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Hi, I am a string theorist and a publicist.


1d
comment Local number operators in quantum field theory
Hi, I actually don't understand it fully, either - I think that in the case of non-relativistic quantum field theory, the statement is really wrong. One may define the number density operator in that limit. The number of particles in a region is nothing else than the "second quantization" (promotion of kets and bras to annihilation and creation operators) of the bilinear expression in bra-kets that would calculate the probability in the 1-particle Hilbert space. There's nothing wrong about it. The nonlocalities, problems, and divergences only start with relativity and loop corrections.
2d
comment Local number operators in quantum field theory
I think he's effectively saying that the number density operator is defined in the phase space, with the cell-of-phase-space resolution. So if you compute the number of particles in a region, you always have to make assumptions about its momentum i.e. allowed relative phases, too.
2d
revised Quantum mechanical proof of Conway's SPIN and TWIN axioms?
added 102 characters in body
2d
answered Quantum mechanical proof of Conway's SPIN and TWIN axioms?
2d
answered Local number operators in quantum field theory
2d
comment Find electric field given the magnetic field
You obviously can't find the electric field itself because the electric and magnetic fields are independent at each point.
2d
comment $m_l=0$ in Hydrogen atom of Scrodinger equation
Yes, the electron in an atom is "vibrating" in the radial direction around the average value that is what you write and that is of the same order for other states of the same atom or other atoms, too. The $x,y,z$ components of the position commute with each other, and so do the 3 components of the momentum. The 3 components of the angular momentum do not commute with each other, but the commutator of two of them is the third one, so the states with $J_x=J_y=J_z=0$ are an "exception" for which the commutator is effectively zero so the $s$-states are eigenstates of all three components.
2d
comment Kinetic energy operator in Dirac's relativistic quantum theory
If you subtract $m_0 c^2$ from the operator i.e. if you add $(-m)$ – I used units with $c=\hbar=1$ everywhere - it just means that $m\gamma_0$ will change to $m(\gamma_0-1)$. Subtraction is subtract, just minus what you subtract. Note that when you do this subtraction, slow electrons will indeed have a very small "non-relativistic" kinetic energy because the corresponding $\Psi$ is "almost" annihilated by the $\gamma_0-1$ operator.
2d
answered How much more efficient is a road bike than a mountain bike?
2d
answered Why aren't units with powers, like cm³, surrounded by parentheses?
2d
answered Kinetic energy operator in Dirac's relativistic quantum theory
2d
comment From where comes the raindrop
I agree with you, Jim. However, one must also be realistic about the altitude from which the droplets are actually falling. The altitude may be as small as 1200 meters in which the case the variation of the wind may be limited.
2d
comment Nikola Tesla vs Einstein?
Einstein wasn't an inventor, he was a scientist.
2d
comment From where comes the raindrop
The cloud from which the droplet came is probably in the direction from which the wind blows.
2d
answered From where comes the raindrop
2d
comment $m_l=0$ in Hydrogen atom of Scrodinger equation
First, it is only not moving in the angular directions; the average value of the momentum in the radial dimension is nonzero. Second, this $|p_r|$ has to be nonzero, much like the average $|r|$, so the particle can't quite stop and can't collapse to the nucleus, due to the uncertainty principle $\Delta p \cdot \Delta x \geq \hbar/2$ which prohibits $r=0$ much like $|\vec p|=0$ etc. The electron finds a compromise between minimizing the kinetic energy (small $p$ is good) and minimizing potential energy (small $r$ is nice), and the sum, total energy is minimized for Bohr-radius-like radius.
2d
answered $m_l=0$ in Hydrogen atom of Scrodinger equation
2d
comment Number of Stars vs Value of Omega (Crtitical Density of the Universe)
They do but there is nothing wrong about that! The branching bubble Universes don't contradict any empirical data, so the theory is totally healthy. That's indeed how the real Cosmos probably behaves. One must distinguish the constant repetitions of the inflation - that's what's ever repeating in "eternal inflation" - and the problem whether one particular expansion episode may terminate. The latter answer is Yes, "graceful exit" etc., and it's been known to be Yes since the early 1980s, too.
2d
comment Negative energy/mass bounds on de-Sitter spacetime
They're related because any notion of energy has to be linked to something that is conserved in the case of the time-translational symmetry of the laws of physics. This is what the notion of energy means. If you don't "conflate" it in this way, then you are sloppy about the meaning of the word "energy". You could then very well redefine energy to be the balance account of someone U.S. dollar account and indeed, it can be negative. But the genuine energy density cannot.
2d
answered Why does Pluto's orbit cross Neptune's orbit?