Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
How experiments differentiate between valence quarks and sea quarks The picture that baryon consist of three quarks and mesons consist of a quark,anti-quark pair is inaccurate.However this simple picture is enough to explain many properties of the hadrons as mentioned in the answer here What is the experimental evidenc... | Well in a baryon there are three quarks that are not virtual. Then there is the quark and the gluon field which constantly creates quarks and gluons and those are destroyed and created again. For a pion(neutral) there is not even these valence quarks. There is only the quark field. The charged pions are a little differ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510163",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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How many images are formed when an object is placed between two plane mirrors with angle $72^\circ$? I'm a little confused here since there are varying answers on the internet, and I cannot find any legitimate sources explaining this problem.
According to what I've seen, the formula is simply
$$
N = \frac{360^\circ}{A}... | The images formed and the object will always lie on a circle. This interesting property can be utilised here.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510285",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Does the wavelength of a particle depend on the relative motion of the particle and the observer? The de Broglie wave equation states:
$$\lambda = \frac{h}{p},$$
where $\lambda$ is the wavelength of the “particle”, $h$ is Plank's constant, and $p$ is the momentum of the particle.
Momentum is usually written $\,p=mv$, w... | Yes, the de Broglie wavelength of a particle depends on the relative velocity between the particle and an observer. I find it easier to think about the de Broglie frequency instead of the wavelength. They are related by $v=f\lambda$ or $f=v/\lambda,$ where $v=p/m.$
If the particle is moving towards the observer, the f... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510506",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Question about changing mass under conservation of momentum In class today, my professor was teaching conservation of momentum. One example she used was an open cart rolling on a frictionless track while in the rain. As the cart collects water, the mass increases; and due to conservation of momentum the velocity must d... | This is really the same situation as an inelastic collision between two objects, the cart and the water. Before the "collision", the cart has mass $M$ and horizontal velocity $v$, and the falling rain has mass $m$ and horizontal velocity $0$. The horizontal momentum of the system is therefore $P = Mv$.
After the "coll... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How does the tiling pattern of magnets influence the effective flux? Problem: A flat irregular shaped surface (A) need be affixed securely to a flat magnetic surface (B). The available means is small disc magnets of uniform dimensions and flux (the flat sides are N and S) to be glued onto (A). For a given thickness of ... | Definitely number '2'.
The flux from multiple magnets is not a constant. For example, if I place two magnets against each other N to N, much of the flux is cancelled. But if I place them N to S, they both add to the external flux. You can then move one of those magnets along the flux lines of the other magnet, keeping ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/510984",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Why does a chain or rope move the way it does when suspended and rotated on a vertical axis? I have always been interested in why objects like chains, ropes, etc. move the way they do when "rotated" around a vertical axis while being held only where it is suspended. It forms a shape if you will, resemblant of a "C" or ... | I think it is hard to study your problem, however, I try to justify why a chain/rope hanging from the ceiling makes a $C$ shape as it dangles freely. For a better perception, simulate each ring of the chain as a separate tiny ball which tends to move on a circular frictionless surface. Due to different radii of these s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/511105",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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In adiabatic expansion does the internal energy of an ideal gas decrease? By First Law of thermodynamic, for an ideal gas, if there isn’t heat transfer, work done by the gas is equal to decrease in internal energy of the gas.
Suppose that I have a perfectly-insulated syringe closed at one end and a frictionless piston... | The ideal gas inside the syringe is always applying a force on the piston, because of its pressure. Therefore, for the piston to remain motionless, there must be another force from the outside that contrasts the push of the gas inside. From the text of your question it seems that in the initial situation, e.g. when the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/511444",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is the volume of spacetime we can survey? How large is the fraction of spacetime volume we can observe within a sphere with the radius of the present particle horizon distance?
| After studying the many answers (related or not - but many thanks anyway) to my question, I can now summarize my understanding: As the 3D (= 2D surface + time) past lightcone shell has zero spatial depth, its fractional extent within a 4D (= 3D space + time) spacetime object like the particle horizon "volume" must be a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/511575",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Why standing wave is needed in microwave oven? In microwave oven, standing wave is created in chamber by reflecting from metal surface. Do we create it intentionally? Is there any special advantages of it?
| The chamber is designed to be a microwave resonator . The first and foremost reason for this would be that it would not be desired to radiate these frequencies out into your living space, as they can heat biological material. For the same reasons, the door has a window with a mesh over it. The wavelengths of the radiat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/511897",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Confusion about expressing an inner product using the Einstein summation convention I think this likely comes down to the following expression,
$$g’^{ab}e’_a e’_b = \delta ^a_b $$
Is this in agreement with the Einstein summation convention? Because even though the two indices are summed over, they still appear on the r... | I assume that you're using Latin indices to mean abstract indices, whereas Greek would imply concrete indices. This would be the modern convention (as opposed to in older publications where Latin vs Greek would indicate timelike vs spacelike coordinates).
Why are the primes there?
This is a notational clash between the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512152",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Hermiticity of spin-orbit coupling in real space In the Kane-Mele model, the spin-orbit coupling is defined in real space as
$$\sum_{\langle \langle i j \rangle \rangle \alpha \beta} i t_2 \nu_{ij} s^z_{\alpha \beta} c_{i \alpha}^\dagger c_{j \beta}$$
where the sum is over next-nearest-neighbor sites on a honeycomb lat... | In the first expression after the equals sign on the first line you have $c_{i\alpha}c^\dagger_{j\beta}$. It should be $c^\dagger_{j\beta}c_{i\alpha}$ since
$(AB)^\dagger = B^\dagger A^\dagger$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512370",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions? What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions?
| In $D=4$ the $R$-symmetry group is $U({\cal N})$, cf. Ref. 1, which also lists $R$-symmetry groups in other spacetime dimensions $D$.
References:
*
*D.Z. Freedman & A. Van Proeyen, SUGRA, 2012; Table 12.1 p. 240.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do I experimentally measure the surface area of a rock? I hope this is the right place to ask this question.
Suppose I found a small irregular shaped rock, and I wish to find the surface area of the rock experimentally. Unlike for volume, where I can simply use Archimedes principle, I cannot think of a way to find ... | *
*Fully wrap stone really tight in aluminium foil. (Of course it will crinkle; press the crinkles tightly down.)
*Soot the whole thing with a candle, just enough so it's completely black.
*Carefully unwrap foil.
*Photograph flattened foil together with a reference scale square. Make sure there's a light background... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512834",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "140",
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When the direction of a movement changes, is the object at rest at some time? The question I asked was disputed amongst XVIIe century physicists (at least before the invention of calculus).
Reference: Spinoza, Principles of Descartes' philosophy ( Part II: Descartes' Physics, Proposition XIX). Here, Spinoza, following... | After the invention of modern calculus and notions like continuity and differentiability, the answer is quite trivial in Newton's formulation of mechanics assuming the body is moving along a line. The second derivative of the position should be always defined as it equals the total force acting on the body. Therefore... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/512902",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "11",
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What determines whether we use a vector or scalar potential? I understand that electrostatic potential is scalar because the curl of the field is zero, and this implies the electrostatic field is the gradient of the scalar potential to satisfy this. Similarly the divergence of a magnetostatic field is zero so a magneto... | The good hint is in the scalar or vectorial properties of the sources.
For the magnetic field, the sources are currents, which are vectors since currents flows in specified direction: it’s no surprise the associated potential should be a vector.
For (time-independent) electric fields not induced by magnetic fields,... | {
"language": "en",
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"source": "stackexchange",
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Why do we feel weightlessness during free fall? An object in free fall accelerates towards the Earth at a acceleration equal to $g$ (the accleration due to gravity). Now if we ignore the air resistance, why do we feel weightlessness? I could not understand the reason that we could not feel the pulling force that the Ea... | When in free fall, neglecting air drag, the only force acting on your body is gravity, which is a non contact force, and you feel weightless. In other words the feeling of “weightlessness” is that of not experiencing the sensation of any contact forces. Stand on the ground and you feel the upward contact force of the g... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513206",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Newton's 3rd law in lami's theorem I'm a high school physics student dealing with the following problem:
Despite solving the problem correctly, I don't understand the diagram (b) supplied with the problem:
These are my questions:
*
*Why are vectors ${ F }_{ RB }$ and ${ F }_{ RC }$ in opposite directions in diag... | There's a tension in the rope that exerts a force in both directions.
Think about it this way: suppose you're participating in a tug-of-war with your friend. You pull him, and he pulls you. Although you're exerting a force on the rope, the rope is certainly also exerting a force on you (that's why you feel you are pull... | {
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Is there a way to construct a Hamiltonian from a set of DE? Let's say I have a set of first-order differential equations for set of position $x_i$ and conjugate momenta $p_i$, which might be complicated and time-dependent
$$ \dot{x}_i = f_i(x_j,p_j,t)$$
$$ \dot{p}_i = g_i(x_j,p_j,t)$$
and I know that these equations or... | Well, given
$$
\dot{p} = - \frac{\partial H}{\partial x}
\quad
\text{and}
\quad
\dot{q} = \frac{\partial H}{\partial p}
$$
we have
$$
H = - \int dx_{i} \, g_{i}(x,p,t)
$$
and
$$
H = \int dp_i \, f_{i} (x, p, t).
$$
You deal with the constants of integration using the obvious constraint:
$$
- \int dx_{i} \, g_{i} (x, ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Why does Heisenberg’s Uncertainty Principle not take wavelength into account? In class today we were taught about Heisenberg’s equation, $\Delta x\Delta p\ge\frac{h}{4\pi}$.
Why isn’t De Broglie wavelength a factor here - or is it, but it’s represented behind the deltas instead? After all, if we’re dealing with indete... | It was precisely De Broglie who hypothesized that $p=h/\lambda$. So you can also write $\Delta x / \Delta \lambda = 1/4\pi$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513564",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Do liquids continuously boil in a pressure cooker? First, I understand that the boiling point of water is increased as the pressure is increased. At 15 PSI, the boiling point is about 250F.
My question, which seems like nobody can answer with certainty, is this: Is there a continuous boil within the pressure cooker on... | It seems likely that the lid of a pressure cooker would be at a slightly lower temperature than the heated bottom. This could allow the steam from a very slow boil to condense without venting.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513687",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Is Newton's first law an "If and only if" On Wikipedia, Newton's first law is stated as:
In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
I read this as $$\mathbf{F}_{\textrm{net}}=0\Rightarrow \mathbf{a} = 0,$$ but does it ... | In my personal opinion, second law is more or less enough, as other two laws can be derived from it.
First law:
$$ \sum\vec{F} = m\frac{\textrm{d}\vec{v}}{\textrm{d}t} = 0 ,\\ \Rightarrow \vec{v}=\textrm{const}
$$
Third law
$$
\vec{F}_{A\to B} \neq 0, \vec{v_{_B}}=\textrm{const},\\
\Rightarrow \vec{F}_{A\to B} + \su... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/513775",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Do the logarithmic corrections to black hole entropy imply corrections to their energy or temperature? Could somebody help guide the thinking in this situation?
Do the corrections to entropy $S$, like those of https://arxiv.org/abs/hep-th/0111001, affect the temperature of a black hole, or its mass, or both, or neither... | It seems that the answer is that only entropy has logarithmic corrections. Neither energy nor temperature has such corrections. The logarithmic corrections of entropy are due to statistical fluctuations. These fluctuations have no effect on temperature or mass/energy.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/514098",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Principle of stationary action vs Euler-Lagrange Equation I am a bit confused as to what I should use to derive the equations of motions from the lagrange equation.
Suppose I have a lagrange function:
$$L(x(t), \dot{x}(t)) = \frac{1}{2}m\dot{x}^2-\frac{1}{2}k(\sqrt{x^2+a^2}-a)$$
Method 1: Principle of least action
$$\d... | First, I think there is something wrong with your partial derivative of the Lagrangian with respect to $x$.
Second, the Euler-Lagrange equations are nothing more than the process that you performed in Method 1, done without committing to a specific form for $L$ but leaving it generic. In your first step you took partia... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/514225",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Are the EM radiation categories objective or subjective? We were taught at school that EM radiation can be categorised as radio waves, microwaves, infrared waves, visible light, ultraviolet radiation, X-rays, and gamma rays, but how arbitrary is this categorisation?
I understand that for humans the 'visible light' cate... | Any classification of electromagnetic radiation is probably going to have at least a few basic components, which can be derived purely from observing the way radiation interacts with atoms and molecules:
*
*Ionizing radiation vs. non-ionizing radiation: Radiation above a certain frequency has the ability to ionize a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/514301",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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Schrieffer-Wolff Transformation for conventional superconductors I was trying to follow the discussion in Radi A. Jishi's book (Feynman Diagrams in Condensed Matter Physics), Chapter 12 on superconductors. They basically have a Hamiltonian that comprises of a quadratic electron part and a quadratic phonon part, which i... | As you describe, the Schrieffer-Wolff transformation does not "integrate out" the phonons in the sense of a path integral or partition function. Instead, the transformation returns an effective Hamiltonian where electrons and phonons are decoupled, up to 2nd order in perturbation theory. The phonons are still there, bu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/514555",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
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Ground → ship Wi-Fi bandwidth in my fast moving spaceship I have a hypothetical question that hopefully makes sense considering only the rudimentary amount of knowledge I have on relativity.
Assume I am in a spaceship orbiting around a spherical satellite, at a certain fixed radius. The satellite sends data to the shi... | If you are in a perfectly circular orbit, then your received signals are affected by the relativistic transverse Doppler effect.
The signals you would receive would be blueshifted by the Lorentz factor of the orbital speed. That is the information transferal rate would (potentially) go up (if you can tune to the new fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/514883",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 5,
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Showing that the $A$-$j$ coupling in classical electromagnetism is gauge invariant I am attempting an early exercise from Altland's Condensed Matter Field Theory. The electromagnetic field's action is given as:
$$S[A]=\int d^4x(c_1F_{\mu\nu}F^{\mu\nu}+c_2A_\mu j^\mu),$$
and I wish to show that the second term is invari... | *
*Assuming the continuity equation $d_{\mu}J^{\mu}=0$, the gauge symmetry is more precisely a gauge quasi-symmetry, meaning that the action is only invariant up to boundary terms.
*It seems relevant to stress that no boundary conditions are imposed in Noether's theorems. In contrast, boundary conditions are necessa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/515209",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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How can the mechanism of electrons in an atom be explained? I am a high school student who takes both Physics and Chemistry.
Recently I learnt about the quantum mechanical point of view of looking at electrons or nuclei. I also learnt that the wave functions can be obtained by solving the Schrodinger's equation with va... | In addition to the comments mentioned, when you solve for 2 electron problems in quantum mechanics, you do include a term of the form $\frac{kq_1q_2}{r_{12}}$ which represent the interaction between the two wavepackets. For more information on how the 2 electron system is solved, see https://en.wikipedia.org/wiki/Two-e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/515438",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"Contradiction" about Hubble parameter $H_0$ in the future? The Hubble parameter $H_0$ is expected to level off asymptotically in the far future as dark energy becomes dominant over matter, radiation, and space curvature. I think it's predicted to go down to 55 km/s/Mpc.
Yet dark energy is also the cause of a galloping... | The Hubble parameter does not measure the rate of change of expansion. It is the ratio of the expansion rate to the size of the universe. $H(t) = v(t)/d(t)$.
If the expansion is accelerating, then the size of the universe gets bigger faster than the expansion rate gets bigger - hence the Hubble parameter gets smaller.
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/515562",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is orbit that could place satellite to be always under the Sun? I just thinking that, if we could place satellite to orbit earth in opposite direction of earth rotation, inverse of geostationary orbit. If we carefully choose a speed to sync with earth rotation, it would have that satellite stay exactly the same po... | It wouldn't be geostationary because we would see it move across the sky. I think you mean geosynchronous, which is what the orbit would almost be. If you wanted it to always stay in front of the sun from some special vantage point, then you would need to somehow have the satellite correct its orbit based on the changi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/515879",
"timestamp": "2023-03-29T00:00:00",
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How do physicists compare the relative strengths of the four forces? Since the four forces are different, with different force carriers, how are they (seemingly) directly compared? I often read that the weak force, for example, is many orders of magnitude stronger than gravity, and that electromagnetism is several ord... | It is the history of how the SU(3)xSU(2)xU(1) standard model of physics was built up making a consistent whole of the grand majority of data up to now, and giving good predictions.
A whole lot of scattering experiments showed that there were different strengths and different lifetimes in the interactions, and these are... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/516169",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Different apparent brightness of a distant star from a moving frame - an apparent paradox Consider a stationary star at a distance $L$ from the Earth.
A spaceship at Earth moving with velocity $v$ towards the star will find the star to be at a distance of $\dfrac{L}\gamma$ in its own frame.
But it won't actually see th... | You can't do special relativity just using gamma! If you really want to know what stars look like when you are traveling quickly relative to them, you need to use the correct method.
I would suggest this source - the maths is as simple as it can be, but I'm not saying it will be an easy ride! The meat of the answer beg... | {
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"url": "https://physics.stackexchange.com/questions/516652",
"timestamp": "2023-03-29T00:00:00",
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Might a cast iron pan set on top of a microwave oven affect the operation? Our microwave seems to take longer to get the job done these days. I notice that someone is storing a large, heavy cast iron pan on the top of the microwave. Is there any way at all that it is possible that the iron pan is interfering with the m... | Assuming that you have not drilled holes into your microwave (that can be really dangerous and should never be done) the enclosure forms a Faraday cage from which the microwaves cannot escape, therefore they can also not interact with the iron pan.
However, with some imagination one could certainly come up with weird r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/516764",
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"source": "stackexchange",
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Energy cannot be created nor destroyed, but can it be lost in expanding space? It is said that there are extremely distant stars and galaxies that we will never see, because overall, the space between us is expanding faster than their light travels towards us. Does this mean some radiation can travel forever through ex... | I do understand your question and your confusion.
Photons are massless particles, they travel along null geodesics, meaning that the spacetime distance between emission and absorption is 0.
You are thinking about information (photon) being emitted somewhere, and then its very purpose should be to receive (absorb) it. ... | {
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Spin of higher string excitations I am trying to better understand spin in string theory.
There is already a good post here:
Ssecond and third level excitations of open string
But I have these questions:
1) Why would the second excited stated be spin-2?
If I use the spin operator then I find states which have
spin eig... | You need more careful extract irreducible representation of little group.
See for example 4.2.2. in Gleb Arutunov notes Lectures on String Theory
| {
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Phase transition on magnetic materials Is ferromagnetic to paramagnetic phase transition a reversible process?
If I start with a ferromagnetic material with a spontaneous magnetization below the Curie temperature, and then I start to heat it, it will become paramagnetic above the critical temperature. If I then start t... | Yes, locally it will have the same magnetization as before due to spontaneous ferromagnetic ordering within magnetic domains. But without an applied magnetic field, the domains will arrange in such a way that the large-scale magnetization will be zero.
I once made this Curie pendulum: https://www.youtube.com/watch?v=Cv... | {
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Roche lobes in binary star systems While studying mass transfer in binary star systems, I came across the concept of Roche lobes and the role of the inner Lagrangian point $L_1$, as shown in the adjoining figure.
However, I am having a doubt in understanding the reason of the fact that one lobe is larger and the other... | You are right: the size of the Roche lobe depends on the mass of the components. It scales linearly with the separation of the components and in addition is a function of the mass ratio. See https://en.m.wikipedia.org/wiki/Roche_lobe
| {
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What happens when a weapon breaks on impact? Here is the situation:
You are attacking someone with a wooden pole (such as a pole arm or tree branch). You either (1) hit as hard as you can and the pole breaks into two pieces on impact OR (2) hit quite hard but the pole remains in tact. Assume that you are hitting the sa... | The force applied on an object is proportional to the change in momentum:
$F = m (v-u)/t = dp/dt$
Momentum is a vector, so direction matters. The largest change in momentum happens when the object you're swinging reverses direction. For example, if you're swinging a stick at a pillar, if it bounces backwards after cont... | {
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Is time slower on the far galaxies? Since far galaxies move away faster, what would be the speed of their time relative to us?
If there is a difference:
*
*What determines whose time would be faster?
*(If I haven't understood it wrong) To resolve the twin paradox, acceleration is required. Is the expansion of the... | Time measured in the frame of a galaxy that is moving relative to us would appear to us to be running slowly. The effect is reciprocal, so our time will appear to be running slowly to observers on the galaxy moving with respect to us. For both sets of observers time ticks away at the same rate in their respective refer... | {
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Witten's description of WZW conformal blocks I am reading this paper by Witten - Geometric Langlands From Six Dimensions. In section 4.1, he gives a description of the vector space of conformal blocks of the current algebra associated to a simply-laced and simply-connected Lie Group $G$ at level 1. He claims that on a ... | I am no expert on this, but it sounds as though the blocks are labeled by the Wilson lines around the 1-cycles. This is what happens on a torus.
| {
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How come Goldstone boson, PQWQ axion, be able to have mass at all? Quote:
Goldstone's theorem: For every spontaneously broken continuous symmetry, there is a massless particle created by the symmetry current.
However, under $U(1)_{PQ}$ symmetry, I read that PQWW axion can obtain mass from $G\tilde{G}$.
Both these s... | Like the pions, the axion is a pseudo-Golstone boson, so it has a mass. The $U(1)_{PQ}$, as a chiral symmetry, is broken by quantum corrections by the axion's coupling to gluons, and so is no longer an exact symmetry. Goldstone's theorem them does not apply. This is completely analagous to the so-called '$U(1)$ problem... | {
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Observed speed of a receding light source Let’s say there’s a planet 4 light years away from Earth and we send a rocket ship towards that planet at 99.9% light speed. We stay behind on Earth and watch the rocket ship travel towards the other planet.
Eventually we should be able to see our rocket ship reach it’s destina... |
Will it appear as if the trip took 8 years to complete?
Yes.
| {
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What is a Past Event Horizon? I've recently been informed about a few things from a reliable source:
1) Wormholes can't form via gravitational collapse
2) The event horizons in an ER bridge can't collide
I understand what a future event horizon is by realizing that once reaching any point on its "surface" there is no ... | A past event horizon would be a surface such that one could only pass it on past-directed curves. Inside it, anything within would be forced out, and then once past the horizon, could not enter again. This object is a so-called 'white hole', the opposite of a black hole. We know of no physical processes that could crea... | {
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Why do we use cross products in physics? We can define cross products mathematically like if we take two vectors, we can find another vector with certain properties but why do we use it in physics, if we consider a hypothetical physical quantity like force which is equal to cross product of certain vectors?
For exampl... | This is a great question. The dot and cross products seem very mysterious when they are first introduced to a new student. For example, why does the scalar (dot) product have a cosine in it and the vector (cross) product have a sine, rather than vice versa? And why do these same two very non-obvious ways of "multiplyin... | {
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Do colors differ in terms of speed? Here is a very simple question about light. As far as I remember from the school program, each color is merely one of the frequencies of light. I also remember that each color's wave length is different. On the other hand, when talking about the speed of light, I've always heard only... | The speed of a wave is given by:
$$c=f\lambda$$
Where $c$ is the speed of the wave, $f$ is the frequency and $\lambda$ is the wavelength. You're right that different colours have different frequencies, but light with a lower frequency has a longer wavelength, in other words if $\lambda$ goes up then $f$ has to come dow... | {
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Light beam vs sound beam Why is it that it's very common to have beams of light but not beams of sound? Laser beams are widely available, and I am aware that it is also possible to direct sound, however, we rarely see examples of it.
Is it more difficult to direct due to longer wavelength or is it more dispersive in a... | The beam width is proportional to the wavelength $\lambda$ divided by the aperture width $L$. Audible sound frequencies are are in the KHz range with wavelengths between approximately 17 m and 17 mm. Whereas visible light wave lengths are in the micrometer range. So sound apertures would have to be vastly larger than l... | {
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Where does the power delivered to car's wheels go? Okay, so power is work/time. Most cases, when power is provided to something, energy is gained as kinetic energy or lost to friction.
But in a car, the engine puts power ( torque x rpm/5252) to wheels, but very little ends up in the wheels, assuming friction keeps them... |
So where does the power go?
Power is just like force and varies from one instant to another.(You cannot say that an object losses $3N$ force! )
What the car/object gains or loose with time energy (whose gain/loss is represented by work done). Power is the rate of work being done(i.e., it represents at what rate the ... | {
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Average value using partition function Let's say I have 4 particles with energy levels $0\,\rm{eV}$ , $1\,\rm{eV}$,and two particles with $3\,\rm{eV}$ energy levels. If I want to find the average value of energy I can say that
$$\bar{E}=\dfrac{(0+1+2\cdot3)\,\rm{eV}}{4}=1.75\,\rm{eV}$$
If I want to use the partition fu... | You are missing a key point about averages.
In your first case you have assumed all energies are equally probable.
In your second case you have assumed energies have a probability distribution $P(E)$ of $e^{-\beta E}/Z$.
In general the average energy is $\sum E\cdot P(E)$.
| {
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Do expectation values of quantum fields behave like classical fields? A famous result in quantum mechanics is Ehrenfest's theorem which states that the expectation values of observables are governed by the classical equations of motion.
Does a similar statement hold for quantum fields?
In particular, in the context of... | The QFT version of Ehrenfest's theorem are the Schwinger-Dyson equations, stating that the classical equation of motion (in presence of a source $J$) $\frac{\delta S}{\delta \phi} + J = 0$ holds as an operator equation $\langle \frac{\delta S}{\delta \phi} + J \rangle_J = 0$ in the quantum theory. If you evaluate this ... | {
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Quantum field theory, interpretation of commutation relation Let $\phi$ be the quantum field
$$
\phi(x) = \int \frac{d^3\mathbf{p}}{(2\pi)^3} \frac{1}{\sqrt{2E_\mathbf{p}}} \Big[ b_\mathbf{p}e^{-ip\cdot x} + c_\mathbf{p}^\dagger e^{ip\cdot x} \Big]
$$
with commutation relations
$$
[b_\mathbf{p}, b_\mathbf{q}^\dagger] =... | The commutation relation $[Q,\phi] = n \phi$ tells you that the field $\phi$ has charge (or eigenvalue) $n$ under $Q$ in our case $n=1$. An easy way to see this is to note
$$\left| \phi \right> := \phi \left| 0 \right> \implies Q \left| \phi \right> = Q \phi \left| 0 \right> = [Q,\phi] \left| 0 \right> = n \phi \lef... | {
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Fermi energy definition Ok, so I'm having a hard time understanding the definition of Fermi Energy. Several sites basically repeat each other, saying that it is the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero 1, and ot... | One can derive the fermi-energy using quntumstatistics and is a more complex derivation. But in condensed matter you find a more vivid explanation about the meaning.
Let us assume a free fermi gas or electron gas. We make the following assumptions
*
*$N\gg 1$ conducting electrons move on a homogeneous charge backgrou... | {
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Why can the masses of the Higgs and top quark determine whether we live in a false vacuum? I read in the paper linked below that the ground state of the universe depends on the potential of the Higgs field, particularly the graph of the Higgs potential with its minima and maxima. I think I understand why the Higgs is i... | The Higgs potential receives quantum corrections from the Yukawa couplings with fermion doublets. The magnitude of the correction is determined by the Yukawa coupling constant, which is itself proportional to the fermion mass. As a result, the heaviest fermions make the greatest contribution to the effective action. Be... | {
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What is the minimum mass for gravity to form objects in a protoplanetary disk? I understand that at smaller scales the strong, weak, and nuclear forces, and chemical bonds have more influence on the formation of objects than gravity. At what amount of mass does gravity become the dominant force that holds together the... | It depends on what the dust is made of, specifically how many coulombs it has (a surplus or deficit of electrons). As mass can be measured in energy, electronvolts/speed-of-light2, and eV is the energy of 1 electron subject to 1 joule of electric potential difference (or one volt [force exerted over distance behind a c... | {
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What would the water pressure be at this point in a static incompressible fluid? I have a bowl full of water. I invert a glass and place it upside down in the water, leaving a small pocket of air.
My question: what would the water pressure at positions P1 and P2 be? I know P1 = P2 because there's no hydrostatic effect ... | The water pressure at both points $P_1 = P_2 = 1 \mathrm{atm}$.
If you placed the entire glass under the water surface, inverted it, and then raised it, there would be no air in the pocket (the one above $P_2$). The water level would rise to $1 \mathrm{atm}$, or about 10 meters.
Conversely, if you inverted the glass an... | {
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Does sound propagate in the same way in both senses through a medium with obstacles? For instance, let's suppose that we are in a room and we hear a person speaking in the hallway. If we start to speak at the same volume as that person do, would he hear us as loud as we hear him?
| Mostly usually yes, in the same way that optical systems show the same attenuation in both directions.
but human mouths and ears are slightly directional and are slightly displaced, so tricks could be played using focusing structures to boost efficiency in one direction, eg: a speaking tube that leads from the mouth of... | {
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Will state of water change in certain condition? Imagine I have an iron tank with a $20~\mathrm{pm}$ hole on it. Then I completely fill it with water and use a pump to get the water out of that hole. What will come out, water or gas?
| Your hole is too small to let even a single molecule through, but let's increase the hole to a size where molecules can come through one at a time. I'm sure this is what you had in mind. What then would be the result?
And the answer is that would have created a molecular beam. That is you would have a beam of isolated ... | {
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Why are topological insulators interesting? Why are topological insulators interesting? Meaning, why should an undergraduate or graduate student start working on this? What are the technological applications? I am not sure how to answer these questions and wikipedia does not help since it does not explain why so many p... | Almost as interesting as sharks with laser beams on their heads are topological lasers. Topological protection can make microreasonators work in unison [1].
[1] Bandres, Miguel A., et al. "Topological insulator laser: Experiments." Science 359.6381 (2018): eaar4005.
| {
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Does stress depend on the intrinsic properties of the body? I'm trying to understand the difference between stress and pressure.
Assume a body, a box with 4 sides.
We apply pressure to this body, and because the body's right side is 'weak', it deforms.
Does this mean that the stress increases in this example because of... | I think the way you are thinking about the weak point, it wouldn't be the stress that is changing in the material.
The weakness is often a material property where the material has a greater strain for the same amount of stress, so the weak point deforms more when the equal stress is applied throughout the body.
The str... | {
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Dimensionless expression for differential equation I am working through Nonlinear Dynamics and Chaos by Steven H Strogatz. In chapter 3.5 (overdampened beads on a rotating hoop), a differential equation is converted into a dimensionless form. I am trying to work out which dimensions the initial equations had, and why t... | Because you take the derivative with respect to $\tau$. Since $\tau$ is dimensionless, the derivative is too.
| {
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Driving a nail with a light object? I was wondering if it is possible to drive a nail through, for example, concrete by dropping a light object on the head of the nail over many iterations.
I.e. is there a certain threshold of force that must be reached for the nail to make even the slightest progress into the concrete... | Hammer is almost always able to transfer phonons, (this threshold is significantly lower than chemical bond energy).
To drill a chunk of concrete, put it in a thermally sealed container and use a non-conductive nail with a higher melting temperature.
Hit a nail, until heat dissipated in concrete melts it.
Disadvantages... | {
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Spacelike separation, special case This is merely a terminology question. Consider two events A and B. Now suppose A and B happen in two different black holes, i.e. there is no way from A to B (or B to A). Is this fundamentally different from a "normal" spacelike separation, where the finite lightspeed hinders to get f... | In GR we don't have displacement vectors (except for infinitesimal displacements). So we can't say, as in SR, that the vector from A to B is spacelike. There can also be things in GR like events that can be connected either by a purely timelike, future-directed curve or by a purely spacelike curve. To describe your sit... | {
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Is Young's modulus a measure of stiffness or elasticity? Young's modulus seems like a modulus of stiffness. It tells us how difficult is it (how much stress is required) to produce longitudinal strain in a solid. It does not tell anything about how an object will react when the deforming force is removed.
How can one o... | It is not true that steel is more elastic than rubber. Not in common language.
Yes, steel has a larger modulus of elasticity, Young's modulus, the ratio of stress to strain $Y=\varepsilon/\sigma$. This is in the region of elastic response as long as the deformation $\sigma=\Delta \ell/\ell$ increases linearly with stre... | {
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Internal force disintegrating a solid body? Let $M$ be a block on a frictionless surface. Now let us mentally divide (not physically) the block into 2:1 ration (i.e $1/3$ of the left be called $M_1$ and $2/3$ right be called $M_2$). So $M_1$ applies force $F_1$ on $M_2$ and $M_2$ applies force $F_2$ on $M_1$ and by 3rd... | Most of your intuition is correct. The piece that you're missing is the constitutive relationship that describes how the force $F$ between the pieces depends on their relative position and velocity.
A decent model for most materials is that the constitutive forces act like some combination of a "spring" holding the pie... | {
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What caused quadrupole anisotropy at the time of recombination? The polarization of CMB requires a quadrupole anisotropy of the incident radiation field acting on the plasma. How did such a special pattern (i.e. hot and cold in two orthogonal directions) generate in the first place? Where does it come from?
| From Quadrupole Types and Polarization Patterns
Quadrupole anisotropies are associated with density, vorticity and gravitational wave fluctuations
Their projection determines the polarization pattern and may be distinguished by symmetry properties
The polarization probe more than just the density or temperature fluctu... | {
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How was the mass of the moon first calculated? How was the mass of the moon first calculated? How do we measure it now?
| In the history of astronomy there was no correct concept of masses before Newton.
The Greeks had found reasonably accurate volumes of the Earth and Moon, but masses were unkwnown.
The planetary mass determination relies on Kepler's third law. Newton indirectly measured the mass of the Moon, trying to estimate the rati... | {
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Could speed of light be variable and time be absolute? I get my "demonstration" of time dilation from the textbook thought experiment.
A laser is mounted on a cart with a reflective ceiling. At $t=0$ the cart starts moving and the laser is fired. When the laser is reflected back at the starting point the (thought) expe... |
Why is the speed of light held constant here?
You are missing one important point of that thought experiment: it is meaningful after considering the Michelson-Morley experiment.
If our interpretation of the Michelson-Morley experiment is that the speed of light is constant with respect to the observer, then we can pe... | {
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Is Griffiths simply wrong here? (Electrostatic Boundary Conditions)
In the above illustration, shouldn't $E_{above}$ and $E_{below}$ be in opposite directions? If not, how did Griffiths end up the following equation? From the above directions, shouldn't the flux add up?
| Two ways of seeing that it’s right:
*
*Consider the case of no charge. Then nothing interesting is happening at the sheet, so the fields should be equal: both sides of the equation are zero.
*Gaus’s law: the sum of the fields going away, which is the outward flux, is given by the charge. Since $E_{below}$ is defin... | {
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What is baking and what are the effects? In their experiment, Davisson and Germer had to bake the nickel mass because it was oxidized.
What is baking and what does it do to the lattice of the metal?
| Usually "baking" a vacuum chamber means heating up the whole installation to over 120 C during a day or so, to drive off adsorbed water etc from surfaces in order to achieve a good vacuum.
Davisson and Germer did something else. From their article:
The investigation reported in this paper was begun as the result of an... | {
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I dont understand the work equation I don't understand how work = force * displacement as if a force of say 1 Newton was to be applied to two objects of different mass until the object reached a displacement of say 1 meter, surely the object of less mass would displace 1 meter in less time (due to faster acceleration) ... | One of the things that we can predict while applying work energy theorem is that the change in kinetic energy is the same for both the given case (faster as well as slower) given the fact that other forms of energy of the system change negligibly. Let's assume that these works aren't the same:
$$W=\Delta K$$
and $$W' =... | {
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How did early radar determine range/ distance precisely? Wikipedia talks about precise timing of the returned radar pulse, with an animation of a clock.
But they didn't have atomic clocks and such before or during WWII.
So how did they determine distances and (possibly) velocities back rhen?
| There were WWII-era electronic circuits that were designed to readily slice time into fractions of a microsecond, for the purposes of timing pulse returns in the first radars and thus deducing range.
The imprecision in the time slicing process could be readily dialed out of the system by aiming the radar beam at a tar... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Finding orthnormal wavefunctions to given wavefunctions Consider a particle in an infinite square well in one dimension. The potential inside the well is 0. The length of the potential well be L. Let the wavefunctions of the lowest three energy states be $\psi_1(x)$, $\psi_2(x)$, $\psi_3(x)$ which are also orthonormal ... | HINT: View the wavefunctions as vectors and use the Gram-Schmidt process.
| {
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Do colliding black holes violate time reversal symmetry? Two black holes can collide and merge into one bigger black hole, but not split into two. Does this mean colliding black holes violate time reversal symmetry?
Related: Do black holes violate T-symmetry? Based on the answer to that question, time-reversing a black... | When two black holes collide and merge into one, a lot of energy is sent out as gravitational waves. This energy spreading out without bound represents an increase in entropy, along with any increase due to the final BH surface area being greater than the sum of the original two.
If we had an exact solution to Einstei... | {
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Local density in SSH model Considering the usual SSH model defined on N sites and parametrized with $\delta $:
$$H = \sum\limits_{j=0}^{N-1} (1-\delta)\ c_{j,A}^{\dagger}\ c_{j,B} +(1+\delta)\ c_{j,B}^{\dagger}\ c_{j+1,A} + h.c $$
In the fully dimerized limit, i.e $\delta=1$, how would one compute the local density for... | If you have obtained the Hamiltonian, and diagonalized it to get the ground state vector, you have presumably chosen a basis, and I would guess that it is labelling sites in real-space, as this is the most "natural" basis to take for a hopping Hamiltonian of this type. Is that right? In that case, the particle density ... | {
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Why does an open ended wire cause the load to the oscillator to increase? Using an ammeter between the wall and signal generator, I noticed that when the lead from a single channel is attached to the signal generator, the power into the signal generator increases by about 100 milliwatts.
When the wire leads are removed... | There are waves in the wire, and they can be reflected back from the closure.
As an example: when I was working with preamplifiers to increase the signal measured in the oscilloscope, I had to use a 50 ohm closure at the end of every wire, to get a good enough reflection otherwise the signal kind of "leaked" , got nois... | {
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Why does a weather vane arrow point in the direction of the wind? It seems that a weather vane will rotate in order to minimize energy and thus orient itself parallel to the wind.
What I do not understand is why it is implied that the weather vane arrow should point in the direction of the wind.
I do not understand wh... | Wind vane will always point to the direction from which the wind is blowing.
I.E., if wind is blowing from East to West,
then the arrow of the wind vane points to 'East'.
The pointed end of the arrow offers least resistance to wind.
Therefore, the arrow achieves the state of equilibrium by pointing itself against the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/524846",
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Properly reporting instrument readings As a first approximation, the uncertainty ($\delta X$) associated to a mensurand can be expressed as $\delta X= \Delta X / 2$ with $\Delta x$ being the resolution of the instrument.
There is also a recommendation indicating that the numerical expression of the result and its uncer... | The problem with your question (and figure) is that the resolution is well beyond the gradation of the instrument, and that is misleading.
So let's suppose can't really distinguish 3.1 from 3.5, all we know is that 3.1 is closer to 3 than 5, and while 3.5 is in the middle, we'll round it to 4.
In this case the uncertai... | {
"language": "en",
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Is Snell’s Law valid in this case? When light travels in a perpendicular path from one medium to another medium of different optical density, is Snell’s law valid?
$\sin i$ and $\sin r$ are both 0, right?
So it isn’t valid.
Is this correct?
| Let me first give an example from Newton's laws. If there is no net force acting on an object, then it will not be accelerating. Therefore, the equation of Newton's second law $F=ma$ is a valid equation, as we have $0=m\cdot 0=0$. But what if we were looking at this scenario with the equation $F/a=m$? This gives us $0/... | {
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Book suggestion about Neutrino effect on Cosmic Structure I am trying to find some nice explanatory books about neutrino effects on the cosmic structure. I did not take GR so I prefer sources that contain not much GR.
I prefer lecture note series or books rather than articles. I mean I want to understand the idea behi... | My favorite book on this topic is Soler, Froggatt & Muheim's Neutrinos in Particle Physics, Astrophysics and Cosmology. They start with neutrinos in the standard model and go over neutrino oscillation, and then go onto look at neutrinos emitted from stellar objects. Experimental neutrino detection is emphasized, and th... | {
"language": "en",
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"source": "stackexchange",
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Pitch of sound in half fill glass I read in my physics book that when we use a spoon and vibrate a glass, the pitch should be according to the air column inside. So, less filled the glass, longer the air column and lesser the frequency according to frequency = 1/4*( v/l) formula. But when I tried to do it practically ... |
I read in my physics book that when we use a spoon and vibrate a
glass, the pitch should be according to the air column inside.
The book is wrong. The pitch depends on the vibration of the glass, not the air inside.
The glass changes shape as it vibrates, and when you add water, the water also has to move to match ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/525346",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Null Geodesics in Anti-de Sitter space time
Would anyone be able to explain how the step was taken in getting the final equation with $R \tan(t/R)$
I understand the steps before where we are finding the null geodesic equation for the AdS space time but not sure how the final equation is produced.
Note: This question ... | Separate the differential relation
$$(\cosh\rho)\,\dot t=R\dot\rho$$
between $t$ and $\rho$ to get
$$\frac{dt}{R}=\frac{d\rho}{\cosh\rho}.$$
Then integrate to get
$$\frac{t}{R}=\tan^{-1}{(\sinh\rho)}$$
or
$$\sinh\rho=\tan\frac{t}{R}.$$
| {
"language": "en",
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"source": "stackexchange",
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How does water vapour replace air molecules? I know that density of moist air is less than density of dry air becuase water molecules replace air molecules, and hence as the average molecular mass of water is less than that of air, the density decreases.
Now my doubt is why do the water molecules replace air molecules,... | I'm not a professional. It is only my thought may you find it useful
If water molecules can dissolve in air then, their would be no change in volume. But as we know, water dosen't dissolve instead it only makes a mixutre with air. So water vapors fight for their volume too therefore increasing volume and decreasing den... | {
"language": "en",
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60 kg on earth is 60 kg on the moon I'm writing a trivia quiz and intend this question, which dates from a high school physics test I took in 1972.
An astronaut tips the scale at 60 kg while on earth, what will she be if she steps on the scale on the moon? Answer 60 kg.
Kg measures mass, which is constant.
The questio... | The answer depends on the type of instrument you are allowed to use for the measurement. The two types are:
*
*Weighing Machine type
*Beam Balance type
This instrument (weighing machine) measures the downward force applied by the object and then divides it by $g$. That is if your body applies a force of $W$ on the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526210",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Understanding lenses for virtual reality and viewing a screen very close to eyes I'm trying to understand the physics of the technology involved in making a simple virtual reality headset.
More specifically, I just care how does one make it so they can see and focus on a screen right in front of their face?
I ask my q... | Two things need to be done.
*
*a sharp image needs to be formed on the retina,
*as perceived by the eye/brain the image needs to be upright.
Because the smartphone is so close to the eye, the rays entering the eye are highly divergent and they need to be made less divergent after passing through the lens.
Th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526345",
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Confused about what a wave is When a wave of something, let's say light or some electromagnetic wave is given, I am confused because I do not understand if shape of a wave represents projectile of it or some value that possess at certain positions. I researched a lot but I have no idea what a wave really is.
My questi... | The most basic definition of a wave might be $f(x-ct)$ which is the equation of a function that moves to the right (translates) with a speed $c$. $f(x-ct)+g(x+ct)$ is the equation of two waves--one moving to the right and one moving to the left--and this equation is the general solution to the 1D wave equation.
So the ... | {
"language": "en",
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"source": "stackexchange",
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How one pair of Schwarzschild coordinates can specify 2 different points on a manifold? My question is regarding Schwarzschild solution. I always heard that coordinate chart is a one to one map from a manifold to real numbers. But when we look inside the black hole using Kruskal coordinates we see that each pair (r,t) ... | Coordinate charts are always one-to-one from the manifold to some open subset to $\mathbb{R}^n$. This is because we use charts as local homeomorphisms to define what a manifold is (it can be defined in other, more abstract ways, e.g. locally ringed spaces, but let's not get into that).
Let's remark another important po... | {
"language": "en",
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"source": "stackexchange",
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Derivation of combination of lenses using different sign conventions In the following derivation of combination of thin lenses, why no sign convention is applied? For the first step, image distance, $u=+v_e$, but shouldn't it be $-v_e$ as the object is to the left of the lens? Also, in the second step, since the virtua... | The author did use a convention, probably just not the one you're used to. From the form of the well-known thin lens equation used ($\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$), we can conclude that the author considers both object and image distances positive towards the right and negative towards the left. It's a simple co... | {
"language": "en",
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Photon vs electromagnetic waves Suppose an electron makes a single transition from higher to lower energy level releasing energy. Would that energy be released in exactly one photon equal to $h\nu$? Also, is saying "one photon is released" equivalent to saying "one electromagnetic wave of $\nu$ frequency is released"... | More than one photon can be emitted but these processes have lower probability. (Rule of thumb: A factor of $\alpha\approx 1/137$ for each extra photon.)
Talking about “one electromagnetic wave” is meaningless. An electromagnetic wave pulse with a small range of frequencies centered on $\nu$ is emitted. (The spread in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/526906",
"timestamp": "2023-03-29T00:00:00",
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Using the uncertainty principle to estimate energies in ground states Suppose, for example, that we want to find the minimum energy of a particle undergoing simple harmonic motion. In classical mechanics, the energy is:
$$E = \frac{p^2_x}{2m} + \frac{1}{2} m \omega_0^2x^2$$
where $m$ is the mass of the particle and $x$... | Building on the last equation in Semoi's answer:
\begin{equation}
\left\langle E \right\rangle = \frac{(\Delta p)^2}{2m} + \frac{m\omega^2 (\Delta x)^2}{2},
\tag{1}
\end{equation}
if you want to arrive at the minimum energy, all you need to do is substitute the uncertainty principle, $\Delta p = \hbar / (2 \Delta x)$,... | {
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"timestamp": "2023-03-29T00:00:00",
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Is the equation $g=GM_Em/R_E^2$ in Tipler incorrect? I was reading my textbook (Tipler et al.), and I am unsure of one of the expressions they used. On page 374, it says (near Figure 11-10) that $g = GM_Em/{R_E}^2$. Is this even dimensionally correct? I got a units of $m/s^2$ on the left hand side and Newtons on the l... | Yes, this is certainly an error. The gravitational acceleration is $g = G M_E/R_E^2$, consistent with the preceding sentence of the text. It would be inconsistent (and a violation of the equivalence principle) for $g$ to depend on $m$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527219",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Gauge ghosts & unphysical states in gauge theory I have a general question about a statement from Wikipedia about ghost states as occuring in gauge theory:
"In the terminology of quantum field theory, a ghost, ghost field, or gauge ghost is an unphysical state in a gauge theory."
I learned gauge theory up to now wi... | There are different ways of defining what "unphysical" state is. Often states with negative norm $\langle \Psi | \Psi \rangle \lt 0$ are considered to be unphysical.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/527340",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
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Entropy change in the free expansion of a gas Consider the adiabatic free expansion of a gas since there is no external Pressure hence Work done on the system is 0 and since the walls are insulated (hence adiabatic) the heat absorbed is 0. However since this is a irreversible process then entropy change > 0 hence dQ > ... |
What am I missing ?
Entropy can be generated without there being heat transfer, i.e., when $Q=0$. That's the case for a free expansion into a vacuum. The classic example given is an ideal gas located in one side of a rigid insulated vessel with a vacuum in the other side separated by a rigid partition. An opening is ... | {
"language": "en",
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"source": "stackexchange",
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What were the experiments and works that suggested kinetic theory of gases and proved that the static theories were incorrect? What are the experiments which could not be explained by static theory?
How can one conclude that these theories are insufficient to explain the experimental results?
| I have searched , and it is a sobering search. All reviews start and stay on the way the theory developed. It does not seem that there was a decisive need to go further than the thermodynamic theory, but the history shows that they did, and it was all theoretical! An example is in this link, ( also of course in wikiped... | {
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Why COM and COG are different things? In the formula for Newton's law of gravitation i.e.
$$F = G(m_1)(m_2)/r^2 $$
here $r$ is the distance between COM of the two objects , so we consider that the object is a single point located at it's COM and at this point gravitational force of attraction acts . Then why is somet... | While your question is essentially a duplicate of the one I linked to, none of the answers have used the equations, so I will supply them here in a comparison.
The COM is weighed based on the mass density $\rho(\mathbf r)$:
$$\mathbf r_\text{COM}=\frac{\int\text dV\,\rho(\mathbf r)\cdot \mathbf r}{\int\text dV\,\rho(\m... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What makes a wheel spin? I don't fully grasp what makes a wheel much easier to move than to push a solid block.
The pressure at the point of contact between a wheel and the ground must be pretty enormous compared to the pressure created by a block of same material and mass as the wheel.
Friction is defined as the pro... | Pushing a heavy block across the ground is going to be hard because as you say the frictional force between the block and ground is $F = \mu F_N = \mu mg$ and for a heavy block this is going to be a large force:
But suppose you split your block into two parts, and you put a layer of oil in between the two parts like t... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
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"answer_id": 2
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If a ball is thrown to a person standing on a frictionless surface, is the impulse of the thrower equal to that of the catcher? If a person throws a ball, exerting a given impulse does the person that catches the ball receive the same impulse assuming that the catcher moves. Is the impulse that the catcher receives les... | As we know from the definition of impulse that $$ J = \int \vec{F} dt$$ and thus as thrower exert a Force for short time while the catcher have longer time for taking a force , So we concluded that Thrower have greater impulse than catcher. But there is also $\vec{F}$ sitting there, To make it simple let us suppose th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Given two states which are close in trace distance, are there purifications of these states which are equally close? Given a pair of state $\rho_A$ and $\sigma_A$ such that they are close in trace distance i.e.
$$|\rho_A - \sigma_A| \leq \epsilon,$$
can one find purifications of these states which are also $\epsilon$ c... | You might want to look at Uhlmann's Theorem: It is not about the trace distance, but a different distance measure, the fidelity, and states that the fidelity of two mixed states is equal to the maximum fidelity of their purifications - that is, their "fidelity distance" is the smallest "fidelity distance" over all puri... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528391",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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Generalising Cutting lens changes intensity of light of image We were told that if I cut a (say biconvex lens) in half, my intensity of light which forms the image is now half.I was wondering if there was a general formula for if I cut a lens horizontally (a variable,say 2/3 of the aperture),what intensity of light wou... | In terms of reducing intensity, there is no difference between adding an aperture to the lens (in front of it or behind it) or cutting out pieces of the lens. In a sense a cut lens is just an ordinary lens with a different type of aperture. In any case, the intensity is proportional to the area of the aperture/remainin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528482",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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What is the fastest moving macroscopic object people have made? The Parker Solar Probe will move at 690,000 km/h (430,000 mph), or 0.064% the speed of light, at its closest approaches to the sun. Parker Solar Probe top speed
Will that be the highest speed yet achieved by a manufactured, visible-size object? If not, w... | According to this Wikipedia page, the current fastest macroscopic man-made object was a shell (mass about 0.1 mg) in an inertial confinement fusion capsule driven by the National Ignition Facility. This particle was measured to be travelling at a speed of $445000\text{m/s}$ or $0.0015c$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528700",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
On the "spectrum" of an operator in quantum mechanics Very simple question, I'm new to this. I'm reading Griffiths book on QM and have a question about the "spectrum" of an observable operator. Does the spectrum of an operator require specification of a particular system? Or is the spectrum of an operator just every po... | The spectrum of a particular operator is the set of all possible eigen values.
In regards to the other answer: since the Hamiltonian of a system has a different form for different systems, also the spectrum of that Hamiltonian will vary with different systems. So talking about the spectrum of a Hamiltonian is equivale... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/528816",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
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$V$-$I$ characteristic of a solar cell please explain the VI characteristics of a solar cell. The characteristics is given in my book without any explanation. How can the Voltage decrease on increasing current shouldn't it be opposite.
Solar Cell I-V characteristics
(Image from Electrical 4 U - Characteristics of a S... | The characteristic is measured under illumination, when the solar cell is a source of electrical power, connected to a load. When the resistance of the load varies, one can get different points on the curve.
Compare with a battery: voltage decreases when a load is connected.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/529053",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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"answer_id": 3
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