft's ideas.
Does quantum co... | Let me first mention a recent paper on quantum computing in the Bohm interpretation - http://arxiv.org/abs/1205.2563 , FWIW, though I cannot offer any comments on it right now, sorry.
Another thing. As nightlight noticed in his posts on hidden variables, there is an off-the-shelf mathematical trick (an extension of the... | {
"language": "en",
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How can I estimate the elasto-optic coefficients ($p_{11}$ and $p_{12}$) of a material? I am attempting to estimate the elasto-optic coefficients ($p_{11}$ and $p_{12}$) of $\mathrm{TiO}_2$ and $\mathrm{ZrO}_2$, where $p_{11}$ and $p_{12}$ refer to the elements of a strain-optic tensor for a homogeneous material as giv... | Boyd is a useful reference. See for example:
E.L. Buckland and R.W. Boyd, "Electrostrictive contribution to the intensity-dependent refractive index of optical fibers," Opt. Lett. 21:1117 (1 Aug. 1996)
where the dielectric constant epsilon is the square of the refractive index n.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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The observation of a non-SM resonance at 38 MeV Was reported here. Of course if this is real it is very exciting. It leads me to the question: given that it took so long to find this resonance at a meager 38 MeV, is it possible that all SUSY particles are hiding down in the MeV or KeV range (or lower)?
| User1247 pointed out my mistaken reading of the scale in a previous answer, now deleted.
Fortunately I found a pi0 mass plot in LHCB which shows that there is gamma gamma mass resolution to clear this point about a 38 MeV diphoton resonance.
By now they could provide us with a definitive plot.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why isn't Hawking radiation frozen on the boundary, like in-falling matter? From the perspective of a far-away observer, matter falling into a black hole never crosses the boundary. Why doesn't a basic symmetry argument prove that Hawking radiation is therefore also frozen on the boundary, and therefore not observable?... | Classically, this is true. Something exiting from a classical static black hole would have had to have started before the universe was created. The frozen-on-the-horizon view of a black hole is the view you get under classical general relativity. When you add quantum mechanics, this view is no longer quite valid, and y... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34812",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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does AdS/CFT implies that there is an CFT in physical horizons? so my rough understanding is that the AdS/CFT duality is some sort of isomorphism between an N dimensional gravitational theory and a N-1 dimensional conformal field theory on the boundary.
The boundary of our 3+1D spacetime is the union of the cosmologica... | The answer is no, not from AdS/CFT, but yes from the holographic principle which gives rise to AdS/CFT, and which AdS/CFT confirms. The reason is the "C" in "CFT", the conformal symmetry is the special property of extremal black holes, that their horizons are in curved space. The cosmological horizon is locally flat sp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/34869",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Bernoulli equation from energy conservation I have derived the energy conservation equation:
\begin{equation}
\frac{\partial}{\partial t} \left [ \frac{1}{2} \rho v^2 + \varepsilon + \rho \phi \right ] + \frac{\partial}{\partial x_j} \left [ \frac{1}{2} \rho v^2 v_j + \rho h v_j + \rho \phi v_j \right ]=0
\end{equation... |
I was trying to derive the Bernoulli equation from the above equation
for time independent flow
If you are studying something time independent then you just let $\frac{\partial}{\partial t}$ to be zero:
$$
\frac{\partial}{\partial x_j} \left [ \frac{1}{2} \rho v^2 v_j + \rho h v_j + \rho \phi v_j \right ]=0
$$
Next... | {
"language": "en",
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Why is current not 0 in a regular resistor - battery circuit immediately after you closed a circuit? In regular open circuits with either a capacitor or inductor element, (when capacitor is uncharged) with a battery, when a switch is closed to complete the circuit the current is said to be 0 because current doesn't jum... | This question is working within the realm of 'circuit theory', which is an idealization useful for introductory teaching of electromagnetism. It is really a simplification of electrodynamic field theory, just a special case making useful assumptions. A lot of conceptual problems in circuit based questions come from f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35042",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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How to choose a suitable topic for PhD in Physics? After completion of graduate courses when a student is supposed to start real research in Physics, (to be more specific, suppose in high energy physics), how does one select the problem to work on? The area is vast, mature and lots of problems remain to be solved. This... | This is what thesis advisors are for.
Indeed it is difficult for a student to identify a problem or topic area which is both interesting enough to potentially get you a job later on, but also has not yet been overgrazed by other physicists. That is why identifying a good thesis advisor, and convincing him to take you ... | {
"language": "en",
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Black-holes are in which state of matter? Wikipedia says,
A black hole grows by absorbing everything nearby, during its life-cycle. By absorbing other stars, objects, and by merging with other black-holes, they could form supermassive Black-holes
*
*When two black-holes come to merge, don't they rotate with an in... | the matter inside a black hole would be a non Newtonian liquid of subatomic particles, the mass being too heavy for an atom to keep itself together.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Does water need to pumped up from deep ocean? OTEC (Ocean Thermal Energy Conversion) utilizes the temperature gradient between cold deep ocean water, and warmer water to do work. I understand the pressure in the depths may be as high as a couple of orders greater than surface atmospheric pressure.
I also remember, vag... | Typically, yes, the water does need to be pumped up.
Because if it released energy by rising, it would already have risen to the surface.
OTEC depends on a high-enough temperature difference between the lower-depth water intake and the higher-depth one, for that temperature difference to do enough work to provide some ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35209",
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"source": "stackexchange",
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Calculating equation of motion from action Suppose my action integral is $$S=\int d^4x(\nabla \times A)^2$$ and $\delta S$ gives $$\delta S =\int d^4x [2(\nabla \times A).(\nabla \times \delta A)]$$
I would like to calculate the coefficient of $\delta A$ from this action integral. But I am stuck. How can I separate the... | Let's do what Heidar says and write it with indices, and identify the Lagrangian.
$$
L=\frac{1}{2}(\vec{\nabla}\times \vec{A})^2 = \frac{1}{2}\epsilon_{ijk}\partial_j A_k \epsilon_{ilm}\partial_l A_m
$$
where, if you haven't heard of it yet, you pretend there is a summation symbol for each repeated index. Then since ... | {
"language": "en",
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Gravitational inverse-square law I was looking at the gravitational inverse-square law:
$$
F_G = G \frac{Mm}{r^2}
$$
This law comes from some experimental data? Why it is an exact inverse-square law? Could it be
$$
F_G = G \frac{Mm}{r^{2.00000000000000001}}
$$
or there is a mathematical method to find exactly this law?... | It is exact in the Newtonian limit, i.e., for speeds slow compared to speed of light, away from strong gravitational fields or horizons, and for big enough objects that quantum effects can be ignored. The 1/r^2 comes from solving Poisson's equation $\nabla^2\phi=4\pi G \rho$. If there would be corrections to this law i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/35457",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Where does the heat flow in the Earth's crust switch from primarily solar to geothermal? Ok, maybe more of a geology question than physics, but maybe somebody has been involved in modeling these heat flows?
Essentially I'm asking if we know what sort of depth the heat source becomes primarily from below rather than fro... | To clarify your question a bit, the average heat flow is towards the surface (if you average over a long enough period) so I guess you're asking to what depth does the heat flow, i.e. temperature, vary with the time of day or season of the year. In that case Google for something like "diurnal variation temperature dept... | {
"language": "en",
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The vacuum light speed: Is it really constant, i.e., independent of location in space-time? I am by no means an expert in this field, however something puzzles me about the speed of light and the relativity of time and space (space-time).
Is is universally acknowledged that the speed of light (299,792,458 m/s) is the u... | As pointed out by Michael Duff here, the speed of light in vacuum is a mere conversion constant. So, just as Michael Duff puts it in his article, you can just as well ask if the number of liters to the gallon is independent of location in space-time.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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A problem of missing energy when charging a second capacitor A capacitor is charged. It is then connected to an identical uncharged capacitor using superconducting wires. Each capacitor has 1/2 the charge as the original, so 1/4 the energy - so we only have 1/2 the energy we started with. What happened?
my first though... | Short answer: this is a textbook example of the limitations of ideal circuit theory. There seems to be a paradox until the underlying premises are examined closely.
The fact is that, if we assume ideal capacitors and ideal superconductors, i.e., ideal short circuits, there appears to be unexplained missing energy.
Wh... | {
"language": "en",
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Do I have the meaning of the property temperature correct? OKay my book just starts out talking about the vague definition we have for temperature and we ended up with the Zeroth law of Thermodynamics which states:
Two systems are in thermal equilibrium if and only if they have the same
temperature.
So does that me... | That would be definition of temperature in thermodynamic framework. However, as Ron has remarked, it can be understood better in framework of statistical mechanics which in some sense is a more fundamental science than thermodynamics.
For a non-isolated system (i.e. a system which is allowed to exchange energy with i... | {
"language": "en",
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Why don't rockets tip over when they launch? Rockets separate from the launch pad and supporting structures very early in flight. It seems like they should tip over once that happens.
*
*Why don't they tip over ?
*Is it due to a well designed center of gravity or do they somehow achieve aerodynamic stabilization ... | More fundamental than the gimballed thrust system or verniers is the relationship between the "center of gravity" and "center of pressure" on a rocket (or any kind of projectile (e.g., bullet).
For the rocket to fly nose-forward and not flip around, the center of gravity must be ahead of the center of pressure. In bui... | {
"language": "en",
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"source": "stackexchange",
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Complete set of observables in classical mechanics I'm reading "Symplectic geometry and geometric quantization" by Matthias Blau and he introduces a complete set of observables for the classical case:
The functions $q^k$ and $p_l$ form a complete set of observables in the sense that any function which Poisson commute... | Any observable $H$ in classical mechanics defines a flow of states by regarding it as a Hamiltonian. This flow acts on observables $f$ by $df/dt = \{H,f\}$ (this is Hamilton's equation). The idea of a complete set of observables is that it is a set for which any observable with constant flow for all members of the set ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Driving a solution of optical isomer molecules with the resonant frequency What happens when we drive a solution of optical isomer molecules (enantiomers) with a microwave radiation in resonance with the tunneling frequency of the molecules (the frequency of the transition between the eigenstates of the Hamiltonian)? ... | Your intuition is right, as far as your solution of optically active (chiral) molecules can be assimilated to an ensemble of harmonically driven two-level systems. For the two level system (left- and right handed molecules being the respective states) which starts out with only left handed molecules, the radiation driv... | {
"language": "en",
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Group Velocity and Phase Velocity of Matter Wave? In quantum mechanics, what is the difference between group velocity and phase velocity of matter wave? How can it also be that phase velocity of matter wave always exceeds the speed of light?
| Actually matter wave describes the probability of finding a particle at any time at any point of space. It is not exactly a sine wave, it is an wave packet. So it contains lots of component of single frequency wave. These the velocity of the single component is called phase velocity. And the overall velocity of composi... | {
"language": "en",
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Zero entropy change If you put a object in contact with a heat reservoir that is infinitesimally higher in temperature than the object and allow equilibrium to be reached the entropy change is zero right?
| When talking about infinitesimals, you need to specify how close to zero it is. The entropy loss is $\delta Q\over T$ and the gain is $\delta Q \over T-\delta T$, so the net gain is $\delta Q \delta T \over T^2$ to leading infinitesimal order, and it vanishes linearly in $\delta T$ and $\delta Q$ both.
For iterated inf... | {
"language": "en",
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Waves travelling with water flow Suppose I use a tool to create a circular wave in the river. If there are two fish swimming 1m from the source (2m from one another), they will both feel the wave at the same time.
What will happen if the river flows from one fish to the other? How will it affect the waves?
| Assuming the river is deep enough or equivalently the waves are small enough compared with the depth.
Relatively to the bank the wave will remain its circular form, however as a whole it will be moving with the river. So, assuming the fishes swim against the current to keep stationary relatively to the bank, the upper ... | {
"language": "en",
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What are distinguishable and indistinguishable particles in statistical mechanics? What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann distribution is used for solving distinguishab... | Assume you have two particle A and B in states 1 and 2. If the two particle are distinguishable, then by exchanging the particles A and B, you will obtain a new state that will have the same properties as the old state i.e. you have degeneracy and you have to count both states when calculating the entropy for example. ... | {
"language": "en",
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Quantum Mechanics- Antenna emitting electromagnetic radiation Radio signals are being transmitted in a frequency of $ 8.4 \times 10^9 \text{s}^{-1} $ and being received by an antenna that is capable of receiving power of $ 4 \times 10^{-21} \text{Watt} $ ($ 1 \, \text{Watt} = 1 \, \text{J s}^{-1} $ ) .
Estimate that n... | It doesn't matter how strong the transmitting station is. The receiving antenna is only absorbing a tiny amount of power. The idea of the calculation is to show that even in a "classical" situation like a receiving antenna, at some level the "granular" nature of electromagnetic energy makes itself apparent.
At least t... | {
"language": "en",
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2D Car Physics including Throttle For a simulation for testing on automatic cruise control, I came across the equation:
$$
v_{n+1} = (1 - k_1 / m) v_n + (1 - k_b) \begin{pmatrix}
T_n \\
θ_n \\
\end{pmatrix}
$$
where:
*
*$T$ = throttle position
*$k_1$ = viscous friction
*$k_b = k_2 / m$
*$k_2 = m g \sin(θ)$
*$v... | The "viscous friction" component is a loss of speed that is proportional to velocity. This proportionality is the same that occurs through viscous losses such as viscous dampers or the losses associated with bearings.
$$k_b= \frac{m\,g\,sin(\theta)}{m}$$
This corresponds to the forward or rearward force on the car due ... | {
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If the earth would stop spinning, what would happen? What would happen if the earth would stop spinning? How much heavier would we be? I mean absolutely stop spinning. How much does the centrifugal force affect us?
If you give technical answers (please do), please explain them in laymen's terms, thanks.
Edit: I am aski... | The centripetal force we feel on the surface would immediately disappear, causing us to feel lighter. The centripetal force is equal to $E=mv^2/r$ and the acceleration is given by $a=v^2/r$. This results in a reduction of the acceleration towards the earth’s centre, also known as gravity. Therefore we would feel lighte... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/37952",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Matrix mechanics for those with wave mechanics background Just curious:
Is there any book or resource that teaches matrix mechanics (quantum mechanics) only without wave mechanics stuff - meaning that the book assumes wave mechanics background.
|
This answer contains some additional resources that may be useful. Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. This answer is left here to contain additional links that do not yet have commentary.
*
... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is Heisenberg's matrix mechanics or Schrödinger's wave mechanics more preferred? Which quantum mechanics formulation is popular: Schrödinger's wave mechanics or Heisenberg's matrix mechanics? I find this extremely confusing: Some post-quantum mechanics textbooks seem to prefer wave mechanics version, while quantum mech... | Ever since Dirac came up with transformation mechanics (kets and bras), and showed both matrix and wave mechanics are special cases of it, physicists have worked with kets and bras. With von Neumann later, this was reinterpreted as Hilbert spaces.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38070",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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Interpretation of field operator Consider a real scalar field operator $\varphi$. It can be written in terms of creation and anihilation operators as
$$\varphi(\textbf{x})=\int \tilde{dk}[ a(k)e^{i\textbf{kx}}+a(k)^{\dagger}e^{-i\textbf{kx}}]$$
where $\tilde{dk}$ is a Lorenz-invariant measure.
If $\varphi$ is interpre... | As the formula clearly shows, $\phi(x)$ cannot be interpreted as a pure creation operator of any type. It is a combination of creation and annihilation operators. Creation operators are those called $a(k)^\dagger$ and annihilation operators are called $a(k)$.
So yes, if $\phi(x)$ acts on a generic state with a well-def... | {
"language": "en",
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Why is the solar noon time different every day? If you check the local time for solar noon is different every day. Why is it so? Is it because Earth doesn't make a complete rotation in exactly 24 hours?
The following is an example of the solar noon differences (also sunrise and sunset), computed by the Python Astral mo... | A solar noon is defined when the Sun is at the zenith (directly above). Since the Earth revolves round the Sun, the point that is directly above would have changed because Earth is in a different point from the previous noon.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38270",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 5,
"answer_id": 3
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Magnitude of New Comet C/2012 S1 (ISON) A new comet (magnitude 18.8) has been discovered beyond the orbit of Jupiter.
Comet ISON will get within 0.012 AU of the Sun by the end of November 2013 and ~0.4 AU from of Earth early in January 2014. It may reach very welcome negative magnitudes at the end of November 2013. F... | The magnitude of any object which doesn't have its own light is dependent on it's albedo i.e. $$\frac{Light \ reflected}{Light \ Received}$$
So, diffrent types of ice have different albedos, so different magnitude. Though, I can't find a relation between ratio of nucleus dust and ice to the comet's magnitude, the albed... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38342",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Are all static solutions of Einstein's equations spherically symmetric? Is it true that all static solutions in GR are also spherically symmetric? Is there a proof of this?
Similarly, are all stationary solutions axisymmetric?
| The answer to your first question is no. In fact, you can find static, stationary solutions to GR corresponding to cosmic strings and domain walls, or even more exotic solutions, like the c-metric.
Your statement about axisymmetry is harder, mainly because I don't know of many non-axisymmetric solutions, period.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38394",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is the Lagrangian "math" or "science"? I've seen in class that we can get from Lagrangian to derive equations of motion (I know its used elsewhere in physics, but I haven't seen it yet). It's not clear to me whether the Lagrangian itself follows from the equations of motion, or whether it represents a fundamentally dif... | It is a mathematical observation that follows from Newton's laws. See for example Lanczos
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38445",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 1
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Determining the center of mass of a cone I'm having some trouble with a simple classical mechanics problem, where I need to calculate the center of mass of a cone whose base radius is $a$ and height $h$..!
I know the required equation. But, I think that I may be making a mistake either with my integral bounds or that $... | I see the problem you have here, change the $r^2\, \mathrm{d}r\, \mathrm{d}\phi\, \mathrm{d}z$ there to $r \, \mathrm{d}r\, \mathrm{d}\phi\, \mathrm{d}z$, then you should get the correct answer
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38624",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
} |
Width of Gaussian Beam and Refractive Index I know that in free space, the width of a Gaussian beam can be written as $W=W_0\sqrt{1+(\frac{z}{z_0})^{2}}$. However, I was wondering if it was possible to express this width as a function of refractive index instead (since I don't believe a Gaussian beam originating in say... | Yes, and the formula you already have still works. Take z to be the optical path length: refractive index n times physical distance. A Gaussian beam in glass diverges in exactly the same way as in free space, only 'squeezed' in the z direction by a factor of n.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38749",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
New physics at high energies, cosmic rays, particle-detectors in space New physics is expected at high energies and cosmic rays have high energies, so have there been or are there any plans to put particle detectors in space to study cosmic rays for new physics ?
| It is difficult to detect very high energy cosmic rays in space. The reason being that to detect them one needs to interact with them. And an interaction is determined by how much material you put in its way. After you interact, you get massive showers of very high energy particles so you need lots of detectors to dete... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38856",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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"answer_id": 1
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Extending the idea of superdense coding I was reading through the superdense coding protocol, that lets A convey two classical bits to B by sending one qubit (assuming B sends A a qubit beforehand). So B creates a 2-qubit state and sends the first qubit to A. A performs a transformation on this qubit and sends it back.... | The problem is that you can't create $2^{n}$ orthogonal states on $n$ qubits using only operations on 1 qubit. The operations you can perform on the single qubit are $I,X,Z,XZ$ (or something of the same form). If you use those four you obtain four orthogonal states on $n$ qubits but any other operations will give state... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38922",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
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Galilean relativity in projectile motion Consider a reference frame $S^'$ moving in the initial direction of motion of a projectile launched at time, $t=0$. In the frame $S$ the projectile motion is:
$$x=u(cos\theta)t$$
$$y=u(sin\theta)t-\frac{g}{2}t^2$$
I know that that at $y_{max}$, $\frac{dy}{dt}=0$ so using this I ... | In the $S'$ frame, your variables are $x' = x - t\cdot u \cos\theta $ and $y' = y - t\cdot u \sin\theta$. If you do the change of variable, you get that the motion now is described by
$$x' = 0$$
$$y' = -\frac{g}{2}t^2$$
So in your new frame of reference you have vertical free fall from rest.
This is not very helpful in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/38983",
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"source": "stackexchange",
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How can the Air friction force be applied to an object? Suppose we have an object and we throw it straight upward in the air. How do we apply the Air friction force to this object while moving upwards and after that downwards? Sorry if it's easy because I'm still a novice!
| You can make a good estimate of the force of air resistance from
Where p is the density of air, v is the speed, A is the cross section area and Cd is a factor depending on the shape (ie how streamlined) of the object - you can look this up for simple shapes.
The tricky bit of the equation is that the drag depends on s... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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quantum entanglement at microwave frequencies Entanglement of optical photons using non-linear crystals has been around for a long time. Macroscopic entanglement using diamonds recently reported in the literature and receiving considerable attention. Quantum mechanics in biology has been the subject of fascinating re... | You can certainly entangle microwave photons with other quantum objects: http://arxiv.org/abs/1209.0441
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39103",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 1
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Schrödinger and thermodynamics I heard that Schrödinger pointed out that (classical/statistical) thermodynamics is impaired by logical inconsistencies and conceptual ambiguities.
I am not sure why he said this and what he is talking about. Can anyone point some direction to study what he said?
| You asked, about logical inconsistencies and logical ambiguities in classical thermodynamics and classical statistical mechanics. As far as classical thermodynamics is concerned, there are no inconsistencies or ambiguities. Classical thermodynamics is based on several axioms (known as laws), and a bunch of definition... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39168",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Definition of CFT A standard QFT cannot be defined as a set of Poincare-invariant correlation functions because this does not take into account the possibility of non-perturbative effects (e.g. instantons)
Can we define a CFT as a set of conformally invariant correlation functions?
What is the correct definition of a C... | The exact correlation functions as defined by a lattice simulation do take into account all nonperturbative effects, they contain all the physics. It is only the expansion of the correlation functions that doesn't take instantons into account. So yes, you can define a CFT by its correlation functions.
This is true for ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39377",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is the number of rays projected by a source of light finite? Take a source of light which gives out infinite number of rays, each ray with finite number of photons and each photon with a finite amount of energy,
Then, Aren't the number of photons become infinite and hence the energy in the beam of light becomes infinit... | I've had the same question but let's look at it differently.
As I a one one dimensional line:
Let's say we have an illuminated line with a finite length.
We know that the photon is a particle hence it has diemensions.
Now let's suppose this lign is illuminated by photons. So the photons are arranged to cover the whole ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39416",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Einstein's mass-energy relation Suppose we have 1 kg of wood and 1 kg of uranium and if we need to find out how much energy would each of the substance give, we'd have to use Einstein's mass-energy relation as follows:
In the case of wood, $E_{wood} = 1 × (3×10^8)^2 = 9 × 10^{16} J$
In case of Uranium, $E_{uranium} = 1... | The Einstein's mass-energy relation, $E = mc^2$, gives the total energy content of the system. But this is not the energy we get from the object. When you annihilate an electron with a positron, both particles vanish so that the released energy is equal to the energy of the two particles according to Einstein's formula... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39475",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Something I don't understand in Quantum Mechanics I've just started on QM and I'm puzzled with a lot of new ideas in it.
1.On a recent lecture I've attended, there is an equation says:
$\langle q'|\sum q|q\rangle \langle q|q' \rangle =\sum q \delta(q,q')$
I don't understand why $\langle q'|q\rangle \langle q|q' \rangle... | *
*The equation is true, if $|q\rangle$,$|q'\rangle$ are chosen from an orthonormal set of vectors, such as an eigenbasis of an operator. Then, by definition, $\langle q|q' \rangle = \delta_{q,q'}$
*$| q \rangle$ just denotes some vector labeled $q$ in some Hilbert space. The dimension equals the number of dis... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39540",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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} |
Why do reversible processes not increase the entropy of the universe infinitesimally? The book Commonly Asked Questions in Thermodynamics states:
When we refer to the passage of the system through a sequence of internal equilibrium states without the establishment of equilibrium with the surroundings this is referred ... | By definition a reversible process in an isolated system cannot increase entropy. If entropy is increased during a process in an isolated system then the process is irreversible, by definition.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39589",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 5,
"answer_id": 4
} |
How does one derive the Lamb shift for the Hydrogen atom? I've been perusing my copies of Srednicki and Peskin & Schroeder, and I can't seem to find an explanation of how one derives the Lamb shift that I can follow.
How does one derive the Lamb shift? What order in perturbation theory do you have to go up to? Does one... | A derivation is here:
http://en.wikipedia.org/wiki/Lamb_shift#Derivation
or in Landau-Lifshitz. Bethe's original derivation is found e.g. in Matt Schwartz's Harvard lecture here
http://isites.harvard.edu/fs/docs/icb.topic792163.files/20-LambShift.pdf
The leading contribution to the Lamb shift is the one-loop level ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What are some of the best books on complex systems and emergence? I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory technical books.
| I like the book Energy Landscapes by David Wales. It deals with various classes of complex systems (clusters, glasses, proteins) in the context of chemistry.
I want to add - emergence is fraught with flaky ideas; a lot of appeals to ignorance are rooted from the idea of irreducible complexity. So because we can't, say,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/39712",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 5,
"answer_id": 1
} |
Time dependent Lagrangian Suppose I have a mechanical system with $\ell + m$ degrees of freedom and an associated Lagrangian:
$$L(\alpha, \beta, \dot{\alpha}, \dot{\beta}, t),$$
where $\alpha \in \mathbb{R}^{\ell}$ and $\beta \in \mathbb{R}^{m}$. Now suppose I have a known $\mathbb{R}^{\ell}$-valued function $f(t)$ and... | Let us reformulate OP's question(v2) as follows:
If we have a Lagrangian $L=L(q^1,\ldots, q^N, \dot{q}^1,\ldots, \dot{q}^N,t)$, and if we eliminate some of the $q^i$ variables from the Lagrangian [by using some given fixed curves $q^i=f^i(t)$], can we still derive the correct Lagrangian equations of motion (LEOM) for... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/40759",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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"answer_id": 0
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Physical meaning of some operators formed by $|Q\rangle \langle Q|$ In Dirac's formulation of quantum mechanics,
Suppose that $q$ represents position observable.
About $|q\rangle \langle q|$: what does this operator mean? I do get that it results in an operator, but unsure of what physical meaning it has. The same with... | It's a projection operator. It measures how much $|\psi \rangle$ a system is.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/40825",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
Distribution of charge on a hollow metal sphere
A hollow metal sphere is electrically neutral (no excess
charge). A small amount of negative charge is suddenly
placed at one point P on this metal sphere. If we check on
this excess negative charge a few seconds later we will find
one of the following possibilit... | Yeah. The right answer would be (B) the negative charge that started on point P will be distributed evenly throughout the surface of the sphere since (as most of the commentators here have mentioned) that point P has too much negative charges in it, so the negatively charged atoms will repel each other more vigoro... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/40993",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 1
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What are the reasons for leaving the dissipative energy term out of the Hamiltonian when writing the Lyapunov function? I have a problem with one of my study questions for an oral exam:
The Hamiltonian of a nonlinear mechanical system, i.e. the sum of the kinetic and potential energies, is often used as a Lyapunov fun... | 1) In the presence of friction, the Lagrange equation gets modified
$$\tag{1} \frac{d}{dt} \left(\frac{\partial L}{\partial \dot{x}}\right)-\frac{\partial L}{\partial x}~=~ -\frac{\partial{\cal F} }{\partial \dot{x}}$$
by the Rayleigh dissipation function
$$\tag{2} {\cal F}~: =~ \frac{1}{2} c\dot{x}^2 ~\geq ~0 . $$
He... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41034",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 0
} |
Calibrating an electronic temperature sensor based on power consumption I'm working with an electronic temperature logger that is being affected by heat generated internally.
How does one come up with a calibration equation to calculate a more accurate reading of ambient temperature based on what the temperature sensor... | Typically you would attempt to measure rather than calculate the effect.
Perhaps by having a second, calibrated device with a long probe that provides an independent measurement of the temperature. You do this in situ if possible or in some reasonable test stand (which might be as simple as disposable cooler filled wit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41140",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
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What is the difference between a spinor and a vector or a tensor? Why do we call a 1/2 spin particle satisfying the Dirac equation a spinor, and not a vector or a tensor?
| Actually, Dirac equation is some what a "square root" of Klein-Gordon equation, so intuitively it can't represent a Vector or Tensor, as "symbolically" spinor corresponds to a square root of "differential", so the transformation rules had to differ from Tensors (actually one is in some vague sense taking "square root" ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41211",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
"answer_count": 4,
"answer_id": 0
} |
Direction of Potential Gradient & Electric field Potential gradient is the negative of the electric field:
$dV=-\vec{E}\cdot \operatorname{d}\!\vec{r}$
Does the negative sign mean that the direction of potential gradient $\operatorname{d}\!V\!/\!\operatorname{d}\!\vec{r}$ is opposite to that of the electric field $\v... | One thing necessary about Potential. It's simply the work done in moving an electric charge against the electrical force. Thus, The negative sign actually says that the work done is against the electric force (either attraction or repulsion). Or in other words, electric potential decreases in the direction of electric ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41283",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Will the siphoning effect help a system pump water upwards if the water's entry and exit points are at the same height? I am looking to pump water from a pool up to a roof for solar heating (black plastic tubing) and then back into the pool with the original source water. Does the gravitational force of the water flowi... | Short answer:
If you have a U-shaped tube full of water with both ends in the pool, and you lift the center of the tube up to roof height, you can pump water through that tube without regard to how high the top is.
The only resistance will be the resistance of water flowing through the tube (and solar collector).
The h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41331",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
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why sometimes touching old flickering tube lights starts them properly In my old house there are two old tube lights. Some times they don't start properly, (specially at evening time, may be it is because of low voltage), they starts flickering i.e. on and off continuously. And when my elder brother touches them, mostl... | I'll throw this into the mix. If I plug in one end of my guitar cable to my amp, turn the amp on, bring up the volume a little, and touch only the center contact on the other end of the cable, I get a loud 60 Hertz buzz from my amp. I believe this is because my body is acting as an antenna - picking up some radiation f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41503",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
} |
Why doesn't my particle simulation end in a flat disc? I've made a 3d particle simulator where particles are attracted to each other by the inverse of the square radius. The purpose of my experiment is to see if this alone would create a flat disk (like some galaxies) since the inverse of the radius is the same as grav... | You get a disk when the particles lose energy (often by radiating it away) but keep their angular momentum.
Galaxies are made of stars, but the stars are born from clouds of gas. The gas has many ways to radiate energy away, which can cause it to settle into a disk. The stars may then be formed in the disk structure.
N... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/41583",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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"answer_id": 0
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