Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Quantum gravity in an accelerated frame of reference It is said that we can't study quantum gravity because gravity is a weak force. But gravity and acceleration are the same. Why can't we study quantum gravity in a strongly accelerated frame of reference?
| This is a classic case of equivocation. The word "gravity" is used in the question with two related-but-different meanings:
*
*When we say "gravity is weak," we mean that a lot of stuff (like matter) is needed in order to give spacetime a noticeable amount of curvature.
*When we say "gravity and acceleration are th... | {
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Why the mechanism of everything in the universe has a pattern? why everything in the universe has a pattern which can be identified and understood to determine outcomes, properties, effects of almost everything. I am saying that couldn't the universe be like patternless, non-deterministic and chaotic. For example why t... | As a matter of fact, we do have a quantifying parameter for chaos, which is Entropy.
In terms of entropy our universe is chaotic, but for better or for worse, this chaos seems to increase monotonically with the passage of time, which is a predictable feature, unlike what you would want. Maybe in future, its possible th... | {
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Will two bodies initially connected to and revolving around each other, start spinning when disconnected? Two extended bodies are connected with a string and revolve around each other (that is, around the center of mass of this system). No gravity, no external forces.
The string is cut, and they start to depart from ea... | The bodies are spinning before the string is cut, once per revolution. Since neither the string nor the cutting of the string apply torque to the bodies, there will be no change of rotational speed for the bodies, so they will keep spinning.
To think of this another way: at the moment the string is cut, the part of the... | {
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Do we hear sound at pressure or displacement antinodes? I have read from Young & Geller (2007), College Physics 8th Edition, Pearson Education Inc. (pg 385) that we hear sound at pressure anti-nodes rather than displacement anti-nodes as microphones sense pressure variations.
When we have 2 speakers facing each other ... | I was visiting a science center which had an acoustic standing wave set up in a long tube through which people could crawl. The standing wave pattern was drawn on the side of the tube and it looked to me that they had made a mistake be showing nodes at the two open ends however, when I did crawl through the tube, I fou... | {
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Density operator in different bases This may sound like a silly question, and it probably arises from a weak understanding of the concept.
What I was wondering is: given a density operator $\varrho=\sum_{i,j}p_{ij}|i\rangle\langle j|$, can we find separate bases for which $\varrho$ is diagonal, but presenting different... | If I understand your question correctly, then the answer is no. The eigenvalues of an operator - which are simply the diagonal entries when that operator is diagonalized - are uniquely defined up to trivial reordering. Furthermore, the vectors belonging to distinct eigenspaces are orthogonal because $\rho$ is self-adj... | {
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Light: reflection and transmission When white light hits a thin "transparent material", is there a general relationship between the spectra of the reflected and transmitted components?
For example, do red filters (that make things look red when viewed through them) also look red when light is shined upon them? Or is th... | "White" light is a bit ambiguous. Let's just call it a mixed spectrum of wavelengths in the visible spectrum for now.
Now, for a given material, assuming it is semitransparent, there is a spectrally varying reflection coefficient. The light that isn't reflected has the complement to that curve (highly reflected light ... | {
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How do I decompose an $SO(10)$ antisymmetric tensor in $SO(4) \times SU(3) \times U(1)$? My guess is that If I denote the $SO(4)$ indices $\mu, \nu = 1,...4$ and the $SU(3)$ indices by $I,J=1,2,3$, I think $N^{mn}$ should decompose as $N^{\mu \nu}, N^{IJ}, N^{I}_J, N_{IJ}$ plus other terms with mixed indices $I,\mu$, ... | Hints:
*
*Firstly,
$$SO(10) ~\supseteq~ SO(4)\times SO(6),\tag{1}$$
so we get the branching rules
$$ {\bf 10}~\stackrel{(1)}{\cong}~({\bf 4},{\bf 1}) \oplus ({\bf 1},{\bf 6}),\tag{2}$$
and
$${\bf 10}\wedge{\bf 10}~\stackrel{(2)}{\cong}~ ({\bf 4}\wedge{\bf 4},{\bf 1})\oplus ({\bf 4},{\bf 6})\oplus ({\bf 1},{\bf 6}\wed... | {
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What is the intuition behind the spacetime interval? In an article that I am currently reading (under the Lorentz Invariants sub-heading), it explains that, just as the distance between two points on a Cartesian plane are obviously invariant of the coordinate system, the “spacetime distance” is also invariant. While in... | The intuition is not too difficult to build. For convenience, I will write $\Delta x$ instead of $x_1-x_2$.
First, we know from the first postulate that the speed of light is invariant. If we write $$\Delta x^2 + \Delta y^2 + \Delta z^2 = c^2 \Delta t^2$$ this is the equation of a sphere of radius $c \ \Delta t^2$. In ... | {
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Induced emf in a rotating disc A question in my book was given as
A conducting disc of radius R rotates about its axis with an angular velocity $\omega$. Then the potential difference between centre of mass of disc and its edge is (no magnetic field is present)
The answer stated that:
*
*There will be a potential d... | Both these questions have been asked (and answered) within the last 3 or 4 weeks on this site. The gist of the answer to your main question is that the 'centrifugal emf' is very much smaller than the 'magnetic emf'. You should show this for yourself by putting figures into your formulae. [Note that a magnetic field of ... | {
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Intensity of reflexion of circular polarization Circularly polarized light, can be caracterized as :
$$E(r,t) = E_0 \cos(kz-\omega t) \hat{x} + E_0 \sin(kz-\omega t) \hat{y}$$
In my course, the Intensity of EM radiation is defined as $I = |U|^2$.
And we defined polarized monochromatic waves as follows (i already put th... | Yes, you take the sum of the intensity along each axis. But you do not miss the factor of $1/2$ by doing that. The reason is that the total input intensity to the reflection is $I_0=U^2=|E_x|^2 + |E_y|^2$ and $|E_x|=|E_y|$; Along each axis the input intensity is ${I_0}/{2}$. With reflection reflectivity $R_s$ and $R_p$... | {
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Newtonian vs Lagrangian symmetry Suppose we have a ball of mass $m$ in the Earth's gravitational field ($g=const.$). Equation of motion reads as:
$$
ma = -mg
$$
From here we can conclude that we have translational symmetry of the form $x(t) \to x(t) + const$ (we are working in only 1D). However, we cannot see this sym... | You can do an integration by parts on the last term (and discard the resulting boundary term) to yield an action with equivalent EOMs:$$
S'= \int \left( \frac{1}{2} m \dot{x}^2 + m g t \dot{x} \right) \, dt
$$
In this context, the symmetry $x \to x + C$ is obvious at the level of the Lagrangian. Moreover, the Euler-La... | {
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Are Newtonian forces real forces or just a useful construct? I am new to physics but not new to science/scientific thinking.
Since I was young I have never really understood how to interpret the Newtonian forces. In some cases they seem very real. E.g. the static friction force can be nicely explained as gluing of atom... |
We see that the objects are not moving so to be self-consistent with
this massive framework of forces we are building we are claiming that
the table is exerting a force towards the object.. Yeah sure! What
kind of atomic interpretation could this have?
Everything we see around us is made of atoms (mostly organised in... | {
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Is there a physical reason behind electromagnetic energy and momentum being derived from the Lorentz force equation? The effect of the EM field upon a charge $q$ is given by the relativistic Lorentz force equation:
$$\frac{dP}{d\tau}= qF^{\alpha\beta}U_{\beta}$$
The expression on the RHS is then substituted via Maxwell... | The relativistic Lorentz force equation ensures that the four force $\frac{dP^\alpha}{d\tau}$ is a contravariant four vector. In particular, the quantity
$$
\frac{dP^\alpha}{d\tau}\frac{dP_\alpha}{d\tau}=\left(\frac{dP^0}{d\tau}\right)^2-\left(\frac{dP^1}{d\tau}\right)^2-\left(\frac{dP^2}{d\tau}\right)^2-\left(\frac{dP... | {
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Why is the angle between the radial velocities at two instants the same as the angle between the tangential velocities at those same instants?
While it is clear that the angle between $v_r$ and $v_r + \Delta v_r$ is $\Delta \theta$, I cannot see a clear geometric reason as to why the angle between $v_t$ and $v_t + \... | The statement is obviously true for motion in a circle. For any short arc (swept out in a short time) a center of curvature can be found so that the arc can be considered part of a circle.
| {
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What will be the angular velocity of a line about a line that is at some angle with the plane of motion? In this book it is written that angular velocity of a rigid body is time derivate of "angular displacement" of any line in the plane of motion of the body. The angular position of the line is measured from any conve... | If a solid object is rotating about fixed axle, all points (and lines) in that object will circle the axle in the same period of time. (They have the same angular velocity.)
| {
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Why do icebergs flip over? Why do icebergs flip over? Are certain shapes of icebergs more "stable" than others, in that it's harder to flip them over? If so, why?
For example, it somehow makes intuitive sense, that a thick iceberg with a certain height (or depth, because 90% of it is below water) would be harder to fli... | This is a nice Newtonian physics question. A very simplified analogue to this is to consider the stable positions of a 2-dimensional table shape iceberg with length $L$, width $W$ ($W < L$).
Typically the material density ratio of $\rho_{\text{ice}} / \rho_{\text{water}} = 0.9$. In a force equilibrium, this leads to th... | {
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Why isn't time reversal a Galilean transformation? I'm a mathematician learning physics from scratch, starting from Newtonian mechanics. As far as I understand, Galilean transformations are defined as transformations of space-time that transform from one inertial frame to another. In turn, an inertial frame is a frame ... | It certainly seems inconsistent to include spatial reflections but at the same time to exclude time reversal.
One reason for excluding both spatial reflections and time reversal from the definition (the convention followed in Wikipedia, for example) is that this means the topological group of Galilean transformations h... | {
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Can an electron near thar the positive terminal of a battery make it all the way to the positive terminal? Following Drude's model of conductivity, can an electron near thar the positive terminal of a battery make it all the way to the positive terminal? The electron is in the wire but near the positive terminal. At le... | Maybe, if the circuit is small enough, and runs for long enough.
The velocity of an electron through a wire is approximately 1mm/second. As a result, if you have a circuit 1cm long, and you let it run for 10 seconds, then an electron that starts off at the negative end of the circuit would reach the positive end of the... | {
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When a person pulls or pushes a cart, why is it advantageous for their body be tilted forward? This is not a homework question. I attempted to draw a free body diagram for a person pulling or pushing a cart.
Based on Newton's third law, the following forces act on the body of the person:
*
*forward reaction force don... | It's similar to why when you pull something with a rope along the ground it can never be vertical. It needs to have a horizontal component to apply a horizontal force.
This is not quite as true with rigid structures like legs, but it similar in that it reduces bending stresses on the leg bones and torques on you knees ... | {
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When a car accelerates relative to earth, why can't we say earth accelerates relative to car? When a car moves away from a standstill, why do we say that the car has accelerated? Isn't it equally correct to say that the earth has accelerated in the reference frame of the car? What breaks the symmetry here? Do the force... | Assuming the acceleration of the earth is immeasurably small due to its vastly larger mass, I think your confusion actually stems from this:
Isn't it equally plausible to say that the Earth has accelerated from the point of view of the reference frame of the car?
It depends what you mean by the reference frame of the... | {
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Find the values of $A$, $B$, and $C$ such that the action is a minimum
A particle is subjected to the potential $V (x) = −F x$, where $F$ is a constant. The particle travels from $x = 0$ to $x = a$ in a time interval $t_0 $. Assume the motion of the particle can be expressed in the form $x(t) = A + B t + C t^2$. Find ... | I suspect that this is not the approach that the problem author wants you to take. Were I confronted with this problem, I would do the following:
*
*Determine what the conditions $x(0) = 0$ and $x(t_0) =a$ tell me about the parameters $A$, $B$, and $C$. I should be able to eliminate two of them in favor of the thir... | {
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Relation between potential energy and conservative force Does potential energy only happen when the work done is by a conservative force? Or does work done by non-conservative forces also create potential energy?
| For a conservative force the following property is true
$$\oint_C \vec F \cdot \vec {dl}=0$$
Using stokes theorom:
$\oint_C \vec V \cdot \vec{dl}=\iint_S (\vec \nabla \times \vec V)\cdot \hat ndA$ where $\hat n$ is a normal vector which gives
$$\vec \nabla \times \vec F=0$$
as a matter of fact if $\vec F$ can be writte... | {
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Why and when can the Earth be considered an inertial reference frame? The question has been asked (e.g., here and here), but I would like to get a more definitive and mathematically formal answer.
The Earth rotates around its axis, around the Sun, and participates in larger scale motions as a part of the Solar system. ... |
The components of the earth rotation at the latitude $\lambda$ are:
$$\mathbf \Omega_E=\begin{bmatrix}
0\\
\cos(\lambda)\, \Omega\\
\sin(\lambda)\,\Omega\\
\end{bmatrix}$$
from here we can obtain the pseudo forces due to the earth rotation
$$ \mathbf F_s=m\,\big(2\,(\mathbf\Omega_E\,\times \mathbf{\dot{R}})+\... | {
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Why exactly is the resistance of a conductor inversely proportional to the area of its cross-section? Before I explain my query, I would like to clarify that I am a ninth-grader who got this question while studying the formula $R \propto \frac{1}{A}$ where $A$ is the area of cross-section.
I have often asked this quest... | Sorry for my poor english. My native language is french.
We can also ask the question about the conductance: why is it proportional to the surface.
The reason is that we are working with a model in which the current density is distributed uniformly over the cross section of the conductor. It is as if we had a lot of id... | {
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Could dark matter be explained by the fact of empty space expanding much faster than space inside galaxies? We know the expansion of the universe is accelerating and mass slows time.
So pockets of empty space experienced more time since the big bang.
That mean the current expansion rate of empty space is much faster an... | No.
We observe the effects of dark matter within galaxies and across galaxy clusters, as well as across the entire universe. So it is by no means just about the rotation curves of galaxies, and your idea can not explain the data.
Yes, current models of structure formation properly take this effect into account - by ign... | {
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Hartree type diagrams in Altland Simons We are told in equation 5.25:
$$F^{(2), 1} = - \frac{T^3}{L^6} \sum_{p_1, \, p_2, \, q} \; G_{p_1} \; G_{p_1 + q} \; G_{p_2} \; G_{p_2 + q} \; V(q)^2$$
$$F^{(2), 2} = \frac{1}{2} \frac{T^3}{L^6} \sum_{p, \, q_1, \, q_2} G_p \; G_{p - q_1} \; G_{p - q_1 - q_2} \;\; G_{p - q_2} ... |
In particular, for the first equation we need small $|q|$, $|p_1|≃p_F$, and $|p_2|≃p_F$. Don't we just need for the second equation small $|q_1|$, small $|q_2|$, and $|p|≃p_F$?
This is correct. But notice, while small $|q|$ requires fine-tuning in all 3 directions in k-space, the condition $|p_1|\simeq p_f$ requires ... | {
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Distances in General Relativity, near massive bodies I've been studying the basics of General Relativity, and my question is: does it make sense to say that near a black hole (or any massive body), distances increase, the way on a topographical map the contours get closer and closer near a steep hill? So that an object... | You can form $\int ds$ along a radial line at some given $t$ and thus create a notion of ruler distance. The ruler distance from the horizon is finite. You can see this also by looking at Flamm's paraboloid: distances along the paraboloid are finite.
However the time required for a particle to move outwards from the ho... | {
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Can one make already separate atoms/electrons entangled? Is it possible to make two separate atoms or electrons entangled on a quantum level? Not photons, those I know can be entangled already
| As soon as two atoms or electrons interact with each other, they become entangled.
Say you shoot two atoms against each other in a collision experiment. At $t=0$ the atoms have a definite momentum $\hbar k$, $|\Psi \rangle = |k\rangle |-k \rangle$. After the collision, they will be in a superposition of different momen... | {
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Normal force shift for ball kept in cavity
Adapted from JEE advanced paper-1 of 2020
If you see the left side of the Planck which the ball touches, it seems so that as we vary $\theta$, the contribution of the force from that point of contact drops to zero. I have marked the point of interest in paint:
As we reduce... | If we assume that the two sides can exert a force only normal to ball, and that they are the only forces on the ball other than gravity, then this becomes just a linear vector solution.
The two forces must sum to zero out gravity and simultaneously have net zero horizontal force. This can only happen if the "downhill"... | {
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What is the meaning of complex distances in relativity? In flat Minkowski space with the metric signature (-,+,+,+) the spacetime interval $ds^2$ is defined as
$ds^2 = -c^2 dt^2 + x^2 + y^2 + z^2$
This interval (or better the square of the distance) can become negative (for timelike intervals) so the spacetime distanc... | The scalar $ds^2:=dx^\mu dx_\mu$ is real, but its sign changes when you switch metric convention. Whether $\sqrt{ds^2}$ is real or imaginary is therefore not purely a physical question.
On the other hand, if $ds^2\ne0$ then $dx^\mu$ satisfies either $dt=0$ or $dx^i=0$ in a suitable reference frame, and which is applica... | {
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Confusion on Normal force and its resolution on inclined plane I had the following doubt regarding normal forces and its resolution on inclined plane. (Also I am quite new to SE, so I have no idea how do we upload diagrams to better represent my arguement).
Consider two cases, in both cases there is a inclined plane wi... |
So in one sense we will be saying that the horizontal component of the block's acceleration is also 0
This would be true if you were to replace 'horizontal component' by 'contribution to the horizontal component'.
However there is an acceleration down the plane, and that has a horizontal component.
| {
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What is light cone? Explain to mathematicians who understand the Lorentz group but not light cone Mathematically the Lorentz group is precisely the $O(1,3)$ is the 4-vector rotation preserving the inner product of 4-vector under this metric
$$
\eta_{\mu \nu}=(+1,-1,-1,-1).
$$
There are four distinct sectors of this $O(... | The light cone is definied to be the set of 4-vectors
$(ct,x,y,z)$ satisfying
$$c^2t^2 - x^2 - y^2 - z^2 = 0.$$
Or written in covariant notation
$$\eta_{\mu\nu} x^\mu x^\nu = 0.$$
(image from Einstein for Everyone - Spacetime)
| {
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Where the reaction force from Newton's third law is acting on this body? In the diagram below I have a fire extinguisher sitting upright on a skateboard. Gas is being expelled out of the fire extinguisher and causing the skateboard to move forward (which is to the right in this picture). This would work in a vacuum as ... | The action force is the substance being pushed out of the extinguisher to the left of the diagram, labelled "force A". The reaction force is then the same substance pushing back on the extinguisher in the opposite direction labelled "force B", and since it is connected to a skateboard,
this force will cause the skatebo... | {
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Do I have to apply more force than gravity to lift my leg above the ground? How much force do I do apply when I lift my leg above the ground? The same amount as gravity does on my leg (mg)? Or MORE than it (greater than mg)? If the displacement from the ground to my lifted leg is h meters, then what's the work done? mg... | Firstly laying out my physics/math assumptions
*
*no friction
*only moving the leg vertically (as if you are lifting a bag)
*constant gravity, $g$
*force on leg, $F$, only varies with time
*for $t<0$ the ground provides the force to stop movement
therefore we can limit movement to 1 dimension, $x$
and from ne... | {
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How does light from distant galaxies reach us? Why doesn’t a ray of light which is emitted by a distant galaxy, say about a thousand light years away, die down in between?
I mean, how do the light rays from different galaxies so far away reach us in this day and age, when they were emitted so long ago? Why aren’t they ... | As other answers tried to explain, it's not about what mechanism would prevent photons from getting lost but finding a mechanism that would remove sufficient photons so we couldn't observe them any longer.
according to our understanding of fundamental physics:
mass less objects travel with the "speed of light"
Accordin... | {
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Where should the reference point be considered during torque measurement? This is an extremely silly and wierd question.
https://en.wikipedia.org/wiki/Varignon%27s_theorem_(mechanics)
While reading about Varignon's Theorem in wikipedia I noticed this sentence,
"If many concurrent forces are acting on a body, then the... | Not so silly. Toppling of a cylinder on a block may help set the stage. A torque is a pair of anti-parallel forces of equal magnitude with a sideways displacement applied to an object.
Suppose you have a pulley supported by a fixed axis. Suppose a bunch of forces are applied to the pulley, causing it to spin. The fixed... | {
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Can we bend a light ray into any closed loop? Suppose we have a medium with varying refractive index and a source of light inside that medium emitting rays. Is it possible to bend the ray into any closed loop?
As the medium has varying refractive index, is it possible?
And if possible, how will it look like if anyone s... | Ok so here are my thoughts. I wanted to construct something like a clock where each circular sector is made of a different material. The incoming angle of the light ray with respect to the boundary of the first to the second layer is $\alpha$ (see image). To make things easy I wanted to choose the second material and c... | {
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Group velocity (open vs periodic boundary conditions) I'm trying to understand the meaning of the group velocity for Bloch electrons given by
$$
\mathbf{v}=\frac{1}{\hbar}\frac{\partial E(\mathbf{k})}{\partial \mathbf{k}}
$$
where $E(\mathbf{k})$ is the energy of the band, and $\mathbf{k}$ is the crystal momentum. So d... | The short answer is, in the thermodynamic limit, k could always be defined as a good quantum number for bulk states despite of different boundary conditions.
This can be shown by considering a finite potential of several equally distributed wells and infinite high walls as boundary.
The solution of wave function is the... | {
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Mixed symmetry of rank $3$ tensor I have rank 3 tensor $T_{ijk}$ with following properties:
$T_{ijk}=T_{jik}$
$T_{ijk}=-T_{kji}$
Is it true that there is the only one tensor of rank 3 with those properties and it is $T_{ijk}=0$.
I'm starting from the following
$T_{ijk}=-T_{kij}=-T_{ikj}=T_{jki}=T_{kji}=-T_{ijk}$
$\Righ... | Your work seems fine. This little fact is sometimes known as the $S_3$-lemma, and it can be stated in a very general way: if $S$ is a non-empty set, $G$ is a (say, abelian) group without elements or order $2$, and $T: S\times S \times S \to G$ is symmetric in the first pair, and skew-symmetric on the second pair, then ... | {
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Is pulling a string instantaneous at both ends? Why is it or isn't it? This is a question that has bothered me for quite some time but I don't have a clue where to start in researching it.
Let's say we have a string which is arbitrarily long, light enough to not take much effort to pull but rigid enough that it would n... | First of all, you can't even imagine the force required to pull a string of length equal to or more than $3×10^8\ \text{m}$. Now, imagine you have the force to pull it, but it is nearly impossible to make a string of that rigidity. It can't withstand that enormous force.
Now, imagine you have both source of force and a... | {
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Conditions for a planet to become spherical I have a question, from which size/mass will a body in space adopt a spherical shape? Over 500 kilometers wide and/or 1/4 the mass of Pluto?
Something like that, I always had this doubt.
| The minimum size has been called the potato radius, as anything too small will look more like a potato than a sphere. The potato radius depends on composition, hereafter assumed uniform. Eq. (9) (ibid.) gives the radius as proportional to $\rho^{-1}\sqrt{\sigma_y/G}$, with $\rho$ the density and $\sigma_y$ the compress... | {
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Why do rain drops fall with a constant velocity? While reading my physics book. I came across a line that says that:
Rain drop falls with a constant velocity because the weight(which is the force of gravity acting on body) of the drop is balanced by the sum of the buoyant force and force due to friction(or viscosity ... | This is Newton's first law: if the force vanishes the velocity is constant. Constant but not necessarily zero.
The resistive force increase as long as speed increases. When it is equal to the gravitational force the speed no longer increases and the total force vanishes leading to constant speed.
| {
"language": "en",
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"source": "stackexchange",
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Confusion with Impulse and Work I get Momentum and Impulse as well as Work and energy but struggle when it comes to connecting the two ideas. I understand that an objects KE can change without its momentum changing, Like in a inelastic collision were the KE of the system decreases but the amount of matter moving to lef... | Impusle is a property defined as: $$\vec{I} = \int \sum \vec{F}.dt$$
and by virtue of this definition, it need not always be accompanied by work.
Consider an example of you standing on a skateboard and pushing on a wall setting yourself in motion away from the wall.
In this case, the force from the wall on your hands m... | {
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Quantum Mechanical Interpretation of Rutherford Experiment Ernest Rutherford performed the gold foil experiment; alpha particles were fired at a gold foil and the alpha particles were scattered. This result disproved Thomson's plum pudding model of atoms.
This got me wondering, how does QM fit into this picture? How do... | There are two parts in the question. First, given potential, how to find the scattering amplitudes as a function of scattering angle. Second, how to obtain the scattering potential in the first place.
The answer to the first question is twofold again. Normally, yes you need QM to compute scattering amplitudes correctly... | {
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What makes the (non-abelian) strong interaction so special that it leads to confinement? The strong interaction has a coupling constant of $\alpha_s(91GeV)\approx 0.1$ whereas the weak interaction has a much lower coupling constant $\alpha_w \approx 10^{-6}$. Both theories are non-abelian gauge theories, the strong int... | Just to state the result for the beta-function associated to QCD
\begin{equation}
\beta = -\frac{g^2}{32 \pi^2} \left(\frac{11}{3}N_c - \frac{2}{3}N_f \right)
\end{equation}
in which $N_c$ is the amount of colours and $N_f$ is the amount of flavours.
Essentially, both terms boil down to antiscreening and screening resp... | {
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Eccentricity of planets based on distance from Sun Are the orbits of inner-solar system planets more circular than outer planets? Or is it the other way around? What's the reason for this? We were taught in our high school Physics class that outer planets had more circular orbits, but some sources online and even on SE... | The eccentricity of a planet's orbit is a measure of how 'circular' it is.
According to this website (14th line down) - there is no clear pattern in the eccentricities of the planets.
| {
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Inverse Laplacian I have seen the following operator somewhere in a paper on cosmology
$$
\frac{\partial_i \partial_j}{\nabla^2} - \frac{1}{3} \delta_{ij}.
$$
What is the definition of the inverse Laplacian? What is meant by this misleading notation? Is this the inverse Laplacian? If yes, what is then $\frac{1}{\nabla^... | Every Laplacian can be inverted using its Green's function. If we have
$$\nabla^2V = \rho$$
the inverse is simply
$$V(x) = \left(\nabla^2\right)^{-1} (\rho) = -\frac{1}{4\pi}\int \frac{\rho(x')}{|x-x'|} \text{d}^3x'$$
and that's what's meant by $\frac{1}{\nabla^2}$, at least in the places where I've seen it.
| {
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Sustaining a current in conductor placed in external electric field Consider the following arrangement-
We have a conducting sphere and a positively charged infinite sheet on the left. The field creates induced charges and the net electric field inside the conductor is zero after a very short time. During this short ti... | In order to sustain a current, one needs to sustain a potential difference between two parts of the conductor. If we have a closed loop, the charges eventually redistribute so as to screen the potential and the current ceases. However, if, for e.g., there is a battery in the loop, which absorbs charges on one side and ... | {
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Graph for Coulomb Force vs $1/r$ My teacher told me that the graph for the coulomb force $F$ vs $1/r$ where $r$ is the distance between the 2 charges should be parabolic but I can't seem to understand why. I am aware that equations of the form $y^2=4ax$ are parabolic but why should $F$ vs $1/r$ graph be parabolic?
| $$F = k_e\frac{q.Q}{r^2} \rightarrow (\frac{1}{r})^2 = \frac{F}{k_eq.Q} \rightarrow x^2 = 4ay$$
where $x = 1/r$ and $4a = 1/(k_e.qQ)$
Hope this helps.
| {
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Clausius inequality leading to absurd result Background: After deriving Clausius inequality, the author of this book derives the following relation:
Consider the cycle shown in the figure in which leg $A \rightarrow B$ is irreversible. In the equation
$$
0>\oint\frac{\mathrm{d}Q}{T}=\int_{A \operatorname{irrev}}^{B} \f... | Considering the result $$\int_{A \operatorname{irrev}}^{B} \frac{\mathrm{d} Q}{T}<S(B)-S(A)$$ for an infinitesimal path, we get $$\mathrm{d}S\ge\frac{\mathrm{d}Q}{T}$$ where the equality holds only for a reversible process (by the definition of entropy).
This means that in your expression $$\int_{A \operatorname{irrev}... | {
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How much longer could Titanic have stayed afloat if it gotten rid of its anchor and chain right after hitting the iceberg? I am wondering how much longer the RMS Titanic could have stayed afloat if the crew had allowed the ship's anchor and anchor chain to fall to the bottom of the ocean immediately after the ship had ... | A detailed question to this answer will, as so often, require a detailed numerical simulation or, better, a scaled-down experiment. But being the gung-ho physicists we are on this site here, we can do a simple guesstimate: According to a quick internet search, the total mass of the titanic is somewhere in the ballpark ... | {
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Are there any physical symmetries that do not form a group? I'm trying to understand the role of symmetry in physics. The overall derivation seems pretty intuitive, reasonable and elegant, but one point I'm curious about is the identification of physical symmetries with groups. It does not seem a priori necessary that ... | Symmetries act on objects. For a symmetry to be nonassociative, it would have to be the case that (doing A and then doing B) and then doing C was different from doing A and then (doing B and then doing C). I don't think that's possible.
There is a previous question about invertibility with some good answers. In short, ... | {
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Could a non-photon massless particle travel at a speed other than $c$? The speed of light is given as $c=\frac{1}{\sqrt{ε_0μ_0}}$ which is in terms of the electric and magnetic constants.
Hypothetically, another massless particle could exist which does not interact with the electronic or magnetic fields. Postulate that... | c is the speed of cause and effect. See Do we know why there is a speed limit in our universe?
The speed of light is a special case of this. If you move a point charge, the "news" that it has moved will spread out at this speed. That is, changes to the electric and magnetic fields from the charge will spread out at thi... | {
"language": "en",
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Why $E$ is neglected at large and small $r$ of quantum harmonic oscillator? In obtaining radial solution of quantum oscillator why E is neglected?
Radial equation:
Resource: nouredine zettili.
| One does this because the original differential equation is overly difficult to solve without first examining the boundary conditions.
The point here is that you are initially only approximately solving the TISE in the regimes of small $r$ or large $r$. This is where the boundary conditions are, so you want to get the... | {
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What is the physical meaning of "correlation length"? I am studying phase transitions right now and trying to understand the physical meaning of the concept correlation length. I saw the equations but I still couldn't quite wrap my head around the physical meaning of it. Like is it the length of the correlation between... | Here's an example using a crystal. The same concept applies to many other physical systems.
Consider an ideal crystal. If you know the position of atom at a, then you can predict the position of atom b no matter how far away it is. But real materials are not ideal crystals. There are inclusions, faults, vibration... | {
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Why proper time is a measure of space? Recently I've been trying to learn General and Special Relativity by myself. There is an specific thing I do not understand perfectly, proper time in the metric of the space-time.
Take the case of an empty space-time:
$$-c^2 \mathrm d \tau^2 = -c^2 \mathrm d t^2 + \mathrm d x^2 +... | In relativity, notions like "space" and "time" depend on what coordinate system you use. However, there are some physical quantities which all observers will agree on. Say there is a clock which travels along some trajectory, from one point $x_i$ in spacetime to another point $x_f$. (Points in spacetime have an invaria... | {
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How does Upthrust/buoyant force act on an object? I came across this question where, In a container there's water at the bottom , kerosene on top and an ice cube floating between them and I was asked to calculate the ratio of height of cube in ice to that in water:
Now till now my intuition for up thrust was that ther... | This diagram was used in an answer to this question Why does a fluid push upward on a body fully or partially submerged in it?
The spring is first at its natural length, then released, showing that there is an up-thrust on the piston due to the height difference (and weight) of the liquid.
In a similar way, even thoug... | {
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Would somebody feel a magnetic field if they are travelling at the same velocity as a charge? I am little bit curious about how magnetic fields are being generated when a charge moves.
I want to check if somebody travelling along with a charged particle, would that person experience a magnetic field?
How are magnetic f... | Magnetic and electric fields are just aspects of what's called electromagnetism. The electromagnetic field is what's unambiguously there, and so is the electromagnetic force on the person.
Whether you see the electromagnetic field as just an electric field or also having a magnetic component depends on your velocity.
I... | {
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A question regarding commutators in quantum mechanics I propose the following thought experiment:
Suppose we have a beam of identically prepared electrons that is splits into two. The first goes through detector A that detects the $x+y$ where $x$ is the coordinate along x direction and $y$ is the coordinate along the $... | It would be far simpler to just directly measure $x$ of your first beam and $p_x$ of the second beam.
Both of which, $x$ and $p_x$ can be measured to arbitrary precision thus violating the uncertainty principle.
There is no violation of the uncertainty principle. If you have an unlimited supply of identically prepare... | {
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Does deceleration require energy? Consider an apple falling from a tree and striking the ground.
The ground decelerates the apple once it hits it, but the force is not applied over any "distance" - it is experiencing the force when it is in contact with the ground - so no work is done, yet there is a change in momentum... | The force is applied over a distance. Both ground and apple are deformed by the impact force. If the apple falls from a large height you can easily see the effect of deformation. In general, the amount of deformation depends on the nature of the objects colliding, their hardness and elasticity. If they are both elasti... | {
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Intuition for Stress and the Cauchy Stress Tensor I'm struggling to get an intuitive understanding of what exactly Stress is, particularly the "direction" associated with it.
In the case of a 1 dimensional bar with just uniaxial loading, the way stress was explained to me was just $\pm\frac{F}{A}$ where $F$ is the forc... | We could start from the Cauchy postulate where we take an arbitrary plane defined by a normal vector $\hat{n}$ and with a finite area $\Delta S$, and compute the traction in that plane $\Delta R$ (here I am neglecting the couples $\Delta M$ since they should vanish in the classical case).
If we take the limit when the... | {
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Normalization constant of blackbody radiation We have the Boltzmann-Distribution: $$~~~~~~~~~~~~~ P_n = N(T) \cdot \exp \left(- \frac {n \cdot h \cdot \omega }{2 \pi \cdot k_B \cdot T }\right) ~~~ , ~n \in \mathbb N_0 ~~~$$ ($n$ = number of photons)
The sum over all the possibilitys $P_n$ must be one.
Now we have to... | From your
$$1 = \sum N(T) \cdot exp(- \frac {n \cdot h \cdot \omega }{2 \pi \cdot k_B \cdot T })$$
$$\frac{1}{N(t)} = \sum\ exp(- \frac {n \cdot h \cdot \omega }{2 \pi \cdot k_B \cdot T })$$
Letting $x = exp(- \frac { h \cdot \omega }{2 \pi \cdot k_B \cdot T })$
and using the identity in your question should give the r... | {
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How much does a radiator at 25˚C affect a room that is 20˚C? This is probably not a very precise question but I'm just trying to get a rough idea how much effect a radiator set at such a low temperature would have on a room. Let's assume that the number of radiators and size of the radiators is generally appropriate fo... | If the temperature of the radiator is higher than the temperature of the room then there will be a flow of heat from the radiator to the room. The rate at which heat flows into the room will be proportional to the difference between the radiator temperature and the room temperature.
If the room is hermetically sealed a... | {
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Eigenfunctions of an Harmonic Oscillator perturbed with an Electric Field Knowing that a particle of mass $m$ and electric charge $q$ is under an uni dimensional harmonic potential of frequency $\omega$ perturbed with and electric field $\vec{E}= E_f \hat{x} $, $\hspace{0.2cm}$ I would like to find the eigenfunctions a... |
My question is: If I use the change of variables I found in the expression of the eigenfunctions of the harmonic oscillator, do I get the orthonormal eigenspace for this specific potential and how I could prove it?
Yes. First, we can see it directly: if $\psi_n(x)$ and $\psi_m(x)$ are eigenfunction of the original ha... | {
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Confusion on molecular dynamics (MD) simulation units leading to absurd acceleration values I am trying to code up a very simple MD simulation in order to learn more about it. I am using the Leonard-Jones potential, expressed as $ V=4\epsilon (\frac{\sigma}{r}^{12}-\frac{\sigma}{r}^{6}) $
The pairwise force is therefor... | I am not familiar with the exact molecular dynamics model you are using, but I have done some simulations with Newton acceleration on mass or Coulomb acceleration on charges. It can be striking what is embedded in those simple accelerations when time-evolved. If the model just simulates Newton's a = G/r2 attraction, we... | {
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Is it the term "telescope" the same as a "detector"? For example, in this reference, MITO: muon telescope they use the term telescope but clearly the "telescope" is a muon detection system. And they also talk about angular resolution, angular aperture, etc. So my question is focused in, is the term telescope the same a... | It is in the sense of definition 2 of wesbster dictionary
any of various tubular magnifying optical instruments
where the detector is used to record rays,(instead of the eye or film) directional vectors, composed of particles (muons in this case)
| {
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Why do the electron and positron creation operators anti-commute? I am learning QFT and is baffled by a minor problem.
The electron and the positron should be distinguishable, as they have different charges. So why do their creation operators anti-commute? They should commute with each other, just like the creation ope... | As far as I remember, you can choose creation operators of different fermions to commute or to anti-commute, both choices should provide correct results if used consistently.
| {
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Why should a dipole have zero net charge? Why can a dipole not have two unequal charges separated by a distance? Is there any significance for the dipole being defined as electrically neutral?
| If we have several charges distributed in space, then the total potential is
$$
\phi = k\sum_{n = 1}^{N} \frac{q_{n}}{\left|\mathrm{r} - \mathrm{r}_{n}\right|}
$$
If charges are concentrated in a narrow region of space (narrow compared to the distance to the observer and, if there are EM waves, to the wavelength) then ... | {
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Why bother buying efficient lights if you are already heating your house? Assume I live in a location where at any time of day and any time of year, I need to heat my house. Assume further that I have a room with no windows. In this case, does it make sense for me to buy efficient light bulbs, considering that any inef... | With more energy efficient lights you can also have brighter ones while still staying within safe watt limits. Less energy used for heat means you can get more light and still not come close to your wiring's tolerance. It's even more important when you have a lighting fixture with it's own maximum wattage. This is due ... | {
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Euclidean space to Minkowski spacetime Can you continuously deform (i.e., shrink, twist, stretch, etc. in any way without tearing) four-dimensional Euclidean space to make it four-dimensional Minkowski spacetime?
| Of course!
It is called Wick rotation. You have to change the time coordinate $t$ to $-it$, which changes the sign of the action in the partition function of a physical system. It is a basic tool is statistical physics. The partition function then changes from $\exp(-iS)$ to $\exp(S)$. As I'm writing its rather backwar... | {
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Weight of Diamagnetic Objects in Lenz Effect I've seen the simple experiment of dropping a neodymium sphere down through a copper or aluminum tube where it falls at less than g. The "Lenz Effect"
My question is:
Has there ever been an experiment when the NeoD sphere is tied to a string attached to a weight scale? Does ... | Someone may have done such an experiment, but it would be messy. It would be a lot easier to measure how long it takes the magnet to fall through the tube to get the same result.
Assuming the magnet falls with a uniform acceleration, since $$y=\frac{1}{2}at^2 \\
\rightarrow a=\frac{2y}{t^2}$$ Since you know the length ... | {
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Is the Integer Quantum Hall Effect a distinct phase of matter? In the Landau classification scheme, phases of matter differ in terms of symmetry. However, we know of many instances where this classification scheme does not apply. I have often heard topological insulators and even the different plateaus in the integer q... | Yes, integer quantum Hall phases are distinct phases of matter with invertible topological order. Any phase of matter can be distinguished from another by the presence of a phase transition, where a smooth change in parameter(s) leads to a discontinuous change in some observable quantity. In the case of the integer qua... | {
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Klein-Gordon Field Quantization and Bose-Einstein Statistics in Peskin & Schroeder I am trying to understand how Klein-Gordon particles obey Bose-Einstein statistics from Peskin & Schroeder's QFT textbook (page no. 22). The excerpt is given below:
From this passage it is clear to me that the two-particle states: $a_\t... | $\newcommand{\Ket}[1]{\left|#1\right>}$
In the Klein-Gordon field, a creation operator $a_p^\dagger$ represents the creation of a single particle in mode $p$. The statement that a single mode can contain arbitrarily particles is simply a statement that, just like the quantum harmonic oscillator, $(a_p^\dagger)^n \Ket{0... | {
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Theoretical minimum temperature required to melt any material Reading about this (New material has a higher melting point than any known substance) got me curious.
Given a pressure level (like 1 atm) and a sufficiently hot temperature, I have the intuition that no material stays solid, and turns to plasma if hot enough... | The outer part of a neutron star is considered solid and its temperature can reach $10^6$ K. This is probably the highest temperature that a solid can reach.
| {
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How often is a non-coordinate and non-orthonormal basis used in GR? I wrote a program that takes as input the basis vectors if electing to use an orthonormal basis, or metric components if using the coordinate basis, and outputs non-zero Christoffel symbols and components of Riemann, Ricci, and Einstein tensors, as wel... | I’ll take the above comment by Sebastian Riese as my answer:
This is typically called vierbein, and used in many ways (e.g. to simplify certain calculations, in Einstein-Cartan theory or for defining spin on curved space times). More info: https://en.wikipedia.org/wiki/Tetrad_formalism
| {
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Scattered radiation factor for diagnostic
I need the confirmation, is it if we put survey meter at 270 degree, does the reading of scattered radiation is same with 90 degree. In my opinion, the reading would be same as the distance is still same (other factor like kVp, Feild size, thickness are constant). or do we nee... | If you need confirmation that scattering at 90° is the same as scattering at 270°, you should measure it.
In one of the first experiments on polarizing Mott scattering of electrons, in 1927, Cox and collaborators built an angular detector like the one you are describing here. They included “redundant” detectors at 90° ... | {
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Existence of Ground State of Dirac equation In chapter four of Ryder, the author showed that there exists a ground state $|0\rangle$ for the Kelin-Gordon equation, just like the case of the linear harmonic oscillator. However, I was not able to extend this to show the existence of a ground state for the Dirac field equ... | The Dirac equation spectrum is not bounded from below, hence there is no ground state. To augment this deficiency Dirac postulated that the spectrum of negative energy states was already filled (the so called Dirac Sea). He then predicted the antimatter state (positron) as a hole In this sea.
| {
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How can we make the energy levels of an one-dimensional infinite square well potential equispaced? We know that the energy values for an one-dimensional infinite square well potential is given by $$E_n = \frac{n^2{\pi}^2{\hbar}^2}{2ma^2}$$ where $a$ is the width of the well. Now, as we can see that the difference in en... | They just wanted you to use the formula for the energy and adapt it very likely. This means if you know the formula for $E_n$, you can see that a cuadratic dependence on $n$ will not lead to equispaced energy levels. So which parameter could you play with so that $E_n$ does not scale cuadratically with $n$?
You might t... | {
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If space is a vacuum, how do stars form? According to what I have read, stars are formed due to the accumulation of gas and dust, which collapses due to gravity and starts to form stars. But then, if space is a vacuum, what is that gas that gets accumulated?
| As people like to think,Vacuum is space that is devoid of matter like air etc. Space is not strictly a vacuum at all places, but it is better vacuum then we obtain in laboratories. when we say space is vacuum it means it doesn't have air to breathe. But space still has matter. You are right universe including stars wa... | {
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Why are time-ordered Greens functions equal to retarded Greens functions at zero temperature? When I calculate a photon polarization diagram:
I get the same answer:
*
*If I calculate it in equilibrium (retarded Greens functions) with finite chemical potential, in the limit of zero temperature, or
*If I calculate i... | This is generally not the case. The reason is that, in addition to zero temperature, you are averaging over the vacuum state with zero particles, which is killed by annihilation operators.
Let us take time ordered Green's function at zero temperature:
$$
G^t(t,t')=\langle 0|T[c(t)c^\dagger(t')]|0\rangle=\\
\langle 0|c(... | {
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Squared Summation of Terms using Einstein's summation convention In working with QFT and Maxwell's equations, terms such as:$$\left(\partial_\mu\,A^\mu\right)^{2}$$ often appear. Since I am new to this, I am not sure of the expansion. That is, is it 4 terms squared or is it 4 squard terms:
$$\left(\partial_0 A^0\righ... | Reference : Squaring the E&M (Maxwell) field strength tensor.
Looking at equation (06) of my answer in above link we realize that this square comes from the expression
\begin{equation}
\left(\partial^{\mu}A_{\mu}\right)\left(\partial_{\nu}A^{\nu}\right)\boldsymbol{=}\left(\partial_{\mu}A^{\mu}\right)\left(\partial_{\nu... | {
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RMS velocity of a gas vs RMS velocity of a gas molecule, which is a more appropriate term? I'm a bit confused by the terminology. Is it the RMS velocity of a gas, or the RMS velocity of the gas molecules or of a gas molecule?
Similarly, is it the mean velocity of a gas, or the mean velocity of the gas molecules or of a... | It is the molecules which have the velocity not the gas as a whole.
The RMS velocity of the molecules in a gas (mean taken at an instant of time) should be the same as the RMS velocity of a gas molecule (mean over a "long" period of time) but given the qualification (and uncertainty) regarding the length of time go for... | {
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Sound proofing: mass-spring-mass or mass-mass-spring? I am trying to improve the sound proofing of a metal box. The box is made of steel of thickness $0.8 \;\mathrm{mm}$. I have additional sheets of steel with $3 \;\mathrm{mm}$ thickness for reinforcement. For vibration reduction, I have access to some bitumen mats (an... | Here are some general rules of thumb:
Before you start designing your sound blocker, you need to know the spectrum of sounds you wish to block. This will determine which wall design will do the trick. For example, if the noise spectrum consists primarily of high frequencies (above, say $3000 \;\text{Hz}$), then two she... | {
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Why only the wavelength and speed of refracted light traveling inside a transparent material changes and not its frequency? When monochromatic light waves travel from one medium to another the frequency never changes.
A transition to a denser medium will result of a slow down of the propagation speed v of the light wav... | Due to continuity if one wavelength of light crosses a boundary, one must emerge on the other side. Hence the number of wavelengths crossing the boundary per second is equal to the number emerging per second. So the frequency of the incident and refracted wave must be the same.
For your second question, energy is lost ... | {
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Polarization of natural light for double slit interference Last week I performed Young's double slit experiment using a laser. As expected, I obtained an interference pattern as predicted by Fraunhofer theory (enveloped by the 1 slit diffraction curve). Then, I added two polarizers with perpendicular axes in front of e... | Both polarizations destructively and constructively interfere at the same points, meaning their sum also shows the diffraction pattern. This is why unpolarized light can be used in Young's experiment with no problem.
However, by letting a different polarization to pass in each slit, you force a situation where each pol... | {
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Projectile motion given angular projection When a body is projected with a certain angle from the ground it returns with the same angle and speed with which it was projected. What if the the body was projected from some height, maybe a building. Will it still reach the ground with same speed and angle?
| No, because once the particle goes below the level of projection, the speed increases, due to conservation of energy. Also the angle of flight, given by $\tan\phi=\frac{\dot{y}}{\dot{x}}$, increases because $\dot{y}$ increases while $\dot{x}$ remains constant.
| {
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Question about dark matter/energy and other dimensions According to drummer and lyricist Henrik Ohlsson, the title Dark Matter Dimensions refers to the "appreciation and acknowledgement of the unseen worlds and dimensions, because without the existence of these unseen forces our physical universe would never be able to... | Dark matter simply refers to matter that does not emit light. In other words it does not interact with the electromagnetic field. We have never been able to observe it directly, since our telescopes can only see incoming light from the universe.
But we can infer it's existence due to the fact that gravitational lensing... | {
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What is the current status of the convergence of the post-Newtonian approximation? In the very well written article by C. Will, On the Unreasonable Effectiveness of the post-Newtonian Approximation in Gravitational Physics, he states:
The one question that remains open is the nature of the post-Newtonian sequence; we ... | The question about PN sequence is raiser mathematical one, nor physical or philosophical. It has a good answer in the paper "Newtonian and post-Newtonian approximations are asymptotic to general relativity" by T. Futamase and Bernard, F. Schutz, Phys. Rev. D 28, 2363 – Published 15 November 1983. The Abstract to this ... | {
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The change of mechanical into electromagnetic waves and vice versa I know that sound is a type of mechanical wave, so the human eardrum changes mechanical energy into electronic energy (impulses) so the information may be processed by the brain.
Question: As satellites transfer info by electromagnetic waves that are al... | Sound waves have frequencies from 40 to 20000 Hz. At a sped of 340 m/s this leads to wabelengths of 8m down to 17 mm. Light waves in this frequency range have wavelengths between 7500 km and 15 km. Usually you are detecting at a much shorter length scale, at which these waves look like AC. This is also why I don't care... | {
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Question about indices and matrix This is essentially a trivial question, which can be answer probably immediately, but i have this doubt anyway.
If, say, $$\Lambda^{a}_{b} = \begin{pmatrix}
f & -fc\\
-fc & f
\end{pmatrix}$$
$$\Lambda^{b}_{a} = \begin{pmatrix}
f & -fc\\
-fc & f
\end{pmatrix}^T or \begin{pmatrix}
f & ... | Here is the rule that always works: always multiply matrices by keeping the indices which are being summed over touching each other. The upper/lower placement doesn't matter. Only the right-left.
The standard matrix multiplication rule is
$$
(AB)_{ik} = A_{ij} B_{jk}.
$$
Notice how the the two instances index that is b... | {
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Selection Rules using Group Theory I was learning about the applications of Group Theory and one important application is looking at the selection rules in a weak EM field. We essentially want to see whether the matrix element $\langle i|H'|f\rangle$ vanishes due to the reasons of symmetry. Here $i$ denotes the initial... |
We essentially want to see whether the matrix element <i|H'|f> vanishes due to the reasons of symmetry
How can we have a right to do this as the perturbed hamiltonian is not necessarily in the group of the unperturbed Hamiltonian ?
The states "|i>" and "|f>" are typically taken to be states of the unperturbed Hamil... | {
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Can we measure $10^{-12}\ \mathrm{N}$ force? I would be interested to measure a very small force, say in the order of $10^{-12}\ \mathrm{N}$? Is this possible? What equipment is needed?
My setup
Assume that I have a relatively heavy machine say between 5-10 kg that I want to measure if it produces this thrust, which ac... | Not to answer your question completely but on the AFM point- we can model the AFM cantilever as a spring in contact mode. The spring constant can be ~0.2 N/m or lower.
Now you can, without much work get z-direction sensitivities of 0.1 nm without too much trouble, taking into account experimental noise.
Very roughly sp... | {
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What does the term "condense" mean in the physics literature? When reading the physics literature, we often see the term "condensate".
Some examples:
*
*in the string net model (Wen, Levin), one will say the string "condensate".
*in QCD, people talk about the quark-gluon condensate.
*In stat mech, one talks about t... | Condense could probably mean :-
*
*to become denser or more compact or concentrated.
*Change of state of matter.
Condensate could mean :-
*
*The liquid phase produced by the condensation of steam or any other gas.
*The product of a chemical condensation reaction, other than water.
*Natural-gas condensate, in ... | {
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Why doesn't a parallel circuit violate conservation of energy? Let's imagine a hypothetical circuit where there are a large number of wires placed in parallel to each other, hooked up to a simple power source.
We know that voltage at each wire would be equal $V_{total}=V_1=V_2=...=V_n$ where $n$ approaches a large numb... | each wire gets q/n charge (assuming each wire has equal resistance). Moreover Conservation of energy is never violated and why would the parallel combination violate the law. Battery does the work which is equal to qV (q being the total charge accumulated throughout the cycle) and this energy (qv) is used in the whole... | {
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Is the circuit unitary in Nielsen's method for calculating complexity? I was trying to learn how to calculate circuit complexity (1707.08570) when I chanced upon a seemingly confusing concept. The "Nielsen method" involves looking at a unitary transformation $U$ that takes a reference state $\Psi^R$ to a target state $... | Let's compute $Q_{aa}^\dagger Q_{aa}$. For the rest of this post, I'll drop the $a$ subscript for convenience. Remember that $[x,p]=i$, so that we have $px=xp-i$.
We have:
\begin{align}
Q^\dagger Q & = e^{\epsilon}(e^{i\epsilon xp})^\dagger e^{i\epsilon xp}\\
& = e^{\epsilon}e^{-i\epsilon px}e^{i\epsilon xp}\\
&= e^\ep... | {
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Interpretation of $\oint PdV\neq0$ I hope you are excellent. I'd like you to help me make sense of the integral $ \oint PdV \neq 0 $ for some thermodynamic process. What can it mean for the integral to be nonzero? I can only interpret it as if there is work, however my deep understanding is very limited. I apprecia... | In thermodynamics, the differential work done on a system is defined as the following:
$$\delta W= -P dV.$$
Work done is an inexact differential, denoted by the symbol $\delta$. This means that the total work depends not only on the initial and endpoints but also on the path taken along the process. To find this total ... | {
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What is the force on a block if another block sits on it? So imagine there is a Block A on top of a block B on Earth's crust. What is the force acting on Block B from Block A? Shouldn't it be the force of gravity acting on Block A because that force is pushing down on Block B?
| Gravity is an attractive force, so we tend to think of it as "pulling" rather than "pushing". But you're right that block B experiences a gravitational force from A.
There is a second force. Block A doesn't fall through Block B, even though there's an attractive gravitational force – according to Newton's Second Law, i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/680037",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why do we take account of the whole solid sphere when calculating potential energy of a point inside a solid sphere? See I know that Newton's shell theorem says that any point inside a spherical shell does not encounter any gravitational force by the (outer)shell and it is zero. The same principle we use while finding ... | The shell theorem relies on the fact that force is a vector, and so the vector sum of forces cancels out inside each shell.
Potential energy is a scalar, and more importantly it is the same sign for all contributions from a given shell. Therefore, the potential energy does not cancel out for each shell and must be cons... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/680156",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
If I lift a body with a force greater than its weight, what will happen to the excess energy provided to the body I will give an example to explain my question.
Case 1:
An elevator lifts body a with force equal to its weight for a distance $d$
*
*Energy given to the body (work done)$=$ Weight $×$ $d$
*Amount o... | In both cases, the work provided by the elevator is turned into kinetic energy of the object.
In the moment the elevator stops (and stops doing work), the object thus carries kinetic energy and therefor will continue flying upwards. Both of your potential-energy calculations are therefore wrong - the actual top height ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/680295",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Is there any *global* timelike Killing vector in Schwarzschild geometry? I have been dealing with the following issue related to the Schwarzschild geometry recently. When expressed as:
$$
ds^{2}=-\left(1-\frac{2GM}{r}\right)dt^{2}+\frac{1}{1-\frac{2GM}{r}}dr^{2}+d\Omega_{2}^{2}$$
one can find a Killing vector $\xi=\par... | A time-line coordinate flips only if one assumes that Schwarzschild's vacuum solution is valid in the interior of a black hole, too. In my view, it is not correct. A solution of Einstein field equations spans the whole spacetime. In case of a constant energy density in some region of spacetime (step function) the solut... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/680739",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 2
} |
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