Q stringlengths 18 13.7k | A stringlengths 1 16.1k | meta dict |
|---|---|---|
Why use Fourier expansion in Quantum Field Theory? I have just begun studying quantum field theory and am following the book by Peskin and Schroeder for that.
So while quantising the Klein Gordon field, we Fourier expand the field and then work only in the momentum space. What is the need for this expansion?
| First of all, this is just a change of basis, which is up to us to make. Furthermore we should always choose a basis that makes our calculations easier, and hopefully makes things more intuitive. For a simpler example - just try finding the volume of a sphere in cartesian coordinates, its just a bad choice.
Second of ... | {
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What happens if an atom absorbs a photon of energy higher than first excited state but lower than second excited state? Since the energy levels of atoms are quantized, I was wondering what happens if an electron is hit by a photon whose energy is higher than electron's first excited state but lower than second excited ... | Let the electron ground state have energy $E_g$, let the first excited state have energy $E_1$, and let the second excited state have energy $E_2$.
Let the energy of the photon be given by $E_p = hf$.
Now it isn't the energy of the exited states that is important in transitions, but the energy differences between state... | {
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3D: Get linear velocity from position and angular velocity I want to find out the linear velocity of a point in 3D space, (Euclidean), given:
*
*Its position
*Its angular velocity
*The point it's rotating around (fulcrum)
(This is a problem I need to solve for 3D graphics programming with a physics engine).
The... | Let $\vec r_0(t)$ denote the point around which the object is rotating and $\vec r(t)$ the position of the object. Then the fact that the particle is rotating around the point $\vec r_0(t)$ can be formalized by the mathematical statement that
$$
\vec r(t) - \vec r_0(t) = R(t) \vec c
$$
for some constant vector $\vec... | {
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Why does Venus transit so slowly? I have calculated that because Venus is $d = 12,103.6~\mathrm{km}$ in diameter and moves at $v = 35.02~\mathrm{km}/\mathrm{s}$, it would take
$$ t=\frac{d}{v} = \frac{12,103.6~\mathrm{km}}{35.02~\mathrm{km}/\mathrm{s}} = 345.62~\mathrm{s} = 5~\mathrm{min}~46~\mathrm{s} $$
for Venus to ... | Your calculation looks like it would be correct for an observer who was stationary with respect to the Sun. However, the Earth is also moving, and I think this accounts for at least most of the discrepancy.
Earth's orbital period is about 365 days while Venus' is 225, so the angular velocity of Earth about the Sun is 0... | {
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What's the exact gravitational force between spherically symmetric masses? Consider spherical symmetric$^1$ masses of radii $R_1$ and $R_2$, with spherical symmetric density distributions $\rho_1(r_1)$ and $\rho_2(r_2)$, and with a distance between the centers of the spheres $d$. What is the exact force between them? I... | If you are looking only for the Newtonian gravitational force, the other answers to this question are correct. The spherically symmetric mass distributions can be replace by the total mass at the center of mass and then the Newtonian gravitational force can be computed for these two masses.
However, if you want EXACT ... | {
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Superconducting gap, temperature dependence: how to calculate this integral? Tinkham (page 63) states that the temperature dependence of the gap energy of a superconductor $\Delta(T)$ can be calculated using the following integral:
How can this actually be carried out? I am not sure how to approach this problem or re-... | I have not tried it on this specific equation, but in principle you can solve problems like this by a combination of numerical integration and a root finding algorithm. For a given variable $x$ you wish to determine for a fixed value $v$ of the integral, the root finding algorithm will find a solution to the equation
$... | {
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Difference between torque and moment What is the difference between torque and moment? I would like to see mathematical definitions for both quantities.
I also do not prefer definitions like "It is the tendancy..../It is a measure of ...."
To make my question clearer:
Let $D\subseteq\mathbb{R}^3$ be the volume occupie... | Moment is the more general term which means quantity evaluated when something is multiplied by its moment arm (perpendicular distance).
Some examples of moments:
*
*Moment of force (torque): $\vec{r} \times \vec{F}$
*Moment of rotation (velocity): $\vec{r} \times \vec{\omega}$
*Moment of impulse: $\vec{r} \times \v... | {
"language": "en",
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Is it possible to calculate atmospheric pressure if given temperature (F) and elevation? I am working on a report at work and need to determine the atmospheric pressure for small intervals over a 24 hour period. Searching Google, I've found charts which give a base pressure of 14.65 psia at sea level. This is at 68F. T... | There is a standard model of the atmosphere
It's also built into matlab, I don't know of any spreadsheets but some googling should find one.
| {
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Please explain this statement about Lorentz transformations I'm reading Sternberg's Group Theory and Physics. I have a question about chapter 1.2 Homeomorphisms.
Background:
A Lorentz Metric is defined as $||{\bf x}||^2=x_0^2-x_1^2-x_2^2-x_3^2$
And a Lorentz Transformation $B$ as one which satisfies $||B{\bf x}||^2=||... | Hints:
*
*Note that the time coordinate $x^0=\frac{1}{2} {\rm tr}(x)$ is given by the trace.
*Note that the trace ${\rm tr}(x)$ is invariant under the $SU(2)$ action.
*The subspace with $x^0=0$ is invariant under $SU(2)$.
*Note that the stabilizer/isotropy subgroup of $e_0$ is $SU(2)$.
| {
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Does gravitational force attract bodies with mass or with energy? On my textbook is written that gravitational force is the force that attracts bodies with mass. But I've seen on a book that It actually attracts bodies with energy. I'm having a class tomorrow and I would like to know some argumments to use with - again... | In relativity gravity is not a force anymore, instead it is geometry of spacetime. Therefore gravity (produced by energy which is equivalent to mass) would also attract massless particles without any force acting.
| {
"language": "en",
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Why can we use Gauss' law to compute electric field? For simplicity I'm considering only the sphere case.
In the Gauss' Law formulation we have some field $E$ introduced by charges $Q$ inside some sphere, then we compute flux and integrate, and we get result $Q/e_0$. Right.
But this formulation doesn't take into accoun... | First of all we use Gauss's law because it is a law of nature!
Second: Gauss's law (together with $\nabla\times\vec{E}=0$, which is only strictly valid in electrostatics) is equivalent to Coulomb's law for the electric field of a distribution of charges. You can prove one from the other.
Third: You a right about extern... | {
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Equivalence between QFT and many-particle QM My understanding from my QFT class (and books such as Brown), is that many-particle QM is equivalent to field quantization. If this is true, why is it not an extremely surprising coincidence? The interpretation of particles being quanta of a field is -- at least superficiall... | As remarked in many references, QFT and QM (many-particle or not) are disjoint theories. The textbooks by Mandl & Shaw, Landau & Lifshitz, Sakurai... report some of the fundamental differences between QFT and QM.
The "interpretation of particles being quanta of a field" is misleading. There is a partial formal analogy ... | {
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Why is electric potential scalar? I can't conceptually visualize why it would be so. Say you have two point charges of equal charge and a point right in the middle of them. The potential of that charge, mathematically, is proportional to the sum of their charges over distance from the point ($q/r$). But intuitively, my... | An explanation based on the definition of scalar quantities in physics.
To see why electric potential energy is a scalar quantity you need to understand the following:
A physical quantity is a scalar property of a system, when its value and its effects do not depend on the orientation of the system.
Let us assume we ha... | {
"language": "en",
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Explanation on the resulting forces of two positive point charges Why will the resulting force lines of two positive point charges be like this:
I would expect this:
| First a comment about the following statements made by Kitchi and Wouter:
Lines of force always have to be smooth, there can't be a sharp bend in them like in your second diagram
and
The comment by @Kitchi basically says it all: lines of force should be continuous and differentiable and they should never intersect.
... | {
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Two ways to form $SU(2)$ singlets? I am trying to reconcile the two ways of forming $SU(2)$ singlets out of a pair of doublets.
Method (1):
If $v=\begin{pmatrix}v^1\\ v^2\end{pmatrix}$ and $w=\begin{pmatrix}w^1\\ w^2\end{pmatrix}$ are two $SU(2)$ doublets, then I can form a singlet by taking the antisymmetric combinati... | OP's two methods are isomorphic. In general one is only interested in classifying representations modulo isomorphism. The point is that for the Lie group $SU(2)$, the spinor representation ${\bf 2}$ and the complex conjugate spinor representation $\bar{\bf 2}$ are equivalent representations ${\bf 2}\cong \bar{\bf 2}$. ... | {
"language": "en",
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Einstein Field Equations and Electromagnetic Stress-Energy Tensor My question is: if we write Einstein field equations in this form:
$$R_{\mu\nu} - \dfrac{1}{2}g_{\mu\nu}R=8\pi \dfrac{G}{c^4}T_{\mu\nu}$$
Then the left hand side is one statement about the geometry of space-time and the right hand side is one statment ab... | Yes, all energy-momentum distributions have an effect on the geometry of spacetime, including the the energy-momentum due to the electromagnetic field. For example, the Reissner-Nordstrom solution (which describes a charged, non-rotating spherical mass) has extra terms in it which are dependent on charge. This is becau... | {
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Why can't we store light in the form of light? We can store cold (ice), heat (i.e. hot water bag) and electrical charge (batteries). We can even "store" a magnetic field in a magnet. We can convert light into energy and then, if we want, back to light. But we can't store light in form of light in significant amounts. ... | It's hard to store light as light because the most common way light interacts with matter is through absorption and emission, which is how mirrors work. However light rays can be bent by gravity, so it would be possible to arrange several massive stars in a way such that a light ray would move in a loop around the star... | {
"language": "en",
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What causes insects to cast large shadows from where their feet are? I recently stumbled upon this interesting image of a wasp, floating on water:
Assuming this isn't photoshopped, I have a couple of questions:
*
*Why do you see its image like that (what's the physical explanation; I'm sure there is an interesting ... | That is a truly amazing picture! I am by no means an expert, but I have an idea.
When the wasp stands on the water, it is curved down slightly. The light that hits these parts will then be bent more outwards than if it just hit regular water. This happens at every side of the circle, so the light is always bent out, an... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/55833",
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Gamma Ray LASER Theory and Technology I am aware that a similar question has been asked by someone else in the past, but in a very general form. Due to the physics interest and technology, in this question I put emphasis on the detail of the physics part and the question becomes very specific.
We know the power of vis... | There are a large number of problems, and a large number of proposed solutions for Graser operation. I published a paper on laser photochemical separation of nuclear isomers to get a population inversion in the 1970s with George Baldwin.
He moved onto LASL where he continued Graser work for some time. His reviews are q... | {
"language": "en",
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Derivative with respect to the nuclear coordinates in the Born–Oppenheimer approximation Reading few sources on the Born–Oppenheimer approximation I don't understand one particular thing.
If you look for example here (PDF, 70 KB) and focus attention on equations 14 and 15 than it is clear that
$$
\nabla_{A}^2 \left( \p... | For each $\mathbf{R}$ there is a complete set of electronic functions $\{\psi_k(\mathbf{r};\mathbf{R})\}_k$, and what these functions are depends on the value of $\mathbf{R}$. As $\mathbf{R}$ is changed continuously, each element of $\{\psi_k(\mathbf{r};\mathbf{R})\}_k$ varies continuously; thus, it is meaningful to ... | {
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Influence of charged particle's own electric field on itself I read this in my textbook: A charged particle or object is not affected by its own electric field.
Since I find this completely unintuitive and my mind is yelling "wrong! wrong! how could a particle even distinguish between its own field and the external fie... | This is the problem with classical electrodynamics. The self-energy of a charged point particle is infinite due to its interaction with its on potential.
Since,
$$W=\frac{q^2}{8\pi\epsilon_o}\int_0^{\infty}\frac{1 }{r^2}dr $$
diverges.
| {
"language": "en",
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How to determine the direction of a wave propagation? In the textbook, it said a wave in the form $y(x, t) = A\cos(\omega t + \beta x + \varphi)$ propagates along negative $x$ direction and $y(x, t) = A\cos(\omega t - \beta x + \varphi)$ propagates along positive $x$ direction. This statement looks really confusing bec... | For a particular section of the wave which is moving in any direction, the phase must be constant. So, if the equation says $y(x,t) = A\cos(\omega t + \beta x + \phi)$, the term inside the cosine must be constant. Hence, if time increases, $x$ must decrease to make that happen. That makes the location of the section of... | {
"language": "en",
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"source": "stackexchange",
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nuclear fission and half life Why is the alpha, beta or gamma decay of an unstable nucleus unaffected by the chemical situation of an atom, such as the nature of the molecule or solid in which it is bound? The chemical situation of the atom can, however, have an effect on the half life in electron capture. Why is this ... | A qualitative argument:
The $\alpha$, $\beta$ or $\gamma$ decay are phenomena that are associated with the weak nuclear, and strong nuclear forces which rule in the nucleus. The electromagnetic force, although it plays an important part in the stability of the nucleus, it does not completely determine what and how will... | {
"language": "en",
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Finding the force of friction of a moving object and its change when it accelerates to a constant speed If an object is moving at a constant speed the force of friction must equal the applied (horizontal) force, and for it to be accelerating or decelerating, the force of friction and the applied force must be unequal. ... | There are a number of wrong assertions in your statement. You say, "surely ... continue accelerating to infinity." Since $ a = \frac {F}{m} $, as long as you apply net force F, you only get constant acceleration a. The acceleration value not only does not go to infinity, but actually does not change, unless the net fo... | {
"language": "en",
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Bat hitting a ball When a bat hits a ball, consider two cases:
1) The batsman goes for a defense, and stonewalls it, to reduce its speed.
2) the batsman goes for a shot, e.g. a home-run, etc.
in which case will the bat have the highest chance of breaking due to the impact?
And am I right in assuming that the force on t... | Every one might have studied about material science . When a body (bat)undergoes repeated stress due transfer of kinetic energy by the ball.this in turn develop micro structural crack in the bat,which keeps on developing when a ball travels with a kinetic energy which is required to develop and break the bat is strikes... | {
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Are two waves being in phase the same as saying that the two waves are coherent? If two waves are coherent, is it the same as them being in phase? Please correct if I'm wrong.
| While I agree with BebopButUnsteady, there is a simpler way to summarize what he said. Coherence and relative phase difference are not the same. Take two signals,
$$s_1 = \sin(\omega_1t + \theta_1)\\
s_2 = \sin(\omega_2t + \theta_2)$$
Two waves can be coherent and out of phase. But they cannot have a constant relati... | {
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What fraction of peak horsepower do typical 4 door passenger vehicles use? I was surprised when I looked at the power rating of the engine used on a Humvee. It's only ~190 horsepower, which is exceeded by many sedan engines.
So an obvious question is why doesn't my Camry SE burn more gas than a Humvee and I think it's ... | You might be interested in my answer to If an electric car were to drive without having to stop, would the range be greatly affected by the speed at which the vehicle is moving?. From just air resistance I calculated that at 70 mph the engine in my Ford Focus is generating about 17 bhp (12.5 kW).
Obviously you need to ... | {
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What Pauli matrices should I use for this two spin system? Consider the Hamiltonian $H = -J_\text{F}S^{(1)}_zS^{(2)}_z + J_{AF}S^{(1)}_zS^{(2)}_z$, describing the graph
Here, F means ferromagnetic and AF means antiferromagnetic interactions. I am having problem with the value of $S^{(1)}_zS^{(2)}_z$.Someone suggested ... | The operator $\Sigma_z$ is the $z$ component of the total spin, and therefore is the sum of the quantities $S^{(1)}_z$ and $S^{(2)}_z$, whereas the operator $S^{(1)}_z\cdot S^{(2)}_z$ is their product. You can easily check that for the matrices in your question the identity
$$\Sigma_z=-2(S^{(1)}_z+ S^{(2)}_z)$$
holds; ... | {
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Potential Inside Conducting Cube A cubical box with sides of length L consists of six metal plates. Five sides of the box { the plates at $x=0, x=L, y=0, y=L, z=0$ - are grounded. The top of the box (at z = L) is made
of a separate sheet of metal, insulated from the others, and held at a constant potential $V_0$. Find ... | The basic steps:
*
*Write the potential $V(x,y,z)$ as a series in products of appropriate orthogonal functions. Often one uses orthogonal functions that arise from the solution to Laplace's equation by separation of variables.
*Impose the boundary conditions (there are six of them) to solve for the coefficients in... | {
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Why planets are orbiting only in one plane? Since gravity is three dimensional why planets are orbiting only in one plane around sun.
| It is believed that the planets formed when a cloud of gas underwent gravitational collapse. Any small angular momentum that the cloud started out with has to be conserved, and since the cloud's moment of inertia becomes smaller, it spins faster. Also, the centrifugal force "throws out" the edges of the cloud and makes... | {
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How to describe heat transfer between two solid materials? A general equation for dealing with heat transfer between one material and a region of insulating material. I've seen basic heat transfer equations for one material, but I'd love to see an explanation of how to do two.
| The one-dimensional heat equation for a solid can be written as:
$$
\rho C_p\frac{\partial T}{\partial t}= -\frac{\partial}{\partial x} \left( k\frac{\partial T}{\partial x} \right) +\sigma
$$
where $\sigma$ is the source term and $ \dot q =-k\frac{\partial T}{\partial x}$ is the diffusive heat flux. At the boundar... | {
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Will we feel right up inside the airplane if the airplane accelerates toward earth at 20m/s^2? Suppose you are in the airplane and the airplane falls toward the earth with acceleration of $20m/s^2$(double of gravitational acceleration $g$). This double acceleration by airplane will cancel the gravitational acceleration... | if this happens, you will be stuck to the ceiling of the airplane but it does not mean that you are pushed up. Actually, the airplane and the person in that airplane, both are falling towards earth simultaneously but the airplane has acceleration=2g, and the person has acceleration =g. Due to this, airplane falls fast... | {
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"url": "https://physics.stackexchange.com/questions/57061",
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Are electrons moving? If so relative to whom? and why is there no magnetic field? electrons on earth moving with us, due to rotation of earth, revolution of earth, sun and our galaxy right?
Then, why is there no magnetic field around a piece of copper wire?
| To good approximation Earth is an Inertial System. Charges at rest with us in this inertial system do not produce a magnetic field, as Maxwell's equations hold in any Inertial system. Viewed from another Inertial system magnetic fields of electrons and protons cancel, as explained in answer (1). Viewed in the Earth's I... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/57140",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
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Place each foot on a scale: can you add the two to find your weight? I frequent a blog from a British psychologist, and every Friday he likes to pose an interesting puzzle or riddle. The Monday after that he posts the answer. They're good fun, and IANAP but this week's answer made my it-might-not-be-quite-as-simple-as-... | Yes, this is not the hardest problem ever, but here's the mechanics calculation that leads to the yes answer.
Draw a free body diagram of your body as you are standing still with one foot on each scale. You experience three forces (I will label their magnitudes): (1) The force due to gravity pulling you down, $W$ (aka... | {
"language": "en",
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Where are we : On level ground or on a ramp - moving in a train? Let's say we are traveling in a train. The path has two parts: one at ground-level and the other moving up on the ramp. The ramp has an inclination of $\arctan\frac{a}{g}$ with the horizontal, where $a$ is the acceleration of the train on level ground and... | If the train is an ideal isolated system, the answer is no, we can't tell where we are. As zhermes pointed out, the equivalence principle states that the gravitational force experienced by a body at rest or moving with a constant velocity is the same as the pseudo-force experienced by that body is a non-inertial frame... | {
"language": "en",
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Capacitance of a capacitor Why does the capacitance of a capacitor increase if the distance between the two plates of a parallel plate capacitor is decreased? I think, with decreasing distance between the two plates, the force of attraction between the charges on the two plates will increase, and as a result more charg... | 1) Capacitance is the ratio of the stored charge Q (+ on either plate, - on the other) to the voltage between the plates.
2) The electric field between the plate is proportional to the plate surface charge density $\sigma = Q/A$, with $A$ the plate area.
3) So if one moves the plates closer together while holding the... | {
"language": "en",
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Have negative pressures any physical meaning? Some cubic thermodynamical equations of state predict negative pressures, have negative pressures any physical meaning? Could they be related to negative mass?
| Thermodynamically pressure is related to the work done in changing the volume. Assuming an adiabatic change the change in the internal energy of a system is given by the work done on it:
$$ dU = \delta W = PdV $$
If you take a volume of an ideal gas and let it expand by $dV$ it does work on it's surrounds and it's inte... | {
"language": "en",
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Path of an electron through an electric circuit When a potential difference is applied across a conductor, and if an electron moves from the negative terminal of the battery and reaches the positive terminal, then I want to know if the electron will remain at the positive terminal or will it again move toward the negat... | In an ideal electrochemical cell case, it should remain at the positive terminal.
The salt bridge should only allow for the ions to flow.
However, practical batteries have other physical phenomenon that restrict the flow of current, and hence introduce this 'internal resistance'. There could be a wide variety of reason... | {
"language": "en",
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Algorithm for identifying planes in a Bravais Lattice I have a lattice with Lattice Vectors $(\vec{t}_1,\vec{t}_2,\vec{t}_3)$ which are NOT orthogonal in general.
How can I identify the atoms/unit cells that belong to a plane - that is normal to a given direction.
I do recognise that the lattice might not be periodic i... | For "simple" planes that "fit" into one or a few unit cells of the lattice, the task is relatively simple, in that you just identify all atoms that belong to the plane in one such block and then use the periodicity of the crystal.
For the most general case, I'm not 100% sure what the best way would be. Here's an idea. ... | {
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Soft Mass and Physical Mass in Softly-broken SUSY In softly broken SUSY, the bare mass parameters may be specified at e.g. the GUT scale, and then we can run these down to another scale using RGEs, similar in form to the RGEs for gauge couplings, with a 1-loop and 2-loop differential beta function. Once these parameter... | The physical masses should be independent of the renormalization scale. We, however, only calculate a finite number of loop corrections, resulting in a scale dependence in the physical mass. This scale dependence can be used to estimate the error in the mass calculation from the missing higher orders.
In principle, one... | {
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2 following gates, permutation matrix I have a circuit that has 4 wires and 2 following each other Toffoli gates.
I have permutation matrix for each Toffoli gate (A and B).
Do I have to multiply that 2 matrices to get the entire permutation matrix of that 2 Toffoli gates?
And if I do that is $A\times B$ or $B\times A$?... | Yes, of course !
This nevertheless suppose that no time is lost between the two gates, but it is a usual assumption in basic lectures.
If the state vector $\left| \Psi_0 \right>$ enters at the left of the circuit, then reach the gate A, represented by matrix $A$, then the B one represented by matrix $B$, and end up a... | {
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"as measured in a local Lorentz frame"? I've seen the phrase "as measured in a local Lorentz frame" tagged on the end of so many sentences.
What does it mean precisely?
To give an explanation with an example, consider the context of measuring the speed of an object, if this applies.
| I think it's safe to say that this phrase means the same thing as "local inertial frame." Assuming that this is actually is a safe assumption, I'll describe, physically, what a local inertial frame is. I can give a lot of mathematical detail in an addendum if you wish.
In special relativity, we assume that spacetime ... | {
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What is the maximum power available from a magnetic field? I just want to validate something I inferred from studying Griffiths (1999).
The instantaneous magnetic field $\vec{b}(t)$ at a distance $r$ from a long infinite conductor carrying a current $i(t)$ is
$$\vec{b}(t) = \frac{\mu}{2\pi r} \hat{\psi} \cdot i(t)$$
T... | First of all, your formula for the energy density is missing a term for the electric field:
$$
w(t)=\frac{\varepsilon_0 e^2(t)}{2}+\frac{b^2(t)}{2\mu_0 }
$$
You will always have an electric field if the magnetic field is time-varying.
However, this is not that important for the more conceptional question you seem to be... | {
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microcanonical distribution We know that in an isolated system, the density matrix is the microcanonical distribution matrix. That this the possibility for all the states with energy in a certain interval is a constant?
But how can I deduce this from the postulate of equal probability?
| The assertion that the density matrix for an isolated system is that of the microcanonical ensemble implies the postulate of equal a priori probabilities since, as you indicate, it assigns equal probabilities to each of the energy eigenstates of the system.
I would then ask you the following question: On what grounds ... | {
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Eye sensitivity & Danger signal Why are danger signal in red, when the eye is most sensitive to yellow-green?
You can check luminosity function for more details...
| I believe you should have googled first:
google hits
Especially the second link very clearly explains the main reason:
The primary reason why the color red is used for danger signals is that red light is scattered the least by air molecules. The effect of scattering is inversely related to the fourth power of the wave... | {
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Deriving torque from Euler-Lagrange equation How could you derive an equation for the torque on a rotating (but not translating) rigid body from the Euler-Lagrange equation? As far as I know from my first class in Classical Mechanics, there is no potential defined for a rotating body, so the only term I see in the Lag... | In my view, you don't derive torque from the Euler-Lagrange equations. It arises naturally from them, as Lagrangian is a formalism of classical mechanics that can explain the behavior of physical systems both in their translations and rotations. For instance, consider a simple pendulum. It's only degree of freedom is $... | {
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A charged sphere with pulsing radius
Radius increases and decreases periodically (as a pulse).And so does the charges on the surface of sphere.
I can't get what is gonna happen.the EM waves are produced perpendicularly to motion of the charges,but here where is the perpendicular ? Will the EM waves get produced into ... | Results with an accurate simulation, near field radiating only :
Simulation of a sphere with a pulsating charge - text in french page 2
| {
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What is the speed of acceleration of the inflation of the universe? Is the inflation speed of the universe accelerating or is it a constant speed of expansion proportional to distance between objects.
| As the universe stands today its not said to be "inflating" but it is "expanding". I think one way to make the distinction is to say that during inflation the radius of the causal horizon ($\frac{1}{aH}$ in FRW universe) falls (linearly) whereas during expansion it increases (being equal to half the conformal time for ... | {
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Direction of the Area Vector (with regards to magnetic dipole) I'm learning about torque on a conductive coil in a magnetic field. I have been taught that $\vec\tau = \vec\mu \times \vec{B}$, where $\vec\mu$ is the magnetic dipole moment. Also, $\mu = I\vec{A}$, where $\vec A$ is the area vector of the loop.
To find ... | The area vector is typically (in the treatments I have encountered) simply defined this way and then all other facts are written in such a way that they are consistent with this convention.
| {
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How Do Electrons "Resonate Against the Restoring Force Of Positive Nuclei?" While reading "Surface Plasmon Resonance," I came across the following:
"The resonance condition is established when the frequency of light photons matches the natural frequency of surface electrons oscillating against the restoring force of p... | This is too long for a comment, so here it goes:
What causes a valence electron of a large atom to feel an effective attractive potential that is similar to a harmonic oscillator?
I hope people following this forum at least understand that in order to have electrons around nuclei display a stable solution and form a... | {
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How old is SUN ☉? How do we know/calculate the exact age of sun ☉ ? ie. 4.57 billion years. What is the way to calculate it?
|
The Sun was formed about 4.57 billion years ago from the collapse of part of a giant molecular cloud that consisted mostly of hydrogen and helium and which probably gave birth to many other stars. This age is estimated using computer models of stellar evolution and through nucleocosmochronology. The result is consiste... | {
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Types of photon qubit encoding How many types of qubit encoding on photons exist nowadays? I know only two:
*
*Encoding on polarization:
$$ \lvert \Psi \rangle = \alpha \lvert H \rangle + \beta \lvert V \rangle $$
$$ \lvert H \rangle = \int_{-\infty}^{\infty} d\mathbf{k}\ f(\mathbf{k}) e^{-iw_k t} \hat{a}^\dagger_{H... | Yeah there is a couple of 'em - off the top of my head I can think of:
\begin{align}
|\uparrow\;\rangle\;=\;
\begin{pmatrix}
1 \\ 0
\end{pmatrix}\qquad&\qquad
|\downarrow\;\rangle\;=\;
\begin{pmatrix}
0 \\ 1
\end{pmatrix}\\
|g\rangle\;=\;
\begin{pmatrix}
1 \\ 0
\end{pmatrix}\qquad&\qquad
|e\rangle\;=\;
\begin{pmatrix}
... | {
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How do Doppler Effect and Time Dilation differ?
Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B).
Edit: I am adding a relativistic space-time diagram below this with
lines of simultaneity drawn. I am also ... | Is important to realize time dilation and the Doppler effect are 2 frame-dependent parts of a single relativistic phenomenon: the constancy of the magnitude of four-velocity (which is always ||c||). Requiring that all inertial observers see a four-velocity with magnitude ||c|| leads to frame dependent observations of t... | {
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The rule breaker, emissivity + reflectivity = 1 If emissivity and reflectivity are inversely proportionate, why does glass have a high emissivity of around 0.95-0.97 as well as being very reflective for IR Radiation?
normally it works but not with glass!
Can anyone explain this?
| Based on the experiments you describe in the comments, it seems like you might very well have a reflectivity of 20-30% in your window, for the spectral region where your camera measure. The question is where you got the high emissivity numebers from. It seems likely that the problem is that you're assuming the emissivi... | {
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Divergent sum in lightcone quantization of bosonic string theory I had the following question regarding lightcone quantization of bosonic strings - The normal ordering requirement of quantization gives us this infinite sum $\sum_{n=1}^\infty n$. This is regularized in several ways, for example by writing
$$
\sum_{n=1}^... | Note that $n$ is really the momentum in the $\sigma$ direction so it has the units of the world sheet mass. The exponent $-n\epsilon$ in the regulator has to be dimensionless so $\epsilon$ has the units of the world sheet distance.
Consequently, the removed term $1/\epsilon^2$ has the units of the squared world sheet m... | {
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Is there a symbol for "unitless"? I'm making a table where columns are labelled with the property and the units it's measured in:
Length (m) |||| Force (N) |||| Safety Factor (unitless) ||| etc...
I'd like not to write "unitless" on several columns...and I'm quite surprised I can't seem to find a symbol for it. Any ... | Units I usually keep in brackets []. Like 70 [kg], 60 [GPa], 5.2 [ms^-1] and for no unit I would say 1.5 [-].
| {
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What is wrong with these ways of determining the mean occupation number? Could anyone point out what went wrong in this argument?
Setup:
We have a system with 2 energy levels say with energies $0,e$ respectively.
We consider the grand canonical ensemble for the system occupied by identical spinless fermions. Then there... | In your Method 1, you forgot that the state (2) also has the occupation number $n=1$ (it has a vanishing energy but you're computing the mean occupation number, not mean energy), so it must be added to the numerator. This changes $1+2f$ in the numerator on the following line to $2+2f$. The simple fraction simplifies to... | {
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Is lattice enthalpy positive or negative? I've learnt that the lattice enthalpy (defined as the energy change from a solid ionic lattice to separate gaseous ions) is always positive, obviously. However, I've seen it explained as the opposite other places, so it's negative.
What is correct?
| When it is explained as opposite, it is usually the heat RELEASED when a crystal is formed, and since the word "released" already makes up for the sign of heat(i.e. if heat is -10 that means the heat released or evolved is +10) , it is taken as positive. Nonetheless, some books also present a negative value to it but i... | {
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How does the freezing temperature of water vary with respect to pressure? I know when the pressure is reduced, the boiling temperature of water is reduced as well. But how does the pressure affect the freezing point of water?
In a low-pressure environment, is water's freezing temperature higher or lower than $0\sideset... | When high pressure is applying on a gas, it gets converted into liquid form. Similarly, if more pressure is applied to the liquid, force of attraction increases so that the liquid is converts into solid state. As the pressure increases the rate of crystallization also increases. i.e., the freezing point also increases... | {
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Difference between slanted indices on a tensor In my class, there is no distinction made between,
$$
C_{ab}{}^{b}
$$
and
$$
C^{b}{}_{ab}.
$$
All I know, and read about so far, is the distinction of covariant and contravariant, form/vector, etc. etc. But what is this slanted business all about?
| Each of the indices in a tensor have a particular left-right ordering. This ordering cannot be changed unless the tensor has some particular symmetry that permits it (or rather, that equates different components on interchange).
The up-down positions of indices tells us about whether the index is associated with using... | {
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$\beta^+$ decay We've been discussing radioactive decay at school, and I grasped everything except for $\beta +$ decay. When I googled radioactive decay, I immediately found out they dumbed down radioactive decay for us, which is probably why they didn't care to explain what they did, they just showed some calculations... | $\beta^+$-decay can be explained as a result of nuclear protons collision:
$p^+ p^+\to p^+ p^+ W^- W^+ \to (p^+ W^-)\: p^+ W^+\to n\: p^+ e^+ \nu_e$
Compare to $\beta^-$-decay:
$n \to p^+ W^- \to p^+ e^- \bar{\nu}_e$
| {
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How to express a Hamiltonian operator as a matrix Suppose we have Hamiltonian on $\mathbb{C}^2$
$$H=\hbar(W+\sqrt2(A^{\dagger}+A))$$
We also know $AA^{\dagger}=A^{\dagger}A-1$ and $A^2=0$, letting $W=A^{\dagger}A$
How can we express $H$ as $H=\hbar \Big(\begin{matrix}
0 & \sqrt2 \\
\sqrt2 & 1
\end{matrix} \Big)$
S... | The matrix element $O_{ij}$ of an operator are defined by
$$O_{ij} = \langle i | \hat{O} | j \rangle,$$
and it is traditional that the $i$ index labels the row and $j$ labels the column. This way matrix multiplication works as you would expect:
$$ (O P)_{ij} = \sum_k O_{ik} P_{kj}, $$
which you can show by inserting a ... | {
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Kinematics with non constant acceleration A particle experiences an acceleration described by
$$
a=kx^{-2}
$$
where x is the displacement from the origin and k is an arbitrary constant.
To what value does the velocity v of the particle converge to as x approaches infinity if the particle starts at some point x0?
If I ... | The solve the first part with just kinematics, use the chain rule:
$$ a(x) = \frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt} = \frac{dv}{dx}v,$$ and then $a(x)dx = vdv$.
Integrating both sides ($x_0$ to infinity on the left and $v_0$ to $v_f$ on the right), we get
$$\frac{k}{x_0} = \frac{v_f^2 - v_0^2}{2},$$
or
$$v_f = \sqr... | {
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Is it possible to "add cold" or to "add heat" to systems?
Amanda just poured herself a cup of hot coffee to get her day started.
She took her first sip and nearly burned her tongue. Since she didn't
have much time to sit and wait for it to cool down, she put an ice
cube in her coffee and stirred it with a metal... | The most important thing about feeling is that its relative and depends on the temperature of sensor point on skin. That's the reason we need thermometer to measure temperature with which everyone could agree.
Energy transfer is involved here, but it has very little to do with Amanda's feeling. Amanda's tongue and mout... | {
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Observer effect, do this mean literally someone or just any interaction with other matter? I am a layman and was wondering, the quantum observer effect. The regular notion to laymen seems to be literally "if you look at it", but as I am coming to understand the world I live in better I feel it means just coming in cont... | This "observation" is actually just a more simple way to state the uncertainty principle. For a one dimensional case involving momentum and position it would be as follows.
$$\Delta x \Delta p \ge h$$
This means that if we know the position exactly then we don't know the momentum.
For energy and time it would be
$$\D... | {
"language": "en",
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Towing of asteroid I recently studied that NASA has planned to tow and place it in the orbit of the moon.
My doubt is when asteroid is placed in the orbit near moon.since the gravitational field of earth is very high.what will it revolve around the moon or the earth.
Can anyone clarify my doubt ??
| There are stable orbits around the Moon, also Nasa, Esa, and many more have satellits orbiting the Moon, and they don't "decay" towards the Earth.
*
*Wiki List of lunar probes Look in the link for orbiters
To look for the physics and no only examples search for Hill sphere:
*
*One google entry
*Hill sphere Wik... | {
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"source": "stackexchange",
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Classical results proved using quantum mechanics Are there any results in classical mechanics that are easier to show by deriving a corresponding result in quantum mechanics and then taking the limit as $\hbar\rightarrow0$?
(Are there classical results that were first discovered through taking the classical limit of qu... | I just came across an example that I'll post as an answer to my own question.
In Brillouin scattering sound passes through a medium causing periodic variations in refractive index and hence forms a diffraction grating that can scatter light. Because the sound waves are moving, the scattered light is doppler shifted. Al... | {
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Does spatial coupling prohibit resonances due to an external source field? The harmonic oscillator coupled to a sinodial external source
$$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$
has the solution
$$x(t)=x(0)\cos(\omega_0 t)+C \sin(\omega_0 t) +\frac{F_0}{\omega_0^2-\omega_\... | Let us denote the field amplitude $\varphi$ (because $x(x)$ does not make sense).
If you drop the term $\omega_0^2\varphi(x,t)$, then your KG equation will look like a field sourced with an external source (force). The corresponding (space) Fourier harmonic $\varphi_{k(\omega_0)}(t)$ will have a growing solution if th... | {
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If photons can be absorbed by electrons, wouldn't that mean light has a charge? I am a biochemistry and molecular biology major. If photons can be absorbed by electrons, wouldn't that mean light has a charge? Electrons only attract positive charges. Isn't it?
| Light does not have a charge. "Charge" is just what we call the tendency of something to affect and be affected by electromagnetic fields, which are what light is made of.
The reason positive and negative charges are attracted to each other is that they both give off these fields. An electron creates an electric field ... | {
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Could some design of a propeller be used in both air and water? Propellers in water are smaller in diameter. They also move more slowly. On the other hand, aircraft propellers are larger in diameter, have narrower blades and operate at very high speeds. An aircraft propeller would break apart in water, while a water pr... | There's two important differences between air and water: Air is compressible, and the densities are about a factor of ~1000 apart - 1 kg/m³ vs 1 t/m³!
For most concerns where you use propellers, compression plays no role because the pressure diferences are very low. The densities, however play a large role.
The thrust ... | {
"language": "en",
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Physical Interpretation of the Integrand of the Feynman Path Integral In quantum mechanics, we think of the Feynman Path Integral
$\int{D[x] e^{\frac{i}{\hbar}S}}$ (where $S$ is the classical action)
as a probability amplitude (propagator) for getting from $x_1$ to $x_2$ in some time $T$. We interpret the expression $... | One interesting interpretation comes from the Wick rotation, where you interpret $it/\hbar=\beta=1/(k_BT)$ - an imaginary time turns many quantum equations into similar equations of thermodynamics / statistical mechanics.
Since $S = \int L\,dt = \int (T-V)\,dt$ has the dimension of energy times time, this means the exp... | {
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What is Transverse Energy? What is transverse energy? Why we use transverse total energy instead of energy and transverse momentum in place of Total momentum in the particle detectors?
| Transverse momentum, $\vec{p}_T$, is the momentum of an object transverse to the beam. Transverse energy is defined as $E_T = \sqrt{m^2+p_T^2}$ for an object with mass $m$ and transverse momentum $p_T$.
The initial longitudinal momentum in a parton collision is unknown, because the partons that make up a proton share t... | {
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Invariance, covariance and symmetry Though often heard, often read, often felt being overused, I wonder what are the precise definitions of invariance and covariance. Could you please give me an example from field theory?
| It helps to remember that invariant quantities are seen as scalars to the transformation (they have no indices in the target space). In the other hand, covariant quantities are objects that transform in a certain way.
Example: Vectors in $R^{2}$, under rotation $R_{ij}$, transform covariantly since $v'_{i}=R_{ij}v_{j}... | {
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What would happen to the Moon if Earth is turned into a black hole? Assume that all of sudden the Earth is turned into a black hole. And the moon revolves around the Earth (before turning into a black hole). What would happen to the Moon after earth changes to black hole will it be sucked to the black hole or continue ... | I think that force of attraction between earth and moon is depend on their masses and the distance between them . Since any of these factors are not going to change if earth becomes a black hole. Hence it will continue to revolve in orbit
| {
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Bremsstrahlung vs energy conservation From Wikipedia:
Bremsstrahlung is electromagnetic radiation produced by the
deceleration of a charged particle when deflected by another charged
particle, typically an electron by an atomic nucleus. The moving
particle loses kinetic energy, which is converted into a photon
... | The short answer to your question is "because of quantum mechanics". If you view the atom and the electron orbit around the nucleus as a classical system then indeed the system would not be stable and the electron would lose orbital energy. This is why Niels Bohr proposed a model with quantized energy levels.
This wa... | {
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Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2? I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part and a radial part. When dealing with t... | The operator $L^2$ is a symmetry of the Hamiltonian, which means that $[H,L^2] = 0$. This means that we can find simultaneous eigenfunctions to $H$ and $L^2$ since $HL^2 | \psi \rangle = L^2 H | \psi \rangle = \ell (\ell + 1) E | \psi \rangle$. The operator $L^2$ does not depend on the radial coordinate, thus the angul... | {
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What is Anderson localization? Could someone give an example worked out in detail? What is Anderson localization, for someone with no previous knowledge on the subject?
I tried to read Anderson's original paper, but it was too terse for me. I have seen a couple of intuitive explanations, e.g. 50 years of Anderson local... | The toy example is localization on the Bethe lattice (AKA the regular Cayley tree). There is a paper by Abou-Chacra, Thouless and Anderson that discusses this. Or you can just google around.
R. Abou-Chacra et al 1973 J. Phys. C: Solid State Phys. 6 1734
or
R. Abou-Chacra and D.J. Thouless, J. Phys. C 7 (1974), 65.
| {
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How long does a supernova last? Is a supernova over instantaneously? Or, does the (for want of a better word) explosion continue for a while? What is/are the order of timescales involved? What is the duration for which the supernova continues to release copious amounts of energy?
| If you're asking about the duration of the explosion of supernovae, then it's done within a few seconds (the number can still be less) - similar to a nuclear fission. But, the cloud surrounding the explosion (i.e) the matter remnant that is thrown off can still remain expanding for years and it can emit EM radiation in... | {
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Some questions about anyons? (1) As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" Hilbert space $V$ would be $V=W_0\oplus W_1\oplus W_2\oplus W_3\oplus...$ , and further we can... | No, “this conclusion” is based on the topological properties of rotation groups. Namely, for any $n > 2$ $\mathrm{Spin}(n)$ is the universal cover of $\mathrm{SO}(n)$, whereas for $n = 2$ it is not. That’s why in $n > 2$ any thing has to be controlled by a representation of the Spin group, whereas in $n = 2$ it has not... | {
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What is the fastest a spacecraft can get using gravity-assist? Assuming normal spacecraft and space objects (no neutron stars, black holes, etc). To what speed can a spacecraft accelerate using gravity-assist?
For example, if a spacecraft is moving at relativistic speeds, it probably won't get seriously sped up by norm... | This limitation would be imposed by the relative speed difference between the starting point and the object being used for a gravity assist.
to steal Wikipedia's example: Imagine you have a train coming at you at 50mph. You throw a ball at the front of the train at 30mph.
From your perspective, the ball was moving 30m... | {
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Ratio of Size of Atom to Size of Nucleus I have the following problem:
In nuclei, nucleons exists in nuclear energy levels and in atoms, electrons exist in atomic energy levels. The order of magnitude of nuclear energy is 1MeV whereas the energy of atomic energy levels is of the order 1eV. Use this info and the parti... | In this case, "size of atom" really means "size of the box that is holding the electron in its place". The "box" is provided by the confining electromagnetic force exerted by the nucleus on the electron. Similarly, the box representing the nucleus is provided by the strong nuclear force between protons and neutrons tha... | {
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Is it physically meaningful to talk about the 'total temperature' of an object? If I had a semi infinite, 1-D object and a finite 1-D object, both heated at the same constant rate at one end each for the same time period and both begin at the same initial temperature, is it physically meaningful for me to integrate alo... | Temperature is the measurement of kinetic energy per unit particle mass. Since you've added the same amount of heat energy to each object, the finite object will have a higher temperature because its heat energy is distributed across a smaller collection of mass. Taking something's temperature is indeed a meaningful me... | {
"language": "en",
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When does Thevenin's theorem not apply (modelling a power source with a ohmic internal resistance) Most physics text books say that a power source can be modelled as an EMF with a internal resistance. This is also know as Thevenin's theorem or Norton's theorem. However I have read in some sources that this is not alway... | Since you mention batteries in a comment:
The voltage source + resistance model works well in many circumstances. At the extremes:
*
*high frequency / fast rise time waveforms: There will always be some inductance, from wiring if nothing else, which appears as an inductance, an easy add to the model.
*low frequen... | {
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What is the most optimal earth's axial tilt in terms of variation of seasons? What is the most optimal earth's axial tilt in terms of variation of seasons?
What would be optimal axial tilt for earth that life would exist and change of seasons would be at minimal level?
| If Earth had 0 inclination to the ecliptic, then life could still exist and there would be no change in seasons. In fact, at latitudes greater than $-23.5^\circ$ and less than $23.5^\circ$, the seasons are already irregular compared with the rest of the planet; they have two points where the Sun shines directly on top... | {
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Inserting metal into parallel plate capacitor
The plates of an isolated parallel plate capacitor with a
capacitance C carry a charge Q. The plate separation is d.
Initially, the space between the plates contains only air.
Then, an isolated metal sheet of thickness 0.5d is inserted
between, but not touching, th... | Yes d=0.5d, Basically start thinking in terms of work per unit charge. So work you do on $1$ coulomb is $E$x$0.5d$. as field in conductor is $0$ in electrostatic condition , you don't have to do any work at all in that region . so $\Delta V$ is 0 in that region . Hence , $\Delta V_{net}= E_{outside}$x$0.5d$. = V for th... | {
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Alpha particle and helium nucleus The symbol for the alpha particle is α or $α^{2+}$, it can be written as $He^{2+}$.
What I want to know is that, are they same? I mean alpha particle and helium nucleus are same or any subtle difference exists?
| They are the same particles. When $\alpha$-radiation eventually gets stopped by an object (a sheet of paper or simply a meter or so of air will do the trick) it attracts two electrons and becomes elementary Helium.
Most of the world's Helium actually originates from reserves underground where Uranium and other $\alpha$... | {
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How can Ohm's law be correct if superconductors have 0 resistivity? Ohm's law states that the relationship between current ( I ) voltage ( V ) and resistance ( R ) is
$$I = \frac{V}{R}$$
However superconductors cause the resistance of a material to go to zero, and as I understand it, as $R \to 0$, $I \to \infty$. Does ... | Ohm's law is generally NOT correct, it's called a law for historical reasons only!! It's a law in the same sense in which Hooke's law is a law... it holds only for certain systems under certain conditions, but it's widely known because it's simple and linear!
It's not just superconductors, diodes are a neat everyday ex... | {
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Polarization of sound Sound can't be polarized because the vibration of such type can't be polarized i.e, it can't be limited or controlled by any barriers and so polarization is not possible in them.
This is what my teacher answered me when i asked the question. But i didn't understand what did he mean by "the vibrati... | It sounds like your teacher's explanation might have been a little misleading. The reason sound can't be polarised is that it is a longitudinal wave, unlike light which is a transverse wave. (Those links have some animated diagrams that should help to make the difference clear.)
"Transverse" means that if a beam of lig... | {
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Elementary question on pion-proton scattering cross-section
Is $E_k$ the energy of the outgoing or incoming pion?
The first peak is supposed to be a delta baryon.
What does the graph tell us, experimentally? A pion of kinetic energy x comes in, then we look at the graph and find the cross-section, so then we have th... | This is a plot where the incoming pion beam is varied and the total interaction cross section is measured , showing higher scattering cross section at the resonances, as the beam kinetic energy is varied. The interactions are measured by looking how many pions are left in the beam direction after the beam has passed h... | {
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Why is the (non-relativistic) stress tensor linear and symmetric? From Wikipedia:
"[...] the stress vector $T$ across a surface will always be a linear function of the surface's normal vector $n$, the unit-length vector that is perpendicular to it. [...] The linear relation between $T$ and $n$ follows from the fundame... | One important thing to remember is that there is the supposition that there is no force that acts on the bulk of the object that's capable of exert net torque (i.e., exchange angular momentum).
This idea changes when you think on something like the interplay between matter and electromagnetic field. Although you can ad... | {
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Gas Laws And Adiabatic Process Air at 20 degrees Celsius is compressed adiabatically from 1 bar to 10 bar, what will its temperature be?
With
$$P_1 = 1,$$ $$P_2 = 10$$
$$T_1 = 293K,$$ $$T_2 = unknown$$
using $$\dfrac{P_1}{P_2}=\dfrac{T_1}{T_2}$$
my solution was
$$\dfrac{1}{10}=\dfrac{293}{T_2}$$
giving
$$T_2 = 2930$... | *The only problem I now have is that $V1=V2$=unknown which is making me think that he may have forgot to add that information to the question. *
I belive that's the problem. You can't have $V1=V2$ in an adiabatic process (suposing that the number of particles is constant).
Your tutor already pointed the right direction... | {
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Are gravitational time dilation and the time dilation in special relativity independent? There are two kinds of time dilation:
*
*One because the other clock moves fast relative to me (special relativity).
*Another one because the other clock is in a stronger gravitational field (general relativity), or acceleratin... | In the calculation of the relativistic precession of Mercury there is a factor of 3. This includes 1 part kinematic time dilation, and 2 parts gravitational time dilation. They are not mutually exclusive.
| {
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How to determine the direction of medium's displacement vectors of a standing wave? Consider the following problem taken from a problem booklet. My questions are:
*
*What is displacement vector?
*And how to determine the direction of displacement vector at a certain point?
*Where is the position with zero displace... | Just because a wave is a standing wave doesn't necessarily mean that the particles themselves do not move, in face if the particles themselves didn't move there wouldn't be any wave motion at all. For a longitudinal wave (made of particles that oscillate in the direction of wave propagation like here as sound waves) pa... | {
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What counts as "observation" in Schrödinger's Cat, and why are superpositions possible? So if I understood correctly, Schrödinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The argument is that the cat now must ... | Superpositions can exist without problem until infinity. Basically everything including me only exists if your look (measure it). QM is very weired and that why most who are responsible for QM like Schrödinger and Einstein felt very uncomfortable with its philosophical side effects. Thats where the cat comes in. From t... | {
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Evolution principle of the physical laws I wanted to know if there is a physical theory that considers that the laws of physics undergo an evolutionary process. That see the law of physics or the absence of them, as something dynamic, and that with time they slowly converge to something we know today. A kind of simulat... | Yes, evolution has influenced physics, though it isn't wide-spread. Cosmologoical natural selection draws upon Darwin's natural selection. It postulates that a black hole, upon collapse, spawns a new Universe, with parameters similar to its Universe, though slightly mutated. By this, it is meant that the fundamental pa... | {
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Eigenfunctions in a harmonic oscillator This assignment is about the one dimensional harmonic oscillator (HO).
The hamiltonian is just as you know from the HO, same goes for the energies, but I get that the wavefunction of the particle, at $t = 0$, is given by:
$\psi \left( x,\,\,t=0 \right)=A\left( {{\phi }_{0}}\left(... | The explicit eigenfunctions of the Harmonic oscillator hamiltonian are given here, but I would highly discourage you from explicitly doing an integral using these expressions to determine $A$. It is significantly easier to use the fact that the eigenfunctions are orthogonal;
$$
\int_{-\infty}^\infty dx\,\phi_m^*(x)\... | {
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How do objects change their axis of rotation? If I hold a pencil at its end and spin it, throwing it upwards, it will spin about its end, but will soon start spinning around its center. How is this?
I would draw the following torque diagram for while it's in the air:
*
*Object: uniform thin rod with length $\ell$ an... | Not sure if I am interpreting your description of the problem correctly, but if I take the initial conditions (using nice round numbers) as a rod of $r = 1\:\mathrm{m}$ length, pivoting about one end at at $\omega = 1\:\mathrm{rad/s}$ at $t=0$, I can decompose the motion as a COM motion of $v=r\,\omega/2$ with a spin a... | {
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North and south of magnetic field
The current I is flowing upward in the wire in this figure. The direction of the magnetic filed due to the current can be determined by the right hand rule.
Can we determine the north and the south of the magnetic field produced by the current I by using a hand rule?
| The concept of magnetic poles only makes sense with respect to permanent magnets/dipoles/solenoids, where the field lines point from one end of the object to the other. In the case of the magnetic field produced by a current, the field lines are in circular alignment around the wire. Hence, there are no endpoints.
| {
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How do you determine the heat transfer from a $p$-$V$ diagram? I doubt this question has been addressed properly before, but if there are similar answers, do direct them to me.
I am currently studying the First Law of Thermodynamics, which includes the p-V diagram and of course, $\Delta U = Q_{to} + W_{on}$.
My questio... | One way is to find out the internal change energy of the system and infer the heat transfer to the system from that and the work done: $$\delta Q_\text{to}=dU-\delta W_\text{on}.$$
If you have a handle on the system's entropy, on the other hand, then you can use the Gibbs relation, $$\delta Q_\text{to}=TdS,$$to find th... | {
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"source": "stackexchange",
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"answer_count": 4,
"answer_id": 2
} |
Angular momentum conservation while internal frictional torque is present So this appears in a problem which looks simple enough in its context; It's something like this:
Two discs, A and B, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ and $2I$ respectively about the common axis. Dis... | The angular momentum of each disk individually is not conserved, however the total angular momentum of both disks is conserved because there are no external torques acting.
Start by calculating the total angular momentum of both disks (I'm going to replace "w" by "v" since "w" is confusingly close to "$\omega$"):
$$\be... | {
"language": "en",
"url": "https://physics.stackexchange.com/questions/64066",
"timestamp": "2023-03-29T00:00:00",
"source": "stackexchange",
"question_score": "3",
"answer_count": 2,
"answer_id": 0
} |
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