Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Limit as $x_1 \to x_0$ for the propagator of the harmonic oscillator
Consider a non-relativistic particle of mass $m$, moving along the $x$-axis in a potential $V(x) = m\omega^2x^2/2$. use path-integral methods to find the probability to find the particle between $x_1$ and $x_1 + dx_1$ if the particle is at $x_0$ at t... | As $T = t_1 - t_0 \to 0$, we have$$\begin{align}\lim_{t_1 -~ t_0~ \to~ 0} \langle x_1, t_1\,|\,x_0, t_0\rangle &= \lim_{T~ \to~ 0}\left({{m\omega}\over{2\pi i\sin\omega T}}\right)^{1/2}\text{exp}\left[{{im\omega}\over{2\sin\omega T}}\left(\left(x_1^2 + x_0^2\right)\cos \omega T - 2x_0x_1\right)\right]\\ &=\lim_{\epsilo... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/160777",
"timestamp": "2023-03-29T00:00:00",
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Why does a magnetic field go anticlockwise of the direction of current? Why never clockwise? How does it 'know' to go anticlockwise?
| The direction of the magnetic field is defined in terms of its effect on a current (or moving charge). Specifically, the magnetic field points in a direction such that the force on a current will be in the $\vec{I}\times\vec{B}$ direction. (That's just a convention; there's no fundamental reason you must define the m... | {
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What are the dimensions, width and length, of a photon? Everyone is always talking about photon's wavelength. But what about its dimensions?
What is length and width of it?
And does it even have a point to think about such things? Or those dimensions are non-existent in such cases?
| For me I prefer an experimental definition of the size of a photon. If you pass light through an aperture you start to see interference effects when the aperture approaches the wavelength of the photon, as if you're clipping the edges. Why do we need to make it more complicated than this?
If the photon is point-like th... | {
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What do quarks look like? I've heard everything from zero-dimensional points, to squares, and I would love to know what they really look like, or if they have any physical shape.
| In physics quarks are point elementary particles. Their existence can only be inferred by fitting mathematical equations derived from quantum mechanical solutions of differential equations.
A simplified description can be found here.
Due to a phenomenon known as color confinement, quarks are never directly observed or... | {
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How do you determine the "phase" of a hydrogen eigenfunction? I've been reading the wikipedia article on the atomic orbitals of hydrogen. They have a nice collection of diagrams, such as this one for n,l,m = 3,1,1
This is apparently showing the wavefunction, not the probability density, and the blue area represents po... | Hydrogenic wavefunctions (as well as anything with well-defined angular momentum about a given axis) come in two flavours.
*
*The first set is 'cylindrical', and has wavefunctions $\psi\sim e^{\pm i|m|\phi}$.
*The second set is 'cartesian', and has wavefunctions $\psi_\text{even}\sim\cos(m\phi)$ and $\psi_\text{od... | {
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Magnitude of the average velocity vector (not the average speed) Thank you ahead of time for taking to look at this. For this following problem we were given an answer however I am almost positive the given answer is wrong. It doesn't even make sense. So here is the question:
The sweep-second hand of a clock is 3.4 cm... | You don't need any integral, even though it is nothing wrong in averaging the instantaneous values to get the average value.
However, by definition, the average velocity is
$ \vec{v}_{ave}=\frac{\Delta \vec{r}}{\Delta t} $ or in words, average velocity is the ration between the displacement and the time taken for this... | {
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Confusion with potential in simple pendulum I'm a maths student taking a course in classical mechanics and I'm having some confusion with the definition of a potential.
If we consider a simple pendulum then the forces acting on the end are $mg$ and $T$. Now I know that the potential is defined such that $F = -\nabla V$... | From the perspective of Lagrangian mechanics, the tension $T$ is a constraint force that does no virtual work. Can you see why? Hence it can the be ignored in the Lagrangian formulation, cf. D'Alembert's principle. See also e.g. this Phys.SE post. The only remaining force in the Lagrangian formulation is gravity, which... | {
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Why does the mathematical constant $e$ enter into quantum mechanics so much? In A. Zee's book Quantum Field Theory in a Nutshell, he mentions on pages 11-12 the following formula which he assumes reader had encountered before:
\begin{equation}
\langle q | p \rangle ~=~ \frac{e^{iqp/\hbar}}{\sqrt{2\pi\hbar}}.
\end{equat... | As a specific case of @ACuriousMind s answer, the $e^{i\phi}$ and $e^{i\phi}$ forms (where $\phi$ is something real) appear as solutions to the differential equation form $$\frac{d^2}{dy^2}f(y)=-\phi^2f(y),$$ where $y$ is some independent variable (not necessarily spatial).
This differential equation shows up quite oft... | {
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Do we know where newly formed quark-antiquark pairs come from in the process of hadronization? The only explanations I have found are very vague, such as "spontaneously created from the vacuum" and because "it is more energetically favorable".
| They don't "come from" anywhere
in the sense that there is a reservoir of these thing sitting around waiting to be used.
Taken together the pair is equivalent to "nothing with some energy". So whenever you have that much energy and nothing, that combination can (not must or will, but might) simply become a quark-antiqu... | {
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Work function definition As in this post How would I calculate the work function of a metal, the definition is given by "the minimum thermodynamic work (i.e. energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface"(from Wikipedia). But when we do photoemission sp... | When an electron is ejected from a metal surface it experiences an attraction due to the image force. However the attraction falls off rapidly with distance. A back of the envelope calculation tells me that (relative to infinity) the potential energy due to the image force is only around -0.001eV at a distance of a mic... | {
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Why is probability proportional to $ \ e^{-E/kT}$? Why is the probability for say the Ising model to be found in state of energy E proportional to $e^{-E/kT}$ ?
Is this some postulate or can it be derived from simpler principles?
| The first law of thermodynamics is that energy is conserved. The second law of thermodynamics states that entropy never decreases. Therefore the equilibrium distribution must maximize entropy while maintaining the same average energy. For a given energy $U$, the distribution that does this is an exponential distributio... | {
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What does the statement "the laws of physics are invariant" mean? In the first paragraph of Wikipedia's article on special relativity, it states one of the assumptions of special relativity is
the laws of physics are invariant (i.e., identical) in all inertial systems (non-accelerating frames of reference)
What does ... | In leyman's terms, it just means that the laws of physics are the same everywhere. Here, on the Moon, even in another galaxy, or in a spaceship travelling at near light speed to another galaxy.
| {
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Tensor product of two different Pauli matrices $\sigma_2\otimes\eta_1 $ I'm solving problem 3.D in H. Georgi Lie Algebra etc for fun where one is to compute the matrix elements of the direct product $\sigma_2\otimes\eta_1$ where $[\sigma_2]_{ij}\text{ and }[\eta_1]_{xy}$ are two different Pauli matrices in two differen... | I think it is easier to compute direct products when you write the matrices in component form; basically, you just have to multiply each element of the first matrix by the whole second matrix:
$$ \mathbf{A}\otimes\mathbf{B} = \begin{bmatrix} A_{11} \mathbf{B} & \cdots & A_{1n} \mathbf{B} \\ \vdots & \ddots & \vdots \\... | {
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If a Killing vector field is timelike, can it be set to $\partial/\partial t$? If one has a Killing vector that turned out to be a timelike Killing vector field because of negative norm. Can we set this Killing vector field equal to $\partial/\partial t$?
| The rough idea: take the local flow of the vector field and use it to get a new "time" coordinate. In general this will work locally, so you have to patch your manifold with small enough open subsets where you can then define the new set of coordinates where now the Killing vector field corresponds to $\partial_t$.
| {
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Can a magnetic field be focused at a distance? There are interesting arrangements of magnets that can strengthen the field in some places while weakening it in others. This is discussed in
Can magnetic fields be redirected and focused at one point? and examples are the solenoid, the Halbach array, and an iron cone.
How... | is there any sort of way to focus the magnetic field similar to boyd bushman beam( also does anyone know is this has been confirmed as working) and using electromagnetic coils? https://patents.google.com/patent/US5929732A/en
| {
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Why do most formulas in physics have integer and rational exponents? I mean, why is $F=ma$? Why not $m^{0.123}$, $a^{1.43}$ or some random non-integers or irrational?
I hope you understand that my question isn't limited just to force, energy, velocity, etc.; it also extends to the area of a square, circle, etc. and all... | Good question, and I don't have a good general answer.
However in the specific example you quote it's because the minimal dimension of space you can inscribe the circle is a surface of some kind ie a plane, or the surface of a sphere.
Similarly, with the formula for the volume of a sphere, the exponent is three - whic... | {
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Units in gravitational $N$ body simulations I am trying to write a code in Python to simulate $N$ bodies interacting through gravity. In particular I am trying to see whether a system of particles with random initial positions and zero velocity will fall into a viral equilibrium.
I understand that in $N$ body simulatio... | Kepler's Third Law is
$$\frac{T^2}{r^3} = \frac{4 \pi^2}{GM}$$
or equivalently
$$
\frac G{4\pi^2} = \frac{r^3}{T^2M}
$$
If you're modeling our solar system you can set
\begin{align}
G &= 4\pi^2\frac{\text{AU}^3}{\text{year}^2 M_\odot}
\end{align}
where "AU" is the astronomical unit and $M_\odot$ is the mass of the sun... | {
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Why does ice melts faster near the surface of water? I had a few frozen bottles and while they were melting I saw this:
in all of the bootles, the ice seems to get thiner near the surface. I have searched a bit and I've found this video that shows better the effect:
https://www.youtube.com/watch?v=sgnlGcB7pDg
(special... | I can't either give you a 100% correct answer, but my thought is that the water at the surface melts faster because of Surface Tension.
Molecules of water like to give off energy to their neighbours and because the molecules of water from the surface can't transfer their energy up, they have more energy.With more energ... | {
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What information do $|\psi(0)\rangle$ and $|\psi(t)\rangle$ represent? I am starting to feel comfortable with the role of the unitary operator in quantum mechanics. For instance, one of the equations I have seen is
\begin{equation}
|\psi(t)\rangle = U(t) |\psi(0)\rangle
\end{equation}
I understand what a unitary oper... | The ket $ | \psi(t) \rangle$
denotes the state of the system at the time $t$,
and $|\psi(0) \rangle$ is nothing but the state of the system at the time $t=0$.
The probability amplitude of the state $|\psi(t)\rangle$ being in some state $| x \rangle$ is $\langle x | \psi(t) \rangle$, which when $x$ represents the spati... | {
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Why is it mandatory to make the string taut/stretched for sending pulse/wave?
In order to send a pulse and to propagate it, the string must be under tension.$^\text{1}$
Why is the tension necessary? Why should the string be stretched/taut for the transmission of the pulse?
$^\text{1}$ Principles of Physics by Walker,... | A wave on a string is like a harmonic oscillator (think mass on a spring). The oscillation happens because of the interplay between the restoring force, which tries to bring the mass to equilibrium, and the inertial quality of the mass, which tends to overshoot equilibrium. If you take away either, you don't get an osc... | {
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Gravity: Is there curved space besides curved spacetime? Wikipedia:
Curved spaces play an essential role in General Relativity where
gravity is often visualized as curved space.
Is the Wikipedia article "curved space" talking about curved space or about curved spacetime? As far as I know gravity is curving spacetim... | Your argument is incorrect: The curvature of a spatial slice is coordinate-independent.
What is true is that in general relativity, there is a priori no preferred spatial slicing. For example, de Sitter spacetime (a universe dominated by cosmological constant) can be sliced into positively curved, negatively curved or ... | {
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Quantum coherence and decoherence In Quantum Mechanics coherent states are defined as eigenstates to some annihilation operator. Afaik this notion is due to Roy Glauber.
Now, I just read that if you have a spin-state for example, then the coherence of the spin-state is measured by the off-diagonal elements of the densi... | Coherent state is one thing and decoherence is something else.
The coherent state has the form
$ (\text I) \ |\alpha \rangle = e^{-\alpha ^2/2} \sum _n \frac {\alpha ^n}{\sqrt {n!}} |n \rangle.$
where $|n \rangle$ is a Fock state of n identical particles. This state is a coherent superposition of Fock states, and its d... | {
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Does the Lorentz invariance of equation of motion guarantee the Lorentz invariance of the solutions? If I have a Lorentz invariant equation of motion, like Klein-Gordon equation, is the solution automatically guaranteed to be Lorentz invariant?
I ask this question because of the discussion from Mark Srednicki's Quantum... | In the spirit of the original post, let $k,x$ be 4-vectors and $\mathbf{k}$, $\mathbf{x}$ the spatial components. Then a quantity of the form
$$\phi(x) \propto \int dk[ a(k)e^{ikx} + a^*(k)e^{-ikx}]$$
is manifestly Lorentz invariant because it does not explicit contain any free Lorentz indices. What Srednicki does is t... | {
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What does $v=c$ in the Lorentz transformation for time tell us? For the simpler cases as boost in the x-direction, the time dilation formula following the Lorentz transformation for time is $$\Delta t'=\gamma(\Delta t-v\frac{\Delta x}{c^2})$$Now, we observe that as $v\to c$, $\gamma\to \infty$. And we also observe that... | You cannot boost a massive particle to the speed of light, which is what you're trying to do. The infinities you are finding when you set $v=c$ are closely related to the fact that it would take an infinite amount of energy to accelerate a massive object, like a pebble or an electron, to the speed of light. So this is ... | {
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On quantum randomness, the longest weather predictions and perfect macroscopic caos
*
*Which is the maximum number of days we can predict future weather conditions with a reasonable degree of accuracy if we knew all of the initial conditions of everything that effects the weather down to the quantum level and with th... | I'll take your statement "down to the quantum level and with the minimal uncertainty allowed" to mean that we can know the quantum state. If, as you ask in your comment " At which point in time $t_0$ [is] the probability $p_s$ for successfully predicting some macroscopic event $E$ is lower than some fixed value $p_0$?"... | {
"language": "en",
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How do quantum fields really couple? The term "coupling" between quantum fields refers to certain terms in the Lagrangian (density) $\mathcal{L}$ where the respective field operators appear together, e.g. $g\phi^\dagger\psi $ with coupling constant $g$.
Knowing the mathematical description/origin of a coupling in QFT, ... | Well, all the fields exist in the same space, right? So they occupy the same volume. Perhaps the different fields are actually different vibrational mode families of something finer; in that case, coupling isn't surprising, since we're observing different vibrational mode families of the same underlying field. There is... | {
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High Pressure Processing(HPP) of juices in a plastic bottle container High Pressure Processing (HPP) is a cold pasteurization technique by which products, already sealed in its final package, are introduced into a vessel and subjected to a high level of isostatic pressure (300–600MPa/43,500-87,000psi) transmitted by wa... | You have to know what method are they using, they are using a tehnique called hydrostatic pressure, here is a good article about that. http://www.eolss.net/sample-chapters/c10/e5-10-04-11.pdf
As you can see the pressure is applied uniformly and there are not pressure diferences as you can see from this video. That mea... | {
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Is there a generalized notion of intrinsic charges which describes a general interaction? Consider classical fields. Lots of parallels can be drawn between different kinds of fields because they are fundamentally similar. Mass can be viewed as a mass charge, [charge] can be viewed as an electric charge. Potentials, pot... | The most successful attempt at a fundamental theory of the interactions in nature is the Standard Model of particle physics.
In it, every interaction except for the self-interaction of Higgs is produced by it being a gauge theory, and the generalization of charge is "simply" the specification in which representation of... | {
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How is the functional integral over momentum performed in the case of the real scalar field? Let's follow Peskin and Schroeder section 9.2, page 282.
The Hamiltonian of a free real scalar field is
$$H=\int{}d^3x[\frac{1}{2}\pi^2+\frac{1}{2}(\nabla\phi)^2+V(\phi)]$$
so the expression for the functional integral is
$$\l... | That's not a handwaving and I think that this particular question is covered in practically every textbook containing path integrals. First of all you should note that we can integrate by $\pi$ not touching the second exponent, i.e.
$$\langle\phi_b\vert e^{-iHT}\vert\phi_a\rangle =\int \mathcal{D}\phi e^{i\int_0^T d^4x... | {
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How to get the magnetic field strength in space near a solenoid I am trying to find the magnetic field strength along the axis of a solenoid.
If I know the strength of the field at the center of the solenoid, and I know the distance from the center of the solenoid, would it be possible to calculate how strong the field... | Absolutely. The answer you're looking for is somewhat surprising.
Suppose the axis of the solenoid coincides with the $z$-axis of our coordinate system. We'll make the approximation that the solenoid is infinitely long (in experiment the solenoid is probably not infinitely long - but this assumption makes this calculat... | {
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How do you quantify the "much greater" operator "$\gg$"? I'm specifically asked to compute the charge in the Earth-Moon system knowing that the gravitational force between the two bodies is much greater ($\gg$) than the electrostatic one. However, I don't know how many orders of magnitude should I take in order to make... | $\gg$ doesn't mean anything about a specific order of magnitude. If you are told to assume $Y \gg x$, what that means is if you have a series expansion of the form
$$\sum C_n \biggl(\frac{x}{Y}\biggr)^n\tag{1}$$
you can neglect all subleading terms (i.e. all except the first one with a nonzero coefficient).
For compari... | {
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Is there a formal proof for the superposition theorem? I was just wondering whether there is a formal prove for the superposition theorem in electric circuits? I tried searching it online but couldn't find anything sufficient. Most of the sources assume it follows from the definition of linear systems, but then how do ... | Superposition is essentially a mathematical concept. Inspection of a physical phenomenon and the choice of the mathematical model to represent it, define the mathematical relations that the phenomenon is suggested to be subject to, and superposition may be one of them.
For example, when we say that a capcitor follows t... | {
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How could a cord withstand a force greater than its breaking strength? How could a 100 N object be lowered from a roof using a cord with a breaking strength of 80 N without breaking the cord?
My attempt to answer this question is that we could use a counter weight. But I don't really understand the concept behind coun... | As far as I see, if you want the object to lower at constant speed the only way is actually fixing at least both the extremities of the cord to the object (can't describe this well, let's say your "grip" is on the middle of the cord).
Whatever happens somewhere else, constant speed means that the balance of the forces ... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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What is the expectation value of the position times momentum operator? Should I write the expectation of the position times momentum operator as:
$$\langle xp\rangle = \langle \psi|x (-i\hbar \partial_x) |\psi \rangle$$
or
$$\langle xp\rangle = \langle \psi| (-i\hbar \partial_x x) |\psi\rangle$$
| In fact $xp$ is not self-adjoint, it can have non-real expectation values. But its symmetrized form $D=(1/2)(xp+px)$ is better behaved (it has a self-adjoint extension). It is the generator of dilatations which scales momenta and coordinates. The complexification of ${\exp}[iDa]$ (i.e. $a$ becomes complex) is importan... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What is basically the difference between static pressure and dynamic pressure? What is basically the difference between static pressure and dynamic pressure?
While studying Bernoulli's theorem, I came before these terms. The law says:
When the fluid flows through a small area, its pressure energy decreases & kinetic e... | To fluid dynamicists, Bernoulli's equation is better known as the 'Energy Equation' since it does indeed account for the energy changes that occur along a fluid path. The energy equation says that the energy is constant along any given streamline. Static or stagnation pressure can exist in the absence of fluid velocity... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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Desynchronised pixels in images of the Sun? NASA published this wonderfull video of Sun from SDO:
https://www.youtube.com/watch?v=GSVv40M2aks
And it occurred interesting question: Sun is very big sphere. Its so big that it took light 4,6 seconds to traverse distance of diameter of the Sun. Every point on Sun surface em... | A dirty little secret of remote sensing: This image of the Pribilof Islands taken by Landsat 8 taken on September 22, 2014 is not time-synchronized.
Landsat, along with many remote sensing vehicles in low Earth orbit, build their imagery one pixel at a time, with each pixel taken at a slightly different time. The appe... | {
"language": "en",
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"source": "stackexchange",
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What made Kepler think that orbits are not circular which came to be elliptical? Kepler formulated his laws in a sort of time where human began to believe in heliocentric universe and telescope was not yet invented/ discovered. So what made Kepler think that orbits aren't circular?
| In respect to above answer, although you are correct but there is a little discrepancy in your last line " a bigger leap was to try the Sun's location at a focus and not the center."
A circle is a ellipsoid with a special case having the two foci at same point, so there could not be so chance putting in centre becau... | {
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If any, what would be the ideal modulation frequency for a phase-sensitive light sensing experiment in a non-dark environment? I have constructed some equipment for sensing a beam of light. The equipment is enclosed in a rudimentary darkbox to block out the majority of the ambient room lighting, but is still partially ... | Do you have access to a dynamic signal analyzer or similar? My most recent setup involves locking in to a signal from a split photodiode that is either singly or doubly modulated. We chose our base modulation frequency by looking at the noise spectrum -- our photodiode when illuminated with a DC signal looks somethin... | {
"language": "en",
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Is there a simple proof that Kirchhoff's circuit laws always provide an exactly complete set of equations? Suppose I have a complicated electric circuit which is composed exclusively of resistors and voltage and current sources, wired up together in a complicated way. The standard way to solve the circuit (by which I m... | The second problem solves the first one. If enough data are known from measurement, then the state of the system is determined uniquely. If more than enough data were measured this will not impact the solution, unless of course Kirchhoff's assumptions are not met or Maxwell's equations are flawed.
As to the requested f... | {
"language": "en",
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"source": "stackexchange",
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Show that, for two large systems in thermal contact, the number $\Omega^{0}(E^{0},E_1)$ can be expressed as a Gaussian in the variable $E_1$ This problem below is from the book "Statistical Mechanics" by Pathria. The author defined the number of microstates of a system with two subsystems exchanging energy as:
$$\Omeg... | Suggestion:
It is not hard to taylor expand to get
$$\ln \Omega_1(E_1) = \ln \Omega_1( \bar E_1) + \beta_1 (\bar E_1) (E_1 - \bar E_1) + \gamma_1 (E_1 - \bar E_1)^2 + \dots$$
$$\ln \Omega_2(E_2) = \ln \Omega_2( \bar E_2) + \beta_2 (\bar E_2) (E_2 - \bar E_2) + \gamma_2(E_2 - \bar E_2)^2 + \dots$$
with $E_2 - \bar E_2 =... | {
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Is a constant transformation still considered a gauge transformation? I've never even considered the possibility that a constant transformation would not qualify as a gauge transformation. But I'm reading a paper that seems to make exactly this distinction. In particular, the title of the paper itself begins with "Ga... | I can't think of any sane definition of the phrase "gauge transformation" which would exclude a function that is identically equal to some constant $C$, but include a function that is equal to $C$ everywhere except for at a tiny region over in the Andromeda galaxy, where it takes on the value $C + \epsilon$ for a tiny ... | {
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Invariance of the QED Lagrangian under charge conjugation Is it true that the QED Lagrangian
$$\mathcal{L} = \bar{\psi}(i\gamma^\mu D_\mu-m) \psi $$
is invariant under charge conjugation?
$$\begin{align}
\psi &\mapsto -i(\gamma^0 \gamma^2 \psi)^T\\
\bar{\psi} &\mapsto -i(\bar{\psi} \gamma^0 \gamma^2)^T\\
A_\mu &\mapsto... | As to your question, yes, the QED Lagrangian is indeed invariant under charge conjugation.
You may have found differently because your transformations under charge conjugation are faulty. The prefactors are correct, however, under charge conjugation $\psi$ goes to $\bar{\psi}$ and vice versa, i.e.
$$
\hat{C} \, \psi \,... | {
"language": "en",
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How eddy current brakes function Take the following example:
where a rectangular sheet of metal is entering a constant magnetic field at $v \dfrac{m}{s}$. Due to Faraday's law of induction + Lenz's law, we can state that an eddy current will be generated to oppose the increase of magnetic flux through the sheet of met... | I think that the most intuitive way of getting a grasp of the phenomenon is by means of energetic considerations. The induced current is due to the relative motion and it dissipates energy to a rate of $RI^2$, where $R$ is the resistivity of the material and $I$ is the induced current. Hence the moving object is losing... | {
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Temperature in statistical mechanics and differentiating entropy In statistical mechanics, the entropy of an isolated system with energy $E$ (with fixed volume $V$ and chemical composition $N$) is defined as $S(E) = k \log \Omega$, where $\Omega$ is the number of microstates with total energy $E$. The temperature $T$ i... | The number of microstates is usually so large that we may approximate using a derivative. After all, look at $10^{23}$ molecules in a jar. It is quite easy to think that you are looking at a continuum.
| {
"language": "en",
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Expression of density operator States in Quantum Mechanics can be thought of as density operators, i.e., positive semi-definite, normalized trace class operators on a Hilbert Space $\mathcal{H}$.
In the case $\mathcal{H}=\mathbb{C}^{2}$ we have that a generic state $\rho$ can be expressed as:
$$
\rho=\frac{1}{2}\left(\... | Every density matrix on $\mathbb C^2$ is of that form because $\rho$ must be Hermitian. This property is clearly satisfied because of the form and the algebra of Pauli matrices. This can then be generalised to higher dimensional Hilbert spaces by introducing a basis for Hermitian matrices which satisfy the same algebra... | {
"language": "en",
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Why are the neutron and proton masses nearly equal? The neutron to proton mass ratio is nearly one. Is there some fundamental reason from this or this simply a coincidence?
| Both protons and neutrons are made up of two types of quarks: up (u) and down (d). Protons are uud and neutrons udd. QCD, the strong force binds these quarks together into protons and neutrons (technically, the binding involves a "sea" of gluons and quark-antiquark pairs). There is an approximate symmetry of QCD called... | {
"language": "en",
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If a black body is a perfect absorber, why does it emit anything? I'm trying to start understanding quantum mechanics, and the first thing I've come across that needs to be understood are black bodies. But I've hit a roadblock at the very first paragraphs. :( According to Wikipedia:
A black body (also, blackbody) is a... | The name "black body" is maybe a bit misleading.
The "Idealizations" section of the wikipedia entry illustrates the idea in the way that always stuck with me. Put a pinprick in a totally "black" cavity. Here "black" means the sides of the cavity do not allow radiation, and the cavity is large enough that the photons th... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "13",
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My physics teacher gave us this equation $v= -3 +3t$ She asked us if the body was accelerating or slowing down, and I immediately said that it was accelerating (because the $a=3>0$). Then she said that I was wrong because the direction of the acceleration vector was the opposite of the direction of initial speed($v_0=-... | The initial velocity and acceleration here are in opposite directions. The magnitude of velocity (represented by $S=|\vec v|$) decreases upto a certain instant. (i.e. where $\vec v=0$).
Edit: Also, consider these graphs. ($t^.$ being the time where $v=0$) Note how the velocity increases but the magnitude of it (in the ... | {
"language": "en",
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Proof of Lorentz contraction? The measurement of the flux of muons at the Earth's surface shows that many more muons are detected than would be expected, based on their mean half-lifetime of 2,2 microseconds. This is a good proof for the time dilatation as predicted by the special relativity theory.
QUESTION: does ther... | As far as I know no-one has ever directly measured the length of a relativistic object. However indirect measurements of Lorentz contraction have been made at the RHIC. This collides nuclei together at relativistic speeds and analyses the resulting shrapnel. The nuclei are far too small to see, but from the results of ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/166932",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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How to find stopping distance of a car? I am trying to calculate the minimum stopping distance of a car once the brakes are applied. I know that $F = ma$, and the braking force is $F = \mu N = \mu m g$, so
$$a = \mu g.$$
Next, by applying the kinematics equation
$$v_f^2 - v_i^2 = 2 a x$$
I found
$$v^2 = 2 a d$$
where $... | When you're using the equation F=ma, the F is ALWAYS the total/resultant/net/unbalanced force, NOT one of the individual forces. It describes the effect (the acceleration) that happens due to the cause (the total force on an object). Here you happen to be right because (at least horizontally) there is only one force, t... | {
"language": "en",
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"source": "stackexchange",
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Why aren't all black holes the same "size"? The center of a black hole is a singularity. By definition, a singularity has infinite density. So how can a black hole with a different mass or density be described?
| It's almost certainly incorrect that the center of a black hole is a singularity as this would be at odds with quantum mechanics. Just how exactly it looks like would be something to ask of a theory of quantum gravity!
Regardless of being a singularity or not, the mass is determined by how much mass you stuff into your... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/167282",
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"source": "stackexchange",
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Is energy of a quantum mechanical moving particle conserved? From the Schroedinger equation
$$
H\psi=E\psi,
$$
if we want to measure the total energy of a quantum mechanical moving particle, then we have to apply the Hamiltonian operator to the wave function and as a result we get the eigenvalue of the Hamiltonian.
N... | Once you measure an eigenvalue, you collapse into a particular eigenstate. Let's call that state $| \alpha \rangle$, such that $\hat{H} | \alpha \rangle = E_\alpha | \alpha \rangle$. Now we use the time-dependent Schrodinger equation:
$$
i \hbar \frac{\mathrm{d}}{\mathrm{d} t} | \alpha (t) \rangle = H | \alpha \rangle ... | {
"language": "en",
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Confused about Lorentz contraction My son asked me the following question which I can't answer in a simple way.
A frame $O'$ has speed $v$ relative to $O$.
A photon travelling along the $x'$-axis in frame $O'$ over a distance $L'$ needs a time $t' = \frac{L'}{c}$.
The speed of light is $c = \frac{L'}{t'}$.
For the obse... | Suppose you are observer $O$, and I am observer $O'$.
Suppose you, I, and the photon all cross paths at a time we can both agree to call $0$ and a place we can both agree to call home.
Eventually, the photon passes Joe's diner, which I say is $L$ miles from home, and --- if we choose units so $c=1$ --- it does so at ... | {
"language": "en",
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Normalization of wave function meaning...? I just have one question.
I'm doing a problem where I'm told to normalize a wave function, which is split up into two regions, namely where $r \leq r_0$ and $r > r_0$. My question is, why am I doing this? I'm not using any of the math I get out of it later on. The only thing I... |
My question is, why am I doing this?
Becase, by convention, we want the probability account for all possible outcomes to sum to unity. The fact that we will get some outcome at a measurement, is guaranteed, and with this normalization it reflects a total probability of 1.
| {
"language": "en",
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White, is it a colour or absence of colours? Our chemistry sir and we had an argument today at the lab, he says that white actually is not a colour, it is the abscence of colour, but we say that it is a colour and we gave the following point to substanciate our point that white is a colour:
When we see an object in red... | The explanation you give is correct. A white body reflects all wavelengths. We call it white when all colors (all wavelengths) are reflected from an object and hit our eye. Black is the opposite.
I would say that white is all colors, as you do. But maybe he sees it from the perspective that since all is reflected and ... | {
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Why did scientists need to invent light years? Why did scientists need to invent light years? What's so important about having a light year? I have been learning that a light year is $9.461 \times 10^{15} \, \mathrm{m}$. My question is, why are light years so important for other people to know. What do scientist use th... | Light years help give an idea of distances through space and time. When we look at a star 100 light years away, that 100 light years not only gives an idea of the immense distance to the object but will also tell us that what we see is light from 100 years in the past.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168226",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
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WKB Quantization Condition - negative? In deriving the quantization condition for a bound state in a potential with "no verticle walls" we start with the WKB connection formulas to find the wavefunction in the interior of the well ($x_1<x<x_2$), namely
$$\psi(x) \cong \begin{cases}\displaystyle\frac{2C_1}{\sqrt{p(x)}}\... | Comments to the question (v2):
*
*Normally we assume that $-\infty< x_1 < x_2<\infty$ are the turning points in the 1D potential well. This means $$\forall x\in ]x_1,x_2[:~~ E ~>~ V(x).$$ Hence OP's third last equation $$0 ~<~ \int_{x_1}^{x_2}{dx\ \sqrt{2m(E-V(x))}} ~=~ -\frac{\pi}{2}\hbar~<~0$$ can never be fulfil... | {
"language": "en",
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Is it possible to "see" atoms? As per my knowledge, atoms are small beyond our imaginations. But there is an image on Wikipedia that shows silicon atoms observed at the surface of silicon carbide crystals.
The image:
How can we see these distinct atoms if they are so small?
| The statement of Martin above:
Now, can we "see" atoms? This depends, as I already hinted at, what you mean by "see". If you mean "make a picture in visible light", then you can't do that.
is actually not quite true. One can take images using visible light that show single atoms. Here is an example:
(1)
The reason t... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168713",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Physical meaning of non differentiatiability of $y(t)$ at a point of an elastic medium Consider two waves $y_1,y_2$ travelling in opposite directions with equations $$y_1(x,t) = A \sin(\omega t - kx) \\ y_2(x,t) = A \sin(\omega t + kx) $$
That create the following standing wave $$y_s(x,t) = y_1 + y_2 = 2A\cos(kx)\sin... | I believe it means that there is a kink or cusp in the pattern the wave makes at that point in time, presumably due to the fact that there was some external disturbance needed to make that change happen.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/168808",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How can gravitions exist without violating GR? How can gravitions exist without violating GR, since GR says that gravity is curvature in space-time.
| GR predicts gravitational waves, which hence exist without violating it. By the wave-particle duality, there must be a particle (or at least a quasi-particle) associated with (the quantization of) such waves. We arbitrarily name them gravitons. Whatever aspect of them may be found to violate GR simply indicates how we ... | {
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"timestamp": "2023-03-29T00:00:00",
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Difference between LO and NLO event generators? I am performing undergraduate research in particle physics.
In our research, we are using two event generators (PYTHIA8 and MC@NLO with HERWIG++) to study open bottom production.
I am unsure of the difference between leading-order event generators and next-to-leading-ord... | It is not limited to the Parton distribution functions (pdfs) only. The difference between LO and NLO event generators is that at the hard scattering level the formers use tree level matrix elements while the latter use one loop matrix elements*. The utility is that when you generate events with NLO matrix elements you... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169042",
"timestamp": "2023-03-29T00:00:00",
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Is there an infinite amount of wavelengths of light? Is the EM spectrum continuous? The electromagnetic spectrum is a continuum of wavelengths of light, and we have labels for some ranges of these and numerical measurements for many.
Question: Is the EM spectrum continuous such that between two given wavelengths (e.g. ... | Yes, there are an uncountable infinity of possible wavelengths of light.
In general the frequency spectrum for Electromagnetic (e.g light, radio, etc) is continuous and thus between any two frequencies there are an uncountable infinity of possible frequencies (just as there are an uncountable number of numbers between ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169209",
"timestamp": "2023-03-29T00:00:00",
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Can the brain detect the passage of a neutrino? On a few occasions either in bed or sitting around a fire, with my eyes closed, I rarely but sometimes see a very quick fast flash of white and then, with my eyes still closed, the flash disappears immediately. It happens so fast that I sit up and rethink if it was even r... | This definitely is not a neutrino. Neutrinos are hard to detect because they are light, quick, and have no charge, making them usually pass through matter. We build giant machines to detect single neutrinos. The chances of this happening extremely low.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169275",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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"answer_id": 3
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Why do microwave ovens use radiation with such long wavelength? According to Wikipedia:
Consumer ovens usually use 2.45 gigahertz (GHz)—a wavelength of 12.2
centimetres (4.80 in).
Typically, I put the dish inside the oven in its center. I suspect most people do the same:
Now, because the plate is in the center, it... | The wavelengths that microwaves use allows the waves to resonate with the water to heat it up, with the added value that they are easily blocked to prevent damage to objects outside of the machine.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169362",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What do spacelike, timelike and lightlike spacetime interval really mean? Suppose we have two events $(x_1,y_1,z_1,t_1)$ and $(x_2,y_2,z_2,t_2)$. Then we can define
$$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2,$$
which is called the spacetime interval. The first event occurs at the point with co... | Let's suppress some dimensions to simplify:
$$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 $$
This quantity $$\Delta s^2$$ is preserved by changes of reference frame, just as in Galilean physics the quantity $$\Delta r^2 = \Delta x^2 + \Delta y^2 $$ is preserved by rotations.
Notice it is also the equation of a hyperbola.... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169631",
"timestamp": "2023-03-29T00:00:00",
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Why does a plane wave leave the position of the particle unspecified? I'm covering a book on QM, and just started recently and I'm stuck at understanding something.
It says that we can describe the state of motion of a particle with an infinite plane wave equation:
$\psi(r,t)=Ae^{i(\mathbf{k}.\mathbf{r}-wt)} $
It says ... | 1) Yes, that's pretty much it - a perfect/ideal wave will extend to infinity. It matters in the sense that a sine wave, $\sin (kx)$ (and similarly a complex plane wave) is only a momentum eigenfunction if it is taken to be infinite in extent, as the domain of sine is all real numbers.
2) If the amplitude was not consta... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Where does this formula for sagging of a beam come from? In one of my physics textbooks there is a chapter on the elasticity of materials which contains pretty basic outline about Young's modulus, stress-strain, elastic potential energy and related stuff. There is only one thing stated in the book which I didn't unders... | The 4's and cubes possibly come from the general physical theory involving a fourth derivative, $$\alpha \frac {d^4y}{dx^4} + \mu ~ \ddot y = W \delta(x).$$ This expression has a Dirac $\delta$-function to locate the weight at $x=0$ and in steady state $\ddot y = 0$. So $y'''(x)$ is discontinuous at $x=0$ by a total am... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169773",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "8",
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What is the mass of a sphere? A solid sphere of mass M is rotating along an axis.
We can consider it as a collection of large number of point masses, every point mass is moving with respect to center of mass with velocity which depends on its radius from rotating axis.
Then, according to relativity, the mass of every ... | Theoretically, a sphere rotating at the speed of light (on its outer edge) would have an infinite mass due to the mass portions on the outer edge. A rotating sphere IS moving and has momentum (that is why flywheels can store energy).
Practically, any such sphere would fly apart far before any kind of relativistic spee... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/169909",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why are stars white? That is may be an easy question, but I am not a professional. The Sun is a star, and when I look at the Sun it is usually yellow. Why are stars in the sky at night white?
I suppose it could be due to their distance. What is the explanation?
| The sun is white. I've seen people say that it just looks yellow because the blue light is being scattered by the atmosphere. Since starlight is also scattered your question is still valid. But based on these pictures, the sun still seems to look pretty white through our atmosphere. My guess is that, since you can safe... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Dielectric constant of Transition Metal Dichalcogenides (TMD)
*
*Why is the in-plane dielectric constant of transition metal
dichalcogenides larger than the out-of-plane dielectric constant? Is
this because of the spacing between monolayers of the TMD?
*Why do these dielectric constants depend on the thickness and i... | The dielectric constant, or more appropriately, the dielectric function, can be thought of as a measure of screening. A simple relation for which to picture this is:
$V_{eff} = V_{ext}/\epsilon$
Therefore, in TMDs, since the electrons are more mobile in the planes, they tend to screen potentials with a greater efficien... | {
"language": "en",
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Helicity angle of electron in $B^0 \rightarrow K^{*0} \gamma$, with $\gamma \rightarrow e^+ e^-$? I haven't been able to find the exact definition of a helicity angle, and the ones that I found don't apply to this particular case, because they'd require to boost to the electrons' 4-momentum to the photon's rest frame. ... | From an experimentalist point of view, I had done something very similar to that for a different decay channel.
For each particle the four momentum in the laboratory frame was stored in the experiment. The analysis proceeds using only these four momenta as input. Due to the helicity amplitudes formalism every momentum... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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A cup of water in ZERO gravity What will happen if I try to pour a cup of water in zero gravity, into another empty cup? Will the water come out of the cup? The adhesive force between the water molecules and the interior of the cup should prevent the water from coming out. Is it correct? Or is there something more to t... | Remember the laws of Newton. In this case the water will only accelerate with the forces you apply when tilting the cup. Assuming not fierce tilting of the cup: By the hydrogen interactions the water will therefore most like just float around shaped as one or more slightly deform bubbles in mid-air, or inside the cup d... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Non-linearity and self-coupling of gravity I have heard that non-linearity of Einstein's field equations has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling?
| *
*In the action formalism a linear Euler-Lagrange (EL) equation corresponds to a quadratic action, i.e. an action which is quadratic in the dynamical field variables of the theory.
*On the other hand, self-coupling or interaction terms in the action correspond to cubic or higher terms. Such terms leads to non-linea... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do photons with a frequency of less than 1 Hz exist? A photon with a frequency of less than 1 Hz would have an energy below
$$
E = h\nu < 6.626×10^{−34} \;\rm J
$$
which would be less than the value of Planck's constant. Do photons with such a low energy exist and how could they be detected? Or does Planck's constant ... | The Planck constant is $h=6.626\times 10^{-34}\;\rm J\,s$ (joule seconds), you cannot compare it to an energy which is measured in Joules - this is the flaw in your argument. To answer the question: Such low energy photons can exist in principle, however the question is how to actually generate them. I'd propose to tak... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/170828",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Continuity of Potential of an electric field Consider a point charge $q$ at $(0,0,0)$, the potential at $\bf{r}$ is given by $V(\bf{r})$ $= \frac{q}{4\pi\epsilon_0r}$. If you consider a path through $(0,0,0)$, you encounter a discontinuity in electric field and the direction of field changes. Is the potential for the f... | A point charge is given at a single, specific location in space. Think of it as an idealized source of charge. At the point where r = (0, 0, 0), electric field is zero and V(r) = $\infty$. As the value of r approaches 0 from any direction, V increases towards infinity but it is never discontinuous.
For any other surfa... | {
"language": "en",
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Chern-Simons action in 4 dimensions I can not understand why we do not have a Chern-Simons action for four or even forms?
And why is it not a good theory for (3+1) dim?
| The rule of the game is to use $A$ and $F=dA$ to write a topological action, and in $d+1$-space time dimension you need to come up with a gauge-invariant $d+1$-form which can then be integrated over the manifold to give you the action. Such an action does not depend on metric at all. Take $U(1)$ gauge field as an examp... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What's the strength of a $B$-field inside a magnet? I understand that the strength of a magnetic field decreases as you get further away from the source of the field.
However, whats the strength of the field within a magnet? Is there a field in a magnet?
Like if I have a bar magnet, is there a $B$-field in that metal c... | Yes, there must be. The solenoidal law tells us that the normal component of the B-field must be continuous across any interface. There are no sources or sinks of B-field. Therefore the lines of magnetic field are continuous through your bar magnet - they come in through one end (very roughly speaking) and out through ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171339",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Why most of physics is somehow related to light? It seems that for the past 200 years, every physicist is concerned about light. For example : Newton's particle model, Young experiment, Photo-Electrict effect and Einstein's formula, Special Relativity (constant speed of light), Bohr's atom model (using Photons to emit ... | Light is a rare phenomenon as it has no mass. Most particles have mass and therefore cannot act in the way that light is, which is to move at the speed of light. At this speed, due to relativity light moves at the same speed regardless of your perspective; no matter how fast you are able to move you can never catch up ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171437",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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What does "receptor convention" mean in electrical circuits? What do the phrases "passive sign convention", "receptor convention", and "generator convention" mean with respect to electrical circuits, particularly for capacitors?
| I think this is really about which way you count current and voltage to be positive. For every element in a network you can define a a current and a voltage. If voltage and and current point the same direction, it's called "receptor". If they are in opposite direction its' called "generator". The most common convention... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/171610",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How much power does it take to keep a massive particle suspended in a gravitational field? For instance if I have a rocket of mass $m$ in a uniform gravitational field $g$, and I want to keep it floating in the air via thrust alone, then how much power in the form of (say) chemical energy would it expend?
This is a sim... | The equation you need is that force is equal to the rate of change of momentum. The force is the weight of the rocket, $Mg$, and the rate of change of momentum is the mass ejected from the exhaust per second multiplied by the exhaust velocity.
$$ Mg = v\frac{dm}{dt} $$
So choose your exhaust velocity $v$, and you can w... | {
"language": "en",
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Can I blow soap bubbles (of air) inside a vacuum chamber? When I blow soap bubbles from a liquid dish soap mixed with distilled water at atmospheric pressure at ground level both internal and external air pressure nullify and the tension of the bubbles holds, can soap bubbles be formed inside a vacuum chamber with all ... | For the question, can a soap bubble exist in a vacuum? Your answer places certain assumptions on the soap bubble.
*
*Asump 1: There is pressure inside the bubble.
*Asump 2: There is no gravity.
*Asump 3: The structure of the bubble has the strength to exert force
against the pressure inside the bubble.
1 A tota... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Angular velocity and instantaneous rotation axis Let's suppose that we have a cylinder of moment of inertia $I$ rolling on the floor without sliding, moving with linear velocity $v$ and rotating around an axis passing through the center of mass with angular velocity $\omega = v / R$. (a composition of translation and r... | The fastest way is to compare kinetic energies in the two cases:
\begin{align*}
KE &= \tfrac{1}{2}I_{\text{cm}}\omega^2_{\text{cm}} + \tfrac{1}{2}M(R\omega)^2_{\text{cm}} \\
KE &=\tfrac{1}{2}I_{\text{inst}}\omega_{\text{inst}}^2 = \tfrac{1}{2} (I_{\text{cm}} + MR^2)\omega^2_{\text{inst}}
\end{align*}
So $\omega_{\text... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172134",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Schwarzschild: Proof that $\{r<2m\}$ is a black hole I saw the following proof to show that $\{r<2m\}$ is a black hole in the Schwarzschild metric.
Consider the Schwarzschild metric:
$$
g=-V(r)\text d t^2 + \frac{1}{V(r)}\text d r^2 + r^2 \text d \Omega^2\;,\quad V(r)=1-\frac{2m}{r}\;.
$$
Introduce the Eddington-Finke... | Choosing $\dot{v}>0$ is equivalent to choosing an arrow of time in your spacetime. Purely from GR, there is now way to determine the arrow of time and therefore it is not possible to prove $\dot{v}>0$. The logic is the following: You observe that there are two equivalence classes of timelike vector fields (which you ca... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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What was Feynman's famous formula? In Welton(1983), Memories of Feynman, Welton mentions two formulas which he denotes as Feynman's Famous Formula (FFF) and FFF #2.
Which famous formulas is he talking about? Is he maybe talking about the Bethe-Feynman efficiency formula? Are these formulas still classified or does som... | There is something famously called "Feynman's famous formula", which comes up in QFT calculations, which I imagine must be the second FFF referred to in Welton's account. It reads:
$$\frac1{a_1 a_2 \ldots a_n} = \int_{x \in \Delta^{n-1}} \frac1{(\sum_{i=1}^n a_i x_i)^n} d\sigma$$
where $\Delta^{n-1}$ denotes the simp... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
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Magnetic field in a wire with constant current
I assume I have a wire parellel to the $z$ axis and with radius $R$. A constant current $I$ flows through it in the $z$ direction. I want to know the magnetic field inside the wire at distance $r<R$.
In the figure, the pink dots represent the flow of electrons in the z di... | The magnetic fields for the currents outside exactly cancel each other... That's just how the law of magnetism works.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172384",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "4",
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Could I break the sound barrier using circular motion? (And potentially create a sonic boom?) Ok, Lets say I get out my household vaccum cleaner, the typical RPM for a dyson vaccum cleaner reachers 104K RPM, Or 1.733K RPS. In theory, this disc would be travelling with a time period of 0.00057692307 seconds, If we take ... | Sure.
It would happen all the time with propellers and rotors if we didn't design them to avoid it.
This is something that is generally avoided in aerospace applications because the shock wave causes pretty significant drag. A lot of work goes into making sure this doesn't happen through careful selection of the blade... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172451",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Binomial expansion of non-commutative operators I would like to determine the general expansion of
$$(\hat{A}+\hat{B})^n,$$
where $[\hat{A},\hat{B}]\neq 0$, i.e. $\hat{A}$ and $\hat{B}$ are two generally non-commutative operators. How could I express this in terms of summations of the products of $\hat{A}$ and $\hat{B... | if $[A,B]=0$ then as you know you get the usual
$$
(A+B)^n = \sum_{p=0}^n C^n_p A^{n-p}B^p
$$
Now if $[A,B]\neq 0$ each term in the sum (for each $p$) splits into a sum of $C^n_p$ terms of all possible permutations of $(n-p)$ $A$s and $p$ $B$s, without regard to the order of $A$s and $B$s. Equivalently to the sum of a... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172512",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "15",
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How to build a MOKE (magneto-optic Kerr effect) magnetometer at home? I'd like to build a magnetometer at home. The type does not matter actually that much but it should be doable at home. The MOKE (magneto-optic Kerr effect) magnetometer at least appears to use relatively simple components.
However, looking at lasers,... | You might find the Faraday Effect easier. Since it was actually done by Faraday it is quite easy. You need a glass or plastic rod aligned with the magnetic field you want to measure, a monochromatic or coherent light source, a couple of polarizing filters and a photodiode. The magnetic field rotates the plane of polari... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172671",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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How do bathroom scales measure body fat percent? My bathroom scale has 2 metal strips each for a foot and the producer claims that it can measure body fat percent. There is a warning in the manual, that if I have heart problems (I guess pacemaker), then I must not use the scale. I tested it, and the results appeared to... | You will get a pretty good answer by reading this paper. In short: fat, water, and muscle each have different electrical properties as a function of frequency. By measuring the (very small, on the order of micro amps) current that flows between your legs when frequency of the driving voltage is changed, you can create ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172761",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "7",
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Why is $F=ma$? Is there a straightforward reason? Why is force = mass $\times$ acceleration? I have searched in many sites but didn't actually get at it. Simply I want to know that if a mass in space moves (gains velocity thus further accelerates), how can I think, postulate and further believe that force = multiplicat... | Let's break this down in two pieces.
First - the proportionality of force with mass. Imagine you need a certain force $F$ to accelerate a mass $M$. Now imagine that instead of one mass, you have two - each with mass $\frac{M}{2}$. Attach a piece of string to each. The total force on the two strings must be the same as ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/172848",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Do Sidebands mean the frequency of an AM radio wave is not constant? I'm studying for A-level now. I have read some other posts explaining how the sidebands generated after the carrier wave is modulated. So, if there is sideband frequency, the frequency isn't constant, right? However, they have written that there is co... | The text and the technical article below may add some insight into the spectral components of a "carrier wave" with amplitude modulation. I am the author of same.
» The variation of r-f output power from the transmitter is the result of the vector addition of the power contained in the upper and lower sideband spectra... | {
"language": "en",
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"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
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Torque wrench units My torque wrench has these markings on it:
(da. Nm.) and on the line below M. KGS.
I can tell from comparing the scale to poundf-foot on the other side that the scale units are kilograms-meter but am struggling to understand those four markings. Can anyone decipher?
| Very cryptic way to write units, but it can be decrypted:
da.Nm= decaNewton.meter (http://www.deprag.se/omvandlare.pdf)
M.KGS=meter kilograms (http://www.thetoolhut.com/Torque-Conversion-English-Metric-Ft-lbs-M-kgs.html)
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/173024",
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Error calculation in parallel resistances This is the question:
There are two resistors with resistance values $R_1=100\pm3$ ohm and $R_2=200\pm4$ ohm. Find the equivalent resistance of parallel combination.
According to what I've learnt, in any expression of multiplication or division, the percentage errors of each ... | The methods you were trying is for finding error when the resultant resistance is to the power one. Like in series.
But here it is of power -1. So differentiating we get
$$\frac{dR}{R^2} = \frac{dr1}{(r1)^2} + \frac{dr2}{(r_2)^2}$$
This implies:
$$dR = \bigg[\frac{3}{10000} + \frac{4}{40000}\bigg] \times 4444.9$$.
$$... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/173149",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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The $g$-force of common objects hitting the floor At my friend's work they have an accelerometer which measures the force with which certain objects hit the ground. He claims that from four feet high, cell phones hit a solid metal surface with a $g$-force of over 2000. Is this right? It seems like that number is way to... | using an accelerometer app I saw that dropping you phone onto a blanket only makes the phone hit like 6 to 8 g's and it doesn't cause harm. Humans in fighter jets widthstand these forces also without harm so it makes sense that it would takes thousands of g's to break it.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/173244",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "10",
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Is this the reason why acceleration is said absolute? I've seem sometimes people saying that although uniform motion on a straight line cannot be detected and hence it is not absolute, acceleration is indeed absolute in Classical Mechanics (I don't know yet how this turns out to work in GR, so for this question I'm exp... | I do not believe your statement to be true, as what you're measuring now is not the absolute acceleration of the train but rather the acceleration of the train relative to the ball.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/173314",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
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Maximum Penetration Depth for Ultrasound How do you define the maximum penetration depth of an ultrasound? I'm assuming it means the depth at which the wave has attenuated to a certain small percentage of the original intensity of the incident beam?
| Yes it is customary when talking about penetration length to mean the length when the intensity has dropped to 36.8% of its surface value. This is motivated by the fact that the intensity decays as $I(z)=I_o e^{-z/d}$. See you need a constant of dimension [Lenght] in the exponent denominator, so you call that $d$ the p... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/173683",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Induced emf problem This is not homework question,just a thought experiment about a general question i have about induction. Let's suppose that we have a closed circuit with only two resistors in series.We also have a changing magnetic flux going through the circuit(we do not care about exact numbers here).
As we know... | OP's question...... "So,in this case,between which two points is the induced potential difference?" ...... An emf (source of voltage) will be induced across any two points bathed in changing flux. Add up all your sources (induced emf) and sinks (resistors) between arbitrary test points as you wish, remembering sources... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/173763",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "2",
"answer_count": 3,
"answer_id": 2
} |
How do these factors affect the free fall of objects? Take an example of two balls of different masses being dropped from about 250 meters from the ground.
How do the following factors affect free fall:
*
*Air resistance.
*Absence of air resistance.
*Conduction of experiment on the moon.
For factor 2, I belie... | Without air resistance all objects are accelerated with gravity $$g = 9.81 \frac{m}{s^2}$$
Only the air causes a "slower" acceleration. This effect depends from the density and shape.
| {
"language": "en",
"url": "https://physics.stackexchange.com/questions/173943",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 3,
"answer_id": 2
} |
Do magnetic fields cause ionisation of gases? I am doing my final year engineering project on Magnetic Field Assisted Combustion and was curious to see what people thought about it.
Companies sell rare earth magnetic arrangements to be attached to fuel lines of gas burners and they are said to improve combustion effic... | The Zeeman effect describes the interaction between the magnetic field and atoms. It lowers or rises the energy level of each atomic state, in your case molecular state. It`s impossible to ionize a gas with magnetic field, since this would mean that that the magnetic field had done work to the system. My guess is that ... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/174031",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "14",
"answer_count": 4,
"answer_id": 0
} |
Florescents and radio waves Okay so if you put a florescent light bulb in front of a certain radio, the radio waves excite the mercury inside a causes them to emit UV light which makes the outer coating of the light bulb light up. But, how can this be if the radio waves are of a lower frequency and thus have less energ... | There are two separate processes going on. Radio waves provide a non-zero electric field throughout the gas. At any time in a gas, some small percentage of atoms are ionized due to thermal collisions. The resulting free electrons are accelerated by the electric field due to the radio waves. These accelerating elect... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/174174",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "1",
"answer_count": 1,
"answer_id": 0
} |
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