Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
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?
| Neutrinos from the big bang have been redshifted to ~2K = ~0.0002 eV, which is considerably lower than the current best upper bound on neutrino rest mass (0.1eV). We have no way to directly detect the flux of neutrinos at this low energy and the indirect methods at deducing it are tentative at best. So primordial neu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17227",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "53",
"answer_count": 4,
"answer_id": 2
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split gravitational force into x, y, and z componenets I am writing a program for a computer science class in which I am doing an n-body simulation in 3-dimensional space. Currently, I have figured out the gravitational force along the hypotenuse between two bodies. Now I have to split these up into the x, y, and z com... | Use $F_x = -x GmM/|r|^3$, similar for $y$ and $z$. This is obtained by taking $F=GmM/|r|^2$ where the direction is $-\hat{r} = -\vec{r}/|r| = -(x,y,z)/|r|$, so the $x$-component is $-x/|r|$.
In the above, $|r| = \sqrt{x^2+y^2+z^2}$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17285",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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What type of substances allows the use of the Ideal Gas Law? I know that I can use the ideal gas law with pure gases or pure liquids. But can I also use the ideal gas law at saturated gases and saturated liquids as long as they aren't two phase substances?
| The ideal gas law is derived from a model (the ideal gas), and like every other model it applies where it's underling assumptions are good approximations to reality.
So, important assumptions for the idea gas law:
*
*Point particles In the ideal gas, the particles occupy no volume. A real gas in which the atoms of m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17362",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
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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
$$\beta H = \frac{1}{(2\pi)^d} \int d^d q \left[\fr... | Yes. It is a merely a convenient choice to fix the term in front of the gradient. You may make some other choice and get some other equivalent RG flow. An interesting toy to play with is a field with kinetic term $K_1 q^2 + K_2 |q|^\alpha$ where $\alpha >0$ is some parameter. You can write an RG flow choosing to fix ei... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17428",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the physical meaning of the affine parameter for null geodesic? For time-like geodesic, the affine parameter is the proper time $\tau$ or its linear transform, and the geodesic equation is
$$\frac{\mathrm d^{2}x^{\mu}}{\mathrm d\tau^{2}}+\Gamma_{\rho\sigma}^{\mu}\frac{\mathrm dx^{\rho}}{\mathrm d\tau}\frac{\ma... | An affine parameter is one which makes the acceleration perpendicular to the velocity. It is the limit of proper time as you take the limit that the geodesic becomes null, rescaled to make the total length stay finite.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17509",
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"source": "stackexchange",
"question_score": "32",
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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... | Normally the transition amplitude is calculated with $e^{i\vec{k}\vec{r}}$. For "small" product $\vec{k}\vec{r}$ one expands the exponential in Taylor series and one leaves only the "dipole" term in the transition amplitude calculation: $\propto\vec{k}\cdot\langle\psi_1|\vec{r}|\psi_2\rangle $. So it is a "dipole" part... | {
"language": "en",
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"source": "stackexchange",
"question_score": "12",
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laser spectral width vs. linewidth I have been racking my brains over the differences between laser spectral width and something called the linewidth. The linewidth was written about in detail by Henry in 1982. The spectral width is the width at -20dB down from peak of the wavelength spectrum of the laser. I am look... | Maybe linewidth of spec is the width of only one longitudinal mode. If your LD is not SLM, the spectral width should be the width between the first and the last longitudinal mode, so the spectral width will be far greater than linewidth.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17717",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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"answer_id": 2
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Why do or don't neutrinos have antiparticles? This was inspired by this question. According to Wikipedia, a Majorana neutrino must be its own antiparticle, while a Dirac neutrino cannot be its own antiparticle. Why is this true?
| here is how I understood the answer. Imagine that we look at the electron in our reference frame, and find that it travels in z direction and has spin projection +1/2. This one we call right-handed electron. Since it is massive, there exist reference frames in which observers see it as left-handed electron. For example... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17750",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Found the answer after drawing a blank with several experts. Two US professors of high GPS pedigree, independently explained that the '10km/day' claim presupposes that between 1 and 3 of the satellites used for a 4 satellite fix do not incorporate the 38us/day clock rate ('factory') offset. They also remarked that the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/17814",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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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... | The resolving power of a telescope with a circular apertre is given by $$\theta = 1.22\frac{\lambda}{D}$$ Where $\lambda$ is the wavelength, $\theta$ is the smallest resolvable angular size and $D$ is the diameter of the aperture (lens/mirror) of the instrument.
The larger $D$ gets the larger the fourier component you... | {
"language": "en",
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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... | The speed of light is being measured very accurately right now for this message to get to you. It's going down a fibre that uses DWDM to separate the channels which requires the speed of light to be very accurately what the engineers expect.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18149",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What is a single word that describes the idea of the second time derivative of energy? I think about position, its time derivative speed, and its second time derivative, acceleration. I would like to identify a single word that can be used as a handle for the second time derivative of energy (i.e., the time derivative ... | Within power systems such as regional or national electricity grids, $\frac{\mathrm{d}^2E}{\mathrm{d}t^2}$ is called the slew rate: it's used to denote the rate of change of power demanded from, or supplied to, electricity grids. It's typically either expressed as MW/s or GW/h, being two time periods of interest in bal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18328",
"timestamp": "2023-03-29T00:00:00",
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"question_score": "4",
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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... | I think the more interesting question to ask is if there is something fundamental about uncertainties?
You are free to ignore uncertainties if your calculations match experiments to the order you are interested in. In my view, a theory is at its strongest when supported by experiments.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18443",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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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?
| Multiply both sides of your equation
\begin{equation}
\det(I-U(t)e^{itE})=0
\end{equation}
by $e^{-intE}$ where $n$ is the number of dimensions of the state vector space. We obtain
\begin{equation}
\det(e^{-itE}I-U(t))=0
\end{equation}
(See below for how this works.) This is a special case of the following equation
\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18539",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Addendum: an other important point of criticism raised (Newman and others): why search for such a theory at all? Its predictions will be nil.
While Maimon thinks that my prediction that true quantum computing will be impossible implies that my theory will deviate from true divine qm. No to both: my theory implies that... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18586",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "31",
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"answer_id": 4
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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 a consequence of the fact that there is no positive frequency function which is zero outside the light cone. If you have a particle in relativity, its dynamics require that it goes faster than light, and to restore causality, it must go back in time. This is explained in my answer here: Is anti-matter matter go... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18705",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 2,
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Locality in Quantum Mechanics We speak of locality or non-locality of an equation in QM, depending on whether
it has no differential operators of order higher than two.
My question is, how could one tell from looking at the concrete solutions of the equation whether the equ. was local or not...or, to put it another wa... | Here is an experimental physicist's view.
Locality for me means that the solutions representing a particle give the particle as local, i.e. once the boundary conditions are given, all its observables and interactions depend on functions as f(x,y,z,t), (x,y,z,t) a point.
Non local means that the solutions giving the o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18762",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do all planets rotate around the sun with the same acceleration? I have this question in mind. suppose if by any chance, all planet around sun stopped rotating. then as per formula F= M * A. all planet should fall with same acceleration towards sun and ultimately fall into sun.
but even when they are rotating around su... | All planets will not have the same acceleration due to their distances from the sun
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18822",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Reducing General Relativity to Special Relativity in limiting case I understand that general relativity is applicable to gravitational fields and special relativity is applicable to case when there is no gravity. But is there a derivation on how to reduce General Relativity to Special Relativity in limiting case, much ... | A well-known technique is post-Minkowskian approximation. It applies to the weak-field limit of general relativity, and gravity shows up as correction terms to the Minkowski metric in powers of Newton’s gravitational constant $ G $.
If, in addition to powers of $ G $, you expand the metric in powers of $ \left( \dfrac{... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/18904",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
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Gauss's Law vs Newton's Law This is thought experiment. I couldn't get a good answer because I keep getting negative mass.
Gauss's Law say that eletric field is proportional to charge, how much charged is enclosed. Newton's gravitational pretty much says the same thing. More mass, strong gravitational strength.
So to p... | In the equations as you've written them, the constant of proportionality is an outward-pointing vector for the electric field and an inward-pointing vector for the gravitational field. Or in other words, if you take the radial component only: it's a positive constant for the electric force and a negative constant for t... | {
"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... | Well, I for one as a physicist do not believe this because conservation of charge does not mean conservation of baryon or lepton numbers. It just means conservation of charge. Physicists do not "believe" in equal numbers of protons and electrons except when bound in nuclei.
The numbers can increase arbitrarily by pair ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19014",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Is it a total or an explicite time derivative in the Schrödinger equation? I am always dubious when I need write Schrödinger equation: do I write $\partial / \partial t$ or $d/dt$ ?
I suppose it depends on the space in which it is considered. How?
| The most general Schrödinger equation has total derivatives
$$ i\hbar \frac{d}{dt}|\psi\rangle = \hat H |\psi\rangle $$
because the state vector $|\psi\rangle$ only depends on one variable, $t$. It's a complicated object that knows about the probability of anything in the given state, but this is hidden "inside" the st... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19141",
"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... | The physical intuition behind this requirement, or quest, is causality. One feels that given the initial conditions, and given the differential equations thought of as a Law of Nature, then the rest of the solution is caused by the initial conditions and the Law of Nature and so must be unique.
This is a very questi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19194",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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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.
| If humans were able to catch all sun energy reaching the earth for their use, will the climate change? It would depend on how much of that energy ends up as heat. Currently, a proportion is reflected back into space: the Earth has a non-zero albedo - it is not perfectly black, and does reflect back into space. Pretty m... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19406",
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"source": "stackexchange",
"question_score": "2",
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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... | Classical case
The Hamiltonian you have introduced is the one of a nonlinear oscillator. While for a linear oscillator period does not depend on the amplitude for this one it does. This means that quadratic approximation will always fail for some amplitudes.
If you want to describe oscillations of small amplitude you c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19451",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
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Who discovered momentum? I read some text about momentum in Wikipedia, but I didn't find any information who discovered momentum. Is the momentum a philosophic principle?
| Jean Buridan (1295-1358) discovered impetus, the measure of which is called momentum. In fact, there is one recent physics textbook that defines an SI unit of momentum as the Buridan (1 B = 1 kg m/s).
Buridan wrote:
This impetus would endure forever [ad infinitum] if it were not diminished and corrupted by an opposed ... | {
"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 ... | A beam expander takes a parralel beam of light and outputs another parallel beam. A factor of 100 is a little optomistic - even assuming you had perfect optics you would inevitably need an exit lens (or mirror) 100x larger in diameter than the incoming beam.
Unless the incoming beam is very very small - and then you ... | {
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How does a receiving antenna get an induced electric current? From this question, I've noted that an electromagnetic field carries no electric charge but it has two components:
*
*Electric field
*Magnetic field
Now what I failed to understand is how does the receiving antenna get an induced small voltage. Is it ... | If you put an electron in an electric field it moves and this is how a radio wave induces a voltage in the aerial. The oscillating electric field of the waves causes electrons to move in the metal of the aerial and this generates the voltage.
Aerials are normally designed so they have a natural resonance at the frequen... | {
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"source": "stackexchange",
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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]. $$
The anticommutator is defined as... | According to the topic of deformation quantization, the first few entries in the dictionary between
$$ \text{Quantum Mechanics}\quad\longleftrightarrow\quad\text{Classical Mechanics}\tag{0}$$
read
$$ \text{Operator}\quad\hat{f}\quad\longleftrightarrow\quad\text{Function/Symbol}\quad f,\tag{1}$$
$$ \text{Compositi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/19770",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "71",
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Basic question about law of gravitation
Possible Duplicate:
Radial fall in a Newtonian gravitational field
This is how Wikipedia defines Newton's law of Gravitation:
Every point mass attracts every single other point mass by a force
pointing along the line intersecting both points. The force is
proportional to ... | Problems of this kind can be solved with methods of differential calculus.
Let's suppose the acceleration to be constant during some short interval of time. We can find new position of the spheres at the end of this interval and calculate new acceleration for the next period and so on.
This will give us an approximate ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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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... | Time asymetry appears in the solution of the Boltzmann's equation because its solution depends exponientally on the initials conditions. After a few caracteristic relaxation times, the initial conditions becomes exponentially small. So, although the microscopic particles obey Hamiltonian dynamics (with trajectories dep... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "36",
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How are the Pauli matrices for the electron spin derived? Could you explain how to derive the Pauli matrices?
$$\sigma_1 = \sigma_x =
\begin{pmatrix}
0&1 \\ 1&0
\end{pmatrix}\,, \qquad
\sigma_2 = \sigma_y =
\begin{pmatrix}
0&-i\\ i&0
\end{pmatrix}\,, \qquad
\sigma_3 = \sigma_z =
\begin{pmatrix}
1&0\\0... | Spin is an angular momentum, so in the rest frame it is a 3-dimensional vector, or 4-dimensional vector with zero time component:
$\vec{v} = (v_1,v_2,v_3)$
Each 3D vector can be associated with a 2x2 matrix by the following rule:
$V = \begin{vmatrix}
v_3 & v_1-iv_2 \\
v_1+iv_2 & -v_3
\end{vmatrix}$
In particular, i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20201",
"timestamp": "2023-03-29T00:00:00",
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What is the physical definition of causality? Maxwell's equations give a physical relationship between the electric and magnetic fields $\vec E$, $\vec B$ at the same time, which some interpret as changes in one causes changes in the other etc. I find this confusing because to me, the cause of both is charge and cause ... | There is no need for physicists "determine if there is a causal relationship" because in this context the word "causal" is entirely subjective. Your question addresses the distinction between proximate and ultimate causes - by way of analogy, if I (the charge) throw a ball (the electric field) at a lamp, was the cause... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/20326",
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"source": "stackexchange",
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Are matrices and second rank tensors the same thing? Tensors are mathematical objects that are needed in physics to define certain quantities. I have a couple of questions regarding them that need to be clarified:
*
*Are matrices and second rank tensors the same thing?
*If the answer to 1 is yes, then can we think ... | $$
\def\cR#1{\color{red} {#1}}
\def\cG#1{\color{green}{#1}}
$$
They seem so similar, but...
There is often confusion regarding indices when we transform a rank-2 tensor, $T_{ij}$. Because matrices can represent rank-2 tensors, it's tempting to just start multiplying. But index order is crucial.
Now, regular matrix mul... | {
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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... | You are right, if you assume the velocity of the fluid is more or less constant across the pipe, then conservation of mass dictates that $AV$ is constant.
Now, if you have a pipe, with no constraints at the bottom to let the water accelerate, this will change. The issue to consider here, is that when the water is accel... | {
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Can x-ray radiation be compared to background radiation? I've been trying to learn about the possible effects of x-ray radiation from dental x-rays and most of the resources I come across compare the exposure to that of natural background radiation.
Here's an example (not specific to dental x-rays): http://www.hpa.org... | This very good article on radiation explains that one unit of uSv measures the amount of damage done by that dose of radiation. If this dose is put entirely in one small part of the body then presumably the damage is confined to that small space. If this is the brain and the mouth then this would appear to be a much bi... | {
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What is the most efficient way to use hand dryer? What's the most efficient way to place your hands under the hand dryer?
Let's assume that dryer creates simple downward flow of hot air.
Here are some examples:
| Neither of these examples are efficient by any standards. Instead of heating up the air which is consuming a lot of energy it is much better to increase the pressure and blow of the water instead of evaporating it. The currently most efficient hand dryer is the Dyson Airblade.
There are similar dryers available but the... | {
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Electrodynamics textbooks that emphasize applications Please recommend undergraduate-level textbooks on electrodynamics which emphasize practical applications and real life examples. Please describe the book's level and contents and its intended audience in as much detail as possible.
Please provide both applications ... | 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 provide little or no commentary.
... | {
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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... | To your 3. question:
*
*QM in Hilbert Space formulation
*QM in $C^*$-algebra formulation
*QM in lattice formulation (compare Blank, Exner Hilbert space operators in quantum physics Ch. 13)
*Approach to QM using deformation quantization
| {
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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... | The analysis of Lorentz violations is found in Coleman and Glashow's "High Energy Tests of Lorentz Invariance": http://arxiv.org/abs/hep-ph/9812418 .
The discreteness leads to Lorentz-violation arguments turn out to be bogus in light of holography (in this I believe I completely agree with t'Hooft), they assume that th... | {
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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... | Here, they are looking for self capacitance. Self capacitance is basically the charge divided by potential of a conductor. One way to look at is is that the conductor is one plate of a capacitor with the second plate at infinity(or wherever your datum for 0 potential is) . From this, we can easily see that capacitance ... | {
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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... | Each particle that makes up a mechanical system, can be located by three independent variables labelling a point in space.
You can choose any particle in the rigid body to start with and move it any where you want, giving three independent variables needed to specify its location.
Choosing a second particle, you choo... | {
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Conservation of Energy and the Poynting Theorem Conservation of energy in an electrical circuit can be expressed by Ampere's law $$\nabla \times \textbf{B} = \mu_o
\textbf{J} + \epsilon_o \mu_o \frac {\partial \textbf{E}} {\partial t}$$ when both sides of the equation are dotted with $\textbf{E}$ and the input pow... | It is not an answer, but more a hint. From school I remember the simple problem which forces to accept the concept of a Poynting vector. If one considers two charged particles moving in perpendicular directions and write energy/momentum conservation for this system, the solution will contain Poynting vector explicitly.... | {
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Would a metal enclosure (such as a shipping container) protect its contents from the effects an electromagnetic pulse? I was watching a program about disaster preparedness, and it was suggested that the metal enclosure of a common shipping container (of the intermodal variety) would be sufficient to protect its content... | Looks like a metal enclosure would be OK, provided its seams and joints are electromagnetically closed , see http://www.wbdg.org/ccb/FEDMIL/std188_125_1.pdf , however, I am not sure this requirement is satisfied in off-the-shelf containers, so some extra electromagnetic hardening of seams and joints may be required.
| {
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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 ... | The simplest explanation I know of requires only one test charge and two reference frames with a relative velocity between them.
Frame 1: The charge is at rest. It is the source of a (purely) electric field.
Frame 2: The charge is moving. It is a current, and the source of a magnetic field.
| {
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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... | And what stops the second balloon rising to the height at which it bursts?
High altitude weather balloons are only partly inflated at launch, they rise until the outside pressure is low enough that they pop, or they have vents that release gas to maintain pressure. The life is normally set by the power to the instrume... | {
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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?)
| TL;DR: The frequency of a light wave does not change from medium to medium while the speed of light (and thus wavelength) does. By knowing the frequency of an EM wave you know it's color in any medium.
Building on prior answers, the facts are: Color is determined by the energy of the EM Wave that reaches your eyeball... | {
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Reduction of a sum to the first Brillouin zone in a band structure calculation this might be a "standard trick" for many solid state physicists,
however it's one that I'm not familiar with so maybe you can help me.
Here's the Problem:
Suppose we're given a Hamiltonian of the form
$H=\sum_{k} \epsilon_{k} c^{\dagger}... | The terms don't disappear--- they are the same as previous terms when you shift the dummy summation variable $k\rightarrow k+Q$.
| {
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How to calculate the charge and the potential across a charged capacitor charging an uncharged capacitor? Initially, there is a single capacitor $A$ attached to a power source that charges it to a certain voltage $V$. Once it is charged, it is instantaneously removed and placed in a circuit with an uncharged capacitor... | Your approach is not correct.
Once you connect the two capacitors what happens is that the plates that are connected with a wire will have the same potential because they form a conductor. Suppose the initial charges are $Q_{1i}=Q$ and $Q_{2i}=0$. Because the potential difference across both capacitors is equal you ge... | {
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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 ... | It is a fictitious force owing to the fact that the key is not in an inertial reference frame, but is in fact in circular motion (it is under tension by string to the car which is in circular motion relative to the ground)
| {
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Can we determine the force an object exerts by its mass and acceleration? I understand that the objects acceleration is determined by the force exerted on it, and that the force exerted on it is determined by its acceleration.
But, does an object's (named A) acceleration (and mass) tell us anything about how much forc... | No, in general it will not. The acceleration and mass tell you only the total (net) force being exerted on object A at that moment. That is equivalent to the total force object A is exerting on all other objects (B, C, etc.) it is interacting with at that moment. However, the mass and acceleration do not tell you anyth... | {
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Why do electron and proton have the same but opposite electric charge? What is the explanation between equality of proton and electron charges (up to a sign)? This is connected to the gauge invariance and renormalization of charge is connected to the renormalization of photon field, but is this explanation enough? Do w... | On the level of QED and above, the equality of the charges has no theoretical explanation. But it is extremely well established experimentally, as even small deviations would add up to huge amounts of electricity in bulk matter.
On the level of the standard model, the value of the charges of the up and down quark comes... | {
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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... | From a fundamental (i.e., statistical mechanics) point of view, the physically relevant parameter is coldness = inverse temperature $\beta=1/k_BT$. This changes continuously. If it passes from a positive value through zero to a negative value, the temperature changes from very large positive to infinite (with indefinit... | {
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Decomposition of SU(N) adjoint representation under SU(2) I am having trouble in demonstrating that under SU(2) transformations the adjoint representation of SU(N) transforms as one spin 1, 2(N-2) spin $\frac12$ and singlets. I am trying to demonstrate it from $N \otimes \bar{N} = 1 + A$ where $A$ is the adjoint repres... | Write things out more carefully. Under the decomposition $\mathfrak{su}(N) \rightarrow \mathfrak{su}(2)$, you decompose the $\mathfrak{su}(N)$ vector representation into
$$
N \to \tfrac{1}{2} \oplus 0^{\oplus(N-2)}\,.
$$
Then,
$$
N \otimes \bar{N} \rightarrow (\tfrac{1}{2} \oplus 0^{\oplus(N-2)})^{\otimes 2} = 1 \o... | {
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Is putting a charged balloon up to a neutral wall polarization AND temporary induction, or just polarization? Is putting a balloon that is charged up against a wall and having it stick polarization AND charging by temporary induction, or just polarization?
| It's just polarization. Inductive charging requires at least three objects two of which must be conductive. The two conductive objects can be charged by induction by first inducing a difference in charge between them with the third object. This is only possible if charges can flow between the two conductive objects. Th... | {
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What's the difference between “evidence of a new particle” and “discovery of a new particle”? Today’s exciting press release from Tevatron on the Higgs boson keeps its head cool and say that physicists saw a “hint” of the Higgs boson because the signal is barely above the two-sigma level. In an effort to explain the re... | Evidence and Discovery are both meant in a probabilistic way. Although physics is commonly known as an "exact" science, you always have uncertainty in your measurements due to human errors and/or the measurements precision. Having said that, physicists in this area have ARBITRARILY chosen to accept a new discovery if a... | {
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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.
| Broadly fermions are associated with matter, and bosons are associated with exchange (force mediation), at least if we are considering elementary particles. A given matter particle will produce and absorb many many exchange particles in its lifetime, so we can guess that there are more bosons than fermions.
It is not, ... | {
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Lorentz invariance of the 3 + 1 decomposition of spacetime Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example
$$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$
($N$ is called lapse, $N_a$ is the shift vector and $q_{ab}$ is the spatial part of the metri... | As I understand it, you're right that splitting the metric into spatial and temporal parts does break the Lorentz symmetry of the metric. When you define a lapse function and shift vector, you start by foliating spacetime into a bunch of spacelike "slices," and these slices can be used to identify a particular referenc... | {
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Resistor circuit that isn't parallel or series What's the equivalent resistance in this circuit (between points A and B)?
| Following on from A Googler's comment to Carl Brannen's answer:
But I think $R_1x_1=R_4x_4−R_3$ and $R_5x_5=R_2x_2−R_3.$ What I'm doing wrong? Please explain
If you follow this correction through, (ie. swap your subscript 1's and 4's, and 2's and 5's in your opening horizontal consideration - the vertical statements ... | {
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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... | This is in addition to @JohnRennie's excellent answer. First thing, the "more this less that" depends upon if the motor is being operated under constant voltage or current. I'm talking about torque only, RPM will increase if torque increases generally, but other friction forces and self-induction make it a headache to ... | {
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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... | The rainbow formed by caustics, which are concentrated rays. This is why only portion of water drops reflect light to the given observer.
http://en.wikipedia.org/wiki/Caustic_%28optics%29
| {
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Faster-than-$c$ photons As far as I know, according to quantum field theory, there are some photons that go faster than c, which is the speed of light in vacuum.
However, there seems to be a paper and a corresponding experiment that show every photon obeys the speed limit of $c$. (http://physics.aps.org/synopsis-for/1... |
As far as I know, according to quantum field theory, there are some photons that go faster than c, which is the speed of light in vacuum.
No, this is not correct. Photons always travel at $c$. This is an accepted fact throughout the physics community, and it is based on many different experiments.
Regardless of the... | {
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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... | I don't know much about this, but I know one thing:
Lower frequences carry easier over distance than higher frequences. Specially if there are physical obstackles in between, which will stop/dampen high frequences, but not low frequences.
So 'far away' will often have less sharp and high pitches, and low pitches will s... | {
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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... | A neutron star is mostly neutrons, but it contains protons to a certain extent allowed by the gravity, since a pure neutron state is unstable to beta decay. The protons collect on the surface due to their electrostatic repulsion, and form a fermi-gas like state there.
The fermi-gas of protons will reflect long-waveleng... | {
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Generators of the lorentz group I have the following minus sign problem:
Consider an infinitesimal Lorentz transformation for which $\Lambda^{\mu}_{\nu}=\delta^{\mu}_{\nu}+\lambda^{\mu}_{\nu}$, where $\lambda^{\mu}_{\nu}$ is infinitesimal small. Define the vector fields $M_{\mu\nu}=x_{\mu}\partial_{\nu}-x_{\nu}\partia... | You get a sign ambiguity because of your notation, as you simplify both ${\lambda^\mu}_\nu$ and ${\lambda_\nu}^\mu$ (which differ by a sign) to the same symbol $\lambda_\nu^\mu$.
| {
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AdS/CFT correspondence and M-theory Three questions:
*
*What can be some applications of AdS/CFT correspondence on M-theory? For example, would it be possible to represent 11-dimensional world using 10-dimensional surface?
*It seems that using AdS/CFT correspondence, we can project our world as being 100-dimensiona... | Something obvious to me is that this relation, so-called ADS/CFT, is not a fundamental concept, and at smaller scales (Planck scale) this correspondence doesn't apply anymore. I can firmly say all or almost all fundamental and important questions of quantum gravity remained unsolved within this framework. On the other... | {
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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... | Introducing magnetic charge into Maxwell equations is not a problem at all, and it does not require any strings etc. Moreover, it makes Maxwell equations symmetric w.r.t. magnetic and electric fields/charges. The equations are as follows:
\begin{split}
\mathop{\mathrm{curl}} E + \frac{\partial H}{\partial t} &= -J_m \\... | {
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Moment of inertia of a coin I have a a coin infinitely thin, rotating along the diameter.
How to derive the formula for it's moment of inertia passing through the diameter.
I was suggested to use the surface density and infinitely small part of the surface area, equidistant from the axis of rotation (marked as $dS$ on ... | You need to specify the integral to your coordinate system of choice and the problem at hand. This will involve explicitly writing out the infinitesimals for each of the coordinates to figure out the exact form of the integrand, as well as setting the integration limits to completely cover the body.
What does the infi... | {
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"url": "https://physics.stackexchange.com/questions/23086",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
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How does matter transform into energy and vice versa? In what ways can energy transform into matter and vice versa? Annihilation is one way to tranform matter to energy. Fission is another (when splitting and atom, what happens to its two parts?)
Are quantum fluctuations one way to transform energy to matter?
| One cannot obtain "clean" energy which is completely free off momentum, and cannot obtain "clean" matter which is free off momentum and potential energy.
So question is ill-posed, there is no "clean" states which can be described as "energy into matter". That just cannot happen.
When we consider reactions of elementary... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23154",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 7,
"answer_id": 6
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Maximum range of a projectile (launched from an elevation)
If a projectile is launched at a speed $u$ from a height $H$ above the horizontal axis, $g$ is the acceleration due to gravity, and air resistance is ignored, its trajectory is
$$y=H+x \tan θ-x^2\frac g{2u^2}\left(1+\tan ^2\theta\right),$$
and its maximum rang... | Adapting concepts from the question and solutions here, we have
$$R_\text{max}=\frac {uw}g=\color{red}{\frac ug\sqrt{u^2+2gH}}$$
and
$$\tan\theta^*=\frac {\ell-H}{\sqrt{\ell^2-H^2}}
=\frac {\frac {u^2}g}{\frac ug \sqrt{u^2+2gH}}=\color{red}{\frac u{\sqrt{u^2+2gH}}}$$
where $\ell$ is the linear distance between the laun... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23186",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 1
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Conservation of Energy and Momentum Regarding Forces - clarification needed The other day, my teacher stated something along the lines of, "Conservation of momentum is not violated by the actions of internal forces, but the conservation of energy is violated. Energy is conserved only when/if internal forces are conserv... | Energy is always conserved if the system considered is closed. So, depending upon the reference considered you can state whether energy is conserved or not relative to that reference.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23231",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 2
} |
How fast is heat transferred by conduction? How fast is heat transferred by conduction? Is there some simple, but quantitative way that starts from some properties of the material (e.g. its thermal conductivity) and makes rough predictions, for example about how much time is needed for temperature to change at one end ... | One can easily estimate the time of reaching a steady state. If you have a layer of a certain thickness and you know the thermal properties of the material, the problem is solved in any textbook on heat conduction. The temperature at the other end varies with time and the final stage is very simple (called a regular re... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23316",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
light ray 'entropy' Is there something like an entropy law for light rays?
I came up with the following experiment: A black box has two circular holes in it, a small and a large one. I don't care about there placement. Now I like to build something into the box that any ray entering the large hole will exit the box t... | (I'm copy-pasting from @user2963's comment into this community wiki.)
There is indeed, excellent intuition! This is called conservation of
etendue. en.wikipedia.org/wiki/Etendue
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23383",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 1,
"answer_id": 0
} |
Subjectivity of decoherence I read that quantum decoherence is subjective, in the sense that two observers may not have the same "environment" and after each one has traced over those degrees of freedom they will end up with a different density matrix for the couple system-apparatus.
I kind of understand the idea, but... | There are two observers and one qubit in the state $| 0 \rangle$ (known to both of them).
Then the qubit is randomly with equal probabilities either intact $U=\mathbb{I}$ or reversed $U=\sigma_x$ (i.e. $| 0 \rangle \mapsto | 1 \rangle$), but only the first observer knowns which action was applied.
Consequently, the fir... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23428",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
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Which ferromagnetic material has the lowest Curie temperature? It is hard to search for materials by their properties in general and I am trying to find a material with a very low Curie temperature. At the moment I am browsing different sites but can only find a number of 'normal' ferromagnetic materials but few with a... | Here is a data sheet for Inconel 625 which claims a curie point of -196C / -320F it is available in powder form, starting with it a metallurgist might be able to add Ni or Fe to get whatever curie point they wanted -- nota bene: the literature indicates that if the alloy is quenched or annealed, makes a big difference.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23512",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 3
} |
How does Newton's 2-prism experiment help to explain why light does not get dispersed into 7-colors in a parallel glass slab?
In a real parallel glass slide(with two prisms imagined to be touching each other to form a parallel glass slide),
The ray of light should pass through the Z in between without any dispersion o... | Whenever light rays of different colors emerge from a refracting surface parallel to each other, they mix up to form white light. When they're not parallel to each other, such as after refraction from a single prism, they remain separate and we see seven different colors.
After the second prism refraction, the light r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23667",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Autocorrelation Functions <---> Pair Correlation Functions Are there any ways to convert an autocorrelation function to a pair correlation function, and vice versa?
| You define the density auto-correlation function as
$$S_{\rho\rho} = \langle \delta \rho(\mathbf{x}_1) \delta \rho(\mathbf{x}_2)\rangle$$
where $\delta \rho(\mathbf{x}) = \rho(\mathbf{x}) - \langle \rho(\mathbf{x}) \rangle$ is deviation from the local mean value.
The Fourier transform of $S_{\rho\rho}$ is related to t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23719",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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} |
How do you calculate instantaneous velocity in projectile motion?
An object is thrown horizontally with a velocity of 30 m/s from the top of a tower. It undergoes a constant downward acceleration of 10 m/s2. The magnitude of its instantaneous velocity after 4.0 sec, in meters per second, is:
To approach this question... | In $y$ direction you have accelerated movement with constant acceleration, thus
$$v_y = v_{y0} - g t$$
and after putting initial conditions
$$|v_y| = g t$$
I have no idea whatsoever what did you want to do with your calculation.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23806",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why there is a $180^{\circ}$ phase shift for a transverse wave and no phase shift for a longitudinal waves upon reflection from a rigid wall? Why is it that when a transverse wave is reflected from a 'rigid' surface, it undergoes a phase change of $\pi$ radians, whereas when a longitudinal wave is reflected from a rigi... | Great question!
You might have learned that the amplitude of compression and the amplitude of particle displacements are not synonymous. In fact, the maximum amplitude of pressure and the maximum amplitude of particle displacements are out of phase for $\pi/2$. And twice $\pi/2$ (one for original, and one for the ref... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23847",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 3,
"answer_id": 0
} |
Equations instead of psychrometric charts I want to create a program that will accurately simulate a condensor. I want to use the data in psychrometric charts. But I cannot and hence want to use equations that show similar data. Any idea where to start?
| Data in the psychrometric charts are essentially experimental. If you want to do approximate calculations, you can do the following:
For saturated vapor pressure (100% humidity line) you can use one of many approximate functions:
*
*http://en.wikipedia.org/wiki/Vapour_pressure_of_water
*http://en.wikipedia.org/wi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23917",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Why is glass a good conductor of heat? AFAIK Glass is insulator, it doesn't have free electron. It's said metal is a good conductor of heat because it has free electron, glass doesn't have free electron, why it is a good conductor of heat?
| Glass is a very poor heat conductor. It has one of the lowest possible heat conduction a solid (without air trapped in it) can possibly have, this is mostly due to its lack of ordered crystal structure. Since it's an insulator, the electronic contribution to the thermal conductivity is very small. However phonons can s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/23946",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
} |
Reference paper to support information -- energy relation $\left(kT \ln2 \rm\frac{J}{bit}\right)\;.$ In answer to Maxwell's Demon Constant (Information-Energy equivalence) there is stated that one bit of information allows to perform $kT \cdot \ln2$ Joules of work. Which paper supports the thesis? (there are many publi... | See e.g. page 3 of
http://arxiv.org/abs/0707.3400
It's nonsensical to attribute this simple particular insight to a "discoverer"; all these considerations should be associated with Ludwig Boltzmann who knew the answer even though the information in physics was considered continuous at that time.
One may easily deri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24006",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Why is there a 90˚ phase angle between particle velocity and sound pressure in spherical waves? My text says that in a plane sound wave (or in the far field), particle velocity and pressure is in phase. As we move closer to the sound source (to near field and more spherical waves), the phase angle between these two qua... | Remembering back to my undergrad days, and courtesy of a quick Google: if you define the acoustic potential $\phi$ by:
$$u = - \nabla \phi$$
then the pressure is:
$$p = \rho \frac{\partial\phi}{\partial t}$$
For a plane wave in one dimension the wave equation is:
$$\frac{\partial^2\phi}{\partial x^2} = \frac{1}{c^2} \f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24091",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
} |
Entanglement spectrum What does it mean by the entanglement spectrum of a quantum system? A brief introduction and a few key references would be appreciated.
| For any equilibrium density matrix, we can recover the Hamiltonian if we know the temperature: $$\beta H = - \log \rho.$$ The motivation is what happens if we get $\rho$ by taking a sub-system (tracing over the rest)? In that case, we can still make up a Hamiltonian --- and the entanglement spectrum simply refers to th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24245",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
"answer_count": 3,
"answer_id": 0
} |
Do black holes play a role in quantum decoherence? Sorry for such a vague question but I could have sworn I read somewhere that Hawking proposed the reason we might see a classically appearing universe is due to the possible role of black holes in quantum decoherence. Is there such an idea by him or another physicist? ... | The idea that virtual quantum gravity will cause fundamental decoherence is due to Penrose, Hawking, and many other GR people in the 1960s. It was inspired by the idea that black holes can link up to other branches of GR solutions, and this behavior suggested that perhaps a new universe is created in the process of sin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24354",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
} |
What areas of physics should a mathematician study to understand TQFT? I am studying topological quantum field theory from the view point of mathematics (axiomatic treatise). So it has no explanation about physics. I would like to know physic background of TQFT. But I have only taken several basic physics classes when ... | One book that I liked was Zee's "Quantum Field Theory In A Nutshell". It's written in a fairly informal manner (well, for a textbook anyway) and assumes that you know a decent amount of mathematics. It's also not an introductory-level quantum book, and it assumes that you've had at least one course in quantum mechanics... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24453",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 3,
"answer_id": 2
} |
What is a fluid flux? I need a concise definition of a fluid flux and an accompanying example. I've never taken a single physics course before, but I'm required to understand this concept so I can do the calculations for a Complex Analysis class.
| The flux through a surface is the amount of fluid that crosses the surface in a flow per unit time at any one instant. If the velocity field is $v(x)$, and the surface is S, it is the integral over the surface
$$\int_S v \cdot n $$
where n is the normal to the surface. This is the general definition of flux of a vector... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24526",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Kerr-Newman black holes and infinite charge Recall the first law of BH thermodynamics
$ dM=\frac{\kappa}{8\pi} dA + \Omega dJ + \Phi dQ $
Now, let's consider the Reissner-Nordstrom solution $J=0$ such that $m>Q$ but only slightly greater. Suppose I have a small bit of charge $dQ$ which I bring in from infinity to the B... | This is the "third law" of Black hole thermodynamics. I put third law in quotes, because it isn't the statement that the entropy vanishes at zero temperature, but the original statement that the specific heats become tiny at zero temperature, so that the zero temperature state is unacheivable.
The extremal limit is per... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24593",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
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Solving Poisson-Boltzmann equation for flat surface without excess salt I'm trying to understand the solution of Poisson-Boltzmann (PB) equation as I read it in a review. The surface is uniformly charged and flat. I am only considering the $x$ direction.
The PB equation under these conditions is
$$\frac{\partial ^2 \ps... | I will use the notation of the review that you cite.
We want to solve the Poisson-Boltzmann (PB) equation for the case of a uniformly charged flat membrane of surface charge density $\sigma$ located at $z=0$. Also we want to consider the case of monovalent ions in the solution with no added electrolyte. We thus want to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24635",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Possibility for radiation in dark matter that is not interactive with regular matter? Definition: Radiation in this case does not refer to electromagnetic radiation. It refers to any kind of emission of energy, even energy that does not interact with regular matter.
Just like dark matter does not interact with electro... | In order to address the question :
Just like dark matter does not interact with electromagnetic radiation, could regular matter not interact with "dark matter radiation" (I'm not talking about the usual "really high wavelength radiation" kind)?
One needs experimental evidence, as @dmckee 's comment suggests.
The oth... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24793",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 1
} |
Which is the strongest meteor shower expected in the next years in the Northern hemisphere? Which is the strongest meteor shower expected in the next years in the Northern hemisphere?
Is it possible to give good predictions for this?
| The Perseids in early August is the most reliable shower year in, year out, and the only one I bother watching. The Geminids in early December are also good, but it's too darned cold up here in Canada. I see sporadic meteors just about every night I'm out observing.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24859",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 3,
"answer_id": 1
} |
What do the colors in false color images represent? Every kid who first looks into a telescope is shocked to see that everything's black and white. The pretty colors, like those in this picture of the Sleeping Beauty Galaxy (M64), are missing:
The person running the telescope will explain to them that the color they ... | Astronomers sometimes show objects, such as the Moon and Mercury in their true colors, but, since the color variations are subtle, they enhance the saturation of the colors to show differences more clearly.
Earth scientists often use a special false color palette for observations; the filters are infrared, red, and gre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24895",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 5,
"answer_id": 2
} |
What makes a good set of binoculars? After trying a bunch of binoculars at Star Parties and the like, I have a pretty good feel for about what aperture and magnification I'd like in a new set binoculars. I'm an eyeglass wearer so a long eye relief would be nice, but what else should I be looking for in a good set of bi... | Aside from the factors you've mentioned, nearly all binoculars you consider will be equivalent in terms of optics. Given that, you'll want to look for durability and comfort.
I'm not sure how common roof-prism binoculars are, but you'll probably want to avoid these for stargazing. Roof-prism binoculars have the objecti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/24984",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 2,
"answer_id": 1
} |
How large is the universe? We know that the age of the universe (or, at least the time since the Big Bang) is roughly 13.75 billion years. I have heard that the size of the universe is much larger than what we can see, in other words, much larger than the observable universe. Is this true? Why would this not conflict w... | An snippet from the NASA page titled "How Big is Our Universe?":
No one knows if the universe is
infinitely large, or even if ours is
the only universe that exists. And
other parts of the universe, very far
away, might be quite different from
the universe closer to home. Future
NASA missions will continue ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25076",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 6,
"answer_id": 0
} |
Why are orbits elliptical? Almost all of the orbits of planets and other celestial bodies are elliptical, not circular.
Is this due to gravitational pull by other nearby massive bodies?
If this was the case a two body system should always have a circular orbit.
Is that true?
| Every circle is elliptical since no answer for PI has been or can fully be achieved. The elliptical model fits as well as any. When taking into consideration Higgs Boson and Dark matter and there possible inflection on string theory in the fabric of space with multiple universes, it is very possible that the distortion... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25110",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 9,
"answer_id": 7
} |
What is the current status of Pluto? Pluto has been designated a planet in our solar system for years (ever since it was discovered in the last century), but in 2006 it was demoted.
What caused this decision? And is there a chance that it could be reversed?
Edit: well, http://www.dailygalaxy.com/my_weblog/2017/03/nasas... | Pluto is now classified as a dwarf planet. The main difference between a planet and a dwarf planet has to do with the requirement that a planet clear out the material in and near its orbit. Planets do this, dwarf planets do not.
The reclassification was triggered by the discovery of many additional object (the Edgewo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 7,
"answer_id": 1
} |
Can any telescope be used for solar observing? Can any telescope, such as a 8" reflector, that is normally used at night to look at planets be used or adapted for solar observing?
What kind of adapters or filters are required or is it better to get a dedicated solar telescope?
I'd like to look at sunspots, flares, prom... | You may use mylar filters in front of the telescope, as other said. Another common way is to add a green glass filter at the entrance of the eyepiece (normally screwed in). This solution is normally shipped with the telescope, but I highly recommend against it. The reason is that the glass may crack due to the heat, wh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25198",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 8,
"answer_id": 5
} |
What open-source n-body codes are available and what are their features? I'm interested in doing simulations with large numbers of particles and need a good n-body code. Are there any out there in the public domain that are open-source and what are their strengths and weaknesses. I'm interested in all types of codes,... | http://www.supersci.org/Codes.php
Some of those are open source and some not. You'll have to do some googling to get to the useful information, but it's somewhere to start, at least.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25241",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 3,
"answer_id": 0
} |
Video of Earth spinning? If the Earth is spinning or rotating at a really fast speed, why haven't we seen any videos from space of it spinning when we get a lot of photos of it?
| Well it is quite expensive to go into space and so taking a video camera for some holiday snaps is not exactly a high priority.
However weather sattelites do exactly this with images of cloud formations and movements. Obviously these aren't typically very glamorous so rarely make into the public domain.
However they d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25278",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 5,
"answer_id": 1
} |
What's the best way to start out with astrophotography on a tight budget? I'm new to astronomy and I don't have a great deal of cash to spend. I currently have a 3" reflector telescope which I've had great fun with. I also have a Pentax DSLR which I've been using to take long exposure photos of various constellations... | If you already have a DSLR then a T-mount is pretty cheap and will give you steadier photos. The first issue you may hit is that you can only do short exposures unless you have a motorized mount.
I use a lens mount adapter on my Pentax K-x to attach a 1.25" barlow (http://www.amazon.com/gp/product/B00009X3UV/) and i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/25319",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 0
} |
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