Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What is the physical meaning of the third invariant of the strain deviatoric? In continuum mechanics of materials with zero volumetric change, the material condition can be expressed by the strain deviatoric tensor instead of the strain tensor itself. To express the plasticity of the materials, the plasticity surface i... | If $E\equiv \varepsilon_{dev}$ describes a tension state then $-E$ describes a compression state. Now, $I_2(E)=I_2(-E)$ meaning, as you say, that $I_2$ cannot distinguish traction from compression. However, in 3D, $\det(-E)=-\det(E)$. Thus, $E$ and $-E$ have opposite third invariants. This difference can be exploited t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403220",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Does increasing tension on a string reduce or increase the harmonic wavelength for a standing wave? I had thought that increasing tension on a string increases the frequency and thus decreases the wavelength. My book says otherwise. Which is correct?
| The question is really about how the harmonics in a string change when its tension is increased. Because nothing is said about the length of the string, I guess you need to assume that the length is constant.
The frequencies of the harmonics for an initial string tension are $1F_0, 2F_0, 3F_0, ... nhalF_0$. The text ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Polyakov Loop and Chemical Potential I have read in a paper (http://arxiv.org/abs/1203.3556) that in a thermal field theory, the chemical potential is $\mu=T \ln P$ where $$T^{-1}=\int_{0}^{\beta} \sqrt{-\xi^2}dt,$$ $\xi$ is $\partial_t$, and $P$ is the Polyakov Loop: $$P=e^{\int_{0}^{\beta} A_a \xi^a dt}.$$ How chemic... | I think the second formula is also not very profound. This is just based on the fact that the chemical potential
$$
\Delta S = \int dt \, \mu Q
$$
enters the action like the zeroth component of an (imaginary) $U(1)$ gauge field $A_\beta=(i\mu,\vec{0})$. Note that this is the Polyakov line for a $U(1)$ background fiel... | {
"language": "en",
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Confused with heat as a form of energy I have quite a simple question. Energy can be defined as capacity to do work.
But I have read
When energy is exchanged between thermodynamic systems by thermal interaction, the transfer of energy is called heat.
I can't understand what is the work done. For example, what is the... | Heat is energy, you are correct. Here is an analogy. Think of temperature as a kind of measure of an atom's velocity. The faster an atom jiggles the higher it's temperature. So far so good? Now let's take the analogy one step further - if something has a velocity, you can calculate it's kinetic energy by computing... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/403616",
"timestamp": "2023-03-29T00:00:00",
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Can I change solid into liquid, gas or solute by cutting again and again until it is a molecule particle? If I have small piece of solid, for example, pure iron powder, fine sand , (at room temperature) then I cut it slowly into half again and again. Every times, after I cut it, I wait for temperature back to room temp... | Solid, liquid and gas are properties that belong only to multiple particles, not a single particle. Those words describe the relationship between different particles, not a single particle.
If you end up with a molecule, all you have is a molecule.
Now if you end up with zillions of molecules all whizzing around more ... | {
"language": "en",
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What would qualify as a deceleration rather than an acceleration if speed is unchanged? The instantaneous acceleration $\textbf{a}(t)$ of a particle is defined as the rate of change of its instantaneous velocity $\textbf{v}(t)$: $$\textbf{a}(t)=\frac{\mathrm{d}}{\mathrm{d}t}\textbf{v}(t).\tag{1}$$ If the speed is const... | Acceleration is the general term for a changing velocity. Deceleration is a kind of acceleration in which the magnitude of the velocity is decreasing. The reason this might be confusing is because the word 'acceleration' is sometimes used to mean that the magnitude of the velocity is increasing, to contrast it with dec... | {
"language": "en",
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How are the apparently unbound degrees of freedom in Einstein field equations filled? Something that has always bothered me in general relativity is the annoying fact that there seems to be too few information in the Einstein field equations themselves.
In order to solve a system we need to calculate both the stress en... | The energy-momentum tensor has to be generated by some matter content of the theory. Suppose the energy momentum tensor is generated by a (free, massless) scalar field $\phi$ satisfying
$$ g^{\mu\nu} \nabla_\mu \nabla_\nu \phi = 0.$$
This will generate an energy-momentum tensor through:
$$ T_{\mu\nu} = \nabla_\mu \nabl... | {
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What is the difference between electrons and holes in silicon? Electrons and holes behave differently in a silicon semiconductor (e.g. mobility of holes is one order of magnitude smaller than that of electrons, the collection time of holes at the same electric field is larger than for electrons... ). I was wondering, i... | For effective hole movement many valence electrons must move. For electron movement only a single conduction electron moves.
| {
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How to tune the frequency of a coil? I'm doing a scientific fair project. I want to do it about wireless energy transmission.
In practice consists of two coils NOT physically connected. One is the transmitter of energy, which is connected to a source of energy. The other (s) is the receiver, which receives the energy t... | Normally, the resonant frequency of the antenna can be tuned with a variable capacitor (varactor) using a bias voltage. In direct inductive coupling of coils there is no resonance involved although capacitors may still be used to match the driver amplifier or receiver detector to the coil. The word antenna in this cont... | {
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Experiment - does mass of a moving body really increase or is it invariant? Suppose we have a mechanical balance, with two identical particles kept in the two sides. Now the balance does not show any deflection.
Now, one of the particles is given some constant horizontal velocity.
Will the balance show the moving part... | Yes, it would -- the elementary pre-general relativity answer is "because gravity (which is what is measured by your balance) depends on the energy (mass plus kinetic energy) of an object, not the rest mass". So although the mass remains the same, a special relativistic correction to Newtonian gravity would be to consi... | {
"language": "en",
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How can a horizontally fired bullet reach the ground the same time a dropped bullet does? I studied projectile motion and now I know that we can treat each component of motion independently. Since gravitational acceleration acts on both a horizontally launched bullet and a vertically dropped bullet in free fall, they b... | It happens in real life just as physics says.
It was tested on the TV show Mythbusters:
https://www.youtube.com/watch?v=tF_zv3TCT1U
| {
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Using complex exponential to represent waves in EM Ever since we've been using exponentials to work with electromagnetic waves, I've been confused about the imaginary portion and want to confirm my thinking.
What does the imaginary portion represent? Nothing, right? It's just a side effect of using complex exponentials... | The exponential function is easier to manipulate than the real trigonometric functions, in particular when it comes to derivatives and integrals: the manipulations can be done completely algebraically using complex numbers. In practice, it's easier to manipulate $e^{i\alpha}e^{i\beta}=e^{i(\alpha+\beta)}$ than
$$
\cos(... | {
"language": "en",
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Why do really cold objects evaporate really quick? So I saw a video of LNG (liquid natural gas) and when it got in contact with water, which was room temp the LNG evaporated instantly...why?
Ice takes a while to evaporate like a sec even when hot water is dumped...why do really “cold” liquids evaporate super quick. Is... | The “boiling point” of LNG is -162°C (-259°F), so putting it in touch with even cool water (10C) is a 170C temperature difference.
That’s like putting water on a 270C (520F) griddle. The water boils quickly.
To add to the effect, water requires an unusually large amount of energy to boil a cc. LNG needs a lots less t... | {
"language": "en",
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Kirchoff's radiation law So, I have some problems understanding Kirchoff's Radiation law.
My textbook, Transport Processes and Separation Process Principles, by Geankoplis, states that at the same temperature T1 the emissivity and absorptivity of a surface is equal, which holds for any black or non black solid surface... | Emissivity and absoprtivity are both functions of wavelength. The plate may absorb 90 % of sunlight ($\lambda \approx 0.5 \mu$m) and have an emissivity and absorptivity of 0.1 in the thermal infrared $(\lambda \approx 10 \mu$m).
These numbers are a bit unlikely, it is usually the other way around.
| {
"language": "en",
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is Work done = Total Energy in System? I have recently learned about three types of energy. Kinetic, elastic and gravitational potential energy. I have also leaned about Work done on a particle.
I would like to know if the Work done on a system is equivalent to the total energy in a system?
I ask this because when we... | The short answer is "no", although it will depend on what you call "total energy".
The point is that work done equals the variation of kinetic energy:
$$W=\Delta E_k$$
(I'm not considering heating, just mechanics).
But, there are two types of forces. We can divide the work in two parts:
work done by conservative forc... | {
"language": "en",
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Einstein field equations to the Alcubierre metric I was wondering how Alcubierre derived the metric for the warp drive? Sources have said it's based on Einstein's field equations, but how did he go from this to the metric?
| Alcubierre started with the metric and used the Einstein equation to calculate what stress energy tensor was required.
The Einstein equation tells us:
$$ R_{\mu\nu} - \tfrac{1}{2}R g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} $$
Normally we start with a known stress-energy tensor $T_{\mu\nu}$ and we're trying to solve th... | {
"language": "en",
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Horizontal Beam Bending Due to Gravity I just thought about this problem recently but am not sure where to find a solution. I am not certain which parameters are important in this problem, so please bear with me.
Assume that a beam of length $L$ with rectangular cross section of width $W$ and height $H$ is pinned on ... | This is a typical cantilever beam with the length L, under uniform load q , its own weight.
Assuming the beam is slender L/H >20 the shear deflection will be of tertiary order and will not have meaningful impact on bending.
then the bending or deflection will be
$$\delta_x = qL^4 /8EI \space ,while\space I = Wh^3/12 ... | {
"language": "en",
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Inertia on a rotating disc? If I toss a ball upwards in a train moving with uniform velocity, the ball will land right back in my hand. This is because the ball has inertia and it continues to move forward at the speed of train even after leaving my hand.
Now consider I'm standing on the outer edge of a rotating disc (... | On the merry-go-round, you are constantly accelerating inwards with acceleration $a=\frac{v^2}{R}=R\omega^2$. When you release the ball, it is no longer accelerating (horizontally) and will move in a straight line (horizontally). So whereas you accelerate inwards to maintain your circular motion, the ball follows a str... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/406384",
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What is the difference between relative time dilation and absolute time dilation I know special relativity says that traveling at high speeds (or really any speed) causes time dilation; and General relativity says that gravity also causes time dilation. I was wondering if relative time dilation (where two observers eac... | It's a sensible thought but no. "A sees B's clock running slow." , which you meet in introductory relativity explanations, is shorthand for "A sees the ticks of B's clock arrive at a certain rate. A knows that with every tick, the clock is getting further away (or, in some cases, nearer) so each light signal has furthe... | {
"language": "en",
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Line element in Kruskal coordinates I try to calculate the line element in Kruskal coordinates, these coordinates use the Schwarzschild coordinates but replace $t$ and $r$ by two new variables.
$$
T = \sqrt{\frac{r}{2GM} - 1} \ e^{r/4GM} \sinh \left( \frac{t}{4GM} \right) \\
X = \sqrt{\frac{r}{2GM} - 1} \ e^{r/4GM} \co... | I don't think you can drive the line element with the jacobian $J$
The Kruskal-Szekeres line element
Beginning with the Schwarzschild line element:
\begin{align*}
&\boxed{ds^2 =\left(1-\frac{r_s}{r}\right)\,dt^2-\left(1-\frac{r_s}{r}\right)^{-1}\,dr^2-r^2\,d\Omega^2}\\\\
r_s &:=\frac{2\,G\,M}{c^2} \,,\quad
... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Approximating sums as integrals and divergent terms I have the following sum (notice that the sum starts from 2, i.e. there's no divergence):
$$\sum_{i=2}^{N}C_i\dfrac{\exp{\left(-k| \mathbf{R}_i-\mathbf{R}_1| \right) }}{| \mathbf{R}_i-\mathbf{R}_1|}$$
Where $\mathbf{R}_i$ are vectors belonging to $\mathbb{R}^3$ and ar... | Make a substitution $\mathbf R' = \mathbf R - \mathbf R_1$
$$\int_V d^3\mathbf{R} \dfrac{\exp{\left(-k| \mathbf{R}-\mathbf{R_1}| \right) }}{| \mathbf{R}-\mathbf{R_1}|} \rho(\mathbf{R}) C(\mathbf{R}) =
\int_{V'} d^3\mathbf{R'} \dfrac{e^{-k| \mathbf{R}'| }}{| \mathbf{R}'|} \rho(\mathbf{R+\mathbf R_1}) C(\mathbf{R}+\ma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/407222",
"timestamp": "2023-03-29T00:00:00",
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In which direction does the normal force point if a rod can swivel? A rod is attached to a wall in such a way it can swivel.
In this case: In which direction does the force (of the wall on the rod) point to? I drew the blue force as I would make a force diagram. Am I wrong?
Here is an example in which the rod can swi... | The pin forces can point in any direction, since all directions are constrained for motion.
You just can't have a normal force in the same direction as sliding is allowed because that would mean the joint can do/consume work.
Now for any example the actual direction is such that all forces converge to a single point. S... | {
"language": "en",
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Connecting a charged capacitor to an uncharged capacitor
I was attending a lecture about capacitors and something confused me.
If I charge a capacitor using a DC supply, the capacitor will gain charge $Q_0$.
Now, if I discharged it along an uncharged capacitor in this arrangement, according to the lecture notes, the c... | When we say that a capacitor is uncharged it means that the net charge on each plate of the capacitor is zero ie equal numbers of positively charged ions and negatively charged electrons.
The charged capacitor also has a net zero charge it just so happens that there is a net surplus of electrons on one plate and an equ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/407459",
"timestamp": "2023-03-29T00:00:00",
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How to check if a thing I have is exactly of 1 kg or not? The definition of a kilogram is as far I know,
Kilogram:
The mass of a cylinder made of platinum-iridium
alloy kept at International Bureau of Weights and
Measures is defined as 1 kg.
But it is not possible to go and check that reference all the time. So is th... | You measure it on a calibrated scale.
But because local gravity varies by 0.25% around the Earth, you generally have a set of calibrated masses with your scale and (at least on digital scales) a software option to perform a calibration.
These masses are checked against a mass at the maker of the scale, and those masses... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/407598",
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Why are there only four fundamental interactions of nature? Is there an answer to the question why there are only four fundamental interactions of nature?
| Because we don't need more.
Well, we haven't found any evidence of any others. And until then, there's no need. Granted, some experiments might show indication of something else going on that pushes revision of the Standard Model.
On the mathematical side, this can be explained from symmetry: the Standard Model Lagrang... | {
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Angle in pair production Assuming a very high energy photon (energy $E$) crosses the atmosphere and produces an electron-positron pair, I would like to know what is the angle between these to leptons produced. I was trying to calculate it by applying the energy-momentum conservation and realized that in this case the a... | The center of momentum frame of the resulting electron-positron would have to be a $0$ momentum frame of the starting photon in order for momentum to be conserved, but photons can't have $0$ momentum. This is why pair production must occur near a nucleus or such to receive some recoil. The usual way to derive the angle... | {
"language": "en",
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Why is this cloud blue? I saw these clouds on the horizon, behind a ridge (apologies I couldn't get more pixels):
Why is the front cloud darker than the cloud behind? There were no other clouds that I saw which could've been casting a shadow on the front cloud. What would cause a cloud to reflect less light?
| A possible reason the cloud reflects less light is that it has a lower density of microscopic water droplets in it as it has more air spaces in between that cloud. Notice how water droplets have almost no preference of scattering so it scatters almost all wavelengths of light so it appears that they reflect all light w... | {
"language": "en",
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Does the neutral charged object attract the positive charged object or the negatively charged object? Consider an electrically neutral object:
*
*Is it going to attract a positively charged object or the negatively charged object?
*What is the type of attraction?
*How does it attract or why does not it?
*Why the ... | Lets look at 2 cases:
i) When the neutral body is a conductor:
If a charged body is brought near a neutral body, the same charge in the neutral body would get repelled and go to the far side hence accumulating the opposite charge in the near side. By coulombs inverse square law the attraction force on the nearer side o... | {
"language": "en",
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When is it appropriate to solve the time-independent Schrödinger equation? I am currently going through Griffiths over the summer but I am a bit confused by one point and I don't have any instructor to ask, so I was wondering if you could help clarify. In Section 2.3, the harmonic oscillator, he writes: "it suffices to... | The time-independent Schrödinger equation is just separation of variables acting on the “true” Schrödinger equation. The eigenvalues (the separation constants) of such equation just so happen to represent the energy of our quantum system. As such, if our interest is solely on the available and accessible states of or s... | {
"language": "en",
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Hydrogen atom- Eigenvalue/function relation I have been given the following Question:
The energy eigenstates of the atomic electron are usually described by wave
functions $ψ_{nℓm}(r)$.
Relate each of $n, ℓ,$ and $m$ to the eigenvalue of a specific operator by giving
the eigenvalue equation for this operator acting on... | n is for the energy of the electron, the eigenvalue of the Hamiltonian. It is called principal, because it should be the basic being related to energy.
It is n because it is natural, in the case of H, it is En=-13.6eV/n^2.
$$\sum_{\ell=0}^{\ell=n-1}(2\ell + 1)= n^2$$
It was first used with Bohr H atom, he used n for th... | {
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Under what conditions can molecules exist? I am curious to know the conditions required for any two or more atoms to bond together and form a stable molecule. Is there a set of rules that should be satisfied?
| In computational chemistry, we approach this question from the Born-Oppenheimer approximation perspective, in a very pragmatic way.
Consider we have an ensemble of electrons and nuclei.
First, we assume that the nuclear and electronic wavefunctions can be separated.
Then, we solve the Schrödinger equation for the elect... | {
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What is the cause of wave impedance? As in electrical impedance,
Causes:
Resistance - collision of electrons with atoms and other electrons,
Reactance - Capacitive and inductive effects.
Likewise, what offers opposition to a wave traveling in a medium?
| assuming we are discussing longitudinal waves (as opposed to gravity or capillary waves), the two factors influencing the movement of waves through a medium are its density and its compliance.
on the other hand, if you are talking about electromagnetic waves, the determinants of their speed (c) in a vacuum are the ele... | {
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Potential difference across a zero resistance wire So I started off with electrostatics and everything seemed nice and mathematical and justified and then "DC circuits" happened!
I just cannot understand the model of electron flow in electrical circuits. Here are my specific doubts-:
1) If potential difference across ... | For a current to flow in a conventional wire (not a superconductor, vacuum, etc.), the potential difference across any segment of the wire and the electric field in it have to be greater than zero.
In most cases, the potential difference in the wires could be approximated as zero, because the resistance of the wires is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/409310",
"timestamp": "2023-03-29T00:00:00",
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Non-zero electric field inside a conductor, when applying an large external field I'm probably missing something, or does not understand conductors well enough. But I have a question related to the title of this message.
In many places you read that there can be no electric field inside a conductor. The arguments typic... | Let’s look at the numbers.
Atoms are typically an angstrom ($10^{-10}$m) across. A metal conductor will typically have one conduction electron per atom.
A Coulomb is a big amount of charge: a macroscopic 1A current for a second. It’s also $6 \times 10^{18}$ electrons.
Combining those, one Coulomb corresponds to the... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is it possible for a lightning strike to hit the ground if there are high rise buildings nearby? Say we have pointed conductors connected to the top of the high rise buildings. Will the strikes hit the nearby ground in such a case?
| It might, if the path of the lightning does not get close enough to the rod or its grounding structure in comparison to alternative targets on the ground.
The lightning strokes originate at the clouds, because the clouds have much higher charge concentration and much stronger local electric field. In comparison, the de... | {
"language": "en",
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"source": "stackexchange",
"question_score": "11",
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Does photon absorption annihilate the associated EM wave instantly? My Understanding
A single photon has an associated electromagnetic wave. The wave is spread out in space, but the photon is considered a point particle. If the photon is absorbed, the entire wave disappears. Photon absorption is instantaneous, so the w... | You are not correct and you are not incorrect. This is the realm of quantum interpretation, and this particular conundrum is called the Einstein bubble paradox. What exactly is happening down there is an unresolved question. All we really know is this: light propagates according to classical electromagnetism, but its e... | {
"language": "en",
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Density function in phase space What does density function in phase space physically mean? How does it indicate, the more familiar density that we are accustomed to ( an analogy may be), in phase space?
| If you integrate out the momentum variables, then you get the usual density as a function of just position. Let's say there are N particles each with mass $m$ so total mass $Nm$.
$$
\int d^3p d^3x \; \; \rho_{phase} (x,p) = Nm\\
\int d^3p \; \; \rho_{phase} (x,p) = \rho (x)\\
$$
So the phase space density is giving mor... | {
"language": "en",
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Why does sound travel faster in steel than in water? I understand that sound travels faster in water then in air. Water is a liquid, and air is gas.
Water still has the ability to roll the molecules over each other (so water can flow), it has some flexibility.
But I do not understand how a solid that is inflexible can... | the speed of sound (a compression wave) in steel is given by the square root of (the ratio of the sum of the bulk compressive modulus and 4/3 times the shear modulus divided by the density of the material). Since steel is very stiff, this makes the numerator very big and even though the density of the steel is signific... | {
"language": "en",
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if light source is bigger than the object, it is possible that shadow of the object is bigger than the object? When sun light falls on my bathe tub i noticed that the shadow of any small particle floating on the water surface is bigger than the particle and also it is quite circular i.e. Deform from It's actual shape. ... | In this case, the likely explanation is that the surface of the water near the "floater" is not flat due to surface tension. This causes the light rays entering the water near the particle to be bent, causing a "shadow" under the particle.
You might have also noticed that the swirling water when the drain is opened ca... | {
"language": "en",
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Energy conservation on expanding universe Due to the expansion of the universe, the photons emitted by the stars suffer redshift, Its mean that the energy is lowered a little bit. Does this mean that the energy is lost? Does the expansion of the universe violate some conservation principles according to Noether's theor... | while photons appear red-shifted for a remote observer who is receding away due to the expansion of the universe, they still retain the same wavelength and energy relative to the frame they originate from, thus no energy has been lost
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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"answer_id": 2
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Massless charged particles in an electric field According to this question, theoretically, there can be massless charged particles.
What will happen if we put them in an electric field?
How will they respond to the increase in momentum/energy? In case of photon the frequency of the associated electromagnetic wave inc... | That is exactly what happens. Their energy and their momentum increase, although their spatial velocity would always be equal to c. You could observe this increase by scattering them with other particles to measure their energy.
| {
"language": "en",
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"source": "stackexchange",
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Torricelli's Law and Variable Density I wish to explore a slight modification of a well known result found in several physics texts - Torricelli's Law of Efflux.
The most common problem on the above result has the following setup:
The container is filled with fluid of a certain density, upto height H and has a hole a... | Let the base of the tank be the datum (z = 0) for zero potential energy. Then the form of the Bernoulli equation that would be valid for this problem would involve an integral of the density variation. Taking the two locations for applying the Bernoulli equation as 1.the upper fluid surface in the tank (assuming it i... | {
"language": "en",
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What would be the charge distribution of a conducting sphere in front of a positive point charge? What would be the charge distribution of a conducting sphere in front of a positive point charge? I mean if it's a positive charge then it should induce negative charge in the near side and positive on the other side. But ... |
if it's a positive charge then it should induce negative charge in the
near side and positive on the other side.
That's correct.
But as it's conducting then it should distribute the charge all over
the sphere. So it should make the sphere neutral.
Since the sphere is isolated, it remains neutral at all times. T... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/410906",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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As the universe expands, do we have any reason to suspect further separation of the fundamental forces/interactions? At some point, all four forces were one force. (another question: what exactly does that mean?). At some point gravity and the strong force separated out leaving the electroweak force. Then the electrow... | Electroweak unification is broken when the temperature is low enough for the Higgs field to settle into its ground state. The ground state of the Higgs field is charged under "weak isospin" and "hypercharge", causing the weak force particles to acquire mass and leaving only the photon massless.
In most theories, grand... | {
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How do bulk regions of clouds conduct charges into a lightning bolt? It's easy to find explanations of the theories of charge accumulation in clouds during storms, as well as ones describing suspected processes leading to lightning channel formation. What I have yet to encounter is any theory describing how a large reg... | The strike does not happen instantaneously - it may take milliseconds for the stepped leader to reach the ground - so there is some time for the charges, spread over a large area of a cloud, to reach the discharge path.
At very high field intensity levels, common in charged clouds, air molecules are easily ionized and ... | {
"language": "en",
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A ball attached on a moving string If there is a ball attached on a string and the string's point of hanging is accelerating horizontally at $\vec{a}$, what will be the forces exerted on the ball that is hanging? It is obvious that there will be a gravitational force downwards and a tension force, and there should be a... | The ball rises until the vertical component of tension equals gravity.
In this stable state the horizontal component of tension is accelerating the ball at the same rate as the vehicle as seen from an external frame of reference.
In this stable state, to an observer in the car, the acceleration of their frame (car) c... | {
"language": "en",
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How do we know the maximum speed of conventional matter is the same as the speed of light? Is there an argument, apart from experiments, that we know this is true?
And if we only know it by experiment, how do we know the experiments are precise enough to conclude this?
Stated differently, what argument is there that p... | We know from Maxwell's equations that the speed of light is constant: $$c=\frac{1}{\sqrt{\epsilon_{0}\mu_{0}}}$$
We know from Galilean Relativity that the laws of motion are the same in all inertial frames.
So for each observer to measure the same value of the speed of light, it must be the same no matter how fast you... | {
"language": "en",
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Plane wave approximation Consider a proton in harmonic motion along vertical direction.
http://physics.weber.edu/schroeder/mrr/MRRtalk.html
Near a point source, direction of electric field is along the curve.
https://en.wikipedia.org/wiki/Plane_wave
But at greater distance from point source, in plane wave approximati... | The electric field of an oscillating point charge consists of a Coulombic component and a radiative component:
*
*the Coulombic part is generally directed away from the charge, and it goes down as $1/r^2$ with the distance from the center of the oscillations.
*the radiative part is generally transversely polarized... | {
"language": "en",
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Calculating Canonical State Sum with fermions? my question is regarding to the fact that we say that $n=0,1$ for fermions/electrons but why not $n=0,1,2$ if a spin up and a spin down electron can simultaneously occupy the same state?
Thanks for the replies!
| Because we count the occupation number for a state in the full single particle Hilbert space (not for orbital states). The full state of an electron is specified by its orbital state and its spin state. That is, there are two states (one for each spin projection) for each orbital state, since the total single particle ... | {
"language": "en",
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What would happen to a 10 meter sphere of room temperature water if released into space? Imagine that we had a space station with a relatively large hangar, and we allowed a ball of water to accumulate that had a 10 meter diameter and a water temperature of 20C. While the hangar is pressurized, someone decides to use a... | It is a perennial but pernicious myth that liquid water would flash into vapor in space if the pressure were suddenly released. Even though the free energy difference (between water and ultra-tenuous vapor) would favor vaporization, evaporation is very endothermic. The water must acquire the heat of vaporization (ove... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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2D ${\cal N}=(2,2)$ Super Yang-Mills with Superspace I'm reading this famous paper by Witten. There is the expression of field strength for the abelian vector multiplet (eq. (2.16)):
$$\Sigma = \frac{1}{\sqrt{2}}\bar{D}_+D_- V\;.\tag{2.16}$$
I'm wondering what is the expression for a non-abelian vector multiplet, writ... | Witten defines it in equation 4.5 of https://arxiv.org/pdf/hep-th/9312104.pdf
| {
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"source": "stackexchange",
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Does the fact that $j^\mu$ is a 4-vector imply $A^\mu$ is, as argued by Feynman? Let
\begin{equation}
\boldsymbol{\Phi}=\Bigl(\dfrac{\phi}{c},\mathbf{A}\Bigr)
\tag{01}
\end{equation}
the electromagnetic 4-potential. We know that if its 4-divergence is zero
\begin{equation}
\dfrac{1}{c^{2}}\dfrac{\partial \phi}{\partia... | Yes the four potential $A^{\mu}=(\phi(\vec{x},t),\textbf{A}(\vec{x},t))$ is a four vector and it can be seen from the equation that it satisfies:
\begin{align}
\partial^{2}A^{\mu}=\frac{1}{c}J^{\mu}
\end{align}
the $\partial^{2}$ operator is a scalar and $J^{\mu}$ is a Lorentz vector leading to $A^{\mu}$ being necessar... | {
"language": "en",
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"source": "stackexchange",
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No sense in the expression $\hat{x}| 1\rangle=\sqrt{\frac{2}{a}}\int_{-\frac{a}{2}}^{\frac{a}{2}}x\cos\left(\frac{\pi}{a}x\right)dx=0$ I am considering a particle of mass m in a symmetric infinite square well of width a in the fundamental state.
$$V(x)= \begin{cases} 0 & \mbox{$|x|<\frac{a}{2}$} \\ \infty & \mbox{ot... | @knzhou already indicated the perfect appositeness of your title.
You apply the definitions of your text, as the chthonian pundit suggests,
$$\hat{x}| 1\rangle= \hat{x}\int dx ~|x\rangle\langle x| 1\rangle= \sqrt{\frac{2}{a}}\int_{-\frac{a}{2}}^{\frac{a}{2}}dx~~\left( x\cos\left(\frac{\pi}{a} x\right)\right ) ~~~... | {
"language": "en",
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Dissapation of photon energy For an incident photon to be absorbed by a material, must it exactly equal a difference in the electron energy levels, or does it just have to be more than one such difference. If more is okay, what happens to the remaining photon energy? Does it continue on as a lower energy photon, if s... | Yes, gamma rays and other high energy light can knock electrons off their orbitals.
https://www.youtube.com/watch?v=NT6foiglgow
This video explains the bohr atomic model in more detail and would answer your question
| {
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How to derive that $pV^k$ is constant in a polytropic process? This is what we did on the lecture:
$$\delta Q=nC dT$$
$$dU=nCdT-pdV$$
$$dU=\bigg(\frac{\partial U}{\partial V}\bigg)_TdV+\bigg(\frac{\partial U}{\partial T}\bigg)_VdT$$
$$dU=\bigg(\frac{\partial U}{\partial V}\bigg)_TdV+nC_VdT$$
$$n(C_V-C)dT=-\bigg(\bigg(\... | We did the same derivation too. But I like it this way:
$$\mathrm{d}U=\mathrm{d}\left(\frac{f}{2}pV\right)=\frac{f}{2}p\mathrm{d}V+\frac{f}{2}V\mathrm{d}p$$
Because $\delta Q=nC\mathrm{d}T$, we have that $\mathrm{d}U=nC\mathrm{d}T-p\mathrm{d}V$, so:
$$nC\mathrm{d}T-p\mathrm{d}V=\frac{f}{2}p\mathrm{d}V+\frac{f}{2}V\math... | {
"language": "en",
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Conformal field theory does not have... conformal symmetry? This post is about 1+1d. It is often said that conformal field theory has an infinite-dimensional symmetry generated by the Virasoro algebra:
$$ [L_n,L_m] = (n-m) L_{n+m} + \frac{c}{12} n (n^2-1) \delta_{n+m,0}. $$
(Similarly for the anti-holomorphic branch w... | The Virasoro algebra is a true symmetry of the theory, in the sense that the action of a conformal field theory is conformally invariant if it exists, and in the sense that the algebra elements map solutions to the equations of motion (quantumly: eigenstates of the Hamiltonian) to solutions of the equations of motion. ... | {
"language": "en",
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"source": "stackexchange",
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Difference between real and virtual objects (optics) I do know the difference between real and virtual images, cf. e.g. this Phys.SE post. I would like to know the difference between the real and virtual objects. I need a real life example.
| Your diagrams say it all. Real objects are points from which light diverges. A normal eye can take these divergent rays and converge them to points on its retina.
Virtual objects are points towards which light converges. If there were no eye or optical instrument in the way, there would be real images at these points. ... | {
"language": "en",
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Sign of work done by friction In Goldstein's classical mechanics (3rd ed.) we read:
"The independence of W12 on
the particular path implies that the work done around such a closed circuit is zero,i.e.
$$\oint \textbf{F}.d\textbf{s}$$
Physically it is clear that a system cannot be conservative if friction or othe... | Of Course, I also have the same question. Technically the work done by friction is negative and what that means is the decrease in the energy of the system. But there is similar principle in thermodynamics that decrease in the energy of the system is due to the positive work done by the system. So if we consider a syst... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Is photon antibunching a requirement for quantum key distribution? While reading up on single photon sources I often came across photon antibunching being a requirement that had to be demonstrated for a specific single photon source. I understand that antibunching behaviour arises from the fact that the radiative excit... | Photon antibunching demonstrates a specific property (indistinguishability) of a specific quantum information carrier (photons).
Most quantum protocols, such as QKD, are not tied to any specific implementation, so photon antibunching is not directly related to them: one could in principle implement a QKD protocol using... | {
"language": "en",
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How do contact transformations differ from canonical transformations? From Goldstein, 3rd edition, section 9.6, page 399 after equation 9.101:
[...] The motion of a system in a time interval $dt$ can be described by an infinitesimal contact transformation generated by the Hamiltonian. The system motion in a finite tim... | Contact transformations were discovered by Sophus Lie in the 19th century. Within this context an infinitesimal homogeneous (time independent) contact transformation:
$$
\delta q^i = \frac{\partial H}{\partial p_i}\delta t,\qquad \delta p_i = - \frac{\partial H}{\partial q^i}\delta t
$$
is a coordinate transformation t... | {
"language": "en",
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"source": "stackexchange",
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Relativistic mass of components gives system rest mass? To put it briefly, in the classic thought experiment of a massless box with mirrored insides containing photons, does the relativistic mass of the photons imbue the box with rest mass?
I take it that's the case, because I think that's how baryons are supposed to g... | The rest mass arises from a difference in the photon pressure against different walls of the box. For example, when the box is stationary in a gravitational field, photon pressure on the bottom of the box is higher than it is on the top, because photons are altered by the field. For another example, when the box is bei... | {
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Misunderstanding of the functioning of the reflective diffraction grating Suppose we have a sawtooth diffraction grating, as depicted below:
where the angle $\beta$ is the angle of inclination of the 'teeth' of the grating with respect to the plane of the grating and incident plane monochromatic waves normal to the pl... | For the light to interfer constructively when propagating at an angle $\theta$, the rays from point $A$ and point $B$ must be in phase. Therefore
$$BF-AE=d\sin\beta-d\sin\theta=n\lambda . $$
This leads to the grating equation
$$\sin\beta-\sin\theta=\frac{n\lambda}{d} . $$
Here $n$ denotes the diffraction order. If $n=... | {
"language": "en",
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Electric potential concept Imagine having two charged plates, one positive and one negative, and a negative point charge is placed at the negative plate. Let's set the negative plate to zero potential. The distance between the negative point charge and the negative plate is zero, so $V$ is zero in the equation $V=Ed$. ... | Potential is defined as
$V(r) = \int_{ref}^{r} \vec{E} \cdot \vec{dr}$
By convention, ref is set to $\infty$, in this reference point, ofcourse the charge has potential energy.
By setting the value of potential to be zero at the location of the plate, you change "ref" to be something other than infinity.
Does this actu... | {
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Work and Voltage Question 1: Is voltage measured as the amount of work a charge can do as it flows between two points because work is proportional to force? Thus by measuring the amount of work a certain amount of charge is doing as it flows between two points, we are able to indirectly measure the electromotive force ... | In answer to questions 1 and 2, voltage is defined this way, not measured. Voltage is usually measured by allowing a small current to flow across a resistor, and measuring the current. Look up "voltmeter" on the internet.
In answer to question 3, no, you cannot increase the voltage between two points by increasing the ... | {
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Virial expansion in terms of pressure I'm studying thermodynamics and I found two forms for the virial expansion:
$$pV~=~RT[1+\frac{A_2}{V}+\frac{A_3}{V^2}+\ldots] \tag{1}$$ and
$$pV~=~RT[1+B_2p+B_3p^2+\ldots]\tag{2}$$ my problem is that I can not find the correct procedure to express the coefficients $B_k$ in terms o... | $$pV=RT\left [1+\frac{A_2}{V}+\frac{A_3}{V^2}+...\right ]\\\Rightarrow p=RT\left [\frac 1V+\frac{A_2}{V^2}+\frac{A_3}{V^3}+...\right] \\\Rightarrow p^2 = R^2T^2\left [ \frac {1 }{V^2}+ \frac{2A_2}{V^3}+...\right]$$
Now substitute for $p$ and $p^2$ into the equation
$$pV=RT[1+B_2p+B_3p^2+...]$$
and gather up terms i... | {
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What would happen to the Moon if the Earth stopped providing it with a centripetal force owing to its force of gravity? Would the Moon really only travel in a straight line then? What about the other planets and their forces of gravity? Wouldn't they prevent this rectilinear and undisturbed motion of the Moon?
| If the Earth just disappeared, the Moon would continue around the Sun on pretty much the same path it has now.
To see this, consider the velocity of the Earth/Moon system around the Sun:
$2\pi \times 150 \times 10^6 \text{ km} / 365 \text{ days} = 2.6 \times 10^6 \text{ km}/\text{day}$
versus the Moon's speed around th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414538",
"timestamp": "2023-03-29T00:00:00",
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What is the general form of the solutions of the 2-electron system? According to Sakurai the solutions of the two-electron system are of the form $\psi=\phi({\bf x_1},{\bf x_2})\chi(m_{s1},m_{s2})$
Since it's a fermionic system, $\psi$ must be a linear combination of antisymmetric states. If $\phi$ is symmetric and $\c... | With:
$$ S \equiv \frac 1 {\sqrt 2}[\chi_{+-}-\chi_{-+}]$$
and
$$ T \equiv \frac 1 {\sqrt 2}[\chi_{+-}+\chi_{-+}]$$
and subbing in:
$$ \omega_A(x_1)\omega_B(x_2) = \frac 1 {\sqrt 2}[\phi^++\phi^-] $$
and likewise for the other $\omega$:
$$ \psi = \frac 1 2 [(\phi^+ + \phi^-)(T+S) - (\phi^+-\phi^-)(T-S)] $$
$$ \psi = \f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414645",
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Heisenberg's uncertainty principle and shape of universe On a TV program with some well-known astrophysicists they sad that the effect of Heisenberg's uncertainty principle shortly after the Big-Bang made matter (normal & dark) expand in a non-homogeneous way.
Now, here's my question: if I understand it correctly, Heis... | A Quantum fluctuation is the temporary change in the amount of energy at a point in space.
This is part of the Heisenberg uncertainty principle.
This allows the creation of particle-antiparticle pairs of virtual particles.
Quantum fluctuations were very important in the early stages of the universe, according to the mo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414746",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can X-rays emitted due to bremsstrahlung radiation have frequency matching with other EM waves like visible ones? The continuous X-ray spectrum has x-rays of widely varying frequencies. Since an E-M wave is characterized by its frequency, is it possible for the X-rays coming out of heavy metals due to bremsstrahlung ra... | The continuous X-ray spectrum comes from Bremsstrahlung radiation, which is the radiation emitted whenever an electric charge is accelerated or decelerated. In this case electrons striking the metal are decelerated by collisions with metal atoms and emit EM radiation as a result. The spectrum is continuous because the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/414877",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do fusion reactors deal with blackbody radiation? The plasma of the ITER reactor is planned to be at 150 million K. Using the Stefan-Boltzmann law, setting the surface area as $1000\,\mathrm{m}^2$ (the plasma volume is $840\,\mathrm{m}^{3}$ so this is being generous), and the emissivity as $0.00001$ (emissivity is ... | Fully stripped atoms can't radiate by having electrons jump between energy levels anymore, because there are no bound electrons. So, that removes the biggest radiation channel unless impurities with high atomic numbers are introduced (such as tungsten). Heavy elements don't get fully stripped of electrons and then the ... | {
"language": "en",
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"source": "stackexchange",
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How does the electric field produced by a simple circuit look? I have not seen anywhere a description of how the electric field looks inside and around a simple circuit. For example let's say we have the circuit shown below. One DC voltage source, two resistors, and a constant current flowing around.
We know that the ... | An electrical circuit is a lumped element model, that does not carry any geometrical information with it. Given a circuit you do not know what is the shape of the resistors, the dimension of the battery, the cross section of the wires, the position of the elements with respect to each other, and so on and so forth.
Un... | {
"language": "en",
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"source": "stackexchange",
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Help with recursion relation for 3D Conformal Blocks I'm trying to calculating the four point function for the 3D Ising model. To do so I need to calculate the 3D Conformal Blocks . I found a paper which has a recursive relation for calculating the Conformal Blocks: equation (3.10). The authors are Filip Kos, David Pol... | To the order $r^2$, the block is given by the contributions of three poles with $k=1$,
$$
h_{\Delta,\ell} = h^{(\infty)}_\ell + \frac{c_1(1)}{\Delta+\ell+1} r^2 h^{(\infty)}_{\ell+2} +\frac{c_2(1)}{\Delta-\nu} r^2 h^{(\infty)}_{\ell} + \frac{c_3(1)}{\Delta-\ell-2\nu+1} r^2 h^{(\infty)}_{\ell-2} + O(r^4)
$$
To the order... | {
"language": "en",
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Weird Reflection Pattern in Reading Glasses While fidgeting with a pair of reading glasses, I noticed a strange reflection pattern (shown in video and photo).
I would appreciate it if anyone that knows more about this could help me figure out why there were eight dots in the reflection instead of four, and why there we... | Think that it's just the reflection of the four lights off your glasses, with one set of four reflections being due to the lights directly reflecting off the glass surfaces. The other four reflections are probably due to the remaining light passing into the glasses and then reflecting off the rear glass-air surface tha... | {
"language": "en",
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"source": "stackexchange",
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Berry Phase for Bloch electrons I am new to the topic of Berry phase.
The definition says that Berry phase depends only on the path in the parameter space of $R$, where the Hamiltonian is $H(R)$, but whatever problems I have seen, the parameter itself has a time dependence. Even for the case of Bloch electrons, we can ... | In real space, the adiabatic Berry phase of a closed orbit just measures the magnetic flux through the orbit's area.
Explanation: (please see Sundaram and Niu )
The semiclassical equations of motion of a Block electron in phase space are given by (Sundaram and Niu equation 3.8)
$$\mathbf{\dot{x}_c} = \frac{\partial \ma... | {
"language": "en",
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Physical intuition behind Poincaré–Bendixson theorem The Poincaré–Bendixson theorem states that: In continuous systems, chaotic behaviour can only arise in systems that have 3 or more dimensions. What is the best way to understand this criteria physically? Namely, what is is about a space of dimension 1 or 2 that canno... | At each point along a chaotic trajectory, the following three directions must exist:
*
*A direction of time, along which the trajectory is going.
*A direction of expansion, along which the phase-space flow is diverging, so you can have sensitivity to initial conditions.
*A direction of contraction, along which the... | {
"language": "en",
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"source": "stackexchange",
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Is everything a resistor? Resistance is due to collision with protons, and pretty much everything contains protons. So technically is everything a resistor? (Or at least, can anything be a resistor?)
| The definition of what a resistor is is not always clear. As an EE, I would recommend phrasing it "Everything has a resistance. Not everything is a resistor." Through every object, if there is a voltage difference from one side to the other, current will flow through it, however minuscule.
I would not call them resi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/416085",
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Pauli exclusion responsible for "solidity"? I have heard Frank Close say that the reason you can't put your hand through a solid object is the Pauli exclusion principle. However Richard Feynman in his "Fun to Imagine" series attributes it to electrostatic forces.
I have two questions: Firstly, who is correct here (or m... | Close and Feynman are both right. If you try and overlap one electron-state with another then, thanks to the Pauli Exclusion Principle,this is impossible. One of the electrons must move to a higher state, which requires energy, which is why the Lennard-Jones potential shoots up, and there is a resistive force. The reas... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/417626",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is a fermion field complex? The Lagrangian of a fermion field is
\begin{equation}
\mathcal{L} = \overline{\psi} (i\gamma_{\mu} \partial^{\mu} - m)\psi
\end{equation}
It is said that the fermion field $\psi$ is necessarily complex because of the Dirac structure. I don't quite understand this. Why is the fermion fiel... | A charged particle requires a complex valued field. For a neutral particle it is believed that a real valued field suffices. For example the Schrödinger and Klein-Gordon current operator is zero for a real wave function.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Why does this paper use 1/cm for units of frequency? Reading this paper from 1963 $^*$, they use units of cm$^{-1}$ for frequency.
Here is an excerpt:
It doesn't seem like wave number, as they clearly call it frequency. What's going on here?
$^*$ Sievers III, A. J., and M. Tinkham. "Far infrared antiferromagnetic reso... | Sometimes physicists use (lenghts)$^{-1}$ to indicate frequencies, expecially in spectroscopy...
As you well now, $\omega = 2\pi \nu$ and $c = \lambda \nu$ so that
$\omega = 2\pi \frac{c}{\lambda}$ which is proportional to $ \lambda ^ {-1},$ since $c$ is a constant.
So when one says $\omega_1 = 29 cm^{-1}$ is actually... | {
"language": "en",
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Terminal velocity to calculate velocity as a function of time? Using the equation for drag force,
$F = c_d \times \rho \times v^2 \times A \times \frac{1}{2}$,
where $c_d$ is coefficient of drag, $\rho$ is air density, $v$ is terminal velocity, and $A$ is reference area for the object, and accounting for acceleration ... | The EOM's are:
\begin{align*}
&\textbf{For the vehicle }\\
& m{\frac {d}{dt}}v \left( t \right) =F_{{d}} \left( {v}^{2} \right) +{
\it Fc}&(1)\\
&\textbf{For the wheel }\\
& \theta\,{\frac {d}{dt}}\omega_{{w}} \left( t \right) =M_{{E}} \left( t
\right) i_{{g}}-{\it Fc}\,\,r&(2)\\
&\textbf{and the condition for a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/418374",
"timestamp": "2023-03-29T00:00:00",
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Understanding what it means that gravitation is proportional to the product of the masses Newton's gravitational law states that
$F = G*\frac{M*m}{d^2}$
Intuitively it means that the greater the masses, the stronger the force, but it is more precise than that, it is proportional to the product of the masses not, for ... | Perhaps it will help to look at the gravitational field strength, which here is measured in units of acceleration ($m/s^2$). Of course we know that force, mass and acceleration are related by $F=m\cdot a$. And we have Einsteins principle that an acceleration and a gravitational field are indistinguishable.
So, the gr... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why is it not possible to dope semiconductors with elements with 6 or 2 valence electrons? As far as I have learnt, semiconductors are often made using elements from the 4th group, and their properties are often enhanced by doping with either pentavalent or trivalent elements. Take the case of pentavalent doping, whic... | Silicon is doped with group III (B, hole doping) and group V (P, electron doping) elements because these form shallow impurities when residing at a silicon lattice position. Shallow impurities in silicon have binding energies of 40-50 meV and are ionised at room temperature so that their electrons reside in the conduct... | {
"language": "en",
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Can an Observer Distinguish between Unruh Effect and Hawking Radiation by Measuring Temperature? In Unruh effect, the temperature of background appears to be proportional to acceleration. On the other hand, the temperature of a black hole is inversely proportional to its mass.
If the two effects have the same origin a... | You are probably assuming an uniformly accelerating observer, then no, because The Unruh temperature has the same form as the Hawking temperature TH =
ħg
/
2πckB
of a black hole.
Assuming an inertial observer makes a difference. An inertial observer doesn't see Unruh Radiation, but far away from a Black Hole will see... | {
"language": "en",
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Questions about shapes and the reason behind the drag coefficient differences
*
*What is the reason that a streamlined body has a drag coefficient that is lesser than the drag coefficient of a streamlined half-body, when the latter has a completely flat bottom, while the former has bulges on either side of the center... | The first thing you need to do when comparing drag coefficients is to check the reference areas. Even though it is not clear from the picture you link to, it is pretty obvious that the frontal area was used. This means for your first question that the half body creates roughly as much drag force as the full body (which... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Decomposition of the symmetric part of a tensor The rate of strain tensor is given as $$e_{ij} = \frac{1}{2}\Big[\frac{\partial v_i}{\partial x_j}+ \frac{\partial v_j}{\partial x_i}\Big]$$ where $v_i$ is the $i$th component of the velocity field and $x_i$ is the $i$th component of the position vector. From what I rea... | In principal component form, $$D_{11}=\frac{1}{3}\left[\frac{\partial v_1}{\partial x_1}+\frac{\partial v_2}{\partial x_2}+\frac{\partial v_3}{\partial x_3}\right]+\left[\frac{1}{3}\left(\frac{\partial v_1}{\partial x_1}-\frac{\partial v_2}{\partial x_2}\right)+\frac{1}{3}\left(\frac{\partial v_1}{\partial x_1}-\frac{\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/419501",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What does it mean if the dot product of two vectors is negative? If the dot product gives only magnitude, then how can it be negative?
For example, in this calculation:
$$W = \vec{F}\cdot\vec{r} = Fr\cos\theta = (12\ \mathrm{N})(2.0\ \mathrm{m})(\cos 180^\circ) = -24\ \mathrm{N\,m} = -24\ \mathrm{J}$$
Why is there a ne... | A dot product between two vectors is their parallel components multiplied. So,
*
*if both parallel components point the same way, then they have the same sign and give a positive dot product, while
*if one of those parallel components points opposite to the other, then their signs are different and the dot product ... | {
"language": "en",
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Is the Bose-Einstein condensation a single particle phenomenon? BEC occurs for noninteracting Bosons. Can we conclude that it can be described with a single particle? What is the significance of the number of the particles?
| What @Árpád Szendrei said is correct. I will add some miscellaneous points.
*
*
BEC occurs for non-interacting bosons
BEC occurs for interacting bosons as well, and non-interacting BEC is actually a pathological example. It has an infinite compressibility. The speed of sound is zero, and any infinitesimal drag wil... | {
"language": "en",
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Can Bohr-Kramers-Slater (BKS) theory examples be generalized to prove that classical gravity is futile? In the comment in What are the reasons to expect that gravity should be quantized? by Ron Maimon, it is mentioned that taking analogy from classical electromagnetic wave to classical grvational wave, one can notice t... |
However, general relativity does not really have conservation of momentum as fundamental concept, and thus it is unclear what this would mean. Can anyone explain this?
GR does have conservation of momentum as a fundamental concept. Specifically, the structure of GR requires that the stress-energy tensor have zero div... | {
"language": "en",
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Why is it necessary to irreversibly erase a memory? I know that the most accepted resolution of the Maxwell's demon paradox was proposed by Landauer and revolves around the fact that the demon's memory is finite and will have to be erased at some point. This is an irreversible process that will generate entropy and pre... | Empty computer memory can be viewed as a thermal reservoir at zero temperature. In a very real sense it is possible to convert information (or rather, in this case, absence of entropy) into energy, something that has been experimentally demonstrated. So the initially empty memory can be viewed as a finite reservoir tha... | {
"language": "en",
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Eigenvalues of a quantum field In the book 'Quantum field theory for the Gifted Amateur", the following is stated, cf. 9.3:
"A quantum field $\hat{\phi}(x)$ takes a position in spacetime and returns an operator whose eigenvalues can be a scalar, a vector (the $W^{\pm}$ and $Z^0$ particles are described by vector field... | I believe the statement is correct, although one can argue that it expands the definition of "eigenvalue" beyond what one can be used to. The quantum field has more than one component in case of spinors, vectors, or tensors, so components of spinors etc. are eigenvalues of the components of the quantum fields. As for e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/420184",
"timestamp": "2023-03-29T00:00:00",
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How does a satellite take pictures when the surface seems to be always cloudy/white? I've just opened ISS video on youtube for the first time, and I must say I'm underwhelmed. There are no oceans/landforms. It's all white everywhere. I'm a bit confused how the satellites can take pictures when the view from space looks... | It is not always cloudy.
Google Earth and various other map and remote sensing image databases work on the basis of multiple images "pasted" together. When a particular area is clear on a particular pass, the satellite takes an image. This image gets added to the database. The collection of images you see on the web si... | {
"language": "en",
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does tension in the string affect its equilibrium? In my textbook (Sears and Zemansky's University Physics), it is written that the vector sum of the forces on the rope is zero, however the tension is 50 N. Then is tension different than the force? And if not, then why force is zero while tension is not?
A body that h... | If you pull the ends of a rope with equal and opposite forces (F on the right hand end and –F on the left hand end), the resultant force on the rope is zero.
But the rope will be in a different state from the state it would be in if no forces were being exerted on it. We say that the rope is under tension.
Tension is q... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/420708",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Hamiltonian operating on a function of time I've seen a few people claiming:
$$\hat{H(t)}[\psi(x)T(t)] = \hat{H(t)}[\psi(x)]T(t)\tag{1}$$
i.e. an explicit function of t is not acted upon by H, even if H itself may be dependent on t.
A more specific example, Griffiths between equation 9.7 and 9.8 (implicitly):
$$\hat{H(... | Hamiltonian operator only have derivatives of space and that too they are partial derivatives, so they don't affect any time-dependent function. Hence your exponential acts as a constant for the Hamiltonian operator.
| {
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If entropy is a measure of disorder, how come mixing water and oil finishes in a well ordered, separate state? By the second law of thermodynamics, entropy tends to increase when the system is let on itself. And if entropy is a measure of disorder, how come mixing oil in water and letting the system reach equilibrium, ... | This is because entropy has almost nothing to do with the apparent order or disorder you can see with your naked eye. That's just a pop science simplification.
Compare the entropy of a dictionary and an identically sized book full of random gibberish. You might think the latter has a higher entropy, because the content... | {
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Why is Copper(I) Oxide Red? This may appear to be a chemistry problem. But, after reading the Wikipedia article on copper(I) oxide, it seems to have more to do with semiconductor-physics. For example:
… light travels almost as slowly as sound in this medium.
Is that true?
What have Kramers–Kronig relations got to do ... | No, it is not true that light moves very slowly in Cu$_2$O. Maybe some polariton extremely close to its resonant energy (I did not look into that), but not generally.
It is red for the same reason why vermillion is red. It has a bandgap of about 2 eV, so that blue and green light are absorbed. And the absorption (the i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421213",
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"source": "stackexchange",
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In a Bell scenario, why can correlations be nonlocal only if there are at least two measurement settings to choose from? In (Brunner et al. 2013), the authors mention (end of pag. 6) that a set of correlations $p(ab|xy)$ can be nonlocal only if $\Delta\ge2$ and $m\ge2$, where $\Delta$ is the number of measurement outco... | Make a $\lambda_{a,b}$ for every pair $(a,b)$.
Then make $q(\lambda_{a,b}) = p(a,b)\,$, and
$p(a|\lambda_{a,b}) = p(b|\lambda_{a,b}) = 1.$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421512",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can Newton’s law of gravitation be derived from Coulomb’s law? I’m casually learning physics and have noticed that Newton’s law of gravitation and the electrostatic force formulas look similar. I’ve asked this question before but would really appreciate another response. Is it possible that the two laws are related? Ca... | To the best of our knowledge they are not deeply related although there is a theory called Kaluza–Klein theory that tried to interpret electro-magnetism as curvature of space-time much like gravity. There are, however, no real indications that this is correct.
To get back to the original question the relation is that t... | {
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"timestamp": "2023-03-29T00:00:00",
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"answer_id": 0
} |
Do photons violate the uncertainty principle, given that they have a constant speed $c$ with no uncertainty? I have a very basic understanding of quantum physics, but as I understand it the uncertainty principle says that the more precisely you know a particle momentum and the less you know the particle's position.
But... | As explained in If photons have no mass, how can they have momentum?, it is impossible to assign photons a classical momentum $p=mv$, because their mass is zero.
Instead, the photon momentum is determined by its wavelength $\lambda$ via
$$
p = \frac h\lambda,
$$
where $h$ is Planck's constant. This means that the only ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/421863",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Check where am I wrong. Here is how information can be sent faster than light If I have a very long rigid rod which is of rectangular cross section and small mass.
Let it's length be 1 light year and total mass be 1 kg now at one end if I rotate that rod, since the rod is rigid it should rotate as a body about the axis... | The solution to this "paradox" is that such a rod simply cannot exist. Relativity prohibits the existence of perfect rigidity.
If you rotated one end, that rotation would propagate from one end to the other at approximately the speed of sound in that rod. Since the speed of sound in any object is slower than the speed ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/422109",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is nesting/ what is a nesting vector in energy contour plots? I am making different plots for a 2-d non-interacting tight binding Hamiltonian
$$ H = - t \sum_{<ij>, \sigma} c_{i \sigma}^{\dagger} c_{j \sigma} + h.c$$
I get the dispersion relation $$\epsilon (k) = -2 t ( \cos(k_{x} a) + \cos (k_{y} a))$$
Plotting... | "Nesting" refers to a Fermi surface where two points on the Fermi surface are connected by half a reciprocal lattice vector. When this occurres, it usually indicates the system is critical or unstable with respect to an interaction.
If your think about adding an interaction term to the Hamilton via perturbation theory... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/422301",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
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