# All Questions

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### Helium Fusion and the Origin of Elements

In the fifth of his Messenger Lectures Feynman mentions the fact that Carbon-12 has an energy level at 7.82 MeV. He then states that this is what enables the fusion of three Helium-4 ions into Carbon ...
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### why do the electroweak vacuum have to be charge and color neutral?

My question is why the electroweak vacuum of the Standard Model have to electroweak charge and QCD color neutral? What goes wrong if electroweak vacuum has either non-zero charge or color quantum ...
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### Quantum Fourier Transform and Entropy

QFT is a nonlocal unitary transformation and so can generate entanglement in a system. It means a separable pure state can be converted into an entangled pure state. Now since the presence of ...
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### Constant of motion

An exercise from Goldstein (9.31-3rd Ed) asks to show that for a one-dimensional harmonic oscillator $u(q,p,t)$ is a constant of motion where $$u(q,p,t)=\ln(p+im\omega q)-i\omega t$$ and ...
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### Higgs mechanism and neutral fields

Consider a Lagrangian $L(\phi,A_{\mu})$ with $\phi$ being some scalar field and $A_{\mu}$ some dynamical U(1) gauge field that minimally couples to $\phi$. Under a global U(1) symmetry the field ...
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### A meaningful distinction between determinism and causality

Causality is generally accepted to be a fundamental physical principle. But quantum mechanics is acausal (e.g. there is no 'why' as to the result of a measurement of the position of a particle in an ...
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### Significance of 'chiral' form for a quibit?

Say I have a qubit with probability amplitude divided evenly among $|0>$ and $|1>$ $$\frac{1}{\sqrt 2}|0> + \frac{1}{\sqrt 2}|1>$$ So it seems that we have a, loosely speaking, ...
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### Cosmological constant doubts

I have read about cosmological constant given by einstein in universe in nutshell as well as in general and special relativity. But still I am not able to understand the aim to use it or to introduce ...
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### Does water turn solid under deep ocean because of high pressure?

I know that we can make water solid with high pressure, so I think water will be solid in the deep ocean? If that is true, the depth of the ocean would be limited because water will become ice? ...
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### Is there a true parallel between Gibbs' phase rule and Euler's polyhedral formula?

Gibbs' phase rule states: $$F=C-P+2$$ where $F$ is number of degrees of freedom, $C$ is number of components, $P$ is number of phases. Euler's polyhedral formula states: $$V+F-E=2$$ where $V$ is ...
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### Electric field in two sphere system

Hi guys I'm really confused by this electric field question. Basically for the given setup shown, draw a graph of how electric field varies with distance from the center, given that radius of ...
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### Derivation of 3-D Potential Flows?

Specifically, spherically symmetric source/sink flow in spherical coordinates, then finding the potential of it. (I understand that the potential is just the integral of the flow function) Also, I'm ...
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### Polar Decomposition of a Complex Scalar Field

People often write a complex scalar field via polar decomposition. What does this parametrization precisely mean? To be more explicit consider the following Lagrangian of a complex scalar field with ...
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### 1. The problem statement, all variables and given/known data [on hold]

The problem statement, all variables and given/known data Consider a thin ring of radius a and mass M. A mass m is placed in the plane of the ring (not in the center!). Determine the gravitational ...
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### When can I use semiclassical approximation?

I know that I can use semiclassical approximation for path integral approach (in quantum mechanics) $\int d[q]e^{iA}$ when action $A >>1$. But how shall I use such condition? For example, ...
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### How does a lightning striking stall a moving car?

I am currently an undergraduate student leading a discussion section for an introductory electricity and magnetism course. I was asked this question that I was unable to answer and I am hoping for ...
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### Universal gravity at small distance

Could it be that there is simply a maximum gravitational force that two bodies of finite mass can exert on one another? This would occur at $r=0$, so maybe there is some really really really small $a$ ...
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### Internuclear Binding Force: Experimental geometric detail

I am looking for the most precise currently available deuterium potential energy curve (generated purely by experimental data) on the nucleon-nucleon scale. This is crucial. I need a radial ...
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### Origins of many-particle interactions

The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. virial expansion - it ...
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### D'Alembertian and Laplacian Green's Fucntions

There is a way to obtain the Green's Function for the Laplacian as a limit of the Green's function of the D'Alembertian? For the Laplacian ($-\nabla^2$) we have $$G_1(\vec X) = \frac{1}{4\pi X}$$ ...
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### Finding the vacuum which breaks a symmetry

I will start with an example. Consider a symmetry breaking pattern like $SU(4)\rightarrow Sp(4)$. We know that in $SU(4)$ there is the Standard Model (SM) symmetry $SU(2)_L\times U(1)_Y$ but depending ...
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### Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with knightian freedom the same things in essence?

In his remarkable works (1,2 and their recent development 3) Thomas Breuer proves by diagonalization the phenomenon that the observer cannot distinguish all phase space states of a system where he is ...
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### Do atoms of a surface excite to reflect the light?

How do surfaces reflect certain colours and absorb the others?
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### Beta Decay Energy

Consider $\beta ^-$ decay. \begin{align*} ^{198} Au \rightarrow ^{198} Hg + e^- + \bar{v_e} \end{align*} The decay energy is given by the difference in mass between multiplied by the speed of light. ...
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### Quantum computers: are they possible or impossible?

I know quantum computers are very complicated and my question is is there any way in "Principle" to create one? Are there already quantum computers being created?
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### The equation of the location of L1

On http://en.wikipedia.org/wiki/Lagrangian_point#L1 it says that the location of L1 can be determined as $\frac{M_1}{(R-r)^2}=\frac{M_2}{r^2}+\left(\frac{M_1}{M_1+M_2}R-r\right)\frac{M_1+M_2}{R^3}$, ...
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### Conservation of Mathematical Constraints when deriving Energy and Momentum from $F=ma$

Background: Starting from $F = ma$, integrating with respect to time, and using basic calc, one can derive $\int Fdt = m (v_f - v_i)$ Starting from $F = ma$, integrating with respect to distance, ...
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### Charged particle between two parallel likely charged plates, is it affected by the plates?

Imagine two parallel conductive plates. Charge up both to have the same amount of positive charge. Then put positive test particle between the two. The Coulomb's law is an inverse square law, so one ...
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### If the universe didn't expand faster than light, would our nights brighter like day?

There's a common QnA which has amused and inspired many kids: There are billions of Stars in the sky. If we combine lights received from all stars, wouldn't it beat Sun? Why is night dark really? ...
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### Collision between 2d circle and flat surface

First of all I want to preface this post by saying that I am absolutely terrible at maths, my level of geometry equals being able to discern a circle from a rectangle but that's about it, as for ...
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