# All Questions

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### What is precisely the energy scale of a process?

Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
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### Lorentz-invariance of step function

I was reading about the Lorentz invariant integration measure $\int \frac{d^3k}{2E_K}$, and ways to prove that this was Lorentz invariant. Many of the proofs I have read use the step function (or ...
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### Induction Oscillation

A bar (m=100g, l=10cm) is moving in a constant magnetic field $B$ as shown above. The resistor $R$ is $1\Omega$. The bar is attached to a spring with spring constant $10N/m$, can you derive ...
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### Why do rings form on microwaved CD/DVDs?

Here's a microwaved CD. As you can see, the disc has been destroyed, but there are very clear circular rings bridged with lines. Why are rings formed when microwaving discs?
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### space contraction near lightspeed

I read a lot of the Time-Life Science books when I was a kid (well, mostly the pictures and captions). One of the things that always stuck in my mind was an explanation of the twin paradox, using ...
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### Why is the rotation not zero and the divergence zero in the figures below?

Why is the rotation not zero and the divergence zero in figure 1 and figure 2 below? Figure 1 Figure 2
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### Interesting approach to Kepler problem

I won't go into the explanation of this idea, because it is explained in this blog post. In this paper, which was featured on John Baez's blog, $\frac {dt}{d\lambda}$ is given as $\frac r V$, where ...
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### Relationship of the volume of a plumbing system to pressure

How does the volume of water a plumbing system holds vary with water pressure? I know the ratio would include the modulus of elasticity of the plumbing material, the total surface area of the plumbing ...
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### Prove $e^Âe^{-Â}=Ê$

I want to prove that the Operatorexponential times the Inverse Operatorinverseexponential equals the Normoperator. I dont really know how to advance here, as I am still really new to the whole ...
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### Weightless person in a cart on a rail

In a problem I'm trying to solve I've having a conflict between my understanding and the proposed solution of the problem. A cart ($m=35kg$) is at rest in the start of a friction-less ("covered with ...
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### Geophysics: Dynamic form factor and Equipotential surfaces [on hold]

I've got the following problem which I need help with. I'm used to calculating coefficients when the problem is about ellipsoids and first order approximations. But when it comes to spheres and ...
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### Propagation of incertitude - specific example

I am setting up an experiment, where I know the force and the incertitude (delta) of that force. However, I need to graph the logarithm of that force with the incertitude of the log. Can someone help ...
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### A question about genus one string amplitude

In BCOV's paper http://arxiv.org/abs/hep-th/9309140 the genus one string amplitude of a Calabi-Yau 3-fold was explained in the B-model as the Ray-Singer torsion (there is a similar discussion in the ...
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### Why is the heat transferring best from within the tube within a tube-heat exchanger

If you've got gas and cooler fluid, you'd run the gas through the tubes, because the gas has a lower h-value. Inside a tube heat-exchanger it is said that the best heat transfer is from within the ...
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### Moment of Inertia Calculation [on hold]

A uniform disc has centre O, radius a and mass 2m. It is free to rotate in a vertical plane about a horizontal axis through O. A particle P of mass m is placed on the highest point of the rough edge ...
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### Determining straining force and reaction forces on a beam

A homogenous beam $OA$ with the length $4a$ and the mass $m$ can rotate in the vertical plane along a horizontal axis through $O$ and is kept in equilibrium by a wire running from the points A and C ...
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### Point charges in a sphere

If we put N point charges (with charge +q) in a sphere with radius R and the charges can move freely in the sphere but can't get out of it, where will the charges go to and what will be the ...
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### Can this RC boat work in thoery? [duplicate]

We're a bunch of friends building an RC boat, this may sound stupid but I had an argument with a friend where he insisted that his design will work. Basically, he's saying that by putting a ...
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### How to derive velocity pressure in English units?

I know that velocity pressure can be calculated from dynamic pressure according to the potential energy of pressure (from Bernoulli's equation): $$P = \frac{1}{2} \rho \overline{V}^2$$ where P = ...
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### Why do electrons, according to my textbook, exist forever?

Does that mean that electrons are infinitely stable? The neutrinos of the three leptons are also listed as having a mean lifespan of infinity.
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### Kirchhoff's junction and loop rules [on hold]

How does the conservation of charge justify Krchhoff's loop rule. Also, how does the conservation of energy justify the junction rule?
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### Why does plugging a hole in an airplane's fuselage result in a huge (10x) atmospheric pressure spike?

While reading about uncontrolled decompression, I came across one famous airline incident, Aloha Airlines Flight 243, where the article I was reading discussed a 1-square-foot hole created in the ...
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### Is the flux through A the same as the flux through B?

In the figure below, the amount of field lines through A is the same as the amount of field lines through B, but can you say the flux through A is the same as the flux through B as well?
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### Why a timelike geodesic maximizes path length?

I'm studying some GR and my book says that in Pseudo-Riemannian manifolds geodesics may even maximize the path locally. That's what happen to the timelike geodesics, for example. My first question: Is ...
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### Electrostatic field in a vacuum

Can an electrostatic field, the direction of which is constant in space, but the magnitude varies in space, exist in a vacuum?
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### SONAR - submarine speed detection [on hold]

A submarine can use sonar (sound traveling through water) to determine its distance from other objects. The time between the emission of a sound pulse (a “ping”) and the detection of its echo can be ...
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### At what distance is lightning dangerous for someone lying down?

My 8 yo child told me that they learned at school that they should lay down flat on the ground in case of lightning. I told him that the more correct position is crouching down with feet together, but ...
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### The wavefunction of the superconductor A consists of two parts: B and C

In reading this article, I come across this paragraph: The pink marked place is where I can't understand, why can we use direct product of the former but not the later? This is may be a basic ...
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### Centre of mass of a system of particles

If the centre of mass of a system of particles is at the origin, does this mean that if there is a particle on the positive X-axis, there must be atleast one particle on the negative X-axis? I feel ...
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### How do you calculate the angular momentum of a dumbbell after a collision? [on hold]

In outer space, far from other objects, a small block of mass $m$ traveling at speed $v_1$ approaches an object initially at rest that consists of two small spheres each of mass $M$ connected by a ...
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### How to relate internal energy to atomic motion?

I am trying to conceptualize how atomic motion leads to the thermodynamically-defined internal energy (denoted as $U$ below) through some broad mathematical relationships. I get that the internal ...
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### What are the limitations of simulating grand unification theories of elementary particles in condensed matter settings?

What are the limitations of simulating grand unification theories of elementary particles in condensed matter settings? I know that condensed matter systems can be constructed to be described by any ...
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### What mechanism creates bubbles in water that stays awhile

If I fill glass jar with tap water and let it stay, small bubbles will appear on the side of jar after a while. I am wondering what processes create those bubbles and what conditions require to ...
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### How to convert from transition dipole moments to oscillator strength?

I'm having some trouble converting from transition dipole moments (in atomic units) to oscillator strength. I've found the following equation in Modeling Molecular Photochemistry by Nick Turro, which ...
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### Are neutrinos weekly interacting particles? [on hold]

Occasionally, I read about weekly interacting neutrinos, and although I know this is a typo, I wonder if it happens to be true. Do average neutrinos, as they fly through the universe, really interact ...
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### Time Reversal Bulk Hamiltonian

This questions is from pages 68 and 69 of: http://fizipedia.bme.hu/images/1/14/Topological_insulators.pdf For a lattice, time reversal invariance of the bulk corresponds to the equation (Eqn 6.11): ...
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### Concerning time and space and illusions [on hold]

Time is a way of measuring durations in a common communicating way that most people adhere to. Space or a coordinated system of length, width, and height is a way of measuring objects and how they ...
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### Hydrogen-boron fusion [on hold]

aRecently I found out that Hydrogen-1 and Boron-11 together are considered a viable nuclear fuel. Fusion of Hydrogen-1 and Boron-11 produces three highly energetic Helium-4 nuclei. Basically the ...
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### Relation between black hole mass and size applied to observable universe [duplicate]

If I apply the relations given in http://xaonon.dyndns.org/hawking/hrcalc.js and http://www0.arch.cuhk.edu.hk/~hall/ag/sw/SpinCalc/SpinCalc.htm to the values for the mass of the observable universe ...
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### If Earth and Jupiter are orbiting around Sun in same orbit, will they have same time period?

Let us suppose that Earth and Jupiter are orbiting around the Sun in same orbit, If we talk about at any particular point. (Which is not possible but for the sake of question) I was wondering that ...
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### Is the second defined arbitrarily? [duplicate]

According to the definition a second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of ...
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### Why do we need complex representations in Grand Unified Theories?

In almost every document about GUTs it is claimed that we need complex representations (=chiral representations) in order to be able to reproduce the standard model. Unfortunately almost everyone ...
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### What causes the black shimmering bands on a sun-lit surface?

I can't figure it out. I thought it was the window causing it, but even without it it happened. It seems to be the motion of the air that causes it, but why shimmering black bands? Sometimes this ...
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### Triodes: Why do mesh fineness and radius of the grid affect amplification factor?

My basic understanding is that a grid which is much closer to the cathode than the anode will be more able to create a repulsive electric field than the anode's attractive field, thus current can be ...
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### Net force acting on the block along the inclined path can be mgcos(theta)? [on hold]

If we take the angled marked with red curve then the net force along the x axis or inclined path comes out mgcos(theta) is is correct?
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### An elevator accelerating upward, tension increases in the rope to which a fish hangs inside the elevator why?

A fish is hanging in an elevator through a rope, when elevator accelerates upward the tension in the rope increases why? When elevator accelerates downward the tension in the rope decreases why?
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### Inertia of a body cancells some amount of force?

If we have a block on a frictionless surface and we apply force F on the block to accelerate it, some amount of applied force will be cancelled by the inertia of the block am I right?
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### Newton's Third law of motion: A hammer hits a wall vs. hits a tire

When we hit the wall by a hammer, Newton’s third law says that hammer applies force on the wall (action) and wall applies force on hammer (reaction) equal in magnitude but opposite in direction ok ...