Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
What does "commuting with the Hamiltonian" mean? In quantum mechanics an observable or an attribute to a particle (like spin) is conserved if and only if it commutes with the Hamiltonian. What does this mean? What observables do not commute with the Hamiltonian?
| In quantum mechanics, observables are represented by Hermitian operators. Mathematically, two operators $\hat A$ and $\hat B$ commute if $$\tag 1 [ \hat A, \hat B]=\hat A \hat B- \hat B \hat A = 0$$
Hermitian operators which satisfy (1) are also called compatible observables meaning that both can be measured simultaneo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/616116",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 2
} |
If quantum entanglement causes the violations of Bell's inequality why don't we see perfect correlation? From wikipedia:
For example, if a pair of entangled particles is generated such that
their total spin is known to be zero, and one particle is found to
have clockwise spin on a first axis, then the spin of the othe... | No. Tsirelson's bound states that, e.g., the value of $2\sqrt{2}$ obtained for the CHSH inequality is optimal within quantum theory, while the maximum value obtainable within all theories which cannot communicate instantly (no-signalling theories) would be 4.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/616267",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Zener effect - how does the probability of tunnelling increase under an increasing potential barrier? From Wikipedia (the basis of my lectures):
Under a high reverse-bias voltage, the p-n junction's depletion region widens which leads to a high-strength electric field across the junction.
Sufficiently strong electric ... | I don't think that the Wikipedia article is correct. The widening doesn't cause tunneling; the shifting of the bands does. Maybe this figure helps (also from wikipedia):
(Zener tunneling is the right-most subfigure.)
In fact, I've never heard of this widening. I guess that it could happen, but I've never seen it in an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/616645",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Physics experiment with sound I am doing an experiment for a school project which consists of blowing into 6 different bottles to create different notes/harmonics. Each bottle is filled with different volumes of water to create a different sound. I have to calculate the theoretical frequency of each, but I do not know ... | I want to add to the answer given about Helmholtz resonator.
What you are expected to calculate (in principle) is the resonance of sound waves in a tube which has one side closed (your bottle). In this simple case the frequency of the different nodes depends on (among others) the length of the tube. As you fill water t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/616765",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
What trigger a capacitor to discharge when I connect a wire externally if $E$ is 0 outside? I know that there is a $Vab$ between the plates but I know also that the charges attract each other in the inside side of plates. So, the questions are:
what happens when I just connect a wire on both plates before connecting th... | Yes some charge from the plate will go into wire. Electric charge of same sign will expand to all available conductor surface due to repulsive force of the charge being stronger than the attractive force of the opposite charge (because that is more distant).
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/617094",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is meant by "spectral resolution of 0.5 GHz"? I sometimes see spectral resolution uses unit Hz. But spectral resolution is defined here and its unit is given as the smallest difference in wavelengths(Δλ) that can be distinguished at a wavelength.
What is the equivalent way of saying "0.5 GHz spectral resolution" i... | The dispersion relation can be written as $c=\lambda f$. Differentiate both sides using the product rule and the fact that $c$ is a constant:
$$0 = d\lambda f + \lambda df$$
Solve for $d\lambda$:
$$d\lambda = -\lambda \frac{df}{f}$$
Usually people consider the absolute value and express $\lambda$ through $f$:
$$|d\lamb... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/617643",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Intuition behind field transfomations Consider a real field $V^{\mu}(x)$ defined on a 4-dimensional Minkowski space. Acted by a transformation $\Lambda = \Lambda^{\mu}{}_{\nu} $ it transforms like
$$V^{\mu}(x) \to V^{'\mu}(x) = \Lambda^{\mu}{}_{\nu} V^{\nu}(\Lambda^{-1}x)$$
My question is: what is the intuition behind... | The components of the vector field transforms the same way as the components of the position vector.
For a scalar field with the value of 7 at point (3,0), for another reference frame rotated $90 ^\circ$, the rotated point (0,-3) has the same value.
But for a vectorial field with value (0,1) at point (3,0), for the new... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/617982",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Lattice spacing in lattice QCD It is known that the lattice spacing in lattice QCD is not an external parameter and needs to be calculated, also the lattice beta parameter scales the lattice spacing ($a$) and goes as a function of the coupling constant as $$β=\frac{2*N}{g_0^2}$$
Where $N$ is a number of colors.
So the ... | The lattice spacing can be obtained in a procedure usually referred to as scale setting for which one requires a physical quantity computed on the lattice. Take as an example the mass of the proton $am_P$ computed at a given value of the bare gauge coupling $g_0^2$ from the corresponding two-point correlation function.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/618131",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 1,
"answer_id": 0
} |
Why is the radial velocity considered zero? I had recently come across a question which is stated as below:
A disc placed on a large horizontal floor is connected from a vertical cylinder of radius $r$ fixed on the floor with the help of a light inextensible cord of length $l$ as shown in the figure. Coefficient of fr... | Some commentators also seem to have fallen into the ambiguity of Radial velocity. Radial normally means toward a centre. and a fixed centre. as the string wraps around the cylinder clearly there is no obvious centre as the motion isn’t circular but some weird spiral and the straight part of string doesn’t continually ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/618389",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 2
} |
Perturbative treatment of infrared divergencies in QED of arbitrary order It is often claimed in QFT literature that infrared divergences of cross-sections of various processes can and should be compensated by taking into account processes of emission of soft photons in any order of perturbation theory.
However in the ... | In the comments, OP clarifies that the issue is with equation (13.2.3). I was confused about this part as well when I first learnt it. The proper way to perform the calculation is as follows.
*
*First, do the $q^0$ integral by contour integration. We assume that the numerator of the integrand (which involves the lowe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/618530",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
If we have a net negative charge in a spherical conductor, why negative charges goes to the surface? So imagine that we have a set of net negative charges, in physics books they said that this set of charges goes to the surface because they repel each other in such a way that this reach to an electrostatics equilibrium... | The question relates only to a charged conductor without current flow. Many students have observed the effects of static electricity generated in the classroom. A test subject stands on an insulator touching a conductive ball which becomes charged from a moving carpet belt and an electrode. Hair standing on end demo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/618685",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 2
} |
What does this Euler-Lagrange equation represent? I have the following Lagrangian:
$$L=\frac{\mu}{2}\left(\dot{r}^2+r^2\dot\phi^2\right)-U(r),$$
The Euler-Lagrange equations are thus:
$$\frac{d}{dt}\left(\mu r^2\dot\phi\right)=0$$
$$\frac{d}{dt}(\mu \dot r)=\mu r\dot{\phi}^2-\frac{\partial}{\partial r}U(r).$$
I am trou... | Yes, the term $\mu r^2\dot{\phi}$ represents the angular momentum, and the first Euler equation telling you that the angular momentum is the constant of motion for the given problem. The second Euler equation is just the radial force equation. If you can try to write newton's equation of motion like
$$F_r=m(\ddot{r}-r... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/618816",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
How do you incorporate friction into kinematics? A small disc of mass $m$ is pushed to $v_0$ on a surface with kinetic coefficient of $\mu$.
Is $v_f = v_0 -{\mu mg} \text{ t} $ ?
(Just based on the idea that increasing $\mu$ , $m$ or $g$ would increase the slow down.)
| Since disc is a continous body the magnitude of friction causing on each part will be different just like in a rope having mass tension force is different at different points
You can solve this by considering torque of friction
$f_r = {\mu } (dm) g$
$f_r = \frac{M}{\pi R^2}2pirdr $
$\int T.dt= f_rr$
After finding expre... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/618952",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Calculate height of a projectile in rotating spaceship reference frame In a rotating reference frame, or in a rotating spaceship, the apparent gravity felt by an object is the centrifugal force. Any moving object also experiences a Coriolis force. When I want to do calculations with a projectile (an object thrown acros... | The efficient way to calculate that is to use the non-rotating coordinate system.
Given is:
1 Launch velocity with respect to the rotating frame
2 Angle with respect to the circular perimeter of the rotating frame
3 Angular velocity of rotating frame with respect to non-rotating frame
The velocity with respect to the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619044",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Baryon to photon ratio In Dodelson's "Modern Cosmology", the current baryon-to-photon ratio is defined as $$ \eta_b \equiv \dfrac{n_b}{n_\gamma} = 5.5 \times 10^{-10} \left(\dfrac{\Omega_b h^2}{0.020}\right). $$
I have tried to found a discussion of the evolution of this parameter, but all I could find was its present ... | The baryon number is conserved. Dating from the baryogensis, the baryonic number density is $n_B=N_B/a^3$, where $a$ is the scale factor and $N_B=\text{const}$.
The number of photons isn't strictly conserved. However, it is approximately $10^{10}$ times larger than the number of baryons. Even if photons are sometimes p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619167",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 0
} |
Divergence of Green function expansion at the origin? The expansion of Green's function in spherical coordinate is given in Eq. (3.125) in Jackson by
$$G\left(\mathbf{x}, \mathbf{x}^{\prime}\right)=4 \pi \sum_{l=0}^{\infty} \sum_{m=-l}^{l} \frac{Y_{l m}^{*}\left(\theta^{\prime}, \phi^{\prime}\right) Y_{l m}(\theta, \ph... | Equation (3.125) is the Green function for a spherical shell bounded by $r=a$ and $r=b$, where it vanishes. If you want to place a charge at the origin, you should first set $a=0$, and the problem will disappear.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619297",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What does 3D buckling reconstruction mean? In condensed matter/material science papers, I often encountered phrases like structural reconstruction, 3D reconstruction, 3D buckling reconstruction, etc. What do these phrases mean (especially the last one)?
For example, this paper (and a non-paywalled link).
| Surfaces of materials don't look like the inside of the bulk, otherwise you'd have dangling bonds and a ton of energy. So the dangling bonds combine in a certain way to minimize that energy. This is what's called a reconstruction. In silicon, the 111 face usually reconstructs into the 7x7 pattern, which is flat and ha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619422",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Significance of the fact the the final expression for acceleration in rolling motion over a slope is independent of friction In accelerated rolling motion on an incline , once we simplfy the equations we find that:
$$ f_s = \frac{I_{cm}}{r^2} \left(\frac{g \sin \theta}{ 1 + \frac{I_{cm} }{mr^2} }\right) \tag{1}$$
What... | I think that as long as $$ f_s \le \mu N$$
there is no sliding and therefore no energy in the system is lost to heat. Under this condition friction can be ignored in the conservation dynamics of the description.
The first example in this link describes the situation in some detail:
rolling motion
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619516",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 4,
"answer_id": 1
} |
What does the concept of an "infinite universe" actually mean? When physicists talk about the universe being infinite, or wondering whether it is or not, what do these two options actually mean? I am not interested whether the universe is infinite or not, I am interested in what are the two options actually looking lik... | Generally when physicists talk about the universe being finite, they are talking about the existence of an upper bound $R$ on the distance between any two points in space. Such an upper bound could arise in several ways - perhaps the universe has an edge - a boundary which cannot be crossed - or perhaps the universe h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619679",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "29",
"answer_count": 5,
"answer_id": 0
} |
Why is electric field across a resistor constant, or voltage gradient linear? Consider this complex circuit :
*
*Consider an ideal resistor with uniform cross section and made of isotropic material with constant resistivity.
*Consider an ideal battery giving a voltage difference of $V$ across terminal.
*Consider... | As to your last question: There will be an excess of electrons on the negative end of the resistor, and a deficiency of electrons at the positive end. A uniform field inside requires a gradient in the charge density.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619801",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
"answer_count": 3,
"answer_id": 0
} |
Peskin & Schroeder, section 12.2, page 409, analytic continuing from $d=2$ to $d=4$? In Peskin & Schroeder section 12.2，page 409, consider the one-loop correction to the propagator in Yukawa theory, it has the form
The authors first spot the pole at $d=2$, and find out that it could be completely absorbed by counterte... | Probably there are some important details that I do not fully understand. But on a high-level, we want to do this because we don't want $\delta_m$ to depend on $M^2$.
If we did it directly in $d=4$, (12.32) would have a pole depending on $p^2$, and therefore we would have to make $\delta_m$ depend on $M^2$. This would ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/619981",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
When is $a_c = v^2/r$ valid? All the derivations I've seen of the formula in the title, namely $a_c = \frac{v^2}{r}$ rely on the tangential speed $v$ being constant. However, I watched this video:
https://www.khanacademy.org/science/physics/centripetal-force-and-gravitation/centripetal-forces/v/yo-yo-in-vertical-circle... | I treat 2D first and then comment on 3D.
The complete formula for acceleration in a plane,
treated in plane polar coordinates, is
$$
{\bf a} = (\ddot{r} - r \dot{\theta}^2) \hat{\bf r}
+ (r \ddot{\theta} + 2 \dot{r} \dot{\theta} ) \hat{\boldsymbol \theta}.
$$
Using now that the velocity is
$$
{\bf v} = v_r \hat{\bf r} ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/620323",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Can internal conversion happen at (close to) absolute zero? My understanding is that, if an atom finds itself in an excited state, for instance following electron capture and gamma emission, the atom relaxes to the ground electronic state because of the perturbation caused by the room temperature. The atom may temporar... | Usually, radioactive decay has nothing to do with temperature and does not at all depend on it. (*)
Radioactive transitions are probabilistic as they are best modeled just like the tunneling effect. There is some potential barrier, but the (quantum) state of the nucleus can tunnel through that and relax to another stat... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/620476",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Combining spins of two particles of spin |1,0> and |1/2, 1/2> I am trying to combine the spin of two particles.
Their individual spins are:
$|1,0\rangle $ and $\left|\frac{1}{2},\frac{1}{2} \right>$
Now I am told that they combine to give a total spin state of:
$$\left|\frac{1}{2},\frac{1}{2} \right>$$
However, I am co... | $
\newcommand{\ket}[1]{{\textstyle\left|{#1}\right>}}
\newcommand{\sqrtfrac}[2]{{\color{lightblue}{\textstyle\sqrt{\frac{#1}{#2}}}}}
%%%
$There is no way to combine $\ket{1,0}$ and $\ket{\frac12, \frac12}$ to get a pure $j=\frac12$ state. The only possible value for the $z$-axis projection $m$ is $0 + \frac12 = \frac1... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/620641",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
What are the Newton's third law pairs in this diagram? In the diagram below, block $C$ accelerates downwards when released. I'm having some trouble identifying the third law (action $-$ reaction) force pairs in my free-body diagrams. Please provide any insights to determining the force pairs.
| *
*B and A - apply force on each other using friction (because they are sliding one over the other).
While it seems that B and C apply force on each other using the rope they are not count as third law because the force do not apply directly on each other - block C apply force on the rope (and vice versa so the rope a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/620942",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Do resistance have to heat? Not a physicist.
Is there a way to build resistances that do not heat when opposing current?
More generally, is it necessary to waste energy to resistance?
If I cut a wire, there will be an almost infinite resistance (unless the tension is large enough to break the air), but no energy cost.
... | If there is resistance then there is momentum being passed from electrons to other electrons and atomic nuclei which we call heat. In superconductors electrons pass some momentum to positive charges but also get it back because superconductors have charges that move in a non random coordinated manner.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/621067",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 3
} |
A light problem: What happens when light completely destructively interferes? So here's the setup. We have a spherical source. It emits a pulse of light in all directions with some wavelength $\lambda$. It reflects off of a spherical mirror that is centered around this source.
Now, when the light comes back, it bounces... | The energy went back into your spherical source. For the first pulse the source had to provide energy. For the second pulse the source had to absorb energy. The mistake is simply assuming that the energy required to drive the source is independent of the external fields acting on the source.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/621202",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 3,
"answer_id": 1
} |
What factors does magnetic field due to a circular loop depend on? I know of three.
*
*Strength of current
*number of loops ( a cheeky way to 'increase' current?)
*radius
I'm having doubts about radius of circular loop affecting the magnitude of magnetic field ta centre of loop. As if magnetic field due to an inf... | The magnitude of the field at the centre is-
$$B=\dfrac{\mu_oNI}{2r}$$
andis thus inversely proportional to radius.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/621279",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
Confusion in Signs when formulation mathematical equations for physics problems One of the common confusion I face when writing and solving mathematical equations for physical problems is regarding signs. Consider this problem;
A ball is dropped from rest from top of the building,it falls down subjected to air resistan... | We must always pick a direction to be positive and stick to it throughout.
A good tip to reduce confusion is to pick the positive direction to be the way you expect the object to accelerate.
So in your first example pick positive to be down. In the second pick positive to be up.
After calculating $a$, you'll have your... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/621454",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 1
} |
Where from is the distance calculated in Newton's law of universal gravitation? In the equation for universal gravitation $(1)$ between two objects, where from is $r$ calculated? From the surface, from the center? Also, are the objects assumed to be particles in this equation or could the be multiple particles like mol... | The object in this law assumed to be points (so the distance is just distance between points). Any two object that are very small compare to the distance between them (no matter from which points on the objects you measure it) can be considered as points.
So, for example if you have a two rigid molecule that are small ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/621606",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Is conduction band discrete or continuous? My question is very simple. I just want to know that is conduction band discrete or continuous?
| As other have noted, it's discrete but with fine enough spacing to treat as continuous.
However I disagree that quantum mechanics is the reason. You see the exact same thing in a classical 1-D chain of masses connected by springs.
The allowed wave vectors $\vec{k}$ in the bands are reciprocal lattice vectors, and the n... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/621737",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 1
} |
How does Dodelson calculate the number density of a particle species? In chapter three of Modern Cosmology, Dodelson models the evolution of a particle plasma as the universe expands. On page 61, the author gives the formula for the species-dependent equilibrium density as:$$n_i=g_i\space e^{\mu_i/T}\int\frac{d^3p}{(2... | I'm afraid your primary error is one of elementary calculus. $\int d^3p$ is not equal to $\frac{p^3}{(2\pi)^3 6}$. Secondly, $E\neq m$ (how could it, since as you correctly say in your next words, $p=\sqrt{E^2-m^2}$??).
To evaluate this integral we go to spherical coordinates, in which $\int d^3 p = \int_0^\infty p^2... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/621902",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why black holes lose energy? It is often said that black holes lose energy throughout the process called Hawking radiation. My question is, since the process of creating particles is random, why do the black holes captures more particles with negative energy than particles with positive energy?
| As Wikipedia notes, when one particle escapes the event horizon but a partner particle doesn't, the latter isn't the issue (as its energy neither enters nor leaves), but the former has more energy due to a gravitational redshift. This amplification produces a partner wave. It's this wave that actually returns negative ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/622102",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
Is it possible to lift an object from rest with constant power? This is inspired by the following question.
Consider some object which I want to lift from rest with a constant power throughout the whole process; the power I apply when lifting the object from rest is the same power I apply to keep lifting it. The force ... | $$\left( \dfrac{dv}{dt} \right)^2 + v\dfrac{dv}{dt} = 0$$
$$\frac{dv}{dt}\times\Big[\frac{dv}{dt}+v\Big]=0$$
When $\displaystyle{\frac{dv}{dt}=0}$, $v$ has to be a constant. But that isn't possible because initially it was at rest but while being lifted, it is not.
$$\frac{dv}{dt}+v=0$$
$$\frac{dv}{v}=-dt$$
$$\int\limi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/622195",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
How does the temperature affect the diameter of a brass ball, and the hole it has to go through (hole is in a thin steel plate)? A brass ball has a diameter of 25.232 mm and a hole in a thin steel plate has a diameter of 25.220 mm at 21.5 C. Both the steel and the brass ball have the same temperature all the time. At w... | The coefficient of thermal expansion describes the increase in a diameter or a circumference, since one is a linear function of the other. You don't need to work with the volume.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/622491",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does the growing up of trees works with respect to energy conservation? We know that the energy (and hence mass) can neither be created nor destroyed. In the light of above statement, I would like to understand views on growing up of fauna and flora on earth.
A small seed is planted in earth. The only visible input... | You are exactly right. A plant like a tree is basically a chemical machine for storing chemical energy by converting water and carbon dioxide into cellulose and other hydrocarbons, using solar energy to do the work. Mass is conserved at every step of the process.
Animals then chemically convert plant matter into muscle... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/622687",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
By how much does the gravitational redshift change a neutron star emission spectrum, thus disturbing the measurement of its surface temperature? How much does the gravitational redshift change a neutron star emission spectra disturbing so the measurement of its surface temperature? I remember some tv-shows talking abou... | The standard gravitational redshift formula applies to neutron stars.
This means that if a distant observer observes a spectral feature that was emitted at a rest wavelength of $\lambda_0$ from the NS surface, then it will be observed at a wavelength
$$\lambda = \lambda_0\left(1 -\frac{2GM}{Rc^2}\right)^{-1/2}\ ,$$
whe... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/623048",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How to explain smooth absorption spectrum of nature (plants, etc.) while the atoms have discrete absorption lines? From quantum mechanics, a photon of energy exactly equal $h\nu=E_2-E_1$ could be captured by an atom that has the energetic level levels $E_1$ and $E_2$ (with $E_1<E_2$). This corresponds to "absorption li... | I'm going to go with an intentionally provocative answer. Atoms don't have discrete absorption lines. Nothing has discrete absorption lines. Any state that can decay or be excited necessarily has a finite lifetime $\Delta t$, and thus its energy is uncertain by an amount $\Delta E$ that can be estimated from a simple F... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/623297",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 4,
"answer_id": 0
} |
How do I find the approximate surface area of a chicken? I'm working on building a chicken army and I'm trying to find out how much metal or kevlar (still deciding) I need to make armor for the chickens. this measurement does not need to be exact I'm just trying to get an estimate for how much I will need. You will be ... | Use the ancient Japanese art of Gyotaku. This method was used to record the catches of Japanese fishermen. They would paint the fish with ink and then roll the fish onto rice paper to get a print.
*
*Dye the chicken in harmless food coloring.
*Carefully roll one side of the dyed chicken onto a large piece of paper... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/623492",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
"answer_count": 8,
"answer_id": 4
} |
Is no acceleration a cause or consequence of no net force? If a body is moving with constant velocity, or is at rest, then the net force on it must be $0$. If the net force on a body is $0$, then it must be moving with constant velocity or must be at rest.
Is $0$ net force a consequence of being at rest or moving with ... | The latter.
Every frame is at rest for observers on it. If they note that the objects on the surroundings are passing by at increasing velocities, how they can decide who is really accelerating, their own frame or the objects on the surroundings?
There is a (fictitious) force in the accelerated frame that can be identi... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/623887",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 14,
"answer_id": 8
} |
Mass-mismatch in the low-lying states of the bosonic string $\newcommand{\ket}[1]{\left|#1\right>}$I've recently been studying the quantisation of the bosonic string (using GSW as my main text). However, I have some issues which I believe should be pretty straightforward, but I can't seem to work out!
We derive the spe... | You've demonstrated that the creation operator $\alpha^i_{-1}$ can map a physical state to a non-physical one. There is no contradiction. If you've seen the BRST approach yet, a succinct way to phrase this is that the action of the oscillators does not preserve the subspace of BRST-cohomology classes (i.e. physical sta... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/623992",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Can speed of image in mirror exceed the speed of light? Suppose I'm moving toward the mirror at the speed of v, then relative speed btw me and mirror would be v.
And I thought that we can think like there exist world that is the same as our world inside the mirror,
so I guessed we will measure speed of the image as 2v/... | Prepare to have your mind blown: hold up a mirror to the night sky, and point it at a quasar. Flip it 45 degrees. You've now made the mirror image of that quasar travel several billion light years in less than a second.
The motion of mirror images is virtual, just a mathematical construct, and relativity does not apply... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/625150",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Characteristic timescale of a can of beer? Modelling a 440 ml can of beer by Newton's law of cooling, the temperature difference between the can and its surroundings (e.g. a fridge) decays exponentially in time at a rate determined by the e-folding time or "characteristic timescale".
Ideally, this characteristic timesc... | No, because this timescale is dependent on the material inside and outside the can.
The can will lose heat to the environment by radiation and conduction from its surface. The rate at which this occurs is dependent on the colour of the surface (dark surfaces are more effective radiators) and the rate at which heat is ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/625250",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
What is the significance of the sign of the velocity for a particle executing SHM? So while deriving equation for the velocity of particle executing SHM at any point, I noticed a difference in the result depending on what wave (sine or cosine) you chose.
For $x=A\cos\omega t$:
$\quad \ \,v=-\omega\sqrt{A^2-x^2}$
For $... | Neither of those expressions are right. If $x(t)=A\cos(\omega t)$, then $v(t) = -A\omega \sin(\omega t)$. You wrote
$$v(t) = -\omega \sqrt{A^2-x^2}=-A\omega \big|\sin(\omega t)\big|$$
If we write $x(t) = A\cos(\omega t - \delta)$, then your two examples correspond to $\delta = 0$ and $\delta = \pi/2$. In the general... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/625408",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Distribution of charge when 2 metallic spheres are connected It is given in my textbook that when 2 charged conducting sphere of different radius are connected by finite wire the redistribution of charges takes place such that the potential just outside of both spheres become equal.
But why potential is the necessary c... | When we connect two spherical conductors with a conducting wire, essentially the potential on surface of both of the conductors become the same. Basically they are equipotential surfaces. Now given $E = dV/dl$, and in this case, $dV =0$, $E=0$. Now you are telling that electric field is zero at only one point between t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/625510",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Can I push something standing on a frictionless floor? Suppose I stand on a friction less floor, and another object of finite nonzero mass stand in front of me. Can I push the mass, so that it has a nonzero acceleration? Also, where does this force arise, since I cannot push the ground, since that would make me slip on... | Absolutely you can apply a force on some other object and make it accelerate. What will happen is that you too will accelerate - in the opposite direction.
You push the thing, the thing pushes you, it's classic Newton's Third Law. This is akin to rocket propulsion.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/625643",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "17",
"answer_count": 6,
"answer_id": 0
} |
How do I go from Planck units to string units? I am not sure exactly what "string units" are. I know that $\alpha' = l_{string}^2 = \frac{1}{M_{string}^2}.$ But these are not units per see, I still need values for $l_{string}$ and $M_{string}$ that could be in whatever units?
My question is, how do I go between string... | *
*The closed-string string coupling constant $g_s$ in both bosonic and superstring theory is the vacuum expectation value of $e^\Phi$, where $\Phi$ is the dilaton field. It is dimensionless: indeed, all dimensionless parameters in string theory arise as VEV's of scalar fields.
*In the bosonic case, the 26D Planck le... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/626037",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
In a sealed chamber, can a vapor be heated enough, that the pressure increases enough, to condense to liquid? Assuming a sealed chamber, containing a vapor, where volume is constant:
Given that the ideal-gas law states $PV = nRT$, if heat is added to an ideal-gas, the pressure will increase as a function of temperature... |
So theoretically you could heat steam into condensing?
Try it (graphically)! Choose an amount of water vapor $n$ and calculate $V$ for a gas-phase $T_0$ and $P_0$ combination on the phase diagram:
Now draw the line $P=nRT/V$ that passes through ($T_0$, $P_0$). (This will appear as a curve on this log-linear plot.) C... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/626170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 0
} |
Why is a large cavity with a small hole at constant temperature approximated as a black body? I can't understand how a large cavity maintained at a constant inner surface temperature T, with a small opening on its surface behaves like a black body.
How is it a perfect emitter and a perfect absorber?
Please explain in a... | The hole is the black body.
The term black body is to do with an object that doesn't reflect anything, and so appears black.
Any light falling on the hole doesn't get reflected, but bounces around inside the box until absorbed. The chance of it re-emerging from the small hole is zero, so it's a perfect absorber.
As the... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/626605",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 3,
"answer_id": 0
} |
Buoyant force on partially submerged bodies When a cylinder is placed on a fluid, it is partially submerged and attains equilibrium at that state.
In equilibrium,
$$F_B=mg$$
where $F_B$ is the buoyant force and $mg$ is the weight of the cylinder.
But we know that $F_B=m_{\text{liquid displaced}}\ g$. Thus, $ m_{\text... | There are two equal and opposite forces on the cylinder, $w = m_{cyl}g$, and $F_B$.
$F_B$ is the force from pressure that water exerts on the cylinder. Since the pressure increases with depth, forces on the bottom are greater, and these are directed upward.
These bouyancy forces are the same, no matter what object with... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/627062",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What is light, a wave or a particle or A wave-particle? What is light?
And how do we know that light is an electromagnetic wave?
I asked my teacher and he said that when you place a compass in light's path, the needle of the compass rotates. Which I think is not a valid answer and thats not what actually happens when w... | This is the simplistic answer that I found useful when I was a kid.
It isn't strictly rigourous, but it was useful. (See also "All models are wrong, but some models are useful".)
Light is something (a "thing", a phenomenom, whatever) which has the property that:
*
*if you do a test that asks "Does this thing behave ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/627177",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 5,
"answer_id": 4
} |
Reconstructing wavefunction from the density matrix Say I have a state, $$| \Psi \rangle = \frac{1}{\sqrt 2} \left( | 0 \rangle + \exp( \text{i} \phi ) | 1 \rangle \right) = c_{0} | 0 \rangle + c_{1} | 1 \rangle.$$
Now I construct the density matrix (DM), $$\hat \rho = | \Psi \rangle \langle \Psi | = \frac{1}{2} \left(... | If you write $c_0 \equiv |c_0|\, e^{i\phi_0}$ and $c_1 \equiv |c_1|\, e^{i\phi_1}$, then you can write the wave function as
$$|\Psi\rangle = e^{i\phi_0}\left(|c_0| \,|0\rangle + |c_1|\,e^{i(\phi_1-\phi_0)}\,|1\rangle\right)\quad . $$
The associated density operator is then given by $\rho_{\Psi}\equiv |\Psi\rangle\lang... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/627322",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
My question is about the concept of acceleration What would happen to the velocity of an object if it is given an initial acceleration of 2 meter per second per second in a case if there is no dissipating force such as gravity, air resistance or friction. I think its velocity would increase by 2 meter per second after ... | An object with mass accelerates only if is being pushed by a force. If the force is removed, the acceleration will stop. The problem with a rocket is that you have to accelerate the fuel until you run out.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/627428",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
What is the exponential (or geometric) rule (or law) for uranium enrichment? Uranium ore starts at about .72% U-235...
At ~20% U-235, it is considered to be about '90% of the way' to weapons-grade uranium, which is about ~90% U-235...
Because uranium enrichment in centrifuges follows a geometric (or exponential) law...... | The equation you are looking for is the SWU calculation (Separative Work Units). The calculations are described at:
https://energyeducation.ca/encyclopedia/Separative_work_unit
Figure 1 shows the exponential dependence that you describe. Enriching from natural to 4-5% takes more energy then going from 4-5% to 95%.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/627642",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
Acceleration of cylinder both rotating and moving under force from a pulley The following states the problem 1.2 from the book Lagrangians And Hamiltonians by Patrick Hamill.
A cylinder of mass $M$ and radius $R$ is set on end on a table at a distance $L$ from the edge, as shown in Figure 1.11. As the string is wound ... | If the cylinder starts from rest and the acceleration, a, is given, then L = (1/2)a$t^2$.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/627725",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 0
} |
According to general relativity planets and Sun bend the spacetime (explaining gravity), but does this hold true for smaller objects? According to general relativity planets and the sun bend spacetime, and that is the explanation of gravity. However, does this hold true for smaller objects, like toys, pens, etc.? Do t... | A large body is an accumulation of many small bodies. Its properties — mass, and with it gravitation and inertia, heat capacity etc. — are nothing but the accumulation of the properties of the constituting small bodies. And vice versa :-).
Remember that all small objects you hold in your hands were once parts of very h... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628115",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 9,
"answer_id": 8
} |
Muon $g-2$ experiment: is there any theory to explain the results? The nature of the experiment has been discussed here, but my main question is this: is there any theory that has predicted the results of this experiment or are we completely clueless about what's happening? In other words, have we come up with a new hy... | This answer was already suggested above. This is another source that has some really nice embedded links on the authors and the university that hosted the study. Very nice reading some might enjoy so I thought it would be nice to share. Assuming I am allowed to put in a link. Not sure it is allowed by stack exchange.
... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628266",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
"answer_count": 4,
"answer_id": 3
} |
Why do images not appear inverted when looking directly through a pinhole camera? I understand that the way light takes through a pinhole creates an inverted image on a surface behind the pinhole. I remember this effect from school experiments, it's also described in this wikipedia article. I punctured a piece of paper... | The directly-through-the-pinhole image is upside down on the retina of your eye. But all images on the retina are upside down. When the lens in your eye forms a real image on the retina it is inverted. It only looks the right way up to you because you brain post-processes the retina image in the visual cortex.
By look... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628424",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "25",
"answer_count": 12,
"answer_id": 6
} |
What is the bare minimum of air density you need to fly a helicopter? How high will a helicopter be able to fly before the propellers have not enough air particles to achieve lift?
What is the minimum air density needed to achieve flight with a helicopter?
Could you give me the air density from $100\%$ to $1\%$ in mete... | The lift generated by a helicopter is linearly proportional to the air density (as it is for planes). To fly we need the lift to be greater than the weight of the aircraft, so as the density reduces there will be a point where the lift generated is less than the weight, so we can't fly.
The minimum air density will dep... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628546",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
What is momentum? Momentum tells you the mass of the object and how fast it is going right? So if I have a 2 kg ball moving at 2 m/s, then the ball has 4 kg⋅m/s of momentum. My question is why do we multiply mass and velocity to get momentum. (From the example above) Why cant we just say the ball is 2 kg moving at a sp... | I think we should let the Original Gangster speak when talking about intuitive definitions of momentum. From Newton's Principia:
"The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.
The motion of the whole is the sum of the motions of all the parts; and theref... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628601",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 8,
"answer_id": 7
} |
How to calculate the amount of standards deviations a measure is from another value I have a theoretical value $\gamma_t$ and a measured values $\gamma_m$, with uncertainties $\sigma_{\gamma_t}$ and $\sigma_{\gamma_m}$ respectively. If the errorbars of $\gamma_m$ is inside of $\gamma_t$-'s, as illustrate below, would t... | When you want to see if two quantities with uncertainty agree, you should compare their difference with zero. If $\gamma_t-\gamma_m=0$ within the uncertainty, they agree. The difference is the best way to check the degree of (dis)agreement, too. The number of standard deviations, $n_\sigma$, is:
$$n_\sigma = \frac{\... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/628870",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why are the wavefunctions of the excited states so symmetric? The excitation from a lower level to an excited state happens through absorption of a photon. But the photon comes from a certain direction. I would expect that the wavefunction of the excited state has to mirror that circumstance and has some non-symmetry i... | When a particle (for example an atom) absorbs a photon, it gets a very small momentum kick in the direction in which the photon was traveling. Usually this isn't large enough to make an appreciable difference, but if the particle is cold enough then this can be observed experimentally. See How does one account for the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629219",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
Finding the final velocity of a car after 8 seconds with energy I'm having trouble on finding how to solve this question that I received.
A 1500kg race car's engine can produce 150,000 Watts of power. Assuming the race car is able to convert 75% of the energy into kinetic energy, how fast could the car go in 8 seconds... | Well, power is just energy over time, one watt is just one joule/second. Hence, convert 150000w to Joules by canceling the seconds. --> 150000j/s * 8s = 1200000j
Now you stated that 75% of the energy is converted to kinetic. so, --> 800000j
now just solve for velocity using the definition of kinetic energy; (1/2)(m)(v^... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629496",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 0
} |
WKB application on symmetric potential well I am a little confused how one can find a wave function by using WKB approximation? I do know the oscillation frequency $$\Omega ~=~ {2E\over h}{\rm Re} \langle L|R \rangle~=~ {E\over \pi\hbar}{\rm Re} \langle L|R \rangle, $$
where $L$, $R$ are the eigenstate of the left and ... | Hints:
*
*In Ref. 1 it is claimed that
$$ \frac{2\pi}{\tau}~=~\Omega~=~\frac{E_n^--E_n^+}{\hbar}~=~\frac{\omega}{\pi}e^{-\phi},\tag{8.63/8.64}$$
where
$$ \phi~\equiv~ \int_{-x_1}^{x_1} \!dx |k(x)|, \tag{8.60}$$
so that
$$ \phi \sim~ \alpha a^2 \quad \text{for} \quad V(0)\gg E \quad \text{where} \quad \alpha~\equiv~... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629711",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Kinetic Energy and Inductor energy violates conservation of energy? Suppose we have an ideal LC circuit (no resistance) and an open switch where the capacitor has an initial voltage $V_o$. Initially, the energy stored in the capacitor at $t=0$ is $\frac{1}{2}CV_o^2$ and the energy in the magnetic field of the inductor ... | Kinetic energy of electrons due to electric current $I$ in an inductor is much smaller than magnetic energy $\frac{1}{2}LI^2$ (provided the inductor has large enough $L$, which is usually the case).
So yes, strictly speaking total energy stored in the capacitor is transformed into magnetic energy and kinetic energy of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629787",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Which types of strain tensor are positive definite? I am taking a look at different types of strain tensor. Specifically, I am thinking about if the infinitesimal strain tensor
\begin{align*}
\epsilon_{ij} = \frac{1}{2} (\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i})
\end{align*}
is positive-def... | The strain tensor does not have to be positive definite, as mentioned before.
On the other hand, you are asking what type of strain tensor are positive definite. A positive tensor would have positive principal strains. That implies a tensor where you have elongation in 3 different directions.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/629994",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Why experiments of electrostatic induction are best done in dry weather? Basic experiments which demonstrate the presence of electric charges and forces..
For instance, when we rub a comb on hairs...it gets negatively charged..and can even suspend bits of paper due to this charge.
And many such experiments of rubbing g... | Electrostatic demonstrations work best when materials classed as insulators do not allow the flow (leakage) of charge. However if even a very thin layer of water adheres to the surface of so called insulators then although the bulk of the material does not allow the passage of electric currents the thin layer of water... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/630090",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 0
} |
Isotopy class of spacetime We know that spacetime is an orientable manifold:
Can spacetime be non-orientable?
But supposing that spacetime is an orientable closed 2D surface, one might envision a variety of non-equivalent solutions in the following sense:
Given a 2D strip, by one rotation(twist), one can create a Moebi... | The orientability of space (rather than spacetime) was first raised by Kant in his 1768 paper, Concerning the Ultimate Foundations in the Differentiation of Regions in Space.
We generally take space to be orientable because experiment shows that it is and Kant alluded to this in his paper, but his paper was really abou... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/630331",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "6",
"answer_count": 3,
"answer_id": 2
} |
Why do my white shoelaces get blue when exposed to UV? My shoes and shoelaces are both white. But when there is a UV light only my shoelaces appeared in a different colour. What is the reason?
| The shoes and shoelaces are made from different materials. The shoelaces contain a substance that fluoresces: it converts the UV light to blue light so that it becomes visible to you. The remainder of the shoes does not contain this substance, so it just absorbs or reflects the UV light, still invisible to you.
There a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/630728",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
How does a copper ring levitates above a AC supply primary coil? Doesn't AC current gives decreasing current and so decreasing magnetic fields or flux. This should then attract the copper ring above primary coil. When magnitude of current increases in AC then due to Lentz law as we know ring will get repelled. But what... | Besides the bad English, I think what you're referring to is the jumping ring experiment, which is a demonstration of Faraday's laws of electromagnetic induction and also of Lenz's law. You can read more about it here.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/630789",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
When putting a floating object in water, why the displacement of mass of water is not equal to only the part of the object inside the water? In this question Will a bathtub full of water weigh more if I add something that floats in the water? the marked answers mentioned a special case where the bathtub is full to a br... | Imagine lowering your rectangular box into a bowl of water. When the box first comes into contact with the water, the upward force upon it from the pressure of water is less than its weight, so it will continue to sink into the water as you lower it.
As the box sinks, the level of the water in the bowl rises because th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/630866",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 2,
"answer_id": 1
} |
Active vs passive transformation in right handed particle People often says that active transformation is equivalent to passive transformation.
Suppose that we have a right handed particle that is, the spin and the momentum are pointing in the same direction, call this direction right. Under a passive parity transfo... | Active & Passive Transformations
Active and passive transformations are not the same. To understand this properly requires a local frame in a space. Now, we can either transform the space itself or the frame. In the first case, the transformation is called an active, in the second case, it is called passive.
It is cal... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/631074",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 3,
"answer_id": 2
} |
In the theory of special relativity speed is relative so who decides which observer’s time moves slower? If for example we have 2 people one moving in speed v relative to the other, according to special relativity the time passing for the moving person is slower than for the stationary person. However from the moving p... | One of the keys to understanding SR is to remember that all the effects it predicts are reciprocal. If Observer A thinks that Observer B's spaceship has contracted in length, Observer B will consider that Observer A's spaceship has contracted by the same proportion. There are many analogous cases in everyday life. If w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/631826",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "24",
"answer_count": 8,
"answer_id": 1
} |
How to determine amplitude of compton scattering using Feynman rules? I am currently studying from Griffiths' introduction to elementary particles.
I started reading about the Feynman rules for caclulating scattering amplitudes, and while I understood them for the cases of electron/muon scattering, I can't understand ... | The incoming photon will contribute with a $\epsilon_\mu(p_2)$, and the outgoing one with a $\epsilon_\nu(p_3)^*$. Note that the $\mu$ index of the incoming photon will be contracted with the one of $\gamma^\mu$, and the $\nu$ index of the outgoing photon will be contracted with the index of the other vertex. You can p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/631911",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Were Kepler's Laws of Planetary Motion the first formal definition of an ellipse? It seems to me that Kepler's Laws necessitate some definition of an ellipse in terms of a coordinate system. I am wondering whether Kepler's Laws mathematically defined what an ellipse is, or if he used an already defined shape in his law... | Due to the geometric formulation, Kepler's Astronomia Nova is full of elaborate illustrations of ellipses, epicircles and whatnot. It is not necessary to spell out the position of points in Cartesian coordinates, because the relation between points are specified in angles, lengths, and geometric constructions.
Kepler ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632199",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What are virtual and apparent forces? Acceleration in a rotating frame can be written as: $$\underline{a}=\frac{\partial^2\underline{r}}{\partial t^2}+\frac{\partial\underline{\omega}}{\partial t}\times\underline{r}+2\underline{\omega}\times\frac{\partial\underline{r}}{\partial t}+\underline{\omega}\times(\underline{\o... | Apparent forces are those that show up as a result of an accelerating reference frame, i.e., they are not forces over the system, but an effect of being in a reference system over which a force IS being applied. Therefore, if you accelerate in an accelerating reference frame, you would start already with some "virtual"... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632465",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
What is the formula for ripple voltage in integrating circuit? With a rectangular wave input Vin and a typical RC circuit with output taken across the capacitor, what is the formula to calculate Delta V due to ripple?
| I guess you know how to calculate the output with a sinusoidal input wave. There are several techcnics for that, but the easiest one is probably using phasors.
And thanks to Fourier series you can write your periodic rectangular wave input as a sum of sinusoidal waves. Let's take for example a square wave $V_{in}(t)$ w... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632604",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Does the shape of a wire affect the electric current in it in any way? Say we have a straight wire connected across two terminals carrying electricity between them. If everything is kept the same (voltage across the two terminals, resistance of the wire, etc.) will there be ANY difference at all if the wire were to be,... | Yes, there is a difference.
If you made the wire as you mentioned, into a spiral, like this:
then there is quite a big difference between this and a straight wire. The difference between a straight wire and a coil or spiral wire is that the spiral wire resists changes in current flow.
This is called an inductor or sol... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632719",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 1,
"answer_id": 0
} |
How can air pressure be equal in all directions? Lay on the ground in a bright sunny day of spring and look the sky. Feel the air pressure on you.
Now lay on your stomach and your back exposed to sky.
You won't feel any change in air pressure. You will breathe normally. Even though air above you ( below you actually ) ... | Actually, the weight of the air above you contributes to the pressure that you feel. Because of this, air pressure drops as you go to higher altitude. This change is not so significant on the scale of you turning your head from pointing down to pointing up, so no real change is noticeable.
Why does pressure only depend... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/632885",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Question about length contraction If an observer A is in motion on a train relative to an observer on the train platform, B, and observer A shoots a laser which hits the wall and comes back, who measures the interval to be the shortest? I don’t quite get it because the train would be contracted according to B, thus dis... | The time is indeed shorter for A. Your reasoning about A is correct. If the time between two events is measured by a single inertial clock between the two vs a pair of synchronized clocks, the time will always be shorter for the single clock vs the pair of synchronized clocks. So A measures the shortest time.
the trai... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/633008",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why electric field is scaled by gamma? Two opposite charges are in a spaceship and are attracted by the electric field $E_s$
But for an observer on earth the Electric force is $$E_e=\gamma E_s$$
Normally the forces are scaled down by $\gamma$ in the earth frame and here also the total force is scaled down.
But why the ... | Electric field E transforms this way:
$$E'=\gamma E$$
Gravity field G transforms this way:
$$G'=\gamma G$$
Force F, be it electric or gravitational, transforms this way:
$$ F'= F / \gamma $$
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/633138",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Why does conservation of angular momentum explain why planet orbits lie in a plane? I just learned about sector velocity and how you can manipulate the equation to show that angular momentum $L$ is conserved by $L/2M$. I know that sector velocity is constant and therefore angular momentum is constant. I have made it th... | The angular momentum is given by a vector product $\vec{L}=m[\vec{r}\times\vec{v}]$. One o the properties of the vector product is that the result is orthogonal to both factors. I.e. both $\vec{r}$ and $\vec{v}$ should be orthogonal to $\vec{L}$. Or you can say that both $\vec{r}$ and $\vec{v}$ lie in the plane orthogo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/633350",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "5",
"answer_count": 2,
"answer_id": 1
} |
How do turbine engines improve compression ratio? As I have learnt from the Venturi tube that Pressure is inversely proportional to velocity. When a general aircraft is flying at say Mach 0.8 and at the same time there is a pressure decrease with increasing altitude. How is pressure achieved in the case. Is there stagn... | I will answer the question in the body of the post.
The venturi effect is not applicable here. The air intake for a small plane with a piston engine is usually exposed head-on to the incoming air and also to the backwash from the propeller. Both of these add ram air pressure to the carburetor inlet.
In fact, it is poss... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/633519",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What does it mean for the gravitational force to be "between" two bodies? What is the meaning of the word "between" in the law that the force between two masses at separation $r$ is given by $\frac{GM_1M_2}{r^2}$? I am confused about how can a force be in-between, either it is on body A or on body B, or on both.
Suppos... | It is not a individual force that exists in the space between them, it is rather saying between in the case that both bodies exert a force on each other, which gradually pulls them to a point between them as they are pulled towards each other, they ultimately simply are counterparts to each other, the equal and opposit... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/633880",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
"answer_count": 6,
"answer_id": 3
} |
In this ray diagram, a plane mirror seems to form a real image In this ray diagram the image formed seems to be real with the given position of the eye. I have learnt that plane mirrors cannot form real images at any circumstance. But at this one it does. Please explain the answer like I'm 5 and how you deduced what y... | Farcher's answer is correct. But it can be elaborated a bit to make it easier to understand.
If you observe the above ray diagram for real images, you can see that the real images are formed when rays from the same point of an object intersect to form an image.
As your image shows, this is not the case. Rays from the ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634014",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 1
} |
Which force came first in Newtonian gravity? Force A on B or force B on A? Can a body $X$ apply a gravitational force on a body $Y$ without itself being acted on by a gravitational force from $Y$? Just per intuition, we deduce from Newton's third law that if $A$ applies force on $B$ then $B$ applies force on $A$. But i... | Neither comes first, they are mutual. In the Newtonian model gravity acts instantaneously at-a-distance (unlike Relativity, where gravity propagates at the speed of light).
Which force you consider the action depends on which one grabs your attention first. The other one then has to be the reaction. But the distinction... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634154",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 2,
"answer_id": 1
} |
Velocity is relative, which means acceleration is relative, which further implies that forces are relative as well So how would we know whether a force truly exists or not. I can be accelerating a car my 5 meters per second squared but another car accelerating with the same acceleration would think that my car is at re... | People in an accelerated car know that it is accelerating due to inertial forces that can be observed inside.
In cases like that, besides the inertial forces, there is the reference of the fixed environement, so it is easy for the passengers to know about their acceleration, just looking outside.
More interesting is th... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634287",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
"answer_count": 8,
"answer_id": 4
} |
What's the meaning of potential energy in quantum physics? We know that the definition of potential energy in classic physics. When we start learning about quantum physics and especially the Schrodinger equation we blindly accept the potential energy part. I would like to know what's the meaning of potential energy whe... | Quantum mechanics is based on Hamiltonian mechanics or if you want, analytical mechanics in general. That means it utilizes the same concepts of kinetic energy and potential energy among others that you may have encountered already in Newtonian mechanics. Their meaning is exactly the same in classical and quantum mecha... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634414",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Do partial derivatives of different coordinate systems commute? Consider an arbitrary set of coordinates $x^\mu$ and another set of coordinates $y^{\mu}$, which is a (lorentzian) transformation from $x^\mu$ given by $y^\mu = f(x^\mu)$.
So I want to know whether $\frac{\partial}{\partial x^\alpha}\frac{\partial}{\partia... | No they don't commute in general. At least not with the usual understanding that
$$
\frac{\partial}{\partial x^2}
$$
is the partial derivative with $x^1$, $x^3$ etc held fixed.
Here is a counterexample:
Let $x= r \cos \theta$, $y= r \sin \theta$ be cartesian and polar coordinates. Then
$$
\frac{\partial x}{\partial y}... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/634888",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
"answer_count": 2,
"answer_id": 1
} |
Is the Least Squares Fit always the accepted Fit in Physics? Is the Least Squares Fit always the accepted Fit in an experiment? Suppose you have $N$ data points and a function $f$ with some parameters. There is a one Least Square sum, it may be obtained for more than one set of parameters but we can find that most opti... | No, it’s not. Sometimes it’s much more complicated than least squares, and sometimes it’s a by-hand “guide for the eye.” Not everybody has the expertise to apply a fancier data analysis, and they don’t let perfect be enemy of good.
Least squares is just sort of default for a typical situation, where you have a curve an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/635008",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 4,
"answer_id": 0
} |
Nonlinear Schrödinger equation in a potential I've recently become interested in the integrability of nonlinear PDEs while reading these lecture notes.
Question 1: Would the equation $i\Psi_t + \Psi_{xx} - (2|\Psi|^2 + V) \Psi = 0$ for a potential function $V(x)$ posses any physical significance?
I was curious as to ho... | The equation you've written is known as the Gross-Pitaevskii equation, which is one of the central concepts used to describe Bose-Einstein condensates.
(Indeed, this is mentioned explicitly in the disambiguation text at the top of the Wikipedia page for the NLSE.)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/635216",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why does increasing tension in a string increase the speed of travelling waves? We know that $$ v = \sqrt\frac{T}{\mu} $$ meaning that increase in the tension of a string increases the velocity of the traveling wave. But how exactly does this happen? If we consider that the travelling wave is just a certain amount of e... | Tension determines the vertical force (perpendicular to wave motion) on molecules of string and hence determines the speed of perpendicular motion. Faster the perpendicular motion, faster the wave has passed by.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/635526",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 1
} |
Why is momentum not quantised in the photoelectric effect? I know that the momentum transfer mechanism in photoelectric effect is pretty complex etc, but why do we quantise the Energy of the photon but not the momentum ?
Edit: had written conserved instead of quantised
| Just because we don't use the equation $$\vec{p}_2=\vec{p}_1+\int_{t_1}^{t_2}\vec{F}\mathrm d t \tag{1}$$
doesn't mean that we ignore momentum. It's simply that there is a large mass (compared to the photoelectron and the mass-energy added by the photon, and that mass absorbs a lot of the momentum of the photon. That i... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/635975",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
$SU(2)$ Symmetry of Hubbard Model I am confused with the $SU(2)$ spin rotation symmetry of the fermion Hubbard Hamiltonian. If the Hubbard model has $SU(2)$ rotational symmetry, it means that the Hubbard Hamiltonian commutes with the global spin operator in all direction:
\begin{equation}
[\vec S, H] = 0 ~~,~~ \vec S ... | From what I understand of the standard notation, the statement that $$[\vec{S}, H] = 0$$ is exactly the same as saying $$[S_j, H] =0$$ for all $j$. Then, to give a proof that a vector operator commutes with some operator simply amounts to proving each component commutes with the given operator.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/637053",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
What would you see dropping a sufficiently strong chain with substantial length into a black hole? Here's a visual representation of the scenario
Here you can see we have a black hole on the left. The event horizon is the edge of the black hole. You are far away from the event horizon, and a chain is passing you by fa... | The first thing to remember is that at the event horizon of a black hole, time dilation is so extreme that, from our frame of reference here on Earth, time has essentially stopped. So you would see nothing happening at all. You could wait for your lifetime, and for the lifetime of all your decedents and nothing would... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/637288",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 6,
"answer_id": 3
} |
Friction between 2 objects stacked on top of each other Let's say I have a particle on top of a block that is resting on top of a rough plane. Let's also assume that there is friction between block & particle as well as block & surface. In which direction would friction act and if we were given some information such as... | Generally speaking, you should always draw each internal force between objects according to the 3rd law of Newton, and then apply the 2nd law of Newton on each object.
Usually one thinks that friction always is in the opposite of movement, but this is not true. For example, put a book on the palm of your hand and slowl... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/637380",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
For how long does the force in $τ=rF\sinθ$ exert on the object that it sets into rotation? When calculating torque using formulas such as $τ=rF\sinθ$, is the force $F$ exerted on the object for an extended period of time (i.e. the force is still exerted on the object even when the object is at a different position on i... | $\boldsymbol\tau=\mathbf r\times \mathbf F$ is just the definition of torque. Its behavior is completely dependent on $\mathbf r$ and $\mathbf F$. So, if you want to know torque as a function of time, look at those values as a function of time: $\boldsymbol\tau (t)=\mathbf r(t)\times \mathbf F(t)$. The definition appli... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/637853",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Why can you not use equation of motion $v^2 - u^2 = 2as$ when attempting escape velocity questions? There is the this question:
Imagine you are projecting a ball with $3/4$th the escape velocity from the surface of the earth. What is the farthest distance will it reach it from the centre of earth? ($R=$ Radius of the e... | That equation is for constant acceleration motions. The value of $g$ decreases with altitude according to $g=\frac{GM}{r^2}$. In this problem, the decrease in $g$ is significant, as you could expect the projectile to reach a great height.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/638045",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Odd or Even symplectic structure in BV formalism I am studying Batalin-Vilkovisky formalism. I am a little bit confused on what an odd (or even) symplectic structure is (i know what the degree of the underlying 2-form is). I can not find a clear definition anywhere. I read that an even bilinear form $B$ is even if $B(x... | *
*An even (odd) symplectic 2-form
$\omega~=~\frac{1}{2}\mathrm{d}z^I ~\omega_{IJ}(z)~ \mathrm{d}z^J $ on a supermanifold means a Grassmann-even (Grassmann-odd) closed non-degenerate 2-form, respectively.
*There is a straightforward generalization to even and odd Poisson structures on supermanifolds.
*The Hamilto... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/638170",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
Computing curvature singularities from a metric Suppose I have the metric
$$ds^2 = f(r)(dt^2-dr^2-dz^2) - \frac{1}{f(r)} d\phi^2. $$
How would you calculate the curvature singularities of this metric if we assume that $f(r)$ takes value $0$ for $r_0$?
| You have to compute some curvature scalars such as $R$, ${R_{\mu \nu }}{R^{\mu \nu }}$ etc. for your spacetime in order to find where those curvature invariants diverge. In order to understand whether there is singularity at all or not, it is enough to show that one of those curvature scalars diverges. But, the informa... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/638227",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 1,
"answer_id": 0
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.