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Studying Einstein's original Die Grundlage der allgemeinen Relativitätstheorie published in 1916's Annalen Der Physik, I came across Equations 66) and 66a) regarding the electromagnetic contribution to the stress-energy-momentum-tensor:
$$ \begin{align} x_{\sigma} = \frac{\partial T_{\sigma}^{\;\nu }}{\partial x_{\nu}... |
When solar wind brings high energy neutrons into contact with Nitrogen-14, a well known process occurs yielding Carbon-14 + a proton. N14 is assumed to exist in upper atmosphere as N2 gas, but the assumption is that in order for this reaction to occur, it must be atomic N14 - if this is correct, the question is what dr... |
I always wondered what happens inside an electronic component during its lifetime. I am aware that passive or active electronic devices can have their performance decreased over a long period of activity, due to exposure to excessive hot / cold temperatures, humidity, corrosion, etc, but how can an electronic component... |
I have the steady state equation with an internal source as
$$\frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2k\frac{\partial T}{\partial r}\right)+Q=0$$
which has the analytic solution
$$T(r)=-\frac{Qr^2}{6k}+\frac{C_1}{r}+C_2$$
where I know $C_1$ and $C_2$ based on some boundary conditions.
However, if I would like ... |
In total internal reflection light inside a dense medium reflects from the boundary to a less dense medium. Since by Snell's law there is no allowed refracted ray, all energy continues along the reflected ray. In the wave picture there is an evanescent wave decaying exponentially in the thinner medium but not transmitt... |
I've been recently been going back over the basics of GR, differential geometry in particular. I was watching one of Susskind's lectures and did not understand the argument made here (26:33 - 35:40).
In short, the argument goes as follows (I think): we have some generic metric ${ g }_{ m n }^{ ' }\left( y \right)$. Sup... |
The definition of sound speed is given by:
$$c_{s}^{2}\equiv \frac{\partial P}{\partial \rho}.$$
In some books of cosmology to calculate the expresion for the sound speed in a baryon-photon fluid they assume adiabatic perturbations.
After of some manipulation they arrive to
$$c_{s}^{2}= \frac{c^{2}}{3}(1+\rho_{B}/\rho_... |
The following question is taken from 10th class science NCERT book chapter 14th.
Most of the sources of energy we use represent stored solar energy. Which of the following is not ultimately derived from the Sun’s energy?
(a) geothermal energy (b) wind energy
(c) nuclear energy (d) bio-mass.
The answer is given as (c)... |
During my course on dielectrics in capacitors, I learned that the dielectric medium if inserted between the plates of a capacitor, reduces the electric field from $E_0$ to $\frac{E_0}{K}$, $K$ being the dielectric constant.
Later while attempting to solve the questions, I happened to come across a question which goes l... |
Why don't the nuclear fusion processes inside the sun produce $\bar\nu_e$ despite having the same mass as $\nu_e$? Is the reason as simple as "there is no production channel for $\bar\nu_e$s." ?
|
Suppose that $\hat{\Psi}^\dagger(x)$, $\hat{\Psi}(x)$ are the usual field operators in second quantisation for some identical particle, and that $\hat{c}^\dagger_n$, $\hat{c}_n$ are the creation and annihilation operators in some discrete single-particle basis, with spatial wavefunctions $\phi_n(x)$ for each mode.
Supp... |
As we know the total cross section can always be obtained from the differential cross section:
$$\sigma = \int_0 ^{2 \pi } \int_{0}^{\pi } \frac{d \sigma}{ d \Omega} d \Omega $$
I understand how the integration is done.
For example, sometimes I see the differential cross section formula is written as: $$ \frac{d \sig... |
While watching Erik Verlinde's lecture on emergent gravity, he showed formulas from Statistical Mechanics,
I want to read more about this topic, at an introduction level, which also mentions how to derive them, especially the $dE = T dS$ equation. What are some known, famous, good books that talk about this?
|
I'm a physics layman, but was reading about ionizing vs. non-ionizing radiation, and it seems unlikely to be a coincidence that visible light (and some UV) spans the shortest wavelengths you can have before getting into ionizing territory. This is perhaps partially a biology question, but is there a reason that things ... |
How is $\frac{dQ}{T}$ measure of randomness of system?
What is entropy really?
The answers to these questions sum up the thermodynamic meaning of entropy. But, I have seen way too many documantaries and YouTube videos explaining that entropy is 'dis-order'. Others say it isn't. Then there is the thing about entropy and... |
First off, a pre-question: if I got this wrong, then probably the whole reasoning is wrong as well.
Studying the lagrangian for a two-particle scalar field with a quartic interaction in the context of SSB and Higgs mechanism, one can find many different cases:
the only fields are the scalars, and the quadratic term is... |
I'm wondering if the mere presence of spin will contribute to the energy of a particle, also in the absence of a magnetic field? For I know that a magnetic field will break the degeneracy between the up and down state via
$$ \hat{H}_\text{precession} = - \frac{g e}{m_e c} \mathbf{S} \cdot \mathbf{B} $$
but suppose I ha... |
So in this video they have an evacuated tube with a golfball at one end, they quickly open one end and the golf ball shoots out the other, hitting a target. Resulting in a rapid unplanned disassembly of the golf ball.
This got me wondering how much energy is 'stored' in an evacuated tube; and how you would calculate it... |
I was solving questions related to circular motion of a pendulum hanging from a ceiling in an inertial frame having angular displacement $θ$ and if I resolve Tension into vertical and horizontal components I get
$$T\cosθ = mg$$
but if I resolve the weight $mg$ in the same scenario I get
$$T = mg\cosθ$$
and both possibl... |
Historically, people measured time with the help of naturally recurring phenomena (say, a day). Then a day was split into smaller chunks (an hour, a minute, a second). Suppose we define an hour as 1/24th of a day. My questions is, how would we split a day into 24 equal parts? How can we be sure that they last the same ... |
note that it's taught that in standard model particles that mediated weak interaction force are gauge bosons: vector particles, spin 1, take one charge.
I'm wondering how to prove these properties in experiment?
|
It seems to me that during the final merger of 2 massive objects there will be a chirp, a sharp increase in the intensity and then it is cut off signaling the merging process is completed. I am wondering what factors help determine the shape of the chirp? is it the drastic difference in their masses or their angular mo... |
I got stuck trying to solve this problem:
Given the potential $$V(x) = \frac{m\omega^2x^2}{2}-\beta x^4,\ \beta>0$$ I need to evaluate the deviation of the energy levels from the harmonic oscillator using WKB.
I tried to use Bohr-Sommerfeld quantization rule but that gives the following integral:
$$2\sqrt{2m}\int_{x_-}... |
Assume that we have an exactly uniform gravitational field like that occur for an infinitely large plate, yet with a finite mass. As we know, two similar clocks located in a specific alignment in the field with different distances away from the plate, and at rest WRT the plate, undergo similar gravity, and thus the clo... |
Why can we apply the variational method to determine the first excited state of a system when the Hamiltonian commutes with the parity operator? Ignoring the information about the commutation, it seems to me that the inequality we need to be able to apply the method isn't satisfied in general, because we would be using... |
The entropy of a photon gas in equilibrium (emitting e.g., black-body radiation; BB) is
$S \propto V \cdot T^3$
where $V$ is the volume and $T$ is the temperature of the gas [see https://en.wikipedia.org/wiki/Photon_gas].
Now, in case of a BB, $T$ is linked to the peak frequency of the BB, $\nu_{\rm peak}$, according t... |
The essence of Wilson RG can be described in tree steps:
Initially we have some theory on scale $\Lambda$.
Lower cut-off $\Lambda^\prime =\zeta^{-1}\Lambda<\Lambda$ and integrate out d.o.f. with $\Lambda^\prime<k<\Lambda$
Place initial and final theory on a level by rescaling momenta and coordinate:
$$
k^\prime = \... |
There's no known interacting CFT in $d>6$, see Interacting CFT in $d>6$
Also we know a lot CFT in $d=2$ (minimal models for example) and in $d=3$ (WF fixed points in $4-\epsilon$ approach to different models in SFT).
But what we know about non-SUSY CFT in $4≤d≤6$? Which examples we can present?
For example, I know abou... |
Maybe my question seems simple, I am reading about general gravity but the first obstacle faced me is the definition of the distance in a four dimension space. Why does the infinitesimal distance in space-time contain a minus sign before the dt squared?
Please someone help me to jump this problem.
|
I'm trying to understand if the microcanonical entropy $S_{mc}=\log(\Omega)$ with $\Omega=\int\frac{d\vec{z}}{h^{3N}N!}\theta(E-H(\vec{z}))$ is somewhat more "fundamental" than the canonical entropy $S_{c}=\beta E-\log(Z)$ with $Z=\beta\mathcal{L}[\Omega]=\int\frac{d\vec{z}}{h^{3N}N!}e^{-\beta H(\vec{z})}$. My guess is... |
I'm confused after reading of a book in which the author proves mathematically that electric and magnetic fields are orthogonal to each other (for TEM mode). I'm calculating it in the same way, however something is missing in his solution.
I begins from Maxwell's equations:
$$\nabla \times \mathbf{E} = - \frac{\partial... |
Quantum theory does not allow a rock to turn suddenly into a duck. It does not allow any other bizarre transformation to happen either. This idea is a myth perpetuated by people who misunderstand quantum theory. Foundational to quantum theory is the concept of particle uncertainty. It is impossible to know a particle's... |
What I have learned after studying QFT on curved spacetime is that we replace the Minkowski metric, used in flat spacetime QFT, with the general metric and partial derivatives goes to covariant derivatives and also take other machinery of GR but the main point: we [formalism used in Birrell or Parker book and I'm not d... |
In classical mechanics we simply have quantities which are simply scalar like momentum, energy of system but when we transit to QM it's an ad-hoc principle, at least to me, that we'll be dealing with quantities which are operator and hence commutativity can't be assumed a priori. Now I want to know if there exist anyth... |
I have tungsten filament. When I apply a voltage and measure the current and calculate the resistance. I can see that the resistance of the filament increases over time (due to the increasing temperature). My measurements suggest that the final resistance after a sufficiently long time is (almost) independent of the vo... |
We all know that if we fill a cylinder with water and then drop the egg into the water it sinks but when we add some three tsp of salt the egg floats.
Let,
$V=$ volume of the cylinder.
$A=$ Volume of the object submersed inside water.
$G=$ Gram of salt to be mixed
Suppose that salt is the only thing we have and it is v... |
I know there are similar questions with answers like this one in physics stackexchange but before I read these I had a completely different argument with a different conclusion which I thought was correct but now I'm suspecting that there is something wrong with the argument. I just want to know what exactly is wrong w... |
Does anyone have a reference how the (lowest-order) Feynman diagrams for the scattering of an electron anti-neutrino $\overline\nu_e$ on a hydrogen atom would look like? I'm a bit confused about the fact that the proton consists of multiple quarks.
|
I was wondering if anyone knows what the maximum distance an induction coil can induce eddy currents on a ferromagnetic material?
I have an induction cooktop and was curious if I could mathematically calculate the distance eddy currents would still heat a cast iron pot. I don’t have a physics background so was hoping s... |
Consider a simple two-body decay process $X\to Y+Z$ where $X$ is a boson, and $Y,Z$ are fermions. If $C$ is violated, $$\Gamma(X\to Y+Z)\neq \bar{\Gamma}(\bar{X}\to\bar{Y}+\bar{Z}).\tag{1}$$
However, if we further assume that CP is conserved and since the CP conjugate of a left-handed fermion is its right-handed antife... |
In the Laplace corrrection for velocity of sound, the bulk modulus is replaced by gamma×Pressure.
$(\gamma=c_p/c_v)$
In its derivation
$$PV^{\gamma} =\text{CONSTANT} $$
is used.
And the reason given is that since the process is very fast, there is no time for heat transfer hence it is adiabatic.
My question is that if ... |
Why do we witness scattering of light from mobile screen even when we have a plane screen to reflect light falling from any source of light (tubelight) onto the screen?
|
I would like to ask this following question. In the picture below we have a spherical and plane wave. For the plane wave we have the angle between k and the x axis, that is θ. I would like to know what this angle is for the spherical wave, =0( ̂ + ̂).
|
In linearized general relativity indices are raised and lowerd by contracion with the flat space metric tensor $\eta_{\mu \nu}$. I don't really understand why we can do that. In the book gravitational waves by Michele Maggiore this is just called a "convention". That seems very weird to me, because raised and lowered i... |
I recently learned about RF direction-finding techniques using antenna arrays, and it got me thinking about whether it would be possible to locate an electrical signal source on a large conductive plane. Imagine a thin sheet of metal around 2m x 2m with a signal source and sink at opposing corners. If you put very prec... |
I'm reading these Cornell lectures on solitons (link doesn't work right now, but it just worked yesterday), and I can't seem to prove what I thought would be a simple analysis exercise.
Namely, suppose you have the Lagrangian density
$$
\mathcal{L}= \frac{1}{2}(\partial_\mu \phi)^2 - U(\phi)
$$
in 1+1 spacetime dimens... |
Suppose $n$ is an odd number. Why can we write $a\llap{/}_1 a\llap{/}_2 ... a\llap{/}_n$ as
$$a\llap{/}_1 a\llap{/}_2 ... a\llap{/}_n = V_\mu \gamma^\mu + A_\mu \gamma^\mu \gamma_5$$
for some $V_\mu, A_\mu$?
I know that $\gamma^{\mu} \gamma^\nu=g^{\mu \nu}-i\sigma^{\mu \nu}$ and I tried to write $a\llap{/}_1 a\llap{/}_... |
If you see my horrible reference picture, you will see that the U shaped tube is placed inside the field where gravitational force exist.
And the bottom of the tube is opened, tube is filled with liquid. the density of liquid is ρ, acceleration of gravity is g, and each column's height is h
I used to conclude that the ... |
So I just noticed that when I filled my bucket with water until it overflowed and then I turned the faucet off, the water kept dripping for like 20 seconds. Why does this happens? Shouldn't it have stopped dripping sooner after I turned the faucet off?
|
In the particle data group table: http://pdg.lbl.gov/2020/tables/rpp2020-sum-leptons.pdf ,only $\tau \rightarrow \pi + \nu_{\tau}$ is documented. But does $\tau \rightarrow \rho + \nu_{\tau}$ as well? I don't see any conservation laws that could forbid such decay to happen.
|
An electron is travelling along the x-axis. It then changes its direction by 45 degrees. Will it emit an electromagnetic wave?
|
In General Relativity we see spacetime as a manifold; in this context vectors can't be defined on the manifold but need to be defined on the tangent space of the manifold. So each point of the manifold has its own tangent space and different vectors in different tangent spaces cannot be easily compared. At last each ta... |
As per wikipedia, "brown" refers to long wavelength hues, yellow, orange, or red, in combination with low luminance or saturation.
So what about the short wavelength hues? Is there any reason why they are not called differently when desaturated?
Specifically, is there any physical reason? That is, is brown in some way ... |
I have trying to get a more precise insight into the calculation of the time to the singularity of a test mass into a non-rotatic uncharged black hole.
Prelude: the lagrangian for a massive particle in GR reads
\begin{equation}
L=-m\sqrt{-g_{\mu\nu} \dot{x}^\mu\dot{ x}^\nu}
\end{equation}
Energy is
\begin{equation}
-E=... |
During my attempt of fully grasping the work energy theorem, I came across this written in my textbook:
The frictional force, which we represented as a constant force is in reality quite complicated, involving the making and breaking of many microscopic welds, which deform the surfaces and result in changes in interna... |
I see that Friedmann's first Equation (for flat space) is:
$$\left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi G}{3}\rho.$$
And I know that Einstein's equation, just considering the time-time component is:
$$R_{00}-\frac{1}{2}g_{00}R=8\pi G T_{00}.$$
And I know that $T_{00}$ in the tensor is $\rho$, so we get:
$$R_{00}-\frac... |
Recent, in articles on QFT and condensed matter new objects appear -- fractons.
As I understand now, fracton is a particle with restricted motion: for example, such excitations can move only along line.
If such excitations have restricted motion, how they deal with uncertainty principle?
Could somebody present simple... |
In learning about the duality of quantum particles, I wonder if a quantum wave stretches out into the distance, essentially forever? And if so, when a particle is observed, is it possible (but highly unlikely) that the particle might be found anywhere along the wave?
|
Y-axis vertical line and the other is X-axis
|
Understood situations:
a) Inelastic, rough collision of free spheres
In such a collision, two coefficients are used. The coefficient of restitution in the normal direction (the ratio $c_N$ of relative normal velocities before and after, between $0$ and $1$) determines elasticity, with $1$ being perfectly elastic and $0... |
When you drive screws into wood with a driver or drill, it is often the case that mid-way through the process the screw will suddenly bind and eject your bit (assuming it's not a Robertson or Torx).
My father-in-law showed me that if you simply drive in little spurts, it will go all the way in without binding.
Now gene... |
I like to think of electric battery as charge separating factory (similar to Van de Graaff generator). I took this idea from "Matter and Interactions" by Chabay and Sherwood. With this view of the battery I would like to understand why there is no potential difference between two different terminals of two batteries. L... |
I am an extreme novice in Physics, I am also a beginner in Physics Stack Exchange, and I'm not fluent in English, so please bear with me, consider my question with indulgence.
I request indulgence especially because $99\text{%}$ of my question is a well-known question with an evident and well-known answer, but the impo... |
It is often said in the physics papers or textbooks that in equilibrium if there is no external potential then number density is uniform $n = N/V$, where $N$ is number of particles, $V$ is volume. I would like to see if this follows from statistical mechanics (or maybe contradicts statistical mechanics).
Let us assume ... |
I know that in quantum mechanics the stronger the force, the shorter the range it mediates between (maybe I have problem in this postulation, if so please correct me). So how can gravitational forces be much weaker than electrostatic forces while both the graviton and photon are massless?
Maybe I have a problem underst... |
I'm supposed to derive a relationship in which the change in gravity $\delta g$ is linked to the change in length of the spring $\delta s$.
When the beam is tilted due to increased weight or gravity, the extra weight will tilt, and this will enhance the rotation. I understand this so far, but I can't figure out how to... |
I am trying to justify the use of $dS=\frac{dQ}{T}$ for the change in entropy instead of the more generic $dS=\frac{dU}{T}$.
According to Schroeder, in order to do so, one has to confirm that the volume change occurs quasistatically.
Consider for example a phase change with a volume change, i.e. ice melting. It is know... |
What is the degree of freedom in kinetic gas theory? How can I determine how much degree of freedom some molecule has?
|
We know, because of baryons such as the triple-strange Omega baryon spin 3/2, that at least the quarks 'up', 'down', and 'strange' must come in 3 colors because of the Pauli exclusion principle.
No triple baryons of ccc, bbb or ttt have (so far) been observed. Thus (I would say) there is no reason (as yet) to suppose t... |
In an electron beam, is the light region under pressure below atmospheric pressure?
Motivation of my question:
In the cathode ray tube, the cathode ray (electron beam) becomes luminous and visible because there is low pressure inside the tube. If the internal pressure drops too low, the light beam disappears. If you t... |
We have built a swimming pool out of pallets, with heavy duty ratchet straps around the outside, holding it in a circle. The pool is $4'$ high and the circumference is $57'$ ($16'$ diameter). The straps are $2''$ wide.
At the bottom of the pool, the outward pressure on the wall is $1.7 \,\text{psi}$. How can I calcu... |
Suppose we have $\vec{F}$ being the force on a proof mass $m$ in the field of a mass $M$ with mass density $\rho(\vec{r})$ given by $\vec{F}(\vec{r})= m\vec{g}(\vec{r})$ and $\vec{g}(\vec{r}) = \nabla \phi (\vec{r})$ which follows the equation $\textrm{div } \vec{g}(\vec{r}) = -4\pi \gamma\rho(\vec{r})$.
Now I am aske... |
On page 154 of Theoretical Physics, By: Georg Joos, Ira M. Freeman the following is stated:
Thus for a given velocity field, $\text{curl} \mathfrak{v}$ represents a vector equal to twice the angular velocity vector.
This is in the context of discussing strain in the study of deformable solids. The argument begins wi... |
If I am standing on a chair, and I point a laser at a coffee table a few meters away from me (that is also below me), the light should reflect away from me. Therefore, no light should be returning to my eyes right? Why is it that I can still see the spot where the laser pointer is hitting the table. How is the light re... |
Disclaimer: Not an engineer
I need some help determining the required performance from a heat exchanger for a pseudo-instant hot water system on a boat. Using a heat exchanger, and a reserve of hot glycol, I want to heat domestic water. I have tried to find the answers and figure it out myself, but am not getting anywh... |
In static rotational equilibrium cases, we learn that the reference axis for calculation of torque is arbitrary. But what if there is a net torque? We use the equivalent of Newton's 2nd law for rotational motion to predict the angular acceleration, but it does not give us the axis of rotation. If there are multiple pos... |
Production of gravitational waves in the early Universe (for example, in the electroweak phase transition) is favoured only if the Universe undergoes a first-order phase transition but not favoured if it suffers a crossover. Why is this so?
|
I have known about the twin paradox for some time and as far as I know that it's not a paradox because one of the twins accelerate in his return journey.
But if this is not the case, then what will they see when they meet each other? If by some means the twins synchronize their clocks when the space twin reaches his en... |
If I had a building of thousands of km in height. Will I experience less weight and gravity in top floor compered to ground?
|
We can prove that gibbs entropy is preserved from Liouville's theorem. We can also prove that its conserved from Noether's theorem and the time reversal symmetry of the Hamiltonian.
But it seems intuitively also that we can prove Liouville's theorem from gibbs entropy conservation, and hence from Noether's theorem. In ... |
In ideal battery the internal resistance is zero whereas in non-ideal battery there is some internal resistance now this internal resistance is due to the battery material (electrolyte) and is present inside the battery between the terminals then why do we represent and eventually do calculations by considering that in... |
For instance, we want to know if cylindrically symmetric de Sitter-type spacetime has an axial geodesic.
This is the metric I am interested in
$$ds^2= \cos^{\frac{4}{3}}\left(\frac{\sqrt{3 \Lambda}}{2} \rho \right)\left(dt^2 -dz^2 \right) -d\rho^2 - \frac{4}{3\Lambda} \sin^2 \left(\frac{\sqrt{3\Lambda}}{2}\rho \right) ... |
Here is an answer by @tparker which makes the following remark
"... a Kosterlitz-Thouless transition, at which the free energy density is smooth but non-analytic..."
The expression for the Helmholtz free energy for the KT transition is $$F=E-TS=(\pi J-2k_BT)\ln \Big(\frac{R}{a}\Big)\tag{1}$$ where $J$ is a parameter... |
I am studying Yang-Mills instanton.
Suppose we have an action in $R^4$
\begin{equation}
S=\int_{M} Tr(F\wedge *F)
\end{equation}
where $F=dA+A\wedge A$.
The instanton number $k$ is defined as
\begin{equation}
k=\int_{M} Tr(F\wedge F)
\end{equation}
Now it can be shown
\begin{equation}
Tr(F\wedge F)=d\bigg[Tr(A\wedge dA... |
Revised Question (07/07/20 14:00 UTC)
Working off of a suggestion by @GiorgioP:
"Would it be fair to say that your question is about the difference of melting behavior of ice if surrounded by air or by water?"
Sort of. Maybe so, but I want to explain in longer form the practical question I'm trying to answer. Perhaps... |
I am trying to derive the "gauge-like" symmetry of linearized gravitation equation, after deriving the latter heuristically from Newton's universal of gravitation. I am roughly following Excercise 7.3 of MTW and the box that follows. (Roughly-because the derivation of linearized gravity done there,is from an action pri... |
I'm trying to revise the Quantum Mechanical model of the Hydrogen atom, and I understand all the methods involved, including separating the wavefunction into its radial and angular parts, solving all the differential equations involved, etc. After we find the eigenvalues and the eigenfunctions and need to normalize the... |
I have recently begun working on a project where I will be modeling some experiment that uses SPDC to generate entanglement. However, I have not formally studied SPDC in any capacity. Is there any reputable resource I can learn (textbook, online lecture notes, etc..) where I can learn more about this process? A quick g... |
Recently I started studying Magnetics and I came across a statement in my book which confused me.It read:
Magnetic force is frame dependent, Electric force is frame dependent but lorentz force is frame independent
I can understand magnetic force being frame dependent as it is a velocity dependent force and velocity d... |
Let's say we have a pendulum and with an initial displacement of 5 degrees, it starts oscillating. Assuming ideal conditions, the pendulum will oscillate forever with its maximum sway angle being 5 degrees.
Is it possible possible to bring the pendulum to a stop or reduce the maximum sway angle by just changing the len... |
As tide approaches in lower part of some rivers (e.g. Ganges), a several feet high tidal wave enters from the sea against the flow of the river (making a great noise), and the water level suddenly rises as the wave proceeds.
I would expect the water level to rise slowly and gradually, as the angle between the moon and ... |
In a Kerr Black hole there is a region where the component $g_{t t}$ of the metric changes sign (the ergoregion). The surface where $g_{t t}=0$ is called the ergosphere.
So, if we consider an observer with four-velocity $u^{\mu}=\frac{d x^{\mu}}{d \tau}=\gamma \dot{x}^{\mu}$, and (for simplicity) with $u^{\theta}=0$ an... |
This approach is seeming intuitive to me as I can visualize what's going on at each step and there's not much complex math. But I'm not sure if I'm on the right track or if I'm making some mistakes. Here it is:
$A$ has set up a space-time co-ordinate system with some arbitrary event along his world-line as the origin. ... |
I'm self-studying Friedman and Susskind's book Special Relativity and Classical Field Theory. The following question popped up while reading section 6.3.4 Lorentz Invariant Equations.
In this Lecture, they derive the Lorentz force law from the Lagrangian given by
$$\mathcal L(t, X^i, \dot X^i) = -m\sqrt{1-(\dot X^i)^2}... |
Let us suppose that there is a block of a ferromagnetic material inside a very long ideal solenoid, the magnetic field lines inside are in a straight line perpendicular to the surface of the block at both the ends.Why does the magnetic field inside the block increases? It is known form the boundary conditions of magnet... |
Recently I have read something about describing FQHE within chern simons field theories. According to Atland's text book,Condensed matter field theory, one can map interacting fermions to composite fermions with chern simons gauge field(statistical field). Follow the text book, we start with partition function and intr... |
Imagine a body with force $F$body and friction force as $F$friction(Friction force is not zero).
When body goes with zero acceleration(no change in speed)
$a$object = 0
the net force equation states that:$F$net=$ma$ then we should have net force as 0.(Since $a$=0)
so $F$body=0.
But $F$net=$F$friction+$F$body=Ffriction
... |
If we had two rigid sheets which were exactly identical and we had the magnets on it as shown in the figure, then would the top sheet float above the bottom, which is fixed on a rigid surface.
The black dots are identical magnets and $N$ and $S$ represent the poles of magnet facing the opposite magnet.
I can see that ... |
Let's think about the following quantities:
Kinetic energy: $K=\frac{1}{2}mv^2$
Lorentz's Force: $\vec{F}=q\vec{E}+q\vec{v} \times \vec{B}$
This two quantities are not invariant under Galilean transformation. I have a couple of questions:
Question one: In classical mechanics how do we deal with the fact that the ener... |
We can raise and lower indices of any tensor with a non-zero rank by applying the metric tensor with indices properly located.
My question is: why is the metric tensor the tool we use for such operations? If we use another tensor we would perform the same raising or lowering operations but obviously with different nume... |
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