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If you have a gas, you can insert a bit of energy $E$ and measure the resulting increase $K$ in the average kinetic energy in your favourite direction. For monatonic gases, $K=E/3$, as the energy is evenly distributed in each translational direction (the "equipartition theorem"). We can plot the ratio
$$C\ =\ \... |
I am reading about Nordstrom's second theory of gravity and have become confused. On the wikipedia page and elsewhere it is said that the theory is completely captured by its equations for the Ricci Scalar ($R=24\pi T$) and the vanishing of the Weyl tensor ($C_\text{abcd}=0$). But according to the Ricci decomposition d... |
I am recently studying the triangle scenario in the context of Bell nonlocality (for reference, see for instance this article). In it, we have three parties, commonly referred to as Alice, Bob and Charlie, with each pair sharing a source.
In the article cited above, they say that observed statistics are quantum compati... |
The most famous instance of this trick is probably in the case of finding the surface charge distribution of a charged conducting disc, where this disc can be perceived as a squashed down version of a charged conducting sphere (which we know to be uniformly charged).
For the disc, we know that the charge of a ring at a... |
I would like to make the computations of twilight sky in mag/arcsec2 based on the solar depression and brightness.
So far I found a nice article about it:
https://articles.adsabs.harvard.edu//full/1966SvA.....9..840D/0000842.000.html
where the following formulas can be found:
In the first one, I don't understand the a... |
According to Wikipedia,
The pressure exerted by the collisions of the N gas particles with the surface can then be found by adding the force contribution of every particle and dividing by the interior surface area of the volume
I have doubt about the multiplication by $N$. It seems to suggest that those $N$ particle... |
I want to derive the Dirac massless equation in curved spacetime from the action. I have the symmetric form of the Dirac action:
$$S = \frac{1}{2} \int \bigg[i\bar{\psi} \gamma^\mu D_\mu \psi - i D_\mu \bar{\psi} \gamma^\mu \psi \bigg] \sqrt{-g} d^4 x$$
where $D_\mu \bar{\psi}= \partial_\mu + \frac{i}{4} \omega_{\mu a ... |
How much the idea of calculating Euclidean path integrals in LQCD is fundamentally tied to using formulations based on the discretized spacetime lattice?
In computational approaches to quantum many-body physics relying on real-time Hamiltonian formulations (quantum chemistry, low-energy nuclear physics, light-front qua... |
In a white dwarf, the star is prevented from collapsing due to the Pauli exclusion principle. If the star is heavy enough, the protons in the star will capture electrons, forming neutrons and bypassing the exclusion principle for electrons. The exclusion principle can come into effect again with the neutrons, forming a... |
When I am learning about phonons, it is taught that acoustic phonons necessarily have $\omega=0$ at $k=0$. while optical phonons have a finite $\omega$ at $k=0$.
But I am confused about two things:
For the acoustic mode, $k=0$ means all lattice points oscillate in phase. But still, they are oscillating so each lattice... |
How can I calculate the time derivative of an electric field from its space derivative? That is, I know $\frac{dV}{dx}$, and I need $\frac{dV}{dt}$. In general, $\frac{dV}{dt}$ = $\frac{dV}{dx} \times \frac{dx}{dt}$. However, $\frac{dx}{dt}$ is the speed of the propagation of the field. According to Newton, it is infin... |
The total power of a powered drill is 850 watts (the rated value written on the drill's casing) and the current at the supply voltage of 230 volts is 3.7 amperes according to the formula $I = P/U$. Calculate the mechanical power.
Now, we keep in mind that the drill produces mechanical AND heat energy. Thus the total po... |
I have read this question (unfortunately this mentions supernova and not black hole):
If it it the latter, then the instabilities that lead to the collapse of a neutron star would begin near the centre of the star at the highest densities.
Collapse timescales go as the free-fall timescale, which is ∝(Gρ)−1/2
where ρ
i... |
The decay products for a muon are an electron, a muon neutrino, and a electron antineutrino. As the decay products for a neutron (electron, proton, neutrino) can combine together to form a neutron again, would it be possible to generate muons using electrons and neutrinos as long as they have sufficient energy?
|
lets say I have an electron moving towards an oppositely charged plate.
Perpendicular to the electrical force vector, exists a magnetic field.
How would I calculate the force on the electron?
Like such?
$$F=qE+q(\int \frac{qE}{m}dt\times B)$$
acceleration of a charge in an electric field is equal to the following.
$$a=... |
I am reading this paper about quantization of the electromagnetic field, and there is a point where the author imposes the fundamental commutation relation between the vector potential and its canonical momentum:
$$[A_i(\mathbf r,t), p_i(\mathbf r',t)] = \frac{i\hbar}{4V}\sum_{\mathbf k}{(2e^{i\mathbf k\cdot(\mathbf r-... |
I would like some clarification around how the Stern-Gerlach filter functions for a single atom.
Consider an SG filter oriented in the $z$ direction with the "down" states blocked, followed by an SG filter oriented in the $x$ direction with both paths open (neither state blocked). Now I understand that if we send "many... |
Consider a rope kept on a surface as shown. The ends of the rope are free.
The FBD of this rope given in the book is shown in the following diagram:
Now, consider the Tension forces at points P,Q and R,
, according to FBD ,the tension forces at these points aren't getting cancelled (vectorially adding upto zero). Bu... |
I am trying to understand the meaning of the "n-particle distribution function" as defined by the three references below([1][2][3]), primarily those by Claudio Zannoni.
Setup: For a system with N classical cylindrical particles each with a location described by $ \textbf{r} _i = \langle r_{i,x},r_{i,y}, r_{i,z} \rangle... |
In the rigid rotor approach we obtain the result that the spacing between different rotational energy levels in a particular vibrational state is $\nu = 2B(J+1)$ and $ B = \frac{ h }{ 8 \pi^2 Ic }$, where $I$ is the moment of inertia and $c$ speed of light.
It seems counter intuitive to me why the energy levels would b... |
It's widely believed that in convential BCS superconductors, only after taking the retardation effect into consideration the weak attractive interaction mediated by phonons can overwhelm the strong Coulomb interaction, which can be modeled by Eliashberg theory. However, though experimental facts like the isotope effec... |
I'm a noob in physics & math, so I'm just looking for a scientific answer for a small fiction project.
My question is : How far can we realistically go in space, if we managed to "use" energy in the best way possible ?
I don't want to take any huge assumptions in technology / science fiction, other than the ability to ... |
This question has been asked a few times here in a few different ways but the answers don't quite seem to land for me. Considering the virtual particle pair; one falls in, one escapes, both become real. Okay.
But then my best understanding is that the escaping particle effectively "borrows" energy from the black hole's... |
A hydrogen atom weighs 13.6eV less than a proton + electron. This missing energy, which is tiny compared to the rest mass of almost a GeV, was carried off by a photon when the atom formed.
Nuclei show a much more pronounced mass defect and can be "missing" up to 1% of their mass.
But the opposite is the case for the qu... |
Why does the beam splitter create superposition ? Ok, in a double slit you have 2 holes in a wall, and thus there are 2 ways through which the particle to go. But in a beam splitter where are those 2 holes ? So my question is: at the molecular/atomic level, what is there in the beam splitter that makes it act as 2 hole... |
I studied about quantum confinement for a presentation on Quantum Well, wire and dots and came across a term 'Quantum Confinement', it said quantum confinement leads to discrete in energy level. And confinement occurs when the de-Broglie wavelength matches the dimension of the confined space. The thing I don't understa... |
I am currently studying antennas and I am trying to understand how to solve the following vector equation $$\nabla^2A+k^2A=-\mu J$$ in the case when there is a point current source at the origin.
The notes I'm following proceed to define the current density as:
$$J = \delta(x)\delta(y)\delta(z)\hat{a}$$ which I totally... |
I'm reading Hawking's book "Briefer History of Time" both in Ukrainian and Russian languages and found a possible translation mistake in this paragraph (last page of "Chapter 6. CURVED SPACE"):
This prediction was tested in 1962, using a pair of very accurate
clocks mounted at the top and bottom of a water tower. The ... |
I was reading about the entropic uncertainty principle, but there is something that is confusing me.
Suppose we have a state $\rho_{AB}$ for a state that belongs to the product of
two Hilbert spaces, that we can identify as Alice's part of the system and the Bob one's.
Now, supposing Alice performs a measurement with o... |
It is envisaged that ,in the future ,Universe can end in a big freeze, where there will be no energy gradient. It is also theorised that Universe was isothermal(with some irregularities I guess) in the beginning.
Also , CMB is almost constant in every direction suggesting almost same temperature in every direction.
How... |
From my understanding, when an object is heated, there is an increase in the average kinetic energy of the molecules of the object. So if the temperature increases the average kinetic energy increases. Consider a molecule in this object. Now kinetic energy of this molecule is proportional to the square of magnitude of ... |
Everywhere I read about the quantum Zeno effect, the phrase used is: <"immediately" after the measurement, the system remains in the observed state>. What does "immediately" mean ? 1 nanosecond ? 1 second ? 1 year ? Why is this phrased even used instead of stating exactly the amount of time that the system remains in t... |
At the limit $\hbar\rightarrow 0$, all "quantum" should tend to "classical", but why is the quantum commutator $[\hat{x},\hat{p}]=i\hbar$ at $\hbar\rightarrow 0$ equal to $0$, but the classical Poisson bracket is $\{x,p\}=1$? Why does it seem that $[\hat{x},\hat{p}]=i\hbar$ does not match with $\{x,p\}=1$ in the classi... |
I have read on papers that argued, when flying, we have constant spin velocities $\omega_x, \omega_y, \omega_z$, that primarily depend on the initial spin setting e.g., topspin, bottom spin and sidespin.
Taking the following coordinate setting. Then topspin and bottom spin affect the spin velocity $\omega_w$, and sides... |
During a course I came across a formula for the quantum effective action of a Yang-Mills theory in euclidean space and it appears like this (some indices may be dropped but I hope that won't be a problem):
$$\Gamma(A) = \frac{1}{2g^2}S(A) + \frac{1}{2}\log\det(-\nabla^2_A\cdot\delta_{\mu\nu}-2i\mathrm{ad}(F_{\mu\nu})\c... |
I am studying quantum field theory and gauge theory, and I am confused about how to take the second-order gauge covariant derivative of a field.
(1) The first way is to write the second order gauge covariant derivative as:
$$
D_\mu D^\mu \phi = (\partial_\mu + i g A_\mu)(\partial^\mu - i g A^{* \mu}) \phi
$$
where $D_\... |
I'm having trouble to solve this problem. In the book Analytics Mechanics, Nivaldo Lemos define two equations:
Equation (8.207):
$$ H' = H + \sum_{m=1}^M U_m\phi_m $$
Equation (8.208):
$$ \Phi_a = \sum_{m=1}^M V_m^{(a)}\phi_m $$
I'm not sure of how to prove that $H'$ and $\Phi_a$ are first-class functions. I know I... |
I'm trying to understand what the parameters in the PMNS matrix mean exactly. For the two neutrino case the single parameter is a fairly intuitive rotation between basis vectors, however the 3 angles + CP phase in the full PMNS matrix is harder for me to understand.
I have also read that particular experiments are sens... |
I am studying the thermal history of the universe and I encountered the definition of effective degrees of freedom $g_{*}(T)$ defined as
$$g_{*}(T)=\sum_{Bosons}g_{B}(\frac{T_{B}}{T})^{4}+\frac{7}{8}\sum_{Fermions}g_{F}(\frac{T_{F}}{T})^{4}$$
Now, in the computation of this factor, we need to consider just relativistic... |
Consider the following quantum two-point function (without assuming radial time ordering),
$$\begin{align}
\langle 0 | \hat{T}(y)\hat{T}(z) |0 \rangle
& = \sum_{n,m}y^{-(m+2)}z^{-(n+2)}\langle 0 | L_m L_n |0\rangle \\
& = \sum_{n\leq -2}\sum_{m\geq 2}y^{-(m+2)}z^{-(n+2)}\langle 0 | L_m L_n |0\rangle \\
... |
I'm coding a program to calculate electronic bandstructures using the Slater-Koster formalism (I am aware that such programs exist already- this is a pedagogical exercise). I notice that the $p-p$ hopping elements can be written as the $\alpha\beta$ component of the matrix
$$
\begin{equation}
V_{pp\sigma}\hat{1} + (V_{... |
I'm reviewing the famous Casimir effect. I'm uploading an image with the starting setup and frame of reference.
The electric field field operator is:
where $\textbf{e}$ is the polarization vector, $\vec{k} = (k_x,k_y,k_z)$ is the wave vector, $\omega_k = c|\vec{k}|$, V is the volume we are considering that is $V = L^... |
I am unsure as to write the resistivity tensor in the most general form in 3 dimensions. Using the following equation. Please can someone explain?
$$\vec{E}=\frac{1}{ne}(\vec{j}\times\vec{B})+\frac{m}{ne^2\tau}\vec{j}$$
|
If we take the first law of thermodynamics:
$$ΔQ = ΔU+ΔW$$
And we consider a system of a ball falling from height $h$ in an Earth-like gravitational field(no air drag and $h$<<$Rₑ$)
$$ΔU = mgh$$ and $$ΔW = -mgh$$
therefore ΔQ = 0 and the process must be adiabatic.
I think I am going wrong somewhere as this means that ... |
If a parallel water wave (water wave with straight wavefronts) is incident on a gap, diffraction happens. However, how much diffraction happens depends on the relative size of the gap to the wavelength of the water wave. The idea is, that a lot of diffraction happens (water wave spreads a lot) when the size of the gap ... |
Background: Equation of Motion
Okay. First I want to see if my "Newtonian Mechanics" lens of the problem is correct.
Let the particle's path be given by $\vec{r}(t) = (x(t), y(t))$ and just as in figure 1, WLOG, assume that the path lies in the first quadrant; according to figure 1, we identify the following forces on... |
Are these the only forces acting on the body. I assumed the COM to be somewhere there in between. since the tension in main string doesnt perfectly coincide with COM theres a small torque being generated which is being balanced by the string on the other side.
If some other force was applied anywhere else say point A... |
I have seen several papers and reports in which the Point Spread Function (PSF) of a microscope is calculated and measured. In particular, as far as I understand, a light point source is placed in the specimen's plane along the focal axis of the objective (i.e. in the objective's focal point), and the light intensity d... |
I am completing a computational project where I am simulating the Ising model using Monte Carlo methods, namely the Metropolis-Hastings algorithm, and the Wolff algorithm.
For the Metropolis-Hastings approach, I found the phase transition in the magnetisation of a cubic lattice with periodic boundary conditions for thr... |
I tried to find the induced charge on two grounded conducting spherical shells due to a charge place in between them. Using method of images, I get a diverging series for the total induced charge on the outer shell, yet we know that physically that induced charge must be finite. Furthermore, by abusing some notations a... |
I've been trying to learn how to multiply two tensors in order to go from
$$g_{\mu\nu} dr^\mu dr^\nu$$
to
$$c^{2}\,dt^2-dx^2-dy^3-dz^2$$
But I can't figure it out.
$g_{\mu\nu}$ is a $4\times4$ matrix, and after the tensor multiplication you get a scalar.
Can someone explain all the steps to me?
|
I see that there are some references in the post PE on the Gribov ambiguity.
However, resolution of this ambiguity, as stated in wiki, is to find the fundamental modular region (FMR).
I looked into the wikipedia page dealing with fundamental domains of modular groups. However, it does not seem to focus on the non-Abeli... |
In order to simulate higher harmonic generation (HHG) using the strong field approximation (SFA), we need to calculate vector potential $\textbf{A}$ from the electric field $\textbf{E}=E_{0}f(t)\cos(i\omega_{c}t+\phi_0) \textbf{e}_x$, where $\omega_{c}$ is the center wavelength of this pulse, $\phi_0$ is a global phase... |
In transmission cables, why does power loss increase when length of conductor is increased? According to the formulas V=IR and P=I²R, When we increase the length, the resistance increases, while the potential difference is same, the power loss decreases as current decreases. So why does the increase in length of wire, ... |
I have been studying an emission mechanism that exploits the ionization, disassociation and subsequent fluorescent recombination of nitrogen molecule by a femtosecond laser for velocimetry.
The literature suggests that the femtosecond laser promotes the ‘tunnel ionization’ of the nitrogen molecule rather than the disas... |
As an example, consider a continuous charge distribution, within Maxwell's model of classical electrodynamics, that is brought from infinity onto a spherical surface at a radius $r$ from the origin. This is held in place by a 'massless' surface providing the necessary Poincare forces. Is it physically consistent to say... |
Can the Kerr metric be used as an exterior solution to analyse the vacuum outside a rotating solid body or does it only apply to a rotating black hole? If it can't, is there an alternative exterior solution that can be used for a solid body? I note that the exterior Schwarzschild solution is identical to the black hole... |
When an elevator decelerates when it approaches the chosen floor (going upwards), the net force is downwards and that is why it decelerates. If the net force is downwards, then why does it not fall downwards? Why does it simply decelerate? Can someone please explain the forces involved in elevators in detail so that I ... |
I do not understand why refractive index of air,when nearly equal to 1,is proportional to the pressure of the air.
If anybody can provide an answer with proper resource from which I can study on the matter,do help me.
|
Suppose I have a Muon in a potential well. Its wavefunction is a solution of the Dirac equation, a relativistic version of the Schrodinger equation for spin 1/2 particles.
Because the particle is "moving" it should have longer half-life than a free muon. But how much longer?
Suppose I use the momentum operator to compu... |
Suppose a object having mass 10kg and surface area of 2cm² and another other object having same mass and surface area of 4cm². What is the pressure required to lift the object? Which one will need more force to lift the object and how surface area relates in term of lifting the object?
|
I am reading the Srednicki's quantum field theory book and stuck at some statement. In the book p.46, the author worte that :
"Now consider modifying the lagrangian of our theory by including external force acting on the particle:
$$H(p,q) \to H(p,q) - f(t)q(t) -h(t)p(t), \tag{6.15}$$
where $f(t)$ and $h(t)$ are speci... |
Can anyone provide me a simple context in quantum mechanics where the $6j$-symbol plays a role? I wish to understand the physical meaning of the $6j$-symbol so such a context will be helpful.
|
I am looking at a derivation for the electromagtic diffusion equation. It starts with Maxwells equations for the magneto-quasi-static case ($\frac{\partial \vec{D}}{\partial t} = 0$).
$$
\begin{align}
\nabla \times \vec{H} &= \vec{J} \tag{1} \\
\nabla \times \vec{E} &= -\frac{\partial \vec{B}}{\partial t} \tag{2}... |
I have been asked to calculate the time taken for a highly conducting hollow sphere to cool down from a certain temperature say $\theta_1$ to a temperature $\theta_2$ ($\theta_1, \theta_2 > \theta_s$) where $\theta_s$ is the surrounding temperature. We are given the inner and outer surface area, which implies it has a ... |
in class we where asked to position a mass (a wooden object on a wood surface) in two ways, so that we have a case where the area of contact with the surface is larger than the initial positioning and then asked if both mass will start moving at the same angle regardless ,knowing that object is at rest in the y di... |
Background
Imagine simple wave equation, say of a string fixed at both ends, in this form:
$$ρ y_{tt} = \frac{T}{A}y_{xx}$$
Or with an added velocity damping term like:
$$ρ y_{tt} = \frac{T}{A}y_{xx} - B y_t$$
$ρ$ is density, $T$ is tension, $A$ is cross sectional area. Subscripts of $x$ and $t$ are derivatives of posi... |
To explain my question lets consider this example:
The wavelength of light in a medium is $\lambda=\lambda_{0}/\mu$, where $\lambda_{0}$ is the wavelength in vacuum. A beam of red light ($\lambda_{0}=720$ nm) enters into water. The wavelength in water is $\lambda=\lambda_{0}/\mu = 540$ nm, assuming $\mu = 4/3$ for wat... |
It seems from the BRST transformation rules that the ghost fields should be dimensionless:
For eg. in the Abelian case in 4D:
$$A_{\mu} \to A_{\mu} + d_{\mu}c.$$
Then the ghost Lagrangian density $\bar{c}d_{\mu}D^{\mu}c$ is of mass-dimension $2$. That's not a top form. How is it well defined then?
|
If I understand it correctly, due to diffusion and something like a concentration gradient, a gate layer is formed at the PN junction (at P there is more space=holes, at N there are a lot of packed electrons). This overflow of electrons from N to P is then inhibited by the emerging electric field — equilibrium is reach... |
My understanding of real physical theory of electromagnetism goes like this:
The Maxwell equations can be used to derive the speed of light;
$$\nabla\cdot\textbf{E}=0$$
$$\nabla\cdot\textbf{B}=0$$
$$\nabla\times\textbf{E}=-\frac{\partial\textbf{B}}{\partial t}$$
$$\nabla\times\textbf{B}=\mu_0\epsilon_0\frac{\partial\te... |
I was studying a very simplified intro to Spectroscopy.
The following diagram shows the emission spectra of Hydrogen Gas:
Credit: NASA, ESA, and L. Hustak (STScI)
My Question: In the spectra, the brightness of the red light is shown as maximum. Doesn't the brightness correspond to the energy emitted by the electron wh... |
Firstly, we solve the Einstein field equations to obtain the metric tensor. After that, we solve the geodesic equations to obtain the geodesics. Is it like this? What is the brief description of solving the Einstein field equations?
|
Consider the Hamiltonian of two spinning particles in a magnetic field with $$H = \vec{B}\cdot\vec{\mu}$$ where $$\vec{\mu} = \alpha \vec{L}_1+\beta\vec{L}_2$$
Now I wish to compute its partition function given by
$$Z = \text{Tr}(e^{-\beta H})$$ Since, the trace would involve tracing over states $|\alpha, jm\rangle$, s... |
Could a black hole be ripped apart if it passed directly between two other black holes that were millions of times bigger?
|
In Shankar's Principle of Quantum Mechanics, Section 10.1, part The Direct Product Revisited (he calls tensor products direct products), he attempts to show that a two-particle state space is the tensor product of two one-particle state space. He begins by letting $\Omega^{(1)}_1$ be an operator on the state space $\Bb... |
Consider the action of the operator $a_k a_l^\dagger$ on the vacuum state $$|{\rm vac}\rangle\equiv |0,0,\ldots,0\rangle,$$ the action of $a_l^\dagger$ surely creates one particle in the $l$th state. But next, when $a_k$ acts on the vacuum, since there was no particle in the $k$th state to start with, it should annihil... |
I do not understand how to take the time derivative of the following Hamiltonian $\hat{H}(t) = \frac{\hat{p}^2}{2m} + \frac{1}{2}m\omega^2(\hat{x}-a(t))^2$, where $a(t) = v_0t$. For instance how does $\hat{p}$ change when taking the time derivative of it? And the same for $\hat{x}$.
|
In the context of Boltzmann's distribution, Schroeder states that an average is defined as
$$\bar{x}=\frac1Z\sum_sx(s)e^{-\beta E(s)}$$
Where $\beta=1/kT$ and E(s) is the energy corresponding to the state ${s}$
Then he states:
One nice feature of average values is that they are additive; for example, the
average total... |
This is very similar to this question, with the main difference being that it doesn't assume that $\vec v=\mathbf0$.
Assume that you have a rolling and sliding sphere with radius and mass 1 with a uniform density of 1, on a frictionless surface with linear velocity $\vec v$ and angular velocity $\vec\omega$.
At time $t... |
I'm currently working on classical mechanics and I am stuck in a part of the derivation of the lagrange equation with generalized coordinates. I just cant figure it out and don't know if it's just basic mathematics or a physics assumption. I hope someone can explain this step to me. I don't understand the transition fr... |
Betaplus: an upquark emits a $W^+$-boson which turns it into a downquark and then decays into a positron and electron neutrino.
Electron capture: an upquark emits a $W^+$-boson which is absorbed by a shell-electron, turning both the upquark into a down and the electron into an electron neutrino. Or the other way around... |
I have a question about the direction of kinetic friction in the following situations:
(1) A wheel is being accelerated ($\Delta \omega>0$) in the air, then it is let on the ground and starts rolling with slipping.
(2) A car is being accelerated ($\Delta v>0$) so that its wheels start slipping.
In both situations: will... |
In a lecture we were taught how the angular momentum operator $\vec{L}$ acts as the generator of rotations in quantum mechanics, which are defined using the following equation:
$R_u(\alpha)=\hat{1}-(i/\hbar) \alpha\vec{L}\vec{u}$
Where $u$ is the rotational axis direction and $\alpha$ is the angle of rotation.
I though... |
When a particle moves in a circle, linear displacement in one complete rotation equals to the circumference of the circle where as the displacement of the particle is actually zero as it comes back to its initial position,
how can linear displacement being a displacement gives two different values,
pl clarify this conf... |
Let's take two small masses from the rod, $dm$ each. One from the point $A$ and another from the point $B$. Now both the masses would have two forces acting on it i.e. tension and $(dm)g$.
From applying second law of motion on each of the masses we will get this same equation:
$dm(a_{tangential})=(dm)g sin\theta$
But... |
Is the square modulus of the cross product between two vectors $\vec{v_1}$ and $\vec{v_2}$ ,i.e., $(\vec{v_1}\times\vec{v_2})^2$, a Lorentz invariant or not? The result of a cross product between two vectors is again a vector but is its square modulus a Lorentz invariant or not?
|
Roy Kerr recently wrote a paper critical of the Penrose singularity theorem. One interpretation of his paper is that the singularity problem might be an artifact of the Schwarzchild metric and that a singularity would not be inevitable in a Kerr metric. Might that mean nature abhors the Schwarzchild metric, i.e., a bla... |
In Introduction to electrodynamics David J. Griffiths 4th edition, section 6.4.2 in magnetization of ferromagnets, after we reach the saturation point (point b in the image)
Now suppose you reduce the current. Instead of retracing the path back to
M = 0, there is only a partial return to randomly oriented domains; M d... |
I am supposed to find the field at a point $P$ in a hole, I initially thought that since the field inside is $0$ initally, now it must be $GM/R^2$ but that is not so, since we cannot assume it to behave a like a point object now, to find the field, one way is to calculate field due to all infinitesimal small parts of t... |
I'm attempting to recreate some plots from this paper on neutrino opacity calculations for interacting matter at supra-nuclear densities. Namely, I'm trying to write a Python script to perform the integration in Eqn. $(15)$, so as to obtain Fig. 3. Eqn. $(15)$ gives the absorption mean free path as:
$$\frac{\sigma(E_1)... |
Here's a thought experiment about the way that heat is transferred through radiation.
Humans can physically feel when a hot object radiates heat on them, such as a campfire or an infrared-based space heater. But can humans feel cold objects the same way?
Say that a scientist is working in a research station in the Sout... |
Consider a particle moving freely, where $\vec{r}(t)$ is the position of the particle. Suppose I move into a frame with
$$\vec{r}' =\vec{r} + \epsilon \vec{F}(\vec{r}, t)\tag{1},$$ where $\epsilon$ is an infinitesimal variation and $\vec{F}(\vec{r}, t)$ is an arbitrary function (e.g. $\vec{F}(\vec{r}, t) = 1 \vec{u}$ ... |
In the paper Analyticity in Spin in Conformal Theories Simon defines the double discontinuity as the commutator squared in (2.15):
$$\text{dDisc}\mathcal{G}\left(\rho,\overline{\rho}\right)=\left\langle \left[O_{2}\left(-1\right),O_{3}\left(-\rho\right)\right]\left[O_{1}\left(1\right),O_{4}\left(\rho\right)\right]\righ... |
Sorry for the length, but this is driving me crazy. And yes, there are other questions on this issue and I have reviewed them, but I cannot see the answer stated simply. What is different about my question is this conundrum - either the end of entanglement can be detected remotely (in which case, faster than light co... |
I'm learning about NMR spectroscopy and I don't understand why saturation occurs when the populations of the higher and lower energy levels of spin are equal. Why wouldn't energy continue to be absorbed until all the spins are in the higher energy level - why is no more energy absorbed once equal numbers are in both en... |
I'm currently reading Andrew Strominger's Lectures on the Infrared Structure of Gravity and Gauge Theory. While I love the reference, the discussion on the gravitational memory effect feels a bit short, and I'd like to dive deeper into it. What are some references, preferably accessible through the internet, that discu... |
I just worked through the derivations of the Yukawa interaction for scalar and spin one particles (i.e. Peskin and Schroeder, end of chapter 4, which covers the tree-level Feynman diagram). It's very satisfying to see that the sign of the interaction is uniquely determined, but I don't feel like doing this calculation ... |
I have a question about the definition temperature, given by $\frac{\partial S}{\partial E}(E,V,N) = \frac{1}{T}$
Is this valid only for isolated systems (and not applicable, for instance, to a (small) closed system in contact with a heat-bath)?
From the above formula (if it's applicable to any thermodynamic system in... |
Can we derive the Minkowski metric from the Einstein field equations? I am still feeling unclear about the general relativity.
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