Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How is a Higgs boson created? I have read a lot on Higgs bosons, yet I do not fully comprehend how they are created and how they are "flicked off" the Higgs field. I have also had trouble comprehending why a Higgs boson quickly becomes unstable and decays into more common particles.
How is a Higgs boson created and how... | A higgs boson is created at an accelerator just like any other particle, by converting energy to mass, according to the famous equation
$$E = mc^2$$
If you take the LHC as example, then protons are accelerated to nearly light speed, having enough energy to create particles as heavy as the higgs.
For a particle to decay... | {
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Why does $\ell=0$ correspond to spherically symmetric solutions for the spherical harmonics? In quantum mechanics why do states with $\ell=0$ in the Hydrogen atom correspond to spherically symmetric spherical harmonics?
| One way to understand it is to recognize that for the spherical harmonic $|l,m\rangle$ with $l=0$ (and obviously $m=0$), we have $\hat L_i|0,0\rangle=0$, where $\hat L_i$ is the angular momentum operator in the direction $i=x,y,z$. It is obvious for $\hat L_z$, which eigenvalue is $m=0$, and can be verified for the oth... | {
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Braiding statistics of anyons from a Non-Abelian Chern-Simon theory Given a 2+1D Abelian K matrix Chern-Simon theory (with multiplet of internal gauge field $a_I$) partition function:
$$
Z=\exp\left[i\int\big( \frac{1}{4\pi} K_{IJ} a_I \wedge d a_J + a \wedge * j(\ell_m)+ a \wedge * j(\ell_n)\big)\right]
$$
with anyons... | How to obtain this braiding matrix from Non-Abelian Chern-Simon theory?
To obtain braiding matrix $U^{ab}$ for particle $a$ and $b$, we first need to know the dimension of the matrix. However, the dimension of the matrix for Non-Abelian Chern-Simon theory is NOT determined by $a$ and $b$ alone. Say if we put four parti... | {
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Wave function of a particle in a gravitational field
Suppose we have a particle with mass $m$ and energy $E$ in a gravitational field $V(z)=-mgz$. How can I find the wave function $\psi(z)$?
It should have an integral form on $dp$. Any help would be appreciated.
What I've tried
One way to solve the problem is use of... | $$
\left[\frac{p^2}{2m}+V(i\hbar\frac{d}{dp})\right]\phi(p)=E\phi(p)
$$
$$
\left[\frac{p^2}{2m}+(-mg)(i\hbar\frac{d}{dp})\right]\phi(p)=E\phi(p)
$$
$$
\frac{1}{i\hbar mg}(\frac{p^2}{2m}-E)\phi(p)=\frac{\phi(p)}{dp}
$$
When integrate we have:
$$
\frac{i}{\hbar mg}(Ep-\frac{p^3}{6m})=Ln\frac{\phi(p)}{\phi(p_{o})}
$$
$$
\... | {
"language": "en",
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When is quasiparticle same as elementary excitation, and when is not? Can anyone shed light on the comparison between these two concepts?
| Dictionary for this answer: Excitation = particle; collective excitation = quasi-particle.
Short answer:
Elementary particles are never quasi-particles, by definition of elementary. This does not mean that what now it is thought as an elementary particle could be a quasi-particle of entities to be discovered.
Mathema... | {
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Does velocity or acceleration cause time dilation? What causes time dilation? Acceleration or velocity?
I've seen multiple comments on this forum that assert velocity is the cause, but that doesn't seem right to me. You can't have velocity without acceleration. It's the inertial force with acceleration that breaks t... | In Special Relativity the time dilation is just a matter of convention in the time measurement between moving frames.
In General Relativity the time dilation is a physical phenomenon which involves a force field (either gravity or acceleration or wathever) that actually slows down the particles of a system. When partic... | {
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1 Tesla electromagnet? Is it possible to create a powerful electromagnet at home?
With use of a ferromagnet it seems so...
Using the following formula: $B(Tesla)= k\mu_0nI$. I understand some ferromagnet's like iron could have permeability above 10,000? That would easily boost the field above a 1 Telsa?
Relative perme... | Let:
*
*$R$: The radius of the coil, $h$ the height of the coil, $n$: spiral density, ie, the number of spirals per height.
*$r$: The radius of the wire, $A$: The area of the cross section of the wire.
*$L$: The total size of the wiring, $N$: The amount of spirals in the coil.
*$\bar R$: The overall resistance of... | {
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How to smooth the spectrum of a light source? Could somebody please tell me if there's a reasonably cheap substance or device can I use to smooth the spectrum of a light source?
For example, if the spectrum has spikes as in the blue graph below, is it possible to smear in terms of wavelength (not spatially, as in ordin... | The phosphors lining the glass tube of a fluorescent light do a pretty good job of smearing the atomic mercury line emission spectrum into something closer to black body radiation. There could be a phosphor mix that accomplishes what you want...
| {
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What gives an object its colour? My understanding of colour is that atoms in a particular object will absorb certain wavelengths of electromagnetic radiation, and the scattered wavelengths give the object its colour. The absorbed wavelengths contribute to lattice vibrations, increasing the kinetic energy and raising th... | In Bunsen burner atoms get heated up which means they absorb energy, and go to some excited states (or even get ionized). And then they de-excite in any way they can which means radiative decay is dominant, as there is almost no other way to dissipate energy. There is no crystal lattice, and compared to luminescence ra... | {
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Work in circular motions Suppose that a satellite circles around a planet that exerts $2000N$ of gravitational force on the satellite.
I understand the fact that since the circular motion and the centripetal force are always perpendicular to each other, the work done by gravity is 0.
However, the satellite is being m... | Centripetal force is always directed towards the center of the circular path and always directed perpendicular to the direction of displacement of particle every where on the circular path.
Therefore angle between centripetal force F and displacement S is 90deg.
Work W= F.S
$$W=FS \cos (\theta)=FS \cos90 = FS\times0... | {
"language": "en",
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How to calculate velocities after collision? I'm currently writing a program for a particle simulator. One of the requirements is that the particles collide in a realistic way. However, I don't know how to calculate the final velocities.
For each collision, I have the $x$-component and $y$-component of each velocity, a... | 2 dimensional collision can be reduced to a 1-dimensional problem in the case of spheres--see here. The $\pm$ you encounter when solving the kinetic energy is likely because there are two solutions and the equations are satisfied by either one. One solution is simply where the particles pass right through eachother, wh... | {
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Is it possible for bubbles to exist in vacuum? In the case of a bubble, the outside pressure is less then the inside pressure.
If that is the case can bubbles exist in vacuum? I am not sure but this should be true if vacuum has zero pressure
| I disagree. If it's a true vacuum then it can't exist. The pressure equilibrium both inside and outside will be zero, thus the surface tension would collapse it into a "drop" rather than a bubble, as there's no internal pressure to hold it expanded.
Were air to be added inside however, then things would get weird. S... | {
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Is it possible to focus the sun in such way?
Imagine the sliding part of the mirror is controlled by computer and opens on intervals.
Is it possible to increase the power of the beam by making it bounce between the mirrors thus going through the lens and then releasing it resulting in beam with more power ?
| Fun fact: You cannot focus the beams from the sun create a hotter area than the surface of the sun itself. This would break the second law of thermodynamics. 6000 °C is hot enough for many spectacular destructive applications, though, a youtube search on "melting steel with sun light" offers hours of entertainment.
If ... | {
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Is it possible to determine the universality class of phase transitions by just analysing symmetry? Since phase transition is closely connected with symmetry, I am wondering whether it is possible to determine the universality class of phase transitions just by symmetry?
Actually, I found it is quite boring to calcula... | At least for the case of the three "conventional" symmetry classes (Wigner-Dyson classes), the symmetry is directly visible in the structure of your Hamiltonian or, if you do numerics, in the matrix elements of your Hamiltonian matrix. For example, if your tight binding matrix contains only real matrix elements and is ... | {
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Holographic Image In a holography set-up, as shown in the figure below, Illumination beam and reference beam both are in phase. The interference pattern generated at the detector contains the whole information about the object. When illumination beam will incident on to the object its phase and amplitude will change ... | I would perhaps answer something like this. Maybe that question helps you also. You have to keep in your mind the proper meaning of whole information; the plate will just contain almost the same information as the one you get from the other side of a window placed there (thorugh it), being its size the same of the plat... | {
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What happens when a charged (negative or positive) object touches an insulator? I know that insulators do not conduct electricity because they do not allow the free movement of electrons. Let's assume the object that's going to touch the insulator is negatively charged. Does some charge get transferred to the the insul... | Well if you don't go into the micro details where the charged sphere may induce extremely low quantity of charge in the insulator before touching and then transfer equally less charge even on touching which would not even be practically noted, NO! There is no charge transfer.
Conceptually you can say the extremely high... | {
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Is it possible to "cook" pasta at room temperature with low enough pressure? It is known fact, that boiling point of water decreases by decreasing of pressure. So there is a pressure at which water boils at room temperature.
Would it be possible to cook e.g. pasta at room temperature in vacuum chamber with low enough p... | Pasta does not really need to be cooked. Instead, it needs to become hydrated. Pasta is just like a dry fruit. If you place it in water for a day or so, it will look at least like it has been cooked.
| {
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Wigner friend experiment Let's supposed we take the Wigner's friend experiment from the metaphysical arena and try to implement it as an actual physical experiment
Assuming Wigner's lab friend is kept as a coherent superposition of states until the external experimenter tries to open the decoherence-insulated lab door,... | As long as the external experimenter does not attempt to measure the phase of each of the arms - and indeed makes a measurement that does not 'touch' this information - he will observe no contradiction. In each of the definite outcomes of the cat experiment inside the lab, the experimenter inside the lab signals this d... | {
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General relativity in terms of differential forms Is there a formulation of general relativity in terms of differential forms instead of tensors with indices and sub-indices? If yes, where can I find it and what are the advantages of each method? If not, why is it not possible?
| Short answer.
Example: The Palatini action, where the action is a functional of a tetrad/vierbein $e$ and a spin connection $\omega$.
$$S(e, \omega) = \int \epsilon_{abcd} e^a \wedge e^b \wedge \Omega^{cd}$$
where $\Omega$ is the curvature associated to the connection form $\omega$:
$$\Omega = D\omega = d\omega + \omeg... | {
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Increase in Mass with Velocity I just had a confusion. Does the mass of the body actually increase when it is moving with a certain velocity? Or does it only look like the mass has increase to another observer. How can the actual mass of the body increase. Please correct me if I am wrong but I feel that it only seems t... | The inertia (resistance to acceleration) increases, and the object's tendency to curve space around it increases as it's velocity approaches the speed of light. But physicists have found it cumbersome to treat mass as a variable, or to keep saying "rest mass" all the time, so we say that the mass-proper stays the same.... | {
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How can space and time arise from nothing? Lawrence Krauss said this on an Australian Q&A programme.
"...when you apply quantum mechanics to gravity, space itself can arise from nothing as can time..."
Can you elaborate on this please?
It's hard to search for!
| The point is that spacetime can be emergent, i.e., you don't put it in by hand from the start, but it sort of pops out at you along the way.
Sometimes the dynamical degrees of freedom (the variables of the theory, if you like) can be different depending on how you describe the system. The best known example is string t... | {
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What exactly is a bound state and why does it have negative energy? Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)?
Why, when a stable bound state exists, the energies of the related station... | Mathematically, bound states are states that decay sufficiently fast at infinity, so that the probability of finding the particle they describe in far away regions of space is negligible.
It has long been conjectured, based on physical intuition, it is the case for the meaningful quantum mechanical states, such as the ... | {
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Meaning of the chemical potential for a boson gas My lecturer told me that $\mu$, the Chemical potential, is zero or negative, and in the following example, mathematically it acts as a normalization constant. But is there any physical insight about why boson gas can be zero or negative?
I think it is due to the fact th... | I think you can consider the zero chemical potential to be an effect of popping up of photon. Both chemical potential and the temperature appears as a undetermined multiplier due to conservation of energy and number of particle respectively. For photon, there is no conservation of particle number and hence the correspo... | {
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At what point is the spin determined in a Stern-Gerlach Apparatus Consider a particle with spin that travels through a Stern Gerlach box (SGB), which projects the particle’s spin onto one of the eigenstates in the $z$-direction. The SGB defines separate trajectories for the particles that travel through it depending on... | The spins are determined when they hit something (i.e. "decoher" by interacting with a macroscopic entity.). You can infer a trajectory for them that extends back to the beginnings of the inhomogeneous field.
| {
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If a Goldstone boson is an excitation moving between degenerate vacua, how do symmetries remain broken? In spontaneous symmetry breaking, moving around the circular valley of the Mexican hat potential doesn’t change the potential energy. These angular excitations are called Goldstone bosons. But doesn't the change of a... | The proposition that the symmetry G is spontaneously broken means that by acting by G on the vacuum configuration, we obtain an isomorphic but different configuration. For the symmetry to be unbroken, the transformations in G would have to map the vacuum configuration onto the same one, not just isomorphic one.
If you ... | {
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Why do high current conductors heat up a lot more than high voltage conductors? 120 volts x 20 amps = 2,400 Watts
However, if I increased the voltage and lowered the current, you can also use a smaller wire size (more inexpensive), also have less heat and achieve the same watt Power.
1,000 volts x 2.4 amps = 2,400 Wat... | *
*The point is that the wire ends are not exposed to a potential difference equal to the full voltage. The wire ends differ in potential only by a (small) voltage drop $\Delta V = R\,I$, where $R$ is the resistance of the wire. Dissipation power equals $P = I\,\Delta V = I^2 R = \frac{(\Delta V)^2}{R}$. Now suppose y... | {
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Does corrosion of iron increase its mass? Does corrosion of a sample of iron increases or decreases its mass? I think that the mass will increase because of additional oxygen atoms.
| The following reactions take place :
$O_2 + 4 e^− + 2 H_2O → 4 OH^−$
$Fe → Fe^{2+} + 2 e^-$
$4 Fe^{2+} + O_2 → 4 Fe^{3+} + 2 O^{2−}$
$Fe^{2+} + 2 H_2O ⇌ Fe(OH)_2 + 2 H^+$
$Fe^{3+} + 3 H_2O ⇌ Fe(OH)_3 + 3 H^+$
$Fe(OH)_2 ⇌ FeO + H_2O$
$Fe(OH)_3 ⇌ FeO(OH) + H_2O$
$2 FeO(OH) ⇌ Fe_2O_3 + H_2O$
(source : Wikipedia )
Now ... | {
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Which of these two different forms of spin-orbit interaction is correct? I am seeing the spin-orbit interaction in two different ways:
*
*$\lambda [\mathbf{p} \times \nabla V]\cdot \sigma$
*$\lambda [\nabla V \times \mathbf{p}]\cdot \sigma$
I don't see how these two expressions can be equivalent though; in (1) th... | Good question. In fact, you can check that $\triangledown V\times \mathbf{P}=-\mathbf{P}\times\triangledown V$. Here is the brief derivation:
$\mathbf{P}\times\triangledown V=(p_y\partial _zV-p_z\partial _yV,p_z\partial _xV-p_x\partial _zV,p_x\partial _yV-p_y\partial _xV)$. Let's take the first component $p_y\partial _... | {
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What is the intrinsic colour of the star? Hey I have this question and I am wrestling with it all day and I am completely lost.
The V magnitude of a star is 15.1, B-V =1.6, and absolute magnitude Mv= 1.3 The extinction in the direction of the star in the visual band is av = 1 mag/kpc. What is the intrinsic colour?
Can ... | A star's color has almost nothing to do with its visual magnitude. The color is a function of size, age, etc. per the OBAFGKMNS classification scale (roughly). The visual magnitude is a measure of the light intensity (in the visual spectrum) which reaches us on Earth, so it depends not only on the star's color but i... | {
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Non-locality and quanta Quantum mechanics is non-local in that long distance correlations are present, though there is no signalling possible. But QFT is Lorentz invariant and contains quantum mechanics as a special case. I assume this is not a paradox as paradoxes do not exist but I do not understand the details. Can ... | Quantum Mechanics is non-local because you are working with particles and interactions all occur instantaneously. This doesn't allow locality. Quantum Field Theory is a framework that instead of working with particles, works with fields. A field has values at each point in space and allows local interactions. However, ... | {
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Delta to Star/Y Conversions and vice versa in Electric Ciruits We all know the basic rules for conversion of $"Delta"$ circuits to $"Star"$ circuits and vice versa. We also know that this is needed for simplification of circuits in complex cases. Can anyone please explain HOW the concept of such conversions came about?... | The concept is a special case of a more general topological notion of graph theoretic duality: see the Wikipedia page for Dual Graph.
Graph theoretic duality is "compatible" with the Kirchoff voltage law (voltages around a loop sum to nought) and charge conservation (currents into a node sum to nought) insofar that no... | {
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The physical interpretation of Newton's constant $G$ It is well known that the speed of light $c$ can be interpreted as the speed limit for information propagation. Similarly, the Planck's constant $h$ is interpreted as the minimum quantum package of action/entropy. Is there a similar interpretation for the Newton's co... | I do not know of any such "limit" interpretation of $G$. The universal gravitational constant $G$ is defined by the Law of universal gravity:
Magnitude of the mutual attractive force two bodies exert on each other is given by
$$
F = G\frac{m_1 m_2}{r_{12}^2},
$$
where $m_1$, $m_2$ are masses of the two bodies and $r_{1... | {
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Recovering 4-vector Lorentz transformation from spinor formalism I'm trying to recover the 4-vector transformation laws using spinors. I have defined
$$v^{\dot{a}b} = v^{\nu} \sigma_{\nu}^{\dot{a}b}$$
as usual, with $\sigma_0=1$.
Now with the rules for dotted and undotted spinor indices i get the transformed v for a bo... | First thing is that you are missing the imaginary unit in the exponential. The correct transformation matrix should be
$$M=e^{i\frac{\theta}{2}}.$$
Up to this small misprint, the first expression you wrote actually gives the desired transformation of the components $v_1$ and $v_2$. If we do the computation
$$
\begin{al... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What form of energy is released in $E = mc^2$? In the famous mass energy equivalence $ E = mc^2$ whenever any form of mass, lets say mass defect in nuclear reactions or any other example of mass is converted to Energy, the released energy is in what form ? Heat ? Light ? Other ?
| See Can we make usable energy from subnuclear particles? for a related discussion. The energy is released both as the kinetic energy of the reaction products and as (usually gamma ray) photons.
| {
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Will density of a metal increases during forging? This question is metallurgical engineering, but I had a similar doubt regarding density of liquids and what causing it.
Forged parts refines defects, dislocations will be moved strengthening the metal. But will the density of forged metal change?
My earlier question was... | The answer is that in principle yes, the removal of defects will increase the density. The question is by how much.
You specifically ask about forging. The forging process doesn't remove dislocations but instead moves them until they become pinned, which is what causes the work hardening. Well, that's an oversimplifica... | {
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Does black hole formation contradict the Pauli exclusion principle? A star's collapse can be halted by the degeneracy pressure of electrons or neutrons due to the Pauli exclusion principle. In extreme relativistic conditions, a star will continue to collapse regardless of the degeneracy pressure to form a black hole. D... |
Does this violate the Pauli exclusion principle? If so, are theorists
ok with that?
The short answers are "yes" and "yes".
Recall that we are talking about what happens inside the event horizon ...
Perhaps the density of states diverges as volume decreases.
However iirc most thinking is around the idea that there ... | {
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Does a photon instantaneously gain $c$ speed when emitted from an electron? An excited electron loses energy in the form of radiation. The radiation constitutes photons which move at a speed $c$. But is the process of conversion of the energy of the electron into the kinetic energy of the photon instantaneous? Is there... | MC Physics would suggest that photons are formed from the joining of 2 opposite electro-static charged mono-charges that are emitted from particles or atoms due to excessive vibration. Those joined mono-charges are (almost) instantly accelerated to c by surrounding electric-magnetic forces then any excess force is appl... | {
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Minimum seperation between two Airy disks as a function of the distance between two point sources of coherent light passing through the same objective I have two coherent point sources of light, $A$ and $B$, separated by a distance $L$, which I focus down to the diffraction limit using a high-powered objective (e.g. a ... | Having spent rather a lot of years designing and building adaptive optic systems, I've seen this sort of problem in a number of guises.
Certainly you can apply some fitting function to the image of each of your spots separately and determine the centroid of each spot alone. If your detector has sufficient resolution, ... | {
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Efflux speed of ideal fluid dependent on diameter? I have a cylinder full of water with diameter $D$ with a round opening on the bottom with diameter $d$. The water is friction-free and incompressible. Now I need a relationship for the efflux speed $v$ with which water exits the cylinder and I shouldn't use the approxi... | While calculating velocity of efflux you use bernoulli's theorem as follows :
At the top of container :$ P + \frac{\rho {v_1}^2}{2} + \rho gh_1 = k$
At the efflux : $P_a + \frac{\rho {v_2}^2}{2} + \rho g h_2 = k$
$P - P_a + \rho g (h_1 - h_2) = \frac{\rho ({v_2}^2 -{v_1}^2)}{2} $
Now, in accordance with equation of ... | {
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Potential energy curve for intermolecular distance
(source: a-levelphysicstutor.com)
I'm trying to understand this curve better, but I can't quite figure out what "negative potential energy" means.
The graph should describe a molecule oscillating between $A$ and $B$, however where I'm stuck in reasoning this is that ... | Suppose that two molecules are at distance $B$ and have zero kinetic energy. There's a lower potential energy position in $C$ and therefore the molecules will attract.
They will convert $\epsilon$ potential energy into kinetic energy and reach $C$.
Now, the law of inertia states, and the fact that they have positive ki... | {
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During reflection does the emitted photon have same properties? When light (photon) is reflected the the original photon is absorbed by an electron and then emitted again. Does this "new" photon have the same wavelength, frequency etc. as the original?
| Like any quantum field you can approximate light as either a particle or a wave. However you need to be clear that both are just approximations to the true nature of light and like all approximations they work well in some circumstances and badly in others.
In this case the photon model is a poor way to describe the pr... | {
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How do I explain to a six year old why people on the other side of the Earth don't fall off? Today a friend's six year old sister asked me the question "why don't people on the other side of the earth fall off?". I tried to explain that the Earth is a huge sphere and there's a special force called "gravity" that tries ... | There's a good chance you won't be able to make her understand how it works.
According to developmental psychologist Jean Piaget, children at her age tend to see themselves as the "center of the world", and are incapable of reasoning about it from any other viewpoint. The process is called egocentrism, and is the same ... | {
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Dielectric constant of water I need the dielectric constant of water from $10^{-2}$ Hz to $10^4$ Hz. As stupid as it may seem, I cannot find much info. I've googled for days. All I can find is close to GHz. And the only info close to Hz, ($100$ Hz) shows a great variation. A relative dielectric constant at $100$ Hz of ... | There is some data in http://www.nist.gov/data/PDFfiles/jpcrd487.pdf (J. Phys. Chem. Ref. Data, vol. 24, No. 1, 1995, p. 33) See, e.g., Table 2 there. Looks like dielectric permittivity of water is about 78.
| {
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What is the 'resolution' of the reality in pixel terms?
*
*What resolution should a TV screen have so that its image were so faithful as reality as if the TV were a window?
*Also what would happen if Physics could reproduce a 'pixel' of the size $ l_{p}^{2} $ the square of the Planck length? Would be then this the r... | It is important to understand that Planck's theory of the existence of length which can be divided by zero is hotly disputed. Einstein famously said about this theory: 'madness is trying the same over and over again and expecting different results'. Theory of continuos space has never been disproven, it works in practi... | {
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Energy spectrum, mass spectrum, and mass gap In Arnold Neumaier's nice answer to this question:
The energy spectrum in quantum field theory
it is remarked that
'If there is a mass gap (i.e., if no representation of tiny positive mass exists), the states can be restricted to their rest frame, where the spatial momentum ... | The lack of a mass gap goes in all interesting cases together with the existence of a massless particle. These don't have a rest frame. See, e.g., the section ''What is the mass gap?'' in my theoretical physics FAQ at
http://arnold-neumaier.at/physfaq/physics-faq.html
| {
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How can the commutator operation not be transitive? I noticed the following:
$$[L_{+},L^2]=0,\qquad [L_{+},L_3]\neq 0,\qquad [L^2,L_3]=0.$$
This would suggest, that $L^2,L_+$ have a common system of eigenfunctions, and so do $L^2,L_3$, but $L_+,L_3$ don't. How is that possible?
| NOTE. Since $L_+$ is not normal (normal means $A^\dagger A = AA^\dagger$) it does not admit a basis of orthonormal eigenvectors. However your question can be safely restated replacing $L_+$ for $L_2$ and I will assume it henceforth.
The most elementary case of this phenomenon is given by a triple of normal matrices in... | {
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Can a mass matrix be asymmetric? I am developing a mathematical model of a mechanical device consisting basically of coupled harmonic oscillators. It turns out that the system mass matrix is asymmetric. I seem to read somewhere that a mass matrix has to be symmetric, but I am not sure. So I would like to know whether i... | Whenever the mass is expressed as a real matrix $M$, the mass term or something else that matters is a bilinear expression. For example, the effective mass in condensed matter physics is the mass matrix $M$ so that the kinetic term of the Hamiltonian is written as
$$ E_k = \frac{\hbar^2}{2m} \vec k \cdot M^{-1} \cdot \... | {
"language": "en",
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Why does ice form on bridges even if the temperature is above freezing? So with this "arctic blast" continuing, I've noticed that for my area, the temperature drops below freezing just long enough to cause freezing rain, but then the sun comes out and the temperature rises immediately. However, on bridges, ice continue... | The wind's "chill factor" is a surface area effect. In a bridge, the surface area exposed to the wind is at least twice as much as a comparable section of the road, so with the proper conditions, the bridge's surface will be colder than the freezing point while the road is above this point.
For example, assume the sti... | {
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light beams of the sun
We receive sunlight on earth surface. What type of light beams are these?
Random/Parallel/Converging/Diverging
I think it should be Diverging as Sun is radiating these beams away. But in one book, answer is given as Random, in another it's Parallel.
| It is difficult to answer this question. An EM wave is generated by vibrating charges and nuclear reactions. Sun is full of vibrating charges and nuclear fusions. Because of this full range of frequencies are emitted. At distances close to sun we observe the directions of waves to be random. But at far away distances t... | {
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How do photons 'connect' during wireless connection? So wireless router broadcasts a signal and then your device searches. So what actually happens when the photons 'meet' it's kind of like saying, 'ah your one of us, so we will follow you, show us the way'
It's so bizarre, how do photons connect during wireless connec... | In the sense of routers (transmitters and receivers) it is preferable to consider the wave-model for the electromagnetic field.
The router has an antenna that, due to how it is shaped and how the current running through it is modulated, creates an electromagnetic field that propagates depending on direction and constr... | {
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What is average life in radioactivity and what is its significance? By definition, average life of radioactive sample is the amount of time required for it to get decayed to 36.8% of its original amount.
But what is the significance of 36.8% and why has that value been chosen?
| When radioactive element A decays to produce element B, the (infinitesimal) number of decayed elements A, $dN$, that occurs in a small time interval, $dt$, is proportional to the initial population of A, $N$:
$$
-\frac{dN}{dt}\propto N
$$
Assuming the proportionality is a constant, then the above becomes
$$
-\frac{dN}{... | {
"language": "en",
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Idea of Covering Group
*
*$SU(2)$ is the covering group of $SO(3)$. What does it mean and does it have a physical consequence?
*I heard that this fact is related to the description of bosons and fermions. But how does it follow from the fact that $SU(2)$ is the double cover of $SO(3)$?
| I'd like to add to Josh's answer, because he didn't really explain what a universal covering group is. Essentially, a space $T$ is a covering space of another space $U$ if, for an open subset of $U$, there's a function $f$ that maps a union of disjoint open subsets of $T$ to the subset of $U$. Or, more simply worded, p... | {
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Why are temperatures generally hotter in the Middle East than in Europe? How come the average temperature in the middle east (Israel, Saudi Arabia, Sudan or lower) is always so much significantly higher than in Europe (say Germany, England etc.)?
I know that the sun rays pass a greater distance to Europe than the midd... | The distance of the Sun from Europe or the Middle East plays virtually no role. After all, many people on the Northern Hemisphere might be surprised that the Earth is closest to the Sun in January – it was on January 4th, 2014. It was 3 million miles or 3 percent closer than it is in July. Nevertheless, the winter is c... | {
"language": "en",
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is there any relation between resistance and magnetism? i was holding a resistance wire(insulated) coiled up and both of its ends were connected to a Ohm-meter it was showing 18 ohms while the circuit was on i pulled the coil from both ends and made that a straight wire with barely a knot in between and observed that t... | There are a few possibilities here, Wikipedia shows many types of ohmmeters but I am going to consider only two; 1. Constant voltage and current measurer, 2. Constant current and voltage measurer.
In your case as you stretch the wire two things happen :
1. Resistance increases as length is slightly increased and cross... | {
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Temperature: Why a Fundamental Quantity? Temperature is just an indication of a combined property of the masses of the molecules and their random motion. In principle, we can explain "no effective energy transfer between two conducting solid bodies in contact" via a condition in terms of the masses of the molecules and... | It is just a scale to get thermal equlibrium problems easily but defined in such a way that it can not be expressed only in the terms of the other fundamental quantities.So it is a fundamental quantity.
| {
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If the k of a wave is negative, is the wavelength negative too? My friend went to an interview for a reputed scholarship program and was asked this question.
A wave has an equation $a\sin(\omega t-kx)$.
Sometimes k surely can become -ve.
We know that $k=\frac{2\pi}{\lambda}$.
So $\lambda$ is -ve?
How can this be?
Wha... | Your equation for the wave is really a vector equation:
$$ \psi({\bf x}, t) = a \sin(\omega t - {\bf k . x}) $$
This tends to be glossed over when students are first taught the equation, and to be fair in 1D the dot product $\bf k.x$ is simply $kx$ or $-kx$ depending on whether $\bf k$ and $\bf x$ point in the same or ... | {
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Is tripleaxis planet possible? Imagine. Our solar system. Our sun. Then earth and moon orbiting it. And you have "powers" to create any planet you want, any size, any density, any weight and any velocity. Would it be possible for you (using all knowledge of earth), to create a natural satellite to moon? Whose trajector... | If things are in close, you have the three-body problem (four, given the sun - but it is distant). Three-body orbits are not uncommon in the universe. Orbit evolution prediction is fundamentally impossible, though abundant special solutions exist,
http://en.wikipedia.org/wiki/Three-body_problem
http://news.sciencema... | {
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Understanding Triplet And Singlet States We know, that for SU(2) representations $$\textbf{2}\otimes \textbf{2}=\textbf{3}\oplus \textbf{1}$$ where $\textbf{2}$ stands for the fundamental representation of SU(2). This means that we have a spin triplet of states and a spin singlet. Can we regard these states as the spi... | The spin part of the quantum state of any system consisting of two spin-$1/2$ particles (including a Deuterium nucleus) can be described as a general linear combination of the singlet and triplet states.
The the symbolic manipulation $2\otimes 2 = 3\oplus 1$ is telling you that the Hilbert space of the system of two ... | {
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Why isn't quantum entanglement just a lack of information? From this question and answer from joshphysics, I didn't understand one thing, even after reading the comments:
Why should assume that entangled electrons will only "decide" their state after observation?
Isn't it just a lack of information? For instance, knowi... | Suppose you have four marbles, each either black or white. Because you haven't looked at them yet, you're only aware of certain probabilities. One way or another, suppose you know that Marbles 1 and 2 have only a 5% probability of being differently colored. Likewise, Marbles 2 and 3 have only a 5% probability of bei... | {
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Does optical fiber preserve the angles of incoming light? I am reading up on optical fibers and there's one thing I haven't understood yet:
*
*Does an optical fiber preserve the angles of incoming light?
For example, if we light two LEDs in front of an optical fiber (within its acceptance cone) and hold the other... | An endoscope uses a bundle of multimode fibers. The number of fibers determines the resolution of the image transported through the fiber bundle. The angle of light isn't preserved in a single fiber. Usually - depending on the length and bending of a such a multimode fiber - angles/modes will be mixed in some way; ther... | {
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The difference between $\mathcal{N}=2$ short multiplets and BPS states I have some questions about the construction of $\mathcal{N}=2$ supermultiplets for chiral matter. I know that the supermultiplet should not include spin one states since they are always in the adjoint representation. So my first question is: why ar... | Spin one fields are in the adjoint representation because of the specific transformation behaviour of such modes under gauge symmetries. This is a symmetry requirement on the lagrangian.
Regarding your second question: the two multiplets are different. In one case we have a central charge and in the other we do not. H... | {
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Why does the windshield of my car freeze even if the outside temperature is above freezing? Under what conditions does the windshield of a car freeze even if the outside temperature is above freezing?
It is not clear whether this is related to the question why bridges freeze with non-freezing outside temperatures (see ... | This can happen if the windshield itself has a lower temperature due to earlier freezing. This effect can also be seen in freezing rain: Air producing rain is advected over frozen ground and suddenly the traffic is in trouble.
| {
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Ensuring globally hyperbolic geodesically-complete spacetimes Let's say we have an incomplete spacetime A that is globally hyperbolic, does there necessary exist a globally hyperbolic completion?
My guess is no, in which case what further restrictions can be placed on A to ensure that it can always be extended to geode... | Consider Kruskal manifold (omitting the future and past singularities at $r=0$). It is a globally hyperbolic spacetime as well known and it is a maximally extended manifold. However there are incomplete causal geodesics: These reaching the singularities. It is impossible to complete them. So the answer to your first qu... | {
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What makes a rainbow happen? A rainbow is formed when a raindrop refracts light, but why then does the whole sky not become a huge rainbow when it rains? Would the light not be dispersed into ordinary white light? What causes it to look as if each end is nearly touching the ground?
| It depends on the position of the sun. A rainbow does not exist at a particular location in the sky. Its relative position depends on the position of the observer and the sun. All raindrops refract sunlight in the same way, but only the light from some raindrops reach the observer's eye. This light is what constitutes ... | {
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What are the correct initial conditions for the moon (in a simulation)? So I've modeled the interactions between the sun and all the planets (and the interactions between the planets) using Verlet integration.
I've used data from Wikipedia for masses, distance from the sun etc.
I initialized the initial velocities of ... | The moon orbits the earth with a near circular trajectory relative to the earth. So add earth's orbital velocity (around the sun) to the moon's orbital velocity (around the earth).
This will put the moon into an orbit around the earth, but might make it a bit more eccentric (elliptical). To correct this you can use ang... | {
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Basic Thermodynamics: Quasistatic Adiabatic Process I'm going through the exercises in a Thermodynamics book, just to revise and build my intuition. Right now, I'm working on:
Show that for a quasistatic adiabatic process in a perfect gas, with
constant specific heats:
$$PV^\gamma = \left[\text{constant}\right]$$
wi... | As an alternative to the popular proposal of using $dU = c_V dT$, I find it more intuitive to use the equation for the internal energy of an ideal gas, and its differential:
$$
U = \frac{3}{2} N k T = \frac{3}{2} p V\quad \rightarrow \quad dU = \frac{3}{2} p \, dV + \frac{3}{2} V \, dp
$$
where I've assumed (in using ... | {
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Water in vacuum (or space) and temperature in space
*
*So, water in vacuum will boil first and then freeze. I don't know how the freeze happens. As pressure lowers to zero, what happened to freezing point? (I know heat taken by vapor, and the water cool down, but I don't think it will be that cold, will it? In vacuum... | The phase shift (sublimation) of water from Ice to vapor occurs in a relatively narrow window. If the ice sample could remain at a temp above a certain level it would all boil away in the vacuum of space.The evaporation and the sub zero temps of space actually cool the sample below the phase shift window thus remain as... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Integration over the state space I came across the concept of average fidelity
$\int f(\psi)d\,\psi$ where the integration is with respect to the uniform Haar measure on pure states.
I've only seen Haar measures in connection with topological groups, so I don't understand what measure is used in this context. Could any... | The group $U(n)$ has a unique Haar measure, both right and left invariant, since it is unimodular as it is compact. Now consider the complex projective space $$\cal{P}(\mathbb C^n)=
\left({\mathbb C^n} / \sim\right) - [0]\quad \mbox{when}\quad v \sim v' \quad \mbox{iff}\quad v = cv'\:, \quad c\in \mathbb C -\{0\} \:.... | {
"language": "en",
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Is crystal momentum an operator? My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and uses it consistently. However, does this not assume that there is an operator that has eigenstates $|\vec{k} \rangle$? If so, how would such an operator be defined... | Sure, it is certainly possible to define a crystal momentum operator, although I haven't heard of people doing this.
You define it by saying that the eigenstates of this operator are Bloch states, and the eigenvalue of each Bloch state is its crystal momentum (translated into the first Brillouin zone). There is a uniqu... | {
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Boosts are non-unitary! Unlike rotations, the boost transformations are non-unitary. Therefore, the boost generators are not Hermitian. When boosts induce transformations in the Hilbert space, will those transformation be unitary? I think no. If that is the case, what is the physical significance of such non-unitary tr... | On the actual Hilbert space of a consistent relativistic quantum mechanical system, the Lorentz transformations including boosts actually are unitary – which also means that the generators $J_{0i}$ are as Hermitian as the generators of rotations $J_{ij}$.
We say that the Hilbert space forms a unitary representation of ... | {
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Why does gravity decrease as we go down into the Earth? We all know that gravity decreases as the distance between the two increases. Hence
$$ F = G \frac{Mm}{r^2}. $$
Hence the acceleration due to gravity
$$ g =\frac{F}{m}= G \frac{M}{r^2} $$
increases as $r$ decreases. Then why does it decrease as we go deep into t... | It's actually not entirely true that the strength of the Earth's gravitational field decreases as a function of depth. It is true for certain regions in the Earth, but it's untrue for others because of the non-trivial dependence of the Earth's density on depth.
To see what's going on, assume that the Earth is a sphere... | {
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Atomic nearest neighbor notation I recently got a correction to a paper that I am writing. The correction references a section in which I talk about nearest neighbors. The comment says:
Do you mean NN, NNN, etc., or NN, 2NN, 3NN? It's different.
To clarify: here is the (111) face of an FCC crystal with nearest neigh... | hmm this is usually the standard notation with
\begin{align*}
\text{NN} &= \text{NN}\\
\text{NNN} &= \text{2NN}\\
&\ldots
\end{align*}
The only thing I could imagine is some kind of numbering of the nearest neighbors: If you have 5 nearest neighbors like in your example with 1NN, 2NN, 3NN, etc. you could mean the first... | {
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Definition of Ohm in SI basic units in words One way Wikipedia defines Ohm is (this is also teached in school):
$$1\Omega =1{\dfrac {{\mbox{V}}}{{\mbox{A}}}}$$
They describe this definition in words, too:
The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1.0 ... | Not sure whether this is correct, but if you have to do it, I think you can say that it is:
the work done by the conductor per unit charge per unit current through the conductor, or in terms of SI units, $\mathrm{\frac JC\cdot \frac1A}$
which is the same as:
the work done by the conductor per unit current per unit time... | {
"language": "en",
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Drift speed of electrons when the object is grounded So I know that the drift speed of electrons is usually pretty slow. Let's say I have a charged sphere and I would ground it over a wire. How fast would the electrons leave the sphere? Would that drift speed be a lot faster than usual? I just want to get the general i... |
So I know that the drift speed of electrons is usually pretty slow.
Yes, if $10A$ of current is maintained in a conductor of cross-section $10^{-4}m^2$, with number density of electrons equal to $9X10^{28}m^{-3}$, drift velocity of free electrons will be $0.000006ms^{-1}$ (with the centimeter scale in your geometry b... | {
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How much power would a space craft's magnetic shield require? I've read over the decades that a magnetic shield might protect a spacecraft from cosmic radiation. Its a fascinating idea that might only be theory or science fiction at the moment. In regards to that here is an article just in case someone isn't sure wha... | If it is a supercon magnet, it runs without losses until the field is deformed by a solar coronal mass ejection blasting by. It offers no protection against energetic photons.
Consider a one tesla field filling a 200 m diameter bubble. How many joules is 4.2 million m^3 of one tesla field? (Suppose the field collaps... | {
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Is the $N$ factorial in the Partition function for $N$ indistinguishable particle an approximation? I suspect that the $N$ factorial in the partition function for N indistinguishable particles
$$ Z = \frac{ Z_0^N } {N!} $$
is an approximation. Please someone correct me if I am wrong and why or why not. Thanks.
A simp... | Actually, it's exact. The flaw is "regarding the whole system consisting of these two particles, we can also write" $Z = 1 + e^{- \beta E} + e^{-2 \beta E}.$ Assuming the two particles are distinguishable, we have
$$Z=\sum_ig_ie^{-\beta E_i}=1+2e^{-\beta E}+e^{-2\beta E}=Z_0^2,$$
with the $2e^{-\beta E}$ since the st... | {
"language": "en",
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Physical distribution of salt anions and cations during electrophoresis If I have a volume of $L$ liters of salt water at a concentration of $\approx N$ mM NaCl and I pour it into an electrophoretic apparatus (like this one: ). Once we turn the apparatus on, and set the power level to some number of volts $V$, we woul... | The ion transport is by convection and diffusion. Only a very small part is by migration. As long as there is no anodic and cathodic reaction I would say the concentration is not changing in any part of the solution.
| {
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Can a car skid while moving in a circle? How can a car skid if it is moving around a circular road? It is understandable that it can topple but I feel it impossible that a moving car can skid. It is hard to imagine that a car would skid while traversing a circular path. The wheels of the car are rotating so it seems ... | If you understand that a car can topple while negotiating a sharp turn at high speeds, then you just have to consider the fact that skidding happens when the tyres don't have enough grip to prevent the car from being thrown out the trajectory. Newton first law states that any solid tends to continue in a straight path,... | {
"language": "en",
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Can Flow of time become still?
*
*According to theory of time dilation, flow of time slows down significantly at the speed of light.Is there any conditions practically or theoretically when flow of time is reduced to zero means it comes to still?
*Whether time & space are infinite?
| Time is relative. When it comes to Time Dilation, you actually see dilated time of another observer. So, your own time flow won't get frozen in any case.
Hypothetically, you can see another one's time frozen if she is traveling at speed of light (time dilation by speed) or she is at event horizon of Black Holes (gravit... | {
"language": "en",
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How to get conductivity from Green function $\mathcal{G}(x_1,x_2,\tau)$ of inhomogeneous system? I'd like to study an inhomogeneous system, i.e., momentum is not a good quantum number therein. Therefore, I tried to calculate temperature Green functions like $\mathcal{G}(x_1,x_2;\tau)$, or its twofold Fourier transforma... | There are a few ways to extract transport properties from your single-particle temperature Green's functions. By analytically continuing it to real time $t$, one gets information about how a particle propagates in the medium. More exactly, you get the probability of the particle traveling a distance $x = |x_1-x_2|$ in ... | {
"language": "en",
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The physics of sound boards As a kid I was bemused at why soundboards worked. A small sound could be demonstrably amplified simply by attaching the source to a surface that is rigid and not too thick. How could the volume increase so much given that there was no extra energy added?
As an adult I kind-of-think I know, b... | The comments above that say the sound is louder because the soundboard itself begins to vibrate are correct. This is called resonance. It sounds louder because the motion of the board is mechanically more efficient at converting the energy of the system into sound waves than the string alone. The board is an effective ... | {
"language": "en",
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"source": "stackexchange",
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Rms value of rectified output from a half wave rectifier The rms value of an alternating quantity which is the input to a half wave rectifier is $\frac{I_{max}}{\sqrt2}$.
Then the rms value of output should be $\frac{I_{max}}{2} \sqrt 2$. But it is given every where that it is $\frac{I_{max}}{2}$. Please tell me wher... | In a half wave rectifier note that the only a half cycle is transmitted In other half cycle, current is (approximately) zero. How will it affect the rms value of output?
$Hint :$ Consider that the rms value in the first half cycle is same but in next half cycle it is zero. How do you find the rms value of current? Will... | {
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Does electron in wave form have mass? I heard from my lecturer that electron has dual nature. For that instance in young's double slit experiment electron exhibits as a particle at ends but it acts as a wave in between the ends. It under goes diffraction and bends. But we don't see a rise in energy. It has to produce 5... | *
*mass=energy(actually mass is a form of energy) so everything who has energy(wave) has mass also
*if you squeeze all wave in a very little place you get a solid item(like you).
*if you squeeze a solid(like you again) in a very little place you will get a black hole
| {
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Non-symmetric Lorentz Matrix I was working out a relatively simple problem, where one has three inertial systems $S_1$, $S_2$ and $S_3$. $S_2$ moves with a velocity $v$ relative to $S_1$ along it's $x$-axis, while $S_3$ moves with a velocity $v'$ along $S_2$s $y$-axis.
So I constructed the Lorentz transformation by mul... | Indeed NowIGetToLearnWhatAHeadIs's comment answers your question:
"Simply because I hadn't encountered one that was not." A rotation is a lorentz transformation which is not symmetric.
Indeed the transpose of a rotation matrix is its inverse, and only trivial rotations or rotations through half a turn are involutary ... | {
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Divergent thin lens producing real images The question is as in the title, can a divergent lens produce a real image, when backed by a convergent lens?
Which are the conditions to be respected?
This was a homework and I have received the solution but I think is wrong.
Basing this on research already done online, the o... | You have two good fundamental answers, but a slightly different take on your answer is that yes, this is done all the time in optical systems to compensate for various distortions, aberrations and errors. A good example is an achromatic doublet, where a convex (converging) lens of one material is put in direct contact ... | {
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How far could the LHC "fire" a proton into space if we (outside LHC) ignore all interactions but gravity? Very simple question, and frankly quite a silly one, but I'm currently writing a lecture for secondary school kids and I'd love to tell them how far the Large Hadron Collider could fire a proton.
The talk is actual... | I think I get what you're after. You're looking for a qualitative handle on just how fast those protons are slinging it...
You might try considering the speed differential between an LHC proton and a photon that is launched at the same time. As others have noted the proton is ultra-relativistic (its kinetic energy is w... | {
"language": "en",
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free energy and entropy my understanding of free energy and entropy is that as entropy of a system increases its free energy decreases. As sun has free energy and this energy is being converted to useful work, and its entropy is increasing. Its entropy will continue to increase till its material is exhausted to cease f... | A large entropy is beneficial to a system, in that it lowers the total energy of the system. So a large increase in entropy would decrease the activation energy. Together with the change in enthalpy, they decide the spontaneity of the reaction. If the expression for the Gibbs free energy is negative at a given temperat... | {
"language": "en",
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Enthalpy Change in Reversible, Isothermal Expansion of Ideal Gas For the reversible isothermal expansion of an ideal gas:
$${∆H}={∆U}=0 \tag1$$
This is obvious for the case of internal energy because
$${∆U} = \frac {3}{2} n R {∆T} = 0 \tag2$$
and
$${∆U} = -C_P n {∆T} = 0 \tag3$$
For the case of enthalpy it is easy to ... | $$H = U + PV \Rightarrow$$
$$dH = dU +PdV + VdP\tag{6}$$
In other words, equation 6 is missing the $VdP$ term.
$$dH = dU + nRT \frac{dV}{V} + nRT \frac{dP}{P}\tag{7}$$
$$ \Delta H = \Delta U + nRT \ln\frac{V_2}{V_1} + nRT \ln\frac{P_2}{P_1}\tag{8}$$
$$P_1 V_1 = P_2 V_2 \text{ (isothermal)}$$
$$\Delta H = \Delta U + nRT... | {
"language": "en",
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Bulk flow of air in a long tube between Antarctica and Australia? I have a 5km diameter clear plastic tube which is open at each end and runs from the center of Antarctica to Lake Eyre in Australia. The tube is on the ground where it can be and at sea level on the ocean.
Will there be bulk flow of the air in the tube? ... | Natural circulation in tubes is driven by pressure gradient between warmer and colder parts of the fluid. The pressure gradient results from density gradient, which is induced thermally by heating/cooling the tube at different points. However, tube dimensions You've set, make it a very complex problem, probably impossi... | {
"language": "en",
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Taking pivot about an accelerating point Given this question:
A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small oscillations?
The standard solution is to write Newton's second law for the ball and then t... | In fact, you are right in that you should consider the fictitious force in accelerated reference frame. As such, using the point of contact between the mass and the bowl is actually not ideal. In the center of mass reference frame, notice if you consider a fictitious force for the accelerated reference frame, it is app... | {
"language": "en",
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Confused about Impulse Encountered a problem that involves impulse while studying for my exam and I'm not sure how to even approach it. I know that momentum is conserved, but I'm not sure how to relate that to avg force. Maybe someone can help point me in the right direction? I know that it's in quadrant III, through i... | This post has some information about impulse that you might find useful.
Homework Question involving Momentum
You will not find conservation of momentum useful here. True, the total momentum of object + wall is unchanged by the collision. But the momentum of the object does change.
Since $\Delta P = J = F_{avg} \Delt... | {
"language": "en",
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Orbital angular momentum selection rules for three identical particles I'm trying to figure out if there are selection rules for the total orbital angular momentum for a system of three identical particles, say bosons.
For two identical bosons one can argue that the exchange symmetry implies that the state must be par... | For 3-particle systems the relevant permutation group is $S_3$, which is significantly different from $S_2$ in that not all representations of $S_3$ are 1-dimensional.
Whereas 2-particle states can always be written so they transform back to themselves under permutation of labels, i.e. always possible to write
$$
\psi... | {
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Does the equation of continuity hold for turbulent flows? My textbook mainly deals with laminar flows. The book derives the equation of continuity, which states that the cross-sectional area times the velocity of a flow is always constant. But nowhere in the derivation does the textbook explicitly assumes that the flow... |
The book derives the equation of continuity, which states that the cross-sectional area times the velocity of a flow is always constant. But nowhere in the derivation does the textbook explicitly assumes that the flow is laminar. So, does the equation hold for turbulent flows too?
That is only a special case of the e... | {
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Does a mirror help a near-sighted persion see at a distance clearer? A near-sighted person without eye-glasses can not clearly see things at distance.
If he takes a photo of the things at distance, he can see the things from the photo much clearer, because he can place the photo much closer to his eyes.
If he turns his... | I am suffering from myopia (nearsightedness). I tried the same (with out wearing my lens), result was I could see things clearer in front of me than when I saw the same things in the mirror.
The below figure shows image formation for a person suffering from myopia.
Lens in our eye is more convex at its back than in... | {
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x-ray in oil droplets experment In oil droplet experiment, x-ray makes the air molecules negatively charged. How does that work? X-ray carries high energy and ionizes air, doesn't that make air positively charged?
| According to this link, the x-rays ionize the gas molecules in the apparatus, not the oil drops directly. So yes, you are right, the air is positively ionized. The newly freed electrons from the gas then adhere to the oil droplets (probably due to an induced dipole moment), producing negatively charged oil.
| {
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"url": "https://physics.stackexchange.com/questions/101811",
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What are circles on broth (eating soup) surface? Think about broth in the soup, usually it has circles on its surface. What are their properties? Why there are many of them (not a few big blobs)? Are they depended on liquid's temperature? What needs to be added to water so these kind of circles appear?
I can only guess... | The circles are droplets of fat (triglycerides: triesters of glycerol and fatty acids). The two phases (water and fat) are immiscible because the water molecules are more attracted (hydrogen bonded) to each other than to the fat molecules.
Absent gravity, energy would be minimized by the droplets being spherical, bu... | {
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Why doesn't diamond glow when hot? In an answer to this SE question, the respondent explains that heating a perfect diamond will not cause it to glow with thermal blackbody radiation. I don't quite follow his explanation. I think it comes down to: there is no mechanism for diamond to generate light in the visible re... | This is because of Kirchhoff's law of thermal radiation. The corollary from it is that emissivity of a material is equal to its absorptivity.
As diamond is transparent even at large temperatures, which can be seen in this answer, its absorption coefficient is very low. Thus its thermal radiation in that spectral region... | {
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Why does my kettle only make a noise when it is turned on Almost as soon as I turn my kettle on it starts to make the familiar kettle noise, yet very shortly after turning off the power the boiling noise stops and the kettle is totally silent. The temperature of the water is (almost) the same as when I turned it off. S... | Formation and collapse of immature water vapor of micro bubbles with a range of radii caused by a high temperature gradient between the heating plate and the ambient water. The noise-like sound is due to different micro bubble sizes.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102032",
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"source": "stackexchange",
"question_score": "7",
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How are velocity and dispersion maps of galaxies made? How can I get the velocity dispersion and velocity maps of galaxies given 3D data cubes obtained using an integral field spectrograph?
| The first thing you have to calculate is the overall redshift of the galaxy. When working at this level there are better and worse lines for doing this — for example, $\mathrm{Mg}$ lines frequently trace AGN outflows, so they'll be biased.
Once you have the galaxy's overall redshift, you can look at individual pixels i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102102",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
} |
How does a half-life work? Carbon-14 has a half-life of 5,730 years. That means that after 5,730 years, half of that sample decays. After another 5,730 years, a quarter of the original sample decays (and the cycle goes on and on, and one could use virtually any radioactive isotope). Why is this so? Logically, shoul... | Suppose you start with two kilograms of C-14. After 5730 years you have one kilogram left. Call that piece A. Now get another kilogram of C-14, call it piece B, and put it next to piece A.
You now have two identical pieces of C-14, and yet one of them (A) is supposed to half-decay in 2865 years and the other (B) is sup... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/102222",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "33",
"answer_count": 13,
"answer_id": 7
} |
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