# All Questions

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### The meaning of scale invariance in power law distribution

A function $f(ax)$ that satisfies $$f(ax)=a^\Delta f(x)\,\,\, (\Delta \in R)$$ is said to be scale invariant. The most general function $f(x)$ that satisfies the previous condition is of the form ...
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### Conservation of angular momentum in helicopter

I have a small RC-controlled toy helicopter with removable tail rotor. Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and ...
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### Did anyone claim that quantum theory meant lasers would never work

I've been reading 'How the Hippies saved Physics', which describes a design for a superluminal communication device, of which the crucial part was a laser which duplicated an incoming photon many ...
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### Solving for initial velocity required to launch a projectile to a given destination at a different height

I need to calculate the initial velocity required to launch a projectile at a given angle from point A to point B. The only force acting on the projectile after launch will be gravity – zero air ...
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### How to determine n equidistant vectors from point P in three dimensions

As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces. For the first part of the assignment, the particle has mass $m$, ...
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### What's the distinctions between Yang-Mills theory and QCD?

So Yang-Mills theory is a non-abelian gauge theory, and we used a lot in QCD calculation. But what are the distinctions between Yang-Mills theory and QCD? And distinctions between supersymmetric ...
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### speed of sound relative to density of medium through which sound travels

I know that sound travels faster in water compared to air and say faster in steel than in what're so What would the density have to be to cause sound to approach the speed of light
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### observation and implied time since creation

I read on a post Big Bang and Cosmic microwave background radiation? We detect light from another 13 billion years ago does this mean that one billion years ago we could only detect light from about ...
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### Will a black hole increase the speed of sound above the speed of light in this medium

For the sake of this question we are inside the EH and a sound wave enters from our perspective as the sound moves closer to us at the EH would it speed up. Specifically how would the extreme ...
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### how does heat energy start to speed up a gas molecule?

If it was possible to place a single gas molecule in a cell and freeze it to near absolute zero. What would the molecule do as it thawed out? Would it translate the heat energy into it's electrons ...
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### Newton's Law of Gravitation, Gauss Law and GR

From One of My Unpublished Papers $$\frac{d^2 x^{\alpha}}{d\tau^2}=-\Gamma^{\alpha}_{\beta \gamma}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau} \tag{1}$$ For radial motion in Schwarzschild’s ...
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### Examples of exact many-body ground state wavefunction

Is there any non-trivial many-body system for which the exact solution to Schrödinger's equation is known? (By non-trivial, I mean a system with particle-particle interactions.) Perhaps something like ...
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### How is it possible that we see light from shortly after the big bang?

How can astronomers see light from shortly after the big bang? How did we get "here" before the light that emanated from our "creation"?
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### Interaction speed between electric charges and magnetic materials

Einstein said that the speed of a matter in universe cannot exceed the speed of light. Is it correct for electric force transmission speed from one electric charge to other one? What is ...
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### What is the difference between an accelerometer and an inclinometer?

When looking through papers for a controls project I found one that seemed to be referencing the fusing of sensor data from an inclinometer and an accelerometer. I always had thought that it was ...
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### Dynamics - Beginner question

I am trying to understand this question, but I keep coming to a dead end: Two identical rectangular masses rest on top of one another, the top is tied to a wall on the left, while the one on the ...
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### Eigenvalue of $L_z$

In section 4.3 of Griffths' "Introduction to Quantum Mechanics", just below Figure 4.6, the sentence begins Let $\hbar \ell$ be the eigenvalue of $L_z$ at this top rung... Why is this valid? ...
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### Curvature of spacetime in only required to explain tidal forces?

I'm a bit confused about the equivalence principle in GR. I'm quoting from Wikipedia: An observer in an accelerated reference frame must introduce what physicists call fictitious forces to ...
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### Difference b/w Kinetics & Kinematics w/concrete example

(I know whether I understand this or not doesn't matter much to my work & study but am just curious.) I still can't differentiate in my head kinetics and kinematics (similar thread is found but ...
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### Can a force in an explicitly time dependent classical system be conservative?

If I consider equations of motion derived from the pinciple of least action for an explicilty time dependend Lagrangian $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ under what ...
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### Backward causality: A question/extension to Ma et al.'s “Experimental delayed-choice entanglement swapping”

In a philosophically rather interesting experiment, Ma et al. show that backward causality exists in quantum physics. An Ars Technnica-article gives a less technical account. From Ars Technica: ...
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### Why is force described as rate of change of momentum? [closed]

momentum = mass * velocity Differentiating both sides leads to force = mass * acceleration since the mass doesn't participate in the differentiation as it is constant. Is this a sound ...
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### How does a voltage independent current source work?

So I'm having some trouble understanding what a voltage independent current source is. How can you have a current without a voltage. as I understand it voltage or EMF is the force that drives the ...
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### is the voltage drop of a battery that is being short circuited the same as the battery's advertised voltige

So I know this is a pretty fundamental question, but I'll ask it any way. lets say you have a 12V battery, and the positive is connected to the negative directly by a wire with negligible ...
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### Equipotential Contour mapping and making it 3D [closed]

I have seen Contour diagrams for Equipotentials . That are drawn like so: I also saw One image for these contours that was in 3D (Negative Point Charge) : I was Wondering If there's any ...
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### How much water is destroyed in photosynthesis, relative to the world's supply?

Water is involved in the photosynthesis. How much water are we talking about compared with the total amount on water on Earth? Is it enough to have an effect on the average age of water molecules?
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### Fermi statistics and Berry phase

When the positions of two fermions are exchanged adiabatically in three-dimensional space, we know that the wave function gains a factor of $-1$. Is this related to Berry's phase?
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### Polyakov action as broken symmetry effective action

I would like to ask if it is possible to regard the Polyakov action as an effective action that describes the broken symmetric phase of a more general model. Could someone draw an analogy with O(N) ...
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### How to deterministically distinguish the following quantum states?

(1) How to deterministically distinguish the following quantum states: $$\frac{1}{\sqrt{2}}[|+0\rangle|0\rangle+|-1\rangle|1\rangle$$, $$\frac{1}{\sqrt{2}}|-0\rangle|0\rangle+|+1\rangle|1\rangle$$, ...
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### Producing photons with same frequency, different amplitude wave [duplicate]

I don't understand how two photons of the same frequency can have different amplitudes, neither how to produce them. I know that classically the square of the amplitude is proportional to the energy, ...
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### Branch-point twist fields and operator insertions on a Riemann manifold

I am having trouble understanding how Eq (2.6) in this paper (PDF) $$Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}$$ generalizes to ...
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### Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$?

For elastic collisions of n particles, we know that momentum in the three orthogonal directions are independently conserved:$$\frac{d}{dt}\sum\limits_i^n m_iv_{ij} =0,\quad j=1,2,3$$ From this, it ...
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### Apparent non-aberration of gravity waves

Since GR assumes that gravity waves travel at speed c, we expect we would be able to some day detect an aberration effect similar the that of light. Of course, gravity waves are so tiny in magnitude, ...