Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What happens if we increase the quasimomentum in a crystal above the edge of the Brillouin zone? If we apply an electric field to a 1D lattice so that the quasimomentum increases as $$\langle\dot q\rangle=eE$$
what happens when we reach the limit $\frac \pi a$? Does the quasimomentum cycle round to $-\frac \pi a$ or do... | It cannot jump to a higher Brillouin zone, since the Brillouin zones are just equivalent descriptions of the toroidal momentum space of a system with a discrete translation symmetry. In a way the choice of the Brillouin zone is a choice of coordinates. So if we keep using the same choice of coordinates then the momentu... | {
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Can you sail up/down a moving river on a windless day? It's not possible to sail into the wind directly, but only at an angle. It can be shown (it may help for below) by considering the pressure forces on a flat sail and flat keel that sailing upwind is only possible because of the angle between the sail and keel.
Supp... | Although it doesn't look like traditional sails, it's possible to go faster than the wind both upwind and downwind with a combination of air-propellors and drive-propellors. It's even been done experimentally:
Last time around, the Blackbird cart raced downwind at 2.86 times the speed of the wind. Earlier this month,... | {
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Dark Matter and Gravity If gravitational lensing implies that Dark Matter exerts gravity onto light then why are the stars and regular matter not clustering around Dark Matter?
| Stars and other objects do cluster around dark matter. ~90% of the mass of a galaxy is in the form of dark matter. For the purpose of visualising, you may think of dark matter as a fluid with zero drag that the stars and regular matter are immersed in and move around through.
On small scales, comparable to the size sol... | {
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When can we consider dipoles? A dipole is a collection of two oppositely charged particles held at some distance, but if two charges are unequally charged (but oppositely charged) how do we take the dipole between them? Do we only take the parts of charge that are equal?
| Such a distribution of charges will also have a dipole moment and therefore a non-zero dipole term in the potential of the electric field produced (along with higher order pole terms). Just use the definition of the dipole moment to compute it:
$$\vec{p}(\vec{r}) = \sum_i q_i (\vec{r}_i-\vec{r})$$
As people have pointe... | {
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What does the spacetime diagram for accelerated/non inertial observers look like? Suppose that we are in flat Minkowski spacetime. There are many inertial observers moving at constant speeds relative to eachother and a single non-inertial observer moving with constant acceleration. In all of the inertial frames, the sp... | The Penrose Carter diagram for flat Minkowski spacetime looks like:
The Penrose-Carter diagram of the flat Minkowski spacetime f
or an inertial observer looks like a diamond, in which
coordinate lines connect opposite apexes which are the spac
elike and timelike infinities. Borders of this diamond are
the ligh... | {
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How can gamma rays affect a human body if they can move through atoms without colliding with them? I found this answer on this SE about why mirrors don't reflect gamma rays, and the answer says that it is because gamma rays are so, so small that they "see mostly empty space between the atoms of the solid.".
If that is ... | Based on your question: Yes, it is extremely unlikely that a gamma ray will hit an atom; however, Avogadro's number ($N_A$) is large: there are many atoms in your body, so it is likely it will interact.
Also: a single gamma interaction is not a problem, but for any appreciable source, there are many gamma rays. For ins... | {
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What construction materials could enable a capillary effect to raise water? Are there materials (possibly in research stage) which are investigated as replacement for piping and pumping systems in construction work to transport water from the ground to elevated floors in civil buildings?
| note that capillary lift in a vertical column only exists as long as a meniscus exists at the top of the capillary column. as soon as you begin to pull the water in the column out of it, the meniscus disappears and now you have to perform the usual work against gravity to move more water up.
This means that capillarit... | {
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What does this imaginary number mean for time and velocity? As some have pointed out in the chat, perhaps the question that I should have asked is, am I really integrating for velocity? My integration might be misleading in that it integrates for something but probably not velocity. Velocity could not be in the same di... | Complex velocity doesn't make sense in physics so you have to choose the parameters $a,b,c$ so you don't get an imaginary velocity.
\begin{align*}
& \sqrt{a v^4- b v^2+\frac{c}{a}}\quad\Rightarrow\quad a v^4- b v^2+\frac{c}{a} \ge 0\\
&v^2 \mapsto x\quad\Rightarrow\\ &g_1=a x^2- b x+\frac{c}{a} \ge 0\\
&g_1=(x-\ta... | {
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Could a black hole's dark matter content be determined? I recently attended a talk where the speaker said that it is impossible for us gain information about the history of particles which make up the black hole. i.e we won't know if the black hole was formed due to huge lump of hydrogen or if it was due diamonds. I no... | In GR, we have the no-hair theorems, which state that all stationary black holes are equivalent except for their mass, spin, and electric charge.
But my main question is that- Is the above principle(?!) applicable only to standard model particles or is it a general one for all particles interacting through gravity?
T... | {
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Why does an axially loaded column break along a 45 degrees plane? In this video, at 7:57, the speaker mentions that columns under compression roughly break along a plane that is at 45 degrees to the axis of loading. If this is true, can someone explain why this happens in terms of inter-molecular forces between the col... | The model assumes the material is isotropic, so inter-molecular forces are (on average) the same in all directions. Under this assumption, there is nothing special about inter-molecular forces along the 45 degree plane. The column breaks along that plane because it has the greatest shear stress, as the presenter states... | {
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Long time tails in Brownian motion
*
*Rings, D., et al. Theory of hot Brownian motion. Soft Matter 7.7 (2011): 3441-3452, doi:10.1039/C0SM00854K.
In this paper the author has mentioned that vorticity diffusion is disregarded due to it's finite time scale. Is the time scale of vorticity diffusion too large when comp... | I believe that they are assuming that the vorticity diffusion decays faster than the timescale for the particle motion, and in fact they say so in the opening section of a later paper: EPL 96 60009 (2011).
It is not completely self evident that this assumption is justified, since the vorticity diffusion is responsible ... | {
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When does my fidget spinner spin longer? Just wondered if it has an impact on duration of spin if I hold it horizontally or vertically. After a few tests, I could not figure out which was actually longer - beside the fact that I can't put the same power on it twice.
| If you spin your fidget spinner horizontally, the weight will be symmetrically distributed around the center of mass and the rotation axis. It should therefore spin for a longer period of time in comparison to doing it vertically.
But if you're looking for the perfect conditions to spin your fidget spinner forever, tho... | {
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Abrupt changes in direction and loss of energy
In the picture that I drew above, I was thinking that there is definitely loss of energy when the ball rotates off of the inclined plane to the small section of horizontal plane. However, I do not know the mathematical equation to model the theoretical change in velocity.... | There are two types of coordinates.
*
*The angle of the ball with respect to the surface, and the conjugate momentum is the angular velocity in this case. (Rough metal surface)
*The ordinary linear translation along the tilted ramp, with momentum ordinary linear momentum. (Slippery ice surface)
The louder the ba... | {
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Massive versus Massless $\phi^4$ Sunset Diagram - does $\frac{1}{\epsilon^2}$ term vanish for $m=0$? In a real scalar massive $\phi^4$-interacting theory consider the amputated sunset diagram. This is the integral out of Kleinert and Schulte-Frohlinde Critical Properties of $\phi^4$-Theories:
The above two-loop integr... | The power counting of momentum $p$ has nothing to do with the divergence power like $1/\epsilon^a$, actually what we are doing here for calculating loop diagrams is translating(mapping) divergence into the language of Gamma function. I think we can call it Gamma function regularization. I will show you examples as the ... | {
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Show that Propagator satisfies Schrödinger equation I want to show that
$$K=K(x,x',t-t')=\sum_{\beta}\exp\left[\frac{-iE_{\beta}}{\hbar}(t-t')\right]$$
satisfies the Schrödinger equation
$$ H|\psi\rangle = i\hbar\partial_t|\psi\rangle$$
with respect to $x$ and $t$, where the $\beta$'s are the Eigenstates of the Hamilt... | Note that, in bra-ket notation, if the $\{|\beta\rangle\}$ are the eigenstates of $\hat{H}$,
$$
\begin{aligned}
\hat{K}(t-t')
&= \exp\left[-\tfrac{i}{\hbar}\hat{H}(t-t')\right] \\
&= \sum_\beta |\beta\rangle \exp\left[-\tfrac{i}{\hbar}E_\beta(t-t')\right] \langle \beta|.
\end{aligned}
$$
Therefore, in the position rep... | {
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Does Democritus's "Atom" exist? Everything is made up of atoms, those are made up of particles like protons, neutrons and electrons. protons and neutrons are made up of quarks, is there a limit to this or can it go on for ever?
Was Democritus right or wrong when he said if you kept dividing something on and on you woul... |
Everything is made up of atoms, those are made up of particles like protons, neutrons and electrons. protons and neutrons are made up of quarks, is there a limit to this or can it go on for ever?
Sure, this can go on forever.
However, according to the standard model of particle physics the electrons and the quarks a... | {
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Is the string-net model Hermitian? In Kitaev and Kong's paper, they define the Hermitian inner product on morphism spaces in Eq. (11).
My question is that:
Given that F symbols satisfy the pentagon identity, does that the string-net Hamiltonian (13) is Hermitian follow from the Hermitian inner product on morphism spac... | The string-net Hamiltonian $H=\sum_{p}(1-B_p)+\sum_{v}(1-Q_v)$ is Hermitian, this is because that $B_p$ and $Q_v$ are all projectors. The fact that $Q_v$ is projector is obvious from the definition of $Q_v$. The argument for $B_p=\sum_k\frac{d_k}{D^2}B_p^k$, where the sum runs over all labels of simple objects in unita... | {
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Paramagnetic material in a coil If we hold the voltage constant, will (and how) the current through a coil change if we put a paramagnetic material in the coil ?
| magnetic dipoles in paramagnetic materials can align under the influence of an outside magnetic field, but this alignment much weaker and never stays permanent in comparison with feromagnetic materials, so placing a paramagnetic object in a coil with current flowing through it would temporarily increase this current de... | {
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Good sources to get velocity/position vectors for all planets and moons in the Solar System for building an orbital simulator? I’m building an $N$-body simulator, and I have everything ready to begin simulating. But my issue is is that I have no idea how to get all the starting positions and velocities for the celestia... | https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
There is links for the planets, it is also in basic text/html which makes it good to automatically parse, don't know how often updated though?
Seems to have velocities and then mean elements to choose from, don't see Cartesian position though. But all info... | {
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How to average the loudness of a audio file from its amplitude? I would like to average the loudness of different sounds so that their means could be used as a dependent variable in a statistical regression, but I have some troubles to understand how loudness works.
Assume that I have large number of different audio ... | In general, you would first ensure the signals you are using have no DC component (likely the don't have a DC component), and more specifically, you could choose to band limit the signals to a frequency range of interest; but this may not be necessary. You will also need to ensure that if you are using different signal... | {
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How the Heisenberg principle holds for protons? Does this principle holds for protons since their position is, in a manner of speaking, known and they are also assumed to be stationary at every popular physics book that I have read, including the school textbooks.
| If you consider the Hydrogen atom (1 proton, 1 electron), you can reformulate the 2 bodies problem in two equations, one for the motion of the center of mass of the atom, and one for an effective mass representing the relative motion of the electron and proton around each others.
Wikipedia : two bodies system (classic... | {
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Direction of wave propagation unchanged after superposition? It's quite confusing.Principle of superposition states that the amplitude of two superposing wave eqauls their indivisual amplitude vector sum.But what about direction.Souldnt't wave direction of propagation should also add up and the most confusing part is t... | The direction does not change due to the same superposition principle.
Let's look at two waves, red and blue, at the diagram below.
The waves intersect and interfere with each other in the area A. The direction of the red wave at point B, beyond the intersection and interference with the blue wave ("after superpositi... | {
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Why is inflation described by a scalar field? Textbooks on cosmology describe the phenomenon of cosmic inflation in terms of the existence of a scalar field (or many scalar fields, as the answer and comments pointed out), called inflaton. Such as choice without motivation seems ad hoc. Is there a reason why inflaton sh... | There are hundreds of inflationary models, and some of them indeed use vector fields (I'm sure you can come up with spinor models as well). But then you can ask yourself - why describe inflation with "100" scalar fields, when you can just as well describe it with only one? Of course you should keep in mind those other ... | {
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How come I can kick a football further when it's moving towards me? If a ball is moving towards me, I can kick it further than if I were to kick it if it was stationary. But surely if the ball is moving in the opposite direction, it should take more force to kick it the same distance as I am accounting for the initial ... | I will give a simpler explanation. A ball hitting a wall, reverses direction and if friction is small, it is elastically scattered, i.e. keeps its speed. Momentum is conserved because the mass of the wall is very large . It is more complicated in real situations, see the answer here for details.
So, if your leg, wher... | {
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Null geodesic eqaution / Timelike geodesic equation I'm taking my first course in GR. We were told in lecture that to find null geodesics, we can solve:
$$g_{ab} \dot{x}^{a} \dot{x}^{b} = 0,\tag{1}$$
and to find timelike geodesics, we can solve:
$$g_{ab} \dot{x}^{a} \dot{x}^{b} = -1 \tag{2}$$
[if the Minkowski sign co... | The expression $g_{ab} \dot{x}^a \dot{x}^b$ can be thought of as being equivalent to the Lagrangian $\mathcal{L}$. The geodesic equation can be be obtained by substituting $\mathcal{L}$ in the Euler-Lagrange equations.
$$g_{ab} \dot{x}^a \dot{x}^b =
\begin{cases}
-1, & \text{if timelike },\\
... | {
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Why are oscillations so ubiquitous in nature? I'm aware that you can always approximate a potential by a quadratic term. But is this the most 'fundamental' reason for the pervasiveness for oscillations?
| Marbles on a hilly surface will tend to roll downhill and settle in the nearby pockets. The reason they stay in the pockets is because the gravitational potential increases in all directions from the bottom of the pocket. A pocket potential can be approximated by a parabolic potential, for small displacements from the ... | {
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Does a vibrating string produce changes in tension in the string? A taut string anchored at both ends increases in tension as the string is displaced to a side. When released the string will vibrate at whatever frequency to which the system is tuned.
If this were a simple standing wave it seems that tension would drop... | This question covers a lot of area, so let's work through it piece by piece.
First, the normal approximation for a vibrating string is (a) a transverse (perpendicular to string) displacement that (b) is a small where (c) the string acts like a spring: (small) changes in length result in (small) changes to the tension.... | {
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How is voltage proportional to current? The question came up in another forum - "What causes current to flow". Many knowledgeable people explained that what causes the flow of charge are electric field forces or Coulomb forces. If there is a distribution of charge such that there is a deficit of neg. charge in one plac... | To understand how a current is created we need to understand the dynamics of the charges. To do this, it is easier to calculate how much work the system can do on a charge rather than just the force in the static case. The potential different can be seen as a measure of the system's capacity to do work on a charge. The... | {
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Definition of an operator in quantum mechanics In J.J. Sakurai's Modern Quantum Mechanics, the same operator $X$ acts on both, elements of the ket space and the bra space to produce elements of the ket and bra space, respectively. Mathematically, an operator is simply a map between two spaces.
So, how can the same op... | Just think of the operator as a matrix (as per your "matrix-elements" tag). Then it operates to the right on a column-vector $\left|\mbox{ket}\right>$, and to the left on a row-vector $\left<\mbox{bra}\right|$
| {
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What's the reaction force on a charge moving in a magnetic field? According to newtons third law, all forces occur in pairs. What is the reaction force that the third law predicts when a magnetic force acts on a charged particle moving in a magnetic field?
| Why do you ask about a magnetic field specifically? Wouldn't we have the same problem with a eletric field? Or a gravitational field?
The answers are the same for all of those fields: the particles that generates the field "feels" the other half of the pair force.
In your case, we have, for nonrelativistic $(v<<c)$ ve... | {
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In which direction would a single atom go if it absorbed heat through radiation? if a single atom with an absolute zero temperature was suspended in space, and it then received energy through radiation from a nearby object:
if that atom was in a lattice, it would vibrate, but since it's just a single atom, what would h... | The direction of movement can only be affected by the relative position of the radiating source. Thinking about conservation of momentum, the atom must require a momentum that is in the direction of movement of the absorbed radiation, namely radially away from the emitting source (assuming a point particle or spherical... | {
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What does it mean that Gravity itself has mass which will in turn generate more gravity? In today's announcement from Netherlands Institute for Radio Astronomy, as discussed in a video about two-thirds down this page.
At the 1:30 mark, the video says "Gravity itself has mass, which will in turn generate more gravity." ... | It is a bit confusing to say that "gravity itself has mass". It would perhaps have been less confusing if they had said, "the source of the gravitational field is energy, and the gravitational field itself has energy. Of course, through the equivalence of mass and energy expressed by $E=mc^2$, it can be said that the... | {
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Information loss in black holes Doesn't quantum collapse or decoherence mean that information is being lost all the time? So why is the loss of information in black holes such a big deal?
| Decoherence does not mean that information is lost - it just 'degrades', like it would happen in a big classical system with the increase of entropy. But the information is still there.
Quantum collapse is another matter. Yes, if quantum collapse was an objective non-unitary process, then it would imply the loss of inf... | {
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Why isn't work done when carrying a backpack with constant velocity? Here's an excerpt from my textbook:
In the following situations, state whether work is being done, and why or why not.
A) A person carrying a backpack walking across a floor
B) A person shoveling snow across a driveway at a constant speed
The soluti... | In situation a), if the person is walking perfectly smoothly in a vacuum then no work is being done on the bag, if there is air resistance then both the person and the air do work on the bag, if there is jiggling then gravity does work too.
Situation b) is clearer, the snow is initially at rest and accelerated by the s... | {
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Expansion wave in a hermetically sealed room Suppose there is a human in a hermetically sealed room who takes in a small amount of air without letting it out. The room is initially at atmospheric pressure. The suction is similar to the case in which a piston is withdrawn to generate an expansion wave in the surrounding... | It would be easier to answer your question, if a human taking in some air is replaced by an expanding or contracting mechanical object, say a sphere.
Either expansion or contraction will generate a spherical acoustic wave which will bounce off the walls (ceiling, floor, etc.) a couple of times, before it decays.
In t... | {
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Why does evaporation cause cooling? I am aware that the evaporation process causes cooling in the remaining liquid, but why?
If anyone can give me the maths and or equations to prove / show this I would be most appreciative.
| No need to use equations to show this. You just need to think about what is happening thermodynamically. To evaporate water, you must add energy to it and this energy must come from somewhere. The energy is initially in the liquid but once it evaporates, the liquid carries the energy away with it (otherwise it would co... | {
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Can you isolate a system from conduction and convection, but not radiation? Can you create a 'box' that isolates the inside from conduction and convection, but lets infrared and visible light pass?
| You mean like a Dewar or Thermos bottle?
They usually have silvered glass to reduce heat transfer by radiation, but you could omit or remove that to let as much radiation through as you'd like.
The long neck is to support the weight, while greatly reducing conduction along it. You'll also sometimes see baffles insi... | {
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Why does a Tulsi leaf always fall with the dark side down?
When it comes to tossing a coin in Kerala, Tulsi leaves are considered to be a good substitute for coins. Or at least they say it is!
It just occured to me long ago that my mother tossed a tulsi leaf to decide whether or not to send me for a class excursion. A... | I flipped a margarine packet lid seven times. It landed with the convex part facing down all seven times. I theorise that with the concave face downward (the "empty parachute" position), it is in unstable equilibrium, the air resistance increases, there is turbulence around the edges, and the chances of flipping increa... | {
"language": "en",
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Where does the negative sign of the Laplacian in the four-divergence go? As far as I'm aware from my course notes and what I've found online, the four vector gradient expands as
$$
\begin{align*}
\partial_\mu x_\mu &= \left( \frac{1}{c} \frac{\partial}{\partial t}, -\frac{\partial}{\partial x^1}, -\frac{\partial}{\part... | Your first expression is not well-defined. According to the Einstein summing convention, you sum over double indices, where one index is upper and the other one is lower. Such indices are called silent. Such an expression is then explicitly written as:
$$x^\mu y_\mu = x^0y_0 + x^1y_1 + x^2y_2 + x^3y_3 = x^0y^0 - x^1y^1... | {
"language": "en",
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Vortex motion in superconductors In mixed state of a type-II superconductor, when we allow a transport current to pass through it, we say that the Lorentz force acts and as a result the flux starts flowing, when the force is greater than the pinning force. What i want to know is whether the Lorentz force acts on the el... | This is a subtle--- and occasionally contentious--- issue. It's too complicated to explicate here, but a good basic reference is P. Nozieres and W. F. Vinen "The motion of flux lines in type II superconductors" Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, 14:130, 667-688, DOI: 10.1... | {
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Are microwave-generating devices (gyrotrons) in the ITER system phased to heat plasma? Provided electricity from grid is converted and supplies 24 gyrotrons, which generate electromagnetic waves, which in turn, will transfer their energy to the electrons of the ITER plasma to heat it up.
In general, electromagnetic wa... | In my experience, it is not very common to call two signal "phased", as you have done it (but different communities have different conventions). I guess what you mean is: "are the signals from the various gyrotrons in phase?"
The answer is: no, they are not.
Phased-locked gyrotrons (i.e. gyrotrons which are in phase) i... | {
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Why do we need to include impulse by string?
There is this paragraph in the solution of the question :
Since ball A is suspended by an inextensible string, therefore, just after collision, it can move along horizontal direction only. Hence, a vertically upward impulse is exerted by thread on the ball A. This means th... | Since the ball(falling) collides with the hanging ball it will give the hanging ball an impulse $I_1$which will have two components one along the vertical direction and one along the horizontal direction and so the ball will tend to go downward but as it is connected to a string which is ideal so the string will have t... | {
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What effect does gravity have on a spinning object? If gravity was the only force present would gravity, beside pulling, also stop the rotation / spin of a small object its pulling towards it over time?
What would be the effect on an uneven object and what would be the effect on a perfect sphere?
| I assume you are talking about two interacting bodies orbiting about one another, one of which at least is asymmetric. Gravity would stop the self rotation by tidal forces, such as cause the tides on Earth. This would convert rotational energy into heat leading ultimately to body or bodies rotating with the same freque... | {
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Suppose the speed of individual photons reduced over time. Would that explain the apparent speeding up of distant galaxies? The observation that distant galaxies seem to be speeding up has led to the theory of dark energy.
However if the speed of individual photons actually reduced over ( very long ) periods of time wo... | The speed of light from distant galaxies has been measured, and it is (as near as we can tell) precisely equal to c.
More specifically, by radio telescopes (treating 'radio' as a form of 'light' since they are both electromagnetic fields and both show the same observed redshift behavior when looking at distant galaxies... | {
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If object size increases, shouldn't magnification decrease by formula According to the magnification formula, magnification is the image size by object size
According to this if object comes near and its size increases shouldn't magnification decrease?
| Magnification is an inherent property of the lens, independent of the height and distance of the original object. Let’s say we are moving a toy car towards the lens, then the distance between object and the lens decreases, but the distance between the image decreases too. The formula is $M=\frac{d_i}{d_o}$.
On the ot... | {
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longitudinal polarization of the electromagnetic field I'm just trying to quantize the electromagnetic field. It has four independent components, where two of them are physical and belong to the (transverse) polarization. But why does it not have a longitudinal component. Is it because photons are massless?
| Yes, because photons are massless. A 4-vector describing a photon gauge field has initially 4 degrees of freedom. Temporal degree of freedom is fictitious, because it (edit: its time derivative) does not appear in the kinetic term of the Lagrangian (thus it does not propagate). Then, you can fix gauge symmetry (say, $\... | {
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When will hydrogen no longer be the most abundant nucleus? In a recent question, we learned why hydrogen is currently the most abundant nucleon or element in the universe.
Here I ask a follow-up: For how long will hydrogen be the most abundant nucleus? It is most abundant now, but is slowly being consumed by nuclear f... | We can only give an answer on the basis of what we currently know about cosmological parameters. If indeed these have been correctly estimated, and that the cosmological constant is constant, then the universe will continue to expand at an accelerating rate.
Given that about half the baryons in the universe currently e... | {
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How does tilting a bike make it turn sharper? Note that my question is not why do you tilt your bike when on a curve. It's about the reduction in turning radius when one tilts the bike inwards.
Short to-the-point answers are welcome.
| This is called countersteering. see an in-depth physics explanation here.
As you turn, the top part of the bike wants to go keep going straight (because of inertia), whereas the wheels are bound to the ground by friction. This is experienced by the bike as a torque trying to flip the the bike in the direction opposite ... | {
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If gravity reaches infinite intensity on the all event horizon surface, doesn't this fact exclude the black holes central singularity? Aren't this two singularities an excess or an unnecessary redundancy?
|
If gravity reaches infinite intensity on the all event horizon surface
The spacetime curvature at the horizon is finite and gravity is spacetime curvature. Thus, gravity doesn't "reach infinite intensity" at the horizon:
Courtesy of Google books, here's the relevant section from "Gravitation":
Misner, Charles W., e... | {
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Why the pressure at siphon 1 atm at the bottom of the pipe?
I assume the area of horizontal cross section of beaker at the top to be way larger than the area of horizontal cross section of pipe
I think at the same depth pressure of a specific liquid which are connected to each other, as in manometer, should be same. B... | I think you are right because $P_1$ and $P_3$ are occurring at surface molecules and when all the water has been filled up by siphon, there is no point of any other force acting on it. Here $P_3>P_1$ as there are more air molecules in $P_3$ than on $p_1$
| {
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Something special about energy eigenstates when it comes to time evolution? A particle is subject to an infinite square well potential with
$$V(x)=
\begin{cases}
0 & −a \lt x \lt a\\
\infty & \,\,\,\,\text{otherwise}
\end{cases}$$
At a time $t=0$ its wavefunction is given by $$\psi(x, t=0)=\frac{1}{\sqrt{5a}}\co... | An energy eigenstate is an eigenstate of the Hamiltonian $H$. If the Hamiltonian is not time-dependent, then the time evolution operator is $U(t) = \mathrm{e}^{\mathrm{i}Ht}$, so every energy eigenstate is also an eigenstate of the time evolution operator, meaning it remains the same state under time evolution.
No othe... | {
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What does $\Lambda^{-1}_{\frac{1}{2}}\gamma^\mu\Lambda_{\frac{1}{2}}=\Lambda^\mu_{\phantom{\mu}\nu}\gamma^\nu$ mean? \begin{equation}
\Lambda^{-1}_{\frac{1}{2}}\gamma^\mu\Lambda_{\frac{1}{2}}=\Lambda^\mu_{\phantom{\mu}\nu}\gamma^\nu
\end{equation}
In P&S, p. 42:
Equation (3.29) says that the $\gamma$ matrices are inva... | Usually when we see an object with a Greek index like $\gamma^\mu$, we assume that the object contains the components of a vector and that the way to rotate it involves a sum over the index $\mu$. Since $\{\gamma^0, \gamma^1, \gamma^2, \gamma^3\}$ are matrices, we can transform them by multiplying them by matrices fro... | {
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Why do physicists assume that dark matter is weakly interacting? IceCube, XENON, etc, keep yielding negative results. If dark matter exists, it doesn't interact with baryonic matter at the energy ranges they can detect. The response is to build even bigger detectors to search for even fainter energy signatures.
Why? Is... | It's not just the "look under the lamp post" effect. There's also the "WIMP miracle". A new heavy (i.e. about the mass of the top quark, the heaviest SM elementary particle) weakly interacting particle would have an annihilation cross section of about $10^{-26} \text{ cm}^3/\text{s}$. Very general thermodynamic princip... | {
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Can any type of wave produce an interference pattern from two sources? Can any type of wave produce an interference pattern similar to the one in a double slit experiment? So for example, could a radio wave create an interference pattern through the airwaves?
| Yes any two wave can interfere having same nature like we can do double slit experiment through the sound wave, for two wave to show interference pattern, phase difference should be constant what I am saying is this.)
Consider say two electromagnetic wave, whose phase difference changes with time.
$$E_1=E_0sin(wt_1-... | {
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Einstein@Home - what is the purpose of "gamma pulsar binary search" tasks? I participate in Einstein@Home program.
My question is - what is the purpose of "gamma pulsar binary search" tasks?
What signatures are being searched?
How gamma pulsar binaries can help in study of GR and gravitational waves?
EDIT:
After some ... | Self-research is everything :)
Now I have at least partial answer.
Gamma pulsar binaries are consisted of pulsar and normal star (usually very bright) rotating close enough to each other.
This paper tells about millisecond pulsar found by gamma ray pulsations analysis. But millisecond pulsars are of direct interest in ... | {
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Why do wormholes necessarily alter time? Why don't they just make two places causally linked? I've heard many-an-explanation of wormholes. From as a kid with the hole punch through paper, to the sci-fi something something magic, to popular YouTube science channels talking about how it could be used for time travel.
I ... | Suppose in the year 3000 the planet Splot passes the Solar System at a speed of $c/\sqrt{2}$ (I chose this value because it makes the time dilation a factor of 2). The Splotians like our calendar so they decide to reset their calendar to also be the year 3000 as they pass, which means we all agree on the dates. At the ... | {
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Why do I see red light reflecting from my normal glasses when I wear anti blue-ray glasses? Today when I went for eye checkup, the optician presented to me an anti blue ray glasses. This type of glasses reflect blue light, and hence, while wearing my original glasses and holding this new pair of glasses under the ligh... |
When I put on these anti blue ray glasses, and put my normal glasses under the light, I saw red light reflected. This confused me because under normal conditions, it would at most reflect the colour of the light.
The light available to be seen depends on the office lighting and sunlight filtered through the glass. Di... | {
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Magnetic field from displacement currents in a capacitor, and an applied exterior magnetic field
If an exterior magnetic field ($B$) is applied to oppose or support the magnetic field produced by the displacement currents ($B_D$), what would happen to the electric field within the gap? And the capacitor in general?
D... | In general, the only practical way to produce a magnetic field supporting or opposing the magnetic field produced by the displacement current (presumably, in all points in space), is to generate another current spatially aligned with the original current and flowing in the same or the opposite direction.
The spatial al... | {
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Why arent black holes bright due to the bent light from nearby stars? If black holes change the path of incoming light in a gradual way (from very slight changes to 180 degrees), only depending on how close the light is passing by, the black hole external layer (where a perpendicular light beams are curved but are not ... | As you can see in the raytracing animation, the observer at the center bottom of the scene does not receive any rays that come from the direction of the black hole:
Therefore a black hole has a shadow which has approximately 2.5 times the radius of its event horizon.
| {
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What does electrical potential at a point mean? From my understanding, potential difference (or voltage) between point A and point B is the difference in electrical potential at the two points. The potential difference is also, the work done per unit charge in moving charges from point A to point B.
But apparently, the... | You can think of it in such a way. Let $\phi(x)$ be the potential function of an electric field $\vec{E}$ with boundary conditions $\lim\limits_{x\to \infty} \phi(x) = 0$. For the potential we obtain
$$\phi(x) = \phi(x) -\phi(\infty) = \int_\infty^x \quad \vec{E}(y) dy.$$
If you bring your charged object from the point... | {
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How is work transferred to the system recognised? For example, a potato initially at room temperature $25 \sideset{^{\circ}}{}{\mathrm{C}}$ is baked in an oven that is maintained at $200\sideset{^{\circ}}{}{\mathrm{C}}.$
I made potato as the system and the outer surface of the skin as the system boundary. While the ove... | There definitely is work being done.
There is power being used to keep the oven hot at the mentioned temperature; power used to increase the temperature of the potato; and water vaporization. However, for your particular application, only the power used to increase the temperature of the potato is of interest. This... | {
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Why do distinct temperature layers form in bodies of water? This may not be the correct place to ask a question about limnology (which I just found out is the science of lakes) but it seems like the place most likely to produce a good answer.
In my diving lessons I learned that there is a layer of water in lakes where ... | The three layers are depicted here (from Wikipedia):
The top and bottom layers are distinguished by mostly constant temperature across their depth.
The top layer mixes due to external factors like wind.
The bottom layers mixes because all the water is close to its highest density and the density is approximately the s... | {
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A slipping cylinder comes into contact with friction Suppose a cylinder is slipping rigidly on a frictionless horizontal surface. Then, at $t=0$ it reaches a different ground. The coefficient of friction between the cylinder and this new type of ground is $\mu$. What happens?
- assuming usual high-school friction to b... |
is the friction force discontinuous?
Your analysis is correct, but it includes the assumption that the cylinder is rigid. As a result, the friction force in theory drops from a finite value to zero as soon as pure rolling starts. You can actually see this happen in bowling, or billiards where initially the slipping ... | {
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Superior Mirage I've been fascinated about mirages and never thought I'd get to see a superior mirage. I live on the south coast of England and enjoy a distant view of the English channel. Last Friday 3 August 2018 at about 5pm, I took some photographs from my balcony which I'd love to hear whether they are superior mi... | I’d love to talk more if you get this comment. I have been researching mirages for four years. I have multiple playlists if you’re interested. I am persuaded all mirages are inferior. If you notice in your captures there is a dark band within which the mirage happens. That’s the “aetherband” and the ship is actually at... | {
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Understanding Feynman derivation of probability current density On page 21-4 of vol. III of The Feynman Lectures on Physics, he derives the formula for the probability current density. Starting with the Schrödinger equation, he presents the time derivative of the probability density, and then states,
"The potential te... | The question is how we simplify $\partial_t P=\frac{1}{i\hbar}(\psi^\ast\frac{1}{2m}(\frac{\hbar}{i}\nabla-qA)^2\psi+q\phi\psi^\ast\psi-\psi\frac{1}{2m}(-\frac{\hbar}{i}\nabla-qA)^2\psi^\ast-q\phi\psi\psi^\ast)$ to $\partial_t P=-\nabla(\frac{1}{2m}\psi^\ast(\frac{\hbar}{i}\nabla-qA)\psi+\frac{1}{2m}\psi(\frac{\hbar}{i... | {
"language": "en",
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Electric field from disc versus point charge A uniformly charged disc of radius R and net charge Q with an x-axis through the center of the disc will have an electric field in a point $x_0$ on the x-axis
$E=kQ(1-\dfrac{x_0}{\sqrt{x_0^2+R^2}})$
if my calculations arent wrong.
If a point charge of charge Q replaces the... | This can be thought of using vector addition ,if u see carefully some components will cancel out giving a net lesser effect in case of a disk but u will see if u continuously decrease the distance the field strength will approach what we call not defined.
| {
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Delta function from poles of Green's function In quantum mechanical scattering theory, we often use Green's functions which contain poles. For example, in Schroedinger quantum mechanics the free Green's function is given by
$$
G_0(\vec{p}) = \frac{1}{E-\frac{p^2}{2m}+i\epsilon}
$$
in momentum space where the infinitesi... | The Green functions $G$ and $G_0$, as well as the scattering potential $V$ are operators. Therefore, if we choose to work in the momentum space, the string of operators, e.g. $G_0 V G_0$, have to be written as a convolution and all the dummy variables have to be integrated out. Doing this, you will never obtain a squar... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Relation between topological insulators and breaking of time reversal symmetry Whenever one talks about topological insulators, the breaking of time reversal symmetry is always mentioned.
Is there an intuitive reason as to why one need time reversal symmetry to be broken in order for topological effects to appear?
| The easiest way to understand this is as follows: Those systems that you hear people talking about are most usually either the IQHE or analogs of it. In that case, you have two space dimensions and the (bulk) invariant is the Hall conductivity. If $P$ is your Fermi projection (derived from a Hamiltonian $H$), then the ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Shouldn't the infinite sea of electrons contribute to gravity? According to my understanding of the dirac equation, there's an infinite sea of electrons occupying all negative energy states which prevents an electron from dropping to lower and lower energy states down to negative infinity.
Since these are electrons, th... | Do not confuse models with reality/data.
The hypothesis of infinite seas of electrons has been left behind because better mathematical models were developed, and the problems of real electrons in infinite seas are model problems.
The solutions of the Dirac equation described fermions for us and started the way to quan... | {
"language": "en",
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"source": "stackexchange",
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Tensor (anti)symmetrization for non-adjacent indices: how can I notate $T^{(ab)c}$ but symmetrizing over $a$ and $c$ instead? Refer to the following passage from Robert Wald's General Relativity:
More generally, for a tensor $T_{a_1\cdots a_l}$ of type $(0,l)$ we define
\begin{align}
T_{(a_1\cdots a_l)} & = \frac{1... | Good question which, I am afraid, has no good answer unless one is willing to use a graphical notation like Feynman diagrams.
Here is a snapshot from the book Group Theory by Cvitanovic:
Note that when using tensors in an irreducible representation for a Young diagram other than a single row or column, the $[ab]$, $(c... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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A harmoinic oscillator in the Heisenberg picture Considering the Hamiltonian of a harmonic oscillator
\begin{equation}
H=\frac{p^2}{2m}+\frac{m\omega^2 x^2}{2},
\end{equation}
the time evolution of the Heisenberg picture position and momentum operators is given by
\begin{align}
\dot{x}&=\frac{i}{\hbar}[H,x]=\frac{p}{m... | You're not imposing the initial conditions correctly. The initial conditions are:
\begin{align}
x(0)&=x_0=x_S, \text{ and} \\
p(0)&=p_0=p_S.
\end{align}
That is, at $t=0$ the Heisenberg and Schrödinger picture operators coincide. So, the solution to this ordinary differential equation (ODE) for $x(t)$
$$\ddot{x}=-\omeg... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Symmetric and antisymmetric states of spin singlet/triplet I'm studying the book "Quarks and Leptons: An Introductory Course In Modern Particle Physics". When I reach chapter 2 (page 33), I encounter this exercise problem that I couldn't understand:
EXERCISE 2.1 Justify the decomposition shown in (2.1) by either (1)
... | If you interchange the spins, then the states are either symmetric or antisymmetric under permutation: this is more explicit if you write
$$
\sqrt{2}\vert S=1,M=0\rangle=\vert\uparrow\rangle_1\vert \downarrow\rangle_2 + \vert\downarrow\rangle_1\vert\uparrow\rangle_2\, ,
\tag{1}
$$
where $\vert \uparrow\rangle_1$ denote... | {
"language": "en",
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Why do spheres roll so far? Say you have a sphere and a cuboid, both of equal mass and material. You push both on a ground of the same material over the same period of time with an equal force. Intuition tells you that the sphere would roll much further than the cuboid. Why is this?
The most common model of friction, $... | The block moves by sliding. When an object slides, the two surfaces are moving relative to each other and friction acts opposite to the motion. This opposite force does negative work on the block and slows it down.
While the sphere might slide at first, it will normally be rolling. When an object is rolling, the two... | {
"language": "en",
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Feynman and Perpetual Electron In the paragraph 1–2 "Matter is made of atoms" of the first Volume of his lectures, the great Feynman says that electrons are in a perpetual motion.
Now, i'm new to physics and i don't know quantum mechanics, but for what i understood about Classical Mechanics, perpetual motion is not pos... | Since he was talking specifically about atoms being in perpetual motion, I believe the idea is essentially Heisenberg's Uncertainty Principle.
Now Feynman did not refer to that here. His point was, rather, that as a matter-of-fact atoms are always in motion, flying about and vibrating against other atoms and so on. Bu... | {
"language": "en",
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"source": "stackexchange",
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Air velocity flowing out of a pierced can How can I calculate the velocity of air that would come out of a pierced can of compressed air if I assume that the pressure inside the can is 7 atm and the size of the hole is that of a regular nail?
| The method proposed below is rather primitive and I am not sure how accurate the result would be, but that's how I would attempt to do it, if I did not want to deal with equations.
You can ballpark the initial velocity (flow rate) using a calculator (like this) for the air flow through an orifice.
As the air is coming ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Strain compatibility From this link, strain compatibility for 2D problem with strains as
$$
\varepsilon_{11} = \cfrac{\partial u_1}{\partial x_1} ~;~~
\varepsilon_{12} = \cfrac{1}{2}\left[\cfrac{\partial u_{1}}{\partial x_2} + \cfrac{\partial u_{2}}{\partial x_1}\right]~;~~
\varepsilon_{22} = \cfrac{\partial u... | The compatibility conditions are important to ensure the existence of a displacement field $u_i$ when a strain field $\varepsilon_{ij}$ is given. They are integrability conditions. You get them from the definitions of the strains:
$$
\varepsilon_{11}=u_{1,1}\\
\varepsilon_{12}=(u_{1,2}+u_{2,1})/2\\
\varepsilon_{22}=u_{... | {
"language": "en",
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Woodworking clamps, does force add up? I was watching a woodworking video about glue, and the guy was clamping two pieces of wood together using a total of 8 clamps. He argued that by doing so he would apply 8 times the maximum force of 150N (a property of the clamp), resulting in 1200N in total.
I think he's wrong. I ... | If the area stays constant the pressure will increase as the total force increases when more clamps are used.
The wood is probably flexible and not perfectly flat so the force will only be exerted over a region close to a clamp where the two bits of wood are in contact.
| {
"language": "en",
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"source": "stackexchange",
"question_score": "2",
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Can a photon be called a disturbance in the electromagnetic field? Total noob here.
I know that electromagnetic waves do not need a medium to travel. I analogize a photon as a single pulse/oscillation in the electromagnetic field and its propagation is the motion of that pulse through the electromagnetic field. Kind of... | There is a close connection between the optical field as it is described by the electromagnetic field and a single photon. It is stated that a photon is a single excitation of the field. In that sense it inherits all the properties of that field. So, if the electromagnetic field is a single pulse that only exists for a... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Rope with no slack tied around the world Imagine a "rope" (for want of a better word) is wrapped all the way around the Earth, to the point that you can hold both ends.
There is no slack on the rope, i.e. it doesn't stretch.
It also isn't caught on anything on the Earth's surface and no friction applies to it, if that ... | The other end would not move instantaneously. The speed at which the signal of you moving one hand will move is at the speed of sound in the rope. In fact, the speed of propagation of any signal cannot be faster than the speed of light.
You can see this easily by just wiggling a rope up and down. It takes time for the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/424197",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pulley problem, wrong decomposition of forces The mass of the red block is $M$. The rope is inextensible and its mass isn't relevant. The mass of the sphere is $M\sqrt{2}$. The angle between the rope and the horizontal is $45°$.
I'm looking for the acceleration of the body but I'm doing something wrong. I want to und... | Try to avoid answering questions by looking at the results you are trying to obtain.
Start from the very beginning, without any prior knowledge of the acceleration and tension. All you know is the mass of the objects and the inclination of the rope. This eliminates the factuality of the $\vec F_{p}+\vec F_{my}=0$ relat... | {
"language": "en",
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"source": "stackexchange",
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Black body radiation net intensity The question says:
A body $X$ of emissivity $\epsilon$ is at temperature $T_1$ . $X$ is inside a box whose walls act as a black body of temperature
$T_2$ . $T_1$ is greater than $T_2$ .
What is the net intensity of radiation leaving body $X?$
The answer states that it is $I_{\text{ne... | The question asks about the net radiation of X, not of the whole system/scene. If blackbody X radiates $\psi_1$, and it absorbs radiation $\psi_2$, the net radiation of X is $\psi_{X}=\psi_1-\psi_2$. For the sake of this question you can assume that the effect $T_2$ would have on $T_1$ is already included in $T_1$ (the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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The definition of the hamiltonian in lagrangian mechanics So going through the "Analytical Mechanics by Hand and Finch". In section 1.10 of the book, the Hamiltonian $H$ is defined as: $$H = \sum_k{\dot{q_k}\frac{\partial L}{\partial \dot{q_k}} -L}.\tag{1.65}$$
And then author affirms that this quantity is constant and... | The Hamiltonian is constant if the Lagrangian has no explicit dependence on time. I think you are getting confused by the difference between $\partial L / \partial t$ and $d L / dt$. The quantity $dL / dt$ is a total derivative, encoding all time dependence of $L$. If the Lagrangian is assumed to be a function of coord... | {
"language": "en",
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"source": "stackexchange",
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Calculating angular velocity of rolling object with just gravity? From what I have learned, you can calculate what the angular velocity of an object will be based on its potential energy.
Say there is a situation where:
*
*acceleration due to gravity = 10 m/s²
*friction = infinite (object is in pure rolling motion)... | I found the angular acceleration using this formula:
-5g/7r * sin θ
where
*
*g = acceleration due to gravity
*r = radius of sphere
*sin θ = angle of incline
Then used that to get velocity by multiplying it by time.
| {
"language": "en",
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Calculating the Instantaneous speed When we are calculating speed from the graph for a uniform motion the speed which get as an answer is actually the average speed and since in uniform motion the average speed is same as that of instantaneous speed so its correct,right? Now if this is right if we calculate the variabl... | Uniform motion is a special case. The instantaneous speed is the same at all times. If you draw a graph, it is a figure where the slope is the same at all points. That is a line.
For a line, the average slope between two points is the same as slope of the tangent at any point. So yes, the average speed and the instant... | {
"language": "en",
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Multi-instanton contribution to path integral Briefly, I would like to have a reference to a clear detailed exposition of the computation of the multi-instanton contribution to the path integral while computing the energy levels splitting of the Hamiltonian with symmetric double well potential on the line.
In more deta... | There are many standard sources for this, the main one being the book of Sidney Coleman "The Uses of Instantons".
A source which is very explicit and quite good, especially for the energy splitting, is "ABC of Instantons" by A I Vaĭnshteĭn, Valentin I Zakharov, Viktor A Novikov and Mikhail A Shifman.
I highly recommend... | {
"language": "en",
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What causes Lorentzian broadening of X-ray diffraction peaks? In X-ray diffraction, the pseudo-Voigt model is a combination of Gaussian and Lorentzian distributions, and is often used to model peaks. The form of the peak is often described as
$V(x)$ = (1-$\alpha$)$G(x)$ + $\alpha$$L(x)$
G(x) and L(x) are the gaussian ... | I'm afraid $\alpha$ has no physical meaning here.
The line profile (i.e. the profile of the diffraction peak) is a convolution of the instrument and physical broadening. The latter means broadening caused by the microstructure of the sample, which is typically divided into the size and strain components. (keyword: size... | {
"language": "en",
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Stress Energy Tensor in language of differential forms The motivation for this is that quantities like the electric current $J$ in maxwell's equations of motion can be expressed as a differential 3-form, so that the continuity equation can be written just as
$$dJ=0$$
Which is really nice because it can all be done with... | If you invite "vector bundle-valued differential forms" then you can define $$ T^\mu=T^\mu_{\ \nu}dx^\nu $$ as a "vector field-valued 1-form", then you have $$ d^\nabla\star T^\mu\sim\nabla_\nu T^{\mu\nu}. $$
However the metric is needed both for the definition of $T$ and to take the covariant exterior derivative $d^\n... | {
"language": "en",
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Lowering of temperature in expansion valve of refrigerator We know that the high pressure liquid refrigerant (comming from condenser) passes through the expansion valve and lowers the temperature (due to decrease in pressure).
My Question:
From the formula pV = nRT:
(p1V1) / T1 = (p2V2) / T2 [ n & R are constant]
So... | As you noted, the refrigerant is a liquid as it passes through the expansion valve, and it is not appropriate to apply gas laws to a liquid. To understand what happens in the expansion valve you have to start at the compressor. After the compressor exhausts high temperature and high pressure gas to the condenser its ... | {
"language": "en",
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"source": "stackexchange",
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Various regions of fluid flow
In the image above, there is this plot between sound velocity and flow velocity. I want to check if my interpretation of the plot is right or not. Here are my observations:
(1) The c-a plot is a plot of how speed of sound varies with the variation of speed of fluid (through which the soun... | Yes, your interpretation of the plot is correct: it is showing how the local speed of sound in the flow varies with the speed of the gas, assuming ideal gas and adiabatic conditions. You are also correct that, as the flow speed increases, the local speed of sound decreases, until it reaches zero. In practice, this sets... | {
"language": "en",
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Evaporation amount of water for a Storm How much water from the ocean is evaporated for a storm over water?
I am trying to figure out what conditions will cause the most evaporation or how to calculate the amount of water evaporated for a given storm.
| No vapour is needed to form a storm, only deep convection is required, there are storms on ice and on deserts but dont have any precipitation.
https://en.wikipedia.org/wiki/Dry_thunderstorm
the evaporation of ocean water in a wet storm is the same water in its rainfall
a number is for example 2.1 x 10^16 cubic centimet... | {
"language": "en",
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Reaching critical point in a fluid I have carbon dioxide in a pressure reactor. I can control both temperature and pressure inside the container (or, equivalently, temperature and amount of fluid). I need to reach the critical point in an experiment.
What is the best experimental procedure to reach the critical point?... | Finally we performed the experiment and we could nicely reach the critical point. We relied on the temperature - specific volume phase diagram (the plot is extracted from these lecture notes):
The region under the curve is the vapor dome, where liquid and vapor coexist. At lower specific volumes there is only (compres... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/425877",
"timestamp": "2023-03-29T00:00:00",
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Joining poles of bar magnet What happens when 2 poles(i.e. noth and south) of the same bar magnet joined to each other to form circular loop?
| A pole, in mathematics, is a point at which a function is singular
(undefined/infinite/divide-by-zero). A good mathematical approximation of
the external field of a bar magnet is the combination of two
singular functions, one positive and one negative, whose
singular points lie near the tips of the bar.
In that "dipo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/426004",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Reason for black and white colour We always say that an object is black to a person's eyes if it absorbs all incident light or doesn't reflect anything, and white if it doesn't absorb and reflects all.
My question is which specific property allows black objects to absorb and stops white objects from absorbing.
| Not sure I understand your question. Keeping my answer somewhat colloquial, less technical.
Visible light consists of a mixture of electromagnetic radiation of different wavelengths (=different colors of light). See: Visible Spectrum
Something appears black to us, if no (or only very little) light is coming from it tow... | {
"language": "en",
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Why isn't average speed defined as the magnitude of average velocity? Speed is usually defined as the magnitude of (instantaneous) velocity. So one could assume that average speed would be defined as the magnitude of average velocity. But instead it is defined as
$$s_{\textrm{average}} = \frac{\textrm{total distance t... | It's quite simple really. "Average speed" is the average of the speed. In general, the average of any function $f(t)$ is
$$\frac{\int_a^b f(t)\ dt}{b-a}$$
In the case of $f(t)$ being the speed $s(t)$, The integral of the speed $\int_a^b s(t)\ dt$ gives the total distance traveled, and $b-a$ is the time elapsed, resulti... | {
"language": "en",
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"source": "stackexchange",
"question_score": "5",
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How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories? Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the conta... | "The jar is empty at present" just tells you $f(0)$. You also need $f'(0)$, $f''(0)$, etc.
| {
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What does the spherical-harmonic notation $Y^{m}_l(\hat{\textbf{r}})$ mean, and how does it relate to the usual $Y^m_l(\theta, \varphi)$? By using the plane wave expansion, the decomposition of stationary harmonic plane wave into partial waves can be given by
$$
e^{i\textbf{k}\cdot\textbf{r}} = e^{ikz} = e^{ikr\cos\the... | Nothing: a vector is defined by modulus and angles; but a unit vector has fixed modulus, so it's just another way to indicate the angles $(\theta, \ \varphi)$.
You can also write $Y_l^m (\Omega)$, since the solid angle is also related to them.
Note: we should name those three harmonics differently, but we the physici... | {
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Why is the pressure same in a horizontal plane in a static fluid? One of the common explainations involve a cylindrical flask filled with fluid and Newton's second law. But such explainations is specific. What could be possible explanation in a case in which the fluid is filled in some randomly shaped flask?
| Suppose that you have a very small ball at depth h in the liquid. Suspending disbelief, imagine that the ball expands by a volume $\Delta V$. The net result will be that a volume $\Delta V$ of liquid rises to the surface from depth h.
Now if we have an ideal frictionless liquid, and neglect atmospheric pressure (which ... | {
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How to calculate the dipole potential in spherical coordinates I want to calculate the dipole potential in spherical coordinates. I know that the potential can be calculated with
$$ \phi = - \int \mathbf E \cdot\mathrm d\mathbf r,$$
but I don't know the electric field. I would say
$$ \mathbf E = \frac{1}{4 \pi \epsil... | The easiest derivation is probably to start with the potential, and then calculate the electric field as the gradient of that potential.
Consider a dipole at the origin aligned along the z-axis, with two point charges of charge $ \pm q $ positioned at $z = \pm\frac{a}{2}$. By symmetry, the potential will be independent... | {
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Why don't we use infrared light to heat food? Why don't we use infrared (IR) or even the far IR just to heat food in a microwave oven instead of, of course, the conventional 2.45 GHz microwaves? Don't people call IR heat waves?
| We do.
That iron on the top of the device is a simple ohmic resistor, which gets the 230V network current directly. There is no need for any converter or stabilization of the temperature or the electricity, because
*
*increased resistivity of the iron due to the temperature
*and the second law of the thermodynamics... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/426954",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "51",
"answer_count": 4,
"answer_id": 2
} |
$\sqrt{-1}$ coefficient in a function In a simple harmonic oscillator with $\ddot{x} = -\omega^2x$, it can be shown through differentiation that one solution can be given by $\dot{x} = i \omega Ae^{i \omega t}$. What does the factor of $i$ do here? What effect does it have on velocity?
| Note that $i$ can be written as follows
\begin{align}
i = e^{i \pi/2}.
\end{align}
Therefore, we have the velocity $\dot{x}$ written as
\begin{align}
\dot{x} \; &= \; i \omega A e^{i \omega t} \\
\; &= \; \omega A \; e^{i \pi/2} \, e^{i \omega t} \\
\; &= \; \omega A \; e^{i \big(\omega t + \pi/2\big)}.
\end{align}
If ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/427068",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
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