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I wish to implement a computer simulation of fish swimming in water in a best-effort physically accurate way.
I would need this simulation to be fast. This means that I can't simulate the dynamics of the whole body of water.
All I need to simulate is the linear and angular position/velocity/acceleration of one fish: ho... |
Today during an intro to vectors class, my physics teacher said that in physics unlike maths addition and subtraction of 0 does have a meaning.
He said " $t + 0$ would be greater than $t - 0$"
Can someone give any real-world example of what he meant? Or do I assume it to be a "dumbed down" way of expressing $\mathrm{d}... |
So I have a high school physics project and I essentially have this experiment idea where I use spectroscopy to find the surface temperature of the sun. Now I'm essentially going to assume the Sun is a black body, then using a spectroscope I can analyse the spectra of the sun light and hence determine the peak waveleng... |
On Peskin & Schroeder's QFT, page 387, the book gives a general analysis about renormalization and symmetry.
For the example of $\sigma$ mass in the linear sigma model, the classical relation is
$$m-\sqrt{2\lambda}\langle\phi\rangle=0 \tag{11.104} $$
I am troubled for following sentences bellow (11.104)
Eq.(11.104) is... |
I’ve been reading a lot about the interaction picture, and I’m trying to string the ideas behind it together.
Essentially, the goal is to calculate something like $<f(\infty)|i(-\infty)>$. We can use states because we assume that they are free in asymptotic times, so they are eigenstates of the free Hamiltonian.
To cal... |
A solid sphere is spinning about z axis. I know that its angular momentum about the z axis will be L=Iw. Where I is the moment of inertia about its central axis and w is its angular speed about z axis. But, what will be the angular momentum about x or y axis or about any arbitrary axis other than z axis ? Is it zero or... |
First of all, is it possible to have a DC generator with 4 poles and a single armature winding?
If so what is the difference in DC output generated between a DC generator that has four poles and single armature winding vs a DC generator that has 2 poles and 2 armature windings (along with two pairs of split rings)?
Bas... |
I am computing the scattering matrix using the LSZ reduction formula in a semiclassical limit. The result that I am getting has the following form:
$$
S = \lim_{t_i \to - \infty} \lim_{t_f \to \infty} f(t_i,t_f),
$$
where $f(t_i,t_f)$ is a function that is expressed in terms of a path integral and $t_i$ ($t_f$) is the ... |
This is a screenshot from Edward P Tyron's article "Is The Universe a Vaccum Fluctuation?"
The explanation Energy-time uncertainty principle from Griffiths:
$Δt$ represents the amount of time it takes the expectation value of $Q$ to change by one standard daviation. $Δt$ depends entirely on what observable $(Q)$ you... |
The following article states that because of the diffraction, the egg is visible, I don't think that's correct, because diffraction occurs at every edge that light passes but it will just slightly increase the field of view, not the whole egg.
https://www.jordanthrilla.com/post/how-does-the-mirror-know-an-object-is-the... |
I am confused about the difference between a spontaneous process and an irreversible process. Based on what I read so far, both processes increase universe's entropy. I never heard of any reversible spontaneous processes before. Is it safe to assume that they both mean the same thing? I can't find any rigorous definiti... |
I've heard that the predicted vacuum energy by quantum mechanics is way far away from what we can actually calculate according to general relativity. The current patch is to include a cosmological constant that cancels out with the expected QFT's predicted vacuum energy.
But how do these cancel out? Does QFT vacuum ene... |
I have heard that the phase transition of a material for example liquid water to vapor or ice propagates faster (assuming it was initiated at critical point $t=0$) over the volume of the material than sound would have?
Is this true and why is this?
Any references about this in the literature?
|
In QCD, even the cross sections of the simplest processes have lots of terms, but we can of course use the spinor helicity formalism to massively simplify the expression.
My question - say we have a scalar field coupled to an $SU(2)$ gauge field instead of the usual spinor field, then would we still have the spinor-hel... |
For a single matter species, the equations of hydrostatic equilibirum for a star are
\begin{eqnarray}
\nabla^2 \phi &=& 4\pi G \rho\\
\vec{\nabla} P + \rho \vec{\nabla}\phi &=&0
\end{eqnarray}
These can be combined with an Equation of State $P=f(\rho)$ (degenerate case), or with both the equation of state $P=f(\rho,T)... |
This is something that completely blew my mind. Last week I was playing randomly with a mirror and my pen and then I noticed that the image of the pen was also having its shadow on a nearby wall.
How is that even possible? For something to form a shadow it must physically block the path of light but a virtual image is ... |
Electron energy loss spectroscopy (EELS) is related to the imaginary part of the inverse dielectric function $−(^{−1}(,)).$
If the dielectric function $\epsilon(q, \omega)$ is actually a tensor and there is anisotropy in the system, which component of the tensor is used to generate EELS in calculations and which compon... |
To start off with, I'm a first year undergrad and do not have much knowledge at all about fluids, and am simply working with context that has been provided to me from a lab script (of a lab I did not do personally- I am doing a peer review assignment). Also, I am fully comfortable with the maths that is being done.
The... |
In my condensed matter course my professor writes: "The lattice potential causes scattering that connects k states, and when these states are degenerate a gap opens. For example, the $\cos(2\pi/a)$ term connects the degenerate states at $k = −\pi/a$ and $+\pi/a$ (i.e. $⟨\psi_{k=-\pi/a}|\hat{V}|\psi_{k=+\pi/a}\rangle \n... |
I am currently researching the skin effect within a wire for my project. In the Wikipedia entry for the skin effect, an approximation for the effective DC resistance is given. I understand the second approximation, but I cannot comprehend the first approximation for the cross-sectional area in the denominator.
$R\appro... |
Suppose you are in a cage suspended by a massless rope that goes around an ideal frictionless pulley. You are supposed to pull yourself up using the rope. You and your cage together are of mass $m$. Let's say you are pulling yourself up at a constant velocity, so the acceleration is zero. We can solve for the force $T$... |
A dielctric resonator was constructed in a sandwitch like structure.
The middle layer is saphire er=11.5 ,the top and bottom layers are diamond with er=5.68.
A special mode was excited artifficially in eigenmode solver.
The electric field rotating around the saphire core and magnetic field with a peak in the saphire ... |
If a force $\vec{f}$ is conservative in a frame $S$, is it such in another, generic, frame of reference $S'$? How do you show this, and how are the potential energies in the two frames related?
|
I am currently in high school and we were just learning about the speed of light. I am fascinated by it but this question was bugging me for a while now. The system is as follows:
A stationary observer
A massless object moving close to the speed of light(or at the speed of light, whatever serves the explanation better)... |
I faced some problems with understanding the process of light absorption in 2D (e.g. graphene). Suppose we have Dirac graphene hamiltonian, skipping all numerical factors:
$$ H = \hbar v\begin{pmatrix} 0 & k_x-ik_y \\ k_x+ik_y & 0 \end{pmatrix} $$
All '$\hbar v$' and similar things will be omitted further. Diagonalizin... |
We know that if the potential energy of a body, say $U(x)$ of a body is known as a function of its x-coordinate, for equilibrium, $$\frac{dU(x)}{dx} = 0$$ Also, several sources suggest that for the state of neutral equilibrium, $$\frac{d^2U(x)}{dx^2} = 0$$
I understand that the sources try to convey that neutral equili... |
I don't know anything about lattice QCD. Therefore, at first glance it seems to me that lattice QCD should be computationally intractable for all practical purposes.
Let's assume that we only care about the two lightest quark types and their corresponding antiquarks. Then the QCD state should be a joint wavefunction of... |
I've been reading about the classical magnetic dipole-dipole interaction and I'm wondering how it would work in a ferromagnet element like iron (theoretically under the assumptions I will write below).
The $B$ field generated by a magnetic dipole is given by:
$$\vec{B}(\vec{r})=\frac{\mu_0}{4\pi}\frac{3(\vec{\mu}·\vec{... |
Suppose we have a charge $q$, which produces an electric field $E$. As the title says, I want to know what will happen to the electric field (E) if the charge q disappears suddenly? Does the electric field (E) disappear instantaneously (after q disappears) or does it persist and propagate through space for a while befo... |
My book says that the interaction energy between the two plates is actually the energy of the electric field that exists between the two plates. I would love to know if the experiment or the theory proves it. I would love to get an answer on this. Thank you!
|
Assume a rope of mass $M$ is connected to a fixed wall and is free from other end
Now,I pull on the end of the rope
My simple questions are:
1.What is the reaction force/Newton's 3rd law pair force to my pull(F) on the end of the rope?
2.What is the restoring force(force to make it go back to it's original length) pro... |
We know the pressure can be determined in a water by: $p = ρ*g*h$.
The whole reason of trying to bring h in the formula is that we are aware that pressure changes with the depth of water and we include h to account for it.
The problem with this in my head is that it's still not correct. density is different at differen... |
Does there exist a "simple", "polynomial-like" quantum field theory (unrealistic, not describing our world, in any spacetime dimension $d$) which does not yield infinities in computations as QED does?
I ask this question because I red it is believed that QED is an effective theory. But I ask myself if this theory can e... |
My Teacher is always writing that work done by external forces is equal to the negative of work done by conservative internal force and both of these are equal to change in potential energy. I don't understand it , can u please tell? Even I read in my book that we cannot change potential energy by doing work by extern... |
Can we compress a solid cone parallel to the axis of rotation, into a disk of same mass to find moment of inertia of solid cone (uniformly dense)?
What I think...
As we are compressing the cone parallel to the axis the distance of every elemental point mass from the axis remain same...
Where i am wrong..?
|
My layperson's understanding is that, although solids and liquids usually radiate across a wide variety of wavelengths modeled by the blackbody spectrum, gases do not because the geometry of their molecules can only be affected by absorbing/emitting certain discrete wavelengths, a la quantum mechanics.
However, from NA... |
I was reading Shankar's Principles of Quantum Mechanics when on page 65, he starts talking about infinite spaces and operators in them. He introduces an operator $K$, which in the $x$ basis takes the form $K=-iD$ with $D = d/dx$ in this basis. He then solves the eigenvalue and vector problem for this operator and finds... |
In the first law of thermodynamics
$$\Delta U=Q+W=\int TdS-\int PdV$$
it is known that $U$ is a state function while $Q$ and $W$ are path functions. However consider the case when there is no work done on a system
$$\Delta U=\int TdS$$
and the case when there is no heat flow
$$\Delta U=-\int PdV$$
In these two cases, I... |
In Griffiths quantum mechanics, there's a discussion of hyperfine splitting for the ground state of hydrogen - this gives rise to a small level splitting corresponding to an emitted wavelength of $21$ cm. Though I don't have much background in cosmology, I believe that an emission spectrum showing such lines is used to... |
Imagine a scene when a massless spring of spring constant(100N/m) is connected to 2 blocks of mass $M$ being pulled by 100N each.
(All surfaces are frictionless.)
by N3L,block also pull external agent by 100N,and since 100N force is acting on block,blocks would move away from spring,therefore applying a pulling force ... |
I've read conflicting information on us being 4D beings (length, width, depth, time) and in what dimension we are able to see. Interested to hear your thoughts, especially if you provide sources.
|
We know that $$ F_n = m*a $$
where $F$ is a net force.
From this equation and gravity law, we can get $a = g=9.8$ for which case we mention $F = m*g$.
But This is only true when an object is falling and there's no upward force exerting on it. The reason I'm saying this is we derive it from the following: $$\large m * a... |
How can I foolproof decide the correct sign of the constraint function in Lagrangian mechanics, particularly in rotations?
In a simple example, lets consider a cylinder rotating around its main axis in positive direction. Accelerating the cylinder further in positive direction with constant $\dot{\omega}$ requires a to... |
T.W.B. Kibble "Classical Mechanics" (1973) gives a few examples of the application of the centrifugal force. One such case is a liquid that is rotating inside a cylindrical vessel. Kibble assumes that the liquid particles all obtain an angular frequency $\omega$. He then chooses this rotating frame, claiming that the l... |
Good time of day. I need to solve system of differential non-linear equations for 3D system. It requires parallel computing on a cluster. Our lab lacks the license on Comsol. It is necessary to determine the heat capacity in a disordered system experiencing the glass transition process.
What's the good open-source alte... |
I have confused myself massively and would like some help.
In my situation we have a cell with emf $V$ and no internal resistance, we hook up 2 lamps of resistance $R$ ohms in series, I have calculated the power of the circuit to be $V^2$/$2R$, meaning each bulb has a power of $V^2$$/$$4R$. Now if we put these bulbs in... |
In John Anderson's Fundamentals of Aerodynamics the following expression for the total induced drag is given on page 442
$$D_i = \rho_\infty V_\infty \int_{-\frac{b}{2}}^{\frac{b}{2}}\Gamma(y)\alpha_i(y)dy$$
On page 191 of Applications of Modern Hydrodynamics to Aeronautics Prandtl uses the small angle assumption to si... |
What is exactly charge apart from an intrinsic property. What is that thing/property on electrons or property due to which we can run devices or new compounds are made? I mean if electric charge is a property that causes a force of attraction/repulsion, then how is it different from any mass? What is charge and why it ... |
In every derivation of solution to Stokes second problem (where we need to find the flow of a fluid under an oscillating plate on the $x$-axis), the pressure gradient is always taken to be 0 to simplify the Navier-Stokes equation. Why is that the case? Surely he closer we are to the plate the higher the pressure would... |
Consider a situation like a magnet which produces a magnetic field, or a point mass which produces a gravitational field. It seems that for practical physical calculation, the physical object's properties are always seen through its fields. Eg See this question.
But is there a clean mathematical description with the ob... |
Suppose we have a $d$-dimensional quantum system with a rotationally symmetric Hamiltonian $\hat{H}$. Extrapolating from the two and three dimensional cases, one might expect that the eigenstates of $\hat{H}$ can be labeled by $d-1$ rotational quantum numbers along with the energy level $n$: $|n,\ell_1, \dots \ell_{d-1... |
Imagine object is falling down and has a mass of 1kg. There's an upward force on it of 50N. Let's calculate what the acceleration is.
$$ F_n = ma = 50 - mg = 50 - 9.8 = 40.2 $$
where a becomes 40.2.
How is it possible that when object is in free fall (no upward force acting on it), acceleration is much less 9.8 than wh... |
As we all know the deeper we look into the space the further we look into the past... So if the Hubble diagram shows the most distant objects at a 20 Mpsec or ~60Mly distance from us (and as for not so large distances where the expansion of the space does not considerably affect the time the light travel to us) we can ... |
Imagine you have a photonic rocket (powered by something like antimatter). If it accelerates at a constant $9.8m/s^2$, it'll reach a velocity of $c$, the speed of light, in around 350 days. What happens when to the velocity when it's approaching at at this speed? If it's throwing out photons at say, $0.5c$ do they conv... |
Recently I was thinking how small local perturbations keep the topological order invariant in some Lattice Gauge Theories, like for the simplest one - Toric Code mode, which is defined as $$H_{TC} = H_0 = -J_s \sum_{site} A_s -J_p \sum_{plaquette} B_p.$$
Now consider Perturbation of the kind, such that:
$$H = -J_s \sum... |
First a disclaimer: This is just an idea I had last night, so if my reasoning here is way off, please let me now.
Let's say that we have an initial thermodynamic system which is in complete balance. We assume, in order to have an easy number to work with, that the incoming radiation is 100 $W/m^2$ and this is perfectly... |
Let $M$ be a Riemannian manifold and $\sigma$ the world function. From page $197$ of Fulling's Aspects of Quantum Field Theory in Curved Spacetime:
$[\sigma_{\mu\nu\rho\tau}]=\frac13(R_{\rho\mu\nu\tau}+R_{\tau\mu\nu\rho})$ so that $[\sigma^i{}_i{}^k{}_k]=-\frac23R$.
I tried to verify this statement, but according to ... |
I have this paper arXiv:1410.4193 which contains a complete list of pre-EWSB dimension-7 EFT operators, and I have taken them and 'converted' them to post-EWSB operators. As an example, from the $\psi^4H$ operator
$$
\mathcal{O}_{\overline{L}uddH} = (\overline{L}_id_R)(u_R^TCd_R)\tilde{H}^i
$$
we get
$$
\frac{v}{2}(\ov... |
To obtain the resultant force, colored in purple, of two parallel and concordant forces $\vec{F_1}$ and $\vec{F_2}$, I apply a vector $\boldsymbol f$ (colored in brown) to the bar $AB$; similarly there will be a vector $-\boldsymbol f$ that when added to $\boldsymbol f$ will give me with the null vector involving no m... |
I was reading about the Taylor expansion of the scale factor from visser,2004
He writes:
$$ \frac{a(t)}{a_0} = 1 +H_0 (t -t_0) - \frac{q_0}{2} {H_0}^{2}(t-t_0)^2 + \frac{j_0}{3 !} {H_0}^{3}(t-t_0)^3 + \\ + \frac{s_0}{4 !} {H_0}^{4}(t-t_0)^4 + \frac{l_0}{5!} {H_0}^{5}(t-t_0)^5 + \mathcal{O}(t- t_0)^6
$$
where $q,j$... |
The energy radiated by some free, real-valued, scalar massless field $\phi$ in flat $1 + 1$ time and space dimensions is the vacuum expectation value of the $\{$00$\}$ entry of energy-momentum tensor.
Introduce:
$$\phi = \int d\omega \ (a^{\dagger}_{\omega} \phi_{\omega} + a_{\omega} \phi^{*}_{\omega})$$
where:
$$\phi_... |
I came across this integral studying QFT regarding what I think it may be the calculation of a 2$\rightarrow$2 particle scattering cross section.
$$I = \int \frac{dp_3}{(2\pi)^32E_3} \frac{d p_4}{(2\pi)^32E_4} \delta^4(p_1+p_2-p_3-p_4) \delta (t-(p_1-p_3)^2)$$
where $p_i$ is the 4-momentum of each particle ($p_1,p_2$ i... |
We can see magnetic field lines by putting compasses or iron filings around a wire that carries current, is there a way to see electric field lines so we can see electric field lines just like we can see magnetic field lines when we put compasses or iron filings around a wire?
|
I'm an EE, so please forgive if this question is dumb.
The word "easiest" means, "What requires the least amount of optics experience?"
"Short distances" means 0.01 to 1 m.
I need to measure the distance between some datum and a moving object. Therefore, I don't necessarily need to measure absolute distance. It is suff... |
I am studying the phenomenon of pair production and I learned that it cannot occur in a vacuum. Rather it occurs near a nucleus which absorbs momentum to keep the momentum conserved.
Instead of a nucleus, can we have pair production with two photons? For example, the two photons collide to produce an electron-positron ... |
Background:
Concerning the use of periodic boundary conditions for systems of $N$ (identical) particles, Ref. 1 considers a cube $\Lambda$ with volume $L^3$ and notes regarding the interaction potential of the form $V(x_1-x_2)$:
It is often useful, for calculations, to express $V$ in the plane-wave basis $|k\sigma\ran... |
In observing blackbody radiation, the cavity radiation is modelled as standing waves in 3 mutually perpendicular directions. However, I am unable to understand how we observe the radiation since the standing waves are confined inside the cavity. I mean how do the standing waves come out of the cavity so that they can b... |
We interpret the electron's wave function as a probabilistic wave function. During a measurement, it has the probability to collapse to any of the eigenstates of the measurement operator based on the square of the amplitudes of the wave function expressed in terms of the eigenstates.
On the other hand, photon is the re... |
I'm in the market for a textbook dealing with classical electromagnetism for someone who already knows the basics (e.g. up to the derivation of the Maxwell equations and the basic expressions for electromagnetic waves). I'd like a well-written book that is rigorous and rooted in vector calculus but also provides intuit... |
Let us consider a cup that I'm holding vertically in my hand
I physically don't go through the cup because of the pauli's exclusion principle where electron with opposite wave function(spin)s dont want to be near each other and also due to the electrostatic repulsion of electrons and protons.
Then comes the case where ... |
Consider a Riemann-Cartan 4-dimensional spacetime with torsion. In such a spacetime, I have been asked to compute the d'Alembertian operator acting on a scalar field. Here's what I tried:
$$ g^{\mu\nu} \nabla_{\mu}\nabla_{\nu} \phi = g^{\mu\nu}\nabla_{\mu}\left(\partial_{\nu} \phi\right) \\ = g^{\mu \nu}\left(\partial_... |
While reading about blackbody radiation, I am seeing the textbooks saying that a cavity with metallic walls that are perfectly reflecting, with a small hole, can be approximated as blackbody as any radiation entering into the cavity would suffer multiple reflections from the walls and eventually be absorbed. But since ... |
The most general Fokker-Planck equation for a probability density $f$ over phase space is
$$\partial_t f = -\partial_i(u^i f) + \frac{1}{2} \partial_i \partial_j (D^{ij} f)$$
where $u^i$ is the drift vector field on phase space, $D^{ij}$ is the diffusion matrix field, and the repeated indices $i,j=1,\ldots,2d$ are summ... |
I've done a latent heat experiment and measured the mass of nitrogen over time while applying heat. These are the results::
Which looks fine, most of the measures are in the linear fit. But when I calculated statistical parameters, they were horrible:
Chi-squared reduced: $131.7$
P-probabilty: $4.577*10^{-22}$
I can't... |
Suppose we have a sphere, with a radius a and a total charge $Q_{0}$, immersed in a conductor, with a conductivity $\sigma$ and a permittivity $\epsilon$ .The sphere releases a current density: $$ j= \sigma E$$
So, utilizing Maxwell's first law for an imaginary sphere of radius r, we can find the electric field: $$E = ... |
Let's say we have a constant (homogene) magnetic field $\boldsymbol{B}$ and a rigid object. Now let's say there are magnetic dipoles $\boldsymbol{p_{m,1}}$, $\boldsymbol{p_{m,2}}$,... $\boldsymbol{p_{m,n}}$ at locations $\boldsymbol{r_{1}}$, $\boldsymbol{r_{2}}$,... $\boldsymbol{r_{n}}$ inside that rigid object.
Of cou... |
Can someone explain me this equation. This is braking distance equation that applies all reaction times ect.. Taken from Bosch Automotive Handbook.
But what does the 25,92 mean there?
v= velocity
tvz = reaction, foot to brake ect.. time, average 1 second
a = max acceleration (decceleration here for braking, 9,81 * fri... |
In studying string theory, one sees the argument that we can gauge-fix the worldsheet metric to become the Minkowski metric. The argument usually goes that general coordinate transformations (GCTs) fix two components, and Weyl transformations fix one. Moving on to an arbitrary number of dimensions ($d$), I have been tr... |
I have an exercise where I have to determine the luminosity of a star with 10 000K. However, I'm confused about how to read off the $y$-axis on the graph when the scale is uneven. What is the function of the horizontal lines and am I supposed to use them to determine the reading of the $y$-axis.
The acceptable range of... |
First of all, please forgive me for my messy and inexperienced question.
I'm not yet familiar with higher-level physics but the question I'm posting here has bugged me for quite some time.
Why do we require a particle of exchange to understand strong nuclear force?
Like, For in electromagnetic force, we introduced the ... |
We know for EM waves undergoing destructive interference, there's constructive interference somewhere else that compensates for the loss in energy during destructive interference. However, I tried constructing a case (below) where such arguments seemingly don't apply.
Statement:
Laser A, placed at the origin, produces ... |
For background, I'm a high school physics Student, and I was recently looking at special relativity out of personal interest, and I read a summarized statement "Time slows down as your approach the speed of light" and so I went googling around and I saw an answer like this on this stackexchange, and I've seen other ans... |
While reading capacitance I found out this statement that for large C, potential difference is small for a given charge means that a capacitor with large capacitance can hold large amount of charge at relatively small potential difference. "High potential difference implies strong electric field around the conductor". ... |
I'm attempting to calculate the modulus of elasticity, or Young's modulus, of various types of wood.
However, I'm confused by the strain component. It's calculated by the change in length divided by the original length.
I have various planks of wood and I want to see how much each bends under a known weight with one en... |
I'm watching a Physics MIT lecture about classical mechanics and I'm on the episode about Work and Energy. I'm stuck at this point in the video
https://www.youtube.com/watch?v=9gUdDM6LZGo&list=PLyQSN7X0ro203puVhQsmCj9qhlFQ-As8e&index=12&ab_channel=LecturesbyWalterLewin.Theywillmakeyou%E2%99%A5Physics.
because I can't w... |
A point mass slides with speed v on a frictionless horizontal surface between two fixed parallel walls,
initially a distance L apart. It bounces between the walls perfectly elastically. You move one of the
walls towards the other by a distance 0.01L, with speed 0.0001v. What is the final speed of the
point mass?
You ca... |
About the alleged duplicates: " Quantum entanglement vs classical analogy" "Show quantum entanglement to a classical thinker" refer to black and white balls that would have a correlation at time zero, and this "anticorrelation of color" would be maintained later on. Clearly, if you read what I'm talking about, I am giv... |
The Cosmic Microwave Background Radiation is the oldest thing we can directly observe. To explain the near uniformity of temperature of the CMBR and the flatness of space, Cosmic Inflation was invented, which has its own problems, such as the failure to explain the initial conditions of the Big Bang and the fine-tuning... |
Let $U$ be a four-vector and $\nabla$ denote the covariant derivative in the Levi-Civita connection. Is it always true that $$\left(\nabla_{\mu}U^{\nu}\right)U_{\nu}=\left(\nabla_{\mu}U_{\nu}\right)U^{\nu}~?$$
I have tried expanding the covariant derivative out. On the LHS you will get a positive Christoffel symbol, wh... |
Note to duplicate concerns: How is that the same question as asking if different orbitals are entangled? I am talking about paired electrons in the same orbital orientation.
Paired electrons in an atom, have anticorrelated spin (pauli exclusion principle).
Does that mean they are entangled?
I am asking this because I a... |
I solve a system of coupled equations numerically. One of the most important, is equation of the gravitational potential,
$$\nabla^2 \phi = 4\pi G m \rho(r)$$
But I have physical problem with boundary condition, I take
$$\nabla \phi(0) =-\infty $$
I want to know if I can take this boundary condition or not?
|
For an ideal gas, we have
\begin{align}
pV = Nk_B T
\end{align}
Considering a monatomic ideal gas specifically, the internal energy is
\begin{align}
U = \frac{3}{2}Nk_BT
\end{align}
so that
\begin{align}
pV = \frac{2}{3}U\quad\quad\quad \tag{1}
\end{align}
If we interpret the term $pV$ as "the energy a gas has due to b... |
I'm just thinking about the efficient algorithm to calculate the photovoltaic conductivity
$$
J(0) = \sigma^{(2)}(0, \omega, -\omega)E(\omega)E(-\omega)
$$
in time domain calculation. In the case of linear conductivity, $\sigma^{(1)}(\omega) = J(\omega)/E(\omega)$, we can get this by Fourier transform of the current re... |
Two objects are moving towards a gravity well. They are at $x$ distance from each other and moving at a fixed speed. The gravity well is massive enough for the objects to experience significant time dilation when near the well. As the first object approaches the gravity well, it will appear slower to the second object,... |
Gauss' Law tells us that for a point charge q at the origin and a spherical surface of radius r centered at the origin, we have
$$\iint_S \vec{E}\cdot d\vec{a}=\frac{q}{\epsilon_0}\tag{1}$$
If we have $n$ charges $q_i$ within the spherical surface, then using the more general result that "the flux through any closed su... |
We know that all actions are invariant under their gauge transformations. Are the equations of motion also invariant under the gauge transformations?
If yes, can you show a mathematical proof (instead of just saying in words)?
|
As we already acknowledge, we can see magnetic field lines by putting compasses or iron filings around a current-carrying wire. Same goes to electric field lines where we can see them when we are looking at plasma balls/plasma globes and what these clips show https://youtu.be/zz9l8e4Rq00?t=48 and https://youtu.be/7vnmL... |
Recently I have been quite confused in determining a phase transition for anyons in Toric Code model. Here the ground state does not have any particle, and loops (in real and dual lattice, which for $Z_2$ are equivalent) proliferate. This means $A_s=1$ and $B_p = 1$ in the Ground State, with which you can give some tho... |
while calculating the self-energy of a continuous charge distribution using the formula
the potential $V$ here is due to the whole charge distribution but we need potential due complete charge distribution except the element dT(volume element). How is this correct?
On the other case while calculating that for a point ... |
Can the Einstein-Yang-Mills black holes be calculated and investigated in the dS space? If this is possible, has there been any special work done so far, and if not, what is the reason why such a structure is not investigated in the dS space?
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