Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How to start moving in at $Re\ll1$ I find it difficult to see how something can accelerate (and therefore increase its velocity, e.g. start to move) in a $Re\ll 1$ situation.
It is customary, at low Reynolds numbers, to ignore inertial effects. This means that the nonlinear terms in the Navier-Stokes equations vanish. ... | In the frame linked to the sphere, you would have to add an inertial volume force $-\mu a$ if $a$ is the acceleration of the sphere.
With dimensional analysis, $\mu a\to \frac{\eta V}{{{L}^{2}}}\times \frac{\mu a{{L}^{2}}}{\eta V}$and so, we have an additional term in the dimensionless Navier Stokes equation $\frac{\mu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/459620",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Why some forces follow superposition principle? Let there be a system of $n$ source charges and a test charge $Q$. When we say superposition applies to electrostatic force, we conclude that the interaction between a given source charge and the test charge is independent of interaction between other source charges and t... | Force is a vector quantity: vectors add in predictable ways, so forces
are capable of being considered separately or of being added together.
We say 'superposition' if force fields (vector fields of
a type OTHER than force) act on some part of an object, like
mass or charge or surface area. An electric field, for ins... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/459708",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Faster ways of computing feynman diagrams Obviously the machinery of QFT allows us to calculate processes, such as QED diagrams, to great precision, and whilst it is effective, it seems there are many processes that make calculations (say by hand) significantly slow.
Are there any recent developments in our machinery t... | Nowadays, less and less people use Feynman diagrams for precision calculations (that is, anything beyond a tree level 4 or 5 point amplitude). There is a whole field dedicated to finding better methods of calculating scattering amplitudes (using recursion and unitarity for example). In fact this is how most calculation... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/459787",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Pressure due the atmosphere Usually when we consider the pressure exerted by gas, there is nothing to do with the weight of the gas. On the contrary the atmospheric pressure is defined as the weight of the gasses. What is the difference here?
| when we say pressure exerted by gas we say about pressure exerted by gas on container due to collision of particles with wall of container when kept in closed container we use PV=nRT to define it here pressure due to weight of air is very small so it is negleted ( it is same case as variation of pressure in sound wave)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/460182",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Computation of $e^{i \hbar \omega a^{\dagger} a} a e^{-i \hbar \omega a^{\dagger} a}$ I need to compute terms like :
$$e^{i \omega t a^{\dagger} a} a e^{-i \omega t a^{\dagger} a}$$
Where $[a,a^{\dagger}]=1$ (they are the bosonic annihilation/creation operators).
I wonder if there is a simple formula for this. Indeed,... | I define the following operator:
\begin{equation}\tag{1}
\hat{A}(t) = U^{\dagger} a \, U = e^{i \omega t \hat{N}} a \, e^{- i \omega t \hat{N}},
\end{equation}
where $\hat{N} \equiv a^{\dagger} a$. We have the following commutator (notice that there's a sign mistake in yours):
\begin{equation}\tag{2}
[a, a^{\dagger}]... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/460321",
"timestamp": "2023-03-29T00:00:00",
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How many temperatures has a plasma? In nonthermal plasma, not all particles move in the same way. The electrons are different from other particles. Both can be described as having a temperature separately. But that would mean, one piece of substance could have
Two temperatures at the same time
No temperature at all.
... | Thermodynamic equilibrium is not a trivial condition. Feynman, in his Statistical Mechanics lectures start writing that a system is in thermal equilibrium when all the "fast" things have happened and all the "slow" things not.
It may happen in some systems, for instance in the case of a plasma, that thermal equilibriu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/460461",
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How can I determine a planet's mass based only off of information about its orbit and its parent star? I'm coding a video game with procedurally generated planetary systems and I want some and I want to make sure I'm at least somewhat scientifically correct. I've reached the part in my code where I know where a planet ... | When a body is in orbit around a planet, the centrifugal force is balanced by the gravitational force:
$$
{{mv^2}\over{r}} = {{GMm}\over{r^2}}
$$
where $M$ is the mass of the planet and $m$ the mass of the orbiting body.
You can transpose this to get the velocity for a given radius or whatever you want.
$$
v = \sqrt{GM... | {
"language": "en",
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"source": "stackexchange",
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Parity transformation and mirror reflection I have some trouble understanding what exactly is parity transformation.
The definition of parity transformation is a flip in the sign of all three spatial coordinates, ie
$$(x,y,z) \rightarrow (-x,-y,-z).$$
Consider a stationary particle at a position $(a,b,c)$ in space des... | First of all, there are two conventions - 'active' and 'passive' points of view. Within the former, you would say that under the parity transformation the particle has changed its position in space from $(a,b,c)$ to $(-a,-b,-c)$. Within the latter, you'd say that the particle stays at the same point of space, but the c... | {
"language": "en",
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What is the theory behind imaging a precision pinhole? In my efforts to characterise a 0.67 NA microscope objective (working distance of about 15mm, effective focal length of 25mm), I have placed a 20 micron precision pinhole at the focal plane of the objective, and back illuminated the pinhole with a 767nm laser. The ... | This looks like an interference pattern caused by the laser's coherence when passing through the pinhole (see e.g. here). Can you try illuminating the pinhole with an incoherent source, instead, such as an LED? I believe that should produce a flatter profile similar to the one in your model.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461100",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Why is the friction force on the bed opposite of the gravity
So here is a simple problem and here is a diagram that I find found online.
Why is the frictional force pointing downwards. I mean I get the correct answer if I follow this diagram and math checks out but intuitively. I thought the frictional force should be... | Suppose there is no rotational motion. Then the frictional force must point upwards along the plane to keep the person from falling.
Now consider the situation when there is no friction and angular speed of rotation is very high. In the rotating frame, the centrifugal force will point outwards and its component along t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461234",
"timestamp": "2023-03-29T00:00:00",
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Why do electromagnetic waves have the magnetic and electric field intensities in the same phase? My question is: in electromagnetic waves, if we consider the electric field as a sine function, the magnetic field will be also a sine function, but I am confused why that is this way.
If I look at Maxwell's equation, the c... | The E and H fields in a time-harmonic EM wave are in phase in the time domain when the medium's polarization (electric and magnetic) are in phase with the corresponding fields. You can see that polarization fields inherently act as 'source' terms in Maxwell's equations, and hence, instantaneous polarization implies in-... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/461393",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
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How can we derive from $\{G,H\}=0$ that $G$ generates a transformations which leaves the form of Hamilton's equations unchanged? In the Hamiltonian formalism, a symmetry is defined as transformation generated by a function $G$ is a symmetry if
$$\{G,H\}=0 ,$$
where $H$ denotes the Hamiltonian.
On the other hand, a sym... | A generating function$^1$ $\epsilon G(q,p,t)$ [where $\epsilon$ is an infinitesimal parameter] can to first order in $\epsilon$ be identified with a generating function $\epsilon G(q,P,t)$ for a type 2 canonical transformation (CT), $P=p+{\cal O}(\epsilon)$, cf. Ref. 1.
On the other hand, a CT takes Hamilton's equation... | {
"language": "en",
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Coulomb's Law Question The presentation of Coulomb's Law in various books occasionally has a note that the test charge, q2, must be small enough that it doesn"t alter the field of the first charge, q1. The same limitation applies to a test charge in any other stationary electric field. If those are the facts of life, t... | Some of them could be complicated, if they don't have symmetry. The good starting point is by assuming symmetry. For example, Gauss' law can be used to solve for the electric field due to a sphere, plane charge density, cylinder etc.
These derivations use Coulomb's law as a starting point.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Unification of gravity and electromagnetism Have there been any attempts at unifying gravity and electromagnetism at least at classical level since Hermann Weyl's idea of gauge principle (1918)? We now have Standard Model which is very successful and many other theories. But gravity and electromagnetism are long range ... | There is no acceptable field theory of gravity, which should describe gravity as a field defined on Minkowski space like electromagnetism, and there is no acceptable theory that describes electromagnetism as a curvature of space . It will take one or the other to make a unified theory at all possible.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462122",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
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Momentum Space Representation of the Tight Binding Hamiltonian I am trying to represent the tight-binding Hamiltonian
\begin{equation}
\hat{H}_{TB} = \sum_{\sigma} \sum_{\alpha,\beta} \sum_{\mathbf{R}_1,\mathbf{R}_2}
t^{\alpha,\beta}_{\mathbf{R}_1,\mathbf{R}_2}
\hat{c}^{\dagger}_{\alpha,\mathbf{R}_1,\sigma}
\hat{c}_{\... | In (2) we can substitute
$t^{\alpha,\beta}_{\mathbf{R}_{1}-\mathbf{R}_{0},\mathbf{R}_{2}-\mathbf{R}_{0}}$. Then since the left hand side of (2) does not depend on $\mathbf{R}_{0}$, if we sum on it we have M times the same thing, so if we divide by M, we have a relation equivalent to the previous one
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462248",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Scintillator decay time=1000 nsec,does that mean dead time is really high? What I'm really confused about is, say my scintillator is really slow, and has a decay time of about 1000 nsec. Does that mean, if one neutron is being read by the electronics, for that particular 1000nsec decay period, no other neutrons can be ... |
That within that long decay time only one neutron is being read and that others are being ignored?
It means exactly that. After one particle is detected, it takes some dead time until the detector is ready to measure another particle. Any events during that time are not recorded.
For scintillators this is typically d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462378",
"timestamp": "2023-03-29T00:00:00",
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Why wasn't the Stipa-Caproni plane efficient in its flight? The Stipa-Caproni was an experimental italian plane design. Though it has a very peculiar shape, it seems at first glance like it would have pretty good aerodynamic profile since its reference area looks rather small. However, its Wikipedia page cites:
Unfor... | I guess Stipa didn't realize that a wimpy looking 2 blade prop was not going to make the air flow do what he hoped. Even modern ducted fans are less efficient than conventional aircraft propellers in cruise conditions, though they are much more efficient for generating thrust at low speeds and hence useful for hovercra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462502",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why do objects rebound after hitting the ground? When an object, say a shoe, falls from a height (under the influence of gravity), it rebounds after hitting the ground. For an object to move upwards, it requires a force to overcome its weight. When the shoe hits the ground some of its energy is lost and the ground push... | Whatever the object lands on and the object itself acts as a spring and in compression the objects store elastic potential energy which comes from the downward motion (kinetic energy) of the objects.
That elastic potential energy is then converted into kinetic energy due to the upward motion of the object which was ori... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462618",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Non-renormalizeable Interaction Implies Trivial Interaction? It has been rigorously proved that the $\phi^4$ theory is trivial, i.e. is a generalized free field, in spacetime dimensions $d>4$. It is also the case that this theory is non-renormalizeable in spacetime dimensions $d>4$. Is this a general feature of renorma... | No, it's not that simple, although the two notions are related.
Renormalizability is a notion that is relative to a renormalization group fixed point. It is possible to have a QFT which flows from a nontrivial UV fixed point to a trivial/free fixed point. In this case it would be non-renormalizable from the point of vi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/462921",
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Confusion over units in force equation? While discussing Newton's laws, our book says
Force is proportional to rate of change of momentum
so they say
F is proportional to mass * acceleration if mass is constant
So $F=kma$ where $k$ is a constant.
They then say we choose a unit of force such that it produces accele... | If you have a proportionality $F\propto m\,a$ (or $F \propto \frac{dp}{dt}$) then using a constant $k$ produces an equality $F=k\,m\,a$ or ($F= k\, \frac{dp}{dt}$).
In terms of dimensions $[F]=[k]\,[m]\,[a]\Rightarrow [F]=[k]\rm \,M\,LT^{-2}$.
The BIMP booklet on SI units (page 118) states that the name of the derive... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463036",
"timestamp": "2023-03-29T00:00:00",
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Symmetry operations on an infinite uniform sheet of charge My book has a section on symmetry operations.
It says, (if the plane of charge is the yz plane) translation symmetry along the y-axis and z-axis implies that the electric field is constant if one translates along the y and z axes respectively. Also, due to rota... | The potential of all points on a plane parallel to the sheet is same and the electric field vector at every point on such plane is same.
Now, because of the symmetry of the 3D space with respect to the infinite sheet, the field vector at $x=d$ is negative of that at $x=-d$ and is along positive and negative x-axes resp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463154",
"timestamp": "2023-03-29T00:00:00",
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Does theoretical physics suggest that gravity is the exchange of gravitons or deformation/bending of spacetime? Throughout my life, I have always been taught that gravity is a simple force, however now I struggle to see that being strictly true.
Hence I wanted to ask what modern theoretical physics suggests about this... | Exchange of particles (gravitons) is a mechanism. Bending of space is a phenomenon for which, the mechanism is not known yet. If that mechanism is known, we can likely manipulate gravity. It is simple to understand repulsion in terms of particle exchange, but I struggle to understand attraction via particle exchange ev... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463327",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "28",
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Does a colored filter reflect their color of light? At the moment I'm somewhat confused by the concept of colored filters; common sense states that they allow only their color of light to pass through(i.e. red filter lets red light through), but, if they appear to be a specific color, wouldn't that indicate that they r... | The filters transmit only the light that the colour of the filter shows. For example, if you had a red filter, then it would mean that only red light would get through. The filter does not reflect light. In my example, all other colours apart from red would not go through the filter. If the filter was a secondary colou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463474",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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How do you measure the chemical potential? It is clear how to measure thermodynamics quantities such as temperature, pressure, energy, particle number and volume. But I have no idea how to measure chemical potential.
Could someone please provide some examples of how one could measure the chemical potential?
| It's possible to measure chemical potential directly. Chemical potential is exactly analogous to pressure, via the fundamental relation S(U, V, N).
While P is what is equalized under a moving wall, $\mu$ is what is equalized under a permeable wall.
While V is what changes to equalize P, N is what changes to equalize $\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463572",
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Why Neutrino is a ghost particle? why neutrinos are called ghost particle.why it is not affected by strong magnetic field. why it does not interact with matter. why it does not interact with gravitational field? I am unable to understand it
| It is called a "ghost particle" because it can pass effortlessly through solid objects "as if it were a ghost". This is another way of saying that it interacts very little with ordinary matter.
The reason it does not interact much with ordinary matter is that it has no electric charge (and so will not be acted upon by ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463651",
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Why the entropy change is not zero in the irreversible adiabatic process? Why the entropy change is not zero in the irreversible adiabatic process?
...while it is defined as the integral of the heat added to the system over its temperature.
| The statement
$$
dS = \frac{\delta Q}{T}
$$
is only true of reversible processes. The generally true statement is
$$
dS \ge \frac{\delta Q}{T}.
$$
For an adiabatic process, $\delta Q = 0$, but that still allows for $dS > 0$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/463988",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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When the voltage is increased does the speed of electrons increase or does the electron density increase? I am just a high school student trying to self study, please excuse me if this question sounds silly to you.
I know that current is a product of the speed of electrons and the electron density.When current is incre... | Increasing the voltage applied to a circuit of a given resistance will increase the current flow. That flow is defined in electrons per second past a point. So increasing the voltage increases the speed of the electron flow.
The number of electrons free to flow is a constant for a material.
For Copper that is one elect... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/464109",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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How much time does it take for a broken magnet to recover its poles? I understand that when you cut a magnet you end up with 2 magnets but I wonder how much time does it take to the magnetic domains to rearange and form the new pole. I know the answer may vary depending on the size of the magnet, the material, and some... | I believe you seem to be worried about the effect of the physical disturbances on the domain arrangement caused by the cutting process. If my assumption is right, then to return both derivatives to their former glory (being much of half of the strength of the original), I'll recommend keeping them in a relatively stron... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/464256",
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"question_score": "4",
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Train and lightning bolts: why the time difference does not depend on the position of the moving person? So imagine two lightning bolts hit the ground, simultaneously to a stationary observer. There is also a person on a train traveling to the right at a constant velocity.
I know that if he started in the midpoint, he ... | The position of the train will affect the time difference between when the person receives the light from each of the lightning strikes. However, this is different from the time difference between the strikes in the train's frame. This is because the person can calculate how much time it took for each light to reach th... | {
"language": "en",
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Why this constant is included in the tortoise coordinate? In the Schwarzschild spacetime, the tortoise coordinate $r_\ast$ is defined by the property that
$$\dfrac{dr_\ast}{dr}=\left(1-\dfrac{2M}{r}\right)^{-1}$$
Now, we cam integrate this. Multiply by $r$ on the numerator and denominator to get
$$r_\ast = \int \dfrac{... | Physicists really don't like to put dimensional variables inside a function like $\ln$, $\sin$, or $\exp$. By choosing $C = 2M - 2M \ln (2M)$, you can combine the logarithmic terms into the logarithm of the dimensionless ratio $(r-2M)/2M$.
Further details on why having "naked" dimensional variables inside a function l... | {
"language": "en",
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If sound is a longitudinal wave, why can we hear it if our ears aren't aligned with the propagation direction? If a sound wave travels to the right, then the air molecules inside only vibrate left and right, because sound is a longitudinal wave. This is only a one-dimensional motion. If our ears are oriented perpendic... | Re. from one of your comments: "But when the air molecule from the centre keeps moving away ,won't there be a vacuum created at the centre" and also this one: "But if the sound wave is emitted for long periods, wouldn't there be a complete vacuum and the sound wave would stop"
I think part of you confusion comes from t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465203",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Observable universe radius for distant observers The radius of the observable universe is about 46 Gly. Is that figure true for all current observers in our universe? Is it true if the universe is finite or infinite, flat or curved?
| If the universe has a FLRW metric, then there is a cosmological time $t$ that all observers at rest relative to CMB or the matter in the universe will experience at the same rate. This is true regardless of the curvature and whether the universe is infinite or merely unbounded.
The radius of the observable universe (i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465439",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Potential in open branch of a parallel circuit with grounding
If the switch is still open, what will the electric potential at Q be, i.e. negative, positive or zero?
Is there a potential difference across the grounded point and point Q, or R3, even though the branch is open? I suppose the current would be zero in that... |
The electric potential at $Q$ will be negative, why? I'll explain in a bit.
Of course there's a potential difference across $Q$ and ground point and $Q$ and $R_3$, which are different.
You're right there isn't current through the branch leading to $Q$, and there isn't "voltage" also based on $V=IR$. Voltage doesn't al... | {
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Initial values of creation/annihilation operators I have a question about creation/annihilation operators. For example, if I have an evolution equation for annihilation operator of photon
$$ \frac{da_k}{dt} = -i \omega_k a_k$$
I obviously obtain
$$a_k(t) = a_k(0) e^{-i \omega_kt} $$
I not fully understand how to find i... | $a$ is an operator. There isn't a specific value to it, and even if you do provide a certain expression in the matrix form – it won't give you much information, as the expression entirely depends on the choice of the basis.
One example would be the generalization of the standard matrix form of the oscillator's lowering... | {
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Work when there is more than 1 force I know that for an object with an applied force, the work done is
$$W = Fd \cos \theta.$$
I was wondering what would happen when there is another force (e.g. friction)? Is it better to say that the work done for a general case is
$$W = F_{net} d \cos\theta.$$
| To specify a work one must specify a force. E.g. the work of friction depends on the friction force, the net work depends on the net force, and so forth.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465793",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does friction not accelerate a wheel? It seems like a silly question because this defies common sense, but it appears that friction is supposed to accelerate a wheel (not attached to anything).
We can derive from Newton's laws that $\mathbf{F} = m\mathbf{a}$ works for an extended object just as it does for a point ... |
Consider the left hand wheel: it is either stationary or rolling at constant speed, without slipping.
For rolling without slipping the condition:
$$v=\omega R\tag{1}$$
holds, where $\omega$ is the angular velocity about the CoG of the wheel and $R$ its radius.
As both $v$ and $\omega$ are either $0$ or constant, this ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Physical example of line charge Electric field due to an infinite line charge, sheet of charge, point charge, etc are popular problems solved in most text on Gauss's law of electromagnetism.
My question: does an (exact or approximate) example of "infinite/finite line of charge" exist in the physical world?
While we fi... | Line charges are used in wire chambers, an apparatus used for high energy physics experiments.
There are lots of ways to make a line of charge. The easiest ones involve putting a charge on a wire. For example, make a large, thin metal ring of conducting material. Place the ring on an insulated stand. Place a positive o... | {
"language": "en",
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Why do prism split light at angle instead of curving it? I assume that when light goes through matter, it doesnt really slow down, but the waveform is pushed back due to some resonance with the atoms.
EDIT: Interference is probably a better word than resonance here
I also assume that the above effect is responsible for... | Light changes speed as it moves from one medium to another (for example, from air into the glass of the prism). This speed change causes the light to be refracted and to enter the new medium at a different angle (Huygens principle). The degree of bending of the light's path depends on the angle that the incident beam o... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is meant by "collective behavior" in the definition of plasma?
"Plasmas are many-body systems, with enough mobile charged particles to cause some collective behavior ." [M.S. Murillo and J.C.Weisheit Physics Reports 302, 1-65 (1998)].
In the above definition what is meant by "collective behavior" ?
| Collective behavior in Plasmas is the phenomenon where the way the plasma as a whole reacts/behaves is dependent on the behavior of each and every particle in the plasma. The overall behavior is the sum of the individual particles' behavior.
| {
"language": "en",
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Do scalar quantities have magnitude only? I've heard that vector quantities have both magnitude and direction but I've never heard that scalar quantities have magnitude only. Magnitude of vector quantities cannot be negative but what about scalar quantities, like temperature (-1°C)?
If scalar quantities don't have magn... | A vector quantity, $\vec V,$ can be written as $$\vec V=|\vec V|\ \hat V$$in which $|\vec V|$ is the magnitude of the vector, a scalar quantity which is non-negative. $\hat V$ is the unit vector in the same direction as $\vec V.$
The convention is that $|\vec V|$ is the product of a number and a unit, while $\hat V$ ha... | {
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Why is a delta resonance decay not a radioactive decay A delta resonance decays as given in http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/delta.html . I wonder, why is it not a radioactive decay? In principle, most/all decays should be radioactive as it is a quite broad description:
Radioactive decay (also know... | Usually we use the word "decay" for a state that's either metastable or that decays through the electroweak interaction. States that fall into these categories will tend to be relatively long-lived.
An example similar to yours that is not usually described using the word "decay" is neutron emission. Because there is no... | {
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"timestamp": "2023-03-29T00:00:00",
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Why is there so much iron? We all know where iron comes from. However, as I am reading up on supernovas, I started to wonder why there is as much iron as there is in the universe.
*
*Neither brown dwarfs nor white dwarfs deposit iron.
*Type I supernovas leave no remnant so I can see where there would be iron relea... | Iron comes from exploding white dwarfs and exploding massive stars(Wikipedia).
(One of many amazing images by Cmglee )
Periodic table showing the cosmogenic origin of each element. Elements from carbon up to sulfur may be made in small stars by the alpha process. Elements beyond iron are made in large stars with ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466889",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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As the universe expands, ultimately, will it continue to reach closer and closer, to absolute zero but never get there? First law of thermodynamics, the conservation of energy, doesn't this law all but guarantee that regardless of how far the universe expands it will forever contain its original amount of energy? All t... | In a dark-energy-only far future, the Universe will asymptote to the de Sitter temperature ($T_{ds}$), the minimum temperature possible in the Universe, which is NOT absolute zero (absolute zero is un-physical, the 3rd law of thermodynamics was actually quantified in 2016). In natural units:
$T_{ds}=\frac{1}{2πl} \appr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467119",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can Mars have an oxygen atmosphere? It is my understanding that, in its gaseous state, oxygen molecules move fast enough to achieve escape velocity. On Earth, we see this more clearly with helium. Regardless of what's happening on Earth, my question is about Mars.
Given the mass/gravity of Mars, would it be able to... | Ignoring escape, by whatever means, let's look at how much mass is needed to at least temporarily provide an atmosphere with a partial oxygen pressure of 0.21 atmospheres (the partial pressure of oxygen at sea level on Earth) at Mars surface. This is a simple calculation:
$$m_{\text{oxygen}} = \frac{A_\text{Mars}\,p_\t... | {
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Is naturalness meaningful for non-fundamental theories? Naturalness has been a guiding philosophy for particle physics for a long time, but a few years ago I heard a talk by Nima Arkani-Hamed where he pointed out that it seems to have failed us as it relates to the Higgs boson mass and the little hierarchy problem. He... | I can only recommend Sabine Hossenfelder's book: "Lost in Math: How Beauty Leads Physics Astray" on this topic. I think everything that needs to be said about naturalness is written down in that book. She argues that by demanding, that our fundamental theory has only natural parameters and no fine tuning, we assume to ... | {
"language": "en",
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Lorentz contraction of the wavelength of light I couldn't find this question on the suggested "similar questions". If this has been asked before please direct me to answer. My question is "why isn't the wavelength of light,which is in the direction of motion, going at the speed of light Lorentz contracted to zero inste... | I mean basically, it's because light is weird. Light is simply not intelligible as a classical thing which is moving and keeps an internal clock that is oscillating in time and has a wavelength by virtue of having some spatial extent. There is no classical thing that a photon easily corresponds to. Our best guess about... | {
"language": "en",
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Can electromagnetic waves apply forces on matter? Basically I want to know whether non-mechanical waves apply forces on matter?
| An electromagnetic (EM) wave is a particular realization of an electromagnetic field. Just like other electric fields, the field in the wave can apply forces to charged particles.
This is partially how radio receivers work. In a conductor like a radio antenna, the atomic nuclei and inner electrons are fixed in place,... | {
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Can quantum deletion error-correcting codes be constructed? I'm wondering whether or not we can construct quantum deletion error-correcting codes. The quantum deletion error is defined by the partial trace. If we can, could anyone give an example?
| It is well known that quantum error correction can also correct erasure errors. In fact, a code that can correct $k$ general errors (in arbitrary locations) can correct erasure errors in $2k$ locations. Thus, any quantum error correction code serves as an example.
To learn more about that, you could e.g. consult Pres... | {
"language": "en",
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Effect of earth's rotation in ballistics For this purpose, let's consider earth's rotations constant. Do earth rotation momentum get transfered to any object (a missile for example) that get's lauched? If so, why do we have to consider earth rotation when lauching the missiles? Wouldn't just follow earth rotation? (Btw... | When an object is launched, it initially shares the earth's rotation. That is one reason why most spacecraft launching sites are situated fairly close to the equator: it gives the spacecraft a free initial velocity of 1600 km/h (at the equator).
The atmosphere also shares the earth's rotation. If it didn't, the equator... | {
"language": "en",
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Feynman diagram for semileptonic decay of neutral kaon I am unsure how to draw a feynman diagram for a reaction that occurs as follows
$$ K^0 --> l^+\nu_l\pi^- $$
Any tips would be helpful.
| Drawing the most appropriate Feynman diagram can be a little tricky sometimes. I find it best to work backwards with the general rule of thumb being to try to minimize the number of vertices. We know that the lepton pair $l^{+}, \nu_{l}$ must come from a $W^{+}$ boson as that's the only mediator that conserves charge a... | {
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inertia tensor of rigid body in generalized coordinate frame? Assuming we know the inertial tensor of a homogeneous rigid body about a coodinate frame at its COM and aligned to it principal axes, how do we find the inertial tensor for the body in some other general coordinate frame which has a linear transformation (4x... | The general 4×4 transformation matrix has a structure where the top left 3×3 submatrix is the rotation + scaling factors. If there is no scaling, then extract the this matrix $ \mathrm{R}$ from $$\text{transform}= \left| \matrix{ \mathrm{R} & \vec{t} \\ \vec{0}^\intercal & 1 } \right| $$
Then you do the standard
$$ \m... | {
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Why doesn't a table tennis ball float on a surface of steel balls? How do we calculate buoyancy here? Place the beaker full of steel balls and submerge the table tennis ball under the steel balls. The table tennis ball does not float up. Why does it not float up? Do table tennis balls float when the diameter of steel b... | The ball bearings are behaving as a solid because the forces between the steel balls (i.e. friction) are large enough to hold the balls in position relative to each other.
If you apply enough force to a solid you will cause it to fracture or to cause plastic flow. So for example if you attached a string to the ball and... | {
"language": "en",
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Is there a physical difference between the colors of quarks? Is there any physical difference to the way, say, red quarks behave compared to green or blue ones? Or is it just an intrinsic property that they have that doesn't provide any physical difference other than that it allows two of the same to be in the same had... | Flavors are to designate the weak interactions of the quarks.
EM charge is to designate the EM interactions of the quarks.
Colors are to designate the strong interactions. The color with the strong force is always attractive, but it can come in neutralized combinations so that you can get stable bound quarks.
Your ques... | {
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Minimum Angular Velocity
A bead is free to slide on a vertical circular frame of radius $R$ comes to equilibrium when $\cosθ = g/Rω²$.
The minimum value of angular velocity comes out to be $\sqrt{g/R}$, which we can find out by balancing Gravitational and centripetal force with Normal reaction to bead from the frame... | The angular velocity can definitely have values in that range. It's just that you then lose that equilibrium position you reference.
If $\omega<\sqrt{g/R}$ then you only have two equilibrium positions. One at $\theta=0$ (the bottom of the ring) and the other at $\theta=\pi$ (the top of the ring).
If $\omega\geq\sqrt{g/... | {
"language": "en",
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Absence of phase transitions in quantum 1D systems at positive temperature While it is generally said that there are no phase transitions in classical lattice systems in one spatial dimension, there are also exceptions to this rule. Rigorous proofs involve some fairly strong assumptions about the statistical weights, s... | For translationally-invariant finite-range lattice 1d Hamiltonians, the absence of phase transitions at positive temperatures has been proved by Araki:
H. Araki, "Gibbs states of a one-dimensional quantum lattice," Comm. Math. Phys. 14 (1969), 120-157.
Later he gave a different (and less computation-heavy) proof which ... | {
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How do I Fit a Resonance Curve with Respect to Known Data? In an experiment, I collected data points $ (ω,υ(ω))$ that are theoretically modelled by the equation:
$$ υ(ω)=\frac{\omega \, C}{\sqrt{(\omega^2-\omega_0^2)^2+γ^2 \omega^2}} \,.$$
How can I fit the data to the above correlation? And how can I extract $\gamma$... | Don't try using any general-purpose curve fitting algorithm for this.
The form of your function looks like a frequency response function, with the two unknown parameters $\omega_0$ and $\gamma$ - i.e. the resonant frequency, and the damping parameter. The function you specified omits an important feature if this is me... | {
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If the water is not viscous, will the board rise? When no water passes, the board hangs downward; when water passes, the board rises. Why is that? Someone told me this is because water has viscosity or tension. Is this explanation correct? I found that even if the experiment was done under the water, the plate would st... | I think the main reasons are adhesive forces of water and board, pressure force due to flowing water has less pressure than atmospheric pressure. This force is even responsible for airplane's take off, peeling away of rooftops at the time of hurricanes.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470011",
"timestamp": "2023-03-29T00:00:00",
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Is it possible to trigger a nuclear reaction with physical force? In Mission Impossible Fallout, they're dealing with 3 plutonium cores. If one of those cores was thrown against a wall by Ethan Hunt, could it start a chain reaction and explode? For that matter, could any blunt force cause the nuclear reaction to initia... | Blunt force over a limited area of fissionable material does not cause a nuclear explosion. Over the years there have been two main ways to detonate a fission bomb, neither of which requires a radioactive trigger.
The first way is to bring two sub-critical masses together to form a single critical mass, and that's all... | {
"language": "en",
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What is the difference between linear and plane polarization? What is the difference between linear and plane polarization?
| I don't think there's any difference. Linear polarization is the more modern and, in my view, better term.
The idea is that in a linearly polarised wave, if we represent the displacement vector at a point in the path of the wave by an arrow, then the arrow tip oscillates back and forth along a straight line. [For circu... | {
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How does $r$ depend on $\varphi$ in the Schwarzschild metric? I am confused about the Wikipedia derivation of the equation
for geodesic motion in the Schwarzschild spacetime. The derivation of this equation involves variation with respect to the longitude $\varphi$ only then the variation with respect to the time $t$ ... | $\let\lam=\lambda \let\th=\vartheta \let\phi=\varphi
\def\cS{{\cal S}} \def\D#1#2{{d#1 \over d#2}}$
Your question can be answered from a more general viewpoint, without thinking of Schwarzschild metric and its geodesics.
You have a 4D spacetime $\cS$ with coordinates $t$, $r$, $\th$, $\phi$. A curve in $\cS$ is meant ... | {
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Black hole photography I recently read an article that said that the event horizon telescope took a picture of a black hole (Sagitarius A*) and it will be presented on the 10th of April. I was wondering how this picture is taken and what a picture of a black hole even means?
The only explanation I could think of was t... | The project is using a network of radio telescopes to measure radio waves emitted by ionized matter in the accretion disk around the black hole, and by ionized matter in relativistic jets that are being ejected along the rotation axis.
| {
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If atmospheric pressure is 76 cm of $\text{Hg}$ , why won't 76 cm of mercury stay in an open tube when suspended in air? If we keep an hold a tube in air with the closed end up and open end downwards, containing mercury upto a length of 76 cm, why does the mercury not stay in place? Shouldn't atmospheric pressure exert... | In an open tube there is atmosphere pressure acting on mercury from top end of tube.
In a closed tube,there is no air trapped above mercury. In fact there is vacuum.
In the construction of mercury barometer, for instance, we take a tube filled with mercury and carefully invert it into a cup filled with mercury. The pr... | {
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Quantum energy levels of a point mass rotating about a fixed point The question is: A particle of mass m is attached to a fixed point in space by a massless rigid rod of length a and can freely rotate about this point. Find the quantum energy levels of the system. What is the degeneracy of each energy level?
I used rot... | For each $l$ there exists $2l+1$ possible values of $m$. Since $m$ must be an integer, and $-l\leq m\leq l$, expanding out the associated Legendre function:
$P_l^m(x)\equiv (-1)^m(1-x^2)^{m/2}(\frac{d}{dx})^mP_l(x)$
where $P_l(x)$ is the $l$th Legendre polynomial in $x$, will show that there is $2l+1$ degeneracies. The... | {
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Why is Earth's gravitational acceleration $9.8 \frac{m}{s^2}$? How was the value of $g$ determined as 9.8 $\frac{m}{s^2}$?
I am not requesting the derivation but the factors/parameters that influence this value.
| 9.8 m/s^2 is not 'the Earth's gravity', it's the at-mean-sea-level acceleration
due to Earth's gravity. The acceleration would be quite different
if measured elsewhere, like at the lunar orbit.
The effective gravity constant also varies due to local mineral density,
and latitude.
Earth's gravity, in the universal sen... | {
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Potential by Assembling Charges For finding electric potential energy of a uniformly charged sphere, we can assemble the sphere by brining charges from infinity to that point. So to make a uniformly charged sphere of radius $R$ and total charge $Q$, at some instant, charge will be assembled up to a certain radius $x$. ... | Two cases described are completely different. In first case you find the true potential of the sphere by taking the charge from infinity to the surface of the sphere. In another case you take the charge from the middle of the sphere or the centre of the sphere to the surface of the sphere which is not the potential of ... | {
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Commutator of spacetime translation In Srednicki's textbook Quantum Field Theory, eq. (95.7) reads:
\begin{equation}
[\Phi (x, \theta, \theta^{*}), P^{\mu}] = -i\partial^{\mu}\Phi (x, \theta, \theta^{*}).
\end{equation}
where $\Phi (x, \theta, \theta^{*})$ is a superfield and $P^{\mu}$ is a generator of the Poincare gr... | Remember! Those are operators, and as such they act on some state $\varphi$. The second term, when operating on this $\varphi$, includes in fact two components
$$P_{\mu}(\Phi\varphi)=(P_{\mu}\Phi)\varphi+\Phi(P_{\mu}\varphi)$$
Put this back into the commutator to get your answer.
| {
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How to deal with motion on a 2-D lattice in terms of dimension? I am reading a paper titled: Random walks of molecular motors arising from diffusional encounters with immobilized filaments. There the authors consider the molecular motor moving on a 1-D protein filament in a 2-D unbounded media. They have used the frame... | I think that the $v$ they means is in Lattice units/Time step.
Probabilities are dimensionless usually (not a decay probability, that is $s^{-1}$) and indicate the jump probability during an unit of "time step" in your lattice simulation. How long to take this time step, you can choose to match the real situation. In t... | {
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Do working physicists consider Newtonian mechanics to be "falsified"? In the comments for the question Falsification in Math vs Science, a dispute around the question of "Have Newtonian Mechanics been falsified?"
That's a bit of a vague question, so attempting to narrow it a bit:
*
*Are any of Newton's three laws c... | One of the problems of Newton's law of universal gravitation, $$F_\text{Grav} = G \frac{m_1m_2}{r^2},$$ is that it does not correctly describe the precession of Mercury's orbit. Mercury behaves slightly different than predicted by Newton's law and general relativity does a better job.
See also the corresponding Wikiped... | {
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Magnitude of vector field I think this is more of a mathematical question, but since it's for a physics problem I decided to ask it here.
I have this complicated magnetic field in spherical coordinates $(r, \theta,\phi)$,
$$ \mathbf{B} = \left( B_r(r,\theta,\phi) , B_\theta(r,\theta,\phi) , B_\phi(r,\theta,\phi) \right... | Depends whether the components given are in terms the coordinate vectors, or unit coordinate vectors. If it's in a GR or field theory book it's probably the former, if it's in something like Jackson or Griffiths (an EM book) it's probably the latter. What you did is right in the first case. But if the basis vectors are... | {
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Expansion of an ideal gas at constant pressure I approach these expansion problems like so:
The gas and the surroundings(piston+outside) are at the same pressure at first. We heat the gas. The pressure rises inside the syringe a bit. The gas expands so the pressure remains constant. Then I use P(the constant pressure ... |
As in the as soon as pressure rises because of the temp rise the volume expands to "counter it". So pressure never really changes much. So it's okay to ignore it for calculations
If the piston moves by a little bit, then the pressure is literally the same. Considering $\Delta V \to 0$ which would mean $\Delta V \app... | {
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Can lasers cause glare or reflections? When going to the movie theater I sometimes notice reflections from the projector on my glasses and I find it very annoying. What happens is that the light hits the back of my glasses and i can see a reflection of it.
I am gonna watch a movie which is going to be projected using ... | Having a laser projector tells you very little about how the projector actually works. The only thing to know for sure is that the light source is some kind of laser (as opposed to e.g. Xenon arc lamps). The advantage is usually that they can be made a lot brighter and with a wider color gamut (they can generate more c... | {
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What is the electric potential inside a point charge? We know that electric potential of spherical charge is inverse proportion with $r$ from $V = \frac{kq}{r}$ , So if $r$ is getting less then electric potential will be higher.
But , What about point charge ? Is it infinity inside it ? My teacher told me that it's zer... | This post does not really answer your question, but still it is worth reading what I would like to highlight.
Point charge refers to electrons or protons.
But in no way does the electron seem to have a size, although it is still debatable today. So, what mathematics and our reality assumes today is that the electron i... | {
"language": "en",
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Is polarization complementary along its different axes? Is polarization complementary along its different axes -- much like the spin of a particle is -- thus implying that the uncertainty principle holds for polarization measurements on these different axes?
| The complementarity principle, formulated by Niels Bohr, states that objects have certain pairs of complementary properties which cannot all be observed or measured simultaneously. The type of measurement determines which property is shown, to be intended as the impossibility of any sharp separation between the behavio... | {
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Are there anti virtual particles (mediator bosons)? I have read these questions:
Can bosons have anti-particles?
Is there a possibility for discovery of anti-graviton, i.e. the graviton antiparticle?
Antiparticle for Higgs boson?
According to the accepted theory, the SM, all elementary particles do have their anti p... |
are there anti virtual bosons?
As you know, a virtual particle is a mathematical construct and is connected with the real particle of its name by the quantum numbers identifying the particle.
Also, you should know that all particles can be virtual within Feynman diagrams if they are not within the incoming and outgo... | {
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Field operator commutation: If two operators commute, then their fourier transforms also commute? Im doing this in the context of field operators $$\psi(x)=\sum_k a_k e^{ikx},$$
$$\psi^T(y)=\sum_k a_k^T e^{-iky},$$ and their being defined as the fourier transform of the creation/annihilation operators $a_k,a_k^T$. Spec... | A plug in will work.
The operation is very common in quantum field theory.
Please refer to any QFT textbook for canonical quantization techniques.
$[\psi(x),\psi^{\dagger}(y)]_{\xi} = [\sum_k a_{k}e^{ikx}, \sum_k' a^{\dagger}_{k'}e^{-ik'y}]_{\xi} = \sum_{kk'} e^{ikx-ik'y} [a_k, a^{\dagger}_{k'}]_{\xi} = \sum_{kk'} e^{i... | {
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Is positron creation operator times electron creation operator equal to the ground state? This is part of a larger problem, but the important part is that at one point I have:
$$
bb^\dagger+bd+d^\dagger b^\dagger + d^\dagger d + b^\dagger b +db + b^\dagger d^\dagger+d d^\dagger
$$
where $b^\dagger$ and $b$ are the crea... | The proof that the anticommutator of different annihilation operators and its complex conjugate can be shown as follows (demonstrated in Srednicki's notation, i.e. in "west coast Minkowski metric", in particular $e^{ipx} = e^{i(\mathbf{p}\mathbf{x} - \omega_p t)}$ , furthermore it requires some relations of spinor alg... | {
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How does light 'choose' between wave and particle behaviour? Light exhibits wave behaviour in phenomenon such as interference but particle behaviour in the photoelectric effect. How does light 'choose' where to be a wave and where to be a particle?
| The fundamental experiment showing the apparent contradiction is Young's double slit: How can particle characteristics be transmitted when there is only an interfering wave between the point A of emission and point B of absorption?
However, for photons in vacuum (moving at c) there is a simple answer: The spacetime int... | {
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If a satellite speeds up, does that make it move farther away or closer? If a satellite is in a stable circular orbit and goes about 41% faster (escape velocity) then it leaves its host forever. I get that. However, what if it speeds up by less than 41%?
Intuitively, it would seem to make the satellite move farther awa... | An orbit of a mass $m$ in the Newton potential of an immobile (for simplicity) mass M can be characterised by two constants of the motion energy, $E=mv^2/2-GMm/r$ and angular momentum L. E fixes v as function of r and L subsequently its direction. For a circular orbit v and r are constant. The increase r for a circula... | {
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Lorentz Transformation: Message sent before finish line As she wins an interstellar race, Mavis has a “hooray” message sent from the back of her 300m long ship as she crosses the finish line at v=0.6c. Stanley is at the finish line and at rest relative to it. He claims the message was sent before she crossed the line... | First note that if Mavis has received this message while she is at finishing line, it'd mean the message was sent earlier, before she cross the finishing line.
I wish you had explained it more clear than this, but do note that
while in Mavis frame the signal had to travel 300m plus the contracted distance between the ... | {
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If an electric field passing through a dielectric medium, back into the original medium, is it "back to normal"? Suppose there is an electric point charge causing an electric field E in a medium with a dielectric constant $\epsilon_1$. You can calculate the scalar potential $\phi$ at a given distance $r$, as well as th... | This can be compared to the setup of a parallel plate capacitor with three layers of mediums inbetween, parallel to the plates: layer one with $\epsilon _1$, layer two with $\epsilon _2$ and layer three again with $\epsilon _1$. The electric field is created by charges on the two plates.
Now if you separate this one ca... | {
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What had Feynman meant when he told nobody understands Quantum mechanics? What do we mean by understanding Quantum mechanics? What had Feynman meant when he told nobody understands Quantum mechanics?
What do we mean by understanding Quantum mechanics?
|
What had Feynman meant when he told nobody understands Quantum mechanics ? What do we mean by understanding Quantum mechanics?
He probably meant that there is no inherent in our classical physics training, intuitive expectation of the behavior of matter in the quantum framework.
In the classical framework, we under... | {
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CFT in momentum space Is there a way to see the conformal symmetry in momentum space in a CFT? I mean if I can recover the conformal group in some way in momentum space.
| The generator of special conformal transformation act, schematically, as
$$
K\sim x^2\partial_x+x\partial_x.
$$
In momentum space this becomes
$$
K\sim p\partial_p^2+p\partial_p.
$$
Since $K$ is a second order differential operator, $e^{\lambda K}$ does not act in a local, geometrical way on functions.
So while it is p... | {
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Will tsunami waves travel forever if there was no land? If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?
| To answer this, I would appeal to the general principle which we call the 2nd law of thermodynamics. One way of expressing it is that the entropy of an isolated system cannot decrease. This means that in order to keep going for ever, a wave motion would have to involve no entropy increase. But almost all processes invo... | {
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Difference in the direction of propagation of em wave How are kx-wt and kx+wt in terms of the direction of the wave. I have been stuck at this or an hour, still can not find a definitive answer.
| Generally, the phase of the eletromagnetic wave is going to be $\phi = \vec k \cdot \vec r \pm wt$; from this expression, we can interpret the direction of the wave. Take a fixed time, then look for direction of the $\delta \vec r$ that maximizes your $\delta \phi$. That's the direction of propagation of the wave. It w... | {
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How is the relative force of the fundamental forces measured? My physics textbook includes the following table:
My question is about the fourth row, where it compares the relative strengths of the fundamental interactions. How are these determined? Is the ratio of electromagnetic and gravitational simply the ratio of ... | There is also another good answer re the strengths of the known forces in this blog
Summary:
Take two objects of some type, perhaps elementary particles, and place them a distance $r$ apart. Suppose each exerts a force $F$ on the other. Then we will say this force is weak if $F$ is much less than $ℏc\over r²$ where $... | {
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Transformation connecting two representations - Quantum mechanics I am working on Dirac's paper The Lagrangian in Quantum Mechanics. He looks for the analogy between a classical transformation between two sets of coordinates and momenta $p_r$, $q_r$ and $P_r$, $Q_r$ ($r = 1,2,\dots n$) and the transformation in quantum... | Note that
$$\langle q|p_r|q'\rangle
= -i\hbar \frac{\partial}{\partial q_r}\langle q|q'\rangle
= -i\hbar \frac{\partial}{\partial q_r}\delta(q-q').$$
| {
"language": "en",
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What should be the independent variable in a resistance experiment? I was asked a question by a student today and I have been pondering about it for a while now. In an experiment to measure resistance of a conductor, should we vary voltage across the conductor and measure the current or should we vary current flowing i... | In addition to what @The Photon has suggested, have you considered using a Wheatstone Bridge? Although it is an old method and digital multimeters provide a simple way to measure resistance, a Wheatstone Bridge can be used to measure very low values of resistances in the milli-ohms range. Whether or not it is useful w... | {
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What is the temperature of the black night sky, outside the atmosphere? The sky at night is rather black. If it were completely black, it would correspond to a black body at absolute zero. But the sky is not completely black. Is there a way to assign a temperature value to the actual black night sky?
The question is no... | It depends on what you mean by “sky”. The Earth’s atmosphere has a large range of temperatures at various altitudes, generally getting colder and colder from the surface temperature as you go up.
If what you are actually asking is the temperature of deep space, then it is 2.725 K, the temperature of the cosmic microwav... | {
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Why can I throw a larger stone farther than a smaller stone? Recently I was throwing stones(don't ask me why) when I noticed that there seems to be an optimum weight of stone so that it travels the farthest.
If I generate the same amount of force each time(and assuming all other variables like air resistance, angle of ... | That is because a smaller stone though experiences less air resistance, it is more affected by the same than the larger stone. A larger stone on the other hand is not affected by gravity as much as the smaller stone is and also has the advantage of inertia of motion which does depend upon mass and size of object (Try s... | {
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Z and $\gamma$ bosons as mixtures of W and B: Part I When it is said that the photon is "a mixture of W and B" ($B$ being a gauge field associated with the $U(1)$ hypercharge)
I have a question on this:
*
*When speaking of "mixtures", this is meant as analogous to the quantum mechanics terminology as the linear comb... | Physics SE has a one-question rule, so I will answer your second one.
The photon being a “mixture” of the $B$ and the $W$ means that the photon’s quantum field is a linear combination of the $B$ quantum field and one of the components of the $W$ quantum field:
$$A_\mu=B_\mu\cos{\theta_W}+W^3_\mu\sin{\theta_W}$$
The mix... | {
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Why does it takes so much time for photons to reach surface of sun from its core? I have read somewhere that the time taken by photons to reach the surface of sun is very large as compared to time it takes to reach earth from the surface of sun . Is the presence of dense gases in sun reason for that.
| Yes, you can model the path of the photon as a random walk (https://en.wikipedia.org/wiki/Random_walk).
This means that the distance a photon reaches after a certain amount of time is given roughly by:
$$ D(t) = \lambda_\text{MFP} \sqrt{N_\text{coll}},$$
where $\lambda_\text{MFP}$ is the mean free path of the the phot... | {
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How much energy is required to perform the Saitama's moon-jump? I have no real knowledge of physics beyond the very basics of classic Newtonian mechanics, but as far as I understand, when a particle moves closer to the speed of light, its "relativistic mass" becomes greater, which means it requires more and more energy... | The average velocity is given by the same formula from Newtonian physics, so $v=\frac{1 ls}{10 s}=0.1 c$. The Lorentz factor corresponding to this velocity is $\gamma=\frac{1}{\sqrt{1-0.1^2}}=1.005$, so relativistic effects are not that great.
By energy "consumed," I'm guessing you mean the kinetic energy they have, wh... | {
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Current in the inductor at $t=0$ $L_1 = 5H, L_2=0.2H, M=0.5H, R_0=10 Ω$, and $i_g=e^{-10t}-10 A$. I need to find $i_2$.
I've started with DE
$$i_2R_0+L_2(di_2/dt)+M(di_g/dt)=0$$
and solved it for $i_2$, so $$i_2=0.625e^{-10t}+Ce^{-50t}A,$$
where C is constant.
I can't find C because I don't understand how to obtain... | Accidentally seen this question again and found the solution. Maybe someone needs it too. I've started with stating that initially
$$v_2=M(di_1/dt)=-5e^{-10t},$$ so $v_2 (0)=-5 V$. Besides, $$v_2(0)=L_2(di_2(0)/dt)=0.2*(-6.25-50C),$$
so C=0.375. Thus $$i_2=0.625e^{-10t}+0.375e^{-50t}A,$$
and answer in the end of the bo... | {
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Is throwing dice a stochastic or a deterministic process? As far as I understand it a stochastic process is a mathematically defined concept as a collection of random variables which describe outcomes of repeated events while a deterministic process is something which can be described by a set of deterministic laws. Is... | Look up Diaconis's work on flipping coins. While it is technically deterministic, what happens is that extremely small changes in the initial conditions flip the outcome. The same would be true of dice. When you shake them in your hand and throw, small changes would give different outcomes. What makes it seem random is... | {
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Magnetic field at boundary of electromagnet iron core Assume you have an iron core in the interior of the solenoid. It is well known that the strength of the field should increase by a factor of several hundred inside the solenoid as a result of the iron core.
However, at the boundary between the iron core and the sur... | Solenoid has a core in the shape of a cylinder. When magnetized, such cylinder produces its own magnetic field $\mathbf B$, orders of magnitude stronger than the external field due to electric current, but this is apparent mostly near its poles - ends of the cylinder and it is also true inside the core.
This magnetic f... | {
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Is there a temporal difference between planets due to the sun's gravitational field? since the Sun generates a gravitational field it also generates gravitational time dilatation. Hence, time further from the Sun should pass quicker than in its proximity.
Can we, therefore, say that the time on Mercury is different fro... | Clocks on the surface of each planet tick at different rates. It is a small effect, amounting to a moderate number of parts per billion.
I used Mathematica to calculate the time dilation on the surface of the Sun and the surface of the planets, relative to a clock far from the solar system that is stationary relative t... | {
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Shape of orbitals in atoms with multiple electrons I found this statement when browsing the Wikipedia article for atomic orbitals:
"Orbitals of multi-electron atoms are qualitatively similar to those of hydrogen."
Is this true? Googling around I could only found this article where in page 50 it seems to address how to ... | What is meant is that the quantum numbers of the hydrogen solutions are still relevant for multi-electron orbitals. You still have shells 1s, 2sp, 3spd, etc.
There is not a "proof". What is there is excellent agreement between quantum chemical calculation and experiment.
| {
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Can you change the wavelength of light keeping frequency constant and can you do the opposite as well? Can you change the wavelength of light keeping frequency constant and can you do the opposite as well?
I understood the basics but please don't hesitate to go deeper into the concept. Also, If you happened to have an ... | As mentioned, wavelength changes in different media depending on the index of refraction. Changing the frequency can be done with non-linear optical effects, notably frequency doubling and similar effects. This change in frequency has a corresponding change in wavelength however, as opposed to the change in wavelength ... | {
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Why does electrical resistivity have units of $\Omega \cdot \mathrm{m}$ rather than $\Omega \cdot \mathrm{m}^3 ?$ Electrical resistivity has units of $\Omega \cdot \mathrm{m} .$ However, since resistivity can be described as the resistance of a unit cube, shouldn't the units therefore be $\Omega \cdot \mathrm{m}^3$ in... | The resistance $R$ of a body grows with bigger length $l$
(a longer wire has greater resistance)
and shrinks with bigger cross-section area $A$ (a thicker wire has smaller resistance).
Hence you have
$$ R = \rho\frac{l}{A}$$
and resistivity $\rho$ must have unit $\Omega\cdot$m.
| {
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"answer_id": 0
} |
Why wavefunction becomes exponentially smaller during quantum tunneling? I am interested in quantum tunneling and I am wondering why the wavefunction of a particle would becomes smaller so that there is a slight possibility of finding it at the other side of a big energy barrier? Is there any interaction otherwise how ... | The classic step barrier is the easiest to solve but the general behavior holds for other functions. The comment addresses the physics of your question, i.e. "the presence of a potential barrier is what defines an interaction". This is the same for classical mechanics. One could ask, "How does the earth know to move... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/479161",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
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