Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Could the acceleration of universe expansion be caused by gravity itself? Dark energy is suggested to be a repulsive force in the universe causing an accelerated expansion. If the amount of mass outside our observable universe is greater than inside (higher mass density), would it not cause an accelerated expansion fro... | I have been working on a similar theory for years, since the type 1a supernova project showed the unexpected acceleration. I tried to publish several times, unsuccessfully. My idea is; yes, it is gravity which causes the expansion because a static universe would be isotropic and homogeneous but a dynamic universe is io... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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How does one calculate the force applied on an object by a magnetic field? I've tried very hard to find an answer to this question, and every path leads me to an abstract discussion of fundamental forces. Therefore, I will propose two very specific scenarios and see if they yield the result that I am looking for.
Scena... | If you have a steel ball bearing with high permeability, then the magnetic potential energy of this configuration will be proportional to the square of the B-field at the position of the ball bearing. For a simple dipole magnetic field on-axis, this will be proportional to $r^{-6}$, where $r$ is the distance from the c... | {
"language": "en",
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Mathematical Universe Hypothesis What is the current "consensus" on Max Tegmark's Mathematical Universe Hypothesis (MUH) which claims every concievable mathematical structure exists, including infinite different Universes etc.
I realize it's more metaphysics than physics and that it is not falsifiable, yet a lot of peo... | Tegmark, Hut and Alford wrote an article at http://arxiv.org/abs/physics/0510188 . Penrose had the idea of a causal loop between matter, mind and math. The authors don't like causal loops and tried to cut them at various points. Tegmark is the Platonist who believes math is fundamental and the ground of being.
Is that... | {
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Why is the energy density of the electric field produced by two unlike charges positive, even though their potential energy is negative? Consider two stationary charges, one positive the other negative. Their potential energy is clearly negative. So you would expect that the energy density of the associated electric ... | Here, you should refer to the definition of energy density, the electric field energy density is defined as following:
$u = \frac{1}{2}\epsilon |\vec{E}|^2$
where $\epsilon$ is the permittivity of media.
therefore this energy density should always be positive.
The derivation of the electric energy density can be referr... | {
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"url": "https://physics.stackexchange.com/questions/15826",
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What is a black hole? Is there a definition of a black hole in a generic spacetime? In some books, for example Wald's, black holes are defined for asymptotically flat spacetime with strong asymptotic predictability, although the definition makes sense without the second condition. Is there a notion of a black hole in g... | What the definition needs to capture is that a black hole is not (1) a naked singularity, or (2) a big bang (or big crunch) singularity. We also want the definition to be convenient to work with so that, for example, it's possible to prove no-hair theorems.
Since we want to exclude naked singularities, it's natural tha... | {
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Could a ship equipped with Alcubierre drive theoretically escape from a black hole? Could a ship equipped with Alcubierre drive theoretically escape from a black hole?
Also, could it reach parts of the universe that are receding faster than the speed of light from us?
| The drive works by warping normal space, creating a bubble that kind of surfs through space time. I don't know what would determine the speed such a ship could achieve so not sure if a natural law would limit the ability to travel beyond visible space. Black holes exist because their extreme mass has warped space bey... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/15960",
"timestamp": "2023-03-29T00:00:00",
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Problem with an electricity / thermodynamics assignment I've been trying to figure this one out for a while on my own, so I'd like to ask for your help if you could offer some.
The task states:
A heater made out of a wire with a diameter $R = 0.2\text{ mm}$, length $4\pi\text{ m}$ and electrical resistivity of $0.5\ti... | Find the resistance of the particular wire. Then calculate the power it uses. Assume this power is dissipated as heat. Find how much energy is converted to thermal energy by heat in 10 minutes. Use the equation Q = mc ΔT to find the mass of the water.
| {
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Momentum and indirect bandgap When an electron is excited from valence band to conduction band, it has to have a finite momentum in the case of indirect bandgap. Does that mean that the electron cannot be created at rest ? does it have a non zero "speed" ?
| It means that to fulfill momentum conservation law, the momentum should be taken from somewhere: from phonons, impurities, etc.
The speed is a derivative of the energy (remember Hamilton's equations), thus the speed is zero at the minimum of the energy, wherever this point is located in k space
| {
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Is the cooling rate of a (very) cold object, sitting next to an AC higher or lower? In more detail:
If i have two soda cans, both are cooled to exactly 4 degrees celsius,
And i put one in a 25 degrees room, and the other next to an AC vent set to 16 degrees.
After three minutes, which one should be colder than the othe... | The answer for the question as posed is easy:
It could be either
This applies for the initial rate of heating. Of course, over time, the story is quite different. The temperature of the one in front of the AC could initially become higher than the one in the static room air. However, given sufficient time, of course... | {
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Which subjects in physics should I choose if I want to help tackling today's energy and environment related problems? I was wondering what subjects a freshman in mathematics ought to choose in the future if s/he wanted to help working on energy and environment-related issues we are currently facing, and will very likel... | Can I recommend hot fusion, instead of cold fusion?
It works in the sun and other stars and may yet work here on earth.
If it works well, it will have many advantages.
A standard general physics sequence will be a good start for this.
Pay particular attention to electromagnetism.
Eventually you would specialize in nucl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16119",
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Does conservation of momentum really imply Newton's third law? I often heard that conservation of momentum is nothing else than Newton's third law.
Ok, If you have only two interacting particles in the universe, this seems to be quite obvious.
However if you have an isolated system of $n$ ($n > 2$) interacting partic... | No, but Newton's third law of motion implies the conservation of momentum. In other words, Newton's third law is a special case of the more general law, which is the conservation of momentum.
| {
"language": "en",
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Is Thirring model a particular case of Gross model? In the Wikipedia entry for the Gross–Neveu model, it is said that
If one takes $N=1$ (which permits only one quartic interaction) and makes no attempt to analytically continue the dimension, the model reduces to the massive Thirring model (which is completely integra... | Yes, because the grassman expansion of a quartic fermi interaction can only be $\psi_1\psi_2\bar{\psi}_1\bar{\psi}_2$ in 2d, because there are only four grassman fields, so all other quartics are zero.
| {
"language": "en",
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Are specific heat and thermal conductivity related? Are there any logical relationship between specific heat capacity and thermal conductivity ?
I was wondering about this when I was reading an article on whether to choose cast iron or aluminium vessels for kitchen.
Aluminium has more thermal conductivity and specific ... | TLDR - heat capacity comes from how phonons behave in the harmonic approximation, while thermal conductivity comes from how anharmonic phonons are.
In more detail, thermal conductivity comes primarily from two channels:
(1) Conduction electrons carrying heat
(2) Anharmonicity of the crystal lattice (i.e. phonons scatte... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16255",
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Chance of "macro tunneling"? We know that subatomic particles can and do tunnel through barriers, so it is theoretically "possible" somewhat that a grain of sand could tunnel through a paper, but Id like to get some perspective on it.
Can anybody give any sort of estimate of how long one would have to wait to expect to... | That is hard even to estimate correctly. For a grain of sand to tunnel through a sheet of paper the probability is so small not because of the tunnel barrier but because it would require the whole grain to move in one direction spontaneously.
Starting with the Transmission probability (from Wikipedia)
$$
T = \frac{e^... | {
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How do we perceive hotness or coldness of an object? Some objects, especially metallic ones, feel cold on touching and others like wood, etc. feel warm on touching. Both are exposed to same environment and are in their stable state, so some kind of equilibrium must be being reached. What is this equilibrium?
And how do... | I don't know the actual biological process, but I know that our body detects heat transfer, not temperature. That's why an object with a higher heat transfer coefficient (such as metallic objects) appear colder than wood at the same temperature, for example.
| {
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Why are infinitesimal rotations commutative, whereas finite rotations are not? Infinitesimal rotations commute and every finite rotation is the composition of infinitesimal rotations which should logically mean they also commute; but they don't. Why?
| Infinitesimal rotations don't commute exactly if you're accurate enough. An infinitesimal rotation may be written as
$$ \exp( i a A ) $$
where $a$ is an infinitesimal "angle" and $A$ is a combination of generators. Such an object doesn't commute with the analogous object $\exp(ibB)$ in general. Instead,
$$ \exp(iaA) \... | {
"language": "en",
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Numeric method to calculate the charge distribution on a conducting surface? If I have an arbitrary (closed?) conducting surface and a nearby charge density, is there a simple numeric way of computing the induced charge distribution on the surface?
| There is no simple way. The "standard" way is to solve Poisson equation with proper boundary conditions (constant $\varphi$ at the surface). Out of potential distribution it is easy to extract charge distribution.
For simple shapes (infinite plane, sphere, etc) it is possible to solve the problem analytically. For arb... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16430",
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Is there any anti-gravity material? I want to know if there is any anti-gravity material. I am thinking of making flying vehicles which are made up of anti-gravity material so that they will not experience any gravity on them and can easily take off and be more fuel efficient. Is there any such thing? Or any workaround... | When you say "anti-gravity material", the closest thing I can think of is the hypothetical concept of negative mass:
In theoretical physics, negative mass is a hypothetical concept of
matter whose mass is of opposite sign to the mass of the normal
matter. Such matter would violate one or more energy conditions and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16474",
"timestamp": "2023-03-29T00:00:00",
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Should annealed disorder be characterized by the average of the partition function? Most of the literature says that for a quenched average over disorder, an average over the log of the partition function must be taken:
\begin{equation}
\langle \log Z \rangle,
\end{equation}
while for the annealed average, it's
\begin{... | If your disorder is not annealed but quenched, the distribution of impurities does not obey the thermal (Gibbs) distribution. Non-annealed, "quenched" disorder is an externally given background, and you need to average extensive quantities, such a free energy ($\propto \log Z$). It is hard for me to guess the exact co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16523",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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About the Ether Theory acceptance Why was the Ether Theory refused by Modern Physics? If you please explain me, I just wanted to understand it more.
| There never was really any experimental or observation evidence that the luminous aether ever existed in the first place. It was merely an invention to pave over a gap in the Newtonian model of light.
Up until the mid-19th century everyone thought that Newton's experiments with prisms and slits had conclusively demons... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is beta negative decay more common than beta positive? In simple terms, why is beta negative decay more common than beta positive?
I know it's something to do with occuring inside/outside the nucleus - but I can't find a simple, easy to understand explanation!
| The beta-decay may be "locally" reduced to a decay of a proton or a neutron inside a nucleus. The beta-minus decay contains the microscopic process
$$ n\to p + e^- + \bar \nu_e + O(1{\rm \,MeV})$$
where the last term indicates the rough increase of the kinetic energy of the decay products. On the other hand, the beta-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16653",
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"source": "stackexchange",
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Can there be black light? I mean is it possible to devise a machine that outputs darkness? I understand there are various colours that light can have. But i was wondering why there is no 'black' light. What is the logical explanation for this? I mean I am expecting an answer that goes beyond mentioning the spectrum det... | There are a couple of things here to clarify.
What is darkness, just (a shade of) black color (as per @anna's answer), yes a machine can do that.
Is it a about a machine that outputs passive darkness (as per @DavidZ's answer), yes it can be done (just dont output anything, it outputs darkness).
Is it about active darkn... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16691",
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Reality constraint What is the "definition" of a reality constraint and why is it called that way?
(I mean how it is used for example in quantum field theory and string theory.)
| A reality constraint typically cuts a quantity with complex degrees of freedom down to the same number of real degrees of freedom.
An example of a reality constraint is to impose that a complex $n\times n$ matrix $M\in{\rm Mat_{n\times n}(\mathbb{C})}$ should be Hermitian $M^{\dagger}=M$.
A bit more abstractly, one ... | {
"language": "en",
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How long does it take for expanding space to double in size? I have been reading about Hubble's constant and trying to make 'sense' of the theory of the expanding Universe. Is is possible that space in the universe expands uniformly? If so, absent of other forces (ie gravity), how long does it take for the distance b... | You are correct that the expansion of the universe hasn't been constant over time. A period of the very early universe is considered to have undergone exponential inflation doubling in size continuously to result in a $10^{78}$ increase in size between $10^{-36}$ to $10^{-32}$ seconds after the big bang.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16781",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Desperately Need Help with Grade 9 Static Electricity I am preparing to teach Grade 9 Static Electricity next week and am going crazy trying to figure out what is happening in one of my experiments. I have a short piece of PVC pipe, 4 inches diameter, and I rub it with wool to charge it negatively. I can observe excell... | Great question. If you can rule out magnetism (based on the material of the foil and the material of the screw under the brass plating, or by demonstrating that there is no force on the foil when the PVC pipe is not charged), you are seeing the effect of induced electric charge on the screws. They are electrically neut... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/16922",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Time, what is it? If you ask any person about time, she/he will give you some answer.
I suspect that it is extremely difficult, (if not impossible) to define time.
Is there a definition of what it is in physics? Is it an "axiom" that has to be taken as it is, without explanations? I also noticed that the tag "time" ha... | Neuroscience tells us our perceptions are stored in short term memory and after much processing, are backdated in time to give the perception of "now" at a later time. This can take many many milliseconds later, even close to a second. Or imagine watching a family movie filmed years or decades ago and becoming so engro... | {
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"source": "stackexchange",
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AdS space - Poincare Patch How can I work out in detail the explicit coordinate transformation formulas needed to go from the "canonical" coordinates to the "Poincare patch"? I'm reading about AdS but the text takes the validity of the Poincare patch for granted, which troubles me. It only has a drawing showing the Poi... | I can recommend the article Introduction to the Maldacena Conjecture on AdS/CFT, arXiv:hep-th/9902131, by Petersen. I suspect that the first 8 pages would be helpful.
| {
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Inertial Mass of a scalar field Does it make sense to talk of the inertial mass of a scalar field? By the equivalence principle, it must be equal to its gravitational mass. We know that the scalar field contributes towards the stress-energy tensor, so, shouldn't it have an inertial mass too?
| Yes, indeed
This is exactly why it is assumed in the Standard Model that mass is the result of an interaction with a scalar "world potential" (The Higgs field) while for instance the changes in energy/momentum of a charge are due to the electromagnetic vector potential $A^\mu$
Regards, Hans
| {
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How do we know Dark Matter isn't simply Neutrinos? What evidence is there that dark matter isn't one of the known types of neutrinos?
If it were, how would this be measurable?
| Cold neutrinos which clumped together would form a Fermi-Dirac condensate. Unlike electrons in an atom there would be no mutual repulsion and the quantum numbers could increase truly "astronomically". For a large concentrate all but the early neutrino contributors would be far from cold. Such a concentrate would behave... | {
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Proof of the Hydrostatic weighing equation? I've been trying to derive this equation for about two hours:
$$\frac{\text{density of body}}{\text{density of water}} = \frac{\text{weight of body}}{\text{weight of body} - \text{weight of immersed body}}.$$
But I can't seem to get it. In my class, we are using it to accurat... | If you place an object with volume $V$ in the water, the buoyant force on it is $\rho_w g V$, with $\rho_w$ the density of water and $g$ gravitational acceleration. This is because the force on the body from the water is the same as it would be on a thin bag of the same shape but filled with water; the surrounding wat... | {
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RG of the Gaussian Model: Finding the scaling factor I'm studying how the Renormalization Group treatment of the simple Gaussian model,
$$\beta H = \int d^d r \left[ \frac{t}{2} m^2(r) + \frac{K}{2}|\nabla m|^2 - hm(r)\right]$$
In momentum space, the Hamiltonian reads
$$\beta H = \frac{1}{(2\pi)^d} \int d^d q \left[\fr... | You have to remember what $t$ means in the Hamiltonian. Usually it stands for $t\equiv(T - T_c)/T_c$, i.e., $t$ is the reduced temperature. Now, since we are interested in the critical behavior, the physical relevant fixed points have to have $t = 0$.
| {
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units and nature I am wondering whether the five$^1$ units of the natural unit system really is dictated by nature, or invented to satisfy the limited mind of man?
Is the number of linearly independent units a property of the nature, or can we use any number we like? If it truly is a property of nature, what is the num... | Even seasoned professionals disagree on this one. Trialogue on the number of fundamental constants by M. J. Duff, L. B. Okun, G. Veneziano, 2002:
This paper consists of three separate articles on the number of
fundamental dimensionful constants in physics. We started our debate
in summer 1992 on the terrace of th... | {
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What is the physical sense of the transition dipole moment? So if the states are the same we achieve the expectation value of the dipole moment for a given state. I mean
$ \langle \mathbf{\mu} \rangle = \langle \psi \vert \hat{\mathbf{\mu}} \vert \psi \rangle$
But I don't feel the physical sense in the case of transiti... | The dipole transition matrix element has a classical interpretation as the time Fourier series of the classical dipole moment of the Bohr orbit corresponding to one of the energy levels. The interpretation is only exact at high levels, at the correspondence limit, and the m,n matrix element is the m-n-th Fourier series... | {
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Is it possible to recover Classical Mechanics from Schrödinger's equation? Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the probability density of finding a particle in classi... | @Arnoques
Sorry, but I think there is an error in your answer:
The spatial extent of the particle wave-function, must be much smaller (and not longer) than the variation length-scale of the potential, to transform $\langle \nabla V(x)\rangle$ turns into $\nabla V\left(\langle x\rangle \right).$
Only in this case, it i... | {
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That 10km/day error predicted if GPS satellite clocks not corrected for relativity Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the GPS (by building the satellite clocks to run 38us/day slower than GPS t... | I looked at the 10km/day-if-38us/day-uncorrected claim several years ago and found it was based on a model of one or all-but-one of the GPS satellites used to fix the observer's position having an uncorrected clock. This model bears no relation to any sensible GPS system. Many lecturers appear not to realise this so 10... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17814",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is there a limit to the resolving power of a mirror telescope? Like, if you grabbed the asteroid 16 Psyche and hammered it out into a disc of 1 mm thick iron foil and curved it into a telescope mirror with 2.4x the radius of the Sun, could you resolve details on the surface of an exoplanet? At what resolution?
Could... | Some theoretical answers were provided, but here's a practical answer from an astronomer's point of view.
(First off, the resolving power is given by diameter, not surface area. So we will talk about diameter here.)
For visible light, the practical resolving power of a 100mm diameter mirror is 1 arcsec. A 200mm mirror:... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Sinusoidal vs exponential wave functions with Schrodinger's equation When solving Schrodinger's equation, we end up with the following differential equation:
$$\frac{{d}^{2}\psi}{dx^2} = -\frac{2m(E - V)}{\hbar}\psi$$
As I understand it, the next step is to guess the wave function, so let $\psi = {e}^{i\kappa x}$ or le... | The most general solution is $Ae^{-ikx} + Be^{ikx}$
Depending on the coefficients $A$ and $B$ this can be equal to either of the example wave functions you gave, and these coefficients will be determined by boundary conditions.
| {
"language": "en",
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What is escape velocity? In reality, how can something no longer be under the gravitational influence of something else? Isn't G a continuous function and although you leave the immediate vicinity of the earth with an escape velocity won't it always exert a force, however small it may be. Won't that force eventually pu... | No, because the fall-off of gravity is $1/r^2$, the force becomes weaker and weaker as the object moves away, at such a rate that it will never pull the object back in, even though the force is never actually zero. If the gravitational force only fell off as $1/r$ then you would be right, it would always pull the obje... | {
"language": "en",
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"source": "stackexchange",
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When has the speed of light been measured, recently? Yes, it is weird, absurd, but I can't stop thinking that the would-be superluminal
neutrino speed has been computed by an arithmetic operation (space/time) and not by direct comparison with a simultaneous light ray running in "parallel".
So the "unspeakable", outrag... | A $2 \times 10^{-5}$ shift in the speed of light would have shown up in a variety of ways. For instance, the laser ranging that is used to monitor the distance to the moon.
The reason no one has attempted to run side-by-side speed test is related to the difficulties of doing neutrino speed measurements. Between needing... | {
"language": "en",
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"source": "stackexchange",
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Do multiple permanent magnets aggregated together approach the same strength as a single magnet of the same size? Here's an applied physics question. ;) If I buy some cube or sphere magnets like these, can I aggregate them together to create a stronger magnet (almost as strong as a single magnet)?
| Although the combined strength will be larger, it will not be exactly the same as the strength of single large magnet. This is because the magnets lower down in the stack are being shielded slightly by the magnets above and below them.
| {
"language": "en",
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"source": "stackexchange",
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Define Pressure at A point. Why is it a Scalar? I have a final exam tomorrow for fluid mechanics and I was just looking over the practice exam questions. They do not provide solutions. But pretty much I have to define pressure at a point and also say why pressure is scalar instead of a vector.
I am thinking pressure at... | A gedanken experiment to illustrate the scalarness of pressure:
*
*take a rubber glove over a glass container and make it hermetic so that water will not penetrate.
*take the glass container under water. Measure the inward curvature of the rubber surface and take it as a rough measurement of the force that water i... | {
"language": "en",
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Difference between Clausius-Clapeyron and Van't Hoff equation I was wondering what is the difference between the Clausius-Clapeyron equation and the Van't Hoff equation. They appear to have the exact same physical meaning and are often used interchangeably.
| They're two forms of the same equation, but Clausius-Clapeyron uses vapor pressure ($p^*$) where Van 't Hoff uses the reaction equilibrium constant ($K$).
Why does this work out? Well, think of vaporization as a chemical reaction:
$$ \text{X} (l) \longrightarrow \text{X} (\text{g}) $$
The equilibrium constant is define... | {
"language": "en",
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Are Uncertainties in Measurements Important? In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is meaningless."
He measures the length of a student and an aluminium bar both in their... | For the purpose of solving problems in physics class, uncertainties are not that important, as the solution will usually be stated to 2,3, or 4 significant figures. However, it is important to understand the concept of uncertainty to be able to do lab work, and to understand if your data are reasonable or not. Uncertai... | {
"language": "en",
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What does a unitary transformation mean in the context of an evolution equation? Let be the unitary evolution operator of a quantum system be $U(t)=\exp(itH)$ for $t >0$.
Then what is the meaning of the equation
$$\det\bigl(I-U(t)e^{itE}\bigr)=0$$
where $E$ is a real variable?
| I would like to elaborate Adam Zalcman's answer, from a physical angle. What Adam actually showed is that all the eigenvalues of the time-evolution operator are of the form $e^{i\phi}$ where $\phi$ is real. The mathematical implication is that $U$ does not change the norm of states.
Let's look at the systems eigen-stat... | {
"language": "en",
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Deterministic quantum mechanics I came across a very recent paper by Gerard 't Hooft
The abstract says:
It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinge... | Even great physicists sometimes write weak paper, and this is the case. Any attempt to find some classical deterministic theory behind quantum mechanics failed, so far. And that is because there is not any.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18586",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "31",
"answer_count": 8,
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Projective Transformations in GR A Thought Experiment:
We are in flat spaceime provided with a reference frame—a rectangular Cartesian frame. The coordinate labels[the spatial labels] are visible to us. Each spatial point is provided with a clock—and the different clocks are synchronized wrt to each other. Gravity is n... | Interesting discussion.
This is my 2 cents contribution:
1- as @RonMaimon stated above, the term "projective transformations" is probably inappropriate and misleading in this context. "Projective" has specific meanings in mathematics, none of which seems to me to be applicable in this case. The OP should perhaps justif... | {
"language": "en",
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Complex numbers in optics I have recently studied optics. But I feel having missed something important: how can amplitudes of light waves be complex numbers?
| Isaac, let me say you are not the only one who feels this way. I had recently been tutoring an undergrad course (on nonlinear optics) and was almost shocked to find most of the students getting muddled in the usage of complex no.s. In fact, in the process, they had a hard time in also understanding/appreciating the bea... | {
"language": "en",
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"source": "stackexchange",
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Causality and anti-particles How can I quantitatively and qualitatively understand the fact that there is a relevance between the existence of anti-particles and causality?
| This is mainly an issue of the complex Klein Gordon field (There's no such requirement for the Dirac field for instance) It's most easily shown with the self propagator of the complex Klein Gordon field using plane waves in the x-direction:
The Klein Gordon equation is.
$\frac{\partial^2 \psi}{\partial t^2} ~~=~~ \left... | {
"language": "en",
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How do we visualise antenna reception of individual radiowave photons building up to a resonant AC current on the antenna? I am a chemical/biological scientist by trade and wish to understand how quantum EM phenomena translates to our more recognizable classical world.
In particular, I want to get a mechanistic picture... | Here is an experimentalist's view of the question:
1) one photon hits the antenna and raises a molecular electron band to a higher energy level, and it will fall back to its lower one, with the characteristic electromagnetic transition time of the order of 10^-16sec, giving the energy to the antenna grid of molecules.
... | {
"language": "en",
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"source": "stackexchange",
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Software to simulate and visualize atoms? Not sure if this is a physics or chemistry question. But if the motion of atoms and it's particles can be described by quantum mechanics, then is there a software that simulate full atoms and it's boundings, in a way you can visualize them, and that can be used, for instance, t... | There are many, many algorithms and pieces of software to do this. In addition to Molecular Dynamics, there are also methods based on statistical simulations in Quantum Monte Carlo, and density functional theory as implemented in programs like Quantum Espresso. It is a simple and worthwhile exercise to program these... | {
"language": "en",
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Why do physicists believe protons and electrons are present in equal numbers? I tended to consider that negative and positive charges are present in equal numbers in the universe to be a known, obvious fact. But is it so? How can we rule out the possibility that there is some kind of asymmetry in the numbers of protons... | I think one of the reasons could be that charge cannot be created. So if initially universe was neutral (at the time of big-bang) it must remain neutral.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19014",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why, intuitively, must a solution in physics be unique? When solving Laplace's equation or Poisson's equation say, we require that the solution must be unique, which can be shown.
*
*In general, what is the physics behind seeking a unique solution?
*Are there differential equations which, for some mathematical rea... | (1) There is a correlation between symmetries, conservation laws and boundary conditions (in the language of differential equations) such that if you have enough symmetries (i.e. enough conservation laws) you will obtain a unique solution.
If you have a system with some free parameters left over and there is genuinely ... | {
"language": "en",
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Why is it concluded that the cosmos is expanding when in fact the observations are for events further back in time? Why is it concluded that the cosmos is expanding at an ever increasing rate when looking further out and therefore further back in time?
Surely, if the time were reversed to play forwards, the conclusion ... | You should try to think of the Universe expanding in terms of the space itself expanding. Not objects moving away from each other in a fixed space. The accelerated expansion refers to the way space in between objects is growing. This is where quantities like proper and comoving distances become very important. If you w... | {
"language": "en",
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If humans were able to catch all sun energy reaching the earth for their use, will the climate change? I guess that energy will be used up and, at the end, will contribute
to heat the earth, so I see no big differences...
please explain your point of view.
| Taking the question at face value, the answer is yes. In order to collect all the solar energy arriving at the Earth you would have to completely cover its surface in solar panels. These solar panels would have to encase the entire atmosphere, because otherwise some energy would be reflected by clouds. This would le... | {
"language": "en",
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Can the quartic oscillator Hamiltonian be made quadratic? I'm interested in turning a quadratic + quartic oscillator Hamiltonian,
$$H = \frac{p^{2}}{2m} +\frac{kx^{2}}{2} + \lambda x^{4},$$
into a purely quadratic problem. One of the simplest things I can think of is replace the quartic term by
$$x^{4} \rightarrow \la... | This is an extraordinarily famous approximation, perhaps the most famous one, called the "Hartree Fock" or "Self-consistent field" approximation. It is the earliest and most famous approach to solving complicated self-interacting systems.
But in the case you are using it, it is very poor. The problem you state can be s... | {
"language": "en",
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Is there a known optical design for a beam compressor? With my little knowledge of optics I have come across some 'known' designs such as the Double Gauss for example, is there a 'beam compressor'.
My requirements are to reduce an incoming parallel wavefront (source at infinity) to either an outgoing parallel beam (ie ... | You can use two parabolic mirrors (either one concave + one convex or two concave) in an afocal Gregorian-telescope arrangement but with multiple reflections. Every second reflection would give you an extra magnification.
For example, if you take two parabolic mirrors with 100mm and 20mm focal length (5:1) then you wi... | {
"language": "en",
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Does a moving escalator make it easier to walk up the steps? I was discussing with my colleagues why it feels easier to walk up an escalator when it is moving. My natural assumption was that the movement of the escalator imparts some extra acceleration on the rider that helps to move up the stairs. But my colleagues in... | Once you get yourself moving, the escalator does not accelerate you and does not assist your running up hill. The only advantage an escalator gives you is that you keep moving up even if you don't put any effort into it.
Next time you feel like running up an escalator (which is not entirely safe), you might consider re... | {
"language": "en",
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What is the connection between Poisson brackets and commutators? The Poisson bracket is defined as:
$$\{f,g\} ~:=~ \sum_{i=1}^{N} \left[
\frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} -
\frac{\partial f}{\partial p_{i}} \frac{\partial g}{\partial q_{i}}
\right]. $$
The anticommutator is defined as... | Both the commutator (of matrices) and the Poisson bracket satisfy the Jacobi identity,
$[A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0$.
This is why Dirac was inspired by Heisenberg's use of commutators to develop a Hamilton-Jacobi dynamics style of Quantum Mechanics which provided the first real unification of Heisenberg's matrix me... | {
"language": "en",
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"source": "stackexchange",
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Infinite quantum well width $L$ to $2L$ adiabatic process If we change width of the infinite quantum well $L$ to $2L$ slowly enough, how it does change energy levels.
| After the process ends, the new energy levels will be just the normal energy levels of infinite quantum well with width 2L.
moreover,
by the Adiabatic theorem:
A physical system remains in its instantaneous eigenstate if a given
perturbation is acting on it slowly enough and if there is a gap
between the eigenvalue an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19931",
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Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution?
I have never seen dissipation explained, although what I have seen a lot is descriptions of dissipation (i.e. more det... | Although summarized as an objection of macroscopic irreversibility when microscopic laws are reversible, Loschmidt's objection originally points that there has to be something breaking the time reversal symmetry in Boltzmann's derivation of the $H$-theorem.
I think that Boltzmann's answer was to say that high $H$ state... | {
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How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments? How does physics scattering experiments relate to real life? And what does the scientist gain from such experiments? I am having a hard time figuring the answer out. Please help.
| Depending on how you define scattering, its not only scientists who do these experiments, it is you, especially your eye.
Most likely you are referring to things like Rutherford backscattering or what is done at CERN, DESY, LHC & Co.?
In the end, the entire world can be seen as particles that are getting scattered by e... | {
"language": "en",
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Physics book for 15 year old boy
Possible Duplicate:
List of good classical physics books
my name is Bruno Alano. As stated in the title, I'm 15 years old (I'll do 16 on 7 of Feb) and much love Computer Science (C, C++), Mathematics and Physics.
Some information may have been unnecessary, but my question is: What is... | Even if it doesn't answer your question directly i think these videolectures are a great place to start and really motivating (and for free):
*
*Walter Lewin ot the MIT:
http://web.mit.edu/physics/people/faculty/lewin_walter.html go to --> take a class Physics I, II, III
*Foundations of Modern Physics: Leonard Sus... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20149",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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How are the Pauli matrices for the electron spin derived? Could you explain how to derive the Pauli matrices?
$$\sigma_1 = \sigma_x =
\begin{pmatrix}
0&1 \\ 1&0
\end{pmatrix}\,, \qquad
\sigma_2 = \sigma_y =
\begin{pmatrix}
0&-i\\ i&0
\end{pmatrix}\,, \qquad
\sigma_3 = \sigma_z =
\begin{pmatrix}
1&0\\0... | The Hilbert space for spin 1/2 is two-dimensional - there are two possible values spin can take: $\hbar/2$ or $-\hbar/2$ (this is taken from experiment).
Now, in two-dimensional Hilbert space spin operator has to be self-adjoined (this comes from foundations of QM). Furthermore, sum of its eigenvalues has to be 0 - bec... | {
"language": "en",
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What is the physical definition of causality? Maxwell's equations give a physical relationship between the electric and magnetic fields $\vec E$, $\vec B$ at the same time, which some interpret as changes in one causes changes in the other etc. I find this confusing because to me, the cause of both is charge and cause ... | If we define some event which we will call $p$ to be the cause and $q$ to be its effect, then $p$ and $q$ should satisfy the following rules,
*
*$p$ implies $q$ but $q$ doesn't imply $p$.
*in the absence of $p$, $q$ shouldn't exist either.
*$p$ and $q$ shouldn't be simultaneous events as viewed from any inertial f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20326",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Synchronising the Earth's rotation via mass redistribution How much material would have to be moved per year from mountain-tops to valleys in order to keep the Earth's rotation synchronised with UTC, thus removing the need for leap seconds to be periodically added? Would it be a feasible project to undertake in order t... | That seems like a fun question!
According to Wikipedia the day is currently 2ms too long, so that's a factor of 2.31e-8. So we need to reduce the angular momentum of the earth by this factor.
To make life easy consider a mountain on the equator, with a mass $m$, treat it as a point mass and assume we manage to move it ... | {
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Was the universe a black hole at the beginning? Big bang cosmology, as far as I understand it, says that the universe was super hot and super dense and super small. It looks like that all the current matter, seen and unseen, were compressed to infinitesimal distance, which means it was a black hole.
*
*Is the big b... | The observable universe exists inside a black hole created by the total mass present in the observable universe.
If we find the size at which the mass distribution with the average mass density of the present universe forms a black hole.
The above expression means that if the present universe has a critical mass dens... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20394",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Are matrices and second rank tensors the same thing? Tensors are mathematical objects that are needed in physics to define certain quantities. I have a couple of questions regarding them that need to be clarified:
*
*Are matrices and second rank tensors the same thing?
*If the answer to 1 is yes, then can we think ... | *
*All scalars are not tensors, although all tensors of rank 0 are scalars (see below).
*All vectors are not tensors, although all tensors of rank 1 are vectors (see below).
*All matrices are not tensors, although all tensors of rank 2 are matrices.
Example for 3: Matrix M (m11=x , m12=-y , m21=x^2 , m22=-y^2) .... | {
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What is the velocity area method for estimating the flow of water? Can anyone explain to me what the Velocity Area method for measuring river or water flow is?
My guess is that the product of the cross sectional area and the velocity of water flowing in a pipe is always constant. If the Cross sectional area of the pipe... | What you refer to is conservation of mass under some assumptions:
*
*Constant density
*A steady state flow
I'll bring us back to your equation by starting with the very fundamental mass accounting for a given fluid flow. To be comprehensive, we need to recognize that velocity isn't constant over the entire area... | {
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How can a human eye focus on a screen directly in front of it? I am asking this question here because I think the answer has something to do with the way light is bent as it's captured through the eye.
I saw a show a while ago about tiny screens on contact lenses to pull up data on objects you see in the real world, I ... | The answer is that your eyes would be focusing not at the concrete distance where the mechanism is placed, but at a virtual image which appears farther away.
This is just basic optics.
It is (one aspect of) what happens when you use a magnifying glass, for instance.
The virtual image of some point viewed through an opt... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20670",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
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Why can't we think of free fall as upside down rocket? /\
/ \
| |
| m |
| |
------ <--- floor (Rocket A)
This rocket is accelerated (g) upwards then mass(m) falls on the floor.
------ <--- floor
| |
| m |
| |
\ /
\ /
\/ (Rocket B)
This rocket is accelerated (g) downwards then mass(m) ... | In fact, in case B, if the rocket really accelerate at g, downward, in the vicinity of earth, it is "free-fall" : m stay midair.
Except this detail, the main difference between the rockets and the elevator is the thrust.
No thrust pushes the elevator during free fall.
No thrust means no force applied on its inhabitants... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20706",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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What formulations of QM are there? It is usually said that there are different formulations of QM, for example historically there was Schrodinger's (wave mechanics), and Heisenberg's (matrix mechanics), then Dirac's (which showed they are equivalent)
Since they are all physically equivalent I have a few questions:
1-Is... | http://www-physique.u-strasbg.fr/cours/l3/divers/meca_q_hervieux/Articles/Nine_form.pdf
See this article by Styer et al entitled Nine formulations of quantum mechanics
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20821",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Discreteness of Spacetime and Violation of Lorentz symmetry It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows such analysis.
My other question is: if Lorentz symmetry is... | There are nontrivial discrete subgroups of the Lorentz group. It is easy to construct an SO(3,1) matrix that has only integer entries and yet is not just a simple rotation. A rectangular lattice in Minkowski space is invariant under the group of these transformations. Different space-time lattices have different discre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20860",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
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How is capacitance defined for three concentric spheres? If we have a configuration of metal concentric spheres (each of negligible thickness) of radii $r_1,r_2,r_3$ respectively and $r_1<r_2<r_3$, and we are given the potentials of the spheres to be $0, constant,0$ respectively. How might we find the capacitance of t... | Although there is a theoretical ambiguity because there are 3 conductors, the particular specification of the potentials here implies that the desired capacitance $C$ is the ratio of the charge $Q$ on the middle sphere to its voltage $V$: $C=Q/V$.
Note that the inner and outer spheres are grounded so $V$ is the (only)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20910",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
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Degree of freedom paradox for a rigid body Suppose we consider a rigid body, which has $N$ particles. Then the number of degrees of freedom is $3N - (\mbox{# of constraints})$.
As the distance between any two points in a rigid body is fixed, we have $N\choose{2}$ constraints giving $$\mbox{d.o.f} = 3N - \frac{N(N-1)}{2... | These constraints are not independent.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20954",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 7,
"answer_id": 5
} |
Reynolds number with hyper-viscosity Is it possible to evaluate a Reynolds number when viscosity operator is substituted by hyper-viscosity operator at the power H (Laplacien to the power H) in the incompressible Navier-Stokes equations ?
| For the equation:
\begin{equation}
\partial_t u_i + u_j \partial_j u_i=-\partial_i p+ \nu_{hyper} \Delta^H u_i
\end{equation}
with $u$ the velocity in $m.s^{-1}$ and is characteristic order $U$, $p$ the pressure in $m^{2}.s^{-2}$, $\nu$ the hyper-viscosity in $m^{2H}.s^{-1}$. The characteristic length scale is note $L$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21108",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
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Speed of a dynamic hydraulic system We all have noticed that changing the temperature of the water in the shower is not instantaneous, rather the result is felt when the water that was in the tap works its way up to the showerhead. However, changing the pressure does feel instantaneous. I wonder at what speed the chang... | The pressure wave does indeed travel with the speed of sound of the media. This is much higher for water then for air with a speed of $\approx$ 1500 m/s.
This effect is well known and feared under the name water hammer. Basically by rapidly closing a valve you create a longitudinal pressure wave that can be powerful e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21184",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Mechanism by which electric and magnetic fields interrelate I read that force due to electric field on some particle in one reference frame can exhibit itself as force due to magnetic field in some other reference frame and that electric and magnetic fields are two aspects of same underlying electromagnetic field.
My ... | Fundamentally they are both the interaction between charges. Magnetic fields are the results of moving charges. When charges move, its time slows down (relativity), therefore, the effect (field) of the charge is weakened. Eg. electrons are moving in a wire relative to a stationary proton, the field of the electron is w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21238",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 4,
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Long-Life High Altitude Balloon Normally high-altitude balloon experiments end with the balloon popping and the payload falling back down to be reclaimed.
But if a second balloon was attached to the payload, one which was only partially inflated at launch, then could you keep the balloon aloft for a very long period o... | There are two limitations to your proposal: the volume of the balloon will be very large at higher altitudes and the gas such as hydrogen and helium will leak even through solid walls with time.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21295",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
What determines color -- wavelength or frequency? What determines the color of light -- is it the wavelength of the light or the frequency?
(i.e. If you put light through a medium other than air, in order to keep its color the same, which one would you need to keep constant: the wavelength or the frequency?)
| Colour is defined by the eye, and only indirectly from physical properties like wavelength and frequency. Since this interaction happens in a medium of fixed index of refraction (the vitreous humour of your eye), the frequency/wavelength relation inside your eye is fixed.
Outside your eye, the frequency stays constant... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21336",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The speed of tachyons The other day I was wondering: When a tachyon is coming towards you faster than the speed of light, will you see it before it hits you? Then I thought of course not, since the light waves aren't traveling faster than the tachyon then how could you see it before it hits you? Now I thought today, if... | If you fire a beam of photons at an object receding away from you at a speed greater than the speed of light, your photons will never reach it to reflect off it
OTOH, if such an object emits photons, you should eventually be able to see the object as it was at the time the photon was emitted.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21485",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 2
} |
Example in the book: A simple accelerometer A simple accelerometer
You tape one end of a piece of string to the ceiling light of your car and hang a key with mass m to the other end (Figure 5.7). A protractor taped to the light allows you to measure the angle the string makes with the vertical. Your friend drives the ... | Did you forget to include the D'Alembert forces in the Free Body Diagram?
http://en.wikipedia.org/wiki/D'Alembert's_principle
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21553",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 2
} |
Have red shifted photons lost energy and where did it go? I think the title says it. Did expansion of the universe steal the energy somehow?
| Energy isn't a nice concept in GR, so all I'm giving is an intuitive way of looking at it.
For gravitationally redshifted stuff:
A photon has energy, thus it gravitates (as energy can gravitate analogous to mass from $E=mc^2$), thus it has some (negative) gravitational potential energy when on the surface of a planet. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21603",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 2,
"answer_id": 0
} |
Can you safely draw sparks from the nose of an electrified boy? From Purcell's Electricity and Magnetism
A spectacular conclusion of one of the popular exhibitions of the time
was likely to be the electrification of a boy suspended by many silk
threads from the rafters; his hair stood on end and sparks could be
... | What is required for sparks across a gap is a high voltage, while what determines whether something will do you harm is the amount of current.
You can theoretically survive almost any voltage so long as the current is sufficiently low. It's just that most sources of electricity that have high voltages tend also to hav... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21652",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
Is sea water more conductive than pure water because "electrical current is transported by the ions in solution"? Apparently, electrical charge is transported by the ions dissolved in water, is this true?
| Yep. Pure water is an extremely bad conductor of electricity, it has very few ions. Water with an electrolyte (like NaCl) is a much better conductor of electricity; as the ions can migrate. Migration of ions is just like migration of electrons. If you place an imaginary surface inside the cell, there will be net negati... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21813",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Prove that negative absolute temperatures are actually hotter than positive absolute temperatures Could someone provide me with a mathematical proof of why, a system with an absolute negative Kelvin temperature (such that of a spin system) is hotter than any system with a positive temperature (in the sense that if a ne... | For the visually inclined, this article explains it simply. The maximum hotness definition is the middle image instead of the expected right image:
Due to the unintuitive definition of heat, a sample that only includes hot particles is negative kelvin / beyond infinite hot, and as clear from the image would give energ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21851",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "43",
"answer_count": 8,
"answer_id": 4
} |
What do the dimensions of circulation mean, and how is circulation related to action? The dimensions of circulation $\int_C \vec{v}\cdot d\vec{r}$ seem strange, but if you include
(even a constant) density $\rho$, then $\int_C \rho\vec{v}\cdot d\vec{r}$ has dimensions
the same as action/volume. Is there any significan... | The best way to gain intuition about circulation is to think of it as a measure of the number of vortex lines through a surface. By Stokes' theorem, $\int_C \vec{v} \cdot \vec{dr}$ = $\int_A (\vec{\nabla} \times \vec{v}) \cdot \hat{n} \, dA$. The quantity $\nabla \times \vec{v}$ called the vorticity, and you are threa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/21987",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
} |
Are there more bosons or fermions in the universe? The question is in the title: are there more bosons or fermions in the universe? Or is there the same number of bosons and fermions?
I think there is the same number but I don't know why exactly.
| The question may be unanswerable because I'm pretty sure the number of photons is variable depending on your relativistic frame. At least that was an interesting observation that Feynman made, almost apologetically, in some of his early work; I'd have to look up the specific reference. (Hmm. Feynman's idea there would ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22066",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 5,
"answer_id": 3
} |
Is ground energy of interacting fermions always higher that that of bosons? Consider two systems, each made of $N$ particles. In both systems particles interact pairwise and the interaction is given by the same Hamiltonian for both systems. Any other constraints and/or requirements you'd like to add should be the same.... | The question makes sense in a nonrelativistic setting, where either symmetry or antisymmetry can be imposed on the wave function.
The symmetric ground state always has lower energy, as it is also a ground state of the non-symmetrized system. (Proof: The symmetrization of an arbitrary ground state is again a ground sta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22101",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 1
} |
Differentiating inside an integral sign I'm reading John Taylor's Classical Mechanics book and I'm at the part where he's deriving the Euler-Lagrange equation.
Here is the part of the derivation that I didn't follow:
I don't get how he goes from 6.9 to 6.10 by partial-differentiating the term inside the integral. If... | It's known as the Leibniz integral rule. As long as $\alpha$ is not the variable being integrated over, then $$\frac{\mathrm{d}}{\mathrm{d}\alpha}\int f(x,\alpha) \mathrm{d}x=\int\frac{\partial f(x,\alpha)}{\partial \alpha}\mathrm{d}x$$
$x$ will not be present outside the integral anyways (due to limits of the integra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22163",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
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Ropes and Pulleys - Really unintuitive answer I usually don't want to do this, but please go to this link, the solution is too big to post it here
http://engineering.union.edu/~curreyj/MER-201_files/Exam2_2_26_09_Solution.pdf
And go to page 5 of the pdf.
Briefly, the problem say
Determine the velocity of the 60-lb b... | 2 - the block 'A' is on a pulley, when it moves 1 ft the rope moves 2ft. It has a 2:1 mechanical advantage, normally you would use this to move block 'A' half the distance you pull the rope and with twice the force - the point of a pulley is to use a smaller force for a longer distance.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22207",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Factors affecting torque and RPM of a motor I am not a physics guy, so not even the basic concept of a DC motor is easy for me. My question is as follows:
How do these parts of a motor affect its RPM and Torque?
I had my research a while ago so I filled out some of it; please correct if there is something wrong.
More t... | The RPM is restricted by frictional losses in the engine and the tendancy of the engine to explode if you rotate it too fast. In that sense the RPM limit is down to how well the engine is made and what it's made of rather than any fundamental EM properties.
The torque is dependant on how large a magnet field the engine... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22303",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
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Why the shape of rainbow is semicircular after rain why not the whole atmosphere is colorful? I have a very simple question.
Everyone must have seen the rainbow after rain. According to the theory the rainbow is created due to the passing of sunlight from small drops of water in the atmosphere(means by dispersion of li... | This is just a guess, as I have no formal training.
My guess would be that it is due to the spherical nature of the atmosphere the light is passing through. If you have a glass globe and shine a light through it the light is bent as it passes through and the pattern that is made on the object on the other side of the g... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22348",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 3
} |
How can people do music with Tesla coils? I saw a lot of videos of Tesla coils doing music on YouTube. And I wonder how can they do that sort of things.
How they can calculate what tone it is going to do? And what are the factors to consider?
| In short, the Tesla coil is converting air into plasma, which changes its volume, which causes pressure waves to spread out in all directions (sound).
The sparks are created by a self-oscillating coil, which happens at a high, inaudible frequency (20 to 100 kHz).
The self-oscillating coil, though, is driven by pulses... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22526",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Can black holes be created on a miniature scale? A black hole is so powerful to suck everything into itself. So is it possible that mini black holes can be created? If not then we could have actively disproved the rumors spread during LHC experiment.
| The search is on at the running LHC experiments for signatures of black holes from large extra dimensions. Despite what @Ronmaimon claims in his answer, experimentalists are not convinced that the probability of some of the models that expect large extra dimensions to be right is zero.
A search for microscopic black ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22578",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
} |
Difference in timbre between 'quiet' and 'far away' I'd like to know what are the differences in timbre - or the acoustic properties of a sound - that allow us to differentiate between a sound which is quiet (but close-by) and one which is far away.
For example, you can tell when someone near to you is playing an instr... | Mostly the effect is due to things other than "timbre", such as reverberation.
The one thing that does affect timbre is the fact that air absorbs higher frequency sound more than lower frequency sound.
http://www.sfu.ca/sonic-studio/handbook/Sound_Propagation.html
So as the waves travel to you, higher frequencies will... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22665",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 5,
"answer_id": 2
} |
Do neutron stars reflect light? The setup is very simple: you have a regular ($1.35$ to $2$ solar masses) evolved neutron star, and you shine plane electromagnetic waves on it with given $\lambda$. Very roughly, what shall be the total flux of absorbed/scattered EM radiation?
Shall the result change if the neutron star... | Martin, the infalling light is blue-shifted, and red-shifted on reflection. No overall change, I think.
However, a suitably mechanically strong light-source on the surface of the neutron star (!) will be seen to emit light that is redder than usual.
If the neutron star had its normal matter scraped off (left as an exer... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22722",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 4,
"answer_id": 2
} |
Why is the conductor an equipotential surface in electrostatics? Since the electric field inside a conductor is zero that means the potential is constant inside a conductor, which means the "inside" of a conductor is an equal potential region.
Why do books also conclude, that the surface is at the same potential as we... | The change in potential between two points is
$$ \Delta V = \int_a^b \mathrm{d}\vec{\ell} \cdot \vec{E} $$
but inside the conductor $\vec{E} = 0$ so that integral between any two interior points is also zero, accordingly the interior is all at the same potential.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22776",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 5,
"answer_id": 0
} |
Decoherence when no one is looking? I understand that in the single-electron-at-a-time double slit experiment, if a detector is placed before the slit, the interference pattern vanishes.
Suppose I left the detector on, but put a bag over its screen (I can't tell what state the electron is before it passes the slits), d... | In the following, I have replaced "photon" going through slits with "electron", and the measuring device with a "photon". This is the traditional Heisenberg setup.
The interaction of the photon and the electron entangles the photon and the electron, so that the electron cannot make the interference pattern. It has noth... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22824",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Is there an explanation for the 3:2:1 ratio between the electron, up and down quark electric charges? I understand that the NNG formula relates $Q$, $I_3$, and $Y$ and can be derived in QCD; does this unambiguously predict the electric charge ratios without making assumptions about the definitions of isospin and hyperc... | There is a nontrivial relation between the electric charge and the strong business, namely that there are instantons which will cause proton decay. So it is not completely true that there are no relations--- the requirement of anomaly cancellation requires that the proton decay process conserve charge, and so relates t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22921",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 1,
"answer_id": 0
} |
Can one introduce magnetic monopoles without Dirac strings? To introduce magnetic monopoles in Maxwell equations, Dirac uses special strings, that are singularities in space, allowing potentials to be gauge potentials. A consequence of this is the quantization of charge.
Okay, it looks great. But is this the only way t... | Below it is explained how a string free monopole theory can be constructed.
Monopoles have not been found in experiments. Therefore the main issue to be defined
are the principles used as cornerstones for the required monopole theory.
The first step is to formulate a theoretical definition of monopoles. This is done ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/22967",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 4,
"answer_id": 3
} |
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