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My question is somewhat related to this one. I want to know if
$$ \frac{d}{dk}\left\langle \hat{f}_k \right\rangle_{\psi_k} = \left\langle \frac{d}{dk} \hat{f}_k \right\rangle_{\psi_k} $$
holds for some quantum-number like parameter $k$ and any operator $\hat{f}_k$. I am using the letter $k$ because it might be some va... |
After reading the question and answers in Definition of short range entanglement I wonder why the definition of a short-range entangled state is given in terms of its possible deformations -
A SRE state is a gapped state that can be smoothly deformed into the trivial product state without a phase transition (all the s... |
Knowing Lorentz Transformation and knowing the differential formulation of Maxwell Equations:
Precisely, what is the meaning of the statement: "Maxwell equation are invariant under Lorentz Transformation"?
What do we mean when we say this?
|
In my Physics textbook there is sample problem in which a firecracker placed inside a coconut of mass M, initially at rest on a frictionless floor, blows the coconut into three pieces (A, B and C) that slide across the floor. Mass of piece C is 0.30M and its final velocity is 5.0 m/s. We have to find speed of piece B, ... |
To describe the behavior of a relativistic point-particle, we have the standard action
$$S=\int d\tau \bigg[\frac{1}{e} \dot X^\mu\dot X_\mu +m^2 e\bigg], $$
where $e$ is the worldline einbein. Then, it has been shown arXiv:hep-th/9510021 and arXiv:hep-th/9508136 that do describe a spin-1/2 particle, we must supersymme... |
Basically, what the title says. Is the difference in mass between the sum of the masses of individual nucleons and the nucleus itself the mass of all the force carrying particles I.e. $W$ and $Z$ bosons?
|
Consider a phenomenological modelling of a continuous phase transition, where the Lagrangian of the system is given by
$$L=\frac{a}{2}\phi^2+\frac{\lambda}{4}\phi^4-h\phi.$$
Here $\phi$ is the order parameter, $h$ is the external field, $a=a_0(T-T_c)$, and $a_0>0$ and $\lambda>0$. I have not written the kinetic term he... |
In my experimental particle physics introductory class it was often said that quantum electrodynamics (QED) is very predictive for sufficiently small center of mass energys since the $W^\pm$-propagators are suppressed by the mass of the boson.
I am a beginner in quantum field theory (QFT) so if you spot a misconception... |
Given we observe that light do follows path A (gravitational lensing) instead of path B, is there any direct empirical evidence about how photons and gravity interact, other than stating that photons are massless particles when we observe massless behavior and massive when we observe massive behavior (gravitational len... |
Consider a linearly polarized harmonic plane wave with a scalar amplitude of $A$, propagating along a line in the x-plane at $45^°$ to the $x$-axis with the $xy$-plane as its plane of vibration. We assume that $k_x$ and $k_y$ are both positive. The wave propagates in vacuum.
So first, we know that
$$\vec{E}(\vec{r},t)... |
Let us say we have a square frame of side $a$. We project a magnetic field $B$ perpendicular to the plane of the frame to only one half of the frame.
So in this case to find the induced emf what should be the flux associated with the frame, $B*a^2$ or $B*a^2/2$, i.e., should I consider half the area or the complete one... |
In this paper by Y. Zhang and E-A. Kim, the authors have designed a novel pre-processing step for machine learning topological classification.
The gist of the paper is that the authors compute chained products of correlation functions between the vertices of a triangle generating 'quantum loops'. By this method they'r... |
Let's estimate the size of perturbations in the very early (GUT scale or earlier) universe required for consistency with CMB.
The CMB fractional temperature (and hence density) perturbations are of order $10^{-5}$. Those whose wavelengths are above the Jeans length had been growing, and in a radiation-dominated univers... |
We have a current carrying circular wire kept in uniform magnetic field $\vec{B}$, as shown, I tried to derive the torque $\vec{\tau}$ acting on it
For 2 elemental parts on wire subtending angle $d\theta$ at center right at opposite to each other
$$d\vec{\tau} = 2idl B \sin\theta r$$
it gives
$$\tau = -2i
r^2 \cos \... |
When it comes to measuring the phonon dispersion at the edge of a Brillouin zone, why are neutrons chosen and not photons?
|
I found a similar question but I could not solve my doubt. So, if you consider this question to be a double, I am sorry.
Consider a system $S$ that undergoes a cyclic transformation and the $n$ sources from which it receives heat have temperatures $T_1, T_2... T_n$. Let $Q_i$ be the heat received/given by the $i$-th so... |
I've found the following paradox, and I wonder how to resolve it.
Two discs are floating in space, call them A and B. They are at a fixed distance D, coaxial, and rotate at the same speed. Each of them has a hole near the border.
The position of the hole in disc B lags behind the position of the hole in disc A, by a sm... |
Please show that the derivative of some atomic density $\rho_{I}$ with respect to its nuclear coordinate $R_{I}$ can be expressed in terms of its electronic coordinate $|\textbf{r - R}_I|$
$ \frac{\partial \rho_{I}(|\textbf{r - R}_I|)}{\partial R_{I}} = \frac{\partial \rho_{I}(|\textbf{r - R}_I|)}{\partial |\textbf{r... |
In positronium, the electron and positron can be anti-parallel which gives us a total spin = 0.
And for electron and positron parallel we have a total spin 1.
Is my reasoning correct if i say :
In the case of the hyper-fine structure splitting the state with total spin 0 has lower energy then the one with total spin 1... |
Suppose a particle of negligible mass is placed at e.g. $x=1$ inside a one dimensional space with a force field generated by the gravitational attraction of a point mass at the origin $0$. I.e. the force is (normalized) $$-\frac{ {\rm sgn} (x)} {x^2}.$$
Then after finite time, the particle will move to the origin.
Howe... |
So electric fields are produced due to presence of charged particles and magnetic fields are produced due to motion of charged particles. In DC circuits, a current-carrying wire involves the motion of electrons, which are charged particles, so both magnetic and electric fields are produced. So why is it that only Alter... |
If we consider a theory of GR (the standard Einstein-Hilbert action) and a complex scalar field, we can easily see that we have a global $U(1)$ symmetry for the scalar field. Now, via Noether's theorem we can build a conserved current from which we obtain a conserved charge:
$$Q = \int d^3x \sqrt{-g}\, J^0.$$
The probl... |
Consider a triatomic linear molecule with unequal masses $m_A \neq m_B \neq m_C$ where $m_B$ is in the middle. If the molecule would rotate, the axis of rotation (center of mass) would therefore be somewhere distant from the middle, its distance to each of these masses would be $S_A, S_B$ and $S_C$ respectively.
If the... |
I am currently working through the problem 4.10 in Kotkin and Serbo's book "Collection of Problems in Classical Mechanics". The problem consists in showing that the quantity
\begin{equation}
\frac{\partial L}{\partial \dot{q}_{i}}\left(\dot{q}_{i}X - \Psi_{i}\right) - L X
\end{equation}
is an integral of motion if the ... |
I have some samarium cobalt magnets and I need to estimate the characteristics of the magnetic field they produce. They are spec'd to give 16 lbf of pull against an iron plate. Is it possible to estimate the magnetic field strength as a function of distance from the magnet using that force rating? I also, of course,... |
Relativistic effects become relevant when $v\sim c$.
Quantum effects become relevant when $|\vec{p}|\sim\hbar c$.
But when do gravitational effects become relevant? It cannot be when the typical size of the system is about the size of the Schwarzschild radius $\left(d\sim\frac{GM}{c^2}\right)$—here, we'd be already in ... |
In the Debye model, for temperatures $T \ll T_D \equiv \frac{\hbar\omega_D}{k_B}$, the molar heat capacity $c_V$ can be calculated as follows:
$$c_V = \frac{12\pi^{4}}{5}R \left(\frac{T}{T_D}\right)^3$$
(where $12\pi^{4}/5\approx 234$).
Now if we take the limit $T\rightarrow 0$, we would expect from the Debye-model $c_... |
Suppose we have two rooms A and B that are the same size and connected by an open doorway, so the air has the same pressure and volume in both rooms. This means that
$P_AV_A = P_BV_B$ and $n_AT_A = n_BT_B$.
If room A is warmer than room B then $n_A < n_B$ so room B contains the greater mass of air.
I understand it fr... |
The XY-model on a 2-torus ($L_1,L_2$) has a lagrangian given by
$$
L_{XY}[\theta] = \int d^2 x \frac{\chi}{2}\big{(}\dot{\theta}^2 - (\partial_x \theta)^2\big{)}
$$
Fourier expanding $\theta$ as
$$
\theta (\boldsymbol{x},t) = \theta_0(t) + \frac{2\pi}{L_1}m_1x_1 + \frac{2\pi}{L_2}m_2x_2 + \sum_{\boldsymbol{k}}\lambda_... |
The Bernoulli equation as a statement on the conservation of energy as I understand it is the observation in an idealized flow that the bulk fluid velocity relates to the kinetic energy of the fluid and must therefore increase/decrease to agree with the conservation of energy in the system. The internal energy of stati... |
Given any arbitrary current carrying Line in a plane whose shape is defined by the function y = f(x) which is kept under a non uniform magnetic field vector B now calculate the net torque about the origin on the current line due to the field . neglect any other forces.
I am a total starter when it comes to both physics... |
From what I understand humans has a capacitance and are able to store charge, and we also have a velocity, we know that the magnetic force is $\vec{F}=q\vec{v}\times \vec{B}$.
I assume while we standing on earth we are grounded so no net charge in our body, but what about while we fly in a plane? and what about birds? ... |
From Wikipedia
[...]below, and symmetric in flavor, spin and space put together. With three flavors, the decomposition in flavor is
$$ \mathbf{3} \otimes \mathbf{3} \otimes \mathbf{3} =\mathbf{10}_{S}\oplus \mathbf {8} _{M}\oplus \mathbf {8} _{M}\oplus \mathbf {1} _{A} $$
The decuplet is symmetric in flavor, the singl... |
Recently I saw the case of creating two entangled electrons with opposite spins from the Higgs boson (which has no spin). The electron spins are always opposite to equal zero as a sum - conserving the Higgs zero spin. So we always create opposites. Why would anyone find that remarkable? People have expressed amazement ... |
Lets assume that we have sourceless anisotropic medium with $\epsilon_1 , \epsilon_2,\epsilon_3 $ as the diagonal values. Also assume $\vec{k}=k_z\hat{z}$ and $e^{i \omega t} e^{-i \vec{k} \cdot \vec{r}}$ form.
We have $\vec{k} \cdot \vec{D} = 0 \implies \vec{k} \cdot \underline{\underline{\epsilon}} \vec{E} = 0 \impli... |
How can we prove that the charge is conserved in particle experiment? Or lepton and baryon conservation.
I think it is easy to say that the charge is conserved, but might be hard to measure. I guess in experiment one could not measure a single particle, instead, it should be a beam of particles.
|
A virtual particle is defined to be the internal line in a Feynman diagram which usually mediates force.
I'm wondering if it's a pure relativistic effect? If the system is non-relativistic (quantum mechanics), does it still make sense to talk about virtual particles?
By the way, I'm wondering that if virtual particle i... |
I am currently studying in atom physics the different "ways" you can "produce" spectral splitting of an atom. But because this is new stuff to me, i find most of it a bit complicated and confusing.
So i would really like for someone to be able to give me a detailed explanation ( a summary) of all these cases.(if it is ... |
Cyan (blue light + green light) + red light = white light,
but is the same true for cyan wavelengths ($490-520$ nm) and red wavelengths ($630-700$ nm)?
|
I know Maxwell relation in MKS unit
$$\begin{cases}\nabla\times E=-\frac{\partial B}{\partial t},\\
\nabla \times B = \mu_0 \epsilon_0 \frac{\partial E}{\partial t} + \mu_0J,\\
\nabla\cdot E = \frac{\rho}{\epsilon_0},\\
\nabla\cdot B =0\end{cases}$$
and the derivation of this equation into Gaussian units
$$\begin{cases... |
I'm trying to understand the definition of relativistic phase space given by Rovelli in his book Quantum Gravity. At chapter 3 he states those following definitions
The relativistic phase space $\Gamma$ is the space of relativistic states - p.107;
The relativistic phase space $\Gamma$ is the space of orbits of $d\thet... |
An Nd:YAG laser that has the following properties:
$\lambda=1024$ nm (wavelength)
$d = 5.8 $ µm (spot size)
$\tau=30$ ps (pulse duration)
$E_L=50$ µJ (energy per pulse).
Given any two of the above parameters, can the other two be derived? Or are all 4 independent?
I am asking because in this paper it appears like only ... |
As far as I know, magnetic fields are created by either magnet or running current, which both can be changed by changing the permeability of the medium and thus change the magnetic flux through the coil.
So will there be induced current in a coil in a uniform magnetic field with changing permeability? If yes, what perm... |
For a given metal, light below a certain frequency will not eject an electron. Once the threshold or minimum energy is met to eject an electron, what happens as light frequency increases past the photoelectric work function? Do more and more electrons eject from the metal and thus the metal becomes increasingly positiv... |
Perhaps this has been asked before and perhaps it's rather trivial, but what would an observer on the most distant astronomical object see? Would they see only the CMB in one direction and us in the other direction, or would they see essentially the same thing as us, i.e. a universe of diameter $8.8\times 10^{26}$ m wh... |
I know that several questions on this topic and one with even the same name exists, but I don't think they fully answer my questions. I request you to first hear me out, and then point out any possible duplicates
If I understand this correctly, potential energy is simply potential work "stored"(?) inside a system of $2... |
Near a charged wire a moving electron is deflected. Since the deflection is an acceleration, the electrons emit photons.
What about an electron's radiation, which is affected by an interference grating?
|
In this link about finding equations of motion of cart pole problem,
There is an equation about acceleration of center of mass of the pole.
Screenshots of them below.
I don't understand why they have more than two parts about angular acceleration - $\varepsilon \times r_p$ and $\omega \times (\omega \times r_p)$?
If ... |
The formula for gravitational potential energy,
$$-G\frac{m_1 m_2}{R},$$
is found by using the fact that the change in potential energy is equal to negative of the work done ( by conservative forces). One of the assumptions is that the 2nd larger mass remains stationary relative to each other, and thus only the work do... |
As it is described in standard textbooks I looked at, the Maxwell equations were first established for electromagnetic fields created by electric currents. Then it is stated that it was discovered experimentally (by Kohlrausch and Weber) that the electric constant in these equations equals the speed of light. From that... |
So the actual question is this-
To two plates of parallel plate capacitors, charges $Q_1$ and $Q_2$ are given. The capacity of the
capacitor is C. Then the switch is closed. [assume both $Q_1$, $Q_2$ to be
+ve]
There were options to this problem but that's not the part of my question.
Once the switch is closed, the po... |
I know that in the standard train tunnel paradox, the train shrinks in the tunnel frame and the tunnel shrinks in the train frame. Paradox is resolved by the fact that even though both doors of tunnel close simultaneously in tunnel frame, the further door closes first in the train frame.
Now, suppose we consider a sce... |
I am doing a PhD in AdS/CMT. In order to have a better understating of the physics of the systems the correspondence aims to describe, I am looking for accessible reviews or online seminars about the mostly commonly used experimental techniques for probing strongly coupled materials such as the cuprates in their strang... |
I currently worked on a type of modified Tolman-Oppenheimer-Volkoff (TOV) equation. Usually people have this equation from a static spherically symmetric metric that has this form:
$$
ds^2= -C(r) dt^2+\frac{dr^2}{1-2Gm(r)/r}+r^2(d\theta^2+\sin^2\theta d\varphi^2).
$$
From what I understand from the textbooks, e.g. Spac... |
I have a doubt concerning a scenario of Doppler Effect wherein the source and observer are on the same relative frame.
A car is moving towards a stationary observer with speed 10 m/s. The horn has a frequency of 640 Hz. What is the frequency of the horn as heard by the driver?
The answer given to this states that dri... |
I started studying Weyl physics in condensed matters, but I got confusing about the difference between the Weyl point and Weyl node. I understood that when the Weyl points connect continuously, the Weyl node is created. Is it right?
In addition, is there any difference about the condition to realize Weyl point and node... |
On this Wikipedia page you can find the following equation for free fields
$$:\phi(x)\chi(y):=\phi(x)\chi(y)-\langle0| \phi(x)\chi(y)|0\rangle\tag{1}$$
But I don't understand where this comes from while it seems a very fundamental equation. I tried understanding it by switching the terms:
$$\langle0| \phi(x)\chi(y)|0\r... |
I have a cube, with a side of 50. The only point is that the top of the cube doesn't exist.
What I have in mind was that because the cube is homogeneous then the x and y part of the center of mass are definitely at 25cm and 25 cm. Then I had a hypothesis and it was that because it has 6 sides, and 1 side doesn't exist... |
This part from University Physics turned my world upside down. What is the difference between ions, free electrons, and excess charge? Also, ions and free electrons make up a neutral conductor? Bloody how?
In practical problems we often encounter situations in which we want to know the electric field caused by a charg... |
I found myself tired of by searching what is the exact definition of magnetic moment.
I have also come across two formulas for same quantity
$\vec{M} = \vec{m} \times \vec{d}$
where $\vec{M}$ is the magnetic moment, $\vec{m}$ is the magnetic pole strength and $\vec{d}$ is the distance between two poles
Another formula
... |
In the context of defect conformal field theory, we consider in operator product expansions "local excitations" of the defect (see e.g. text between eq. $(1.1)$ and $(1.2)$ in the paper Defects in Conformal Field Theories). But what is a local excitation of an extended operator?
For example consider the Maldacena-Wilso... |
If you take two capacitors, one with capacitance C and the other with 2C, and charge them to voltages V and 2V volts, assuming CV = Q, they'd have charges Q and 4Q.
Now when these two are connected in parallel with oppositely charged plates connected, charge flow takes place till terminal potentials are equal. I assume... |
I'm trying to learn friction (only - nothing else - just skin friction) on a surface as it moves through water. I'm hoping to find a working formula, including all necessary units, in terms of wetted area, viscosity, and velocity (while, along the way, absorbing the subject well).
More than twice now, I've encountered... |
While reading about some new (now older technology), it said that vacuum tubes could run on electron field emission rather than photoionization. https://spectrum.ieee.org/semiconductors/devices/introducing-the-vacuum-transistor-a-device-made-of-nothing
It is some interesting stuff. In reading wikipedia (I know it's cre... |
I was taught that the potential decreases in direction of electric field but when we place a positive charge in between it's electric field is too in that same direction but the negative charge has exactly opposite direction of electric field to the parent electric field....so why is it opposite?
|
I am referring to the book 'Semiconductor Physics and Devices' by Donald A. Neaman.
Chapter 4.4.1 says that
"Each donor level has two possible spin orientations for the donor electron; thus each donor level has two quantum states. The insertion of an electron into one quantum state, however, precludes putting an electr... |
The Gubser-Klebanov-Polyakov-Witten (GKPW) prescription relates the partition function of a CFT to that of a bulk theory of quantum gravity. Since the CFT partition function is fixed, does that mean that there's only one consistent theory of quantum gravity with all the bulk fields and the action fixed?
|
Okay, I really have three questions, but I can only post once every 40 minutes and they’re all related.
Say I have a balloon with the inside supported by a collapsible frame and made from a very strong substance. When you make it not in it’s collapsed position, it would become a vacuum inside. Since that’s lighter tha... |
Given a path integral for a system
$$Z(\phi) = \int [D\phi] e^{-S[\phi]},$$
where I am working in the Euclidean signature, necessarily mean that the system described is quantum mechanical? In the equation above, I am looking at $(d+1)$ dimensional field theories, such that $d=0$ Feynman path integral is standard quantu... |
Because the presence of pressure in all directions also demands the presence of random thermal motions. And then in the presence of random thermal motions how do you define a streamline? I mean how can you merge the two(a random motion and a steady motion) to explain the net result? What does the velocity at a point in... |
I'm studying from these lecture notes by S. Pascoli. She mentions several times the leptonic flavour problem but she never actually defines it. I've looked a bit online but I only found vague expression of the problem. So I ask you,
What is the flavour problem?
In particular, what is the leptonic flavour problem?
As ... |
Why is it that the field configuration that minimizes the Higgs potential is said to be a constant one (meaning $\phi(x) = \phi_0$)? Is it a physical reasoning, which kind of makes sense, since a non flat ground state of the field would be rather strange? Or is it a mathematical reasoning that the field configuration w... |
I don't understand the following statement: Any pair of Dirac spinors verifies $(\bar{\Psi}_1\Psi_2)^\dagger=\bar{\Psi}_2\Psi_1$ and it is valid for both commuting and anti-commuting (Grassmann-valued) components.
In the case of Grassmanian number, shouldn't I add an extra sign when I flip them? Is there anything else ... |
It is well known result that Photon BEC was achieved in slightly curved cavity, because curved mirrors provide trapping potential (https://www.nature.com/articles/nature09567).
We can see that this is possible from the following dispersion relation for energy:
$$ E(r, k_{||}) = \hbar c \sqrt{k_z+k_{||}^2} =\hbar c \sq... |
This was a claim made by my professor in my mechanical metallurgy class. I don't see how it is true. I could very well have a solid (which is incompressible) and have isotropic properties. We deal with such types of materials every day.
I have no idea as to how to even begin approaching this problem.
Any help would be ... |
Is there any way to compute the Legendre Transformation of a Hamiltonian which is linear in momentum, for example, a crazy Hamiltonian like
$$H(q,p) = \alpha p q + m\omega q^2 .$$
This function is convex (and also concave) in $p$, which is a sufficient condition for the Legendre transformation to work (as far as I know... |
Why is there an upper bound to the frequency at which an electronic device can be operated? For example, the frequency of electricity that we receive at home is 60Hz (in the USA).
What will happen if we increase the frequency?
Is there any relation between speed of the device and its operating frequency? For example, ... |
Let's suppose there are two electrons in a potential box. The Schrödinger's equation of a system includes a factor representing electric potential of their interaction. How is it computed? Do we have to integrate over a square of an amplitude of all the wave function values for one electron to get a potential it genera... |
Suppose there is a $N$ body hamiltonian, suppose $N=2$ for simplicity:
$$
H = - \frac{1}{2} \nabla_1^2 - \frac{1}{2} \nabla_2^2 + V(r_1,r_2) + \frac{1}{|r_1 - r_2|}.
$$
If we make a measurement for position (for example that $r_2 = x_2$) and the particles are in the state $\psi$ (which is a stationary state), then the ... |
In Newtonian mechanics the expression for the velocity of the center of momentum frame is $v_{CM}=\frac{\sum_i m_i v_i}{\sum_i m_i}$, where $v_i$ is the velocity of the particle $i$ in the lab frame.
Is there any expression similar to this one in special relativity?
|
The standard treatment is that once we measure a spin along the z-direction, it will be aligned with +1 or -1 spin along the z-direction.
Then, when we measure it again along the z-direction, it has a 100% chance of showing the same spin as it did last time. On the other hand, if we measure it along the x-direction, it... |
The data gathered led physicists and astronomers to the conclusion that the universe is accelerating its expansion and therefore to theories about dark energy. My question is, could certian constants like plank's constant and the G, the universal constant of gravitation, and perhaps other so called constants that have... |
So, I was reading Schutz First Course in General Relativity and in chapter 5 is states that " If SR is to be valid in a gravitational field, it is natural guess to assume that laboratory frame at rest on Earth is a Lorentz frame." I am not able to get why is it so?
Then, it goes on to show that from Pound-Rebka-Snider ... |
In this paper by Alba Cervera-Lierta the following transformation is performed:
$$
a_k=u_kc_k+iv_kc^\dagger_{-k} \\
a^\dagger_k=u_kc^\dagger_k-iv_kc_{-k}
$$
where $c_k$ and $a_k$ represent annihilation fermionic operators and $u_k$, $v_k$ are mere constants. According to the article, the gate (or matrix) that perform... |
Say you had a broad spectrum white LED (all visible wavelengths) and you wanted to make a RGB LED (just red-green-blue wavelengths) that could produce white light of equal brightness to the broad-spec one.
Would you need the wavelengths in the RGB LED to be of a higher intensity than the wavelengths in the broad-spec L... |
Given this image, $2$ objects are connected via a spring (its mass is negligible)
The spring constant is $k$ and that is all that is given.. mass of $A$ is just $m_A$ etc.. and $g \approx 9.8 \frac{m}{s^2}$ (on Earth)
I need to find the maximum displacement ("stretching") of the spring ($L$)
I tried to draw the force... |
So, as soon as star radius becomes smaller that Schwarzschild radius it becomes a black hole. But as matter continues to fall on it attracted by the gravitational pull its radius sooner or later will exceed Schwarzschild radius and it will become a visible heavy object again. This oscillation in/out of black hole state... |
When a Galilean transformation on a quantum system is performed, the states and the operators change:
$$|\phi\rangle \rightarrow |\phi\rangle'$$
$$\hat A \rightarrow \hat A'$$
I don't understand the interpretation of the transformed objects. What confuses me is that both the state and the operator change. Maybe my inte... |
I'm self-studying Friedman and Susskind's Special Relativity and Classical Field Theory.
They define a general Lorentz transformation (which keeps the origin fixed) to be a Lorentz boost in $x$-direction composed with some spatial rotation(s). I've proved myself that such a general Lorentz transformation $L$ (leaving o... |
Penrose explained that a trapped surface is a region of spacetime where the null expansion $\theta$ is always negative. A black hole is therefore a trapped surface that cannot communicate with null infinity.
On the other hand, Hawking's area theorem says that the expansion $\theta$ is strictly non-negative on the horiz... |
I'm studying Friedman and Susskind's Special Relativity and Classical Field Theory and follow them in using $c=1$.
They derive the above relation by first using Lagrangian of a free particle $\mathcal L=-m\sqrt{1-v^2}$ to show that conjugate momenta are given by $P^i = mU^i$ (where $U^\mu$ is the 4-velocity). Then they... |
One can naturally think of the vielbein $e_\mu^a$ as a gauge field corresponding to local translation invariance. Moreover, the metric may be written
$$g_{\mu\nu}=e_\mu^a e_\nu^b \eta_{ab}.$$
I have always seen the graviton $h$ given by
$$g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}.$$
Obviously, the graviton is the gauge field... |
The Einstein Equivalence Principle states that in a sufficiently small frame of reference is impossible to know if we are into a gravitational field or not. Equivalently we cannot say if we are in an accelerating frame or not. This is because gravity and inertia are equivalent (hence the name of the principle).
So beca... |
The geodesic equations of a 2-sphere are the following:
$$\ddot\theta - \sin\theta \cos\theta\dot\phi = 0$$
$$\ddot\phi + 2\cot(\theta)\dot\theta \dot\phi = 0$$
For $\theta$=$\pi$/2, $\phi(s)$=a$s$+b. In order to avoid solving the differential equations, I was trying to do an axis rotation of the equatorial solution, b... |
The width decay $\Gamma$ is the probability per time of a decay and the more accessible states there are in a decay, the more $\Gamma$ grows. Are these accessible states the decay's channels, or the states of phase space at a given energy related to the kinematics of the process, so $\rho(E_f)=\frac{dn}{dE_f}$?
|
I was considering the statistical lifetimes of various light bulbs at first. However, upon further reading it seems that they tend to be approximately Weibull distributed with a shape parameter $k \approx 4,$ not $k=1$ (the latter being required for them to coincide with the exponential distribution).
A great example w... |
I may be flat-out wrong here, but it seems to me there is a very common misunderstanding of what the double slit experiment results mean, at least by non-physicists, because of the way it is often explained.
The experiment shows that photons behave differently, as particle or waves, depending on how we choose to observ... |
My professor in his lectures has stated that a consequence of Einstein Equivalence Principle (EEP) alone is that light bends in a gravitational field.
The proof went as follow: Imagine to be a free falling observer (so an inertial observer in GR by definition) in a box, and imagine to shoot a beam of light through a ho... |
In this lecture, around 44:00
https://youtu.be/KU94cMZif8Y?t=2635
The lecturer mentioned quickly that the 2nd neutrino (of muon) results in a Nobel prize earlier than the 1st neutrino (of electron's).
Puzzle: Could some experts please explain why and how the research results happened? Naively
the 2nd neutrino (of muon... |
Since quantum entangled particles can transfer the data of their spin properties faster than the speed of light and without any problem of weak signal, can we use quantum entanglement to transfer phone calls and internet connection? Why are we not building up a telecommunication structure based on this technology? What... |
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