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Given the velocity of a particle as a function of time V(t), and a distance between two points on a straight line (from point A to point B), I would like to find the time it will take the particle to travel this distance.
To solve this, I first obtain velocity as a function of position V(x). I do this by integrating V(... |
I've seen many examples about a particle moving relative to field.
But I never saw a field moving relative to observer (or a particle).
So, can field have a speed?
I thought about some possibilities:
Field is just a theoretical concept, so it doesn't exist and cannot have a speed.
A speed of field is same as wave on ... |
Consider the example of a linear triatomic molecule. Now at low temperatures, where we can exclude vibration, quite clearly degrees of freedom, $f=5$, with 3 translational and 2 rotational degrees of freedom. But if we calculate it using, $f=3N-k$, we get $k=2$, and hence $f=7$. How do we explain this?
Also, in additio... |
$\rm SiO_2$ substrate is widely used for the research of 2D materials but charging impurity of amorphous $\rm SiO_2$ degrades their performance, e.g. reduces the conductivity of graphene.
Inserting something between $\rm SiO_2$ and the 2D material such as a few layers of hBN or gas or molecules reduces this influence. ... |
For
i) an ideal rotation ellipsoid entirely covered with a thin shell of water
ii) locked mutual rotation
iii) non-rotating earth
iv) further conditions (?)
the idea of equilibrium tides with a stationary state do apply. In an inertial, non-rotating frame (with origin e.g. at the c.o.earth or c.o.mass) there is collect... |
I would like to know if an acceleration number would remain squared in
$$ v=v_{o}+at $$
Such as 1.35 m/s^2, for example, would end as
$$ v=v_{o}+(1.35^2)t $$
or simply as
$$ v=v_{o}+(1.35)t $$
Thank you very much for any help!
|
I want to know how to design a classical mechanical system that has a phase space $M$ with a nontrivial global topology. If I naively consider a system in which the generalized coordinate $q_1,\cdots,q_n$ lives on some manifold $M_q$ and if I take the standard kinetic energy $K=\sum_{i=1}^n\frac{1}{2}\dot{q}_i^2$ then ... |
I don't understand the meaning of following path integral measure
$$
\frac{[df]}{U(1)}
$$
What is the difference between $[df]$ and $[df]/U(1)$? A naive idea is the latter measure is more physical since it removes some gauge degrees of freedom from $U(1)$? The symbols are from equation (1) of the supplementary material... |
I understand that a diatomic molecule has 3 translational and 2 rotational degrees of freedom. But since there is only 1 vibrational mode associated with a diatomic molecule and 1 vibrational mode is associated with 2 degrees of freedom, shouldn't the total degrees of freedom be f=7? I've seen it given as f=6 in many s... |
We know that the lagrangian function of a holonomic system subject to fixed constraints has the form
$$\mathcal{L}(\mathbf{q,\dot{q}})=\frac{1}{2} \langle \mathbf{\dot{q},A(q)\dot{q}} \rangle - U(\textbf{q}) $$
where $\mathbf{q}$ is the vector of lagrangian coordinates of the system, $\mathbf{A(q)}$ is the mass matrix ... |
I'm currently going through Goodman's Introduction to Fourier Optics, Fourth Edition and I'm at the Wigner distribution function section, where he states the definition:
$$W_{g}(x,y;f_{x},f_{y}) = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} g(x + \Delta x/2, y + \Delta y/2) g^{*}(x - \Delta x/2, y - \Delta y/2)\time... |
How does the lighting falling into a room differ in color temperature, shadow productions, directionality and other aspects, in relation to the positioning of the sun and the room?
For example, if the sun was high facing a window from the North, how would the natural lighting differ to the room on the opposite side wit... |
Consider picture below where a force applied to a water by a piston and suppose the gauge reads an arbitrary pressure. If I lock the piston to its position and remove the force applied to piston, will the pressure on the gauge read the same?
Consider that the manometer is below water level so it is filled already.
|
Electric Potential definition is as follows:
Electric potential (also called the electric field potential,
potential drop, the electrostatic potential) is defined as the amount
of work energy needed per unit of electric charge to move the charge
from a reference point to a specific point in an electric field
But
its... |
I had a question on symmetry operations that exactly resembles this post. The selected answer there mentions the required symmetry operation to be scale symmetry, and says:
An infinite plate looks the same no matter how far away from it you are.
However, an infinite linear charge configuration would also look the sam... |
• My first confusion is why the endothermic one is still being called ΔHeg considering the definition states "loss of energy by isolated gasious atom upon gain of an e-"?
• Why can't I compare both? They have same dimensions right?
If the question is not clear, take it as comparison of 1st and 2nd electron gain enthalp... |
Consider a delayed choice quantum eraser:
There is an interference pattern at D1. There is an interference pattern at D2. There is no interference pattern at either D3 or D4.
I also understand there is no overall interference pattern (if you count all photons regardless of which detector has been hit), and the questio... |
Consider a sphere $S_1$ radius a and another concentric hollow sphere $S_2$ of radius b and small thickness t. Let us charge the inner sphere by some amount q. As a result -q charge shall appear on the inner surface of $S_2$ and +q on it's outer surface. Now let's connect the outer surface of $S_2$ to the inner sphere ... |
"A hypodermic syringe contains a medicine with the density of water (Figure 6). The barrel of the syringe has a cross-sectional area A = 2.50 * 10^-5 m2,
and the needle has a cross-sectional area a = 1.00 * 10^-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F of magnitude... |
While reading Kardar's 'Statistical Physics of Particles', in section explaining Zeroth law of Thermodynamics, Kardar claims that each of the system's i.e A & B , B & C are assumed to be separately in mechanical equilibrium. If they are allowed to do work on each other, additional conditions like constant pressure is r... |
Summary: Eigenvalues of a "non-normalized" covariance matrix of time-series measurements from a linear system have units of Action (energy * time). Can we interpret this to obtain meaningful statistical thresholds?
Recently I've been doing some volunteer work on an open-source system identification tool for mechanisms... |
From Poisson's, A Relativists Toolkit, problem 1.12 on page 27:
"A particle moving on a circular oribit in a stationary, axially symmetric spacetime is subjected to a dissipative force which drives it to another, slightly smaller, circular orbit. During the transition, the particle loses an amount $\delta \tilde{E}$ o... |
On the flat earth website, they prove that the gravitational pull of an infinite flat earth is finite. Is their proof correct?. I'm not that good at physics and can't determine if they're correct myself. For a school thing.
https://theflatearthsociety.org/home/index.php/blog/infinite-flat-earth-mathematics
Additional q... |
In the image below, the negative charged particle with a velocity v experiences of force in a magnetic field F perpendicular to the velocity v. The work done on the particle is said to be 0, but why? Shouldn't the work done be Fcos(theta)xdisplacement vector where theta is the angle between the Force and the displaceme... |
Suppose that, in the standard model, the lightest particles were the electron, electron neutrino and $W$ boson.
I want to calculate, at 1-loop, the $\beta$-function of $g_{2L}$ in the regime where only these three particles are 'active'. For that, I need the wavefunction renormalization of the electron and neutrino, e... |
In the book Quantum Optics by Scully and Zubairy it is mentioned that the finite linewidth of the laser is essentially due to spontaneous emission events that randomize the phase. My question is; why does spontaneous emission randomize the phase, but stimulated emission doesn't? Their model uses a single cavity mode co... |
The scenario is this: a large mass $ M $ is made of matter and anti-matter in equal amounts. If given a little energy, it will self-annihilate. Another mass $ m $ is in vicinity. The potential energy of both systems is given by:
$$ U = -\frac{GMm}{r^2} $$
Both of them have gravitational potential energy. Now, the large... |
I am currently immersed in the study of quantum mechanics for an upcoming exam, specifically focusing on the demonstration of the Heisenberg Uncertainty Principle. While I believe I can successfully replicate the demonstration, I find the process somewhat circular, as it appears we are demonstrating it because we alrea... |
Why is it said that as long as the normal contact force remains the same or constant, the frictional force is independent of the area of the surfaces in contact?
Does it mean when the normal force starts varying, the frictional force will start depending on the area of surfaces in contact?
I sound dumb but please clari... |
In their 2009 Free Will Lectures, John Horton Conway claimed that there is no evidence for determinism. Specifically, in the sixth lecture, around 38 minutes in, Conway says:
This is perhaps the most contentious thing that I have to say: there is no evidence for determinism! This absolutely shocked me, and if any of y... |
Sakurai and Wikipedia proove the golden rule in the interaction picture. As the reason of that choice is not clear for me, I ask you what are the difficulties that rise up when you try to get the rule in the Shrodinger picture.
It appears that there are no difficulties, but the result you get is different (and that is ... |
For first law of thermodynamics, what the law states can be matched with the equation, U=q+W
, could anyone provide me insight on how does H=U+PV
equation comes up? What is the physical meaning of H ?
|
When I throw a ball at a wall and it bounces off of it and there is conservation of momentum we can say that the springiness of the ball and the wall is the action reaction force responsible for the conservation of momentum but if we zoom in at the atomic or subatomic scale at the interface of interaction what is speci... |
Let's say I am using a long wrench to unscrew a tight bolt because the formulas developed in rigid body statics states that the moment arm should be longer for minimal force application. But how long till the force/torque travels to the bolt periphery, receives a reaction torque from the friction of the bolt fitting fo... |
Every formula and every discussion about kinetic time dilation uses Velocity (or we could say relative velocity). But velocity is a vector with both direction and magnitude. But it seems to me that an object bouncing back and forth or going around in circles or in any other random direction would have the same kineti... |
I know that Richard's rule states that entropy of fusion is constant for metals, and that it is ~2.2 cal K-1 mol -1. I am struggling to find the origin of this statement, is it empirical? What is its derivation? And how does it relate to the melting enthalpy ranges for metals to be between 1-1.5R Tm?
|
In this question, it is explained that parallax measurements of distance are affected by length contraction. This should be true on both ends, since movement is relative and not absolute, and that appears to create contradictions in some scenarios.
Consider 3 spaceships disposed roughly in a straight line: A B C
and ... |
The image above is to help illustrate what I observed, although in this image the line is grey, while what I saw was a bright white line.
This question arises from an experience i had about two years ago, while in my home. I observed a single white line that ended up curling in on itself, and I immediately recognized ... |
Could a cold plasma be densified until its particles are so densely packed together that it behaves like a solid without reaching extreme temperatures? If so how?
Edit: okay there seems to be a confusion. I’m not trying to cool the plasma but simple push the particles so close together that they are equal in density to... |
I recently watched a video on the diffusion equation for neutrons in a fissile material, and at about 2:30 minutes into the video, the author points out that the right hand side of the continuity equation (bottom) should not be 0 because new neutrons are created and consumed in each reaction.
$$\left \langle \vec{\nabl... |
Consider an infinitesimal coordinate transformation,
$$ x^{\mu} \rightarrow x'^{\mu} = x^{\mu} + \epsilon^{\mu}(x). $$
We can show that the metric tensor under such a transformation, up to first order in $\epsilon$, becomes
$$ g'_{\mu \nu}(x') = g_{\mu \nu} (x) - \partial_{\mu} \epsilon_{\nu} - \partial_{\nu} \epsilon_... |
The theoretical coefficient of performance of a heat pump for warming is $\frac{T_h}{\Delta T}$. Take an example of an outdoor temperature of -15C and an indoor of 20C, one then has COP = 293/35 = 8.37. Next, look at all actual heat pumps (for example the list at https://www.ahridirectory.org/) and one finds that at ... |
I am considering the view of object moving at near light velocity
It is described in
https://physicsworld.com/a/the-invisibility-of-length%E2%80%AFcontraction/
I have some comments mainly to the first picture
about the Lorentz contraction disappearing for a cube moving at near the speed of light.
The issue has to do wi... |
I have 50 data for each velocity components ux, uy in vector form in two columns. so $\mathbf{U} = u_x\hat{x}+u_y\hat{y}$.
Moreover, $\mathbf{U} = \mathbf{U_0} + \delta \mathbf{u}$ where the equilibrium part $\mathbf{U_0} = mean(ux)+mean(uy)$ () and $\delta \mathbf{u}$ is the perturbed part. The perturbed part $\delta ... |
Are there any materials that can function as efficient high-energy neutron multipliers? I have read about the utilization of Beryllium and Lead as neutron multipliers, but they seem to only be discussed in the context of neutrons with energies in the tens of MeV. Do these materials have similar properties for neutrons ... |
Almost all the imaging experiments use $4f$ lens combination for imaging. What I don't understand is what is there a need for this combination. From my understanding, we can just use a convex lens. Place it at $f$ distance from the object and we will get the inverted image at $f$. How is a $4f$ lens combination useful ... |
When simulating rigid body physics with joints(say unconstrained for simplicity) you normally have a constraint force binding the two objects together applied at the point of the joint.
This results in a system with too many degrees of freedom so we use that the force does no work to provide an additional constraint.
I... |
I have been trying to read Penrose diagram to understand what white hole can do, but can the white hole collapses into a black hole and if so then what kind of conditions would turn a white hole into a black hole? I know the event horizon of a white hole would repel everything including light but is there anything in G... |
The total energy density $(U)$ of an electromagnetic wave is given by the equation
$$U=\frac{1}{2}\epsilon_0{E_0}^2+\frac{1}{2}\frac{{B_0}^2}{\mu_0}\tag{1}$$
Also quantum energy $(E)$ of a photon in the electromagnetic wave is given as
$$E=hf\tag{2}$$
This might sound absurd, but
can we arrive at Equation $(1)$ by mean... |
This is a repost from MathStackExchange (https://math.stackexchange.com/q/4840786/) where however no solution has been found so far.
Given the tensor product of Hilbert spaces $\otimes_{i \in \mathcal{Z}} (\mathcal{H}_i, \psi_i)$ (here $\mathcal{Z}$ is the set of integer numbers, $\mathcal{H}_i = \mathcal{L}^2(\mathcal... |
In my calculations, I have to use the units in which the Planck constant and light velocity must be taken as unity.
Now, what would be the value of Earth's gravitation force $\implies g = G\cdot\frac{M\cdot m}{R^2}$ (G-> Gravitational Constant, M -> Mass of Earth, m -> mass of Other Body, R -> Radius of Earth) in these... |
Previous discussions on this forum regarding the derivation of the law of conservation of angular momentum from Newton's Laws have pointed out that it supposes the strong form of Newton's Third Law. My question concerns why that law is reasonable for contact forces in rigid bodies and in fluids. To illustrate the form ... |
There is a rigid body undergoing general planar motion (translation+rotation) in 2D. I dont know the translational velocity and center of mass(CM), all I know is the velocity at geometric center (which is not the CM) and rotational velocity. So if I knew either translational velocity or CM, I can find the other and cal... |
For Schwarzschild metric we have invariants:
\begin{equation}
\begin{aligned}
& r^2 \frac{d \varphi}{d \tau}=\frac{L}{m} \\
& \left(1-\frac{r_s}{r}\right) \frac{d t}{d \tau}=\frac{E}{m c^2} .
\end{aligned}
\end{equation}
Which, after being put into metric give us orbit equation:
\begin{equation}
\left(\frac{d r... |
I have a question regarding the spin-orbit interaction in zinc blend materials. As far as I understood, the split-off valence band (VB) forms as a result of this interaction, and it is a shift in energy that causes the formation of the split-off band.
On the other hand, spin-orbit interaction causes a splitting of spin... |
I read in textbooks that the electric conductivity of a semiconductor is $\sigma=q(n\mu_n+p\mu_p)$, where $q$ is an electron's charge, $n$ and $p$ are the concentrations of electrons and holes, $\mu_n$ and $\mu_p$ are their mobilities. In an intrinsic semiconductor $n=p$ but $\mu_n$ may be different from $\mu_p$.
In de... |
Why is a (solar) analemma, photographed (Multiple exposure imagery)in the morning or afternoon at latitudes other than geographical poles or the equator, slanted?
(For further examples of slanting see this imagery: https://www.perseus.gr/Astro-Solar-Analemma.htm)
|
In 1976, John Bell proved that any locally causal theory can't account for certain observed correlations, he formulated the local causality hypotesis in terms of "local beables".
In particular, he argued that this was necessary to distinguish between theories that are relativistic and theories that aren't. For instance... |
In non-relativistic quantum mechanics, the spin operators associated with a particle of spin 1/2 are proportional to the $2\times 2$ Pauli matrices
$$
\widehat{\sigma}_x = \begin{pmatrix} 0 & 1 \\ 1 & 0
\end{pmatrix},\qquad
\widehat{\sigma}_y = \begin{pmatrix} 0 & -i \\ i & 0
\end{pmatrix}, \qquad
\widehat{\sigma}_z=... |
I've started reading three papers, one by Luttinger, one by Eich and by Tatara, and I'm confused to how they relate to one another.
My understanding is that in Luttinger's paper a "gravitational" field is added such that it emulates a thermal gradient, by satisfying the Einstein relation. For this he has to introduce a... |
I'm reading the Gravity Hartle book (ed.2003) and I'm having trouble with the question in the last part of Example 5.9 - Frequency Measured by an Accelerating Observer. More specifically the problem is to consider an observer staying on the bridge of a starship following the accelerated worldline described by $$t(\sigm... |
When holding a book from its corner with two fingers in a pinched position, the fingers act as a sort of hinge, and the book is free to rotate about this corner only. The external forces acting on the book are $mg$, and the contact forces from the fingers.
Since contact forces act on the axis of rotation, they don't ex... |
In post-Newtonian approximation of gravitation, the metric on and around the Earth is taken to have the expression
$$
\begin{bmatrix}
-1+\frac{2}{c^2}U+ \frac{2}{c^4}(\psi-U^2) + \mathrm{O}(c^{-5})
& -\frac{4}{c^3} V_x + \mathrm{O}(c^{-5})
& -\frac{4}{c^3} V_y + \mathrm{O}(c^{-5})
& -\frac{4}{c^3} V_z + \mathrm{O}(c^{-... |
Given a Hamiltonain $H(p,q)$, I know that the classical partition function for a single particle is given by an integral over the phase space
$$
Z_1 = \frac{1}{h^3} \int e^{-\beta H(p,q)} d^3pd^3q
$$
Suppose that the Hamiltonian also depends on some continuous parameter $\sigma\in \mathbb{R}$. I believe $Z_1$ would bec... |
I've seen the picture of nematic phase in liquid crystals like this one
https://saylordotorg.github.io/text_general-chemistry-principles-patterns-and-applications-v1.0/s15-08-liquid-crystals.html, which is quite intuitive.
However, I find it confusing when considering it with crystal solids. It's said that in the nemat... |
If the tension in a string with fixed ends is slightly increased then does the wavelength of a wave travelling along the string change, or does only the frequency change?
|
Consider a system that described by the Hamiltonian $H(t)$, contains non-adiabatic time-dependent external fields and the evolution drives the system away from equilibrium.
Now the partition function $Z$ is given by-
\begin{equation}
Z = \dfrac{Tr\Big[U_{C}\rho(-\infty)\Big]}{Tr[\rho(-\infty)]}
\end{equation}
Where $U... |
[This question is connected with this one. Since the estimation and measurement of spatial gradients and time derivatives have very different levels of difficulties, I thought it best to ask two separate questions]
In post-Newtonian approximation of gravitation, the metric on and around the Earth is taken to have the e... |
Given a $4$-dimensional spacetime described by four coordinates $(t,r,\theta,\phi)$, we usually define the null coordinates by,
\begin{equation}
u = \frac{t-r}{2}, \quad v = \frac{t+r}{2}
\end{equation}
which can be solved for $(t,r)$ so that,
\begin{equation}
t = v+u, \quad r = v-u
\end{equation}
where we can view thi... |
I am currently working with bitensors and plane waves but I'm getting some results which don't seem to make sense and can't figure out why. So first of all we know that Synge's world function $\Omega$ corresponds to half the square geodesic length $\sigma$ and we therefore should be able to write
$$\Omega=\frac{\sigma^... |
I came across this page in the "Cosmic rays and particle physics" by Gaisser. I cannot find any explanation to the notation of $n$ (eqn. 6.8 and forward). Intuitively it should be something like no. of particles, number density etc. but according to 6.11 it should be in units m/s.
|
I'm trying to re-construct an explain for how an optical tweezer traps a neutral atom with a non-zero dipole.
It began something like this:
"The vacuum is filed with short-lived dipoles form by electron-positron pairs (vacuum fluctuations). If a coherent field is applied to the vacuum, these electron-positron pairs wil... |
Let's consider the circular motion of an arm with the angular velocity vector directed in the z+ direction. If an object attached to the arm (so that it is completing the circular motion along with the arm) also has a constant speed in the x and z direction (so the magnitude of the radius of curvature is increasing and... |
Consider two spherical capacitors with Identical radii for the inner and outer spheres (let them be a and b). +q and -q charges are in the inner and outer sphere on Both the capacitors. Now I connect only the outer sphere of one capacitor to the inner sphere of the other . What is the potential difference of the inner ... |
What is actually resistivity?
I read that when the temperature increases the the resistance of the conductor increase. Length and area of a material doesn't change so it means that the resistivity of the material increases with temperature in conductors.
But in semiconductors when the temperature is increased its said ... |
We have two containers (the fridges) each made of the same thermal insulation. They both consume continuously energy just enough so that their inside temperature stays the same. They consume energy because the insulation is not perfect. Which consumes more energy the one with more mass in it, or the one with one less m... |
It is my understanding that ballistic conduction mainly occurs at very short distances. Now a redditor claimed it only takes place under extremely cold temperatures but I found an article published 22 years ago describing room temperature ballistic conduction in carbon nanotubes.
|
The physical model of inflation includes a metastable false vacuum, or a slow-roll field on a flat potential. In either case, I just realized how this is completely insane. With the exponential growth of physical volume, there is exponential growth in the total energy. I understand that there isn't energy conservation ... |
My understanding of Wilson loops
Let's work with classical electromagnetism. The 4-potential $A_\mu$ determines the electric and magnetic fields, which are the physical entities responsible for the electromagnetic force. The 4-potential has a gauge symmetry $A_\mu \rightarrow A_\mu +\partial_\mu \lambda$ with $\lambda$... |
I am reading the paper PRB 106, 035102 (2022). In the supplementary materials, it says, within the Green’s function formalism, the thermal and quantum average of an observable θ is expressed as,
$$\langle\theta\rangle=-\mathrm{i} \int \frac{\mathrm{d} k}{(2 \pi)^d} \int \frac{\mathrm{d} E}{2 \pi} \operatorname{Tr}\left... |
My teacher just said the number of electrons in the universe always stays the same, that's not how I understood weak force interactions and electron capture. Is there some rule that states that the number of electrons will always be the same in the universe, is the number of particles in the electron quantum field some... |
My question is about the ways to derive these expressions. Why in the case of the thin circular plate dm = (M/A) * dA is used while in the thin rectangular plate dm = (M/V) * dV is used? Can they be derived using the other ratio instead of the one I already mentioned? For example, can you derive the expression for the ... |
I have noticed in the solutions of the problems of Friction of a physics book I'm studying from that in cases of limiting equilibrium, the force of friction $f$ to be equal to the coefficient of static friction multiplied by the normal contact force (N).
I know that should be used in cases of limiting equilibrium, but ... |
A parallel bundle of monoenergetic photons is used for imaging in the configuration below. The bundle passes through a layer of water with a thickness of 1 cm, then through a zone where a cube with a thickness of 1 mm is placed, and then through another layer of water with a thickness of 1 cm. Upon exiting the second ... |
This is a phenomenon I've noticed quite a few times when eating, and thought it interesting enough to be asked here. I am not sure, however, if a similar question has been posed before.
When I set a hot bowl of miso soup to cool on the table, I noticed that the sediments (probably micro-particles that make up the paste... |
In Leptogenesis models, a Baryon asymmetry $B$ is obtained from the conversion of a $B-L$ (i.e. Baryon-Lepton number) via Sphaleron processes.
In the literature (i.e. here), the conversion rate $C_{sph}$ with which Sphalerons convert the $B-L$ to a $B$ asymmetry is often given as $C_{sph} = \frac{28}{79}$ if the conver... |
I have two states, $|\psi\rangle$ and $|\phi\rangle$. I have in mind that they live on a length $L$ spin chain with finite local Hilbert space dimension.
I know that for every Schmidt decomposition bipartitioning the system into a region $A$ and a region $B$, the following is true:
$$|\psi\rangle = \sum_{i=1}^n \lambda... |
Many quantum computing systems, most notably trapped ions, propose to use optical heralded entanglement schemes to entangle small 'modules' of qubits that are further apart. Typically one puts two atoms into two different cavities and then repeatedly tries to catch photons from both at the same time (really just one ph... |
if I have 10 data in each column for speed (2D), how to connect those data as wave form?
I need to find the components of wave vector ($k_x, K_y$).
I request any suggestions regarding this.
|
When using Einstein convention, with explicit indices, we usually write
$$
A_{\alpha\beta} = \eta_{\alpha\mu}\eta_{\beta\nu}A^{\mu\nu}
$$
But in matrix form, the order of the operations matters, and we often see the tensor $A$ being put in the middle, like here, when it was stated that the correct order is:
$$
(A_{\alp... |
I have X amount of speed measurements of an aircraft, each measurement includes a heading and a forward ground speed.
What I want to do is to calculate the wind speed affecting the craft.
For example:
Measurement 1: Heading 0 (North), Speed 10 m/s
Measurement 2: Heading 90 (East), Speed 15 m/s
Measurement 3: Heading 1... |
I found this question in a test paper and the answer was all the three pieces must be in same plane because three vectors must be in same plane to cancel each other but if we consider a case like this-If three vectors such as i+j, k-j, -i-k are the velocities of the three pieces and all the pieces have same mass then w... |
Question: When a sky-diver jumps out of a plane (ignoring air resistance) the skydiver is at rest with regards to forces acting on him. So I have some questions:
What does it mean in terms of relativity that the earth rises to meet the sky-diver? if the sky-diver is accelerating downwards, that isn't a force (in Einst... |
Information cannot be transmitted faster than the light. However, I am confused about the meaning of 'transmission' of information. How does the information 'move'? If I calculate the future state of a particle using physics laws, did the information about particle 'move' with negative speed?
|
Consider a star perceived under an angle $\alpha$ from the earth. In the Hanbury Brown Twiss experiment, they say that the coherence length $L_{coh}$ of this light is given by
$$
L_{coh}= \frac{\lambda}{\alpha}
$$
where $\lambda$ is the wavelength of the incoming light . So they measure the coherence length of the ligh... |
I have been reading on higher category and symTFTs. It appears to me that, for higher categories, people seldom mention the consistency relations (like the MacLane coherence theorem in the category case). A few years back, I heard that people didn't even know all the consistency relations for 2-categories.
So, my quest... |
During sublimation, the solid phase transitions to a gaseous phase. If you were to place this solid inside of a constant volume V at a certain temperature T, the system would reach a steady state. I am wondering how one would find the number of particles in the vapor at a certain temperature.
What I thought would be th... |
The LIGO Gravitational-Wave Observatory and CERNs Large Hadron Collider both have some impressive ultra-high vacuum systems. For my project proposal I need to demonstrate some understanding of how much power it takes (in practice) to maintain an ultra-high vacuum. This could be Watts as a function of vacuum level and v... |
Consider a Hamiltonian $H$ on some spin chain of length $L$.
Suppose we have a subset of $n$ eigenstates $\{|\psi_i\rangle \}$ of $H$ obeying the following special condition. First, a couple quick definitions: $$|0, \{a_i\}\rangle = \sum_{i=1}^n a_i|\psi_i\rangle,$$ $$|t, \{a_i\}\rangle = e^{-iHt}|0, \{a_i\}\rangle$$
T... |
I want to check my understanding on the difference between symplectomorphism and canonical transformation. This is a follow-up of my previous post.
(A) A map $(q,p)$ to $(Q,P)$ is called a symplectomorphism if it preserves the symplectic two-form: $dp\wedge dq=dP\wedge dQ$.
(B) A map $(q,p)$ to $(Q,P)$ is called a ca... |
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