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### Running fo the fine structure constant: meaning of $\alpha(Q^2=0)$?

In Measurement of the Running of the Fine-Structure Constant, the L3 collaborations writes At zero momentum transfer, the QED fine structure constant $\alpha(0)$ is very accurately known from the ...
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### What are the symmetries of standard model and its conservation laws?

Is there like a list of symmetries in the standard model with associated conservation laws?
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### What causes the electric field in a Daniell Cell?

I would like to know what causes the e-field in a Daniell cell. From a chemistry point of view, I do understand that this is initiated by a redox reaction in which Gibbs free energy is decreased. The ...
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### Superconductor behavior near absolute zero

How does critical current change for superconductors as temperatures approach the millikelvin realm, particularly High-Temperature Superconductors?
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### How to reduce magnetic field between two magnetic shield sheets?

I put 2 parallel silicon steel sheets between magnetic field as below: As silicon steel has much bigger permeability than air,magnetic line will go through 2 silicon steel sheets. What I can do to ...
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### Time differential between two signals sent at two different near-relativistic speeds

There is something I don't quite get about relativistic velocities, which I am hoping to clarify with this question. Suppose you have an emitter and receiver both located somewhere far away from one ...
1 vote
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### How is surface charge induced on the surface of circuit wires when connected to a battery?

Understanding: I watched the newest Veritasium electricity video and he said that the electric field inside the wires of the circuit that causes the electric current to flow is created by both the ...
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1 vote
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### The chronology of taking approximation changes the answer?

The problem is to find the time it takes a particle dropped from a height $h_0$ above the surface of the earth to reach the surface (exactly, not approximately i.e. $g$-value is not constant, in the ...
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### Does an observer experience stronger gravity on the way towards the singularity?

I have read this question: Clearly as you approach the singularity the tidal force on a body increases. Are the fundamental forces unified in a black hole? Based on the questions on this site, ...
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1 vote
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### What is a "massive phase" in the string theory or CFT?

When reading through some articles, one encountered a vocabulary termed as a "massive phase" in the string theory or the CFT, in the case where a theory followed an RG flow between UV and IR....
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1 vote
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### Spherical harmonics with 2 cosmological probes : considering $a_{\ell m, photo}$ as a constant and $\hat{a}_{\ell m, spectro}$ as an estimator

I am in cosmological context where the survey on which I am working has 2 probes : a photometric galaxy clustering ($GC_{ph}$) probe and a spectroscopic galaxy clustering ($GC_{sp}$ probe). We use an ...
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1 vote
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### Do electric fences such as those typically used to fence cattle generate magnetic fields?

I'm using magnetometers near electric fences and I'm wondering if the electric fence should be detectable and if so, how close do I need to be to the fence for there to be a "measurable" ...
1 vote
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### Equation for the simultaneous eigenfunction of three operators in spherical coordinates

If I'm considering the three operators $H,L^2,L_z$ with the condition $[H,L^2]=[H,L_z]=[L^2,L_z]=0$, I can find a complete set of simultaneous eigenfunctions. If I study this problem in spherical ...
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The time dynamics of an atom interacting with a reservoir of spectral density $J(\omega)$ are obtained by solving the following integro-differential equation $[1]$: $$\dot{c}(t) = \int_0^t dt'\int_0^{... • 99 -1 votes 0 answers 72 views ### I have found a serious error in a Wikipedia page? [duplicate] From WP Signal Velocity article: https://en.wikipedia.org/wiki/Signal_velocity Signal velocity is usually equal to group velocity (the speed of a short "pulse" or of a wave-packet's middle ... • 2,982 0 votes 0 answers 32 views ### Please help me calculate on two resistors. The scheme is very strange [closed] Good afternoon, I can't figure out where the current will go. It seems that this scheme does not make sense at all, but it is necessary to calculate the voltage on the resistors 0 votes 0 answers 11 views ### How does a spring's maximum compression ratio change with decreasing it's free length for a coiled helical spring(compression)? I'm just looking for a simple expression formula for how maximum spring compression changes with free length of a coiled helical spring, say a Compression spring. A way of understanding what I mean by ... -2 votes 0 answers 14 views ### A solid, insulating sphere of radius a = 4.9cn has a uniform charge density / . Find the magnitude A solid, insulating sphere of radius a = 4.9cn has a uniform charge density on its volume of rho = 25.5 muC / (m ^ 3) . Concentric with ( this sphere is an uncharged (بالمركز conducting, hollow () ... 0 votes 2 answers 48 views ### For someone staying on Earth, what is the minimum possible time to send a spaceship to Alpha Centauri and have it back? Suppose we want to send a spaceship to Alpha Centauri and calculate the minimum possible time it will take for us here on Earth to have the spaceship back. We are not interested in how fast the time ... 0 votes 0 answers 8 views ### Interlink among different length scales of simulation and modelling techniques I found this figure in the following paper A Review on Multiscale Modelling and Simulation for Polymer Nanocomposites However, I am skeptical about its correctness, as this paper is not peer-... • 109 0 votes 0 answers 19 views ### What is the correct derivation for particle concentration from one frame to another? I. The simplest derivation I can think about is based on conservation of the number of particles and length contraction. In frame S, say we have a volume V (surface S, length l) of particles of ... -2 votes 2 answers 119 views ### What is the real world interpretation of E = mc^2? Why I am asking this question: There appears to be a logical contradiction in the notion that gravity is "one thing" mass moves in gravity much differently than light (a massless particle) ... • 293 3 votes 1 answer 37 views ### What curve does a rod form when bent to intersect 3 or more points? Suppose that we have a sufficiently thin, flexible cylindrical rod of length L made from a homogeneous, isotropic material, and that initially [at rest?] the central axis of the rod is a straight ... • 593 1 vote 0 answers 26 views ### What is the structure group of the SU(3) manifold? It has been known for many years that the manifold of the Lie group SU(3) is the non-trivial fiber bundle of the spheres S_5 \times S_3, in which S_5 is the base and S_3 the fibers. What ... 0 votes 1 answer 25 views ### Eigenfunction of a free particle going in the x direction quantum mechanics When we talk about a free particle we have the Hamiltonian H=\frac{p^2}{2m} and the TISE \frac{-\hbar^2}{2m}\psi''(x)=E\psi(x) and, saying k=\frac{\sqrt{2mE}}{\hbar}, we have two particular ... • 609 0 votes 1 answer 27 views ### Why is current same even if the area of the conductor differs? Current is directly proportional to area if area of conductor increase Current increases but in conductor like a horizontal frustum as area increases current remains same I have learned this equation ... 0 votes 1 answer 65 views ### Arbitrarity of i in the propagator My question is simple: how arbitrary can the factor in front of the propagator be? What I mean by that is, if we call the wave operator K and the propagator G, I've seen different books use ... • 4,502 0 votes 1 answer 67 views ### Units make speed of light dimensionless..? We shall now adopt a new unit for time, the meter. One meter of time is the time it takes for light to travel one meter ... (page-4, Bernhard Schutz's A first course in relativity) I am confused, how ... • 5,259 0 votes 1 answer 30 views ### How to harvest water passivley? I have been reading recently about methods to collect moisture from the air passively and turn it into water. However, is there any attempt currently for small-scale water harvesting? Methods I have ... 0 votes 0 answers 23 views ### How do I determine the relationship between initial and final volume in this case? Some total volume contains two compartments separated by a wall that allows for mechanical and thermal interaction, each compartment having a different amount of an ideal gas. For the initial ... • 183 0 votes 2 answers 28 views ### Instantaneous current and average current Imagine a simple electrical circuit with a battery and resistor. We know that the average current in any part of this circuit remains same . My question is : is the instantaneous current also same ... 0 votes 1 answer 25 views ### Sources to learn Gauge Theory, Groups, Lie Algebra, etc [duplicate] As seen in previous questions, I'm interested in gauge theory, although I have no idea how to do any of the mathematics, though i'd like to start. With that in mind, Are there any good sources that ... 4 votes 0 answers 35 views ### Is there a Lagrangian L (equivalently an action functional S) which yields the Navier-Stokes equation? The Navier-Stokes equation or the Euler equation are usually derived as the conservation laws. However, I wonder if there exists a Lagrangian L or equivalently, an action functional S[\... • 1,049 3 votes 1 answer 68 views ### How fast would these clocks tick relative to each other? Lets say you have two clocks, you attach one to a mirror and drop in into a black hole, while you keep the other next to you, point it towards the black hole and view it's reflection on the mirror. ... • 1,082 1 vote 1 answer 40 views ### Why lead plate was used in Rutherford's gold foil experiment? I have read that lead plate is used to concentrate the beam of alpha particles which are being directed towards the gold foil as it is a heavy metal. But there are other heavy metals like manganese, ... 4 votes 3 answers 364 views ### Why would black hole rip me apart? According to my understanding of General Relativity, gravity is not a force and an observer which is falling freely under the influence of gravity should be considered inertial. Now, I have come ... 0 votes 0 answers 16 views ### What exactly did Lagrange do, historically? [migrated] I'm tying to understand, historically, what lead to Lagrangian mechanics (LM). What did Lagrange actually do? In the time (year 1788), when Lagrange published his work (that we nowadays call "... • 402 0 votes 0 answers 22 views ### Given the time dilation at the event horizon plus black hole evaporation, can anything really ever enter a black hole? [duplicate] There are many thought experiments about what it would be like to fall into a black hole, spaghettififaction, the singularity at the center and so on. But to me it seems that no object could actually ... 0 votes 0 answers 9 views ### Decay time of rotational frequency of the ring This is a question for one of my exams. I have uploaded my way of solving below. I have some queries: (i) The time I derived is independent of minor radius a but by commonsense, I know with the ... • 11 1 vote 0 answers 13 views ### Understanding the derivation of the variational principle in classical density functional theory I am trying to understand the derivation of the variational principle as presented in Bob Evan's 1979 work.[1]. The part that is tripping me up is when he presents the following result. He starts by ... • 51 0 votes 0 answers 39 views ### Can we apply lens makers formula when medium on both side of lens is different? [closed] A symmetric biconvex lens of radius of curvature R and made of glass of refractive index 1.5, is place on a layer of liquid placed on top of a plane mirror as shown in the figure. An optical ... 1 vote 2 answers 25 views ### How to predict deviation from ideal gas behaviour? Molar masses of H2, N2, CO2, and NH3 are 2g, 28g, 44g, and 17g and respectively. The gases deviate from ideal behavior in the following order:$$\require{mhchem} \ce{H2<N2<CO2<NH3}$$... 1 vote 0 answers 18 views ### Why the Tokamak Fusion Reactors need to be so big if electromagnetism works better for small distances? I'm probably asking something dumb, but for the little I think I know, I assume that the bigger the electromagnetism field, the bigger the energetic requirement. I'm assuming that the square cube law ... • 25 1 vote 0 answers 14 views ### Why does expressing the Faddeev-Popov determinant as this lead to such problems? Background In the following, I am interested in the Schwinger function associated with the gluon propagator when one considers the Gribov no-pole condition in the partition function. Defining \nabla^{... • 1,782 0 votes 1 answer 32 views ### How can one calculate the torque around this point? I'll link to one of my previous problems, since the setup is very much alike this one for the problem I'll be solving: What happens with the pendulum when we choose this angular velocity for a ... • 303 1 vote 0 answers 33 views ### Are there any other significant radii around Schwarzschild black holes besides the four I know of? A Schwarzschild (non-rotating, non-charged) black hole has an event horizon with radius r_s = \frac{2 G M} {c^2}, where M is the mass of the black hole, G is the gravitational constant, and c ... • 253 4 votes 2 answers 130 views ### Essential self-adjointness of the kinetic energy operator I'm studying the mathematics of quantum mechanics, and specifically, I'm trying to understand Kato's paper. In practice essentially self-adjoint does not mean that the operator is self-adjoint and ... • 61 4 votes 1 answer 87 views ### Does the neutrino interact with the photon? I know that the straight answer is no, but in my EFT course, where we're interested in nonrenormalizable operators of the Lagrangian, things aren't so straightforward. The non-minimal QED Lagrangian ... • 4,502 0 votes 1 answer 23 views ### Hartree-Fock on a lattice: how to deal with non-diagonal charges For a Hubbard hamiltonian,$$\hat{H} = \sum_{i,j,\sigma} t_{i j} \hat{c}^\dagger_{i \sigma} \hat{c}_{j \sigma} + \sum_i U_i \hat{n}_{i \uparrow} \hat{n}_{i \downarrow},  the mean-field solution can ...
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On page 191 of Peskin and Schroeder, they state: Since $q^2<0$ for a scattering process… where $q$ is the momentum of the incoming photon in the electron vertex function. Why is this so? Shouldn’...