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bio website motls.blogspot.com
location Czech Republic
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visits member for 3 years, 7 months
seen 2 hours ago

Hi, I am a string theorist and a publicist.


6h
comment Possible Error in deriving conformal generator
There are several issues, I've mentioned some of them, and one must be careful about the conventions and strategy used by someone else. If you have a problem with someone's derivation, try to check the "big claims" only and derive it yourself - all the hard ideas of the derivation may clearly be seen even in the derivation following slightly different strategy, conventions, and active vs passive distinction. I feel that if you can't derive it yourself even while looking at the "template derivation", it's useless to follow someone else's derivation, anyway.
2d
comment Possible Error in deriving conformal generator
Also, the most general transformation always fixes some point, so it may be obtained from a transformation fixing the origin, by conjugating it with a translation by $Y$ which is the point that is fixed.
2d
comment Possible Error in deriving conformal generator
Hi, thanks. I wasn't quite able to figure out what the first question is. The full transformation is composed of two things: finding the right $x'$ for a given $x$, and evaluating the components at the new point (that's the orbital part); and mixing the components with each other (that's the spin part). The full generator may be divided in this way. If we specialize to transformations that do not change $x$, the orbital part is trivial so it may be subtracted or added without spoiling the formula.
2d
comment Possible Error in deriving conformal generator
The commutators like $[J_{\mu\nu},x^\alpha]$ vanish because $x$ is a vector of $c$-numbers, so in each representation, it is simply proportional to the unit matrix that commutes with all the actual generators. Here $x$ is not meant to be something like the $x$ operator acting on a wave function in QM.
Aug
20
comment Feynman Lectures: Trigonometry Error in Rotational Dynamics?
Yes, that's very right that you're used to that notation. But Feynman's talk is supposed to be directed even to undergraduates who haven't heard of calculus, or at least who haven't internalized it, so he's just "emulating" much of the wisdom of the calculus without the modern notation for derivatives and infinitesimals.
Aug
18
comment Classical probability explanation for quantum non-locality and Bell's inequality?
If you are saying that the classical Malus' law is enough to calculate the absorption by polarizers, then it's because the classical Malus' law is mathematically identical to the probailities for 1 photon in QM - and that's because the classical law is actually an emergent consequence of the quantum law when the same absorption rate is applied to many photons in the same state.
Aug
18
comment Classical probability explanation for quantum non-locality and Bell's inequality?
If you claim that you have a classical local model that gives the same correlations, then you are wrong. It is not possible. If you are manipulating with the probabilities computed from QM and see that the manipulations are consistent with classical probabilities, they are because there's nothing such as "classical and quantum probabilities". The concept of "probability" means exactly the same thing in quantum mechanics - it's just being differently, more directly, calculated.
Aug
18
comment What is the motivation for the definition of a manifold?
No but every theorem about manifolds does.
Aug
14
comment Glashow-Weinberg-Salam mass terms
You've copied the error of missing $i$ in front of $W^2_\mu$, didn't you?
Aug
14
comment Must length equal distance?
Apologies, user, I don't understand these thoughts of yours. You are doubtful about some aspect of the notion of "distance" or "length" that others probably find obvious, and I don't know what it exactly is.
Aug
14
comment Reduced mass and harmonic mean
An underlying reason/explanation for a mathematical claim - like any claim about harmonic averages - is ultimately mathematical. So the "mathematical deduction" and the "underlying reason" is really the same thing. Of course it's no coincidence that the reduced mass is proportional to the harmonic average.
Aug
13
comment What is the status of massless photons traveling through a medium?
You surely don't mean a pure state in the sense of an element of the Hilbert space, do you? Every physical system may be in a pure state. A pure state is the right description whenever our information about the system is maximized one allowed by the uncertainty principle.
Aug
12
comment Why are the energy eigenstates realized in atomic transitions?
Dear @queueoverflow, nope, you still completely misunderstand how it works. First of all, the ket vectors with several terms are not "mixed states" - mixed states are described by density matrices, not by vectors in the Hilbert space - they are just "superpositions". Second, general superpositions have transitions to other superpositions. The coefficients in the superpositions dictate the probabilities that it happens. If you write two pure states with different coefficients, they are not "mutually exclusive". They describe the probs that one or another option is realized.
Aug
12
comment Length in polar coordinates
even if $d|\vec X|=0$ i.e. if the tiny infinitesimal line interval $d\vec X$ goes tangentially along a circle with a fixed $r$, i.e. if it goes in the angular direction. Because the length of the arc given by angle $d\phi$ is simply $r\cdot d\phi$, the formula for $ds^2$ must contain this squared, i.e. $r^2\cdot d\phi^2$. At the end, the opposite-signature time coordinate is added to both expressions in the obvious way.
Aug
12
comment Length in polar coordinates
Forget your 3D spacetime. Take just the two ++ coordinates. Then $X\cdot X$ is just the inner product of the vector $X$ with itself which is simply $r^2$, the squared distance from the origin. The distance from the origin is called the radial $r$ coordinate. But $dX\cdot dX=ds^2$ is something else. It's the squared length of an infinitesimal vector $d\vec X$ which is located everywhere. So it's not the squared length of a line interval starting in the origin $(0,0)$, which was the case of $X\cdot X$. Now the tiny line interval $dX$ is at any point $X$ and it has nonzero length even ...
Aug
12
comment Length in polar coordinates
No, your question and guess are perfectly right! But $\partial_a X\cdot \partial_b X$ - which is similar to $dX\cdot dX=ds^2$ - is something else and behaves differently than $X\cdot X$ without the derivatives. The two formulae (first and second in your original question) are just very different.
Aug
12
comment Why are the energy eigenstates realized in atomic transitions?
Wow, thanks a lot, but only see modest 99,996 here! Maybe I got two downvotes since your party. :-)
Aug
12
comment Why does the sky suddenly look gray through this window?
Hi, I don't think it's right to talk about a "filter". The grey light you are seeing is not obtained by filtering the blue light from the sky - it wasn't reflected by droplets at random points of the sky first. Instead, the grey light is scattered white light that goes directly from the Sun, and changes the direction in the dirt on the glass. I tried to point out that your whole way of looking at the question is upside down from a physics viewpoint. The normal color is grey - the abnormal color that needs an extra explanation is blue.
Aug
12
comment simplification of Green's intergral for diffusion
The original integral was a simple gaussian, $\exp(x^{\prime 2})$, why would you make a substitution that would turn it into a hard and bizarre $\exp(x^2)$? I am sure you have misunderstood the substitution.
Aug
12
comment How to test that a flat metric represents a global three-torus geometry
In general relativity, we never imagine that the space or spacetime is a submanifold in a higher-dimensional one (your "4D space") - the embedding is just a tool to visualize curved spaces in popular texts for children. ... Otherwise, the toroidal shape - with its finite volume and periodicity - clearly has lots of potential consequences. One may sail around like Magellan, see multiple images of the same celestial objects in many directions, etc. For any of these to be observable, the torus must be small enough - not too much bigger than the visible Universe.