Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Does Big Bang predict the size of the fluctuations in the CMB? From this Ethan Siegel’s article
The temperature fluctuations in the CMB are only 1-part-in-30,000, thousands of times smaller than a singular Big Bang predicts.
Does big bang predict the size of the fluctuations in the CMB?
Do we know what caused the ... | The big bang model does not predict the size of the CMB fluctuations - rather, the universe we see today is a consequence of those fluctuations since all the structures we see today (clusters of galaxies and superclusters, filaments etc) must have grown from structures that are traced by those fluctuations.
Given that,... | {
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A Number State of Light through a dielectric If a number state |1> picks up a factor of $e^{-i\phi}$ on going through a certain medium, what factor will a number state |N> pick up? Will it be $e^{-iN\phi}$ or $e^{-i\phi}$ or something else? And what is the justification? Thanks.
| As long as it is a linear optical medium - which is typically the case up to good accuracy - it will act as $a^\dagger\to e^{-i\phi} a^\dagger$ on the creation operators (i.e. in Heisenberg picture). Thus, it acts as
$$
|n\rangle =\tfrac{1}{\sqrt{n!}}(a^\dagger)^n|0\rangle \ \to\
\tfrac{1}{\sqrt{n!}}(e^{-i\phi}a^\dagg... | {
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Why do lights appear like straight lines on a windshield of a car? (becomes more prominent at sunset and night)
i think thats the Diffraction of light caused by the scratches in the glass. or the wiper blade leave a pattern of dirt and grime in an arc. i hope someone can confirm my logic.
my seconde question is why t... | It is probably not diffraction unless you can see a separation of colours.
The most likely explanation is scratches on the windscreen (and the covering of dirt) caused by the wiper blades.
More prominent at sunset because the Sun is low in the sky and the windscreen is being hit by a shaft of light.
You will note f... | {
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Only sea water appears blue in color, why this is not happening in river water? Is the salt in the water the reason for scattering sunlight into blue?
| The color of a body of water is usually due primarily to light reflected from the sky and surroundings. Of course the ocean usually doesn't have a lot around it except the sky, but in a place where a lot of light from vegetation reflects off the water, the ocean can appear green.
This is a fresh-water lake; you can se... | {
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Electric field of an infinite sheet of charge I am trying to derive the formula for E due to an infinite sheet of charge with a charge density of $ \rho C/m^2$. I assumed the sheet is on $yz$-plane. I used Coulomb's law to get an equation and integrated the expression that over $yz$-plane. But, I have not succeeded in ... | Use cylindrical coordinates. The field (on axis) of a ring of charge (radius $R$, charge density $\lambda$) goes like:
$$ E(z) = \frac{1}{2\epsilon_0}\frac{ R z}{(z^2 + R^2)^{\frac 3 2}} $$
then integrate over $R$, using:
$$ \int{\frac{ R z}{(z^2 + R^2)^{\frac 3 2}dR}}=-\frac z {\sqrt{z^2+R^2}}\rightarrow 1$$
| {
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Meaning of the word 'canonical' in physics I often encounter the term canonical in my study of physics. What does it mean? There is canonical momentum, canonical transformations and I have even heard the phrase 'proving something more canonically'. What does the word mean in each of these contexts?
| Sometimes it just means "official" or "standardized" or "really important", but usually it has the more precise meaning "relating to the Hamiltonian formulation of classical mechanics". The canonical momenta are usually first introduced in the Lagrangian framework, but they are the momenta that appear in the phase spac... | {
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Galilean transformations of velocity If I perform a Galilean boost $$x' = x - vt \\ t'=t$$ between two frames $S$ and $S'$, observers in each frame would disagree on the velocity of a particle because
$$ \frac{dx'}{dt'} = \frac{dx}{dt} - v. $$
Well Galilean transformations preserve the spatial intervals $\Delta x$ and... | The confusion is in what $\Delta x$ really is.
Let's say two observers, one in S and the other in S', see a meter stick. They will both agree it is one meter long. So if $\Delta x$ is a set length then yes, this is invariant under the transformation.
Now let's say an observer in S is holding this meter stick. Over any... | {
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In a vacuum can a cooler body radiate Infrared radiation to a warmer body? I mentioned vacuum, because I want to discount the effects of conduction or convection. I simply want to know if some of the infrared radiation(IR) goes from the cooler body to the hotter body? How does each body know how much to radiate at any ... |
How does each body know how much to radiate at any particular time?
They don't. If you assume that both bodies are "black", that is they radiate electromagnetic waves due to their temperature as described by the black body radiation equations, they do it because that's the way nature is.
[...] how does the hotter bo... | {
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How can a transformer produce a high voltage and a low current? I understand that in ideal transformers, power is conserved. Because of this the product of voltage and current in the secondary winding is a constant.
This means that voltage and current are inversely related, which seems unintuitive because they are dire... | Here is an analogy which might help you grasp how a transformer works.
Think of an electrical transformer as if it were instead a car transmission. The ratio between torque and RPM at the input shaft is altered by the gears to yield a different ratio of torque to RPM at the output shaft.
As an example, in first gear t... | {
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Why not free electrons in atom doesn't radiates em waves\photons? Why not free electrons in atom doesn't radiates em waves\photons, although they move with acceleration? Like 1s electron of Titan, it doesn't emits em waves, yes? Why?
| In quantum mechanics there are no individual electrons which dart about like ping bong balls. But there is an electric charge density which can be derived from the total wave function of the system. In general this charge density is not stationary. To the extent that it is moving, oscillating or accelerating, it will e... | {
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Woodworking clamps, does force add up? I was watching a woodworking video about glue, and the guy was clamping two pieces of wood together using a total of 8 clamps. He argued that by doing so he would apply 8 times the maximum force of 150N (a property of the clamp), resulting in 1200N in total.
I think he's wrong. I ... | He's right - the forces of the clamps will add up. You seem to be confusing force and pressure. The pressure from each clamp would reduce radially outwards from each clamping point, as you describe (although adding clamps will increase the average pressure acting across the entire length of the planks, thus increasing ... | {
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All central forces are conservative forces, but are all conservative forces central forces? I have just been introduced to the concept of central forces, and to the fact that they are per definition conservative forces. I have looked up several examples of central forces (gravity, electric, and spring), but they cover ... | A constant force is conservative but not central.
For example: $\vec F=F \hat x$
You can check that the curl of this force is $0$, hence it is conservative. Its potential energy function in 3D space would just be $V(x,y,z)=-Fx+V_0$, where $V_0$ is some constant value.
An example of this is the approximation of gravity ... | {
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Demagnetising $H$ field If we have a permanent magnet we know that we have a $H$ field opposite in direction to the residual magnetic field $B_r$. The $H$ field causes a demagnetisation, but how does it do it? We know that the physical field (the field which causes the Lorentz force) is the magnetic field $B$.
| The H field is caused by the positive and negative poles that develop at the end of the magnet in the opposite direction of the B field. Whether H or B is the real field is somewhat a matter of taste, for neither is directly measurable in any easy way and both are the result of averaging; some even say that within the ... | {
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On Harmonics In Physics I am an IB physics student. I am very confused about the concept of first, second, third, etc harmonics.
My questions are:
*
*How does a wave get from first to second harmonic, and from second harmonic to third harmonic etc? What do we need to do to a wave to get it there? Increase the spee... | Harmonics are derived from a mathematical concept called fourier series. If you have a $1\lambda$ standing wave and you have a measuring device in the middle, you'd find a 0, if you then created a standing wave with $2\lambda$ and you measured at the exact same spatial coordinate, you'd find another 0. So, by measuring... | {
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How to derive this expression for the free scalar field in QFT? (Peskin & Schroeder) In the introductory text to quantum field theory by Peskin & Schroeder, they state that in analogy to the simple harmonic oscillator in quantum mechanics, the free scalar field can be expressed as:
$$\phi(\vec{x}) = \int \frac{d^3 p}{(... | I'll adopt the abbreviation $kx:=k_0x^0-\mathbf{k}\cdot\mathbf{x}$.
The Klein-Gordon equation $(\square +m^2)\phi=0$ can be solved by a Fourier transform. Writing $\phi(x)=\int d^4ke^{-ikx}\tilde{\phi}(k)$ we get $(k^2-m^2)\tilde{\phi}(k)=0$, i.e. $\tilde{\phi}(k)=\tilde{\varphi}(k)\delta(k^2-m^2)$ for some function $\... | {
"language": "en",
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Potential difference across the strips of an inductor The voltage across the ends of an inductor is $L (di/dt)$. Applying the loop law $V = L(di/dt)$, so the voltage across the strips at a distance x measured from the "LEFT END" should be $V \frac xl$ because the inductance of x length is $ L \frac xl$.
But according... | There are 2 different potential differences in this question. One is the PD along each strip in the direction of $l$ - ie horizontal. I shall call this $V_x$. The other is the PD between the 2 strips in the direction of $b$ - ie vertical - at the same horizontal position $x$. I shall call this $V_y$, but note that like... | {
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On String Theory, Supersymmetry and prospects of a theory of everything The fundamental postulate of string theory is that matter is composed of tiny vibrating loops of string, and each vibrational mode of the string corresponds to a different fundamental particle. Now, since there exists infinitely many possible vibra... | QCD is already a little like this. Mesons and baryons form families of increasing spin and mass ("Regge trajectories "). Nucleons are bound together by exchange of spin-0 pions, but heavier spin-1 vector mesons also play a role, and even tensor mesons of spin-2 and higher. The attempt to develop a theoretical framework... | {
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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... | You're right that it's a bit circular as stated. The more rigorous way to state a conservation law is something like:
The rate of change of [quantity] in a bounded system is equal to minus the rate at which [quantity] leaves through boundaries of that system.
A "closed system" is then a system for which both of thes... | {
"language": "en",
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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... | There are some reasons I can think of, and they are not mutually exclusive if true.
1) There is more moisture in the sky. This enables sunlight to scatter more, and so the sky appears to be brighter.
2) The rain is able to clear dust, pollutants, etc. which normally block sunlight. With less of these particles in the a... | {
"language": "en",
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What is the educational path to properly understanding the Higgs Boson? I want to understand the Higgs Boson. Not in terms of analogies and metaphors, but in terms of hard math.
Assume I have a solid background in pre-university maths and physics. (I have many bits and pieces of higher-level stuff, but let's ignore tha... | The basic answer is: learn quantum mechanics, then quantum field theory, then the standard model.
By the way, it's the Higgs field that does all the interesting things - the Higgs boson is, to our knowledge, the most useless aspect of the Higgs field. It does nothing of any importance, and yet, because the Higgs field... | {
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derivative of the electric field along the normal to the surface near the conductor how to derive the formula approves the derivative of the electric field along the normal to the surface near the conductor is inversely proportional to the principal radii of curvature?
$\frac{\partial E}{\partial n}=-E \left(\frac{1}{R... | This formula can be deduced by applying the Conservation of Flux : the flux through any volume above the conductor is zero because it encloses no charge.
Imagine such a volume close to the surface of the conductor. In profile this volume (vastly exaggerated in size) looks like the shaded region ABCD in the diagram belo... | {
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Intuitively, why do attempts to delay hitting a black hole singularity cause you to reach it faster? In general relativity, proper time is maximized along geodesics. Inside of a black hole, all future-oriented timelike trajectories end at the singularity. Putting these two facts together, we find that any deviation fro... | My (very limited) intuition for this is that once you cross the event horizon, the singularity is not so much a distant point in space as it is a moment in future time.
In other words, within the event horizon you're firing your rockets not to avoid some point $(x,y,z)$, but rather to avoid next Thursday. From here,... | {
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What is the value of absolute zero: $-273.15\ \rm °C$ or $-273.16\ \rm °C$? What is the value of absolute zero?
0K=
-273.15 °C
Or
-273.16 °C
It has been confused in different scientific scriptures. The first definition on Dictionary.com, for example.
| According to BIPM (International Bureau of Weights and Measures),
The kelvin, unit of thermodynamic temperature, is the fraction $\frac{1}{273.16}$ of the thermodynamic temperature of the triple point of water.
Hence the triple point of water is $273.16\ \rm K$. Comparing to the $0.01\ \rm °C$ reference (i.e. $273.16... | {
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Spin glasses overlap Suppose you have a spin glass simulation in which the standard Metropolis MC algorithm is used to sample phase space.
The we calculate the equivalent for the lattice system of the self intermediate scattering function, namely:
$$
C(\tau) = \frac{1}{N}\sum_i^N\left<\sigma_i(t)\sigma_i(t+\tau)\right>... | This is called the Temporal Autocorrelation Function. A bit like spatial correlations, it is related to critical dynamics. For example, in a simple, non frustrated 2d Ising model, time autocorrelation is low in the high temperature phase (which is noisy and therefore forgets quickly), and also in the low temperature ph... | {
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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... |
So it seems there is an absurdity in claiming that the solution of the differential equation is unique. Where am I wrong?
You seem to be taking that the fact that an equation has a unique solution to imply that that equation is the only one with that solution.
An even simpler example:
The solution of $x=1+2$ is uniqu... | {
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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... | The Heisenberg Uncertainty Principle does not involve speed. It involves momentum, and this is one of the places where that distinction is very important. Photons all travel at the same speed, yes, but their momentum can take on any value. As such, the uncertainty in its position and the uncertainty in its momentum are... | {
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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... | Given about the same size of a balloon and a football, the main difference in how far they advance horizontally is their kinetic energies, not air resistance.
Since the velocity of an arm is limited, the initial velocity of a balloon would be similar to the initial velocity of a football and, since the football is much... | {
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Difference between pressure and temperature If I am given the average kinetic energy of the molecules of a gas or a liquid, how can I tell if the fluid will burn me/crush me/both if I immerse my hand in it?
Equivalently, what is the difference between heat transfer and momentum transfer at a molecular level?
| Both pressure and temperature can be thought of as forms of kinetic energy density, but they are divided over different quantities. Pressure is proportional to kinetic energy per unit volume, while temperature is proportional to kinetic energy per particle. The conversion factor between the two measures (per-volume vs.... | {
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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?
| No, it doesn't. Velocity is a vectorial quantity, it has magnitude (speed) and direction. Uniform circular motion can be given as an example in order to help you with your question. Even though the speed is constant in this particular example, the direction changes all the time.
The velocity of an object changes when ... | {
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Half-life of $W$ and $Z$ bosons $W$ and $Z$ bosons should decay through weak interaction. But their half-life is around $\tau = 10^{-25} s$ which is a typical value for particles decaying through strong force (instead of a $10^{-12}-10^{-6} s$ for a weak interaction decaying particle).
Why this can be?
| Both are weak decay processes but the intermediate vector boson decay occurs at very much higher energies of 80-90 GeV compared to 1 GeV for beta decay.
| {
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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... | The cathode source frees up lots of thermal electrons continuously and the electric field between cathode and anode accelerate them toward a specific direction.
and until these two is working electron beam continues to exist with no problem.
| {
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How to identify an MRI artifact on Fourier space? I am trying to find the frequency of the artifact on the MRI image of the knee below both manually and with ImageJ:
As you can see the artifact results in a bar pattern extending horizontally along the image - i.e. a spike artifact.
After transforming to Fourier space,... | I agree that 4.8 is pretty close to 5.02. There is nothing else in that neighborhood that grabs my attention.
The higher frequency spike looks like the next harmonic of that first spike frequency. It probably represents some additional structure to the artifact.
Note, unless it is windowed funny, this is NOT a classi... | {
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Degeneracy of anisotropic oscillator I was working on the 3D isotropic harmonic oscillator and I found that the energies are given by:
$$E=\hbar\omega(n_x+n_y+n_z+3/2)$$
Which has a degeneracy of $\tfrac12(n+1)(n+2)$. However, when dealing with the anisotropic case, I'm not sure if there's a degeneracy in energies. For... | The states
*
*$n_x=3$, $n_y=0$
*$n_x=0$, $n_y=1$
are degenerate in energy.
$\tag{QED}$
More generally, any harmonic oscillator of the form
$$
E = \hbar \omega_1 n_1 + \hbar \omega_2 n_2
$$
will be degenerate if $\displaystyle \frac{\omega_1}{\omega_2} \in \mathbb Q$. It is an important exercise to prove that tha... | {
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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... | There is an article here: (the optimal driving force is shown to be $90^{\circ}$ out of phase of the motion)
Phase difference of driving frequency and oscillating frequency
Also any vector like $4j + 3i$ can be expressed in phasor form as $5 \angle 41^{\circ}$ or in complex form $4+3i$. Adding $90^{\circ}$ is just a v... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Speed of sound in a gas and speed of a typical gas molecule Why is speed of sound in a gas less than the average velocity of the gas molecules? Is there an intuitive way to explain this?
| Gas molecules moving with an average speed and sound propagation are two different things. Something you have to keep in mind is that sound is not transmitted by the net motion of particles. Sound is transmitted via pressure waves (or you can just say sound is pressure waves). Furthermore, that the gas molecules have a... | {
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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?
| here are some general rules.
Low-frequency EM waves (up to about 500kHz) propagate mostly by ground wave.
Medium-to-high-frequency EM waves (500kHz to 30mHz) propagate by ground wave and by ionospheric reflection.
High frequency waves (above roughly 50mHz) propagate by line-of-sight.
| {
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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]
\,.
$$
I'm trying to get an understanding of how this represents energy.
If I'm in a vacuum, and I push a block with a force of $1 \, \mathrm{N},$ it will move... | Think of a unit of work as what you do when you lift a kilogram to a height of a metre. How do you do 2 units of work? You lift that kilogram 2 metres. 3 units? 3 metres. Etc. If you lift something the work you do is the force you exert times the distance traveled (height raised).
For your example of pushing a body in... | {
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Why doesn't a charged particle moving with constant velocity produce electromagnetic waves? A charged particle moving with an acceleration produces electromagnetic waves. Why doesn't a charged particle moving with a constant velocity produce electromagnetic waves? As far I understand, the electric and magnetic fields i... | Ok so if you take maxwell equations and manipulate them a little you can get $$\begin{aligned}
\frac{\partial B}{\partial t} \quad & = -\quad \nabla\times E, \\[5pt]
\frac{\partial E}{\partial t} \quad & = \frac{1}{c^2} \nabla\times B - \frac{1}{\epsilon_0}J \\[5pt]
. ... | {
"language": "en",
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How does a particle know how to behave? How does a particle know it should behave in such and such manner?
As a person, I can set mass is so and so, charge is so and so - then set up equation to solve its equation of motion but who computes that equation of motion for a particle in real life?
I, as a person, employ sm... |
How does a particle know how to behave?
Already the title is about metaphysics, a consciousness is attributed to the particle by the verb "know".
Physics is about modelling observational measurements with mathematical formulae which can predict future behavior. The "knowledge" is collective and comes from an accumula... | {
"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... | The idea of presenting gravity as a standard quantum field of interacting gravitons is naive, because it does not explain how spacetime becomes curved. All other fields do not affect the background like pens writing on a sheet of paper. The sheet may be flat or curved, but writing on it doesn't change the curvature. GR... | {
"language": "en",
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Velocity of separation and velocity of approach Can I have a clear cut dimension or difference between velocity of approach and velocity of separation?
In just simple 1D motion.
Considering two rigid spherical masses of different masses and moving with different velocities.
| The problem is that the velocity of approach is a term which introduces ambiguity.
In one dimension, if bodies $A$ and $B$ are travelling at velocities $\vec v_{\rm A}$ and $\vec v_{\rm B}$ the velocity of approach can be said to be either $\vec v_{\rm A} - \vec v_{\rm B}$ or $\vec v_{\rm B}-\vec v_{\rm A}$.
Taking t... | {
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Triangulating Sol's position from another star Let me pose this question as a hypothetical.
Your ship makes a warp/jump through space. There's a malfunction. You're definitely not at your intended destination. You've warped to an unknown star, but you have managed to land you and your crew on a habitable planet orbi... | If the star is in our galaxy, then you can in principle triangulate your 3d position in the Galaxy from the positions of M31 and the Magellanic clouds.
With access to more specialised equipment (telescopes, spectrographs etc.) it should be possible to identify a set of well-known globular clusters to obtain more accur... | {
"language": "en",
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How can four-momentum be conserved in every frame in an elastic collision? I have this problem:
A particle B is standing still while another one, A, is moving towards it with initial 4-momentum $(E,p,0,0)$. Calculate the change in particle A's 4-momentum as viewed from the particle B's rest frame, in terms of the init... | I think you've been (understandably) misled by the wording of the problem.
...as viewed from the particle B's rest frame...
That's badly written because there are two different reference frames that could reasonably be called "particle B's rest frame": the one in which particle B is at rest before the collision, and... | {
"language": "en",
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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 answer is no, for using it with the theoretical models, as the other answer says.
BUT
Neural networks are used as tools in deciding kinematic states in particle detectors, assigning momentum and energy to possible new particles and thus identifying them by using a neural network "fit" even by the time I retired ... | {
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Why can we see the cosmic microwave background radiation? This radiation (CMBR) is said to have its origin at the surface of last scattering that exposed itself when the big bang universe had expanded for less than a million years.
In order to see radiation from a source, one has to be on its future light cone. In a un... | The answer by anna v is in line with what I have seen previously, but is it clear enough?
The "light cones" I mentioned can be shown in a graph in which one axis represents time and the other any spatial dimension. The scaling of the axes can be chosen so that a light cone is represented by a pair of lines inclined at... | {
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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... | Let us suppose that you are indeed left with one unstable nucleus with a half life of $\tau$.
The half life is the time interval during which the probability that the nucleus will decay is $\frac 12$.
So you start the clock at time $t=0$ and wait for one half life when the time is $t=\tau$.
The probability that the n... | {
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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?
| To answer this, lets use a single atom as an example. Essentially, the energy contained in that atom (bonds between the sub-atomic particles in the atoms nucleus) radiates away at the speed of light away when released, mostly in the form of Gamma radiation. the gravitational field would radiate out in exactly the same ... | {
"language": "en",
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Work done by friction on a body which is rolling on an inclined plane Why is the work done by friction zero during translational motion but nonzero when the body is rolling on an inclined plane?
| The work done by friction is zero in both cases. This is easiest to see in the formula for power:
$$P=F\cdot v$$
Friction acts at the point of contact where the velocity of both the body and the ground is zero, so P is always zero, so no work is done by friction.
On the other hand, gravity acts at the center of mass w... | {
"language": "en",
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Formally from $Z=\mathrm{tr} \,e^{-\beta H}$ to $Z=\sum_{n_1, n_2} e^{-\beta (E_1 + E_2)}$ for two non-interacting quantum harmonic oscillators Suppose we have a Hamiltonian of two noninteracting quantum harmonic oscillators. Then the Hamiltonian can be written
$H = H_1 \otimes I_2 + I_1 \otimes H_2$.
When I start with... | Let $\{|1, n_1\rangle\}$ be an orthonormal basis for the Hilbert space $\mathscr H_1$ of oscillator 1, and let $\{|2, n_2\rangle\}$ be an orthonormal basis for the Hilbert space $\mathscr H_2$ of oscillator 2, then the set of all tensor products $\{|1, n_1\rangle\otimes |2, n_2\rangle\}$ is an orthonormal basis for the... | {
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Hydrostatic force on spillway gate? I'm designing an spillway gate that, as the water exceeds a specific height, then it opens pure mechanically, it means the hydrostatic force compensates for the weight of the gate. As you can see the gate is hinged in point $A$.
If i try to find out how high water can reach before th... | Imagine that the water height is at a point where the force at B is exactly zero but the gate has not yet moved upward.
Part of the weight of the gate will now be supported by the hydrostatic force, and part of the weight will be supported by the hinge at point A.
In other words, the hydrostatic force must only lift a ... | {
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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?
| Yes. Dense-phase pneumatic conveying does exactly this. A powder is fluidized with air and then flows under gravity. It is widely used in process industries. For example, it is widely used in aluminium smelting to convey alumina (aluminium oxide) with particle sizes similar to sand. The solids flow like water when... | {
"language": "en",
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"source": "stackexchange",
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In quantum mechanics, is $|\psi\rangle$ equal to $\psi(x)$? So I'm going through my notes and I think I've confused myself. We often imply
$$
|\psi\rangle \to \psi(x)\\
\langle\psi| \to \psi(x)^*
$$
for instance when we talk about eigenvalue equations we interpret
$$
\hat{H}|\psi\rangle =E|\psi\rangle
$$
as simply
$... | To start, the kets are vectors, which means if we want an explicit realization of them, we would need to write them with respect to some basis. The first basis most people see is the position basis, where the basis kets are the states of definite position. Then, an arbitrary state $|\psi\rangle$ can be written as
$$ |\... | {
"language": "en",
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Relativity of Jerk Popular expositions of general relativity start with a thought experiment showing that it is impossible to distinguish a constantly accelerating frame of reference in a free fall from a free floating frame of reference.
Thought Experiment:
Person A is a small closed box, free-falling towards earth... | Gravity happens to measurably correspond to a constant acceleration, not jerk. So, no, this doesn't lead to a new theory of gravity. At least not immediately. On the other hand, strictly speaking, there is actually a slight jerk involved in free fall if an object falls long enough for the increasing gravitational field... | {
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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... | Electromagnetic energy can be converted into other forms, like heat or mechanical energy as in the case of motors. So the total energy is conserved, but it need not be in the form of the electric or magnetic field.
| {
"language": "en",
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Canonical quantisation: How to find the scalar product? I am trying to understand the canonical quantisation procedure. I understood that one takes the classical field equation and replaces the field by an operator Φ which solves the field equations. Then one imposes the commutation relations on Φ and Π.
Since Φ solves... | The general answer to your question is given by holomorphic quantization (a good treatment of which can be found in Woodhouse, "Geometric Quantization", especially chapter 5 & section 9.21). The idea is that you can build a scalar product from two ingredients:
*
*a symplectic form $Ω$, which is a non-degenerate anti... | {
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Question regarding average velocity We know average velocity in its strictest sense, means total displacement over total time taken: $$\frac{X_f-X_i}{T_f-T_i}$$
There's a special case, when a body is moving in a straight line with a constant acceleration. Of course since its acceleration is constant, it has to be a rec... | It's incorrect to use the word "only". (1) is always valid if acceleration is constant, but that doesn't exclude the other situation. It still can be valid in certain special situations.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/432049",
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How are particles in a collision chosen? In synchrotron particle colliders, how are the particles which are collided chosen? For the most part, collisions of different types of particles don't do anything like you might expect in a video game; there is no secret recipe list of cool things, each which require different... | It comes down to a trade-off between collision energy and collision 'purity'. Accelerating lighter particles, like electrons, to high energies is difficult because they have higher synchrotron losses. It is easier to accelerate protons to higher energies, however their collisions are 'messier' - the interactions that h... | {
"language": "en",
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How to measure angles in Minkowsky space, and how do they transform? I want to know how an ordinary angle $\theta$ transforms under a Lorentz boost. For that purpose I consider a 4-vector given by
$$ a ^ \mu = ( t , \cos \theta , \sin \theta , 0 ) .$$
The angle I will analyze is the one between this 4-vector and the ... | If you're moving, the angle is going to change. What you want to do is to define the origins of your reference frames $S$ and $S'$ at $t_0 = t_0' = 0, x_0 = x_0' = 0$. That is, $t_0 = t_0'$ is when observers in each frame perform their angle measurements. But how do they make a measurement? There was some event at $(x,... | {
"language": "en",
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Closed field lines in case of a Bar magnet Field lines in case of charges go from +ve to -ve but incase of magnet, they dont start or stop anywhere. They form closed loops. Is this consequence of the fact that single poles dont exist or something else is going on here?
| Yes. In an alternative universe where north and south charges can exist independently just as positive and negative charges can exist then magnetic field lines could start and end at these charges. In such a universe the alternative maxwells equations become symmetric, moving electric charge generates magnetic field an... | {
"language": "en",
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Debye Temperature for Copper I am trying to calculate the Debye temperature, $\theta_D$, of copper using the following:
$$
\theta_D = \frac{\hbar v_s}{k_B} \left( \frac{6\pi^2N}{V} \right)^{1/3}
$$
I have the following values: $\rho = 8900$ kgm$^{-3}$, $v_s = 3800$ms$^{-1}$, atomic mass $ M_a=63.5$gmol$^{-1}$. Now, the... | Great post. And thanks Anyon for the clarifications. I will post the complete clear solution for that problem with links and numbers and while doing that I will correct a small mistake that Anyon did.
First, concerning the density and molar mass of copper, I have
$$ \rho = 8960 \text{ kg/m}^{3} $$ and $$ M_a = 63.546 \... | {
"language": "en",
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Why do we describe physical systems in Hilbert space? In quantum mechanics we study physical systems associated with a Hilbert space. Why do we need a Hilbert space to describe the state of a system?
| Although there are many perspectives on this, largely united by the (correct) notion that Hilbert spaces allow for geometric tools to be applied, I'd like to present another overlooked perspective: Hilbert spaces are the tool of choice in QM because they can uniquely mimic probability spaces.
In quantum mechanics, we a... | {
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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... | There will be no shear across plane B. To see why, imagine a very small 'needle' embedded in the solid block, with the needle pointing from left to right in your picture. Also, with the center of the needle residing in the center of the block. I'm imagining the needle penetrating plane B. If there were shear, the needl... | {
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Expected momentum of ground state hydrogen $$ I am trying to calculate the expected momentum of an electron in the ground state of hydrogen atom. This is the wave function.
So far I have done this:$$\iiint_V \Psi^* (-i\hbar) \frac {d\Psi} {dr} r^2 sin\theta dr d\theta d\phi$$
But the answer I am getting is $$\frac {i... | You simply miscalculated the action of $\vec p$ on spherically symmetric functions f(r).
In actuality, your answer should transform vectorially,
$$
\vec p f(r)= -i\hbar \nabla f(r)= -i\hbar~ \hat x ~\partial_r f(r),
$$
so, then, as @KevinDeNotariis suggests,
$$
\langle \vec p \rangle= -i\hbar \int d^3x ~\psi^* \par... | {
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Forces between wheels and road for a vehicle Let’s assume we have a front-wheel drive (FWD) car, and we apply a torque (Cf) to the front wheels. At this point, assuming no slip condition, a friction force (Tf) will occur due to friction between the rotating wheel and the road. This force will be from left to right (acc... | There is a force to the left on the axle of the back wheels $F$ which is accelerating the rear wheels to the right.
The friction force between the tyre and the ground to the left $F_{\rm friction}$ applies a torque about the axle of the wheel to cause it to increase its rotational speed.
The frictional force is try red... | {
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Uncertainty cannot be calculated? I'm doing an experiment on resonance. The phase difference between the driving force and the one oscillating is given by
$$\varphi=\arcsin\left(\frac{y_1}{y_2}\right)$$
where $y_1$ and $y_2$ are measurements of voltages. At resonance $y_1=y_2$ so $φ=\frac{π}{2}$.
However, I'm trying... | The idea that you can use partial derivatives multiplied by the uncertainty in the independent variable(s) to estimates uncertainty in the dependent variable is just an approximation.
It is related to a Taylor series expansion with an implicit assumption that the terms involving the second derivatives and higher can be... | {
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Relationship between strain energy function and strain or stress How one can get the strain or stress from the strain energy function ?
And if one cannot do it, what is the use of that function ?
| The Strain Energy Deformation Function (SEDF) is a scalar $\psi(\varepsilon_{ij},\xi_k)$ defined in term of some strain tensor $\varepsilon_{ij}$ and possibly some internal variables $\xi_k$ (representing non-reversible or dissipative phenomena). This functions is a thermodynamic potential, that can be interpreted as G... | {
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Doppler effect in light (Observer moving away from source) I understand this intuitively and can picture it in my head, but when I do it on paper, the result is a sign difference that I cannot understand
According to this diagram the wavelength = ct-vt = t(c-v)
then the periodic time T = t-(vt/c) which should be t+(v... | For a stationary source the wavelength is $\lambda=cT$. The wavelength does not depend on the motion of the observer. The position of wavefront n is $x=ct-n\lambda=ct-ncT$.
The position of the observer is $x=vt $. Setting those two equal, the observer receives wavefront n at $vt=ct-ncT$ which gives $t_n=\frac{c}{c-v}n... | {
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Why does the position uncertainty of a harmonic oscillator not have the expectation value squared term? My question is about the derivation for the uncertainty of a quantum harmonic oscillator in the non-zero ground state energy. In my textbook A modern Approach to Quantum Mechanics by John S. Townsend there is a discu... | ::chuckles::
I remember being baffled by how this works out mathematically myself, and it's one of those "I can't believe it's that simple!" ones.
Three facts:
*
*$\hat{a}$ and $\hat{a}^\dagger$ are the lowering and raising ladder operators: they take a numbered state to one numbered either one less or one more tha... | {
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In $E=hf$, can $f$ assume any positive value? (Beginner) The energy of photon is given by the equation $E=hf$, where $h=$ Planck's constant, and f=frequency of radiation. Is f quantized, or can it assume any value?
If it can assume any value, then wouldn't this mean that the energy of photons is not quantized? If f ca... | Suppose you have an electromagnetic field(which is made up of photons) oscillating with frequency $f$ inside a cavity(resonator like two mirrors). Because of quantization, the field cannot have an arbitrary value of energy but only integer multiples of $hf$(i.e., $nhf$). This is what is meant by energy quantization.
| {
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Lagrange Equation - Basics The basic equation of Lagrange is given by,
$$\frac{\mathrm d}{\mathrm dt} \frac{\partial L}{\partial \dot{q_j}} - \frac{\partial L}{\partial q_j} = Q_j \tag{1}$$
where $T$ is the kinetic energy, $V$ is the potential energy, $L = T-V$. But at any given instant $$T + V = \text{Constant}\tag{2}... | Think of the difference between the expression $\frac{1}{2}\,\dot{q}^2 - \cos{q} = 1$, which is a special case of the pendulum's total energy, versus ${q}^2\sin^2(\dot{q}) + {q}^2 \cos^2(\dot{q}) + (1- {q})(1+ {q}) \equiv 1$. In the first case it is not true that
$$\cos{q} = \frac{1}{2} \, \dot{q}^2 - 1$$ for all po... | {
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Gravitationally-induced slowing-down of the spreading of a wave packet The spreading of a wave packet is very fast in quantum mechanics: for an electron, a gaussian wave packet spreads from one angström to 600km in one second! In his famous QM book, Sakurai mentions that there are numerical evidence that taking into ac... | At least in the linked paper they discuss using molecules (such as fluorofullerene C$_{60}$F$_{48}$) as the test particle. The molecules are uncharged.
| {
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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?
| The process that was first used to resolve the internal structure of the proton and neutron is called deep inelastic scattering. Basically, you hit the target hadron with enough energy that the probing particle's wavelength is short enough to make out the details of the internal structure of the proton or neutron.
You ... | {
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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 ... | The formula you used, $$\mathrm{d} S=\frac{\mathrm{d}Q_{\mathrm{reversible}}}{T}$$is a simplification for situations where all other factors are constant. Here, you're better off using $$\Delta S=nR\ln\frac{V_2}{V_1}$$
($R$ is the gas constant, and $n$ is the number of moles) It's a more sensible formula since the only... | {
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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 relativistic collisions, the lost kinetic energy appears as rest masses of products. Or the kinetic energy can increase in, say, a $1 \to 2$ decay process, where rest mass energies are converted into kinetic energy.
| {
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Why does current conservation involve an arbitrary function? In section 6.1 of Peskin's quantum field theory introduction, right after equation 6.3, the four current density $j^{\mu}$ is said to be conserved because for any function $f \left( x \right)$ that falls off at infinity, we have
$$
\int f \left( x \right) \pa... | I don't know Peskin's book, so I guess. Maybe the author has defined a quantum field as an operator-valued distribution? Then it would make sense to insert a test function, since to say $T=0$ if $T$ is a distribution means $T(f)=0$ for any test function $f$ and we physicists are used to read $T(f)$ as
$$\int\!T(x)\,f(x... | {
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If a galaxy forms from a spherical stationary cloud, how much of the gas will escape? Let's ignore the dark matter legend and stay with Keplerian physics.
Assuming that there is a cloud with $N$ stationary particles with the same size uniformly distributed in a sphere and they condense to form a galaxy.
$$N>>10^{\text{... | To quote Binney and Tremaine Galactic Dynamics, 2nd et p. 556:
From time to time an encounter gives a star enough energy to escape
from the stellar system. Thus there is a slow but irreversible leakage
of stars from the system, so stellar systems gradually evolve towards
a final state consisting of only two star... | {
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Does time dilation mean that faster than light travel is backwards time travel? Ok. So my question is, I've always heard it that Faster Than Light travel is supposedly backwards time travel.
However, the time dilation formula is
$$T=\frac{T_0}{\sqrt{1-v^2/c^2}}$$
And while it is true that speeds greater than $c$ turn... | When using formulas in physics it is important to keep in mind the assumptions that the formula is based on. In this case $T_0$ is the time on a clock in its rest frame. It is doubtful that tachyons exist, but if they do then they are not at rest in any inertial frame, so the time dilation formula simply does not apply... | {
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IQHE, quantized conductance, and zeeman splitting I've been trying to understand IQHE by reading these lecture notes by David Tong.
Mainly, I was trying to understand the quantized hall resistivity in terms of the number of Landau levels crossing the fermi energy.
Then, I began thinking about why spin induced Zeeman ... | This doubling indeed happens in the "quantum spin Hall effect", but those systems are at zero magnetic field (and moreover enjoy time reversal symmetry, which is key). However, in the usual quantum Hall effect, there is a huge static magnetic field, which polarizes all the low energy electrons (the Zeeman splitting is ... | {
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Commutator of Gauge Transformations for Yang-Mills Theory Following the conventions of "Quantum Field Theory and the Standard Model" by Schwartz, we have that for Yang-Mills Theory, an infinitesimal gauge transformation acts like
$$\delta_{\alpha} A = d\alpha - i\left[A, \alpha\right].$$
I am trying to compute the comm... | Try this:
$$
\left[\delta_{\alpha},\delta_{\beta}\right]A = (A + \delta_{\beta}A + \delta_{\alpha}\left(A + \delta_{\beta}A\right)) - (A + \delta_{\alpha}A + \delta_{\beta}\left(A + \delta_{\alpha}A\right)).
$$
| {
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Relationship between intensity and amplitude of light wave I am confused with the realtionship between intensity and amplitude of wave. My understanding is that energy in a wave is proportional to its intensity; which is proportional to the square of the maximum height of the wave. is that a correct understanding.? If ... | The maximum height of a wave is also referred to as it's amplitude, and yes, you are correct. The energy of a wave is proportional to the square of it's amplitude, and by consequence, it's intensity depends on the square of $A$ as well. If the intensity were to decay as $1/r^2$ then it's amplitude would decay as $1/r$ ... | {
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In textbook thermodynamics, does heat $Q$ have a derivative of volume $V$? I'm just trying to get $U(V_2, T_2) - U(V_1, T_1)$ for an non-ideal gas, given the heat capacity at constant volume $c_V(V,T)$ and the equation of state $P(V,T)$. I know I can start from the equation:
$$ dU = dQ - PdV $$
From here, I want to ge... | You don't have
$$\text{d}U=\delta Q-p\cdot\text{d}V$$
but
$$\text{d}U=T\cdot\text{d}S-p\cdot\text{d}V$$
The first principles assumes
$$\text{d}U=\delta Q+\delta W$$
with
$$W=\int_1^2 \delta W=-\int_{V_1}^{V_2} p_\text{ext}\cdot\text{d}V$$
If the transformation is mechanically reversible, on have $$p_\text{ext}\approx p... | {
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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 ... | Yes, temperature is generally a measure of the average translational kinetic energy of the molecules of an object.
Skin burns occur when the combination of the temperature on the skin and the duration of the exposure of the skin to that temperature exceed the threshold of burn.
Given a solid, liquid (e.g. water), and ... | {
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Can any body be uniform in the universe? If I take any body in the shape of a rod and stretch that, after it reaches breaking stress it breaks at one point.
Even though we apply the same the stress on each and every part of the rod it broke at one point. If it's uniform it should break at all points because breaking st... | Does Prince Rupert's drop count?
It will break explosively and reasonably uniformly when damaged due to accumulated stress. This is of course not due to uniformity but rather to its peculiar composition. I wonder if you could redefine uniformity so that it will be covered.
| {
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Is this possible to focus common light (not laser) to a small point in the wall and control it with mirrors? I want to make something like a laser projector for an experiment but with common light.
My question is: is this possible to focus a small point of common light to the wall and control it with mirrors? What comb... | An alternative to consider is to use a strong light source for example halogen lamp, which is typically used in fiber optic illuminator.
| {
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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... | I offer you two examples.
A) Draw a semicircle on AB as its diameter. Assume semicircle is
reflecting, and you are looking for reflection from A to B. It obviously
happens at C, midpoint of arc AB. I leave to you to show that for any other point P of arc ACB you have AP + PB < AC + CB.
B) Consider two points A, B, with... | {
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Do we need a small displacement to create a oscillatory motion on the spring? Do we need a small displacement to create a oscillatory motion on the spring with a mass attached to it? Whats the limit of the displacement that we can give initally to create a oscillatory motion? Is it has to be small or it can large?
| For an ideal spring the force as a function of position is $F=-kx$. Since this is a restoring force for all $x$, there is no limit on what initial displacement will cause oscillations (anything will do).
Even if your spring is not ideal, the force will probably have the form of $F=-f(x)$, where $f(x)>0$ for all $x\neq... | {
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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 suspect what you were actually taught is either that the velocity component along the string is the same on both ends, or that the force / tension is the same. One might think that both of these imply also equal acceleration component, by way of simple $f(x) = g(x) \Rightarrow f'(x) = g'(x)$ consideration or via Newt... | {
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Wigner $D$ matrix How to derive symmetry relation of Wigner $D$ matrix? I mean this relation
$$
D_{m',m}^j (\alpha,\beta,\gamma)
= (-1)^{m'-m} D_{-m',-m}^j (\alpha,\beta,\gamma)^*.
$$
I want to derive this, but I don't know how. Anyone derive this, please.
| The Wikipedia page that you linked to explains, at the end of the section “Properties of the Wigner D-matrix”, that this property is a consequence of the commutation of the rotation matrix with the time reversal operator $T$. The derivation is given there.
| {
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What is the relation between physical theory and physical law? Gravitational law was explained by Newtons theory of gravity. So a law was described by a theory. What is the theory for Newton's laws of motion?
| Laws, postulates, principles are the the axioms used in physics mathematical models to pick up from the mathematical solutions those that describe data and measurements an predict new situations successfully, validating the theory. As in mathematics one cannot question the axioms, so in physics mathematical models the ... | {
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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?
| The answer would seem to be "no", because you make a medium less dense by removing material from it. Once you get to a vacuum, you are only left with how good is the vacuum?
An experiment for an undergraduate optics lab would be to build a Michelson interferometer with a gas cell in one arm. As the gas is pumped out,... | {
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What is *diagonal* long range order? I have seen this question about off-diagonal long range order in superfluids.
What’s the difference and the significance between long range diagonal and off-diagonal long range order?
| Found the answer. It means density modulation.
While off-diagonal long-range order is defined as $n^{(1)}(r,r')=\langle \psi^\dagger (r)\psi (r')\rangle$, diagonal long-range order is the special case where $r = r'$. Qualitatively, one can see that when $r=r'$ the argument of the expectation value is $|\psi(r)|^2$, i.e... | {
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Is the Hydraulic analogy of a resistor wrong? According to Wikipedia's Hydraulic analogy page
A resistor is analogous to a constricted pipe such at the one in the photo below.
Bernouli's principle tells us that the pressure in both sides would be identical in both of the wide sections of the pipe
and in the narrow sect... | You're probably aware of this; but just to cover all the bases, in the hydraulic analogy, pressure represents voltage, flow rate represents current, and as you mentioned, a pipe restriction represents a resistor.
For starters, there's a comment in your question that should be addressed:
Bernouli's principle tells us t... | {
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How to calculate conductivity / electron mobility from theory? Is there a way to make quantitative statements about the conductivity of materials with band theory?
If not I should still be able to get information about the conductivity from Green-Kubo relations of the electron wavefunctions in the material, right?
| What you are asking are transport properties of materials, which represent the response of the system to an external perturbation (such as electric field) so that you cannot obtain just from band structure.
For the transport of the classical particle, you can solve the Boltzmann transport equation, from which you can ... | {
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Why don't all gasses have infinite entropy? Entropy of an ideal gas is defined as the logarithm of the number of possible states the gas can have multiplied by Boltzmann's constant:
$${\displaystyle S=k_{\mathrm {B} }\log \Omega .}$$
In deriving the Maxwell-Boltzmann distribution, we initially start by counting a finit... |
So why is entropy not always infinite when a continuous distribution is used?
If the space of possible states is a continuous region, then the original definition of entropy is not useful (all entropies would be the same, infinity). One may introduce different definition:
$$
S = k_B \ln \Omega
$$
where $\Omega$ is vo... | {
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Deriving Friedmann Equations without General Relativity Can we derive the analytic Friedmann Equations without general relativity, starting from completely classical/nonrelativistic arguments? (If we consider sufficiently small volumes.)
| A Newtonian approach is possible but of of course it is not rigorous.
We're in a newtonian approximation now, and we want to describe the motion of a unit mass at a point P on the surface of a sphere.
So let's take this spherical distribution of matter, take a point at a distance $l$ from the origin. The equation of m... | {
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Ladder operators and energy levels I am studying how to get the normalization factor algebraically in the exited states of the harmonic oscillator using the beautiful ladder operators technique.
I am stuck at the point where is stated that the product of the ladder operators yields the energy levels (in $\widehat{a}^\d... | I think you misunderstood what he meant. Griffiths did use one of the equations you stated :
\begin{equation}
\hbar\omega\left(a\pm a\mp \pm \frac{1}{2}\right)\psi = E \psi \ ,
\end{equation}
but the other equation he used (2.61 in my edition) wasn't the form of the eigenstates, but the eigenvalues which are written ... | {
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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... | For the first part, you have to remember the work done by a spring. Say we have a coil spring squeezed by amount of x cm and locked in this position, hence loaded with a force of F= kx.
But when you release the lock and allow the spring to stretch back to its relaxed length, F gradually tapers off to zero.
So the work... | {
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Entanglement in atoms, nuclei and quantized fields Are the particles that are bounded by chemical bonds or nuclei joined by nuclear forces entangled or are they pure states?
In addition to that, are the subatomic particles in the atoms and nuclei, excitations of a single electron field, quark field, entangled or are ju... | Quantum systems become entangled through interaction with each other. Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.
| {
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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... | They do not mean that the particle itself moves up and down in a wavelike way. What is meant by wave/particle behavior or duality is something more subtle; something that many very smart people have spent their lifetimes working on and which my answer will treat in a simplified way which I hope you can grasp.
For obje... | {
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"answer_id": 1
} |
A perfectly fitting pot and its lid often stick after cooking I encountered a question that asks for the reason that a perfectly fitting pot and its lid often stick after cooking when it cools down. The answer in the solution manual was that the pressure decreases when the temperature decreases. I understand that point... | You've made the wrong assumption about what a perfectly fitting lid does. Rather than sealing perfectly, it will vent gas when the interior is at a higher pressure (the lid will lift), but seal when the exterior pressure is higher (the lid is pressed down).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/440322",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
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