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If the speed of light has to be invariant for all inertial reference frames is the only extra assumption in Special relativity, why can't we explain Time dilation without the light clock?
Imagine a light bulb that flashes once in every $T$ seconds for an observer stationary to the bulb.
Can someone explain, just using ... |
I'm reading Introduction to Electrodynamics 4th Edition by D.J. Griffiths where after listing the Maxwell equations in empty space (i.e. $\rho = 0, \mathbf{J} = 0, \mu = \mu_0, \epsilon = \epsilon_o$) he says on p.g. 393:
[The equations] constitute a set of coupled, first-order, partial differential equations for E
an... |
The Lorentz boosts are represented by symmetric $4\times4$ matrices. Though the most general Lorentz transformations has no obvious symmetry property, can the symmetry (under transpose) of the Lorentz boost matrices be understood intuitively? Like, from considerations of principle of relativity (that the inverse transf... |
Our lecturer gives study material which contained that Newton's second law could be written as:
$$ \begin{aligned} F &= m \ddot{x} \\ &= m \frac{d \dot{x}}{dt} \\ &= m \frac{dx}{dx} \frac{d \dot{x}}{dt} \\ &= m \frac{dx}{dt} \frac{d\dot{x}}{dx} \\ &= m \dot{x} \frac{d \dot{x}}{dx} \end{aligned} $$
The last line of that... |
This is regarding symmetries and unitary transformations in quantum mechanics. Consider some infinitesimal continuous transformation given by $T$, where
$T = 1 - \frac{iG\epsilon}{\hbar}$.
If this transformation conserves some arbitrary operator $A$, then we will need the following to hold:
$T^\dagger{}A T = A$
If we c... |
Let's look at ferromagnetic system as an example.
The correlation function is defined:
$$G(r,r_{0})=\langle(m_{r_{0}}-\langle m_{r_{0}}\rangle)(m_{r}-\langle m_{r}\rangle)\rangle=\frac{1}{r^{p}}e^{-\frac{|r-r_{0}|}{\xi}}$$.
In my understanding, When $G(r,r')\neq 0$, it means the system is somewhat ordered and $G(r,r')=... |
Consider a point source of light placed $40$ cm to the right of a thin converging lens of focal length $15$ cm. We wish to find the distance of its image from the lens.
We can use the lens formula:
$$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$$
Putting $f=+15$ cm and $u=-40$ cm,
$$v=\frac{-15\cdot 40}{-25}\text{ cm}=+24 \text... |
The path of light is not visible in vaccum,but only the source(reflecting surface) of light is visible to us. But in case of image formation, for example from a concave mirror, we see the image at the point of intersection of rays. That point lies in the path of intersecting rays.
As we can see the image, it is simila... |
If we take vacuum expectation value of two scalar field at the same point (2-point correlation function when 2 points coincide) it diverges. what is the physical reason(interpretation)behind this? Also what happens if i take one scalar and one vector field (or any other field other than scalar one)?
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as shown, in my option one diode looks enough, is there any special reason we have to connect two of them
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$|\psi\rangle$ is the quantum state of a system and $\psi(x)$ is the quantum wave function. Quite simply, what is the difference?
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This is a problem in "Differential Equations: A Modern Approach with Wavelets" by Krantz:
If the length of any small portion of an elastic cable of uniform density is proportional to the tension in it, then show that it assumes the shape of a parabola when hanging under its own weight.
After not knowing how to approa... |
I was preparing lecture notes for an undergrad thermodynamics course, and (due to fiddling with some equations) I stumbled upon a peculiar thermodynamic relation that I couldn't find anywhere else. I have the feeling I'm rediscovering hot water.
The relation is as follows, and holds for a generic reversible process of ... |
I am getting into general relativity, which of course means getting to grips with curvilinear coordinate systems. Repeatedly, the textbook and lectures have emphasized the relationships $$e_i=g_{ij}e^j\quad \text{and}\quad g_{ij}^{-1}=g^{ij}$$
In a problem set, I have been told that, given $$s(r, \theta, \phi) = r\begi... |
I know that in many case, just crashing a naked nucleus with an electron does not reduce the proton number of that nucleus, but the electron just start orbiting the nucleus instead. I understand that this is due to energy conservation, as in some nuclei, the electron energy required is usually very high. Now, the muon ... |
Well I know that the universe is expanding, but is there any equation or letter or simply just an expression that tells us that the universe is expanding...
|
I read on Wikipedia that "An example scale showing power ratios x, amplitude ratios √x" [1], i.e. that the relationship between power and amplitude is squared.
How come? Have this something to do with the relationship of power and electric potential, i.e. P = U² / R?
Where
P = Power
U = Electric potential
R = Resistan... |
I have asked this question a number of times and am still uneasy with it.
I want to know how somebody can derive the equation (also see above, picture from a publication):
$$\epsilon(\omega)=\epsilon_L + \frac{i\sigma(\omega)}{\omega}$$
The sign is completely wrong in my mind! I am aware that physicists and engineers ... |
I am trying to understand Schroeder's treatment of heat engines, and am having a very hard time understanding the Rankine cycle.
I know that efficiency $e = W/Q_h = 1 - Q_c/Q_h$, and the total $PV$ work done during the process is represented by the area enclosed by the cycle. Moreover, Schroeder calculates the efficie... |
My first idea is that number of $\pi ^+$ and $\pi ^-$ mesons in collision of heavy ions with some target made of heavy nuclei should be close to 50/50. But after that I start to think that mass of $d$ and $u$ quarks are different so maybe it will be easier for some mesons to be produced. Heavy ions have more neutrons t... |
I work with PEG hydrogels and use the material to recapitulate cartilage biology and I am really interested in modeling the soft tissue mechanics in COMSOL. I have been studying the work of Caccavo et al closely as the work implements both poroelastic and viscoelastic physics (https://doi.org/10.1016/j.msec.2017.02.155... |
I was asked to compute the energy momentum tensor of a string whose Lagrangian is:
$$\mathcal{L} = \frac{1}{2}\rho \dot{y}^2-\frac{1}{2}\tau y'^2 \tag{1}$$
I've used:
$$T_{\mu\nu} = \frac{\partial\mathcal{L}}{\partial(\partial^\mu\phi)}\partial_\nu\phi-g_{\mu\nu}\mathcal{L} \tag{2}$$
To get:
$$T_{00}=\frac{\partial\mat... |
In the classical incorrect 'billiard ball' model of the atom, electrons are often drawn as smaller balls than the protons and neutrons in the nucleus.
However from quantum mechanics we know the electron is really a non-localised electron cloud.
I assume in the same way protons and neutrons are non-localised. But since ... |
Let us have an integral $I$ over the first Brillouin zone (BZ) of a 2D lattice.
$$I = \int\int \Omega(k_x,k_y) dk_x dk_y$$
where $\Omega(k_x,k_y)$ is some function (let's say it's Berry curvature). what is the correct numerical approximation of this integral? I thought Riemann sums would work i.e.
$$I \approx \sum_{k_x... |
Let's assume I shoot an object from a high tower horizontal to the earth's surface. As far as I understand, depending on the velocity I will get different types of orbits. With decreasing velocity I will go from
hyperbolic orbit where the focal point is the earth's center
parabolic orbit where the focal point is the e... |
Since there are 3 states of oxygen:
3Σ−g: The ground triplet state
1Δg: The ground singlet state
1Σ+g: An excited singlet state.
What happens to the ground triplet state when it is exposed to the 60 Ghz EM wave? I've read that the radio wave at 60Ghz gets mostly absorbed by oxygen, why is that?
Does the ground triplet ... |
In many QFT books and courses people use a non-relativistic approximation to extract potentials from QFT. They do so by comparing the scattering in QFT with the scattering in Quantum Mechanics, in the Born approximation. This is done in Peskin & Schroeder's book, also in Schwartz. Here is an example available online (f... |
I have a question about the meaning of complex conjugation in time reversal symmetry in quantum mechanics.
$T$-symmetry in classical mechanics is defined simply by the substitution $t \to -t$. If I have an external magnetic field it is not enough and I have to substitute $ \textbf{B} \to - \textbf{B} $. This makes sens... |
In my textbook, under the topic of gravitation, it states that if the centres of 2 planets, each of mass $M$ and separated by a distance $r$ and you have a point halfway between the centres of the planets, the gravitational field strength at that point is $0$.
I don't fully understand why that is. Is it because the p... |
I've become a bit stuck on how to calculate commutators. I understand [A,B] = AB-BA
but what exactly is AB, is it AxB (A multiplied by B), or is it A(B) (A acting on B)?
For example if $A=4x$ and $B=2x^2$,
Is AB, $A(B) = 4(2x^2)=8x^2 $,
or is it $AxB = (4x)(2x^2) = 8x^3$
I feel like I've really been overthinking this a... |
The next decade is very promising for cosmology as new surveys such as SPHEREx, Roman, Euclid, DESI which will shed light on inflation, dark matter/energy and more. At the same time there are particle detectors, some of which are still being built, looking to directly detect dark matter, e.g SuperCDMS, XENONnt, LUX-Zep... |
Suppose I have wheels driven by a motor. The wheels make contact with a horizontal surface, so that the wheels accelerate in translational and rotational motion. If I want to know the linear acceleration of the wheels I use: $a=\alpha r$.
The torque on the wheel is given by:
$\tau=I \alpha \rightarrow \alpha=\frac{\ta... |
As I understand it, evaporation is thought of as a phase transition from a liquid into a gas. Individual molecules get enough energy to break surface tension, and flung up into the gas. A gas that's saturated with water vapor can precipitate out when the temperature goes below the saturation point. e.g. dew.
Is it us... |
If I have a typical Drude dielectric permittivity:
$$\epsilon(\omega) = \epsilon_{\infty} - \frac{\omega_p^2 \tau}{\omega^2\tau + i\omega}$$
Now, decomposing $\Re{(\epsilon(\omega))}$ and $\Im{(\epsilon(\omega))}$:
$$\Re{(\epsilon(\omega))}=-\frac{\omega_p^2}{\omega^2+1/\tau^2} + \epsilon_\infty$$
$$\Im{(\epsilon(\omeg... |
In Supersymmetry and Morse Theory (1982) by E Witten,
Concern whether the supersymmetry is broken by checking whether
$$
Q | 0 \rangle=0
$$
exists or not --- Witten said:
SUSY breaking: A solution may be shown not to exist by calculating a reliable, positive lower bound to the energy eigenvalues.
SUSY non-breaking: ... |
I have a basic doubt. Say I am viewing Mars from my window and I used the compass app to get an approximate 2D direction. If at the same instant another person also observes Mars from their window. Say the other person is in the same city separated by a few kilometres. What will be the measured direction by me and the ... |
Does P/N doping a semiconductor affect the color in some straightforward manner? Say the material starts as a yellow color and it is p doped, what can we expect from this information or what information do we really need.
|
I came across this question while studying for a Physics test, with the corresponding answers posted below it.
But isn't the direction of the induced current as a consequence of Lenz's law such that the new magnetic field it induces opposes the original magnetic field, not that it must cause an opposition of motion o... |
Firstly, I am a layman with an interest in physics only so please forgive any ignorance I demonstrate here. This question puzzles me and I'm sure there's a good answer. I've heard it said repeatedly when referencing things like the black hole information paradox that information is preserved. This was the impetus for H... |
The Gibbs free energy is defined as follows:
$\Delta G = \Delta H - T\Delta S$
My professor and I are currently working with a simplified definition of $\Delta G$ for reaction-diffusion systems in which we assume zero enthalpy contribution (for simplicity):
$\Delta G = -T\Delta S$
We are considering a fundamentally ope... |
update/clarification: I have commented and have then been invited to include more here. I didn't say explicitly that I was not restricting physics to a simple Newtonian model, so that is now said.
When we study electrostatics we have the pleasure of both starting and terminating electric field lines on opposite charge... |
We define the Associated Legendre Function as follows:
$$ P_{\ell}^m (x) = (-1)^m (1-x^2)^{\frac{m}{2}} \left( \frac{d}{dx}\right)^m P_{\ell}(x)$$
How would we show that $P_{\ell}^m (-x) = (-1)^{\ell + m}P_{\ell}^m (x) $? I know it has to do with the chain rule, but I'm very stuck
Note: $P_{\ell}(x)$ is defined as:
$$ ... |
As the title suggests, but I'll reiterate.
Since a black hole has an extremely large gravitational pull, wouldn't you be going forward in time relative to Earth the closer you get to the black hole?
|
I'm sorry if this sounds like a silly question. I think I am jsut missing some key insight. But take the Schwarzschild solution, which describes the spacetime around a static spherically symmetric mass (but I also want ask about any other kind of spacetime). The metric is
$$ ds^2 = -(1-\frac{r_s}{r})dt^2 + \frac{r^2}{1... |
Consider the following situation:
We know this is a classic example frequently used when teaching Faraday’s Law, and the voltage/electromotive force (emf) $\mathcal{E}$ induced across terminals of the moving conductor (lighter gray bar in the picture) is
$$\mathcal{E} = B l v$$
where $B$ is the uniform magnetic field ... |
The asteroid Bennu seems to be just a pile of rubble weakly held together by gravitational forces. Newton’s law, -Gm1m2/r2, and Coulomb’s law, +keq1q2/r2, have exactly the same form but opposite sign. So if I add enough charge to the asteroid, it will simply fly apart! The amount of charge needed is sqrt(G/ke) = 8.6... |
I googled that question and found this answer:
https://www.quora.com/If-I-had-a-laserpoint-inside-a-very-fast-moving-spaceship-and-I-point-at-the-wall-in-front-of-me-normal-to-the-direction-of-motion-will-the-light-hit-a-bit-lower-due-to-the-speed
Also sometime ago I watched the video on SR paradoxes explanations, wher... |
I'm trying to prove that if $\psi (\mathbf r, t)$ satisfies
$$
i\hbar \frac{\partial\psi}{\partial t}(\mathbf r, t) =
-\frac{\hbar^2}{2m} \left( \nabla-\frac{iq}{\hbar} \mathbf A \right)^2\psi(\mathbf r, t)
+ q\phi(\mathbf r, t)\psi(\mathbf r, t), \tag{1}
$$
then so does $\psi'(\mathbf r, t) := e^{i(m\mathbf{v\cdot r}... |
For the Hadarmard Hamiltonian, $\hat H = (\hat X+\hat Z)/\sqrt 2$, where $\hat X$ and $\hat Z$ are Pauli matrices. The time evolution of a state under this Hamiltonian could be visualized by a rotation on the Bloch sphere with an axis
$$
\hat n = \frac{1}{\sqrt2}\begin{bmatrix}
1 \\
0 \\
... |
I have a very naive question concerning Feynman diagrams: If we consider the process $\pi^{+}\rightarrow \mu^{+}\nu_{\mu}$ via the weak interaction, then we get this Feynman Diagram according to Wikipedia:
Now, my question is the following: If I drew this diagram, is this also correct?
Or if I only exchanged the posi... |
I know many people (including me) are bombarding this site with questions about the recent Veritasium video about the one-way speed of light, but I think I found a way.
Here it is:
(You can see sort of what I am talking about in the picture I attached. Just pretend the mirrors aren't there.)
You could set up a light s... |
Reference: A. Konda et al., "Aerosol Filtration Efficiency of Common Fabrics Used in Respiratory Cloth Masks", ACS Nano 2020, 14, 5, 6339–6347.
The paper linked above was about experimentally determining the efficiency of different cloth masks.
They say the pressure difference determines the breath-ability and comforta... |
I am trying to understand space groups in crystallography. In Internation tables for crystallography, for a nonsymmorphic space group, they list some symmetry operations. 8 of them are listed under the (0,0,0)+ set and 8 in the (1/2, 1/2, 1/2)+ set. What does this mean? Are there 16 operations in total? How do the sets... |
https://m.youtube.com/watch?v=ljoeOLuX6Z4 in this video they measure the same event at different times does that tell you the speed of light in that direction? Since the event doesn’t appear to happen at the same time instantaneously does that mean that the speed of light isn’t infinite in that direction? Can you measu... |
I'm just a high school student so this may seem dumb but none of my teachers nor my seniors could clarify this.
In the balanced equations of any radioactive decay every atom is represented as $$^x_yZ$$
Wherever an electronic is emitted the 'x' position is indicated by -1 and thus the atomic numbers balance.
But it neve... |
As I understand, the Nagasaki plutonium was made in nuclear reactors by bombarding U238 with neutrons.
There was about 20% of U238 in the gun-type U235 bomb at Hiroshima. Was this for reasons, or was it just the best rate of enrichment achievable ?
My main question is: When Little boy goes off, chain reaction, lots of ... |
Why not one? Well we can't even sigle out a 'one ray' exactly because it's still a thin beam but my question is why do we see the image in a plane mirror only at the point where they all meet? We could have also thought the rays come from some farther point, if we continue it behind the mirror past the point where imag... |
I'm confused about the resistance of superconductors. It is known that the resistance at the the critical temperature goes exactly to zero (the resistance is not very small, its really zero, right?). But in a superconducting state, not all electrons form Cooper pairs right? so why then is the resistance exactly equal t... |
Let $\hat{H}(t)$ be the Hamiltonian of a quantum system depending on time $t$ through $k$ parameters $R(t) = (R_1(t), R_2(t), \dots, R_k(t))$:
$$
\hat{H}(t) = \hat{H}(R_1(t),R_2(t),\dots,R_k(t)).
$$
Suppose that the Hamiltonian changes very gradually. The adiabatic theorem tells us that the system which starts out from... |
The set of equations $$\Box A^\alpha = -\mu_0 J^\alpha$$
can be found in section 12.3.5 of Griffiths's book. From what I understand, the real-valued functions on both side of the equations are the coefficients of some $1$-forms with respect to a chart. Thus, I am wondering how the equivalent index-free equation involvi... |
Is this statement correct? I intuitively believe it is wrong. Simplest example would be shooting a bullet.
I just read this from my little brothers textbook. Is the textbook garbage or did i miss out on something.
Thank you for your help!
|
Here is a problem where you have to calculate percent uncertainty for an angle and its sinus function. It calculates the uncertainty for its angle using the well known formula, then calculates uncertainty for sinus by subtracting maximum and minimum mistake uncertainties to get absolute uncertainty and divides it with... |
In the continuum limit of (2+1)-dimensional compact $U(1)$ gauge field, the instantons are input by hand in terms of nonconservation of magnetic flux $\int b$:
\begin{eqnarray}
\int dxdy [b(x,y,t+\epsilon)-b(x,y,t-\epsilon)]=2\pi,
\end{eqnarray}
by insertion of a monopole operator $\Psi^\dagger$ at time $t$.
My questi... |
A spinless fermion (possessing an electric charge) can move across the sites of
the discrete (translationally-invariant) lattice. The structure
features three kinds of sites: $α_n$, $β_n$, $γ_n$ with $n = 1,...,N$ and $N ≫ 1$.
For each n, $α_n$, $β_n$ and $γ_n$ share the same x-coordinate $t_n$ = $na$. The particle ... |
I have been thinking about it for some time and I have found some explanations. However none of them were concrete enough. More specifically, I believe that there should be at least a little current between our bodies and the air but it sounds unsatisfactory as our bodies are capable of detecting very small currents.
N... |
What if a source of white light is within the prism itself. Let's say it emits a thin beam of white light. Now the speed of different wavelengths is different but it is not being refracted at a surface (atleast until it emerges from the other side), so what will happen to it? Will it stay together as white light only? ... |
In a video from MinutePhysics, I heard that the N95 masks use electrets to trap very small particles electrically.
In the case of cloth masks, silk has the property to electrostatically filter particles.
So my question is, does this make silk an electret? If not, what is the difference between the electrostatic propert... |
I am a coder working on something related to robotics recently. This post is to know something I am not sure about the derivation of direct cosine matrix.
I have two reference materials on the hand right now, where the first one is Wiki and another is a book of robotics.
The problem confused me just comes from the defi... |
One could define temperature as follows:
$$T^{-1} = \left(\frac{\partial S}{\partial U}\right)_{N,V}$$
I was reading Schröder, and he says that we can define temperature in another way:
$$T = \left(\frac{\partial U}{\partial S}\right)_{N,V}$$
But, it is understood that
$$\left(\frac{\partial U}{\partial S}\right)_{N,V}... |
While studying the Renormalization Group, we found the interesting result that states "every field theory is an effective theory" (every FT is only valid for energies smaller than a particular scale $\Lambda$), because the renormalization flow always goes towards the IR regime and going in the opposite direction would ... |
The Lorentz transformations can be derived from (a) Principle of Relativity and (2) group axioms. I was looking at the derivation here, and I have problem understanding one specific step. In the derivation one somehow argues that the determinant of the matrix should be $1$. That is done in the following steps, I quote ... |
I read about how spin and magnetism are related (mathematically) but I found that it is a concept related to classical physics which is in turn related to the idea of electrons actually spinning on their axis (which was later found impossible, at least as far as I know) but I wasn't able to find any relation between qu... |
I'm reading about the uncertainty principle formulated in the language of $ C^*$ algebras. It states that for any state $\omega: A \rightarrow \mathbb{C}$ on a $C^*$ algebra and for any self-adjoint $a, b \in A$, we have
$$
\sigma_{\omega}(a)^{2} \sigma_{\omega}(b)^{2} \geq \frac{1}{4} \omega(i[a, b])^{2}
$$
So, what a... |
Bodies can be subjected to pressure drag or friction drag. But let's consider the overall drag coefficient $C_d$.
My question is: $C_d$ is bigger at laminar or turbulent flow?
This image represents the Cd for both blunt and streamlined bodies.
Horizontal Flat plate: My first argument is the velocity gradient is higher... |
When the phrase "in principle" is used to explain a concept in physics, is a philosophical argument being made? If yes, what is the philosophical argument? If no, what is meant by "in principle" and what value does it add when it is used to explain a concept?
Some examples of the use of the phrase "in principle" (highl... |
What is the right way to evaluate a stochastic path-integral of the form:
$$\int \mathcal{D}x \mathcal{D}\tilde{x} \left( \int_0^T \sin(x(t_2)) x(t_2) dt_2 \int_0^T \tilde{x}(t_1) dt_1 \right) e^{-\int \tilde{x}(t_1) G^{-1}(t_1,t_2) x(t_2) dt_1 dt_2}$$
Where $G^{-1} = \delta (t_2 - t_1) \frac{d}{dt_2}$ and $\tilde{x}(... |
I'm having trouble understanding some derivation from Sakurai's QM, chapter 1. To derive $[x,J(dx)]=dx$ he claimed that $dx|x+dx\rangle \simeq dx|x\rangle$ because the approximation is of second order in dx. I don't understand the meaning of this justification...Also, aren't $|x+dx\rangle$ and $|x\rangle$ orthogonal ke... |
I have been doing substantial research into the inner workings of the common household microwave lately, because of a recent discovery in Wuhan, China, where researchers somehow ionized air, then lit it to create a high-temperature plasma using a conventional magnetron, whose emissions were somehow "concentrated" using... |
As far as I know, fermions are the particles which exhibit antisymmetric states: $\hat{P}\left|n_1\right>\otimes\left|n_2\right> = -\left|n_2\right>\otimes\left|n_1\right>$. Often times, we decompose the state $\left|n_1\right>\otimes\left|n_2\right>$ into its spatial and spin parts:
$$\psi(x_1,x_2) \chi_{1,2} = \Psi =... |
What do I need?
What would the most effective method be to reduce the uncertainty of my outcome?
Should I record the mass and diameter of the marble too or just the height?
If I change mass will it be more effective than height change?
|
I'm in my first year as a PhD student and I'm trying to learn about twistors. I found the question about the book recommendations for twistor theory, but it quickly became clear that my knowledge of differential geometry is vague at best. I looked at some recommendations for differential geometry, but either they're to... |
Can you give me any reference about solving 1 D Ising model with open boundary condition, magnetic field and nearest interaction?
|
Related to a research project I am currently doing I am studying Einstein-type Lagrangians, i.e. field Lagrangians which are second order, but whose Euler-Lagrange equations are also second order differential equations.
Consider a generic field $\phi ^i$ of unspecified type in local coordinates where $i=1,...,m$ is an... |
I am new to QM and have a question regarding bra-ket notation and dual vectors.
I have a vector $|\Psi\rangle = |a\rangle + k|b\rangle$, where $k$ is some complex number k = $x + iy$. I want to find the dual vector $\langle\Psi|$. I have some ideas about this but I'm not sure which (if any) is right.
$\langle\Psi|$ = (... |
In the commonly considered spacetimes with singularities, the singularities - to my knowledge - always have less than 3 spatial dimensions:
The singularity of the Schwarzschild spacetime (describing stationary black holes), the Vayidia spacetime (describing radiating spacetime), or the FLRW spacetime (describing the U... |
The electric field produced inside a uniformly polarized sphere
of radius R is equal to:
$$ \bf E = - {\bf P \over \rm 3 \epsilon_0}$$
It doesn't depend on the sphere radius. Does that mean... as long as I have uniformly polarized spheres made of the same dielectric their size won't matter?
But then, if I have two iden... |
I have a general question concerning the description of a Figure, taken from Griffiths' Introduction to Elementary Particles, page 20:
I'm afraid I do not really understand the last part: How is it possible to determine the mass of the particle by looking at the curvature of the track? I mean, the only question that I... |
How does mechanics help prevent the pipes from bursting?
How does it link to the pressure of a pipe?
How does fluid mechanics link to physics when its about the liquid phase of chemical processes?
|
Page no. 291 of Hidden Unity in Nature's Laws by John C. Taylor says the following -
"Take a spherical water drop.
No special direction is picked out by such a drop. If we rotate it
nothing has changed. A spherical ice crystal (assuming it to be a perfect crystal) does define special directions, by the way the molecul... |
In Wess & Bagger, chapter 3, the infinitesimal supersymmetric transformation is defined as: $$ \delta_\xi \psi = i\sqrt{2} \ \sigma^m \bar{\xi}\partial_m A + \sqrt{2} \ \xi F$$ and $$\delta_\xi A = \sqrt{2} \ \xi \psi$$ and an important exercise claims that $$ \delta_\eta \delta_\xi \psi = -2i\eta \sigma^m\bar{\xi}\par... |
I am wondering why classical electromagnetism predicts (classical, wavelike) photons , but classical Newtonian gravity does not predict analogous wave-like solutions (as far as I am aware)?
Stated differently, classical electromagnetism predicts its corresponding force-mediating particle - the photon (albeit as a class... |
I am working on a project to measure the stress in metals so I am looking for a variable that changes directly with stress. I noticed that when hitting a metal (unstressed) (say iron) by another metal (say copper) a sound is generated with a unique wavelength. When I retry the same experiment, but this time applying so... |
I can not find out the right conjugation relation for an oil immersion objective (oil in the object space, air in the image space).
If I send an incident plane wave in air with angle $\alpha_{air}$ with regard to the optical axis, its angle in oil $\alpha_{oil}$ will be smaller because of refraction.
Where will focus t... |
Ok, this is (probably) my last question about this topic. My other two (here and here) had some misguided assumptions, but I think this one is better. (There is probably something else I am neglecting, but I'll give it a shot anyway.)
Set up a rotating apparatus with two toothed wheels, one attached to each end of a ro... |
I don't know how to imagine open sets in Minkowski spacetime. I have seen that there are many diffrent ways of constructing them — that's OK. But for example. which construction do people mean in the case of the Reeh-Schlieder theorem?
In such an example, do I have to imagine balls in 4-dimensional Euclidean spacetime ... |
I've been reading about Galileo's experiment with inclined planes, and he ends up saying something along the lines of "the ratio of distances is equal to the ratio of the times squared"
My initial thought is that, with initial velocity zero. A first distance can be defined as:
$ s_{1} = \frac{1}{2} a t_{1}^2 $
And a se... |
I need this for a programming project:
B is moving on a circular path at constant speed.
Radius, period and theta are given and my program calculates the position at every update.
A is moving on a straight path at constant speed.
Initial position and speed are given.
Based on the given data I would like to be able to ... |
Apparently the distance between galaxies used to be smaller in the distant past. That means it used to take fewer units of time to get from one galaxy to the next. So either the distance really was smaller in the past or the units of time used to be bigger in the past.
Which of the following is true?:
The spatial di... |
When solving the hydrogen atom, to separate the two-particle Time-Independent Schrödinger Equation (TISE) into two separate equations, we make the change of variables:
$$\vec{r}_{CM} = \frac{m_e}{m_e+m_p}\vec{r}_e + \frac{m_p}{m_e+m_p}\vec{r}_p$$
$$\vec{r}_{rel} = \vec{r}_e - \vec{r}_p$$
Where the subscripts $e$ and $p... |
I am looking for a unitary representation $\hat T$ of the following canonical transformation
\begin{align}
q_1&\rightarrow q_2 &p_1&\rightarrow p_2\\
q_2 &\rightarrow -q_1&p_2&\rightarrow -p_1
\end{align}
which is a 90°-rotation in the $(q_1,q_2)$-subspace of a 4-dim phase-space. It is therefore a point-transformation... |
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