Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Notation for the divergence of a rank 2 tensor I am studying advanced fluid mechanics and sometimes you see equations written in index notation like
$$ Dv_i= \partial_t v_i +v_j\partial_jv_i$$
but sometimes you find this arrow/vector notation (what is the name of this notation?)
$$ D \vec{v} = \partial_t \vec{v} + (\ve... | In this answer I use $x=x_1, y=x_2, z=x_3$ and Einstein notation. Lets take tensor A
$$A =
\begin{bmatrix}
a_{11} && a_{12} && a_{13} \\
a_{21} && a_{22} && a_{23} \\
a_{31} && a_{32} && a_{33} \\
\end{bmatrix}
$$
On wikipedia in this article I found following information (in article they use S instead A) for cartesia... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465284",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Do black holes violate the conservation of mass? This question has confused me for quite some time now. I have searched it up online, and the basic answer is: 'Mass is a form of energy. When black holes die they release the amount of energy that they should. Mass is conserved.' But there's a problem with that answer. E... | Conservation of mass is not a fundamental law of nature so the violation of it is not a problem. Mass is just a form of energy, and energy is the quantity that is supposed to be conserved. So since black holes do not violate the conservation of energy the problem you are worried about does not exist.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465446",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 0
} |
Potential in open branch of a parallel circuit with grounding
If the switch is still open, what will the electric potential at Q be, i.e. negative, positive or zero?
Is there a potential difference across the grounded point and point Q, or R3, even though the branch is open? I suppose the current would be zero in that... | In the lower part of your circuit you are dealing with resistors (including the connecting wires).
If a current $I$ passes through a resistor $R$ then there is a potential difference across the resistor $V=IR$.
No current passes through the lowest branch of the circuit which includes the switch because there is no co... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465593",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Initial values of creation/annihilation operators I have a question about creation/annihilation operators. For example, if I have an evolution equation for annihilation operator of photon
$$ \frac{da_k}{dt} = -i \omega_k a_k$$
I obviously obtain
$$a_k(t) = a_k(0) e^{-i \omega_kt} $$
I not fully understand how to find i... | The problem is that you are not very specific here. Let me try to infer as much as I can, and then you need to correct me. You are working in the Heisenberg picture here. That means your state is independent of time but you time-evolve your observable instead. Your notation suggests that you are considering a periodic ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/465685",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Physical example of line charge Electric field due to an infinite line charge, sheet of charge, point charge, etc are popular problems solved in most text on Gauss's law of electromagnetism.
My question: does an (exact or approximate) example of "infinite/finite line of charge" exist in the physical world?
While we fi... | The magnetic field due to a current in a wire can be derived by considered it to be the resultant of Coulombic fields arising from (a) a line of positive ion-cores in the wire and (b) a moving line of electrons. Bearing in mind length contraction, it can be shown (for example Resnick: Intro to Special Relativity) that ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466055",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Question regarding Lorentz Transformation formula So the Lorentz Transformation formation equation are
$$x′=\gamma(x−vt),$$
*
*Does $x′$ and t represent time and position at one event(one instance) or do they represent two events- meaning is $x'$ actually $x_2-x_1$
*I am rather confused on when to use the Lorentz e... | The equation you've given is not the full Lorentz transformation. There is also a transformation giving t'.
Does x' and t represent time and position at one event(one instance) or do they represent two events- meaning is x′ actually x2−x1
It works for either purpose.
Can't I just use the time dilation and length con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466211",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is meant by "collective behavior" in the definition of plasma?
"Plasmas are many-body systems, with enough mobile charged particles to cause some collective behavior ." [M.S. Murillo and J.C.Weisheit Physics Reports 302, 1-65 (1998)].
In the above definition what is meant by "collective behavior" ?
| Plasmas are controlled by long-range interactions (i.e., Coulomb potentials and magnetic fields) and so the particles respond accordingly. Since electric fields do work to get rid of themselves, a plasma will reach what is called a quasi-neutral state, i.e., equal number densities of oppositely charged particles or:
$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466309",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Do scalar quantities have magnitude only? I've heard that vector quantities have both magnitude and direction but I've never heard that scalar quantities have magnitude only. Magnitude of vector quantities cannot be negative but what about scalar quantities, like temperature (-1°C)?
If scalar quantities don't have magn... | A scalar $x$ has magnitude $|x|$, also known as the absolute value. Celarly, $x \neq |x|$ for negative $x$, but instead of saying the scalar has a direction, we would say that it has a sign (+ or -), which is a much simpler concept. Maybe your confusion arises from the fact that a two-dimensional vector can be describe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466426",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 1
} |
Is there a higher dimension analogue of Noether's theorem? So I have recently read the proof of Noether's theorem from the book variation calculus by Gelfand. Basically, what I have already seen is that for any single integral functional, if we have a transformation that keeps the functional invariant, we can derive a... | In field theory, you often consider "Lagrangian densities" which are to be integrated over space-time instead of just over time.
For example, where as in the one dimensional case you would write
$$
S = \int dt L
$$
in field theory you would write
$$
S = \int d^4 x \mathcal{L}.
$$
The equation of motion will be a PDE.
N... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466705",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Experimental tests of Schrodinger evolution, position distribution, in square well and other simple systems? Have the energy eigenfunctions in position space ever been experimentally tested for the simplest system undergraduates encounter when learning quantum mechanics, the square well? If not, what is the best exampl... | You may wish to consider the exeriment by Crommie, Lutz and Eigler (Nature 363, 524 (1993)), who look at standig waves between step edges in a surface two-dimensional electron gas using scanning tunneling microscopy. Other experiments by the same IBM group have shown the standing waves in quantum corrals. Generally, ST... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466817",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 1,
"answer_id": 0
} |
Why is there so much iron? We all know where iron comes from. However, as I am reading up on supernovas, I started to wonder why there is as much iron as there is in the universe.
*
*Neither brown dwarfs nor white dwarfs deposit iron.
*Type I supernovas leave no remnant so I can see where there would be iron relea... | The nucleosynthesis in the inner of the stars generates energy: The huge amounts of energy form Helium from hydrogen. The star then start generating carbon from helium and so an. This finishes with iron. To generate with larger atomic numbers the star needs more energy. Most of them are generated in supernovae, where ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/466889",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 4,
"answer_id": 2
} |
Confused about forces acting in this simple statics problem I'm trying to solve this statics problem to find the internal tension that results, in each member:
It shows 3 idealised weightless rigid members hinged in a vertical plane, in an isoceles triangle. Two of the members carry identical loads at their midpoint (... | $F_1=0$. Reasoning: forces on left diagonal must be symmetric to right diagonal. Hence $F'_1$ on the left diagonal equals $F_1$. But $F_1$ and $F'_1$ are action and reaction forces. Hence are opposites.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467018",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Counterterms in quantum brownian motion In the part "Quantum Brownian motion" of the book, The theroy of open quantum systems written by Breuer, the author investigates on the Caldeira-Leggett model:
The Hamiltonian of the particle is
$H_{S}=\frac{1}{2m}p^{2}+V(x)$
The particle is coupled to a bath consisting of a lar... | There is nothing quantum or explicitly divergent here, but even at the classical level the extra "push" from the interaction with the bath oscillators changes the potential seen by the particle so that it is no longer $V(x)$. The counterterm is designed to cancell this effect so that the parameters in $V(x)$ coincide... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467134",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at the Killing horizon? Let $\chi$ be a Killing vector field that is null along a Killing horizon $\Sigma$
Why is $\chi_{[\mu}\nabla_\nu \chi_{\sigma ]} = 0$ at $\Sigma$?
| This is a partial answer. It assumes that the Killing field $\chi$ is normal to the Killing horizon. This implies that $\chi$ is null along the horizon, so it is consistent with the condition given in the OP. However, a Killing field that is null along the horizon is not necessarily orthogonal to the horizon; that's wh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467291",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Particle accelerators and the amount of radiation they emit Do particle accelerators emit a lot of radiation? If they do, can someone give me a rough estimate of how much?
I'm also curious as to what kind of radiation they give off.
| The idea of a storage ring is to store the beam, so giving off radiation means either losing beam, or losing energy. The later is accomplished via synchrotron radiation (accelerating charged particles in a circle), and is easily computed from the current, the energy, and the bending radius.
In the usual LINAC (linear a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467407",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Lorentz contraction of the wavelength of light I couldn't find this question on the suggested "similar questions". If this has been asked before please direct me to answer. My question is "why isn't the wavelength of light,which is in the direction of motion, going at the speed of light Lorentz contracted to zero inste... | The Lorentz contraction factor $\gamma$ describes the length of an object in relation to the object's length in its own rest frame. Light doesn't have a rest frame, so the same analysis doesn't apply.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
} |
Strong empirical falsification of quantum mechanics based on vacuum energy density It is well known that the observed energy density of the vacuum is many orders of magnitude less than the value calculated by quantum field theory. Published values range between 60 and 120 orders of magnitude, depending on which assumpt... | This is a very good question. As noted above it is not a prediction of "ordinary" quantum mechanics but of QED/QFT. As it is probably the wrongest prediction ever, something fundamental is wrong. However since predictions of QED tend to be very accurately confirmed by experiment, it cannot be a complete falsification. ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/467939",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 9,
"answer_id": 3
} |
Find the time when tangential acceleration is equal to radial acceleration
A particle begins to move along a circular path of radius R with a constant magnitude tangential acceleration of $a_t$. After time $t$ it's the centripetal acceleration is equal in magnitude to tangential acceleration. Find $t$?
My Attempt:
$$... | You don't want to treat your final equation as a differential equation you need to solve. That equation is only going to be valid at one instant in time, whereas if you integrate it you will be assuming it holds at all times, and hence you won't have a constant $a_t$. Really what you have for a single time $T$ is
$$a_t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468021",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Violation of Stefan's law when shining a light on a black body Suppose there is a black body in a dark room and the room temperature is constant. Now a ray light is shone upon it. Since a black body absorbs all radiation that falls upon it, it must absorb more radiation than it did when no light fell on it, but accordi... | Before the light was shone on the black body the temperature of the black body was constant because the rate at which energy was radiated out to the surroundings was equal to the rate at which it absorbed energy from the surroundings.
When the light was shone on the black body continuously and absorbed by the black bod... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468160",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
How do I find the pulling force required to lift an object in a system of 3 pulleys?
In the image above, assume that the person is lifting the 12.5 kg weight at a constant velocity and the pulleys are frictionless. In this case, what would the pulling force be?
Here's what I've tried:
I assumed that the resultant forc... | While analyzing tensions in the ropes is a valid way to solve this problem, one can also consider that:
$$ F = \frac{dE}{dx}$$
so lifting the weight a distance $x$ off the ground (which is plain old lifting, $F=mg$), you have to pull the rope a distance $x/2$, so the force should be $2mg$.
Note that the main purpose of... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468268",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Buoyancy question Suppose we have a ball of volume V and a block of the same volume V whith same density. We submerge the ball into some kind of liquid so that $\frac{1}{2}V$ is submerged into the liquid. We do the same thing with the block. Now $\frac{1}{2}V$ of both block and ball is submerged into the liquid. At thi... | This diagram might help you understand what is going on?
The initial position of the sphere is shown in grey and the new position of the sphere is shown in orange.
The pressure on all parts of the sphere below $XY$ increases by $h\rho g$ when in the new position $X'Y'$ and those parts all contribute to an increase ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468370",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Velocity of efflux when fluid is itself moving In efflux velocity given by Torricelli equation:
$$ v^2=2gh $$
what is reference frame for this $v$. Is it fluid or ground? I am just a high school level student, so please forgive my ignorance.
| The velocity $v$ is the velocity relative to the container and the fluid in it. That is, the fluid in the container is taken to be at rest, so $v$ is the velocity increase as the fluid is forced through the hole.
Torricelli's law is simpler than you (probably) think. It just uses conservation of energy to say the incre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468536",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Effect of earth's rotation in ballistics For this purpose, let's consider earth's rotations constant. Do earth rotation momentum get transfered to any object (a missile for example) that get's lauched? If so, why do we have to consider earth rotation when lauching the missiles? Wouldn't just follow earth rotation? (Btw... | Earth's rotation velocity does get transferred to any object (a missile for example) that gets launched. The reason why we have to consider Earth's rotation when launching the missiles is the target rotates together with the Earth. Let us consider the following example: a missile is launched from point A to deliver som... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468682",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 5,
"answer_id": 2
} |
Feynman diagram for semileptonic decay of neutral kaon I am unsure how to draw a feynman diagram for a reaction that occurs as follows
$$ K^0 --> l^+\nu_l\pi^- $$
Any tips would be helpful.
| Because neutral currents have not been observed and flavor changing can only be done with the emission of W bosons the strange antiquark will decay to an up antiquark and W- boson . The W- boson will decay to an electron and an antielectron neutrino. The pion formed by the up antiquark and the down quark will decay to ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468830",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why does a single X-ray photon generate 1620 electrons when it hits CCD detector? Fe55 is one radioactive isotope.
It emits X ray photons : mainly k-alpha & k-beta lines.
Why does a single X-ray photon generate 1620 electrons when it hits CCD detector ?
While, in photo-electric effect, single photon generates single el... | The iron K-alpha edge is at around 7,000 eV and that bandgap of Silicon is about 1.1 eV.
Let's assume that all that happens when the x-ray hits the ccd is that the x-ray is completely absorbed to create excited electrons. Then we can expect 7000/1.1 or about 6300 electrons from a single x-ray photon. This is a rough es... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/468945",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why doesn't a table tennis ball float on a surface of steel balls? How do we calculate buoyancy here? Place the beaker full of steel balls and submerge the table tennis ball under the steel balls. The table tennis ball does not float up. Why does it not float up? Do table tennis balls float when the diameter of steel b... | Well, what if the steel balls were extremely small, say molecular size. In that case, the constraining annulus would look like a polished steel collar, and would likely hold down the ball even if the glass was shattered, underwater, in a swimming pool. . (The van der Waals forces, and metallic bonds, would accou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469105",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "16",
"answer_count": 2,
"answer_id": 1
} |
Clarification on isotope notation I am a bit confused about the idea of isotope notation. I know that the top number is the mass number, equivalent to the number of neutrons + protons, while the bottom is the atomic number, equivalent to the number of protons.
What I don't understand is why during beta decay, the elect... |
Can the atomic number be considered as just the charge?
It's not standard to talk about an electron as having an atomic number. However, if you interpret these numbers as charges, then the system you've been taught makes sense.
However, where does this electron originate from if the nucleus originally only contains ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469247",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Minimum Angular Velocity
A bead is free to slide on a vertical circular frame of radius $R$ comes to equilibrium when $\cosθ = g/Rω²$.
The minimum value of angular velocity comes out to be $\sqrt{g/R}$, which we can find out by balancing Gravitational and centripetal force with Normal reaction to bead from the frame... | If your formula was correct, then the maximum $\cosθ = 1 = g/(Rω^2)$. However, it is not correct. Assuming $θ$ is measured up from the (downward) vertical to the radius going to the bead, then: $N(\cosθ) -mg =0$ and $N(\sinθ) = m(Rω^2)$.
Solve the first equation for $N$ and put it into the second. Then: $(mg/\cosθ)... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469344",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Unable to get interference from milk using Time domain OCT (Michelson Morley interferometer) approach I was able to construct time domain Optical coherence tomography based on Michelson Morley interferometer using a LED. While testing the interferometer, I used glass slide, layers of scotch tape. I was able to get frin... | Possibly the milk particles are too small, the light randomly scatters throughout it, the returned scattered light then has random phase variations, and the fringes are washed out.
Ideally, you’ll have optical interfaces from which the light can reflect with a particular phase delay relative to the reference beam.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469458",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How do I Fit a Resonance Curve with Respect to Known Data? In an experiment, I collected data points $ (ω,υ(ω))$ that are theoretically modelled by the equation:
$$ υ(ω)=\frac{\omega \, C}{\sqrt{(\omega^2-\omega_0^2)^2+γ^2 \omega^2}} \,.$$
How can I fit the data to the above correlation? And how can I extract $\gamma$... | If we put:
$$Y = \frac{\omega^2}{u(\omega)^2}$$
and
$$X = \omega^2$$
the equation becomes:
$$Y =\frac{X^2}{C^2} +\frac{(\gamma^2 - 2 \omega_0^2)}{C^2} X + \frac{\omega_0^4}{C^2}$$
You can then extract the coefficients using polynomial fitting. To get the least-squares fit right, you have to compute the errors in $Y$ an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/469754",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 4,
"answer_id": 1
} |
Is it possible to trigger a nuclear reaction with physical force? In Mission Impossible Fallout, they're dealing with 3 plutonium cores. If one of those cores was thrown against a wall by Ethan Hunt, could it start a chain reaction and explode? For that matter, could any blunt force cause the nuclear reaction to initia... | As written in direct comments to the question: in the case of fission bomb designs the critical mass state is achieved by setting off a chemical explosion. .
As written in comments: the problem is to design the chemical explosion in such a way that you get a significant yield of nuclear chain reaction.
By contrast:
If ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470192",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 5,
"answer_id": 2
} |
Micro-world Perception: What does a microbe perceive as it's being, say, sloshed in a glass of water? I've wondered how micro-organisms perceive the larger world, it's forces and the
consequences the relatively massive forces have on such tiny objects.
Let's say E coli (0.5 micro meters width, 2 micro-meters length) i... | As pointed out by PM 2Ring, as animals get smaller, the effects of the viscosity of the water become greater. A human pushes his or her way through the water; a goldfish wiggles their way through the water, and an animal the size of a water flea (1/10th of an inch, or less) crawls through the water as if it were pancak... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470347",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Observing the conserved canonical momenta Suppose I have a Lagrangian $\mathcal{L}[\phi]$ with $\phi$ a cyclic variable, which means that the Lagrangian is symmetric under shift of $\phi\rightarrow\phi+c\quad$.
The equation of motion will be simply the conservation of the canonical momentum:$$\partial_{\mu}\frac{\parti... | Generally I can observe $J^{\mu}$ whenever I add to the Lagrangian a coupling of the field $\phi$ to some other field, say $\psi$, in such a way that there is a vertex containing one $(\partial^{\mu})\phi$ line and only a vector combination of $\psi$ lines, say $b_{\mu}(\psi)$.
This vertex generates an operator $\lang... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470469",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Are microwaves sinusoidal or is that just a model? I know that projectiles are parabolas because I can derive that from constant acceleration. And the height of a Ferris wheel rider vs. time is demonstrably a sine wave. What is the underlying thing that tells us microwaves are sinusoidal vs. some other periodic shape... | The wave equation for light tells us that solutions are sinusoidal:
$$ \frac{\partial^2 E}{\partial t^2} = c^2\frac{\partial^2 E}{\partial x^2}$$
(here, in one dimensions with the electric field $E(x, t)$ a function of position $x$ and time $t$).
If you guess a sinusoidal solution:
$$ E(x, t) = e^{i(kx-\omega t+\phi)}$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470602",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why we fill dU/dT value in Cv(specific heat at constant volume) only and why not in Cp? According to equipartition of energy, the energy ossociated with each degree of freedom is $\frac{K_{b}T}{2}$ for one molecule .
For 'x' molecule which has degree of freedom f it's energy is given by
$U= \frac{f k_{b}Tx}{2} = \frac... | Because specific heat at constant pressure is defined in terms of enthalpy $h$ and not internal energy $u$. It is defined as
$$C_{P}=\biggl(\frac {δh}{δT}\biggr)_P$$
PROOF:
Since
$$h=u+Pv$$
$$\biggl(\frac{δh}{δT}\biggr)_{P}=\biggl(\frac{δu}{δT}\biggr)_{P}+\biggl(\frac{δ(Pv)}{δT}\biggr)_{P}$$
$$\biggl(\frac{δh}{δT}\bigg... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470741",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Rocket Leaving Earth's Gravitational Field I stumbled across this seemingly simple question that really stumped me on further thought:
A rocket is intended to leave the Earth's gravitational field. The fuel in its main engine is a little less than necessary, and an auxiliary engine, only capable of operating for a sho... | In principle, I'll say that it is the same. We can imagine the small auxiliary engine like a little bit of more fuel in the main tank, which is the same as all the other fuel.
In practice, it depends on how efficient the engine is:
Rocket engines generate thrust by pushing back the exhaust gases from fuel burn. More ef... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470875",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 4,
"answer_id": 0
} |
How can the big bang be "observed"? The Big Bang Observer is a proposed spacecraft to study gravitational waves. Especially the one that are thought to originate from the Big Bang. Question. How can we observe waves that has an origin at the beginning of time? Doesn't it implies then that we were there when it happened... | The aim of the Big Bang Observer would be to study gravitational waves generated during the inflationary period that took place some $10^{-32}$ seconds after the Big Bang.
One of the frequently misunderstood aspects of the Big Bang is that it didn't happen at some point, with the universe expanding outwards from that p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/470997",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Quantum energy levels of a point mass rotating about a fixed point The question is: A particle of mass m is attached to a fixed point in space by a massless rigid rod of length a and can freely rotate about this point. Find the quantum energy levels of the system. What is the degeneracy of each energy level?
I used rot... | As @probably_someone wrote in his comment:
It might be easier to think of the equivalent problem: a particle is constrained to move on a fixed sphere, with no other forces besides the constraint (which is what is meant by "free" in this context).
Now I guess that the non-degenerate energy levels you wrote down are c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471357",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Do electrons in a flash of lightning oscillate between Earth and the clouds (or between clouds)? In this video, around 2:24, one can see a flash of lightning that keeps the same form for a little time span. Does this mean that it takes a while before the discharge is complete (which I can't imagine) or that the electro... | Lightning is a rapid transition from a non-conducting to a conductive state.lightning creates an ionized, electrically conductive channel through air inside the cloud,between clouds or between cloud and earth.The high electric field accelerates the electrons between the channel.When they collide with air molecules, the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471502",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Potential by Assembling Charges For finding electric potential energy of a uniformly charged sphere, we can assemble the sphere by brining charges from infinity to that point. So to make a uniformly charged sphere of radius $R$ and total charge $Q$, at some instant, charge will be assembled up to a certain radius $x$. ... | The first thing to note is that the electric potential at a point is entirely different to the electric potential energy of an assembly of charges.
I have assumed that you are finding the potential at a point and you have used two definitions of the zero of electric potential, one at infinity and the other at the centr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471655",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
Density of supermassive black holes So I know that supermassive black holes can have "densities" less than water because black hole density scales as $1/m^2$ since $R_s = 2GM/c^2$. I am trying to reconcile this with the fact that black holes are the most compact objects for a given mass.
For instance, if I had 6 billi... | If I'm understanding the question correctly, then you're trying to reconcile two statements: (1) A Schwarzschild black hole consists of empty space. (2) A sufficiently compact distribution of matter is a black hole.
These statements are not in contradiction to each other, because a Schwarzschild black hole is just one ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471814",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Why couldn't they take pictures of a closer black hole? The latest photos of the M87 black hole capture light from around a black hole at the center of the Messier 87 galaxy, which is 16.4 Mpc ($5.06 \times 10^{20}$km) from our milky way.
Why couldn't / didn't the scientists involved take photos of black holes less dis... | Since this isn't covered by Rob Jeffries' answer, let me add that Sagittarius A* (the black hole in the centre of Milky Way) was considered, but as explained by Heino Falcke at press conference revealing the photo (quoted after Deccan Herald)
Sagittarius A Star is 1000 times faster and smaller. Its like a toddler who ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/471920",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "18",
"answer_count": 2,
"answer_id": 0
} |
Integrability of a non-integrable quantum spin model at critical point Is it right, that non-integrable quantum spin models in one dimension become integrable at their critical points? Or do they stay nonintegrable at the critical point also? Are there any examples known? In the field of 2d classical models, the three-... | If the non-integrable quantum spin chain at the critical points can be described as a conformal field theory (not always the case), we can say that the model is "integrable''. Because CFT can be seen as an "integrable'' theory since it can be solved exactly and Yang-Baxter relation is satisfied naturally. If the critic... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472064",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "9",
"answer_count": 2,
"answer_id": 1
} |
Do working physicists consider Newtonian mechanics to be "falsified"? In the comments for the question Falsification in Math vs Science, a dispute around the question of "Have Newtonian Mechanics been falsified?"
That's a bit of a vague question, so attempting to narrow it a bit:
*
*Are any of Newton's three laws c... | "Falsified" is more philosophical than scientific distinction.
Newton laws have been falsified somehow, but we still use them, since usually they are a good approximation, and are easier to use than relativity or quantum mechanics.
The "action at distance" of Newton potentials has been falsified (finite speed of light.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472215",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "21",
"answer_count": 6,
"answer_id": 1
} |
Expansion of an ideal gas at constant pressure I approach these expansion problems like so:
The gas and the surroundings(piston+outside) are at the same pressure at first. We heat the gas. The pressure rises inside the syringe a bit. The gas expands so the pressure remains constant. Then I use P(the constant pressure ... | If the heat addition occurs very slowly such that the pressure and temperature gradients in the gas approach zero, the process can be considered quasi-static and the pressure of the gas will always be very close to the external pressure. If the process is also frictionless, then we can say it is a reversible isobaric e... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472431",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Angular momentum of a body about a point rotating about its own axes I want to calculate angular momentum of a sphere about point O. The sphere is rotating about its two axes with angular velocities $w_1$ and $w_2$.
I know that angular momentum = $m\vec{r}\times\vec{v} + Iw$, where v is velocity of centre of mass. Here... | A rigid body can only have one rotation axis. When the angular velocity vector has multiple non-zero components, like $$\vec{\omega} = \pmatrix{ \omega_1 & \omega_2 & 0}$$
then the magnitude of rotation is described by the length of the vector $$ \omega = \| \vec{\omega} \| = \sqrt{ \omega_1 ^2 + \omega_2 ^2 } $$
The r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472527",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
What is the electric potential inside a point charge? We know that electric potential of spherical charge is inverse proportion with $r$ from $V = \frac{kq}{r}$ , So if $r$ is getting less then electric potential will be higher.
But , What about point charge ? Is it infinity inside it ? My teacher told me that it's zer... | When dimensions become very small, we are no longer in the realm of classical physics where potentials have mathematical singularities as in the classical 1/r Coulomb potential. Point particles belong to the realm of quantum mechanics and there the laws and computational rules are different.
The electron is a charged p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472691",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 1
} |
How do you calculate the error propagation in a Helmholtz coil? I'm having some trouble with the error propagation expression in a Helmholtz-coil.
Specifically $\frac{\frac{∂B}{∂R}}{B}$.
If anyone could help, I'd be really grateful.
The formula used is
$$B(x) = \frac{NMI}{2R} \cdot \left(
\left(1+\left(\frac{x+\frac{a}... | HINT: The error propogation can be calculated for a relation $Z\pm\Delta Z=(A\pm\Delta A)^n(B\pm\Delta B)^m$ , and $Z\pm\Delta Z=\frac{(A\pm\Delta A)^n}{(B\pm\Delta B)^m}$
$$\frac{\Delta Z}{Z}=n\frac{\Delta A}{A} +m\frac{\Delta B}{B}$$
The propogation for $Z\pm\Delta Z=(A\pm\Delta A)(B\pm\Delta B)$ is:
$$\Delta Z=\Delt... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472818",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is polarization complementary along its different axes? Is polarization complementary along its different axes -- much like the spin of a particle is -- thus implying that the uncertainty principle holds for polarization measurements on these different axes?
| The answer is yes, in the sense of mutually unbiased bases.
Polarization can be expressed in terms of $2\times 2$ Pauli matrices, and the eigenstates of the Pauli matrices are mutually unbiased, meaning that, if $\vert \pm\rangle_i$ are the two eigenstates of the Pauli matrix $\sigma_i$, then eigenstates of any of th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/472919",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
My hairs on my hand stand straight whenever I move my hand to TV screen and feel vibration and sound on TV screen Whenver I try to reach my hands near the screen of my TV . My hairs on my hands get straight and more importantly I can hear and feel a sound and kinda vibration . Please mention if this sound duplicate. My... | Is your television tube-based or LCD?
Tube-based TVs work by shooting electrons at the front of the display. Most of these get recycled back to the back of the tube using a wire that connects on a pad that's just behind the front, under the case where you can't see it. However, the front of the display is not perfectly... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473148",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Interacting term in Jellium model I have a question about the deduction of interacting term in Jellium model. In the text book Condensed Matter Field Theory ed.2 Alexander Altland, Ben Simons, pg.52. Author gives the expression of e-e interaction without deduction details:
$$
V_{ee}=\sum_{k_1,k_2,q} a^\dagger_{k_1-q \s... | Suppose that you have two quartic terms with different orderings, like $a^\dagger a^\dagger a a$ and $a^\dagger a a^\dagger a $, assuming that total momenta and Lorentz spins etc. of the oscillators sum to zero. As you say, if you try to re-order one of them you "wrong" terms via the commutator $[a^\dagger,a]=1$, like... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473312",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
How does light 'choose' between wave and particle behaviour? Light exhibits wave behaviour in phenomenon such as interference but particle behaviour in the photoelectric effect. How does light 'choose' where to be a wave and where to be a particle?
| The light doesn't chose. You as an experimenter chose which observable you want to measure, and thus which operator you use. Such measurement will result in a wavefunction collapsing into one of the eigenstates of this operator.
E.g. a positiin operator will give you a position, i.e. particle.
A momentum operator will ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473566",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "60",
"answer_count": 11,
"answer_id": 3
} |
Why is the ratio of gravitational force and the inertia to resist it 1? Is there a deeper meaning behind how things of different mass fall at the same acceleration? It feels so perfectly balanced...
| This is a priori an assumption.
In Newtonian physics, they are not assumed to be equal but because empirically they are, we often take them to be the same. For example, Newton's second law says $\vec{F}=m_i\vec{a}$ and Newton's law of gravitation says $\vec{F} = -(GMm_g/r^2)\hat{r}$. The standard (high school) calcula... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473684",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How is this derivation of a field transformation, in Weinberg's QFT book, performed? I am reading Weinberg's book Quantum theory of fields.
Could you explain to me the following things? Vol.1, page 60 (transcribed from this image):
To first order in $\omega$ and $\epsilon$, we have then
\begin{align}
U(\Lambda,a) ... | Equation (2.4.9) follows easy:
The coefficient of $\eta$ on the LHS of (2.4.7) is $-U P U^{-1}$. And on the RHS it is $-\Lambda P$ (here we don't have to worry about the indices). Set these two equal and (2.4.9) follows.
The coefficient of $\omega$ on the LHS of (2.4.7) is $U J U^{-1}$. The coefficient on the RHS is $(... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/473937",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
The Meaning of Electromagnetic 'News' in Griffiths Book In the Introduction to Electrodynamics book, by David J. Griffiths, 4th edition, page 60, the author makes the following statement:
"it is not the position, velocity, and acceleration of Q right now that matter: electromagnetic "news" travels at the speed of light... | Imagine that there was an explosion.
You are $3\times 10^8\,\rm m$ (=$1$ light second) away from the explosion.
You will receive "news" of the explosion ie see the flash of light associated with the explosion, one second after the explosion actually happened.
Here the use of the word "news" has the implication of a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/474287",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 0
} |
Lorentz Transformation: Message sent before finish line As she wins an interstellar race, Mavis has a “hooray” message sent from the back of her 300m long ship as she crosses the finish line at v=0.6c. Stanley is at the finish line and at rest relative to it. He claims the message was sent before she crossed the line... | I assume that the signal is sent when she actually crosses the finish line in the ship's reference frame (the issue of how they know when to send the signal is irrelevant).
Now, imagine that there is someone in the center of the ship that, at a time before the ship reaches the finish line, sends a signal to both, the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/474384",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
If an electric field passing through a dielectric medium, back into the original medium, is it "back to normal"? Suppose there is an electric point charge causing an electric field E in a medium with a dielectric constant $\epsilon_1$. You can calculate the scalar potential $\phi$ at a given distance $r$, as well as th... | Andreas Schuldei makes a great point about the parallel plate capacitors and different media between the plates.
On the micro level there are some important factors. An applied field distorts the electron cloud around atoms in molecules yielding a dipole moment. However, this happens among adjacent molecules/atoms. So... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/474569",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 1
} |
What had Feynman meant when he told nobody understands Quantum mechanics? What do we mean by understanding Quantum mechanics? What had Feynman meant when he told nobody understands Quantum mechanics?
What do we mean by understanding Quantum mechanics?
| He certainly meant understandable in terms of principles of classical mechanics (points of matter with masses, subjected to forces in a three-dimensional Euclidean space and satisfying deterministic evolution laws), since we understand very well quantum mechanics. That is evident from the fact that nowadays most techno... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/475662",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Cooling effect caused by evaporation Evaporation is said to cause cooling effect because it absorbs energy from surroundings to change its phase from that of a liquid to gas. I am in doubt as to why would the surroundings be ready to give up energy more than the water molecules. Wouldn't 'lower temperature of the water... | Evaporation requires the liquid molecules to overcome the intermolecular attractive forces and escape to the surroundings. Only the most energetic molecules, near the surface of the liquid, have enough kinetic energy to overcome the attractive forces. As these highly energetic molecules escape from the liquid (i.e., ev... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/475784",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 1,
"answer_id": 0
} |
When air is ionised, which component gases are actually ionised? Air is a mixture of O2, N2 etc. Which gases are ionised at STP, and is there a different level of ionisation for different gases?
| The most common ionizations are of oxygen and nitrogen. Nitrogen ionizes first (at lower levels of energy input) and yields a deep blue color. Oxygen ionizes at a slightly higher energy level and adds a pinkish-white color to the plasma. Once the plasma heats up due to current flowing through it, it begins to emit a bl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/475939",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Will tsunami waves travel forever if there was no land? If there was no land for tsunami waves to collide with, can the waves travel around the globe for forever?
| Waves keep going forever, in a way
As others pointed out already, waves tend to lose energy.
However, what will (theoretically) happen is that at any point in time the wave will lose a fraction of its energy, but never truely 100%. So though you will soon reach a point where random noise will make it practically imposs... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/476360",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "19",
"answer_count": 4,
"answer_id": 2
} |
How to calculate pumping pressure for backfilling of a borehole? I am trying to calculate the pumping pressure needed to backfill a borehole with geothermal grout. The hose is pulled up at the same rate as the borehole fills, so pumping pressure will get lower as the hole is filled. The borehole is initially filled wit... | A force balance on the grout column gives $$P_B+\rho_{grout}gy(1-i)-P_A-4\frac{\tau_w y}{D}=0$$This neglects any acceleration of the grout fluid and any drag caused by the upward motion of the hose. For the water, the force balance is $$P_A=\rho_{water}gy(1-i)$$ So, $$p_B=-(\rho_{grout}-\rho_{water})gy(1-i)+4\frac{\ta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/476928",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Deriving classical Hall effect from quantum Hall effect I'm interested in the derivation of the classical Hall effect coefficient, given in cgs by $$R_{H}=-\frac{1}{nec},$$ where $n$ is the electron number density, $-e<0$ is the electron charge,and $c$ is the usual, ubiquitous velocity in Physics, from the fact that QH... | I think you cannot derive classical case from the quantum case. $g=\text{filling factor}\cdot\frac{2e^2}{h}$ occurs at very high magnetic fields where Landau levels start filling and current is carried only by edge states. In classical regime, magnetic fields are low and Landau levels haven't started filling and there... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477190",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 2,
"answer_id": 0
} |
Can heat increase cutting power? I'm writing a book in which the protagonist has a sword that she closes in lightning. (It doesn't melt because it is made of a special material.) Could the heat generated by the superhot plasma allow the sword to cutt through metal?
| An average lightning bolt is at $30,000 K$ and contains $10^9 J$ of energy and the average sword has a weight of $1.5 kg$. For calculation purposes let us assume that the sword is made of carbon steel which has a specific heat capacity of $490 J/kg K$ and let us also assume that all the energy of the lightning bolt get... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477288",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
No hair theorem and Killing tensors I have 2 questions regarding Killing Tensors :
*
*A practical question is how to guess whether a spacetime has Killing tensors or not. We can guess some simple Killing vectors by looking at the isometry of the metric components. Is there any such simple intuition behind finding K... |
A practical question is how to guess whether a spacetime has Killing tensors or not.
This is very hard and in general case open problem, however for some situations (such as vacuum stationary and axially symmetric solutions) there are techniques. See e.g. this paper for the description of an algorithm (Cartan–K̈ähle... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477377",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Normalize accelerometer data based on non-central location I am trying to "normalize" accelerometer data for a sensor that is not centered on a car. In the image below, you can see how centripetal force changes based on location.
In my case, I only have one sensor on the right side of the vehicle. For logistical reaso... | With only the readings of one accelerometer you're out of luck.
The basic reason is that a particular reading could be due to a high-speed, large-radius turn or a low-speed, small-radius turn and the two cases call for different corrections.
If you have secondary data—such a ground velocity (speedometer speed is only a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477721",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why are orbits $1.5r_{s} < r < 3r_{s}$ unstable around a Schwarzschild black hole? The "Orbital motion" section of the Wikipedia entry corresponding to Schwarzschild metric reads:
A particle orbiting in the Schwarzschild metric can have a stable circular orbit with $r > 3r_s$. Circular orbits with $r$ between $1.5r_s$... | Regarding your first question:
In general relativity the energy of a light object moving around a spherically symmetric mass can be written as:
$E=mc^2(\frac{\sqrt{1-\frac{2GM}{rc^2}}}{\sqrt{1-\frac{v^2}{c^2((1-\frac{2GM}{rc^2})^2(\hat{r}\cdot\hat{v})^2+(1-\frac{2GM}{rc^2})|\hat{r}\times\hat{v}|^2)}}}) $
The strange pa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477810",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Is throwing dice a stochastic or a deterministic process? As far as I understand it a stochastic process is a mathematically defined concept as a collection of random variables which describe outcomes of repeated events while a deterministic process is something which can be described by a set of deterministic laws. Is... | As you commented, rolling classical dice is a deterministic chaotic process, and thus impossible to model in enough detail to predict which face will be up, unless you have very accurate input data.
More accurate than is plausible for dice rolled by hand, unless maybe you're collecting it with high rez / high-speed cam... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/477910",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "26",
"answer_count": 5,
"answer_id": 3
} |
Does a particle exert force on itself? We all have elaborative discussion in physics about classical mechanics as well as interaction of particles through forces and certain laws which all particles obey.
I want to ask,Does a particle exert a force on itself?
EDIT
Thanks for the respectful answers and comments.I edited... | This answer may a bit technical but the clearest argument that there is always self interaction, that is, a force of a particle on itself comes from lagrangian formalism. If we calculate the EM potential of a charge then the source of the potential, the charge, is given by $q=dL/dV$. This means that $L$ must contain a ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/478060",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "127",
"answer_count": 8,
"answer_id": 6
} |
Photoelastic modulator vs. Acousto-optic modulator I am trying to understand the salient differences between photoelastic modulators (PEMs) and acousto-optic modulators (AOMs).
Both of these devices are based on the photoelastic effect - that is, under mechanical stress, a medium's optical properties (e.g., refractive... | I think you are correct that in an AOM we have a traveling wave of phonons. I know experimentally that laser diffracted in the same(opposite) direction as the RF input will be up(down)-shifted in frequency. This makes sense if one thinks about the momenta of the photon and phonon adding or subtracting. Most AOMs also c... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/478213",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Is there a temporal difference between planets due to the sun's gravitational field? since the Sun generates a gravitational field it also generates gravitational time dilatation. Hence, time further from the Sun should pass quicker than in its proximity.
Can we, therefore, say that the time on Mercury is different fro... | Time dilation is a concept from special relativity. GR doesn't have a concept of time dilation, except in the special case of a static spacetime, which is the only case where the metric can be derived from a scalar potential. An observer on the surface of a planet is orbiting the sun, so the spacetime they're in is not... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/478481",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Can you change the wavelength of light keeping frequency constant and can you do the opposite as well? Can you change the wavelength of light keeping frequency constant and can you do the opposite as well?
I understood the basics but please don't hesitate to go deeper into the concept. Also, If you happened to have an ... | Why does frequency remain constant?
The reason that light does not change its frequency is because of conservation of energy. Light is made up of quanta (small discrete particles). The energy of light is proportional (or equal if you use appropriate units) to its frequency.
$$E=nh\nu$$
Where $n$ is number of quanta. Wh... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/478686",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 3
} |
Why does electrical resistivity have units of $\Omega \cdot \mathrm{m}$ rather than $\Omega \cdot \mathrm{m}^3 ?$ Electrical resistivity has units of $\Omega \cdot \mathrm{m} .$ However, since resistivity can be described as the resistance of a unit cube, shouldn't the units therefore be $\Omega \cdot \mathrm{m}^3$ in... | Resitivity can be thought of as resistance of a unit cube, but for a unit cube, the resistance doesn't work out to $\text{material constant} * \text{volume}$.
Instead, restivity ($\rho$) is given by $\rho = \frac {RA}{L}$ (where $R$ is resistance, $A$ is area and $L$ is length of material) or to rearrange in terms of n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/478820",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 2,
"answer_id": 1
} |
Is a hole better for creating a toroidal vortex than a pipe? Does a hole work better for creating a toroidal vortex, where the fluid starts to turn as it exits, than a pipe, where the flow inside is more laminar. Some high power vortex guns have a cone shaped barrel. So, is a cone better?
| enter link description here
Hope this image help you!!!
The thing here assume the pipe only one side, gas is moving similar to given image.
If it is a cone then you can see that almost all the gas entering leaves out. Hence the power is also increased.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/478916",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Viscous flow through a concave tube Consider gravity-driven incompressible flow through a concave tube with known radius $R(z)$, where pressure is atmospheric $P_a$ on both ends.
How does the viscous pressure distribution $P(z)$ compare with that of purely inviscid flow?
I think both flows should definitely have a pres... | In the case of viscous flow, I gave the answer here. Viscous laminar flow during expansion of the nozzle will come off the walls with the formation of a jet and return flow zones - see Figure 1.
In the case of an inviscid continuous flow, the distribution of velocity and pressure is shown in Fig.2. In this case, the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/479052",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 1,
"answer_id": 0
} |
Could one theoretically use the expansion of the universe to travel through it? At least in one direction? Could one theoretically use the expansion of the universe to travel through it? At least In one direction?
That’s it that’s my question.
I’m not a physicist but I do get ideas.
I also wonder if one could theoret... | The expansion of the universe is happening in all points in our surroundings, all three dimensions at a time. All points in three dimensional space were at the beginning of the universe's one point ( classically, ignoring quantum mechanics) in the beginning of time.
Think of the surface of an expanding balloon, where a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/479302",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Why are solar panels kept tilted? I have noticed that, in my country India, most of the solar panels are tilted southward at an angle of ${45}^{\circ} .$ Even on buildings with inverted V-shaped roofs, solar panels are still oriented southward on both the sides of roof.
Research
Many sites suggests that the tilt aids ... | Cleaning issues aside, the best orientation of a solar panel is the one that maximizes solar exposure.
It can be fixed or change periodically if a motor mechanism is provided. If it is static, then it can be horizontal assuming the latitude of the location is close to the equator.
Since India is near the equator, there... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/479515",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "38",
"answer_count": 4,
"answer_id": 3
} |
What happens when in space a basketball flies and hits another resting basketball? We have the following situation:
In space, a basketball flies and hits another resting basketball.
What happens next?
a) Both balls fly in the original direction (but slightly slower) = momentum conservation (inelastic collision)
b) Firs... | The word you are looking for is the Coefficient of Restitution.
The coefficient of restitution$(e)$ decides whether the collision is elastic or inelastic. It depends on the surfaces of contact between the balls. The value of $e$ is generally between $0$ and $1$. With $0$ representing completely inelastic, and $1$ rep... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/479632",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Interpreting the conserved charge in scalar QED In scalar QED, applying Noether's theorem for internal global symmetries results in a Noether current that is dependent on the gauge because of the presence of the covariant derivative.
$$j_\mu=-i(\varphi^*\partial_\mu\varphi-\varphi\partial_\mu\varphi^*)-2eA_\mu\varphi^... | The total current is gauge invariant, because the first term is also not gauge invariant, because of the partial derivative and not covariant derivative. In fact the current is just like for free charged scalar just replacing partial derivative by covariant derivative.
As intuition to the appearance of the second term,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/479733",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
Kinetic Molecular theory ideal gases, deriving the equation $PV = \frac{1}{3}mN C^2$ The problem I have with this proof is how to acquire the fraction $\frac{1}{3}$. In theory we were taught by taking into consideration a rectangular vessel which obviously has three paths which a particle can take when colliding betwe... | (a) I won't reproduce a complete proof (See for example Jeans: Kinetic Theory of Gases), but will outline how the factor of 1/3 enters, even for a container of arbitrary shape.
If we consider a small 'patch' of the container wall, it is straightforward to show that the total momentum of molecules hitting that patch pe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/479860",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Energy density in electrostatics - definition Background:
It can be shown that the potential energy of charge distribution can be calculated by
$U = \frac{1}{2}\int_V \rho(r')\Phi(r') d^3r' $
by means of integration by parts and the poisson equation $\Delta\Phi(r) = 4\pi \rho(r)$ the integral can be rewritten
$U = \fra... | You just showed that $\frac{1}{2}\rho(r')\Phi(r') = \frac{|E(r')|^2}{8\pi}$. (EDIT: as @Fabian said in the comments, it is actually that $\frac{1}{2}\int_V \rho(r')\Phi(r') d^3r' = \int_V \frac{|E(r')|^2}{8\pi}d^3r'$)
So, it does not matter whether you define $u(r) = \frac{1}{2} \rho(r')\Phi(r')$ or $u(r) = \frac{|E(r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/480197",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Write electromagnetic field tensor in terms of four-vector potential How can we know that the electromagnetic tensor $F_{\mu\nu}$ can be written in terms of a four-vector potential $A_{\mu}$ as $F_{\mu \nu} = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}$? In the vector calculus approach, this is not really hard to s... | The Bianchi identity $\mathrm{d}F~=~0$ together with Poincare lemma guarantee the local existence of $A$ in contractible regions of spacetime. See also this related Phys.SE post.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/480324",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 0
} |
Pressure in irrigation water pipe I would like to know the pressure at the bottom of the pipe which I use for irrigation purpose. The land is step cultivated and the pipe goes slanting for the length of 140 meters and the top height would be 45 meters, water is pumped out from borewell using 7.5 hp submersible pump. I ... | I gave in my comment :
use pressure = density * gravity * height. google this as there are several calculators available on the web.
Using 1000kg/m^3 for density, 9.81m/s^2 gravity and 45m
Pressure = 1000 * 9.81 * 45 = 441450 pa
converted to atm is 4.41
Different slightly to the result in the link, as I assumed 1000kg/... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/480399",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Approximation of multiplicity when Ideal gas low density is applied $\frac{M !}{(M-N)!} \approx M^{N}$ Our lecturer today mentioned how a piston's head being at equal pressure maximised the multiplicity of states.
He mentioned the following:
If I have a fixed number of particles $N_A$ on left and $N_B$ on the right,... | $$
\frac{M !}{\left(M-N\right)!}
~=~
\begin{alignat}{10}
M
& \times & \left(M - 1\right)
& \times & \left(M - 2\right)
& \times & ~\cdots~
& \times & \left(M - N + 1\right)
& \times & \left(M - N\right)
& \times & \left(M - N - 1\right)
% & \times & \left(M - N - 2\right)
& \times & ~\cdots~
% & \times & 2
& \times & 1... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/480734",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
Liouville's integrability theorem: action-angle variables For classical dynamical systems, let $I_{\alpha}$ stand for independent constants of motion which commute with each other. 'Remark 11.12' on pg 443 of Fasano-Marmi's 'Analytical Mechanics' suggest that $I_{\alpha}$s can be taken as canonical coordinates.
For a c... | I believe I understand your question. I think Different action-angle variables for a 2D harmonic oscillator is a good example. The 2D oscillator is
$$H = H_1 = \frac12( p_x^2 + p_y^2 + x^2 + y^2)$$
which may be split into
$H = H_x + H_y$
where
$$H_x = \frac12(p_x^2 + x^2)$$
$$H_y = \frac12(p_y^2 + y^2)$$
and then yo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/480959",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Operators acting on a single subsystem within a combined system's state I was reading over combined systems and operators acting on a single system within the combined system, and am confused by the math.
For example, we have individual qubit states for subsystems $A$ and $B$ that, as a combined system, produce the st... | Welcome to SE! Another way of saying what your text claims is
$$(O\otimes I)(A\otimes B)=(OA)\otimes B.$$
To prove this to yourself, you could write a general $O$, say $O=\begin{pmatrix}w&x\\y&z\end{pmatrix}$, and then just evaluate both sides of the above equation directly for $A\equiv\begin{pmatrix}a_0\\a_1\end{pmatr... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/481070",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why is baryon number conservation an accidental symmetry I have to write a report surrounding the subject of baryogenesis and I wanted to start this report off with explaining how the first Sakharov condition: Baryon number violation is possible within the Standard Model. I, however, can't seem to find a good explanati... | I think your misunderstanding is precisely that you think that $U(1)$ gauge symmetry in SM can be associated to any quantum number such as baryon or lepton number. No, it can not. The $U(1)$ coming from $SU(3)_C\otimes SU(2)_L\otimes U(1)_Y$ is related to a quantum number called hypercharge, $Y$
We say that baryon and ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/481279",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
RC circuit: is order of resistance and capacitor important? in a RC circuit is order of resistance and capacitor important?
Typically there is the battery then the capacitor then the resistance, but is it ok if I draw with the battery then the resistance and then the capacitor?
| The two circuits you describe:
are basically the same. For example the change of the current with time when we first connect the battery will be the same. There are some obvious but minor differences, for example in the left circuit when we first connect the battery $V_a$ starts at zero and rises to $V$, while in the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/481447",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Quantum Tunneling and Conservation of Energy According to my understanding quantum mechanics, the probability of any particular particle in the universe being at any specific location in the universe is very small but never actually becomes zero. Thus, a little bit of all of us is everywhere.
Let's assume I suddenly qu... | Here are the basics of quantum tunneling:
Note, the energy level of the particle in the above simple example does not change.
This holds true for all tunneling scenaria:
There should exist wave functions $Ψ$ , i.e. solutions for the quantum mechanical equations applicable to the problem where the specific boundary con... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/481549",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 1,
"answer_id": 0
} |
Why haven't we yet tried accelerating a space station with people inside to a near light speed? Is that something we could do if we use ion or nuclear thrusters?
Wouldn't people in the station reach 0.99993 speed of light in just 5 years accelerating at 1g and effectively travel into the future by 83.7 years?
That wou... | The only current propulsion systems, that I know of, that could achieve high speeds is the same one they've been talking about for decades, setting off nuclear bombs behind a pusher plate. However, I heard somewhere that this would only be feasible for about 10% of the speed of light. And, like in the other answers, ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/481634",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 5,
"answer_id": 4
} |
2 windows - will I see the reflections?
I have a question regarding photons nature. Let's say I have a single source of light - regular bulb and the observer - in the same room.
The observer looks through a glass window (normal glass window-nothing special about it) and sees his reflection, but some of the light is p... | Ok. I am not an expert nor I have enough time to work through an answer comparable to many excellent answers I find here.
Generally your logic is correct, meaning that every time the light goes through a medium like the one you are describing a percentage of the beam will pass through and the rest of it will be reflec... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/481776",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 5,
"answer_id": 4
} |
Why does thermodynamics use the negative of the Legendre transform? So I see how the negative Legendre transform is very helpful in interchanging dependencies and giving us the four different major thermodynamic potentials, from internal energy to Helmholtz, Gibbs, and enthalpy.
But what I'm unclear on is why we use th... | The point is to preserve the intuition we have about energy. The Helmholtz free energy, Gibbs free energy, enthalpy, and internal energy all can be described as some kind of energy (subject to various other things being held constant) that can be used up to do work, and is minimized at equilibrium. If you added random ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/481932",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 3,
"answer_id": 1
} |
Thermodynamic description of few-body systems How large should a system be to become thermal?
Thermodynamic description is well-established for systems with large numbers (say, of order of $N_A\sim 10^{23}$) of constituents. Is there a "lower bound" of sorts, for the number of degrees of freedom $N$ in a system, for wh... | As far as I see it, as it was mentioned in the previous answer - it's all about ergodicity. For example, if we consider a thermodynamic system of $N$ particles, the lower the number of particles in it, the bigger the fluctuations of some physical quantity $f$ ($\langle \Delta f^2 \rangle \sim N^{-1/2}$), and thus the b... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482048",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
How is sound affected by gravity? How would sound be different on a planet with a stronger gravitational field? My reasoning leads to sounds of the same wavelength having higher frequencies - is this correct?
| Sounds travels faster through denser mediums.
In a planet with the same amount of air in the atmosphere, but a larger gravity, the gas would be compressed more tightly and thus be more dense at the surface.
For this reason, the velocity of sound waves would be higher.
For two waves synthesised with the same wavelength,... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482162",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Angular velocity of rotating rod Consider the following system:
Newton's second law for rotational motion:
\begin{equation}\tau=I\alpha \Leftrightarrow rF=\frac{1}{3}mr^{2}\alpha \Leftrightarrow \frac{d\omega}{dt}=\frac{3F}{mr}\end{equation}
Considering RHS constant, we get $\omega=\frac{3F}{mr}t.$
I'm not sure if the... | Consider the FBD of the situation, where the reaction force $R$ below is drawn in a positive sense. Also shown is the center of mass (blue dot), located exactly at $\tfrac{r}{2}$ from the pivot.
*
*Case A, pivoted arm means the linear acceleration of the center of mass is coupled with the angular acceleration $$ \d... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482302",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Fisher Information in Statistical Mechanics I am studying the canonical ensemble and it seems to me there is an analogy between derivatives of the partition function, which can extract energy momenta for the system and Fisher score /information.
In partciular we have expressions like $-\partial_\beta log(Z)=<H>$, $\fr... | There are very useful relations indeed, which I wouldn't necessarily call analogies.
We define a set of thermodynamic variables denoted as {${\theta_i}$} and specify the partition function denoted as $Z(\theta)$. In a typical case where we work with Gibbs measures, we may write
$$lnZ = \psi $$
where $\psi$ corresponds... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482545",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
When I do water electrolysis, which water molecules are split apart? If I do water electrolysis I will get hydrogen at one electrode and oxygen at the other.
Is it because a molecule of water somewhere in the middle splits into H and O and then the H and O travel to the appropriate electrodes? Or is it something more ... | Even in "de-ionized" water, some fraction of the water molecules in the bulk will dissociate into $\rm H^+$ and $\rm OH^-$ ions.
In electrolysis, the $\rm H^+$ ions migrate towards the cathode, where they find each other, steal electrons from their surroundings (including the cathode) and form $\rm H_2$ gas. Likewise ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482658",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why electric potential requires absence of acceleration? As of 28/05/2019, Electric Potential is defined in Wikipedia in the article with the same name as:
The amount of work needed to move a unit of positive charge from a
reference point to a specific point inside the field without producing
an acceleration
What... | An accelerating charge radiates EM waves that carry energy,
the static electric potential difference does not account for the radiative exchange.
To measure therefore the work done by the static potential difference while moving a charge from one place to another, must be performed so that the charge does not radiate... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/482994",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 7,
"answer_id": 1
} |
Initial speed is zero and so is power? If I want to accelerate something from standstill to max speed, with a constant force (acceleration and mass don't change), the equation P = F * v would say that in the beginning we use 0 W power. How is that possible? Since power is the rate of transference of energy to the body ... | $$ \frac{dv}{dE} = \frac{d}{dE} [(2E/m)^{\frac 1 2}] $$
$$ \frac{dv}{dE} = \sqrt{\frac 2 {mE}} $$
which diverges at $E=0$ (i.e. $v=0$), so the velocity is infinitely sensitive to energy for a body at rest.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/483143",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 7,
"answer_id": 2
} |
Is my understanding of vectors correct? I recently learned that a vector in mathematics (an element of vector space) is not necessarily a vector in physics. In physics, we also need that the components of the vector on a coordinate transformation as the components of the displacement vector change. So, if my understand... | You are correct in saying they are different. Physics vectors are mathematical vectors, but not necessarily vice versa.
For example, Birkhoff and Maclane "A Survey of Modern Algebra", p162 of the 1953 edition:
A vector space $V$ over a field $F$ is a set of elements, called vectors, such that any two elements $\alp... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/483477",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 2
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.