Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why is the mean density the same for all nuclei? Tell me if this is a correct theory? So the radius $R$ of the nucleus is directly proportional to $A^{1/3}$ (the nucleon number).
As $$V = \frac 43 \pi r^3,$$ this makes $V$ directly proportional to $R^2$. Also, as the nucleon number increases, the mass also increases an... | Indeed, this is a non-trivial fact about the nuclei, as opposed to atoms. The atoms are held together by the Coulomb forces, and their density increases (i.e. they become more compact) as the charge of the nucleus and the number of electrons increase.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Eddy current confusion Every source tells that eddy currents are produced by change in magnetic flux in conductor, but according Gauss' law for magnetism net flux over a closed surface is 0, then how magnetic flux will change to produce eddy current?
| Assume you have a coil winded along z axis and a large metal plate put in xy plane. Then applying AC voltage across the terminals of coil eddy current induced on the metal but in this case charges are moving and using Gauss' Law considering the change in the magnetic apparently flux changes. With another setup, for ins... | {
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What is the Unruh effect for an accelerated observer in heat bath? The Unruh effect states an accelerated observer in flat Minkowski spacetime sees excited states in a heat bath with the Unruh temperature.
Then, when the initial rest observer is in a heat bath with the uniform temperature $T$ in the Minkowski spacetime... | Because the velocity of the observer has no effect on the temperature of the heat bath (reservoir) or, the other way round the temperature of a get bath is not dependent on the velocity of the bath, the answer is yes.
Of course at relativistic speeds, the mass of the bath will increase. But one can always find a refere... | {
"language": "en",
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Ceiling fans with just one large winglet? I am from India and in India ceiling fans have generally three wings.
Today while laying on my bed a question came in my mind.
First of all, I know that if we use just a single wing at a time of same dimensions as each wings of a three winged fans have then it will reduce the a... | A fan blade is just a wing. At the tip, air spills round creating a vortex in its wake. This wastes energy and reduces the efficiency of the wing.
A long, thin wing has a smaller tip, and hence smaller losses, than a short, fat wing of the same area. So the long, thin wing is more efficient. In other words, you need a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/580965",
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Magnetic, geographic and geomagnetic poles
Can someone explain me in simple terms where and what are the magnetic, geographic and geomagnetic poles?
Some sites say that magnetic north pole is in the south and thus it attracts the south pole of the magnetic needle while some say the north pole of the needle points sou... | The geographic poles are the North Pole and the South Pole of the Earth. These are not the actual magnetic poles, they are the axial poles. The magnetic poles are the actual poles of the Earth's magnetic field, but are not antipodal as they do not pass through the Earth's center. The geomagnetic poles are antipodal as ... | {
"language": "en",
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Universe and Anti-Universe pair Two years ago Latham Boyle, Kieran Finn and Neil Turok, in their work CPT-Symmetric Universe, proposed that the pre and post bang eras constitute a universe/anti-universe pair.
For Anti-universe in general we mean a universe rich in antimatter, that is matter composed of anti-particles, ... | This cosmology is one in which there are two independent expanding regions, one in the $+t$ direction from the origin and one in the $-t$ direction. The thermodynamic arrow of time points away from the origin, and there's an exact symmetry (CPT) that exchanges the two regions, so they're indistinguishable and we could ... | {
"language": "en",
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Why doesn't static friction point down the incline on a ball rolling down an incline?
In the figure above in which the sphere rolls without slipping down an incline, why is static friction directed upward? Static friction is meant to oppose impending motion so it should oppose the object's tendency to slide, and gravi... | The static force pointing upward doesn't mean the ball is accelerated upward. It's the force of gravity that does the job. It pulls on the ball, and if the ball doesn't slip, the static friction causes a torque, together with the force of gravity, which makes the ball roll downward.
| {
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Does a linearly accelerated charge radiate? Does a linearly accelerated charge radiate? And if yes, is the electromagnetic waves emitted detectable from both its non-inertial frame and from other observing inertial frame? And If yes, doesn't this contradict with Einstein Equivalence principle?
|
Does [a] linearly accelerated charge radiate?
"It depends". Accelerating relative to whom?
Is the electromagnetic waves emitted detectable from both its
non-inertial frame and from other observing inertial frame
No.
Doesn't this contradict with Einstein Equivalence principle
This is indeed an apparent paradox in ... | {
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Force on a relativistic laser source Consider a laser source emitting a laser beam in the horizontal direction. If we are given the power of the laser source, we can calculate the force on the laser beam.
Now consider that the laser beam is moving horizontally with a 0.5c. Would the force on the laser source change by ... | To someone riding alongside with the laser source (or in the same system of reference, in relativistic terms) the laser is behaving like it always did, with no increase/decrease in power output.
But the scenario of an observer experiencing a light source moving at relativistic speeds have a name - Doppler beaming, also... | {
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Why does the electric field have non-zero curl for magnetic monopoles? In Griffiths’ Introduction to Electrodynamics, he asks what changes would need to be made to Maxwell's equations to accommodate the existence of magnetic monopoles. Now, it is clear to me that the Gauss’s law and Ampere’s law must be left untouched.... | With the standard caveat that all theory is predicated on experimental validation, I would strongly expect magnetic charge to obey a continuity equation. If you make the modifications you suggest without changing Faraday's law to include magnetic current, then you would find that $\frac{\partial \rho_m}{\partial t}=0$... | {
"language": "en",
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How does light, which is an electromagnetic wave, carry information? We see an object when light from a source strikes the object and then reaches our eyes. How does light, which is an electromagnetic wave, gets encoded with the information about the object? Do the individual photons get encoded with this information o... |
How does light, which is an electromagnetic wave, gets encoded with
the information about the object?
There are several stages to this. Initially there has to be a light source emitting photons. This can be the object itself, but is more likely to be a separate light source such as the sun or a light bulb, usually a ... | {
"language": "en",
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If gravity is curvature of space why are more massive objects "heavier?" How does curved space explain why a denser object of the same shape and volume feels heavier?
| If we are only dealing with weights in a localized place at the surface of the earth, it is possible to use the principle of equivalence: the physical properties are the same as being in a spaceship in the outer space with an acceleration $g$.
Heavier objects here on earth would be equally heavier there. It is easy t... | {
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Meaning of Eigenvalues for position operator To each observable in quantum mechanics there is an operator corresponding to it. I don't understand what's the meaning of the eigenvalues of the $\hat{x}$ operator. Since $\hat{x}$ is hermitian, eigenvalues correspond to real numbers, what's their physical meaning? If they ... | Eigenvalues are the values that are measured in the experiment, i.e. eigenvalues of $\hat{x}$ are the values of the position obtained when measuring it. Every measurement will produce a different result, i.e. a different eigenvalue, unless the system was prepared in an eigenstate of the measured quantity - this is the ... | {
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Doubt on net acceleration during non-uniform circular motion During non-uniform circular motion, the direction of net acceleration is not in the direction of the centripetal acceleration, then why does a particle still move in a circular path, please explain.
| Let's look at a position vector in general polar coordinates
$$\vec r(t)=r(t)\pmatrix{\cos\theta(t)\\\sin\theta(t)}$$
Now define
\begin{align}
\hat r&=\pmatrix{\cos\theta\\\sin\theta}\\
\hat \theta&=\pmatrix{-\sin\theta\\\cos\theta}
\end{align}
to make our lives easier. I dropped the time dependence but remember it's s... | {
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If we repeatedly divide a solid in half, at what point does it stop being a solid? Suppose I have some material in solid-state (say), I cut it into two parts. Take the first cut it into two parts, take the first cut it into two parts, and then repeat this again and again. There will be a point when the substance loses ... | Suppose you start in the thermodynamical equilibrium of the solid at a given temperature and suppose "cutting" means also moving apart from each other by the mean free path in the gas-phase. For doing this you have to apply work. If you are finished with cutting (say you did this in the order of 3*Avogadro number of ti... | {
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Stokes law and speed at equilibrium It is stated that the equation leading to Stokes law describes an equilibrium state, such as the upwards force is equal to the downward force:
$$ 6\pi r\eta v = \frac43\pi r^3 (d_1 - d_2)g $$
Now $v$ is velocity, and velocity at equilibrium is $0$, and this is the breaking point of m... | (a) Your equation does not lead to Stokes's law but $incorporates$ Stokes's law. The law states that a sphere of radius $r$ moving at speed $v$ through a fluid of viscosity $\eta$ experiences a resistive force given by
$$F_\text{res}=6 \pi \eta r v$$
and is in the opposite direction to the body's velocity. It holds pro... | {
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Fourier Transform of $1/k^4$ I am dealing with a higher derivative theory problem and I have to perform the following integral,
\begin{equation}
\int \dfrac{d^3k}{(2\pi)^3}\dfrac{e^{i{\bf k}\cdot {\bf r}}}{k^4}
\end{equation}
This is because i have to solve something like $(\nabla^2)^2f=K\delta^3({\bf r}).$
I know that... | We can proceed exactly as in the case of the Coulomb potential i.e. Fourier transform of $1/k^{2}$. So, performing the same steps as in Coulomb case, we have
$ \begin{split}
\int \frac{d^{3}k}{(2\pi)^{3}} \frac{e^{i\vec{k}.\vec{r}}}{k^{4}} &= \frac{1}{(2\pi)^{2}}\int_{0}^{\infty} \frac{dk}{k^{2}} \left[\frac{e^{ikr} - ... | {
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Measurement of force (statics) body 1 and 2 are pulling the balance by 20 N
what does the balance read?
same question but without 2.
for 1st question I thought the balance will read zero force because they are two opposite forces of the same magnitude but it's wrong. the correct answer is 20N I don't know why
| For every weighing scale the force you exert is always counterbalanced by an equal and opposite force - that's the third Newton's law. If the scale lies on the ground, your weight would be opposed by the normal force coming from the ground, which is fixed; the same would happen with a Newton meter (or a spring balance)... | {
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Why do we use Eigenvalues to represent Observed Values in Quantum Mechanics? One of the postulates of quantum mechanics is that for every observable $A$, there corresponds a linear Hermitian operator $\hat A$, and when we measure the observable $A$, we get an eigenvalue of $\hat A$ as the result.
To me, this result see... | You might want to have a look at the ideas of Quantum Darwinism. I am not sure how popular this thoughts are, so decide for yourself.
As far as I understand there an attempt is made to explain why certain states are measured, based on how "stable" they are compared to other states when interacting with the measurement ... | {
"language": "en",
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Perpetual motion: Conditions for rolling a wheel sliding on a bar This is a basic question about energy conservation and classical mechanics:
Question: Under what situations can this motion be perpetual?
*
*Without gravity and without frictions.
*Without gravity and with frictions.
*With gravity and without fri... | Neglecting GR effects, the answer is clearly meant to be (1) for all speeds and (3) provided the inner gear is moving fast enough, because gravity is a conservative force.
| {
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Confusion about Lorentz Coordinate Transformation A normal Lorentz coordinate problem might say:
At $t=t'=0$, two coordinate systems $S$ and $S'$ have their origins coincide with the $S'$ system moving with speed $v$ in the $+x$ direction relative to $S$. If event 1 happens at $x=a$, $t=0$ in the $S$ system then when/w... | Consider Einstein's train thought experiment that demonstrates non-simultaneity. Let's say the train moves left to right. The lightning strikes at the front and back of the train occur simultaneously for the platform observer (S frame) but for the train observer (S' frame) the strike at the front of the train occurred ... | {
"language": "en",
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Which heat capacity is used in the heat equation? The heat equation is often written as $\frac{\partial T}{\partial t} = \frac{\kappa}{c} \nabla^2T$ where $\kappa$ is the thermal conductivity and $c$ is a heat capacity per volume.
I often see $c$ written as $c_P$ implying that it is the heat capacity (per unit volume) ... | Both options ($C_p$ or $C_v$) are approximations.
In the general situation, a non-rigid solid material will expand non-uniformly and therefore will have a time-dependent stress distribution, which stores internal strain energy.
The simplest assumption is that the object is not mechanically constrained and that the non-... | {
"language": "en",
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Many-world interpretation of double slit experiment Different interpretations of young's double slit experiment is available, I read Copenhagen and Feynman's path integral interpretation of double slit experiment; former uses the idea of wave function and later uses the idea of infinite paths and sum over the weight f... | Mathematically, the path integral is simply a way to derive the wave function.
The three interpretations you mention can broadly be summarised:
*
*Copenhagen The wave function is probabilistic and the selection of any given outcome is otherwise inherently random. Any underlying reality is inaccessible to science. Shu... | {
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Time for an object's afterimage to disappear at the event horizon My understanding is that as someone/something falls into a black hole, they would get dimmer and dimmer until disappearing entirely as they cross the event horizon. Most non-radiant objects would probably become invisible to outside observers well before... | The time will be proportional to the light crossing time of the black hole, which is less than a millisecond for a stellar-mass black hole, or around a day for the M87 black hole.
I don't have a source for the following derivation and it's possible I made a mistake.
An object radially infalling into a Schwarzschild bla... | {
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1-dimensional Heat Equation I have to solve the following differential equation:
$$ \partial _t u(x,t) = D \partial ^2_x u(x,t) $$
with the initial condition $$ u(x,0)=\exp \left( -100^2 \left( x-\frac{1}{2} \right) ^2 \right) .$$
The $x$ and the $t$ Interval is [0,1].
The Boundary Conditions are $$u(0,t) = u(1,t) = 0.... | As others have already pointed out, there exist many methods for solving this equation (separation of variables, integral transforms, Green's function approach, etc.) One thing that is worth noting is that here we are dealing with a problem with initial conditions. Thus, if we pursue the solution using Fourier transfor... | {
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Optics viewing angle and distance Almost all optics like microscope, telescope.. require observer putting their eyes very close to the optics to see.
Can the same optics designed so observer can see like viewing TV screen, i.e. from a larger distance like 30cm from optics? Or is it impossible?
| There are a few laws of optics that come into play here. Probably the most significant one is simply this: if you step back 30 cm from the exit aperture, the aperture now subtends a very small angular field of view. Since all the light coming from the telescope must pass through that aperture, it can't take up a large... | {
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Why amplitudes are rational functions? In Bootstrap and Amplitudes: A Hike in the Landscape of Quantum Field Theory there are few statements about analytical structure of amplitudes.
I want to understand statement:
Tree amplitudes must be rational functions of Mandelstam
variables.
What is the reason for such a prop... | @Anonjohn has given a good answer. I would like to add a bit more. I think, that the author of statement tacitly assumes dealing with massless theory with a linear dispersion relation (kinetic term of form $\phi \Box \phi $) : Why does nature favour the Laplacian?. So each propagator is of the form:
$$
\frac{1}{(\sum_{... | {
"language": "en",
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How to convince myself that capacitance cannot be a function of voltage? My textbook states that:
...The capacitance $C$ depends only on the geometrical configuration (shape, size, separation)of the system of two conductors. [As we shall see, later, it also depends on the nature of the insulator (dielectric) separatin... | $C$ can be a function of $V$, for example the capacitance of a varicap diode is controlled by the voltage across it.
However the voltage does not directly set the diode capacitance. What it does is to control the separation of the charge layers. It is this varying separation which results in the capacitance change.
Thu... | {
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Why doesn't planet Earth expand if I accelerate upwards when standing on its surface? According to General Relativity I am being accelerated upwards by planet earth while writing this question. But a curious person on the the other side of the planet relative to me would have the same experience. That means we are acce... | It comes down to a definition of acceleration. Acceleration is most universally appreciable as a force application contradicting an object's natural position or trajectory. Notice that this does not require that the object move -- only that it is being affected by a force, as in 'experiencing pressure'.
So by this defi... | {
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Why is Schrodinger equation taught while it does not describe an electron? Strictly speaking, it is "wrong" because it does not describe spin-1/2 particle like an electrons. Why in every QM textbook is it taught, not as a historical equation, but as a current equation?
| I think you are confusing the treatment of relativistic (spin-$\frac{1}{2}$ particles) electrons as compared to the non-relativistic case. The Schrodinger equation can perfectly describe the properties of the non-relativistic electron. The Dirac equation describes the interactions of relativistic electrons (and other s... | {
"language": "en",
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Rotating current carrying loop Consider a circular loop of wire fixed on the rim of a wheel. This wire carries a current 'i' in it. When the wheel is at rest, which basically means that the current carrying loop is at rest, the magnitude of magnetic field at the center is, say B1. If I set the wheel in motion with a co... | I'm thinking that with the wheel rotating, the motion of the positive charges will constitute an electric current that offsets the change in the motion of the free electrons.
| {
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When a sphere is in pure rotation, will all particles in its surface have same linear speed? Imagine this sphere to rotate about its diameter, from the centre to the point of surface if we take all of them have equal distance that is 'r(radius of the sphere)'.So same linear speed right? I looked up many sites but they ... | Linear speed of a point on a rotating object will depend on the angular speed and distance between the point and the axis of rotation. All points on a sphere are equidistant from the center of the sphere, but are not equidistant from an axis of rotation through the sphere. Consider the earth spinning about its axis - t... | {
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What will happen if I multiply a ket vector by a complex number? I was reading Zettili’s Quantum Mechanics book. There I have seen
when a ket (or bra) multiplied by complex number, we also get a ket (or bra)
But how do we infer this by mathematics?
| Two things happen, depending on the magnitude and phase of the complex factor. Both can be seen by examining what happens when you insert the factor $f$ in $\mid\Psi\rangle = f\mid\psi\rangle$.
Your primary observables are always bra-ket pairs, so calculate $\langle\Psi\mid\Psi\rangle=\langle\psi\mid f^*f\mid\psi\rangl... | {
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Will any solution to the wave equation be a wave in reality? In the mathematical sense, a wave is
any function that moves. In that sense we can consider that any function that complies with the wave equation (let's consider in one dimension to simplify things) will be a wave. But is this kind of thinking physically val... |
In the mathematical sense, a wave is any function that moves.
Not so, unless one defines the variables of the function, the above has no meaning. Wave equations are used in order to model observations of nature.
What is a wave? From sound and water waves we come to an association with sine and cosine variational beh... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Bernoulli Pipe Flow Equation Physical Meaning I have just been introduced to the Bernoulli Equation for fluid flow. However, I am unable to understand why the pressure and velocity are inversely proportional.
Because, as the fluid goes through a smaller cross-sectional area, the flow velocity increases, but due to the ... | If the pressure in the small diameter, where the flow has greater velocity, was equal or greater, we could take a derivation from that region and inject the fluid back in the region of big diameter.
In this case, the average velocity in the region of big diameter would increase, leading to increased velocity in the reg... | {
"language": "en",
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Is $U^\dagger(R)\hat{H}U(R)=\hat{H}$ always true? Consider a Rotation transformation on momentum state,
$$U^\dagger(R)\hat{\mathbf{p}}U(R)=R\hat{\mathbf{p}}$$
Now the question is whether,
$$U^\dagger(R)\hat{H}U(R)=\hat{H}\,?$$
Here, $\hat{H}$ is the Hamiltonian of a free particle. Is it always true? Is there any counte... | If the operator $U$ is indeed the unitary operator, then
$U U^{\dagger}= U^{\dagger} U = 1$
then expression you have (which appears to be applied incorrectly) above will reduce back to its original form
$\frac{1}{2m} U^{\dagger} p^2 U = U^{\dagger} H U = H$
| {
"language": "en",
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Magnetic field around a current carrying wire and Special Theory of Relativity I understand how the magnetic field and electric field (around a current-carrying conductor) swap their roles depending on the frame of reference, due to the effect of length contraction (in the special theory of relativity); however, this q... | In a frame with two equal charges (a source charge and a test charge) separated by $y$:
The electric field from the source at the test charges is:
$$ \vec E = k_e \frac q {y^2} \hat y$$
and the force on the test charge is:
$$ \vec F = q\vec E = k_e \frac {q^2} {y^2} \hat y$$
If we boost this by $\vec v = -v\hat x$ so t... | {
"language": "en",
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"source": "stackexchange",
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Why can we set $c$ and $\hbar$ to 1 when it changes the result? So in my QFT course, my professor said that you can set $c$ and $\hbar$ to 1. And he gave us an example:
$$E = mc^{2}$$
And then set $c = 1$:
$$E = m$$
This seems completely ludicrous to me to do. Doesn't it change the result? Why can this be done and why ... | If you ask two doctors how much you weigh and one doctor says “you weigh $100\text{ kg}$” and the other doctor says “you weigh $220\text{ lbs}$”, would you claim that they have given you completely different answers? No. They gave you the same answer using different units.
Setting $c$ or $\hbar$ to 1 is simply choosing... | {
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Does the second law of thermodynamics imply that renewable energy also leads to global warming/climate change? So I have this (possibly dumb) question about the implications of the second law of thermodynamics to the use of renewable energy for the world, so please bear with me. Here goes: Apart from the finiteness of ... | There is no increase in heating from solar or wind power, because they're using energy that's already in the system. Yes, it all eventually gets converted to heat--but it would anyway. Sunlight not falling on solar panels would fall on something else; wind hitting wind turbines would otherwise run into buildings, tre... | {
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"source": "stackexchange",
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Charge conjugation of fields This page on Wikipedia says, "In the language of quantum field theory, charge conjugation transforms as -
*
*$\psi \Rightarrow -i\big(\bar{\psi} \gamma ^0 \gamma ^2 \big)^T $
*$\bar{\psi} \Rightarrow -i\big(\gamma ^0 \gamma ^2 \psi \big)^T $
Could someone explain the reason behind choos... | The charge conjugation symmetry is the proper time reversal symmetry.
It becomes an exact symmetry of relativistic quantum systems if we combine with space-time time reversal and parity, due to unitarity.
About the techinical details you are raising I think that this transformation looks complicated just in you notatio... | {
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If you keep the center of gravity of two objects on each other would you never be able to separate them? To find the attractions between planets and stuff like that, you use the center of gravity/mass to apply to Newton's equation. So even if those planets collided into each other, you could separate them if you give e... | The idea that the force between two spherical bodies goes as $1/r^2$ is only valid outside of the bodies.
Once you're inside the bodies, things are different. If the bodies are of uniform density, the "shell theorem" applies, and the force goes to zero as $r$ goes to zero. (It may not be obvious, but if you work out ... | {
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Prove that the elements of the dual frame of an IC POVM cannot be positive I've read a claim about POVMs in my lecture notes, which I fail to prove. Hence, I would be grateful if some of you have some hints for me /can help me.
Let $\{N_i\}_{i=1}^{d^2}$ be an informationally complete POVM on $Herm(V)$, where $V$ is a H... | Suppose $D_k \geq 0$ for all $k$. Notice that all the $D$ operators have unit trace.
For two PSD matrices it holds that, $Tr(AB) \leq Tr(A)Tr(B)$.
This implies that, $Tr(N_k D_k) \leq Tr(N_k)$ for all $k$
Now we know that $Tr(N_k D_k) = 1$. So if all the dual operators were PSD, we would have the $Tr(N_k) \geq 1$ for a... | {
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How do wavelengths add-up? If I have 3 LED lights of following colors and wavengths:
Red 650 nm
Blue 450 nm
Green 550 nm
All three are placed side by side and turned ON.. then what will be the wavelength of the combined light that my eye will see? Most probably the combined color will be 'whitish' because the mixing of... | Wavelengths are one to one only with the spectral colors, and wavelengths do not add up to a new one, they remain distinct .
It is the perception of color which is a biological function, due to the receptors of the eye, which creates new hews and colors when more than one wavelength falls on the retina of the eye.
... | {
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How much energy is in the Universe as photons? The mass of Universe in kilograms is about 10 power 53.
But how much energy exists in the Universe in form of photons?
And if they would all be converted into mass, how much mass that would make?
Dark matter and dark energy are out of the question.
| Mass of the "observable" universe is about 10 to the power of 53. However, the answer of your question would be irrelevant, since what we have observed and measured is practically from the past. For example, the measured mass of a star in 1 billion light years from earth has added up to the calculation to get the "10 t... | {
"language": "en",
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Is the Green function of electromagnetism a scalar or a tensor? When I check classical electromagnetism books Maxwell equations
\begin{equation}
\Box A^\nu (x)=\frac{4\pi}{c}j^\nu (x)
\end{equation}
can be solved using a scalar Green function $G(x,x')$
\begin{equation}
A^\nu (x)=\int G(x,x')j^\nu (x')d^4x'
\end{equatio... | Index $\nu$ has nothing to do with the equation itself. The equation does not know whether $A$ and $j$ are scalars, 4-vectors on spinors. The equation itself is scalar type, so its Green function can be scalar only.
Another argument: let say $A^\nu$ is a solution for $j^\nu$. Then $C^\mu_\nu A^\nu$ must be solution for... | {
"language": "en",
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"source": "stackexchange",
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Why can’t gravitons distinguish gravity and inertial acceleration? If gravitons mediate the gravitational force, couldn’t the detection of gravitons by an observer be used to distinguish whether they are experiencing gravitational acceleration vs. inertial acceleration, contradictory to general relativity? If this is n... | In the language of quantum field theory, the gravitational force is self-coupling, which means that gravitons carry gravitational charge and can feel the gravitational field.
In the language of general relativity, sufficiently small gravitational waves are perturbations of spacetime travelling in a curved background sp... | {
"language": "en",
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Why don't we use the concept of axis of mass in place of center of mass? Being a high school student, I read the concept of center of mass and it was written in my book that
When a spinning ball is projected with some velocity , then all the points on the ball have complicated paths except the center of that ball whic... | If the ball has a single axis of rotation, then all points on that axis will not rotate (that's pretty much the definition of "axis of rotation"). However, it's possible for a ball to have more than one axis of rotation simultaneously, so while their claim is misleading in that it implies that all non-center points alw... | {
"language": "en",
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"source": "stackexchange",
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Effect of coloured filters on white light I am concerned about the accuracy of some information in a science textbook which I would like to clarify please. When white light is shone through a blue filter, only blue light will pass through. When the emergent blue light is passed through a red filter, no light gets thro... | My guess is that the author of the textbook has the common misconception that there are only three colors—red, green, and blue—and yellow is red+green. Therefore, you're expected to answer that the red+yellow filters will let through red light, and the green+yellow filters will let through green light, and the others w... | {
"language": "en",
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How is a free theory defined? In field theory, I've seen a free theory described as
*
*A field with the specific Lagrangian density ${\cal L}=|\partial\phi|^2+m^2\phi^2$
*A field whose equation of motion yields a linear set of solutions
*A field with non-interacting i.e. free normal modes
The first seems too speci... | I believe the problem with all the definitions is that they are not well defined. I can always make a highly non linear field redefinition and make a free quadratic Lagrangian appear interacting. That's why the best way to define a free field theory is to say that it's S matrix must be unity.
| {
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Reduced density matrix: Derive or postulate? Let us consider a quantum mechanical system of interest S that interacts with the environment E. Then, the reduced density matrix
$$
\hat \rho_\mathrm{S} = \mathrm{Tr}_\mathrm{E} \{ \hat \rho \}
$$
is the partial trace over the environment, where $\hat \rho$ denotes the ... | Usually this expression is neither postulated nor derived, but rather a serves as a definition of the reduced density matrix.
For more context let me add:
Reduced density matrix typically appears in certain contexts, notably, when you consider a system coupled to a bath, and want to trace out the degrees of freedom of ... | {
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Why does a capacitor act as a frequency filter? What is it about a capacitor which allows it to filter frequencies?
I understand the construction of a high-pass RC filter, and the mathematics behind it, but I'm struggling to find an explanation of the physics behind the phenomenon.
In my mind I can picture the broad sp... | A capacitor along with a resistor can act like a filter because its impedance is frequency dependent and by division of voltage between resistor and capacitor it works.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/590006",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 10,
"answer_id": 5
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Why is there a density instead of mass in the Navier-Stokes Equation, if it's analogue to Newton's Second Law? I read in Ian Stewart's 17 Equations that Changed the World book that Navier-Stokes equation (I know it's not exactly a scientific book, but still, I'd like clarification on what is wrong if it's the case):
$\... | The Navier-Stokes equation describes the motion of some infinitesimal volume of the fluid. That is we divide the fluid up into tiny volumes $dV$ and the equation tells us how these tiny volumes move. The overall motion of the fluid comes from combining the motions of all these tiny volumes.
So the equation is really:
$... | {
"language": "en",
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How does one determine which signs to take for the Gradient Wind Equations? Under geostrophic balance, one can write
$$\frac{V^2}{R}+fV-fV_g=0$$ where $V:$wind speed, $V_g:$ geostrophic wind speed, $f:$ Coriolis parameter, and $R:$ radius of curvature.
Solving for $V$, we can get a relationship between $V$ and $V_g$ as... | It's a general problem that quadratic equations have two roots when only one is expected. One will then be unphysical and we have to decide which is the one we want.
In this case we can proceed as follows: When $|R|$ becomes very large (either positive or negative) then the centripetal acceleration becomes negligible... | {
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Does mass really exist? In elementary physics, I have learned mass as the amount of matter (naively) and energy as the ability to do work. Now we know that they interchangeable by famous Einstein's equation:
$$E=mc^2$$
It seems from here that they are interchangeable, but then I watched this video, which says, in a nut... | Mass is the proportional coefficient between force and acceleration. In everyday life it's necessary,but in models without particle-like things you can throw it away.
In some particle models it is interchangeable with energy, but the buildup of the model needs its concept.
| {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Properties of the dot product Suppose we have three vectors $\textbf{A}$, $\textbf{B}$ and $\textbf{C}$. If $\textbf{A}\cdot\textbf{C}=\textbf{B}\cdot\textbf{C}$, does that mean that $\textbf{A}$ must be equal to $\textbf{B}$? If so, can this property be proven?
Though the question is mainly mathematical, it has occurr... | If for given $\vec A$ and $\vec B$ the equality $\vec A\cdot\vec C = \vec B\cdot\vec C$ holds for all vectors $\vec C$, or at least for a set of generators (say, a basis), then we can conclude that the two vectors are equal, otherwise we can't.
I will try to make it plausible: If we take the standard basis $\{\vec e_x,... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Can someone explain the measurement problem with little bit of mathematics? Can someone mathematize the statement of the quantum measurement problem? I am only interested in the statement of the problem (and not its solutions). Thanks.
Still confused. Stated in this way (as in the current answers), the measurement pro... | The actual act of measurement and the subsequent collapse of the wave function is not a dynamical process and hence has no mathematical equations to quantify or describe this process.
This is why there are various interpretations of the measurement/collapse process.
| {
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Why does power increase as a constant force accelerates a body? If a constant force is being applied to a body, without any other external forces, F = ma says that that body will accelerate at a constant rate. This acceleration will continuously increase the body's velocity.
According to P = Fv, since the force is cons... | There is no internal mechanism, imagine a ball falling in a constant gravitational field. It basically means that the same force acts for a longer distance (not a longer time) if the speed is larger. Intuitively, for a conservative force like gravity this means that you get potential energy faster
| {
"language": "en",
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Can there be waves in different fields? I am a physics fan, but I am not a physicist. I don't even know that the question I have asked make sense or not.
There can be waves in the gravitational field. So I would like to know if there can be waves in other types of fields, such as electromagnetic field, Higgs field etc.... |
Can there waves in different fields?
Yes. You have already heard about waves in the gravitational field. They were first detected about five years ago!
Waves in the electromagnetic field include light waves, radio waves, microwaves, etc. These electromagnetic waves simply differ in their frequency and wavelength. Oth... | {
"language": "en",
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Orbit with crash Let's assume I shoot an object from a high tower horizontal to the earth's surface. As far as I understand, depending on the velocity I will get different types of orbits. With decreasing velocity I will go from
*
*hyperbolic orbit where the focal point is the earth's center
*parabolic orbit where t... |
transparent for the thrown object
Worth mentioning an alternative to point-mass orbits here. Assuming the Earth was literally transparent to the object, but all the mass was still there, distributed over the full volume.
Assuming uniform density, we now have a central force field where gravity is proportional to $r^1... | {
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Canonical Transformation in Quantum Phase Space I am looking for a unitary representation $\hat T$ of the following canonical transformation
\begin{align}
q_1&\rightarrow q_2 &p_1&\rightarrow p_2\\
q_2 &\rightarrow -q_1&p_2&\rightarrow -p_1
\end{align}
which is a 90°-rotation in the $(q_1,q_2)$-subspace of a 4-dim pha... | Skip the silly hats--everything is an operator.
Observe the obvious invariants
$$
I=q_1^2+ q_2^2, ~~~ J= p_1^2+p_2^2.
$$
Observe the hermitian operator
$$
r=q_1p_2-q_2p_1
$$
commutes with both of them, so it's worth considering its effect on your four variables,
$$
[r, q_1]=iq_2 \\ [r, q_2]=-iq_1 \\ [r, p_1]=ip_2 \\ [... | {
"language": "en",
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Why is the proof that the product of a linear operator with it's adjoint always given in terms of the inner product? The proof that $LL^\dagger$ is Hermitian, where $L$ is a linear (but not necessarily Hermitian) operator, is usually given in terms of the inner product, i.e:
\begin{align}
\langle \phi |LL^\dagger |\psi... | When you write
$$(L^†L)^† = (L^†)(L^†)^† = L^† L$$
you are implicitly using two facts, that $(AB)^† = B^† A^†$ and that $(A^†)^† = A$.
If you already accept those facts then the second version is fine. But if you want to prove those two facts you will need to consider the inner product.
You must consider the inner prod... | {
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Importance of center of mass for ceiling fan I am learning about center of mass these days. While doing so, I encountered the equation
$$\sum {F_{external}} = ma_{com}$$
Then, it was written that with the help of this equation, it can be clearly seen that if the blades of ceiling fan are not kept at 120° the center of ... | The answer to your question can be found here. It is a process called precession which is a change in the orientation of the rotational axis of a rotating body ... other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis.
Because the... | {
"language": "en",
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"source": "stackexchange",
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Black rings in 4D gravity In Introduction to Black Hole Physics by Valeri P. Frolov, Andrei Zelnikov there is a discussion of gravity solutions. They present some examples of solutions with non-spherical horizon topology:
But such solutions are known in 5D.
About the possibility of such solutions in 4D authors say:
I... | Yes, in 4D the topology censorship theorem seems to rule them out:
Every causal curve extending from past null infinity to future null
infinity can be continuously deformed to a curve near infinity.
Roughly speaking, this says that an observer, whose trip begins and ends near infinity, and who thus remains outside all... | {
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Why topologically non-trivial materials are robust againist any external perturbations or defects? Topologically non-trivial materials are insensitive to perturbations or defects. How can I prove it mathematically?
I thought of making the first-order perturbation term zero.
$$\left< \psi \right|H'\left| \psi \right>=0$... | For the sake of this explanation, let's concentrate on systems that have a spectral gap (not the most general scenario but it shall do).
Let $P$ be the Fermi projection of some topological material $H$ such that its Fermi energy is placed inside of a spectral gap of $H$. We have the Riesz formula $$ P = -\frac{1}{2\pi\... | {
"language": "en",
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Destructive interference Take the most simple academic example for interference. Since it is not any real experiment, one can have shocking contradictions.
For example: 2 monochromatic plane waves with (parallel) amplitudes propagating in the same direction. The Poynting vectors of the 2 waves without superposition are... | The energy balance is indeed an interesting problem. For a monochromatic plane wave the source is an infinite sheet of sinusoidal current.
It is not trivial but is straightforward to calculate the Poynting vector for this arrangement. When you do so you find that energy propagates away from the current sheet with equal... | {
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Matsubara sum with log term How do I compute the Matsubara sum
$$\sum_n \log\left(-i\omega_n +\frac{k^2}{2m}+\mu\right)?$$
If I have sums like
$\sum_n \frac{1}{i\omega_n -m}$, I can sum it up by calculating the sum of residues of the function $\frac{1}{z-m}g(z)$ at the poles where $g(z)=\begin{cases}
\frac{\beta}{\exp... | S=$\sum_n\ln(-i\omega_n+\epsilon)=\sum_n\ln(i\omega_n-\epsilon)+C$
(usually this is an action and the constant is irrelevant. This transform is unneccessary just for convenient)
$=\mathrm{Res}\left\{\ln(z-\epsilon)g(z)\right\}$
when $g(z)$ is what you've mentioned. Then the problem is to evaluate this integral. We coul... | {
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Problem with the proof that for every timelike vector there exists an inertial coordinate system in which its spatial coordinates are zero I am reading lecture notes on special relativity and I have a problem with the proof of the following proposition.
Proposition. If $X$ is timelike, then there exists an inertial coo... |
The 3+1-Lorentz transformation is
\begin{align}
\mathbf{x}^{\boldsymbol{\prime}} & \boldsymbol{=} \mathbf{x}\boldsymbol{+} \dfrac{\gamma^2_{\mathrm u}}{c^2 \left(\gamma_{\mathrm u}\boldsymbol{+}1\right)}\left(\mathbf{u}\boldsymbol{\cdot} \mathbf{x}\right)\mathbf{u}\boldsymbol{-}\dfrac{\gamma_{\m... | {
"language": "en",
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"source": "stackexchange",
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Why thin metal foil does not break like a metal stick? Consider a metal stick, say iron or aluminum. From the experience, even if it's resilient, bend it forward and backward a couple of times, it would be broken.
However, consider a thin iron foil or thin aluminum foil. From the experience, we know that it could be be... | "Thin" is a relative term, but let's assume we're talking a foil that's 0.01 to 0.02 mm thick (i.e., kitchen aluminum foil). Let's also assume that our foil is a soft alloy -- i.e. nearly pure aluminum or iron.
If I take a piece of kitchen foil and I bend it with my hands, the bend radius is likely going to be no less... | {
"language": "en",
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"source": "stackexchange",
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Regarding the velocity of waves in even dimensions A few years ago I asked on Reddit about the behavior of wave propagation in even and odd dimensions. I received this answer:
"The answer lies in the solutions to the wave equations. Essentially, in odd dimensions a wave will propagate at a single characteristic velocit... | I assume a wave equation $(\Box +m^2) f = 0$. This is simply the wave version of Einstein's famous relation $E^2 = m^2c^4 + p^2c^2$. Thus $v \in [0,c)$ for $m\neq0$ and $v=c$ for $m=0$ for any positive number of space dimensions.
| {
"language": "en",
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How to solve this problem only using the kinematics of rotational motion? This is a problem from my introductory physics textbook:
A wheel of moment of inertia $I$ and radius $r$ is free to rotate about its centre. A string is wrapped over its rim and a block of mass m is attached to the free end of the string. The sy... | The case with a massless wheel is a bit boring, because it is just the case without a wheel, i.e., a free falling body.
In classical mechanics, there is always multiple routes that lead to the same answer, so you could start from the kinematics equations if you can argue that the angular acceleration $\alpha$ is consta... | {
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Determine the direction of electric and magnetic field in for plane EM wave A problem states that
Measurement of the electric field (E) and the magnetic field (B) in a plane-polarized electromagnetic wave in vacuum led to the following:
$$
\begin{array}{ll}
\frac{\partial E}{\partial x}=\frac{\partial E}{\partial y}=0... | The direction of the fields (perpendicular to the direction of propagation) is determined by the source of the wave. If you consider a positive charge oscillating back and forth, the motion of the charge introduces a transverse component into the (preexisting) electric field (in the direction of motion). The motion al... | {
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Two Cylinders on Ramp Suppose I have two cylinders: a light one and a heavy one. Now, I let the cylinders roll down a ramp without slipping. My question is, which one will get to the bottom of the ramp first, and why?
| There's an intuitive proof that two cylinders differing in only density will roll with the same speed: just superimpose two cylinders with the same mass. The cylinders will roll at the same rate. But together they make a cylinder of twice the mass, that is also rolling with the same rate. As a practical matter, giving ... | {
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Why is gravity considered a negative vector in a pendulum question? In many places and tutorials, gravity is often considered as a negative vector.
I am confused as to why is that? I though I was missing something from trigonometry but it was just negative in first place. It is pointing downwards, but if we negate that... | Other answers are good, but I think there is a misunderstanding of the OP that needs to be addressed.
There is often an ambiguity on the meaning of $g$, that can be used for two related things:
*
*The scalar $g$, that it's about $9.81 \text{m}/\text{s}^2$
*The vector $\vec{g}$, which points downward. $\vec{g}=(0, 0,... | {
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Kinetic energy and curvature In quantum mechanics, the kinetic energy of a particle described by the wave function $\psi$, is related to the curvature of the $\psi$. This is easily seen, but I have confused my self with the negative sign. That is: $\hat{T} = -\frac{\hbar^2}{2m}\nabla^2$, is the kinetic energy operator.... | What you mean by 'curvature' is often negative. Take the sine wave $\psi(x)=A\sin kx$. Larger $k$ means larger curvature. By taking the 1D kinetic energy operator we get
\begin{align}
-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}\psi(x)&=-\frac{\hbar^2}{2m}\left(-k^2 A\sin kx \right)\\
&=\frac{\hbar^2k^2}{2m}\psi(... | {
"language": "en",
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Why is the tension on both sides of an Atwood machine identical?
The field forces $F_{g1}$ and $F_{g2}$ push down on Block 1 and Block 2, respectivley, where
$$F_{g1}=m_1g$$$$F_{g2}=m_2g$$
Since the pully system reverses the direction of each force, wouldn't the following be true?
$$T_1 = F_{g2} = m_2g$$$$T_2 = F_{g1}... |
Since the pully system reverses the direction of each force, wouldn't the following be true?
T1=Fg2=m2g
T2=Fg1=m1g
Technically you are correct. But a few changes have to be made to your statement.
The blocks are not at rest and both travel with acceleration $a$. We can assume that $M_1$ goes up and $M_2$ goes down. S... | {
"language": "en",
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Can coldness be converted to heat energy? We know that the heat can be converted into heat energy with the help of thermoelectric generators, but why can't we generate energy from coldness?
Like the temperature of the universe in 1 K, can this be used in the near future to be used as an energy resource for probes or sa... | Strictly speaking, heat is not converted into energy - instead heat is energy. A thermoelectric generator is sometimes loosely described as turning heat into energy, but what actually happens is that a temperature difference between a heat source and a cold sink (usually the surrounding environment) causes heat/energy ... | {
"language": "en",
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Spin part of the angular momentum from the Lagrangian For fermions of spin $1/2$ the angular momentum has following form:
$$
\mathcal{J}_z = \int d^{3}x \ \psi^{\dagger} (x) \left[i(- x \partial_y + y \partial_x) + i\sigma^{xy} \right] \psi(x)
$$
Here the first term is orbital part and the latter one is the spin part o... | The symmetric EM tensor does contain the spin. There is a discussion by Michael Berry about this, and also some in Wikipedia here
| {
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Integrating cross products I know that while integrating dot product to two vector quantities along a line integral, the limits of the integration implicitly takes care of the direction in which we integrate from here and here.
But would this be true in case of cross products? Would the limits of the line integral of a... | In general, limits on an integral over a subset of $\Bbb R^n$ implicitly take care of integration direction. (The case $n=1$ is familiar; if $a<b$ the directions for $\int_a^bfdx,\,\int_b^afdx$ are obvious.) It doesn't matter whether what's integrated is a univariate dot product, a $3$-dimensional cross product or in g... | {
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Why does ponytail-style hair oscillate horizontally, but not vertically when jogging? Many people with long hair tie their hair to ponytail-style:
Closely observing the movement of their hair when they are running, I have noticed that the ponytail oscillates only horizontally, that is, in "left-right direction". Never... | As @nuclear-hoagie said, the ponytail is basically a pendulum, so vibrations up and down are not really possible (or are much more complicated) as the hair would have to elongate itself in order to store the kinetic energy from the hair falling down so it cannot release it later. However the sideways and back and forth... | {
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Can spacetime be curved even in absence of any source? Einstein's equation in absense of any source (i.e., $T_{ab}=0$) $$R_{ab}-\frac{1}{2}g_{ab}R=0$$ has the solution $$R_{ab}=0.$$
But I think $R_{ab}=0$ does not imply that all components of the Riemann-Christoffel curvature tensor $R^c_{dab}$ be zero (or does it?). F... | What you're asking about is referred to as a vacuum solution to the field equations. This does not mean that there is no mass anywhere, rather that we are considering a region of our curved spacetime in which there is no mass.
The Schwarzschild solution for instance is a "vacuum solution" because we are considering the... | {
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We know a human cannot run on water, but could a much stronger and faster animal? We know a human cannot run on water, but could a much stronger and faster animal?
This viral video shows a moose running across a body of water:
https://www.youtube.com/watch?v=K5-0d00hV1c
Some say the video is fake. Others think the wat... | Humans, always overlooking the world of the small. It is as vast as the big world, hence strength is relative. So the answer is: insects. As long as they are not winged, etc. which of course can be sure death-trapping appendages, many insects are too light to break the surface tension of water. Yet if you want to narro... | {
"language": "en",
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3 pulley atwood machine with 2 blocks and 1 free-moving pulley I'm supposed to use the Lagrangian approach in the solution. I've just recently started classical mechanics course and it's still somewhat confusing to me.
The problem I am working on is as follows: "2 masses $m_1$ and $m_2$ are connected with a line acros... | There is one Lagrangian for both $x$'s, but there is a separate Euler-Lagrange equation for each of $x_1$, $x_2$.
| {
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Physical meaning of $\frac{π}{8}$ in Poiseuille's equation Recently I read about the Poiseuille's equation which relates the flow rate of a viscous fluid to coefficient of viscosity ($\nu$), pressure per unit length($\frac{P}{l}$) and radius of the tube ($r$) in which the fluid is flowing. The equation is
$$\frac{V}{t}... | Poiseuille's law is the result of doing a a force balance on the fluid, applying Newton's law of viscosity between the fluid velocity gradient radially and the shear stress, solving for the fluid axial velocity distribution, and integrating the velocity distribution to get the volumetric flow rate. The $\pi/8$ comes i... | {
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Radiation Within a Faraday Cage - Can It Escape? so we all know that the Faraday Cage prevents most EM radiation from entering the Faraday Cage. But what about, if we place radiation within the Faraday Cage - can it escape outside? I sort of recall working in class on a lab and finding that yes, it does escape - becaus... | In a case of cage being a closed shell made of perfect conductor, no radiation should be present outside, because charges on the inner surface will move in such a way that all radiation is reflected from the inner walls back to the insides. They work like a mirror for all frequencies.
This is why perfectly reflecting c... | {
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Intrinsic relations between two solutions Recently I've encountered a problem stated as follows:
A smooth bowl has the shape of a paraboloid. The equation of the cross-section with the $(x, z)$-plane is $x^2= 2R_Az$, where $R_A$ is the curvature radius at point $A$. One releases at a point with height $z=h$ a point mas... | In your first solution, you have assumed that the centripetal acceleration is $v^2$/R (based on what you know about circular motion). In the second, you have shown that, in this situation, the vertical acceleration is $v^2$/R at point A.
| {
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Near point and focal length of the eye What is the relationship between near point and focal length of the eye?normally in a convex lens when the object is kept at 2f we get the same size image as shown . A healthy human eye can see objects without any trobles. Then is the near point of the eye, 2f of the eye lens? Im ... | As I recall, a relaxed lens of a healthy eye puts the image of nearby (but not close) objects on the retina of the eye. For distant objects, the muscles around the lens must make minor adjustments to the shape of the lens (unless you are far-sighted). For nearby objects, the muscles must work harder to shorten the foc... | {
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What is the velocity $u^\mu$ in the stress-energy-tensor of a perfect fluid? I am currently learning about fluid dynamics in special relativity. We defined the stress-energy-tensor of a perfect fluid to be
\begin{equation}
T^{\mu \nu} = (\rho + P) u^\mu u^\nu + P g^{\mu \nu}.
\end{equation}
We said that $u^\mu$ is the ... | The MCRF is not a single frame: there is a different frame at each spacetime point. The summation for the bulk velocity doesn't run over all particles: it runs over a small region surrounding the chosen point, much smaller than the typical distances we will be considering in our study of the fluid, but much larger than... | {
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Functional derivative in Faddeev Popov method (Lorenz Gauge) When applying Faddeev and Popov method (am using Peskin and Schroeder as reference), we use the identity:
$$1=\int \mathcal{D}\alpha(x)\delta(G(A^\alpha)) \det\left(\frac{\delta G(A^\alpha)}{\delta\alpha}\right) \tag{9.53}$$
to write
$$ \int \mathcal{D}Ae^{iS... | $$\begin{align}{\rm Det} \left(\frac{\delta G}{\delta \alpha}\right)
~=~&\int {\cal D}c{\cal D}\bar{c}\exp\left(\int \!d^4x \int \!d^4y ~\bar{c}(x)\frac{\delta G(x)}{\delta \alpha(y)}c(y) \right) \cr
~=~&\int {\cal D}c{\cal D}\bar{c}\exp\left(\int \!d^4x \int \!d^4y ~\bar{c}(x) \frac{1}{e}\partial_x^2\delta(x-y) c(y) \... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Shouldn't some stars behave as black holes? Some of the "smaller" black holes have a mass of 4-15 suns. But still, they are black holes.
Thus their gravity is so big, even light cannot escape.
Shouldn't this happen to some stars, that are even more massive? (mass of around 100 suns)
If their mass is so much bigger, sho... | If the visible matter became enough dense to be concentrated inside its Schwarzschild radius, it becomes a BH.
Until their inner pressure withstand the gravitation they stay being stars.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/596400",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Applications of representation theory of finite group in physics? Well, I have just finished my study on basic representation theory of finite group from a pure math course. After tortured a lot by abstract constructions, I would like to know the real application of this theory, however, it seems to me not many topics ... | The moonshine phenomenon is a deep subject involving conformal field theory and string theory that is based on the observation of some relationships between the representation theory of finite groups of "big size"(but finite) and modular forms (obtained as partition functions of some CFTs).
References:
Miranda Cheng - ... | {
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Writing a simple sum with einstein notation Is there any shorthand using the Einstein notation to write a simple sum?
$X = X_1 + X_2 + X_3 ....$
Can I write: $X = X_i$ ?
I don't think so because the definition states that only indices that appear twice is summed over. What is the correct way to write a simple sum like ... | The Einstein summation notation includes repeated indices (i.e. summation notation). For vectors (and tensors), $X$ would usually mean the full object, $X = X^{i} e_{i} = X^{0}e_{0} + X^{1}e_{1}...$ etc. The $X^i=X^i (x)$ are the components of the vector and $e_i$ is some basis. The $i$ deonotes the components, and thi... | {
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Mass of the fundamental particles I have always wondered that how do scientists measure the mass of a fundamental particle.
Obviously they can't weigh it in a conventional machine we use to weigh other things in our daily life.
And do they use the formula:
$$E^2=m^2c^4+p^2c^2$$
| The mass of particles can be measure in a variety of ways depending on what's the particle is( and How precise measurement you want). For instance, an electron's mass can be measure as follows
The electron rest mass can be calculated from the Rydberg constant $R_∞$ and the fine-structure constant $α$ obtained through s... | {
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Why a fan make us feel colder instead of warmer in a cold room? Stay in a cold closed room, turn on a fan directed at you, it makes you feel colder instead of warmer. why?
Here is the definition of heat:
Matter exists in different physical forms – solids, liquids, and
gases. All matter is made of tiny particles called... | Others have given wonderful answer. But I think one more point is necessary here.
Why does a wet cloth become dry when the wind is blowing ?
Actually if we take a closed beaker half filled with water and vacuum in the upper half then the upper half is not vacuum after sometimes. This is because some of the higher ener... | {
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Relativistic energy of harmonic oscillator What is the relativistic energy of an harmonic oscillator:
$$\frac{m_0 c^2}{\sqrt{(1-\frac{v^2}{c^2})}}+\frac{1}{2}kx^2$$
Or
$$\frac{{m_0 c^2}+\frac{1}{2}kx^2 }{\sqrt{(1-\frac{v^2}{c^2})}}$$
I think the first one is true but I need an exact logic or derivation.
| First of all the speed $v$ is the property of the particle. The points on spring move at different speeds. So you can't write like the 2nd one. Even the 1st one is wrong. Also practically speaking the Hooks law works only for small distances and velocities, and after that it fails. If you assume there exists a mass les... | {
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How can a bicycle keep its momentum while changing direction? I was riding my bicycle downhill. When the street leveled I realized I had forgotten something so I started turning around without pedaling, pretty much using the momentum I had acquired. Soon I was moving in the complete opposite direction, still without ha... | Your momentum is not conserved because there are external forces acting on the you + bicycle system. Though there are several external forces, the main one is friction.
The friction from the ground will will provide a torque and force on your bicycle, hence your angular momentum will not be conserved.
| {
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How can we find the total weight of a pulley apparatus? I recently have been trying to solve this problem, which asks me to find T3 assuming that g = 9.8:
My idea was to find the acceleration of the two blocks in order to calculate the apparent weights of the 40 and 26 kilogram masses, and add the apparent weights to ... | You haven't taken into account the actual weight of the masses.
$$W_{sys}=-(W_1+W_2+W_P)+(M_2-M_1)a=-(M_1+M_2+M_p)g+(M_2-M_1)a$$
Putting the values, You have calculated :
$$W_{sys}\approx 1155$$
| {
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"timestamp": "2023-03-29T00:00:00",
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Wave function boundary condition in scattering problem The the boundary condition for a wave function in a scattering problem is
$$\psi_{\boldsymbol{k}_{1}}(\boldsymbol{r}) \underset{r \rightarrow \infty}{\rightarrow} A\left(\exp \left(\mathrm{i} k_{\mathrm{i}} \cdot \boldsymbol{r}\right)+f(\theta, \phi) \frac{\exp (\m... | Any correctly posed mathematical problem involving differential equations requires boundary conditions (initial conditions are also a kind of boundary conditions). Otherwise it simply cannot be solved, although the issue is often glossed over in not very mathematically rigorous physics textbooks.
When it comes to the S... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/597810",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
General relativity modifies Newton's inverse square law of gravity. Why do many people do experiments to test the inverse square law? General relativity may induce the so-called post-Newtonian correction to the inverse square law of gravity. For details, please refer to chapter 9 of Weinberg's Gravitation and Cosmology... | Newton acknowledged the $1/r^2$ behaviour his laws expected of point masses and outside spherically symmetric densities would experience $1/r^3$ corrections (which primarily matter at short distances) due to factors such as the central mass being spheroid, and he showed this still leads to elliptical orbits; it just ma... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/597948",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
} |
Why do low-energy waves produce heat, but high-energy waves do not? Radio waves, microwaves and infrared are known to produce heat and even cause burns, while visible light and ultraviolet are not. This seems counterintuitive to me, as the latter contain the highest amount of energy.
Why is this? Does it have to do wit... | We need to clear something up first, which is the difference between photon energy and energy delivered by an absorbed wave. Photon energy is what you’re referring to in your question, but photon energy has nothing to do with total energy delivered. For example, 1 Watt is pretty bright for a laser, but it’s pathetic fo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/598277",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Why do we bend little forward for rising from Chair? How does torque arises when not bending forward and how does it gets cancelled while bending little forward? Please give me a video explanation or figurative explaination if possible.
| Try sitting straight and push the arms of your chair to get up. You will notice that you don't always need to bend forward to rise from the chair instead a reaction force is exerted on you by the chair which helps you to get up.
Similarly, in case you are trying to get up without using your hands you bend your body to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/598365",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
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