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Near equilibrium the potential of a typical steel spring is well approximated by a quadratic function. I'm having trouble finding a reference for the what is the next-to-leading order contribution, and its magnitude, for typical spring-steel springs. For example if I want to predict the period of a mass on a spring for... |
I'm asken to compute $\left(\frac{\partial G}{\partial p}\right)_{S,N}$.
I start using the definition of dG:
$$dG=-SdT+Vdp+\mu dN$$
$$dG=-\left(\frac{\partial G}{\partial T}\right)_{p,N}dT+\left(\frac{\partial G}{\partial p}\right)_{T,N}dp+\left(\frac{\partial G}{\partial N}\right)_{T,p}dN$$
If we want to compute the d... |
Can low energy electron-proton collision produce neutrons (and neutrinos)? I asked many of my physics teachers but they said that it would produce hydrogen atoms instead. Some explained this because of strong interactions and some explained using weak nuclear interactions, but actually i didn't understand anything. Why... |
If we assume that the Sun is at rest in an inertial reference frame, the total mechanical energy ( $E$ ) of the Sun and the orbiting body is constant and equal to the sum of the kinetic energy ( $\mathcal K$ ) and the gravitational potential energy ( $\mathcal U$ ).
Is there a mathematical-physical explanation, for stu... |
An inertial observer in a two dimensional Minkowski space $(t,x)$ is located at the origin with four-velocity $U^{\mu}=\begin{bmatrix}1\\0\end{bmatrix}$. If a photon is detected by the Observer, its energy can be calculated using the scalar product as follows:
\begin{equation}
\eta_{\mu\nu}U^{\mu}p^{\nu}=-\hbar\omega,
... |
Some context:
Let us consider a spinless charged massive particle of mass $m$, charge $q$ in an electrostatic potential $V(x) = \frac{m}{2q}\omega^2x^2$.
The corresponding stationary Klein-Gordon equation is then:
$$
\left(-\dfrac{\partial^2}{\partial x^2} + m^2\right)\phi(x) = (E-qV(x))^2\phi(x)
$$
One may right it in... |
Earlier I asked this question on the Math Exchange but I'm looking for a physics point of view. How do you interpret an equation like $$x^n \delta(x) = 0, \qquad n\in \mathbb{N},$$ around $x=0$? Why does it suffice to show the integral of this expression is zero around the singularity to show the equality is valid? The... |
I'm trying to solve the magnetostatic problem of a magnetized sphere using the expansion of $\frac{1}{|\textbf{r}-\textbf{r}'|}$ in terms of Legrendre polynomials. For simplicity I assume $\textbf{M}\left(\textbf{r}\right)=M_{S}\hat{z}$
inside the sphere and $0$ outside, or in spherical coordinates
\begin{equation}
\le... |
In my general relativity course, we are discussing infinitesimal diffeomorphisms defined by $x^{\mu}\rightarrow y^{\mu}(x) = x^{\mu} + \xi^{\mu}(x)$. We have been examining how different objects transform under this. For example, the metric transformation $g_{\mu\nu}(x)dx^{\mu}dx^{\nu} \rightarrow g_{\mu\nu}(y) dy^\mu ... |
Is there a standard way for me to isolate 2 of N bands of a general $N\times N$ Hamiltonian? That is, I want to make a $2\times 2$ Hamiltonian given a larger one. I was told that there is a general method called downfolding for effective Hamiltonians in condensed matter physics, but to my understanding, these project o... |
How can sine waves be used to describe both alternating current and sound waves? In the case of alternating current, the zero crossing represents zero current, and the waveform below the zero crossing represents current with opposite polarity. What does the zero crossing represent in sound waves? Silence? When repr... |
I'm trying to figure out how the sum of two spin 1/2 operators along an arbitrary direction would work.
These operators are of the form
\begin{equation}
\textbf{S}_j \cdot \hat{\textbf{n}}_j = \frac{\hbar}{2} \begin{pmatrix}
\cos (\theta_j) & e^{-i \varphi_j} \sin (\theta_j)\\
e^{i \varphi_j} \sin (\theta_j) & -\cos (\... |
We draw FD diagram on a paper which is essentially a $2$-$d$ space and then use perturbative Feynman rules to write the algebraic expression of the perturbative term. I want to ask if drawing it on a cylinder, a torus(problem of CTC), sphere, or any other curved surface will make some change in interpreting the FD.
I u... |
Take an earth-star and a spaceship frame. The spaceship is heading at near the speed of light towards the star from the earth. Now let's say that in the earth-star frame, there are three events
the event that the spaceship passes the earth
the event that the spaceship is destroyed by the exploding star
the event that ... |
I was doing the problem described in the following question:
A $0.250\ \mathrm{kg}$ block of cheese lies on the floor of a $900\ \mathrm{kg}$ elevator cab that is being pulled upward by a cable through distance $d_1=2.40\ \mathrm{m}$ and then through distance $d_2= 10.5\ \mathrm{m}$. (a) Through $d_1$, if the normal f... |
I just heard about the photonic propulsion and it looks like light may have a mass ! Which is known by the name of "relative mass".
The question is way too generic but here are more precision:
How could you amplify the relative mass of a laser beam?
How could you calculate the relative mass before and after the amplif... |
Let's just say we have the Earth-Moon system isolated in space, with Earth at rest, and the moon orbiting it.
How can we calculate the total energy of Earth in such a case (Kinetic energy would be effectively negligible I'm assuming, hence only potential energy would be taken into account?)?
We can calculate the Energy... |
I've previously asked a question on here about if it was possible to change the barion number by radioactive decay, for example positron emission, and the answer was of course no, as the baryon number rmains consistent. I've also talked about this problem with some friends, and one of them came up with a process to tur... |
For single spin 1/2 particle, we can use three Pauli matrices as generators to do rotation on Bloch sphere to get any state we want in the Hilbert space.
However, for spin greater than 1/2, I try to use three SU(2) generators to do rotation, and I can not find a rotation which rotates $S_z$ to $S_z-1$ states (for examp... |
This is very basic physics but I'm a little stumped. We're working on 2 dimensional collisions in our lab class, and we have a video of two pucks colliding against each other. After working out before and after kinetic energy, we know that the collision is highly inelastic, as it loses 58% of its initial kinetic energy... |
I've read that everything from fire to LEDs can produce UV radiation. Generally, unless intended otherwise, lightbulbs will have a phosphor coating to prevent UV radiation from escaping the bulb. Although this technically creates a light source that emits a low amount of UV rays, I'm wondering if there exists any possi... |
According to standard electromagnetic theory, if the charge A is stationary and the charge B is moving along arbitrary trajectory then the electromagnetic force on charge A is:
\begin{equation}\vec{F}_A = q_A \left(-\nabla\phi - \frac{\partial}{\partial t}\vec{A}\right)\end{equation}
where $\phi$ and $\vec{A}$ are velo... |
i don't even clue about this question. this is the third example of book which is taking on school but I don't even get it.
can anyone solve and explain the idea here? i need to understand this.
|
I have the following homework assignment:
A spaceship is stationary at the r-coordinate 10M outside a black hole of mass M. The spaceship contains a lab which is measuring the properties of the accretion disk which surrounds the black hole. What is the speed of the particles orbiting in the disk as measured in situ?
... |
Considering the action for induced gravity:
$$S=\int d^4x\sqrt{-g}\left(\epsilon\phi^2 R-\frac{1}{2}(\partial\phi)^2+V(\phi)\right).$$
I was trying to get the metric field equations by doing the usual procedure and for the $\delta(\phi^2 \epsilon R)$ term, using the Leibniz rule twice, I got this:
$$ \delta(\phi^2\epsi... |
I have just read Einstein's famous formula, Energy-mass Equation, that is
$$E=mc^2$$
Or As Einstein wrote it
$$m=\frac{E}{c^2}$$
Now I have learned that any energy of the particle like potential or kinetic energy, actually causes an increase in the mass of the particle. For instance, Suppose I have a moving clock and a... |
What role if any does electronegativity have in superconductors.
Most of the elements used in superconductors on the periodic table are at the low end of electronegativity and I was wondering if there is any correlation?
|
Which of the above setups would have the strongest attraction to a steel plate? You can assume the magnets are secured to a non magnetic structure. My intuition says that A (non alternating) would be stronger, but I don't know enough about magnets to confirm that. I know that the magnets would prefer to be alternating... |
This is a picture of the data of a given measurement by an oscilloscope. I would like to know what the difference between horizontal units and horizontal scale at an oscilloscope is. I would be so so grateful if someone could shed some light on it! :)
|
This is a question on mathematics rather than the physics. It is based on QFT Q3.4, part b on Peskin and Schroeder.
My confusion stems from the fact that we are consider $\chi(x)$ to be a classical anticommuting field,that takes Grassmann numbers as their values and satisfy the following relation:
$$\alpha \beta = -\al... |
How do we calculate the entropy and the enthalpy of compression of R-143a from 1.5 MPa to 5 MPa at 383.15 K giving the following information:
At 1.5 to 5 Mpa and 353.15 to 403.15 K, the compound 1,1,1-trifluoroethane (Refrigerant R-143a) follows the equation of state:
|
If I were to take a photograph of a bullet in mid-air I wouldn't be able to tell which way the bullet is moving. However, the bullet has the property of momentum which is a vector which decides the direction in which it moves.
When I take a photo of a wave though, for example, a rope wave, I also can't tell which way t... |
I have this really basic (probably silly) question about Lorentz transformation on integrals that I couldn't understand:
So I read on Peskin that the Lorentz invariant measure is $$\int \frac{d^3p}{(2\pi)^3}\frac{1}{2E_p} = \int \frac{d^4p}{(2\pi)^4}(2\pi)\delta(p^2-m^2).$$ And I have a few things that I don't understa... |
Here we are talking about the mutual force between the two balloons. This is in the context of Newton's law of gravity (so electrostatics etc. are ignored). You can assume that the cocktail party is held in a room that contains air. It is not necessary to assume that the Earth's gravitational field is present, but if i... |
Light are made of waves in the electromagnetic field, so I wonder what is the shape of that wave. I mean what would be the EM field surrounding a photon in a particular instant?
[Edit]
Or alternatively, how is the (electromagnetic) energy of the photon distributed in space? This would be equivalent to consider a energy... |
On the German Wikipedia page, we can read: "The higher the azimuthal quantum number $\ell$ for a fixed principal quantum number $n$, the more the average distance of the electron from the nucleus increases." Can someone explain to me why this is correct?
I thought that the average distance should decrease for increasin... |
Tghere are a lot of different papers about STU supergravity, for example see this.
As I understand, STU supergravity is N = 2 supergravity coupled
to three vector multiplets.
Could someone explain, what is the meaning of abbreviations "STU"?
Which properties of such theory motivate study it"s? Is such theory special in... |
Let me be a little silly and suppose that when "God" created our Universe - he had these 3 options:
(Most classical): let the energy (contained in any particle = field excitation) spread evenly among all points of it's wave function (like probability actually does; interference included) and without collapse.
There's... |
This site already has several questions about how airplanes fly. Some of the answers do give useful insights, but the only real explanation I've found involves using a computer to solve the Navier-Stokes equations with a no-slip boundary condition (ref 1). By "real explanation," I mean one that actually predicts the am... |
We often talk about chaos, but is chaos an objective term or a subjective term? If it's an objective term, is there a mathematical way to determine it? Is it possible there's a threshold where something is neither chaotic or in a state of order?
|
Is there an analog of the Jordan-Wigner transformation between fermion algebra on a circle and a Pauli algebra? For example, the continuum analog of bosonization of "compact boson $\leftrightarrow$ Dirac fermion" there's an analog of the bosonization map, say on a Euclidean cylinder.
As a reminder, the compact boson is... |
Basically the title. I am wondering if there is a relationship between the two, and if so, what is it?
|
A quasi-symmetry of an action $S$ is a transformation of the fields that leaves the action invariant up to a boundary term (see e.g. the answer to this question). In contrast, let us call a transformation of the fields that leaves the action invariant without producing a boundary term a strict symmetry.
Under which con... |
I have Started reading Hamilton's Principle or Principle of Least Action In first course of Undergraduate classical mechanics.
So, I think it becomes easier to apply the Variational principles if forces can be expressed as generalized potentials.
So my first question was,
$ Is\ it\ possible\ to\ express\ all\ Fundament... |
In quantum mechanics, we know that the spin 1/2 matrices are:
$$S_x = \frac{\hbar}{2} \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix},
\quad S_y = \frac{\hbar}{2} \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix},
\quad S_z = \frac{\hbar}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$$
While I am pretty sure I understand... |
Suppose we have three vectors $\textbf{A}$, $\textbf{B}$ and $\textbf{C}$. If $\textbf{A}\cdot\textbf{C}=\textbf{B}\cdot\textbf{C}$, does that mean that $\textbf{A}$ must be equal to $\textbf{B}$? If so, can this property be proven?
Though the question is mainly mathematical, it has occurred to me a number of times whe... |
In QFT yesterday we were talking about Higgs/SSB and mass terms in Lagrangian. Our professor wrote down some lagrangians
and asked us to explain certain things and also if it is for massive or massless field. One of them was this
Lagrangian (not a realistic one I think)
$\mathcal{L} = \frac{1}{2} (\partial_\mu \phi )^2... |
I have read about the experiment of Torricelli, he filled a tube with mercury and placed it standing in a basin filled with mercury, then mercury poured out into the basin from the tube. He concluded that a vacuum was created.
The problem is I don't think that there is enough evidence to reach this conclusion. Maybe so... |
I have a cylindrical permanent magnet with uniform magnetization $\mathbf{M}=\mathbf{a_z}M$, length $L$ and Diameter $D$.
I'm wondering why the $\mathbf{B}$-field created by this uniform magnetization has no $\phi$-component, that is, the field lines don't "circulate" in the magnet.
The field only has a $r$-component ... |
First Let me write both the laws So Newton's law says that
$$\mathbf{F}=m\mathbf{a}$$
and least action principle says that a particle occupy, at the instants $t_1$ and $t_2$, positions defined by two sets of values of the co-ordinates, $q^{(1)}$ and $q^{(2)}$. Then the condition is that the system moves between these p... |
In the following expression of Lagrangian in General Relativity :
$$S=\int d^{4} x \sqrt{-g}\left(\frac{R}{16 \pi G}+\mathcal{L}_{\mathrm{M}}\right)$$
I understand that we can write for example :
$$c\,dt\,dx\,dy\,dz = \text{det}(J)\,c\,dt\,dr\,d\theta\,d\phi=\text{det}(J)\,d^4x$$
with $J$ the Jacobian between $(ct,x,y,... |
I was reading the rutherford experiment of the $\alpha$ particles. where we conclude that the positive charge and mass are concentrated in the center of atoms. while concluding the above result we use the charge and mass of the $\alpha$ particle.
I am still wondering when we don't know about the nucleus size(before the... |
I understand that the group velocity is computed by $d\omega/dk$. Given the relationship between the wavelength of a waveguide and its frequency:
$$\lambda=\frac{c}{\sqrt{\nu^2-\nu^2_0}}$$
where $c$ is the speed of light.
How can I find an expression of the group velocity without knowing the dispersion formula? Is the ... |
Consider the time-periodical Hamiltonian $H(t)=H(t+T)$. In the Floquet theorem, the Schrödinger equation has a solution of the form
\begin{align}
|\psi_\alpha(t)\rangle=e^{-i\epsilon_\alpha t}|\phi_\alpha(t)\rangle,
\end{align}
where $|\phi_\alpha(t)\rangle=|\phi_\alpha(t+T)\rangle$. This Floquet eigenstates satisfy
\b... |
Why does "lasing" occour with the longitudinal modes of the cavity, that is, why does the longitudinal modes govern the spectral properties of a laser?
|
From my understanding, the mean squared speed are given by the following expressions:
$\langle v^2 \rangle = \langle v_x^2 \rangle + \langle v_y^2 \rangle + \langle v_z^2 \rangle $
$\langle v^2 \rangle= \langle v_x^2 + v_y^2 + v_z^2 \rangle$
However, I couldn't figure the expression for the mean speed of $\langle v \ra... |
So I keep hearing people talking about how physics break down at for example the center of a black hole. And maybe I am just to stupid but, why? How can we say that? For all we know a black hole could just be a very dense sphere. Kind of like a neutron star where are all the atoms sort of combine to become a single obj... |
Consider it has zero orbital angular momentum, what is the total angular momentum?
what I thought is since orbital angular momentum is $0$, what left is the spin angular momentum, which is $\hbar/2$ or $-\hbar/2$, but I'm not sure about that.
|
Does a filament lamp still have resistance when no current flows?
|
Form a textbook i am learning for its says:
All valid wave functions (energy eigenfunction with definite energy and superposition states with simultaneously multiple energies) for a given quantum system satisfy the Time dependent Schrodinger equation.
However only the spatial parts $u(x)$ of energy eigenfunction [defin... |
So, I just saw this Youtube video by Veritasium that discusses how it's impossible to measure the one-way speed of light from a light source to a detector, since it's impossible to synchronize clocks in a fashion that would prevent a directional difference in the speed of light from altering clock speeds via relativist... |
Hello I am trying to find the fourier transform of a plane wave of the form $$\psi(x) = \frac {1}{\sqrt{2\pi \hbar}}\exp\left(\frac {i}{\hbar}p_0 x\right)$$ where $p_0$ is fixed and Real
I've worked through this far:
$$(Ff)(p) = \frac {1}{\sqrt{2\pi \hbar}} \int_{-\infty}^\infty dx \frac {1}{\sqrt{2\pi \hbar}}\exp\left... |
Strip is made of polyethylene and is cold drawn so that all polymer chains are oriented in one direction. Now, if heat is supplied to it via external source then how much will this strip contract. Is there a general formula or any article which contains this data for some other similar material?
|
In one of my assignments for GR there is a question as follows:
Consider the equation
$$A^{\alpha}_{\mu \nu}B^{\mu \nu} = C^{\alpha}$$
where B is a second rank anti-symmetric tensor and C is a vector.
From this I am able to prove that $$(A^{\alpha}_{\mu \nu} - A^{\alpha}_{\nu \mu})$$ is a tensor.
But can I say anything... |
I have a cylindrical permanent magnet with uniform magnetization $\mathbf{M}=\mathbf{a_z}M$, length $L$ and Diameter $D$. The magnet has its center in the origin. So there is a length $L/2$ on each side of the $xy$-plane.
In an example in my book featuring this scenario, the author states:
"As a consequence of $\disp... |
I was fiddling with my little sister's magnets just now and noticed that if I stuck one pole to a coin I can add a couple of coins/paperclips successively to make a chain, which doesn't really happen if there was no magnet
1)First of all, why does this happen?
2)Does the amount of links I can make depend on the magnet ... |
We know that we can obtain AdS$_2\times S^2$ by considering the near horizon limit of extremal RN black holes in $4d$ with various asymptotics, i.e., either Minkowski$_4$, or (A)dS$_4$. How about the effective geometry which appears in the near horizon limit of non-extremal charged black holes? I know that, in general,... |
While watching YouTube, I came across the following popular video:
Why no one has measured the speed of light
It appears to say that speed of light could depend on direction it is traveling and we would never know.
I was under the impression that the Michelson-Morley experiment was intended to verify that very assumpti... |
$$\begin{pmatrix}
1& 0 & 0 & 0\\
0& \cos\theta & \sin\theta &0 \\
0& -\sin\theta & \cos\theta &0 \\
0 & 0 & 0 &1
\end{pmatrix}$$
See this matrix, it represents a rotation in the xy plane for the Lorentz transformation.
I am a little confused, is impression mine or it is a rotation measure as clockwise positi... |
Due to the nature of the Heisenberg uncertainty principle along with the Schrodinger equation, the position of a particle gains uncertainty / loses certainty over time, because its momentum is also uncertain.
If you know the wave function of a particle at time t0, and reevaluate it at a later time t1, have you gained o... |
When we choose a coordinate system any two perpendicular lines may be chosen as $X$ and $Y$ axes. However, once $X$ and $Y$ axes are chosen, there are two possible choices of $Z$-axis. The $Z$-axis must be perpendicular to the $X-Y$ plane. But the positive direction of $Z$-axis may be defined in two ways. We choose th... |
static friction is:
Ff = mu * Fn
So it means, it is just a multiple of the Fn force vector. How is it possible that its always shown in the illustrations in a different direction than the Fn vector?
|
Van der Waal equation: $$(p + aN^2/V^2)(V - bN) = nRT. $$
I am trying to get $(\frac{\partial p}{\partial T})_{V}$ and $(\frac{\partial V}{\partial T})_{p}$.
what I have done:
$(\frac{\partial p}{\partial T})_{V} = \frac{NR}{V - bN}$
$(\frac{\partial V}{\partial T})_{P} = \frac{NR}{p + \frac{aN^2}{V^2}}$
I feel like I ... |
Reading the book on Supergravity from Freedman & van Proeyen I was very bewildered by the so called cyclic identity of $\gamma$-matrices of the Clifford-algebra(eq. 3.67) important in string theory:
$$(\gamma_\mu)_{\alpha(\beta} (\gamma^\mu)_{\gamma\delta)} = 0 $$
(the round brackets indicate a symmetrisation operation... |
According to Penrose's Conformal Cyclic Cosmology (CCC), there were universes prior to ours, prior to the singularity of our universe.
But how is this claim compatible with his famous singularity theorem, according to which spacetime geodesics cannot be extended beyond a singularity?
I believe Penrose doesn't deny the ... |
Following is a small derivation just so I can explain my question. The gravitational potential energy is:
$$(*)U_g = -\frac{GMm}{r}$$
And:
$$ \Delta U =-GMm(\frac{1}{r_{final}} - \frac{1}{r_{initial}}) $$
If some mass $m$ is taken a height $h$ above the ground, we get:
$$ \Delta U =-GMm(\frac{1}{R+h} - \frac{1}{R}) = \... |
I recently asked a question here relating to what it means if we saw "Physics break down". Thus i had a strong look into Black Holes. Or at least some Articles about them. And i couldnt help but ask, could the concept of a Singularity be bs ?
The Idea
Ok so from what i understand, if you fell into a Black Hole, a few t... |
Suppose we have a time-dependent canonical transformation - say generated by a function of the type $F_2(q,P,t)$. The resulting Kamiltonian picks up an extra partial $\partial F_2/\partial t$:
\begin{align}
K= H(Q,P,t)+\frac{\partial F_2}{\partial t}\, .
\end{align}
If we are instead given not the generating function... |
I am trying to implement reflecting boundary conditions of
$
\begin{align}
\psi_N \equiv \psi_{N-1},
\end{align}
$
$
\begin{align}
\psi_{-1} \equiv \psi_0,
\end{align}
$
to the hamiltonian matrix and then trying to find the 101 lowest energy eigen values. I am using a dimensionless schroedinger equation so $\hbar = 1$ ... |
I was thinking and I have this question,
entangled pairs of particles collapse at the same time. Knowing this, could we measure the one way speed of light by having 2 entangled particles, one at the base where the clock is located and one at the end of a tube. At the end of the tube we also place some kind of device th... |
Wikipedia gives the magnetic flux densities of current loops. The magnetic flux density of two infinitly long conductors look the same, but I am not sure about the numeric accuracy of the value of the field. What is the equation for the field, given the current I and the distance of the conductors a?
|
When I heat up a room, this is basically both an isobaric and isochoric process. Since air can be thought of as an ideal gas, the equation of state $pV = NkT$ and thus $NkT$ is also constant. Because the energy of air can be expressed as $E = \frac32 NkT$, $E$ is also constant. How come that heating up the room works i... |
Following a course in dynamical systems I am studying a mass spring damper system. In the particular case it is a cart constrained to a fixed point by a spring whose oscillation is damped by a damper b.
If I understand correctly the resulting position graph is the following (and input):
My question is: why is there a... |
Consider a Lagrangian $L(q, \dot{q}, t)$ for a single particle. The variation of the Lagrangian is given by:
$$\delta L= \frac{\partial L}{\partial q}\delta q + \frac{\partial L}{\partial \dot q}\delta \dot q\tag1$$
When using Hamilton's Principle ($\delta S = 0$):
$$\delta S = \delta \left[ \int L(q, \dot q, t) dt \ri... |
In classical mechanics we talk about Lagrangian, but when we talk about fields (in example- electromagnetic fields), we consider the Lagrangian density instead of "just" the Lagrangian.
I didn't understand why?
In addition I didn't understand the differences between the relativistic Lagrangian formalism and classical L... |
I'm trying to understand the basics of the formalism of Feynman diagrams describing interactions in QED and below I present two examples where I still don’t understand the logic behind them:
Image 1 (found here,
picture 6.8):
Image 2 (found here;
see first image in Jay Wacker's answer):
I learned that both degrees of... |
Are there other equations can be derived from $E = mc^2$?
If mass and energy is interchangeable, does it mean that any other equation that uses mass can be modified by energy/$c^2$? What other equations can be derived from this simple equation in Physics?
|
In a Yang-Mills theory where the fermion fields transform under $\Psi \rightarrow e^{-\theta^A t_A} \Psi$ with $t_A$ generators of a Lie-algebra fulfilling $[t_A,t_B]=f^A_{BC}t_C$ a Noether current $J_{\mu A}$ of the following form can be assigned to the Dirac-equation $(i\not\partial - m)\Psi = 0$:
$$J^\mu_A = -\over... |
Consider a Lagrangian $\mathcal{L}$ which is function of, for example, some vector fields $A^\mu$ and tensor fields $B^{\mu\nu}$. That is,
\begin{align}
\mathcal{L}=\mathcal{L}(A^\mu, B^{\mu\nu})
\end{align}
Then I would like to ask that is it possible to derive from such $\mathcal{L}$ different equations of motion whi... |
Looking at a few problems that are prefaced by Suppose a particle of mass m moves under the influence of a force field along a space curve whose position vector is given by a function r with x, y, z components.
I got v and a, and then did the Fdr integral to get the work, but on a few I'm getting negative work. Should ... |
(This is taken from Introduction to Quantum Mechanics by D. Griffiths, 3rd edition, Problem 6.18 .)
If a system has inverse symmetry, we know that [$\hat{H},\hat{\Pi}] =0$ where $\hat{\Pi}$ is the parity operator.
This means that eigenstates of the parity operator are eigenstates of $\hat{H}$. Namely:
$f(x) = \frac{1}... |
I was lightly tickled by Veritasium video Why no one has measured the speed of light in which the author says that a one-way measurement of speed of light is impossible (or, rather, that $c$ could vary depending on direction).
So riddle me this:
You have a mirror (M), light source (LS) and light detector (LD) at a cert... |
Using the von Neumann entropy definition, the pure states have zero entropy and we have the full information about the system. My understanding is that the whole universe should be in a pure state and unitarily evolves.
But in Page Curve, which describes the entropy change during black hole evaporation, the entropy inc... |
Let's say we have some set of spin matrices based on total angular momentum $j = 1$. We have 2 matrices of importance to consider:
$$ J_x = \frac{\hbar}{\sqrt{2}} \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}, J_z = \hbar \begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{pmatrix}$$
Assume th... |
The first law of thermodynamics states that energy is conserved. $\Delta U = Q - W$ (internal energy change is the difference between external energy supplied and work done on the environment).
The second law of thermodynamics states that entropy is never decreasing and is only constant in reversible thermodynamic proc... |
We're familliar with talking about stimulated emission using energy and time domains (e.g. Wikipedia's Stimulated emission) but what about spatially?
My naive guess is that since the stimulating electric field of an incident plane wave is zero in the incident direction, the stimulated transition in the quantum system (... |
I am reading Peskin and Schroeder's chapter on functional methods. They propose the amplitude:
$$
\langle \phi_b(\vec{x})|e^{-iHT}| \phi_a(\vec{x})\rangle
=
\int \mathcal{D}\phi\mathcal{D}\pi
\exp \bigg[
i\int_0^T \left(
\pi \dot\phi - \frac{1}{2}\pi^2 - \frac{1}{2} (\nabla\phi)^2-V(\phi)
\right) \bigg]
$$
They th... |
Consider a Killing vector $\chi^\mu$ with the Killing Horizon $\Sigma$. From Carroll's book (pg 245), along the Killing horizon, the Killing vector obeys the geodesic equation
$$\chi^\mu\,\nabla_\mu\,\chi^\nu = -\kappa\,\chi^\nu$$
where the right-hand side is non-zero because the integral curves of the Killing vector $... |
My understanding of what's said in the Veritasium video Why no one has measured the speed of light suggests that the one-way speed of light has not been measured and that it being isotropic has not been experimentally verified.
Wouldn't passing a pulsed beam through two identical but widely separated population inversi... |
In a video by Sabine Hossenfelder, it is mentioned that in an expanding universe, energy is not conserved. The reason for this is that there is no time translation symmetry, an experiment performed at one time will not necessarily give the same result as an otherwise identical performed at another time, so Noether's th... |
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