Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
The work-energy principle for particles reversing direction I've been trying to find an answer to this question, but have really been stumped so far.
The work-energy principle says that work done on a single particle is equal to its change in kinetic energy. Now let's say a particle is moving in the +x direction at con... | Let the particle of mass $m$ be the system under consideration.
Look at the diagram below which shows the particle initially moving in the $\hat x$ direction at a velocity $\vec v_{\rm initial}= v \,\hat x $ at position $A$ with a constant external force $\vec F = F (-\hat x)$ acting on it in the $(-\hat x$.
The dir... | {
"language": "en",
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Degenerate parametric amplifier: quadratures The degenerate parametric amplifier is described by the Hamiltonian:
$H=\hbar \omega a^\dagger a-i\hbar \chi /2 \left[e^{2i\omega t}a^2-e^{-2i\omega t}(a^\dagger)^2\right]$
Where $a$ and $a^\dagger$ as just the operators of creation and anhiquilation and $\chi$ is just a rea... | Commonly, the quadratures are defined as $X_1=(\hat{a}^{\dagger}+\hat{a})/2$ and $X_2=i(\hat{a}^{\dagger}-\hat{a})/2$. You can use the equations of motion for the operators $\hat{a}^{\dagger}$ and $\hat{a}$. Solve the differential equations for these, which are not complicated. Then use the quadrature operators. On pa... | {
"language": "en",
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Is this statement of conservation of charge circular? According to Wikipedia:
A closed system is a physical system that does not allow certain types of transfers (such as transfer of mass and energy transfer) in or out of the system.
According to my textbook, the principle of conservation of charge is:
The algebrai... | These statements are not circular but equivalent, you can assume one is true and the other follows. That is:
if
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/425013",
"timestamp": "2023-03-29T00:00:00",
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Is the reason the sunshine is 'extra bright' after rain due to refraction of the additional water in the air? Quite frequently after the sun comes out after rain I experience a 30 minute period where the sunshine is 'unusually bright'. Such that it makes my eyes water.
My question is: Is the reason the sunshine is 'ex... | It may not be direct sunlight that does this.
Any wet surfaces, particularly if the water has not yet had a chance to disperse and runoff, will likely reflect more ambient light as well as direct light at different angles than they would dry (when they'd absorb more without the water to reflect). I would typically not... | {
"language": "en",
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How do I calculate time dilation on GPS satelites due to Earth's mass? I found this answer which gives as the formula
$$T_2 = \frac{T_0}{\sqrt{1-\frac{2GM}{c^2 R}}}$$
that should result in the time $T_2$ passed on a GPS satellite while $T_0$ seconds pass in the center of earth. I assume the following:
*
*$G\approx 6... | The expressions in the quoted answer are pretty misleading (I hesitate to say wrong, but, well). These are time dilations with respect to flat space, so with respect to an observer at infinity which is not moving with respect to objects in the gravitational field of Earth. What you actually need are the dilations wit... | {
"language": "en",
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"source": "stackexchange",
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Forms of transformation Suppose $O$ is an object to be transformed, and $S$ is the transformation operator. Sometime the transformation is in the form
\begin{equation}
O \rightarrow SO. \tag{1}
\end{equation}
But sometime the transformation is in the form
\begin{equation}
O \rightarrow SOS^{-1}.\tag{2}
\end{equation}
I... | (1) is Lorentz transformation, while (2) is similarity transformation.
Lorentz transformation includes rotation and boost. Similarity transformation is performed upon a square matrix that leaves invariant its characteristic polynomial, trace, and determinant. The transformed matrix is similar to the original matrix in... | {
"language": "en",
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Symmetry of the dielectric tensor In the book Principles of Optics by Max Born, in chapter XIV, the rate of change in the electric energy density $w_{e}$ is generalised to
\begin{equation}
\frac{dw_{e}}{dt} = \frac{1}{4\pi}\sum_{kl}\,E_{k}\epsilon_{kl}\dot{E}_{l}
\tag 1
\end{equation}
in order to take into account anis... | The requirement of permutation symmetry in couplings of this form is a pretty universal feature, and the core reason for it is that for the energy to be a well-defined function of the state variables, you need it to be path-independent.
This is easiest to see using a concrete example, so consider a 2D case in which the... | {
"language": "en",
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Binding energy between an $1s$ electron and its nucleus I've always thought that the binding energy decreases as the electron moves/jumps away from the nucleus.
Then when I see the radial probability distribution for $1s$ electron, there is a probability for finding the electron everywhere. Since the binding energy dep... | Before looking at the atom, consider a classical example of a comet on an elongated elliptical orbit around the Sun. While particles are not anything like planets, still even this rough classical analogy seems to address your concern. The kinetic energy farther from the Sun is lower, the total energy is still the same ... | {
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How can the solutions to equations of motion be unique if it seems the same state can be arrived at through different histories? Let's assume we have a container, a jar, a can or whatever, which has a hole at its end. If there were water inside, via a differential equation we could calculate the time by which the conta... | Now imagine you have a jar, and there is a drop of water moving vertically behind the hole. Can you solve this one provided you have the coordinates and the velocity of the drop. Yes, you can. The only difference is that the initial state of the jar is not enough for solving the (jar, water) system, you need the inform... | {
"language": "en",
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Applying the Heisenberg uncertainty principle to photons The speed of light is a universal constant, so we definitely know the speed of the photons. If we know the speed, then we should not have any information about their location, because of Heisenberg's uncertainty principle. But I'm one hundred percent sure when li... | I would like to mention some interpretation that made me understand these concept easier for myself.
Imagine that your window shrank into approximately wavelength size. You would certainly observe diffraction phenomenon under this condition.
You can interpret it as an outcome of uncertainty principle in a case when X a... | {
"language": "en",
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Why is it much more difficult to horizontally throw a toy balloon than a football? If you horizontally throw a sphere of radius $R$ it will feel, in this direction, a drag force due to air. Assume the drag is given by Stokes law, $F_D=6\pi\eta R v$, where $\eta$ is the air viscosity and $v$ is the horizontal speed. Thi... | We know that
Where p=mv is the momentum.
If both the balloon and the ball initialy have the same speed when you throw them, then the ball will have more momemtum than the balloon because it is more massive (p =mv).
So that if the force of friction on both of them is the same, the rate of change of momentum is the sa... | {
"language": "en",
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What is state variable and full differential? e.g. in entropy? I am studying basic concepts of entropy and statistical physics. And red a lot what is entropy, and that it is integrative factor of heat; and getting it with the full differential._
Anyway, what I am trying to grasp in all that story, actually to gain a fe... | The equation should read $dS=dQ_{rev}/T$, where the subscript rev refers exclusively to a reversible path between the initial and final states of the system. This reversible path does not necessarily have to bear any resemblance whatsoever to the actual process path between the initial and final states. If you don't ap... | {
"language": "en",
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A simple question on finding the number of macro states for a system of two Einstein solids Consider two identical Einstein solids each with $N$ oscillators in thermal contact with each other and suppose that $$q_{\mathrm{total}}=q_A+q_B=2N$$
How many different macrostates are there ( i.e. possible values for a total v... | This is more a question of how you define a macrostate in your model. In the conventional Einstein solid model, we consider the energy observable. The reasoning for this is that we are using the model to study thermal energy (specifically heat capacity), and so all internal energy is taken to be heat, and changes in he... | {
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Turning off an inductor: Experimental problems I am trying to measure the current in dependence of time in turning on and off an inductor.
If I choose an inductor with low inductivity (36 mH) it works for turning on (almost) as expected, but for turning off it doesn't.
Here is my setup:
and here is are the results (... | You need to provide a path for your current when the switch is open. See picture for details. At step 1, you have current. At step 2, your current dies out. So at step 3, when you expect your current, it is not there.
If you fix the circuit as in step 4,5,6, you are fine.
| {
"language": "en",
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If an object moves at constant speed, does it necessarily have constant velocity? If an object moves at constant speed, does it necessarily have constant velocity?
| If an object moving at a constant speed, It is not necessarily that it should move with constant linear velocity because Linear velocity is speed along with direction. so if the direction is not constant then Linear velocity will vary.
e.g - An object moving with constant speed in a circular path certainly doesn't have... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Force, work and the apparent disappearance of Mechanical Energy A man exerts force on a wall of bricks. The man must have consumed the energy he possessed (mechanical energy?) to exert the force. The man sweats and tires himself out but the wall does not move.
The force is given as $F = ma$ but no acceleration was prod... | First, it does not require energy to produce a force. A ladder can lean against a wall, exerting a force on it indefinitely without the expenditure of energy. A man exerting the same force sweats and gets tired, not because energy is required to produce force but simply because the human body is a very inefficient mach... | {
"language": "en",
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Confusion about how an electron gun works I'm a little unclear about the charge balance aspect of an electron gun. Referring to this diagram and similar diagrams I've seen, what I don't get is wouldn't the target of the electrons have to be connected to the positive anode so that the electrons fired at a target can b... | Think about it this way. The only reason this connection exists in the TV scenario it to hit a target for illumination display purposes. In other applications such as linear accelerators we shoot the beam thru a window into a vacuum waveguide filled with a resonant Microwave freq. This Acceleration scenario creates ene... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/427735",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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What type of fields existed in early universe? In quantum field theory we associate field to every particle. So how many elementary fields exits in nature? Why are fields associated to particles different from fields associated to fundamental forces? And if fields are fundamental and existed since universe formed, why ... | The fundamental fields of the Standard Model are the various quarks (up, down, ..), leptons (electron, electron neutrino, mu, ..), gauge bosons and the Higgs boson, where the matter fields differ from the force fields by their statistics - gauge bosons are, well, bosonic, like the Higgs field, whereas matter fields are... | {
"language": "en",
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Differentials and small changes in thermodynamics This may seem like an elementary question, but I'm a bit confused right now about this. From the first and second laws of thermodynamics, and from the definition of enthalpy (per unit mass), we have the equation (as an example, and at constant pressure):
$$
dh=c_p dT.
$... | For a perfect gas, $c_p$ is actually independent of temperature, so both equations are equivalent. Some real gases actually show behavior very close to temperature independence of $c_p$, e.g. ammonia.
In addition, because the coefficients of temperature dependence of $c_p$ of most gases are not that large, over a smal... | {
"language": "en",
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Why is conservation of momentum not valid here?
To explain my confusion, I would provide the following system:
The two masses $m$ and $M$, with $M\gg m$, are moving towards each other(as directed by the arrows) with a common constant speed $V_0$. There is no friction between any two surfaces and all collisions are per... |
As $M\gg m$, there will be negligible change in the velocity of $M$
after collision.
Yes, the change in the velocity of $M$ will be negligible, but what is conserved is not the velocity but the momentum and, since $M\gg m$, even a small change in the velocity of $M$ will translate in a relatively big change in its ... | {
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What is a complex phase shift? In a complex methods course I am taking, we were given an equation for a particular driven harmonic oscillator where the driving force is trigonometric. I have worked out the math and obtained an equation that tells me that the driving frequency at resonance is the natural frequency multi... | It is a phase shift by 90 degrees if multiplied by $i$ indeed.
Note that $i=e^{i\pi/2}$. Writing whatever driving signal in complex form, since it is sinusoidally driven, it will have an $e^{i\omega t}$ in it, multiplying by $i$ multiplies by $e^{i\pi/2}$, and when you multiply the exponentials you add the exponents t... | {
"language": "en",
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How are RF Waves transmitted? What is the mode of transmission for RF waves at 1800 MHz. Is it ground wave propagation, Line of Sight Propagation or Atmospheric reflection (from ionosphere).
What are the different ways for different frequencies of RF waves?
| Frequency is essential in this discussion. What happens at 50 MHz is irrelevant at 1800 MHz. At 1800 MHz waves travel by line of site. They can be impacted by tropospheric ducting and I believe also by thunderstorms.
Search for radio propagation in Wikipedia - insufficient prior research.
| {
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Why does work depend on distance? So the formula for work is$$
\left[\text{work}\right] ~=~ \left[\text{force}\right] \, \times \, \left[\text{distance}\right]
\,.
$$
I'm trying to get an understanding of how this represents energy.
If I'm in a vacuum, and I push a block with a force of $1 \, \mathrm{N},$ it will move... | I see several answers that all seem to explain it, but for someone trying to understand the why, perhaps it's best answered simply.
It is going to be a lot more "work" for me to push a heavy trashcan out the door and down the driveway than the amount of "work" for me to just push the trashcan out of the house.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/428525",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "32",
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"answer_id": 6
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Probability of a vector lying in an interval Suppose we have a vector $\vec{v}$ with constant length that is equally likely to be pointing in any direction, specified by $\theta$ w.r.t the $x$ axis .
How can I compute the probability of the $x$ component of $\vec{v}$ lying in the range $v_{x}$ to $v_{x} + \mathop{dx}$... | A slightly less laborious way of writing this is: Let $\theta$ be a random variable describing the angle of the vector relative to the $x$ axis. Then we can write the vector in Cartesian coordinates as:
$$
\vec{v} = |v|.(\cos \theta, \sin \theta)
$$
Thus the probability of $v_x < \vec{v}_x < v_x + dx$ is simply the pro... | {
"language": "en",
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Is there any moon without its planet? Is there any planet without its star?
Is there any moon or any planet wandering in outer space without a definite orbit?
(The name moon or planet used here serves only for size and spherical shape notion.)
|
João Bosco asked: Is there any planet without its star?
They are called rogue planets, and of course there can also be rogue moons: for example, a regular planet can lose its moon when a rogue planet comes too close and disrupts the system the moon can be ejected.
| {
"language": "en",
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Why doesn't a charged particle moving with constant velocity produce electromagnetic waves? A charged particle moving with an acceleration produces electromagnetic waves. Why doesn't a charged particle moving with a constant velocity produce electromagnetic waves? As far I understand, the electric and magnetic fields i... | Riemannium's answer tackles why you need acceleration to form EM waves. I will hit from a different way that I think gets at your question title as to why charges moving at a constant velocity do not produce EM waves. In the subsequent discussion all mentioned reference frames are inertial reference frames.
The easiest... | {
"language": "en",
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Does ferromagnetic material decrease magnetic field intensity in surrounding area? I have a doubt regarding behaviour of ferromagnetic material. I know that magnetic fields are said to increase in intensity inside bulk of ferromagnetic material, or converge into them.
Does this mean or imply that magnetic field intensi... | Yes, it does decrease outside of the iron piece. Imagine the new magnetic field introduced by the iron piece (would look like a bar magnet). When superimposing with the original magnetic field, you'll find cancellation outside the iron piece.
| {
"language": "en",
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String theory and background independence I have read that string theory assumes strings live in spacetime defined by general relativity which make the theory background dependent (although general relativity is a background independent theory). Background independence dictates that spacetime emerge from more fundament... | You're asking a question that deserves an enormous amount and clarifications. I will just want to share some very illuminating references on the idea of "Background independence" in the context of string theory.
What is background independence and how important is it?
At least two philosophers understood background in... | {
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Chirality of the Electromagnetic Field Tensor I have learned that chirality is a concept, that appears for $(A,B)$ representations of the Lorentz group, where $A\neq B$.
An example would be a Dirac spinor, corresponding to the representation $(\tfrac{1}{2},0)\oplus(0,\tfrac{1}{2})$, where we can identify left- and rig... | There's a great existing answer, I just thought I'd check where the "rotation" comes from.
As you know, the electromagnetic field tensor decomposes under $SO(3)$ into two vectors, $\mathbf{E}$ and $\mathbf{B}$, which are preserved under rotation. In fact, any linear combination of $\mathbf{E}$ and $\mathbf{B}$ are pres... | {
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Deriving or building a Hamiltonian from a Density Matrix Is it possible to create a Hamiltonian if given a Density Matrix.
If you already the the Density Matrix, then is the Partition
Function (Z) even needed?
This Q is not about physics. Its about an application of math
to poorly defined and dynamic systems such as p... | No. Suppose you have an admixture of spin-up/spin-down states:
$$
\rho=\left(\begin{array}{cc}
1-\alpha & 0 \\
0 &\alpha\end{array}\right)\, .
$$
There is no information about the evolution of the system, in the sense that there is no reason to suppose that this density matrix must evolve according to $H=\omega \sigm... | {
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Dependency of temperature acquired by a resistor on power A nichrome heating element across 230V supply consumes 1.5kW of power and heats up to 750*C. A tungsten bulb across the same supply operates at a much higher temperature of 1600*C in order to emit light.
Does it mean that the tungsten bulb necessarily consumes g... | A typical incandescent light bulb with a tungsten filament consumes somewhere between $25$W and $100$W (much less than $1.5kW$) and reaches temperatures on the order of $2500^{\circ}C$ (much greater than $750^{\circ}C$).
So, why does it get hotter than a nichrome heating element?
It is because the temperature of a heat... | {
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Why are coordinate systems used in General Relativity if it is a background independent theory? I am studying topological manifolds as a prerequisite to studying General Relativity and although this question is premature since I have not yet begun the latter it is bothering me.
From basic physics I always heard that Ge... | Pretty much the latter: coordinates are the tools we use to describe what is going on: there are no coordinates in nature and it does not really matter which coordinate system we use, so long as it's 'good': it should provide a suitably differentiable 1-1 map of the manifold (or an open subset of the manifold) into $\m... | {
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Reversing magnet polarity to increase/decrease Eddy currents? I have a cast iron wheel with magnets around the inner radius as a braking mechanism. If I were to add additional magnets around the outer radius, would the amount of Eddy currents increase or crease if the polarity of the outer magnets was opposite?
EDIT:
H... | If the magnets in the two sets were facing each other (i.e., if green outer magnets were shifted to the $6$ o'clock position), it would be pretty obvious that, in order to increase eddy currents, the outer magnets would have to be installed with their north poles facing the wheel, so that the magnetic fields of the two... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/430328",
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How does particle physics use deep neural networks to find particles? Does anyone use deep learning: RNN, CNN or any other architecture of deep neural networks to asses the standard model or to detect new or unseen particles? What's the status these days in this frontier?
| The short answer is no.
The verification process for the standard model involved comparing predictions furnished by that model with experimental data, mostly from particle accelerators, including some which were purpose-built to serve in this way. Neither the process of writing down the mathematical underpinnings for ... | {
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What happens to a radioactive material's atom when it disintegrates? Suppose you initial had radioactive $2^n$ atoms (where $n$ is an integer). Now after a number of halflives the number of left out atoms becomes 1. Now what will happen to it will it disintegrate and the leftover would be half an atom? Now if the reac... | Radioactivity does not mean that an atom disappears. It means that the atom splits into one or more different smaller atoms or fragments of atoms. Very little mass is lost. The mass of all the fragments is not much less than the mass of the original atoms.
When the last radioactive atom has decayed, the process of rad... | {
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What happens to gravity and spacetime when mass turns to energy? What will happen to the distorted space and time around a mass when it is converted into energy?
Will it go back to its original configuration (i.e. with $0$ gravity)?
Or does space time oscillate? Or is there something else that happens?
| There are several ways to convert mass into energy. The mass of a star e.g. decreases slowly due to nuclear fusion processes. In this case energy is radiated away which corresponds to a slight decrease of mass. As the mass of the star remains spherical symmetric during this process, so does its gravitational field and ... | {
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Is $\sin\left[2\alpha\right]\cos\left[2\alpha\right]\ge0$ a valid restriction on the angles of the principal stresses in 2D elasticity? This question pertains to Elasticity: Tensor, Dyadic, and Engineering Approaches By: Pei Chi Chou, Nicholas J. Pagano, Section 1.4.
The objective under discussion is to find the direct... | Ref. 1 writes [admittedly somewhat confusingly]:
[...], and noting that the sine and cosine are either both plus or both minus, [...]
Ref. 1 does not say that sine and cosine are either both positive or either both negative in eqs. (1.12a)-(1.12b), which would have been incorrect$^{\dagger}$. Rather Ref. 1 is trying ... | {
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Could you have sand pipes like water pipes? It's common knowledge that sand behaves like water when in small grains. So can you make a pipe that carries sand in the same way pipes carry water? If not, is there another way you could?
| Tricky for sand, most grains of sand are 'sharp' they will lock into each other and form jams in the pipe unless you have some fluid (eg. air or water) carrying them along. There are types of sand with smooth polished grains which flow more freely (eg desert sand) but these aren't used in construction so there isn't m... | {
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What causes clock drift in quartz oscillators? Usually, computer seem to use quartz oscillators. In contrast to atomic caesium clocks they seem to have a relatively big drift and thus we need protocols like NTP to correct them.
What causes this clock drift in quartz oscillators? Is it something that could be improved? ... | The number one factor limiting the long-term accuracy of quartz crystal oscillators is ambient temperature fluctuation. Crystal ovens exist for keeping quartz oscillators at a constant temperature for applications requiring high time keeping accuracy, but that's obviously not a practical solution for things like quartz... | {
"language": "en",
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Once introduced will an electric and/or magnetic field live for ever? So if generate an electric field or magnteic field, will it live for ever? because whenever you get rid of that field for example getting rid of electric field by discharging a capacitor, it will result in changing megntic field and that will result... |
Does it mean then that once introduced electric field or magnetic
field will become immortal?
Not necessarily - as mentioned in a comment and in the praveen kr's answer, EM energy could be converted in other forms of energy - but, if it is not, it may get close to immortality. Take the light coming from stars that... | {
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How are particles in a collision chosen? In synchrotron particle colliders, how are the particles which are collided chosen? For the most part, collisions of different types of particles don't do anything like you might expect in a video game; there is no secret recipe list of cool things, each which require different... | In rough lines, when one is planning a particle collider experiment, one has a theory which will be tested by the experiments in the collider.
There are two streams :discovery machines, as was the Tevatron and now the LHC, which by discovering new predicted by the theory particles validate the theories, and accuracy ... | {
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How does this action in this picture reduce $R$? (Angular Momentum) I was doing a course on Brilliant today when I came across this question:
In the picture, the question asks me what actions that must be done in order to maximize the distance I travel during takeoff from the curved ramp, and presents me with three c... | $R$ is the distance from the center of the circle to the center of mass. By standing up, you raise the center of mass and consequently shorten $R$. The center of mass is the average position of the mass of a body. If a force acts on the center of mass of any body, the body will only accelerate lineraly, but not rotatio... | {
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Why are the Lyapunov and Lindeberg Central Limit Theorem conditions often satisfied in the real world? Some background for the question.
I've been trying to understand why so many things have a Gaussian Distribution. There are a lot of questions about this on StackExchange but none of them were answered in sufficient d... | There are two reasons that come to mind: firstly, many real-world phenomena are collective actions with many, many steps involved. Brownian motion is
a good example, where thousands of collisions with a small particle
can result in its random jiggles seen in a microscope. The familiar
pin-board sorting of balls into... | {
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Closed field lines in case of a Bar magnet Field lines in case of charges go from +ve to -ve but incase of magnet, they dont start or stop anywhere. They form closed loops. Is this consequence of the fact that single poles dont exist or something else is going on here?
| In this answer I explained that macroscopic magnetic and electric fields are created by the alignment of the magnetic dipole moments of subatomic particles respectively a charge separation.
... incase of magnet, they (the field lines) don't start or stop anywhere. They form closed loops. Is this consequence of the fac... | {
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Are there limitations to the type of paths needed in the path integral formulation of quantum mechanics? In some places it is stated that one needs to include all paths in the path integral approach to quantum mechanics. But in the implementations I have seen one has been content with paths that goes in small steps alo... | It depends on Lagrangian. In cases of physical systems, Lagrangian has kinetic energy part and another following from some potential energy. In such systems this terms has certain property: kinetic energy is quadratic in velocity. When potential energy is absent - as in a case of free particle for example - action inte... | {
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Uniaxial stress question Let's have a rectangular profiled bar. Let us introduce force $\vec{F}$ which pull the bar apart. In the picture below let us make a virtual horizontal cut $A$.
Well, everything is in the picture. Nothing fancy. But the part I'm stuck with is this:
Let's instead of cut $A$ make a cut $B$ whic... | I think the force is assumed to be uniformly distributed over the cross section.If uniformly distributed, ther will be no shearing effect.But if applied at a point then the analysis becomes complicated.Refer to the image attached.
| {
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Quantumness of gravity and Padmanbhan insight on holography Padmanabhan (and also Klinkhammer and others) argues that even classical gravity is already "quantum"...since:
$$F=G\dfrac{Mm}{r^2}=\dfrac{L_p^2 c^3 Mm}{\hbar r^2}$$
Is this "naive" argument right? And related to this, how should we understand holography in ne... | As the Planck length $\ell_{\mathrm {P}}$ is defined in terms of the gravitational constant: ${\displaystyle \ell _{\mathrm {P} }={\sqrt {\frac {\hbar G}{c^{3}}}}}$, then yes, trivially we have $G = \ell_{\mathrm {P}}^2c^3/\hbar$. This is no way implies that classical gravity is 'quantum', at least not in any sense tha... | {
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How do base kets satisfy Schrödinger's equation in Schrödinger picture and why don't they evolve with time? According to Sakurai, eigenvalue equation for an operator $A$, $A|a'\rangle=a'|a'\rangle$. In the Schrödinger picture, $A$ does not change, so the base kets, obtained as the solutions to this eigenvalue equation ... | Only kets that represent physical systems ("state vectors") satisfy the Schrodinger equation. Basis kets don't represent physical systems, but just a system of coordinates, so they don't.
Your question is analogous to asking why the coordinates of a random point in space don't satisfy Hamilton's or the Euler-Lagrange e... | {
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Fire-powered thrusters? So recently I have been working on a science project for ideas that could possibly help in space expeditions, and one of my ideas would be a rocket that would be powered by flame, anyone here have an answer?
| what you describe is exactly how rocket engines work today: a very violent chemical reaction inside a rocket motor causes extremely hot gases (there's your flame!) to fly out of the exit nozzle at tremendous speed. the pressure forces that accelerated the hot gas produce a reaction force on the motor which equals the m... | {
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What does the $R$ stand for in $R_\xi$ gauge? The $R_\xi$ gauge fixing condition is a term that can be added to a Lagrangian to choose a certain gauge:
$$
\delta\mathcal L = -\frac{1}{2\xi}(\partial_\mu A^\mu)^2
$$
Here, $\xi$ is the parameter that decides the gauge, but where does the $R$ come from?
| Following the comment by @AccidentalFourierTransform, here are two references:
*
*M. Srednicki, "Quantum Field Theory", 4th Edition, Chapter 62, page 377 (emphasis mine)
Here we have used the freedom to add $k^\mu$ or $k^\nu$ terms to put the propagator into generalized Feynman gauge or $R_\xi$ gauge. (The name ... | {
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Dispersion of cavity photons I read a paper called "strong coupling phenomena in microcavity structure" in that with regard to photons in a microcavity
For small $k$, the dispersion is parabolic, and so it can be described by a cavity photon effective mass $M = hnc/cLc$. This mass is very small, typically ∼$10−5me$ [1... | Yes they do. The horizontal axis of the graph gives the information of the k component parallel to the propagation plane (it is connected to the angle through a sine). So you can see the photon dispersion as (in units hbar=1):
Ephot(k)= omega_o+k^2/2m, where k is the in-plane mometum of the photons.
| {
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Chronology protection: current status I am looking for some fresh references on the Chronology Protection Conjecture. I am aware of this question, but the answer there seems to resort to energy conditions.
But, weren't they shown violated in QFT, even in averaged format?
I heard physicists are mostly "uncomfortable" wi... | Dismissing all closed timelike curves from just physical arguments is hard since a lot of them are fairly benign (such as the classic timelike cylinder where two spacelike hypersurface of a globally hyperbolic spacetime are identified), but those are usually not considered very problematic since you can always just go ... | {
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Energy difference between enantiomers (matter/antimatter) I am aware of the fact that enantiomers have different energies, for example L-amino acids have different energy than D-amino acids. The difference is not significant and is most usually about $10^{-18}$ eV. (1)
Recently I have read that antimatter mirror images... | I will expand on this later, but there is a main difference between regular enantiomeres, in which the particles are the same but in a different configuration, versus an antimatter enantiomere, in which all particles reverse their properties. In the antimater case, chirality relationships for instance, remain the same,... | {
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What is the experimental evidence that the nucleons are made up of three quarks? What is the experimental evidence that the nucleons are made up of three quarks? What is the point of saying that nucleons are made of quarks when there are also gluons inside it?
| When I was in university, sitting on my dinosaur, one of my profs mentioned he worked on a neutron polarization system on a particle accelerator at Chalk River.
I had to ask how you polarized a neutral particle with a magnet, still thinking in terms of classical particles and charges. He explained that since there's an... | {
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Why does increasing the volume in which a gas can move increase its entropy? Let's say we have a box with a non-permeable wall separating the box in half. There is gas on the other side of the wall. Now we remove the wall so that the gas can diffuse to the other half of the box.
It is said that the entropy of the gas ... | A statistical mechanics perspective. The phase space of an atom in the gas is described by the microstates, made from position and momentum values, $(x, y, z, p_x, p_y, p_z)$.
The allowed position states are constrained by the dimensions (l, w and d) of the box, $0<x<l$, $0<y<w$, $0<z<d$.
When you increase the box size... | {
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What is possible intuitive explanation of inelastic relativistic collsion? In classical mechanics, we say an inelastic collision happens when some energy is transferred to heat and noise without changing the total sum of momentum. However, in special relativity, every component of 4 momentum is preserved, but not the s... | In a collision, the total relativistic energy is conserved.
$$E_{rel,total,f} = \gamma_{Ai} m_A + \gamma_{Bi}m_B$$
If, in addition, the particles retain their rest masses in the interaction,
we have for the left-hand-side:
$$E_{rel,total,f} = \gamma_{Af} m_A + \gamma_{Bf}m_B$$
and (without using the "final" labels o... | {
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Can I use time evolving block decimation (TEBD) to simulate the dynamics for many body localized systems? In the many-body localized phase, the system is described by quasi-local integrals of motion ("l-bits"). The entanglement does grow logarithmically with time. So if I use TEBD to get the real-time evolution will it... | If the entanglement entropy scales like $\sim \log t$, then the required bond dimension (and hence, the computational cost) for TEBD scales as a power law in $t$ (because it's exponential in entanglement entropy). If you call that "efficient" then TEBD is efficient. But if you want to go to very late times you're obvio... | {
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What is quantum fluctuation in the Bose-Einstein condensates theory? I would like to understand what quantum fluctuation really means. I think it's the particles that are not in the ground state. Am I right? But then, what are the differences between quantum fluctuations and thermal fluctuations?
Another question. How ... | Dinesh, this subject is also that I do not understand in detail and would like to understand better (especially the LHY correction), but I can say this much: BEC with attractive interaction are unstable in general. Atoms will rush to clump on top of another and decay via three-body loss. However, if there is another, r... | {
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What is a correct loudspeaker connecting scheme and why? Thinking of "what would be best shape for a subwoofer box?" i came to idea of a barrel, with its sides (or covers) "replaced" with speakers:
I have stereo bass amplifier which is fed from single signal source. So there are 2 possible ways to connect a terminals ... | Assuming that, when listening to the music, you are sitting at a point equidistant from the two bass drivers then the sound from them will travel an equal distance from each driver to reach you. If you wire the speakers in antiphase then the sound from the two drivers will be in antiphase when it reaches you and will i... | {
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How to determined the angle of force weight in an incline force vector problem? today in class I was introduced to some basic incline problems. I know that Force weight can be resolved into 2 components-the parallel and the perpendicular. I was given the angle of the ramp to be $30 degrees$. Which makes the parallel co... |
I hope this clears the confusion. Use trigonometry to find the components of force.
| {
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Does time dilation mean that faster than light travel is backwards time travel? Ok. So my question is, I've always heard it that Faster Than Light travel is supposedly backwards time travel.
However, the time dilation formula is
$$T=\frac{T_0}{\sqrt{1-v^2/c^2}}$$
And while it is true that speeds greater than $c$ turn... | I don't know what you mean by "some sort travel in a complex plane". Faster than light travel is by definition some object that changes position from $x_0$ to $x_1$ in such a way that $\dfrac{x_1-x_0}{\Delta t}>c$, where $\Delta t$ is the elapsed time. There is no time travel involved when this happens, but causality w... | {
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IQHE, quantized conductance, and zeeman splitting I've been trying to understand IQHE by reading these lecture notes by David Tong.
Mainly, I was trying to understand the quantized hall resistivity in terms of the number of Landau levels crossing the fermi energy.
Then, I began thinking about why spin induced Zeeman ... | The definition of filling factor is, $\nu \equiv \frac{\text{number of particles}}{\text {number of flux quanta}}$. I guess even if you include the Zeeman splitting this is not going to change.
| {
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Work done by a gas In the expression for work done by a gas,
$$W=\int P \,\mathrm{d}V,$$
aren't we supposed to use internal pressure?
Moreover work done by gas is the work done by the force exerted by the gas, but everywhere I find people using external pressure instead of internal pressure.
| Work is done by the gas against the external pressure.If there is a case of free expansion of the gas (as in vacuum) the work done by the gas is zero as no opposing forces are present to prevent expansion of the gas, hence it is evident that work done by the gas is only due to external pressure. If the process is quasi... | {
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Where is the right place to put the pressure gauge to measure the pressure of a tank? Studying the basic concepts of Fluid Mechanics, applied to pressure gauges, and looking at schematics in many places, a question came into my mind: Where is the right place to put the pressure gauge to measure the pressure of a tank?
... | Unlike a sensor, a gauge has to be where you can see it. Often you dont want the process liquid to get in the gauge, so the gauge is on top of the liquid level.
| {
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Rindler Coordinates and homogeneous Gravity Field I understood from the equivalence principle that an accelerated observer in free space is equivalent to a stationary observer in a gravitational field.
As far as I understood further, this means to analyze systems which occur at the earth's surface it is possible to use... | The Rindler metric describes an homogenous gravitational field (as you say in your title) i.e. a field that is the same everywhere. This means it is only an approximation at the Earth's surface since on Earth the gravitational acceleration changes with height. The Rindler metric will describe the geometry only over a r... | {
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Defining generalized momentum in terms of kinetic energy versus a Lagrangian Reputable authors (e.g., Bergmann, Wells, Susskind) define generalized momentum using the Lagrangian $L$ as $$p_{i}\equiv\frac{\partial L}{\partial\dot{q}^{i}}.\tag{1}$$
Joos and Freeman define generalized momentum for holonomous-scleronomous ... | *
*The canonical/conjugate momentum (1) is the natural/fundamental notion in Lagrangian formalism. (Also recall that there exist velocity-dependent potentials $U(q,\dot{q},t)$.)
*The kinetic momentum (2) only exists if there is a natural notion of a kinetic term $T$ in the Lagrangian $L$. (The kinetic term $T$ is by ... | {
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Why is the power of a filament lamp directly proportional to the cube of its voltage? I was doing a textbook question on how the power of a bulb varies with the potential difference across it. I plotted this graph:
(V is on the x axis and P is on the y axis.)
I was then told that this graph obeys the relationship $P=k... | Think of it the following way. You were right in writing the relationship between power, voltage and resistance:
$$P=\frac{V^2}{R}.$$
But this equation was said to not fit the data, and instead
$$P=kV^3.$$
Comparing these two equations, we arrive at the relationship
$$R=\frac{1}{kV}.$$
This is the thing we need to expl... | {
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Can Heat Transfer occur between two bodies with the same temperature but different states only through Latent Heat Transfer? I understand that temperature difference is the driving force for heat transfer but I have been wondering whether there would be any heat transfer, let's say if steam at 100 degree Celsius and wa... | yes it's possible if the states are somehow not reversible(might not be the proper word for that). For example if you have water and air at ambient temperature then water will evaporate as long as the air isnt saturated.
| {
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Relationship between intensity and amplitude of light wave I am confused with the realtionship between intensity and amplitude of wave. My understanding is that energy in a wave is proportional to its intensity; which is proportional to the square of the maximum height of the wave. is that a correct understanding.? If ... | If you insist on taking a wave, your statements are correct. The energy of the wave IS proportional to the intensity, which is in turn proportional to the square of amplitude of vibrations produced by the wave(in this case being the vibrations of electric and magnetic fields). When you increase the brightness, the ampl... | {
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Physical Significance of $U$ (Internal Energy ) , $H$ (Enthalpy) , $F$ (Free Energy) and $G$ (Gibbs Free Energy)? I know their mathematical definitions and how these terms are interrelated (mathematically) but I fail to understand the physical meaning of none but one which is INTERNAL ENERGY .
It seems implausible to m... | U, F, G, and H are sometimes referred to as Thermodynamic Potentials. A nice (in my opinion) explanation of the physical significance of these properties in relation to entropy (S) and system work can be found on the Hyperphysics web site under "Thermodynamic Potentials".
Hope this helps.
| {
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"source": "stackexchange",
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What causes burns when in contact with hot water? As I understand it thermal energy (heat) is simply a measure of the kinetic energy of an object (For example : water).Hot water is simply water with a larger kinetic energy in its molecules, right ?
So how do my hands get burned if I immerse them in hot water ? Do the ... | It should be noted that this question is not that much about heat, as about biochemistry. The actual damage to living tissues is not caused by kinetic "bombardment" by fast molecules, but proteins permanently switching to a different spatial conformation, which is favored at higher temperatures.
This explains why 310 K... | {
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Introduction to nuclear physics I want to self-study nuclear physics in order to understand nuclear reactors and nuclear weapons, what books can you recommend?
| Here are some available references. The Atomic Nucleus by Evans. Nuclear Reactor Theory by Lamarsh. The Los Alamos Primer by Serber. Building the Bombs by Loeber. Most of the details for nuclear weapons are classified or at least limited distribution. You can also search the web for articles by Drell and Peurifoy ... | {
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What does resonant frequency in the Q factor mean? For the Q factor of a body undergoing force oscillations, does resonant frequency refers to the frequency of driving frequency or the body's natural frequency?
The term resonant frequency seems to mean the body's natural frequency (since this frequency corresponds to r... | In your question, you state that the pendulum is oscillating at a frequency f and that it is being forced by a source. In this context it appears that what the author meant was that the pendulum was being driven at its natural frequency f.
| {
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Example in which light takes the path of maximum optical length According to the modern version of Fermat's principle,"A light ray in going from point A to point B must traverse an optical path length that is stationary with respect to variations of that path.".Is a maximum optical path length possible ?What if we keep... | You are quoting wikipedia
There is no maximum length from point A to point B (the path could be arbitrarily long), the more deviation to that minimum path the more length is added in such a way that the light phase is so mixed up that it ends up cancelling itself (no light).
EDIT: Quantum electrodynamics from Feynman o... | {
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How can a particle in circular motion about a fixed point accelerate, if the point doesn't too? When a particle is performing uniform circular motion attached to a string about a fixed centre, at any instant of time its acceleration is directed towards the centre but the centre has no acceleration. But I was taught in ... | I think what you're asking is "How can a particle accelerate towards a point without ever getting closer?"
Acceleration is "change in Velocity," and Velocity is the combination of speed and direction. So acceleration can mean "a change in speed", "a change in direction", or a combination of the two. In order for any ob... | {
"language": "en",
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"source": "stackexchange",
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Harmonic Oscillator Trial Wavefunction I was learning today about trial wave functions for a harmonic oscillator.
We learnt that the solution to Schrödinger equation for a harmonic oscillator is a Gaussian curve, i.e.
$$
f(x) = e^{-x^2} .
$$
Testing a trial function such as:
$$
\psi = N_{0}e^{-ax^2}
$$
where $x$ is p... | The basic point is that the equation involving $E$ is an identity, which must hold for all values of $x$, not just particular values of $x$. So, all the $x$-dependent parts must cancel identically. Sometimes, identities are distinguished from simple equations by using the symbol $\equiv$ rather than $=$.
Slightly more ... | {
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If $\sum_n \ c_n \ \psi_n(x,t)$ represents an arbitrary state for a given solution to the TISE, what are the bases for a free particle? If $\sum_n c_n \psi_n(x,t)$ represents an arbitrary vector in the Hilbert space of solutions to Schrodinger's equation with a given potential function, this makes makes sense to me. Ea... | The integral is a sum. We just changed from a discrete index to a continuous one, since $k$ isn't bounded by any quantization conditions. The bases are the separatable solutions to the free particle Hamiltonian, but since they aren't normalizable, they can't represent a physical state. Although, we can think of them as... | {
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Is there a medium less dense than vacuum, in which light can travel faster than $c$? Is there a medium less dense than vacuum, in which light can travel faster than $c$? If not, can we make it?
| It depends on the volume! You have to read something about the Casimir effect. Even in a complete vacuum, you always have virtual particles. Reality is quantum, and quantum vacuum is not empty! It cannot be!
So basically when the volume is bounded as in a capacitor, it seems there are fewer possible excitations inside... | {
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Retarded potentials with a dirac delta fail to give Lienard-Wiechert In the derivation of the Liénard-Wiechert potential the expression for the retarded potential is given
$$\varphi(\mathbf{r}, t) = \frac{1}{4\pi \epsilon_0}\int \frac{\rho(\mathbf{r}', t_r')}{|\mathbf{r} - \mathbf{r}'|} d^3\mathbf{r}'$$
and it is appli... | The definition of the Dirac function cannot be applied directly to obtain your third expression, because $t_r'$ in $\delta^3(\mathbf r' - \mathbf r_s(t_r'))$ is a function of $\mathbf r'$.
To evaluate the integral, one must change the integral to new integration variables $\mathbf y$ in such a way that the definition c... | {
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How can I find inlet pressure of a valve by measuring the mass flow rate? I don't have a manometer to measure how much pressure of water my inlet valve is having, can I measure this by just having an empty container and have the valve fill it per x amount of seconds x amount of liters and calculate that to what my actu... | In principle, yes, you can calculate the inlet pressure of a valve by measuring the mass flow rate as it discharges to atmospheric conditions. However, to so this, you need to know something about how the flow rate relates to the pressure drop across the valve, which will depend on the size and design of the valve. I a... | {
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Isotropy of the universe in different reference frames Suppose that we put Bob and Alice into intergalactic space. If they look around they will see the light from distant galaxies shifted according to the Hubble law. More importantly, the light is (on average) isotropic.
Now suppose we accelerate Bob to e.g. $\beta = ... |
According to this reasoning, there exists a special reference frame where the universe is isotropic. This, of course, isn't what we measure.
There is such a special frame, and that is what we measure. The special frame is the frame moving with the Hubble flow, and in that frame, the CMB is observed to be uniform in a... | {
"language": "en",
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Formula for potential energy? Conservation of energy? How would we know what formula to use for potential energy?
In my class, $mgh$ was used, but when dealing with a spring, it's ${1\over2}kx^2$. Is that because that's the elastic potential energy formula?
Also, for elastic and inelastic collisions, momentum is conse... | Both equations for potential energy are of the form $\text{force}\times \text{distance}$ ie $mg \times h$ and $kx \times x$.
The factor $\frac 12$ is there for the spring potential energy because the force does not stay constant as the extension of the spring changes unlike the gravitational force on a mass which stays... | {
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Non-compatibility between relativity and quantum mechanics Is the discrepancy between quantum mechanics and relativity only in the math involved or is it much deeper? That is, do the same interactions have different and non-comparable interpretations in both, or are the mathematical equations involved wrong with respec... | The unified theory of particle physics, $\operatorname{SU}(3)\times \operatorname{SU}(2) \times \operatorname{U}(1)$, uses Klein Gordon and Dirac and quantized maxwell equations to solve for quantum mechanical systems, and at a meta level quantum field theory. All these are 100% compatible with special relativity.
If b... | {
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Wave behavior of particles When people say that every moving particle has an associated wave, do they mean that the particles will move up and down physically, for example when we say that a moving electron has a wave associated with it, does the electron physically oscillate? Or is it some other wave, like a probabil... | The wave is there to describe the phenomena of diffraction and of interference. Particle beams can interfere destructively: no intensity at some spot when both beams are on.
This can be described by a phase and the mathematics of waves. When phases are opposite, the sum is zero. Feynman explains this (in his little boo... | {
"language": "en",
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Hamiltonian for a magnetic field An atom has an electromagnetic moment, $\mu = -g\mu_B S$ where S is the electronic spin operator ($S=S_x,S_y.S_z$) and $S_i$ are the Pauli matrices, given below. The atom has a spin $\frac{1}{2}$ nuclear magnetic moment and the Hamiltonian of the system is
\begin{gather*}
H = -\mu ... | The Hamiltonain is calculated as
\begin{align}
H =& \, g \mu_B \, \left(B_x S_x + B_y S_y + B_z S_z\right) \, + \, \frac{1}{2}A_0 S_z = \\
=& \, \frac{g \mu_B}{2} \, \left(B_x \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} + B_y \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} + B_z \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{... | {
"language": "en",
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Integral formula for inertia tensor Writing down the balance of angular momentum, we introduce the inertia tensor by the formula
\begin{equation}
J(t)a \cdot b = \int_{S(t)} \rho (t,x)\left( a \times \left( x - X(t) \right)\right)\cdot \left(b \times \left( x - X(t) \right) \right) dx
\end{equation}
for some vectors $a... | Welcome to Physics SE!
The definition of the inertia tensor that you seem to be using can also be written, as on the Wikipedia Moment of Inertia page
$$
\mathbf{J} = -\int d\mathbf{x} \, \rho(\mathbf{x}) \,
\big[ \Delta\mathbf{x} \big] \cdot \big[ \Delta\mathbf{x} \big]
$$
where $\Delta \mathbf{x} = \mathbf{x}-\mathb... | {
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Contravariant metric in Newton-Cartan spacetime I'm interested in the geometrized Newtonian gravitation or Newton-Cartan theory. In every reference that I have found begins saying that a Newton-Cartan spacetime is a manifold $M$ with some structures. Among then, is always pointed a contravariant metric $g^{ab}$ that re... | The metric structure in Newton-Cartan geometry is given by two elements (in d+1 spacetime dimensions):
*
*A contravariant metric $h^{\mu\nu}$ of rank d
*A one-form $\psi_\mu$ spanning the radical of $h$, namely $h^{\mu\nu}\psi_{\nu}=0$.
The 1-form $\psi$ allows to distinguish between timelike ($\psi_\mu X^\mu\ne... | {
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Doubt about ray diagrams In a ray diagram, 2 rays are considered enough to locate the image of a point on a given object. But how can we say that the rays other than the one we drew will meet at that same point?
I guess we can justify this by saying that we get only one image of a given object by a single mirror/l... | This is a direct result of paraxial optics. By paraxial, one means that all the rays are nearly parallel to the optical axis.
Let's make this claim more rigorous. Any given ray at some point is characterized by its height $x$ and angle $\theta$ in respect to the optical axis. In this scenario, nearly every optical elem... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/440716",
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Air Pressure in a Mine In Sunday's "60 Minutes" TV program the correspondent descended into a gold mine said to be 2 miles (3 km) deep. What equation describes the air pressure relative to sea level atmospheric pressure?
| Barometric formula is the equation which can estimate the pressure at different heights:
$$
p=p_0\cdot\exp\left(-\frac{mgh}{k_BT}\right)
$$
The $p_0$ is the reference pressure, $T$ is the temperature in K, $k_B$ is the Boltzmann constant, and $h$ is the height.
| {
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Cylinder vs cylinder of double the radius roll down an incline plane, which one wins? A solid cylinder and another solid cylinder with the same mass but double the radius start at the same height on an incline plane with height h and roll without slipping. Consider the cylinders as disks with moment of inertias I=(1/2)... |
My thought process was that since the radius doubled, c=2
$c$ is not the moment of inertia itself, it's the constant in $I = cMR^2$. For your two solid cylinders, the constant will be the same, even though $I$ will differ because $R$ will differ.
Similarly, if it’s moment of inertia increases, it’s angular and line... | {
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What is the measured decay rate of antineutrons? / What is the measured mean lifetime of antineutrons? Please do not post any "answers" dealing with predicted/theoretical estimates. The question specifically asks for measured / experimental evidence.
| According to Fundamental Symmetries, ed. Bloch, P., Pavlopoulos, P., Klapisch, R. 1987, page 82:
The measurement of this lifetime has not yet been attempted as it requires very slow antineutrons. Low-energy antineutrons are created in the antiproton source of antiproton accumulators, and they can be produced in the ch... | {
"language": "en",
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Is the normal force equal to weight if we take the rotation of Earth into account? In my physics class we were doing problems such that we set $N$ (normal force) $= mg$. I understand that by Newton's Third Law, if I exert a force on the ground, then the ground will exert an equal and opposite force on me. However, the ... | Here is a diagram of an ideal spherical Earth radius $R$, mass $M$ rotating at an angular speed $\omega$ with an object mass $m$ in contact with the surface of the Earth.
The object on the Earth is subject to two forces:
gravitational attraction $\frac{GMm}{R^2}=mg$ where $g$ is the gravitational field strength an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/441245",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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"answer_id": 3
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Understanding projective measurements as a special case of POVM measurements ("third postulate" in Nielsen and Chuang) I am working through Nielsen and Chuang's book and am confused about a detail from sections 2.2.3 and 2.2.5.
On page 88 of my copy (section 2.2.5), they write
Projective measurements can be understoo... | https://en.wikipedia.org/wiki/Projection_(linear_algebra)#Orthogonal_projections states:
An orthogonal projection is a projection for which the range U and the null space V are orthogonal subspaces.
Thus, orthogonality is a property of a single projection, not of a set of projections, as you state it (some kind of m... | {
"language": "en",
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Do centrifugal force and gravity differ in their effects on objects? If the type of object matters, consider the human body. If the situation matters, consider standing on the inside wall of an O'Neill cylinder compared to standing on the surface of Earth.
"Differ in their effects on objects" means: Would the object be... | What we normally think of as “gravity” on earth is actually a mix of gravitational and centrifugal force: plumb bobs don’t hang toward the center of the earth, but rather slightly toward the opposite pole. They are both static body forces, so it’s not possible to directly tell them apart locally.
But any rotating fra... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why does the warm air rises up? Warm air has more energy than cold air. This means that according to the Einstein equation $E = mc^2$ the warmer air has a greater mass than the cold one. Why is the warm air rising, if it has a greater mass, which means that the attraction of gravity between the Earth and the warm air i... | Buoyancy and the ideal gas law.
PV = nRT
P is pressure
V is volume
n is number
R is a constant
T is temperature
In a closed container if you increase T then P goes up.
In the open (atmosphere) V goes up
With same mass and more V buoyancy then takes over.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/441954",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Is there some physical interpretation of the parallel exterior region? Let the maximal extension of the Schwarzschild spacetime be given. It admits as coordinates the Kruskal-Szekeres coordinates $(T,X,\theta,\phi)$ with $$T^2-X^2<1$$
since the singularity occurs at $T^2-X^2=1$. This spacetime is divided into four regi... |
Is that really the case? There is no physical interpretation for the regions III and IV? Specially the parallel exterior region, isn't there any known physical interpretation of what it might be physically or how it might really exist in a given situation?
Yes, that's really the case. Those regions don't exist for a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442037",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Capacitor demo explanation I know that for a charged capacitor as one separates the plates further apart the voltage increases while the capacitance decreases.
But surely as the plates are pulled further and further apart the potential difference across the plates or voltage cannot rise indefinitely? Where does it stop... |
to take the gravitational potential energy as comparison feels weird because the further a mass gets from another mass the less force it experiences until a point where the force experienced is so negligible that it counts only theoretically
The same thing is happening with the charge plates.
At a close distance (whe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442152",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Accurate Equation for Earth's Gravitational Binding Energy This is a relatively important question for anyone who can answer it. I am trying to find the equation that accurately solves for Earth's Gravitational Binding Energy. The information below is from the wikipedia page:
Assuming that the Earth is a uniform sphere... |
I am trying to find the equation that accurately solves for Earth's Gravitational Binding Energy.
There isn't a single equation for this (and much of real science does not yield convenient single formulas as solutions). What the PREM produces for density is a set of piecewise approximate polynomial functions that mo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442379",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
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Plasma and helicon wave frequencies in iron according to Drude model The first chapter of Ashcroft and Mermin's Solid State Physics discusses electromagnetic waves in metals. One of the exercises requires calculation of the plasma and helicon frequenies using the Drude model. For iron, I got $2.3*10^{16}$ for the plasm... | For the plasma frequency, you're only about one order of magnitude off; the correct value is $9.89 \times 10^{14}$ Hz (source). The reason for the difference is that because of iron's long-range periodic crystal structure, electrons in iron have an effective mass significantly higher than their physical mass. Note th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442470",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
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What is the shape of a gravitational wave form? What is the shape of a gravitational wave as it hits the Earth, particularly the time portion.
Does time start at normal speed, then slow slightly, and then return to normal speed?
Or does it start at a normal speed, slow down slightly, then speed up slightly, and then ... | The new report here, published today, shows three very nice examples of gravitational waves coming from the merger of two black holes on page 2. So I can see the wave shapes very clearly.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/442588",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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