Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Is energy $E$ in Schrödinger equation an observable/ Can $E$ be measured? Take this quantum approach to estimate mean energy of a molecule:
$$\langle\psi|H|\psi\rangle=\overline E$$
Question:
Is $E$ an observable? How we can compare it to an experimental value? i.e how to experimentally measure it and what are the stat... | You can measure the energy of a molecule in a number of ways.
If what you want is to measure the energy difference between an excited state and the ground state, then you can drive the transition using e.m. waves of suitable frequency. You need a way to determine that the transition has happened, and a way to measure t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361132",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 3
} |
Do gravitational sources move along ‘geodesics’? Assume we have a system of say two bodies which are orbiting each other. Now assume that we wish to find an equation of the orbits of the two gravitational sources. Do they follow a ‘geodesical’ path, if we assume that the sources may or may not be singularities, which i... | First note that in the case of block holes it is not even clear what "following a geodesic of the entire manifold" would mean as the interior of the black hole exists outside of the causal past of the rest of the space time. Even for extended bodies (e.g. stars) it is not immediately clear what this means as you would ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361301",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
How to find error in trigonometric ratios? How do I find the error in measurement of $\sin \theta$, if I am given the error in the measurement of the $\theta$
| In general, if you have a function $f$ of a single variable $x$, you can propagate the uncertainty in the following way:
$$ \delta f = \left|\frac{df}{dx}\right| \delta x$$
If you have a function $g$ of several variables $x$ and $y$ with uncorrelated uncertainties, then
$$\delta g = \sqrt{\left(\frac{\partial g}{\parti... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361466",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Electric power and resistance dependance According to the equations,
$$P=VI =I^2R\,\text{ and voltage } V=IR$$
it seems clear that when the resistance is lower by fixing the voltage at constant, the current is therefore, higher, generating high power. But what confused me was when the resistance is higher by fixing th... | Notice that by fixing a constant voltage $V$, we have that the current $I$ is inversly proportional to the resistence by Ohm's Law:
$$I\propto\frac{1}{R}$$
So, your first assumption is right, when we set the resistence to be lower the current is higher.
When you set a constant current $I$, we have by Ohm's Law:$$V\prop... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361617",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Doppler shift and speed of rotating objects in space I understand the concept of how we can use the doppler effect to know if an object is spinning, in the sense that the part of the object spinning towards us will exhibit a blueshift, and the part spinning away will exhibit a redshift.
However, how can we determine th... | If you consider a rotating body, some parts of the object will be moving towards you and some parts away. These additional velocity components will give you a different Doppler shift, and a different observed frequency of light. When considered the whole visible surface of the rotating object, there will be a continuum... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/361887",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Very basic question about quantum field operators For a matrix $A$, the notation $A^\dagger$ implies the transpose of the complex conjugate of $A$ i.e., $A^\dagger=(A^*)^T$.
What does the symbol $\hat{\phi}^\dagger$ mean for a quantum operator corresponding to a classical field $\phi(x)$? Is it okay to think of $\hat{... | That for a matrix the dagger denotes the transpose conjugate is really just a special (namely the finite-dimensional) case of the general definition of the Hermitian adjoint:
For any operator $A$ on a Hilbert space $H$, the adjoint $A^\dagger$ is the operator such that
$$ \langle v, Aw\rangle = \langle A^\dagger v,w\ra... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362063",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
How to identify binary stars in $N$-body simulation? Binary stars constitute a significant portion of the stars of a globular cluster.
I would like to verify that this is true in my $N$-body simulation, but I don't know how to decide whether a star in the system is a binary.
Visually this is easy to do, as binaries are... | You'd need to calculate the binding energy of pairs of particles in your simulation. If for a pair this energy is negative then the pair is bound forming a binary system.
I assume you already have an effective way of calculating the potential, so this should not add much more execution time, since you just need to chec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362181",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
How to use a galaxy's redshift to measure its distance I know how we can use the spectrum emitted by a galaxy to measure whether it is redshifted/blueshifted, but out of curiosity, how can the redshift of a galaxy be used to determine its distance from us?
| This is the whole idea behind Hubble's law: more distant objects recede faster (higher redshift) than closer objects. So there's a direct correlation between distance $d$ and redshift $z$
$$
d = d(z)
$$
At small distances/redshifts
$$
z = H_0d/c
$$
So, measuring $z$ gives you a direct estimation of distance
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362370",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Work done by the piston versus work done by the surrounding Suppose a massless, frictionless piston assembly initially has a higher pressure than the external (atmospheric) pressure, and it is pinned so that the piston does not move. Once the pin is removed, the piston would expand until the pressure inside the piston ... | The work done varies because the piston will be accelerated at a higher rate.In case of contant pressure expansion(both internal and external pressures are same at all instances) the piston moves slowly.Because the force will be just enough to move the piston.But in your case the force inside will be sufficiently highe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362568",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 5,
"answer_id": 3
} |
White light Hawking radiation If the Hawking radiation is similar in spectrum to a black body, then at what mass of the black hole its radiation would have the same peak energy as the sunlight?
| The equivalent temperature of a black hole (as seen from infinity- since the blackbody radiation will be red-shifted as it moves away from the black hole) is given by $$\frac{1}{8\pi M}$$ in natural units. Or with all the constants in there: $$\frac{\hbar c^3}{8\pi k_BGM}$$
For the Sun's temperature of $5778\rm K$, thi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362721",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
In Young's double slit experiment, why are the two theta values equivalent?
I've read several answers on here to similar questions, and I've also looked at several different picture interpretations to no avail. I can't wrap my head around it. I understand that under the assumption of L >> d, both rays from the slits a... | If you refer to the yellow-shaded triangle, yes, you're on the right path: it is purely geometric. Excuse me I'm not going to work much more than a cheap paint picture ^^
Steps:
*
*(Green) If the angle $\theta$ is that one, you obviously have 90 degrees minus $\theta$ until the slit-wall.
*(Blue) We are supposing t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/362983",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
} |
Why am I getting two different results in emu and SI unit? I am computing force between two magnetic poles each of one unit pole (in emu) and situated one centimeter apart.
In electromagnetic units:
$$F_{dyne}=\dfrac{p^2}{r_{cm}^2}=\dfrac{1^2}{1^2}=1 dyne$$
where $p$ is pole strength in emu
In SI units:
$$F_{N}=k_A \df... | I find this topic to be a quagmire.
The SI unit of magnetic pole strength is the ampere-metre with $1\,\rm Am$ equal to $10$ electromagnetic units (emu) of magnetic pole strength.
The relationship is derived here.
The conversion that you were using was for magnetic flux the SI unit of which is the weber and it is t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/363110",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is $\mathrm{d} \Omega = \mathrm{d} \cos \theta \mathrm{d} \phi$ and not $\mathrm{d} \Omega = -\mathrm{d} \cos \theta \mathrm{d} \phi$? The textbook I am following (Peskin&Schroeder) on QFT takes $\mathrm{d} \Omega = \mathrm{d} \cos \theta \mathrm{d} \phi$. I cannot for the life of me see that its correct. We know t... | Usually, you integrate $\theta$ from $0$ to $\pi$, but $\cos \theta$ from $-1$ to $1$ (P&S don't write the integration boundaries explicitly).
$$ \int_0^\pi \mathrm \sin\theta\, d\theta = \int_1^{-1} \mathrm d(-\cos\theta) = \int_{-1}^1 \mathrm d(\cos\theta) .$$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/363232",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Do any particles exist which are NOT entangled with another? Please accept my apologies for a neophyte question
Do we have evidence that suggests whether a subatomic particle can exist which is NOT entangled (correlated) with at least one other particle in the universe?
Are there reasons this cannot be possible?
Are t... | A system of two spins: the state $\newcommand{\ket}[1]{\mid#1\rangle}\ket{\uparrow}\!\ket{\uparrow}$ is not entangled. In case you wonder what that notation means: the first spin up and the second spin up.
As opposed to the state $\ket{\uparrow}\ket{\downarrow}+\ket{\downarrow}\ket{\uparrow}$ which is a superposition o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/363467",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
} |
Validation of Work-Energy Theorem Is the work-energy theorem valid when there's an impulsive force during motion of considered body?
For eg: Consider a man jumping from some height into a swimming pool of certain depth, if we apply work energy theorem from his initial position to final position (Change in Kinetic Energ... | *
*You are totally correct about your reasoning. Remember, the work-energy conservation theorem is always valid.
*Thus, whenever you see a change in the total energy of a system, it means the energy goes into/out of that system. But you can always include more "objects" into your system and observe that the conservat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/363802",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Spaghettification inside a black hole? Taylor and Wheeler in "Exploring Black Holes" calculate that the spaghettification time, measured from feeling a 1g tidal difference head-to-toe to disintegration at the singularity, is a constant, a little less than one second. For small black holes (3 solar mass) this happens w... | Taylor & Wheeler's spaghettification time is valid for the case of "raindrops", a particular motion where the astronaut fell from rest far away from the black hole (as Brent Meeker commented).
As for inside the horizon, maybe it is unhelpful for you to focus on the description of Schwarzschild $t$ and $r$-coordinates s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/363934",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
With a very intense light on a black object, will it reflect? I was wondering about the nature of object's colour. I know that an object get its colour from the absorption of visible electromagnetic radiation, reflecting all the other wavelength. But if we take the case of a black object that absorbs every visible ligh... | Yes if it's a perfect black body then it would be black. You should read about https://en.m.wikipedia.org/wiki/Black_body
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/364041",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Are the field renormalization factors infinite or finite?
*
*We know that in quantum field theory we include infinities at each order of the perturbative expansion of the renormalization $Z$ factors about the coupling constant $\lambda$ to absorb the divergences of the loop diagrams, so it seems $Z$ must be infinite.... | As you are familiar, the idea is to introduce renormalised parameters and fields in terms of bare quantities, related by various renormalisation factors, $Z_i$.
We then expand $Z_i$ around some classical tree level values; this corresponds to $Z_i = 1$ followed by an infinite series of corrections $\delta_i$, so $Z_i =... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/364178",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
How torque about every point on Axis is same? I read somewhere that torque about every point on an axis is same. But I am really confused about how this can be. Please help me and give an satisfactory answer
| This can be proven using vector algebra.
Let a straight line in space be your axis; a straight line in space can be defined by a point through which it passes and a vector you scale up and down in order to find every point in a specific direction; let these two object be $A_0$ and $\vec{v_0}$ respectively. Your line is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/364303",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 1
} |
Why are position and momentum space examples of Pontryagin duality? https://en.wikipedia.org/wiki/Position_and_momentum_space
https://en.wikipedia.org/wiki/Pontryagin_duality
I am trying to understand logic behind the uncertainity principle. And as far as I understand, it follows mathematically if we assume that wave f... | Practically speaking, the full machinery of Pontryagin duality is way more advanced than physicists need to understand the uncertainty principle. There are several ways to "derive" that the momentum-space wavefunction is the Fourier transform of the position-space wavefunction, which depend somewhat on your choice of s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/364488",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 0
} |
What sound frequency can be heard the greatest distance by humans? What sound frequency can be heard the greatest distance by humans? Assuming a pure tone, single frequency, same source SPL (dB) for each frequency, outdoors with no obstacles between source and listener. I believe the answer would be the result of the... | You ear has a frequency response peak at about 3kHz, meaning that this frequency will be easiest to hear over long distances. In comparison, your ear's response to bass frequencies is much weaker, and to make them as audible as a distant sound source at 3kHz requires much more acoustic power. This among other things is... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/364633",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Why is it "bad taste" to have a dimensional quantity in the argument of a logarithm or exponential function? I've been told it is never seen in physics, and "bad taste" to have it in cases of being the argument of a logarithmic function or the function raised to $e$. I can't seem to understand why, although I suppose i... | There is no reason to give metaphysical arguments like "It's not possible to add a meter with a meter squared". This is a purely mathematical issue.
Physics is, first and foremost, mathematical models. Mathematics doesn't care about units. Mathematics only involves pure numbers.
If, in some universe, we need the law $x... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/364771",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "86",
"answer_count": 7,
"answer_id": 4
} |
Periodic multi-layer scattering of neutrons I am trying to understand the reflectivity plot on slide 26 of Neutron optics,Soldner lecture.
1.Is the peak from $\theta$=0.0 to 0.4 due to total external reflection from the first upper surface?.
2.There is another peak at $\theta$=1.0. Is it because of Bragg's interferen... | Here are the answers:
*
*Yes.
*Yes... But is it better called as Darwin's plateau.
*Those are fine structure arising from multiple wave interference (and are not seen experimentally) (see page 16 of Analysis and design of multilayer structures
for neutron monochromators and supermirrors ,S. Masalovich )
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/364920",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
Integration measure in terms of the Levi Civita tensor For a course in General Relativity I had to calculate the volume of the unit 2-sphere $S^2$, but I have some trouble with understanding the concept.
At first I calculated the volume of a sphere with radius $R=1$, but somehow this should only make sense when I'm in ... | The "volume" of a 2-dimensional space is what we would commonly refer to as the area. Note that for a 2-sphere we have $\epsilon = r^2\sin\theta d\theta d\phi$, where $r$ is just a constant, usually taken to be unity. The integration thus yields
$$
\int_M\epsilon = r^2\int_0^\pi\sin\theta d\theta\int_0^{2\pi}d\phi = 4\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/365356",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Does a permanent magnet attract a positively charged rod? I thought that because the charge on the rod is static, there wouldn't be an interaction with the magnetic field, however the answer to the question states that both poles of the magnet would attract the rod. Thanks!
Edit: The question does not state the materia... | Note that a charged object can attract a neutral conductor by inducing dipole polarization; the fact that your neutral conductor is magnetic is a red herring.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/365808",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Why don't electric charges get attracted to current-carrying wires when they're at rest, when they do feel a force if they're moving? Why does charge placed at rest near a current-carrying wire experience no force, but if the charge starts moving then it gets attracted toward the current-carrying wire?
Why doesn't char... | It is a fact of nature encoded within the system of Maxwell's equations which describe electromagnetic interactions classically.
The definition of charge comes from observations, as well as the definition of the magnetic field.
That a charge is attracted to another charge is a law of nature. That the magnetic dipole... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/365963",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Gas Laws: Why is PV directly proportional to mT? My book mentions that the three informal gas laws (Boyle's, Charles', and Gay-Lussac's) can be combined into a more general relation PV ∝ mT (the precursor to the Ideal Gas Law).
Where:
P is pressure, V is volume, m is mass (taken as a measure related to quantity of ga... | P ∝ m conceptually: for a given volume and temperature, if you increase the mass (get in more particles) the pressure will become higher. Simple, isn't is?
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/366272",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
What does the cut-off $\Lambda$ stand for in the theory of QED? The bare electron mass $m_0$, in QED, changes as $$m_0\to m=m_0+\delta m\Big(\frac{\Lambda}{E}\Big)$$ where high momentum modes from $E$ to $\Lambda$ has been integrated out.
What scale does the cut-off $\Lambda$ stand for in the theory of QED and why? I... | There is usually no unique cutoff scale $\Lambda$ in renormalization. The reason is that generally we don't know what the ultimate microscopic physics is.
So the rationale is to pick any scale $\Lambda$ to be much, much larger than any physical scale of interest (particle mass or energy $E$ of an experiment you're doin... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/366404",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Why do quantum effects of gravity become important at the Planck scale? The standard heuristic argument for why quantum effects of gravity become important at the Planck scale is to consider the length scales at which both quantum field theory (QFT) and general relativity (GR) become crucial in order to explain physica... | User anna v has already given a correct answer. In this answer we try to summarize.
In a nutshell, the Planck scale of quantum gravity is determined by the 3 physical constants $G$, $c$ and $h$.
*
*When the wavelength $\lambda$ becomes of the order of the Schwarzschild radius, the rest energy $mc^2$ becomes of the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/366598",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 1
} |
How to find the direction of velocity of a reference frame where two events are simultaneous in case of a space-like interval Suppose in a inertial reference frame $S$, an event $A$ occurs at $(ct_A, x_A, y_A, z_A)$ and event $B$ occurs at $(ct_B, x_B, y_B, z_B)$.
Now the invariant interval of these two events is,
$$I... |
The answer concerns the case $\:I > 0$, so let in a frame $\:\mathrm{S'}\:$ two events taking place by a space interval $\:\Delta\mathbf{x}^{\boldsymbol{\prime}}\:$ and time interval $\:\Delta t^{\boldsymbol{\prime}}\:$ apart with
\begin{equation}
\left\Vert\dfrac{\Delta\mathbf{x}^{\boldsymbol{\prime}}}{\Delta t^{\bo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/366727",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 5,
"answer_id": 2
} |
Early atmospheric Watt steam engine - how does the steam move from the cylinder to the condenser? Below is a picture of one of the earliest designs of Watt's steam engine.
The basic principle of operation is this:
*
*The weight which is attached to the beam $E$ pulls the piston $P$ up, sucking steam from the boiler ... | tfb's answer correctly describes the working cycle - just wanted to capture some of the extra questions in the comments.
Ideally you want to fill the cylinder with steam to lift it and then have the steam disappear creating a vacuum to pull the cylinder down. In Newcomen's original engine this was done by spraying cold... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367043",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Difference between and diffusion and heat equations? I read everywhere that diffusion and heat equations are similar. The same differential equations can be solved for both.
Consider a finite one-dimensional diffusion or heat transfer where one end is insulated and the other end is kept with a constant flux.
The bounda... | Your observation is good and correct: they are same. Both are diffusions; one diffuses material and the other diffuses heat.
The limit you mentioned also exists for heat transfer as well when you apply fixed temperature as boundary conditions; the temperature cannot be higher that its boundary temperature.
For diffus... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Where does the interference pattern or diffraction pattern due to a single or double slit placed in front of a light source form? I have seen that when we use a spectrometer for performing an Optics experiment involving a single slit or double slit to study , say the Fraunhofer Diffraction pattern or some interference... | The fringes which you have described are non-localised, they occur everywhere where there is which has passed through the slit(s).
When you use your eye to observe the fringes, you are observing them from the slit(s) being focussed on the retina of the eye, just like the telescope of the spectrometer focussing the li... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367343",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Interpreting Schrödinger Equation's solution for a free particle Let's say we have the time-independent Schrödinger Equation for a free particle (without potential):
$$-\frac{\hbar}{2m} \frac{d^2 \psi}{dx^2} = E\psi$$
Whose general solution is:
$$\psi(x) = Ae^{ikx} + Be^{-ikx}$$
Where $k = \frac{2\pi}{\lambda}$ (i am s... | As to your first question: the meaning is that the particle is not a free particle after all. This is the problem of a particle in a one-dimensional infinitely deep square potential well: $\Phi=0$ for $x\in[0,L]$ but $\Phi=\infty$ otherwise. Then (by Schrödinger's equation) $\psi=0$ at those points where $\Phi=\infty$.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367493",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
} |
A single-component simple system thermodynamics The following equation is taken from Callen's Thermodynamics, page 39:
$$(\frac{\partial u }{\partial s})_v=(\frac{\partial u }{\partial s})_{V,N}$$
where $u = U/N$, $s = S/N$ and $v = V/N$.
The notation is conventional.
My question is:
The author doesn't make any assump... | We know that
$$ dU = TdS - pdV + \mu dN$$
If we assume that the internal energy $U$ is an extensive, homogeneous function of degree 1, then it follows that
$$ U = TS - pV + \mu N$$
Now consider the quantity $u \equiv U/N$. We would have that
$$ du = \frac{1}{N}dU - \frac{U}{N^2}dN= \frac{TdS}{N} - \frac{pdV}{N} + \fr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367678",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Books on non-perturbative phenomena in quantum field theory I am looking for any good places (preferably textbooks) to study about introductory non-perturbative phenomena in Quantum field theory.
Any suggestion will be appreciated.
| The following books assume some acquaintance with perturbative quantum field theory. Together they cover a very wide spectrum of nonperturbative techniques for very different situations.
*
*E. Calzetta and B. Hu. Nonequilibrium Quantum Field Theory. Cambridge Univ. Press (2008). A book on nonperturbative quantum fie... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367793",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 4,
"answer_id": 2
} |
Is the gravitational field stronger in the transverse plane of a mass than along its axis of propagation? Is the gravitational field stronger in the transverse plane of a mass than along its axis of propagation? I read somewhere that it was but cannot find the reference again. That is, for a mass traveling at very hi... | If "transverse plane of mass" means the gravitational attraction perpendicular to the mass's velocity, then you are correct.
There is a weak field approximation to GR call Gravitoelectromagnetism in which there is an $\vec{E_G}$ and $\vec{B_G}$ which obey equations similar to Maxwell's equations for $\vec{E}$ and $\vec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/367968",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is classical spin the spin-$\infty$ representation of $SO(3)$, not the spin-$1$ representation of $SO(3)$? Given a classical spin model,
$$H=\mathbf{S}_1\cdot \mathbf{S}_2\tag{1}$$
where $\mathbf{S}_i=(\sin\theta_i \cos\phi_i,\sin\theta_i \sin\phi_i,\cos\theta_i), i=1,2$ is the classical spin.
Given a quantum spin... | *
*The classical angular momentum square $S^2$ should be a continuous variable, and identified with the quadratic Casimir $$\rho(\hat{S})^2~=~\hbar^2 s(s+1){\bf 1}, $$ in the $s$-representation $$\rho: su(2)~\to~ gl(2s+1,\mathbb{C}), \qquad s~\in~\frac{1}{2}\mathbb{N}_0,$$ of the quantum $su(2)$ Lie algebra.
*Appare... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368296",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 0
} |
Does twisting a wire heat it? I was playing with a key chain loop in a (very boring) chemistry class and then I straightened the loop into a wire keeping two end of the loop (now wire) curved so as to easily twist it. It was more or less a S shaped structure of metal with a longer straight part in the middle of S.
On ... | I believe the heat is due to plastic deformation, as you repeatedly twist the wire. So what is plastic deformation?
When the metal is strained no further than $A$, its response is purely elastic and the wire will return fully to $O$. But if the deformation exceeds $A$, the deformation will be plastic and the wire will... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368648",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
How does the LHC separate the protium isotope to have only protons for the collision? I am preparing a presentation for my physics class about the LHC and the following question arose:
Every text about the LHC says that it collides protons from a gas of hydrogen whose electrons were previously taken away.
Can collisio... | Given their charge and mass, as soon as you start accelerating particles around a loop with a given magnetic field to deflect them, only particles with the correct mass/charge ratio survive. In effect you have built a giant mass spectrometer - other isotopes of hydrogen are too heavy, and the Lorentz forces are insuffi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368819",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Variation of Gauss Bonnet Invariant I am trying to do the variation of Gauss Bonnet Invariant, and the Gauss Bonnet Invariant is:
$G$=$R^2$+$R_{abcd}$$R^{abcd}$-$4R^{ab}$$R_{ab}$
The variation of $G$ is:
$\delta$$G$=$2R\delta$$R$+ $\delta($$R_{abcd}$$R^{abcd}$)-$\delta$$(4R^{ab}$$R_{ab}$)
I am having problem in doing t... | You will need
\begin{equation}
\begin{split}
\delta \Gamma^c_{ab} &= \frac{1}{2} \left( \nabla_a h_b{}^c + \nabla_b h_a{}^c - \nabla^c h_{ab} \right) ~, \\
\delta R^a{}_{bcd} &= \frac{1}{2} \nabla_c \nabla_d h_b{}^a + \frac{1}{2} \nabla_c \nabla_b h_d{}^a - \frac{1}{2} \nabla_c \nabla^a h_{db} -\frac{1}{2} ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/368965",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is the equation of relative motion for two objects moving in straight lines? If two objects, A and B, are moving in the same direction along straight lines in a plane, they might be diverging, converging or moving in parallel.
If we wish to describe B's motion with respect to A, what is the equation of motion?
For... | We first rewrite the velocities of the boats so that they're in terms of knots.
Currently, we have written:
$$(x_A,y_A) = (30t, 20t)$$
$$(x_B,y_B) = (35t, 10-15t)$$
So that the velocities are
$$\vec{v_A} = (30, \;\;\;\;\;20)$$
$$\vec{v_B} = (35, \;\;-15)$$
We need to rescale them so that $\vert \vec{v_A} \vert= 10$ and... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369116",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 3
} |
How is Liouville's theorem important to statistical mechanics? I have come across Liouville's theorem in the first chapter of many statistical mechanics textbooks, still I don't quite get how it is important to statistical mechanics.
How is it related to statistical mechanics? How can it be applied to the study of ense... | It is extremely important if you want to understand the reason behind the irreversibility paradox. Basically, classical mechanics are microscopically reversible. Then, why don't we ever see macroscopic reversibility for certain experiments? Why can we see a glass shatters but pieces do never join back into the original... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369198",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 0
} |
Direction of dipole moment How do you find out the direction of the dipole moment in a charge distribution? For example a sphere with charge density $\rho$ in northern hemisphere and $-\rho$ at southern hemisphere? How can you think about the direction in general?
| Generally speaking, the dipole moment of a neutral charge distribution points in a direction that goes from the places with negative charge to the places with positive charge. Moreover, if the distribution has any sort of rotational symmetry axis (either continuous or discrete) then the dipole moment needs to lie along... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369348",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Planck length at relativistic speeds? I'm currently in high school so sorry if the answer to this question seems obvious but I’m only just learning about this stuff. I’ve been learning about special relativity, in particular length contraction and time dilation. I was wondering, if the Planck length is the smallest pos... | This is a very good question, and serious physicists such as Lee Smolin have been wondering about it. According to Special (and General) Relativity any inertial observer should get the same value for the Plank length in terms of its own units. So the Planck length calculated in a frame that I see moving should be the s... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369532",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "20",
"answer_count": 7,
"answer_id": 1
} |
Heat to work or thermal energy to work? A system consists of different forms of energy like thermal energy, mechanical energy, chemical energy, nuclear energy etc. If these energies are to be transferred to another system (call it system 2), it can either be done as heat or work (or mass but here I take system approach... | @Chester Miller So if energy is transferred to a system(as heat or work) and there is no transfer of energy from this system, then the energy transferred to the system will be saved as one of the forms of energy of the system ie increase the energy of the system(which may be thermal energy, mechanical energy, chemical ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Convention mostly used for Fourier transform I know that mathematically it doesn't matter what sign of $i$ we use to Fourier-transform a wavefunction from real- to momentum-space and vice versa, as long as we consistently change the sign when transforming it back to its original space. But I've seen many text-books (le... | A wave that propagates in the $\vec{k}$ direction is given by
$$\left<\vec{r}\Big|\vec{k}\right>=\frac{1}{\left(2\pi\right)^{\frac{3}{2}}}e^{+i\vec{k}\cdot\vec{r}}$$
and thus it is common to decompose a function as
$$\psi\left(\vec{r}\right)=\frac{1}{\left(2\pi\right)^{\frac{3}{2}}}\int\tilde{\psi}\left(\vec{k}\right)e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/369835",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
How to represent a axisymmetric, stationary metric in a coordinate independent way? A classic example of a stationary, axisymmetric metric in GR is the Kerr metric. In Boyer-Lindquist coordinates $(t,r,\theta,\phi)$ it is obvious that the metric is independent of $t,\phi$ and so is stationary and axisymmetric.
Now, oft... | The definition of stationary and axialsymmetric normally comes after one has specified a local coordinate expression, (writing $g_{\mu\nu}$ is still a local coordinates expression, since it has indices).
However as you might know, an abstract symmetry of a metric is associated to a Killing vector as has been pointed o... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370071",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Wrong sign in Conformal Casimir The quadratic conformal Casimir in $d$-dimensional Euclidean space is given by
\begin{equation}
C = \frac{1}{2}L_{\mu \nu}L^{\mu \nu} - D^2 -\frac{1}{2}\left(P^\mu K_\mu + K^\mu P_\mu \right)
\end{equation}
as given for example in the beginning of lecture 6 here http://pirsa.org/C14038. ... | I get
$$
C_2=\frac{1}{2}L_{\mu \nu}L^{\mu \nu} + D^2 +\frac{1}{2}\left(P^\mu K_\mu + K^\mu P_\mu \right)
$$
In Euclidean signature
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370318",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
} |
Comparison between two flavor neutrino oscillation and a system of up-spin and down-spin states of an electron? In the system of up-spin and down-spin states of an electron, we can write a general state of electron at time $t$ as
$$\left|\psi(t)\right>=a\left|\uparrow\right>+b\left|\downarrow\right>,$$
where $\left|\up... | 1) the spin states for the electron are two possible eigen values +1/2 or -1/2 .
2) the neutrino states involve two masses for the neutrino
Spin is a conserved angular momentum variable.
Mass is not a conserved quantity.
A free particle carries a number of conserved quantum numbers and momentum and energy and angular ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370464",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Lorentz transform of force
If a particle of mass $m$ and velocity $v$ is moving due to a constant electric force what would the force be in the the frame where the particles velocity is 0?
To try and solve this I used the four force and did a Lorentz transform of the four momentum. However I got different answers in ... | The Lorentz force must be transformed in the same way as other forces in special relativity.
Avoiding a tensor treatment, you can say that
$${\bf F'} = {\bf F_{\parallel}} + \frac{1}{\gamma}{\bf F_{\perp}}, $$where $\gamma$ is the usual Lorentz factor and the subscripts refer to the components of the Lorentz force ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370692",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why these patterns form in captured image while zooming?
This is a gif format video that shows zooming of an image of computer LCD screen which i captured using my mobile phone. You can see that some fringes are forming and disppearing and hence some patterns are forming while i zoon in or out. How will you explain th... | ERROR: type should be string, got "\nhttps://xkcd.com/1814/\nApparently this isn't enough text so here is a real explanation\n" | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370817",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 2,
"answer_id": 1
} |
Lattice and basis vectors for a NaCl structure I am supposed to obtain the selection rules of a NaCl lattice considering a rhombohedral set of lattice vectors but I am not getting any valid results. My guess is that I am not choosing the basis correctly.
I define my FCC lattice vectors as
$a_1=\frac{a}{2}(1,0,1)$, $a_2... | You should ask this on chemistry forum.
If I remember it correctly, I think NaCl is a cubic lattice where each chlorine atom is surrounded by 6 sodium atoms at equal distance and vice versa. So with this information, we can start like:
The Na basis atom is at (0,0,0) and Cl basis atom is at (0.5,0.5,0.5) or vice versa.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/370937",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Running vs. walking in slippery condition We are experiencing warmer weather than normal, which is causing the snow to melt and re-freeze daily. This has led to very slippery conditions.
A few years ago, I was running in similar conditions, and I got to an area where the ice started to feel more slippery. So my reacti... | https://www.sciencedaily.com/releases/2011/03/110324103610.htm
"Biomechanics researchers Timothy Higham of Clemson University and Andrew Clark of the College of Charleston conclude that moving quickly in a forward, firm-footed stance across a slippery surface is less likely to lead to a fall than if you move slowly. Ap... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/371190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
What's the purpose of shorting the base and collector of a transistor in current mirrors? I often see this diagram of a current mirror (as shown below).
As far as I know, the purpose of a current mirror is the ensure that the collector current for both transistors are equal.
This can simply be achieved by making sure t... | Shorting collector to base is NOT redundant, it serves the useful purpose of making conduction in the two transistors similar. In particular,
the construction of a transistor includes a thin base region between emitter and collector, and that base region has an effective electrical
resistance. Forcing all current in... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/371360",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Does salt affect the boiling time of water? If I have 1 cup of water on the stove and another cup of water with a teaspoon of salt.
would the salt change the boiling time of the water?
| Yes and no.
It will not change the boiling time of water. If you add salt, then it's not water anymore, it is now a new solution (salt + water). It will change the boiling point of the solution. Because that solution now has a different boiling point, if nothing else changes, it will take a different amount of time to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/371577",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 2
} |
How does friction increase energy of a system? I had this doubt while thinking through a question about centre of mass. Consider a system, consisting of a man standing on one end of a plank which rests on a frictionless surface. Now the man starts running towards the other end of the plank(friction is present between t... | There was no work done by friction in your example. Work is force by displacement. Friction is between man's feet and the board they contact. During this contact, each foot does not move relative to the board. Therefore the displacement is zero and so is work by friction. Actual work here is done by man's muscles by co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/371707",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Why are high electronegativity atoms found in the periodic table's upper right corner? Looking at a graphical representation of electronegativity in the periodic table reveals a pattern that, noble gases aside, electrognetivity increases as you move toward the upper right hand corner of the table. What causes this?
Th... | Mendeleev's periodic table of elements is based on the number of protons in an atom. Also, in an electrically neutral atom,
$$no. \ of\ electrons=no. \ of \ protons$$
So for stability, octet configuration is sought by the atom. For electro-negative elements, since they have a higher number of electrons in the ultimate... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372329",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why can the Klein-Gordon field be Fourier expanded in terms of ladder operators? Using the plane wave ansatz
$$\phi(x) = e^{ik_\mu x^\mu}$$
the solution to the Klein-Gordon equation $(\Box + m^2) \phi(x) =0$ can be written as a sum of solutions, since the equation is linear and the superposition principle holds, as
$$\... | The action functional of the real scalar field is:
$$ \mathcal{A} = \frac{1}{2} \int\mathrm{d}^4 x \left(\partial_a \phi \partial^a \phi - m^2 \phi^2 \right) = \int \mathrm{d}t \int \frac{d^3 \mathbf{k}}{(2\pi)^3} \frac{1}{2}\left[ |\dot{q}_{\mathbf{k}}|^2 - \omega^2_{\mathbf k}|q_{\mathbf k}|^2 \right]$$
where the sec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372425",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 5,
"answer_id": 1
} |
Is Heisenberg's Uncertainty Principle applicable to light? Can we apply the Uncertainty Principle to light? If so wouldn't it violate it because we just need to find the position of light, since we would already determine it's momentum(from the wavelength of light used)?
| Using wavelength you can find only the magnitude of momentum $\sqrt{P_x^2 + P_y^2 + P_z^2}$. For finding its direction you will need its wavevector $\vec{k}$. Heisenberg's Uncertainty principle applies to each component of momentum and the corresponding component of position, for example, you can't find simultaneously... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372537",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
Momentum of a photon when considered as a particle According to dual nature of light, it is said to have both particle as well as wave nature. When we think of it as a wave, its momentum can be found out from
De Broglie's equation i.e λ = h/mv, provided we know its wavelength.
But how do we calculate the momentum of a ... | From relativity, we know that the energy-momentum relation is given by:
$$
E^2 = (pc)^2 + (mc^2)^2
$$
We can see that when $m\rightarrow0$, $E = pc$. The energy of the photon can be found using $E=hf$ and you can solve for $p$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372666",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is the neutrino oscillation probability formula independent of the Majorana phases? Is there a simple way to understand why the neutrino oscillation probability formula is independent of the Majorana phases?
| I assume you mean the routine formula, for Greek flavor indices and Latin mass eigenstate indices,
$$
P_{\alpha\rightarrow\beta}=\left|\left\langle \nu_\beta(t)|\nu_\alpha\right\rangle \right|^2=\left|\sum_i U_{\alpha i}^{*}U_{\beta i}e^{ -i m_i^2 L/2E }\right|^2.
$$
Now the standard result of Bilenky et al 1980 extend... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/372935",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Physical meaning of gauge choice in electromagnetism In electromagnetism, it is often referred to gauges of the electromagnetic field, such as the radiation or Coulomb gauge. As far as I know, the definition of a gauge helps us to redefine the problem in terms of a vector potential and a scalar potential that, since we... | The gauge choice or another has the same physical importance as choosing a inertial reference frame or another... the possibility of doing that gets you a lot of truly profound physical implications (by Noether theorem, for example), so both answers are yes, in some sense.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373336",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
For all practical purposes can light be bent (without the help of gravity) or just reflected? For example, if a single beam of light was directed directly at the tangent of a semi circular mirror, would it be considered bending or redirecting many times to form a near circular pattern? When I say bend I mean in a curve... | a beam of light can be bent through an angle by sending it through a wedge-shaped piece of glass, requiring neither gravity nor reflection. this phenomenon is called refraction and can be studied in detail on wikipedia.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373569",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
What if cosmological constant was zero? Physicists always ask why the cosmological constant is not exactly zero!
I would ask here, what if cosmological constant was zero? The universe wouldn't expand and matter would exert gravitational force and shrink the universe into a big crunch!
So, why physicists want the consta... | To add to Anders Sandberg's answer, the Friedmann equations are really the crucial piece of the puzzle here. These equations assume General Relativity, as well as homogeneity and isotropy (i.e. the universe looks the same in every direction + looks the same at every point). Manipulating the Friedmann equations yields a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373659",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 1
} |
Reason for 6π factor in Stokes' law According to Stoke's law, the retarding force acting on a body falling in a viscous medium is given by $$F=kηrv$$ where $k=6π$.
As far as I know, the $6π$ factor is determined experimentally. In that case, how is writing exactly $6π$ correct since we obviously cannot experimentally ... | If you have read that the 6π coefficient is determined experimentally, then you would also have read that this applies to spherical objects with very small Reynolds numbers in a viscous fluid - Stokes' law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.
We cannot d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373780",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 2,
"answer_id": 1
} |
How do partons' spin/orbital angular momenta contribute fractionally to the nucleon spin structure? Experimentally it is found that the spin and orbital angular momenta of quarks and gluons contribute fractionally to the total nucleon spin $1/2$, as in:
$$\frac{1}{2} =\frac{1}{2} \Sigma_q + \Sigma_g + L_q + L_g$$
But ... | The quark spin is (almost*) unambiguous, but the other three contributions to the total angular momentum turn out to be gauge dependent. Except for certain special projections in certain momentum limits, it is not possible to observe the gluon spin, gluon orbital angular momentum, and quark orbital angular momentum se... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/373895",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Matter effects in neutrino oscillation The neutrino oscillation probability in matter is given as:
where
Now what I do not understand is that "As the energy increases, the probability
of oscillation within the sun through the matter effect increases, so the survival probability decreases". I have read this (page 2... | The transition probability $P_{\nu_e \rightarrow \nu_{\mu}}$ is indeed decreasing with neutrino production energy, i.e., the survival probability $P_{\nu_e \rightarrow \nu_{e}}=1-P_{\nu_e \rightarrow \nu_{\mu}}$ is increasing. Why? The first sine term ($\sin^2 2 \theta_m $) in the oscillation equation (your first equat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/374171",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why the unit vector is represented as a partial derivative in GR? Can someone give a good intuitive explanation why we represent the unit vector as a partial derivative in GR and what does it mean?
| We'd like to say that a (unit) tangent vector is a direction on a manifold. But we can only define and distinguish directions because there must be something different about different points on the manifold, that is, we have a non-constant 'testing' function. So, the vector is the direction in which we differentiate fu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/374271",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
Strange interference pattern of light on top of tower, pattern was seen on air. What was it? I was just looking out of window at night when I saw a tower with a light on top. It had a red light.
When I looked at it through my curtains with net on, I saw an interference fringe, one is the main light itself and band of ... | What you are seeing is an interference pattern, similar to double slits or diffraction gratings. You can confirm this comparing the light pattern when you are looking straight through the curtain (when the curtain is perpendicular to the line from you to the light) and when the curtain is at an angle. Angling the curta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/374639",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 2
} |
Photon density in radiation: number of particles in a EM wave Since light spreads out in all directions from it's source, how far it must travel to become individual photons? Can we consider, that is, that as the intensity of light becomes weaker as it spreads, we measure in fact less photons until only a few remain?
O... | This is the double slit experiment one photon at a time.
. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.
In 2003, A. Weis and R. Wynands at the University of Bonn (Germany) designed a lec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/374768",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Is a canonical transformation equivalent to a transformation that preserves volume and orientation? We have seen the reverse statement: Lioville's Theorem states that canonical transformations preserve volume (and orientation as well). Is the reverse true?
If I demand a map from the phase space to the phase space to pr... | In dimension $2n>2$ they are not equivalent since (for time-independent transformations) canonical is equivalent to $$\sum_{k=1}^n dq^k\wedge dp_k = \sum_{k=1}^n dQ^k\wedge dP_k\tag{1}$$
whereas conservation of oriented volume means
$$dq^1\wedge \cdots \wedge dq^n \wedge dp_1\cdots \wedge dp_n = dQ^1\wedge \cdots \wedg... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/375072",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 3,
"answer_id": 1
} |
Why is the normal force $(M+m)g$? I am trying to understand the solution to this problem. The problem asks to find F such that m stays fixed relative to M. In the solution, it is mentioned that the normal force for block M is (M+m)g, I don't understand that. I thought it is supposed to be only Mg.
The solution states ... | I wanted to write this as a comment but it seems I don't have to reputation to do so, so here goes. Since it is given that the masses should be stationary relative to each other, to understand why the vertical normal force exerted on $M$ by the surface is $(M+m)g$, it is probably easier to treat the combination of the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/375421",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 2
} |
An inverted bottle stops water flow, but does not when connected by a tube? I'm wondering why an inverted bottle doesn't overflow a container it fills once it reaches the opening, but when a tube is used then the water drains out completely causing the container to overflow and the bottle to become crushed/implode?
I ... | The tube system implodes the bottle because the height of the bottle above the lower reservoir determines the strength of the suction that develops inside the bottle. This follows from the laws of hydrostatics about which you can learn more on wikipedia. To prevent the bottle from imploding (and therefore draining out ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/375614",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
What is a minimal set of quantities fully describing the source of a magnetic field? Assume I would like to compare different magnetic fields without knowing what generates them. What is the minimal set of physical properties describing a field that would let me calculate all the other properties of this field?
I would... | There is no such set of minimal quantities, unless you know pretty much everything about the fields to begin with.
As a simple example, consider the magnetic field produced by a dipolar surface current distribution confined to the surface of a sphere of radius $a$, given by $\mathbf K(\theta,\phi) = K_0 \cos(\theta) \h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/375789",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What does electric potential mean in a circuit? As we know that electric potential at a point is defined as a work done by me to carry unit charge from infinity to that point. How can I use this definition in an electric circuit that contains a battery? Suppose electric potential at a point in a circuit is 4 volt. Wha... | When we talk about a potential we actually always mean a potential difference i.e. the difference from the potential at some convenient reference point. That's because we can only ever measure potential differences and not absolute values. So when you say:
electric potential at a point is defined as a work done by me ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/375909",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
Venus, Earth and Mars Magnetic fields Why does Earth have a magnetic field, while it appears that Venus and Mars have none or very little?
| A geodynamo requires a fluid that can carry a current. A widely held but incorrect explanation for Mars' lack of a magnetic field is that Mars' core is frozen solid. Gravitational observations of Mars show that its core is at least partially molten, just as is ours. While a frozen core would explain Mars' lack of a mag... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/376032",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 2,
"answer_id": 1
} |
What are the initial conditions associated with solving the geodesic equation in General Relativity? Can we say that initial conditions for solving the geodesic equation in general relativity be intial velocity of a particle?
| The geodesic equation
$$\frac{d^2 x^{\mu}}{ds^2} + \Gamma^{\mu}_{\rho\sigma} \frac{dx^{\rho}}{ds}\frac{dx^{\sigma}}{ds}=0$$
is nothing more than a set of (coupled) second-order differential equations for the particle's coordinates as a function of some parameter $s$. The explicit solution
$$x^{\mu}(s)$$
requires an i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/376296",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
What are the eigenvalues of $L_+$ and $L_-$? I'm studying angular momentum in quantum mechanics. My question involves the operators $L_+=L_x+iL_y$ and $L_-=L_x-iL_y$; in a problem I have a Hamiltonian, $H$, depending an $L_y$, $L^2$ and $L_z$. The solutions suggest to write $L_y$ as a combination of $L_+$ and $L_-$ and... | If you write the matrix representation of $L_y$ in a basis where $L_z$ is diagonal, you should get (assuming $\ell=1$) something like
$$
\hat L_z=
\left(
\begin{array}{ccc}
1 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & -1 \\
\end{array}
\right)\, ,\qquad
\hat L_y=\frac{1}{2i} \left(
\begin{array}{ccc}
0 & 1 & 0 \\
-1 & 0 & 1 ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/376774",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How to get the fourth component of EOM in a relativistic formulation of a charged particle in an electromagnetic field? We consider in Lorentz spacetime, $(x^0,x^1,x^2,x^3)=(t,x,y,z)$, choose the unit of time such that $c=1$.
Given a four vector $A_\mu$, and let the Lagrangian
$$L(x^i,\dot x^i,t)=-m\sqrt{1-\dot x_i\d... | The action you start with is
$$
S = \int d\tau L
$$
and
$$
L = - m \sqrt{ - \eta_{\mu\nu} {\dot x}^\mu {\dot x}^\nu } +q {\dot x}^\mu A_\mu \, .
$$
This action has a gauge symmetry, which is reparameterization invariance, $\tau \to \tau'(\tau)$. In order to write down your Lagrangian you choose the gauge $\tau = x^0 ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/377189",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Where does the fine structure constant come from? I have this question: Where does the fine structure constant come from? Is it derived? Is it assumed? I will be most thankful if you will also include other detailed info that you think is also good to know, or just suggest a reading on it.
| The electrostatic force between two point charges $q_1,\,q_2$ separated by a distance $r$ is proportional to $q_1 q_2 r^{-2}$, but it has the same dimension as $\hbar c r^{-2}$. Therefore, a dimensionless value $\alpha$ exists for which the charge between two "unit" charges (e.g. electrons) is $\alpha \hbar cr^{-2}$. E... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/377440",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "12",
"answer_count": 4,
"answer_id": 1
} |
Why do we use capacitors and not batteries in defibrillator? Why do we use capacitors in defibrillators and not batteries?
I know that capacitors are used to store electrical energy but isn't the function of a battery just the same?
Moreover, I know that batteries are used to make capacitors work in a defibrillator, bu... | The defibrillator requires a high voltage to do its job. ordinarily this would require a very large battery stack (hundreds of individual cells) to achieve the voltage requirement. Instead, defibrillators use a smaller battery pack to drive a chopper circuit that steps the voltage up through a transformer, after which ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/377546",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "64",
"answer_count": 6,
"answer_id": 1
} |
Small inter nuclear separation limit for Diatomic molecule Let’s take the a simple $H_2^+$ molecule, where there is only electron which is $r_a$ away from the first proton and $r_b$ away from the other one.
Let’s call the separation between the two protons $R$.
As $R\rightarrow \infty$, the electron will stick to one o... | Let $\Psi(\vec{r})$ be $1s_a$ wave function and $\Psi(\vec{R}+\vec{r})$ be $1s_b$ wave function. As $\vec{R} \to 0$ we have for ungerade state:
$$
\phi_{-}(\vec{r}) = N_{-}(\Psi(\vec{R}+\vec{r})-\Psi(\vec{r})) \approx N_{-} \nabla\Psi(\vec{r})\vec{R}
$$
Thus the limit (not normalized) is $\nabla\Psi(\vec{r})\vec{n}$, w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/377792",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Is it possible to have a non mathematical explanation of the dependence of Pair Production cross section with energy? Cross section of pair production with interaction of photon increases with energy. But why does that happen? I want a non mathematical answer on this.
| A photon, no matter how much energy it has, will not turn into a pair of particles because of conservation of momentum and energy. The photon does not have a center of mass because it has no rest frame . Any pair of particle-antiparticle will have a rest frame, so there is a reductio ad absurdium.
In order for a pair ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/378077",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
In pilot wave theory where is the wave? As a non specialist, for a single particle system it's easy to appreciate the concept of a pilot wave extending through all Euclidean space, guiding a particle which ends up at a location determined by the pilot wave and its initial location.
For multiple particles however the wa... | The "pilot wave" is just the usual wave function of quantum mechanics.
If you have $N$ spinless particles, it is a map: $\psi: \mathbb{R}^{3N} \to \mathbb{C}$. This means it lives in the 3N-dimensional configuration space of the particles. I should emphasize that this is not a specialty of pilot wave theory but just t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/378246",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Wave in expanding medium How is the behaviour of a wave modelled in a medium that is expanding faster than the wave is propagating within it?
I ask obviously because of the applicability of the question to the concept of an expanding universe.
Also, if energy cannot be created or destroyed but only transferred, and if ... | As the wave is moving, it loses energy due to various forces like friction acting on it. Hence, the wave will come to a stop in the end.
Also, if energy cannot be created or destroyed but only transferred, and if energy has been lost from a part of the system in the emission of the wave, where is (or what is the natu... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/378405",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Mixing Gases for laser Hello stack exchange community! I finally found a way to ionize air for less than $200! 1 small problem is mixing gases is coming out to be very difficult and i dont know if this is the right place to ask but here we go. What is my best way of mixing gases like co2, air, and helium = 1:1:6. What ... | This really isn't the correct forum. Engineering would better address your question, but here's my thoughts.
If accuracy in mix is critical then your best approach is to use flow feedback controllers with mass flow meters that all mix into your chamber or manifold.
But it sounds like you are trying to keep the price lo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/378532",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
why is the photopeak at a higher energy than the compton edge? Why does the photoeffect deposit more energy than interactions via Compton scattering?
Or the other way around: Why is the photopeak right (at a higher energy) than the Compton edge?
https://en.wikipedia.org/wiki/Compton_edge
I know that the interactions ... | In short, the photopeak is formed in the case of complete absorption of the gamma ray's energy in the scintillator or detector, while the Compton edge is the maximum amount of energy absorbed by the scintillator in the process of Compton scattering, where there is an incomplete absorption of the gamma ray's energy as i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/378672",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 1
} |
Stone-von Neumann theorem According to Stone-von Neumann theorem, any two canonically conjugate self adjoint operators following the relation: $$[\hat{q},\hat{p}]=i\hbar$$ cannot be both bounded.
I am confused about how we prove this part and what does it mean physically?
Can anyone explain?
| I commented that the Stone-von Neumann theorem is not a proof for the statement in the beginning of the question. The original proofs of the Wielandt-Wintner theorem (incidentally proved only in 1947-1948, while the Stone-von Neumann theorem had a satisfying proof by von Neumann already by 1931) are found in:
Wintner, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/378951",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
} |
Does radiation cause a change in temperature? If yes, then is there a limit to the temperature decrease? If no, then can the body which radiates heat attain an absolute zero temperature?
| Everything is gaining and losing heat all the time, partly by radiation, and partly by other processes, such as conduction. The temperature of an object changes until all of these heat fluxes sum to zero, at which point it is in equilibrium and the temperature remains constant. If you could put an object in an infini... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/379105",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
Is Mass Flow an Additive Property? Mass ($m$) is an additive property in the sense that the total mass within a system can be simply determined by adding up the mass of each individual substance that's in it.
However, if two mass flows ($m/t$) of different liquids were to be mixed to form a single flow, would the resu... | (Assuming that by "mass flow" you mean the mass flow rate $\dot m$)
Yes. Since mass is a conserved quantity, it obeys the continuity equation in the form
$$\frac{\partial \rho}{\partial t} + \nabla \cdot \mathbf j =0$$
where $\rho$ is the mass density and $\mathbf j$ is the mass flux.
As a consequence, if two flows wit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/379195",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Tesellation: What does the trace of a rotation matrix means? The crystallographic restriction theorem says that you cannot have a periodic lattice with $n$-fold rotation symmetry, with $n$ different from 1,2,3,4 and 6 (for 2D and 3D).
There are many ways to prove the theorem, see the Wikipedia article. I understand som... | Consider transformation of a set of primitive translation vectors $e_a$, $a=1...d$ of a $d$-dimensional lattice under rotation $O$:
$$
Oe_a = \sum_{b=1}^d k_{ab}\ e_b.
$$
If rotation is a symmetry of a lattice then coefficients $k_{ab}$ are integers. Thus rotation matrix written in $e_a$ basis has integer elements and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/379310",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
Physical significance of the zeroth component of 4-velocity and 4-force Is there any physical significance of the zeroth component of the four velocity vector and four force vector? I understand that the space part of u$^\mu$ is related to ordinary velocity and space part of F$^\mu$ is the usual force. But are there an... | The zeroth component of a 4-vector is often referred to as its "time-like" component because it is analogous to the time axis in $(t,x,y,z)$ spacetime. So physically saying, components such as $u^0$ or $F^0$ are simply the same as their spatial cousins, with a difference of a factor of $c$ ($m/s$) for dimensional consi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/379441",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
How to measure a static electric field? I looked up google but didn't find any design for measuring electric field that doesn't vary with time.
My own idea is to use two parallel plates (like a capacitor but without the dielectric). In an electric field E a potential difference V = Ed (d is separation between the plat... | According to this source, there are electric field probes based on three orthogonally placed dipole antennae. Such probes have applications ranging from measuring radiation levels in fields to satellite detection of earthquakes.
A dipole often orients itself in the direction of the electric field.
Thinking something w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/379682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 2
} |
Why are two solutions to the field equations necessary to get the full Schwarzschild metric? For a long time I've wondered why it was/is necessary to have separate solutions to the field equations for the interior and exterior metrics of a Schwarzschild black hole. Is there something weird going on at the event horizon... | They're not two separate solutions. It's just that when you express them in a particular set of coordinates, the Schwarzschild coordinates, the coordinates misbehave at the horizon. There are other coordinates, such as the Kruskal-Szekeres coordinates, that don't have this problem.
The other thing to realize is that it... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/379959",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is chewing gum only elastic for a brief period when pulling it out of your mouth? Assume you are chewing some gum and pull it out of your mouth like so:
If you release the gum quickly it will spring back to your mouth as if it is elastic, but if you leave it for a few seconds then release it will just fall down li... | Gum acts springy on short timescales and like a very viscous liquid on longer timescales. That is, its stress-strain behavior is time-dependent. Here is why:
The gum consists of long molecules with kinks and bends in them, oriented in random directions and tangled up with one another. when you quickly pull on the gum, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/380576",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Gauss's Law for Gravity to find the Gravitational field of a finite rod To find the gravitational field at Point P in the figure:
One solution is to draw the field of a mass $$\mathrm{d}\vec{g} =\frac{G\,\mathrm{d}m}{r^2}$$ and integrate over $\mathrm{d}m$, adding vectorially.
However, if one uses Gauss's Law for Grav... | Gauss's law is a important and when first introduced it is applied to simple situations the show that it predicts values for gravitational fields which are consistent with those found when using the inverse square law.
So you start with a point mass and draw a Gaussian sphere centre on the mass around it.
Applying Ga... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/380675",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
Is the notion of Lebesgue Measure a necessary construct for statistical physics? In chat last night a user and I were discussing the "physical" meaningfulness of the notion of lebesgue measure. In particular, we were curious as to whether physicists can "make do" without it. I mentioned that the dominated convergence t... | edit I have edited the answer to deal with some of the criticism in the comments
To the extent that the Lebesgue measure is needed to define Lebesgue integration, it is central to Quantum Mechanics: in general we require wavefunctions, as a function of position, to be Lebesgue square integrable.
More specifically, in ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/380814",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 3,
"answer_id": 1
} |
Primordial Black Holes mass diference with isomass stellar black holes How can we distinguish, for a given mass (measured from gravitational waves experiments and or other experiments) of a black hole or black hole binary, if they are PRIMORDIAL or they are stellar black holes or any other weird origin?
| That is very difficult. A black hole time dilates and redshifts radiation emitted by objects so it becomes virtually impossible to detect. As a result a black hole formed in the big bang and one formed by stellar collapse appear indistinguishable. The classical idea of a black hole is that it has “no hair,” which is to... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/380897",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Has anyone driven a bell or tuning fork using light? In principle a metal bell or tuning fork of sufficiently high quality factor could be driven by audio frequency radio waves of sufficient power to produce an audible hum. Has this been done, yet? If not, what combination of quality factor and transmission power would... | You can use, for example, photoacoustic effect in gas inside a resonator (https://www.ibp.fraunhofer.de/content/dam/ibp/de/documents/Kompetenzen/Akustik/Photoakustik/pdf1_tcm45-48829.pdf)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/381076",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.