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Hi, I am a string theorist and a publicist.


Oct
21
revised Why higher frequencies in Fourier series are more suppressed than lower frequencies?
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Oct
21
revised Why higher frequencies in Fourier series are more suppressed than lower frequencies?
added 73 characters in body
Oct
21
revised Why higher frequencies in Fourier series are more suppressed than lower frequencies?
added 386 characters in body
Oct
21
answered Why higher frequencies in Fourier series are more suppressed than lower frequencies?
Oct
20
answered Why does charge conservation due to gauge symmetry only hold on-shell?
Oct
19
comment Modern avatar of Englert's solution?
I see, thanks for the clarrified connections etc., @José.
Oct
19
comment Non-unitarity of wave function collapse
Dear @Jonathan, in some modest sense, you may be able to "define" the square root of the delta-function but you won't be able to calculate with it. For example, you won't know what it evolves to. It's easy to see why. An ordinary delta-function evolves to the well-known nonzero functions at time $t$, calculable from the Green's functions. However, the square root of the delta-functions is proportional to delta-function but infinitely times smaller. So it will evolve into "zero" and unitarity will be violated, anyway. This is just not how the calcuations may be done.
Oct
18
comment Is there a theortical limit to the amount of sound-energy air can contain?
I actually think it's a fun question. It depends what configurations of the air you're ready to call sound. For example, you may allow sound waves that make the air pressure drop everywhere except for $1/N$ of the volume. I guess that the work this system may perform while switching to the uniform pressure goes like $C.p_{\rm average}V_{\rm total}\ln(N)$ or so. Of course, if you may compress all the air to very small regions, you will get more energy. Then there are lots of questions whether you allow heat (hot air), phase transitions, hot air, nuclear reactions etc.
Oct
18
comment What is a simple intuitive way to see the relation between imaginary time (periodic) and temperature relation?
Nice, Moshe! Qmechanic: fun terminology. I guess the opposite is not true: the Heisenberg representation isn't an important representation of the Schrödinger algebra. However, what is true is that Wigner's friend is an important representation of Schrödinger's cat and Wigner's friend could even be Heisenberg himself, see e.g. this picture en.wikipedia.org/wiki/File:Heisenberg,W._Wigner,E._1928.jpg :-D
Oct
18
comment Modern avatar of Englert's solution?
Dear @José, sorry for being redundant then. I also added (into my answer) a link to a seemingly related paper on the octonionic membrane by Duff et al. Conical singularities in general don't solve Einstein's equations at the singular point except that sometimes they can when the UV physics governing the singular loci is favorable. After all, orbifolds are allowed and some of them may also be viewed as deficit angles etc. But I am afraid that if a full-fledged embedding of Englert's solution to a UV complete theory exists, it's not known.
Oct
18
answered Modern avatar of Englert's solution?
Oct
18
comment Non-unitarity of wave function collapse
This is a meaningless statement, lurscher. Of course that if you want to imagine that there exists a non-existent, non-local, inconsistent, non-unitary operation that messes up the wave function, you follow this pathological procedure at least by another procedure that rescales the wave function so that it has the same norm as before. But this is by additional fudging: there's no inherent preservation of the norm in the operation. It's wrong to say it's by "definition". By the most natural definition, the pathological non-unitary non-local operation you propose also modifies the norm.
Oct
18
comment Non-unitarity of wave function collapse
"measurements in the most basic formulation given in QM courses always assume that you are able to measure the state in a non-local way" - Nope, there is no contradiction between locality and the postulates of quantum mechanics, as demonstrated by the important example of local quantum field theories such as the Standard Model which are perfectly local. They also describe reality: all physical processes in this Universe are demonstrably local, which proves that all mechanisms that are nonlocal are unphysical.
Oct
17
comment Non-unitarity of wave function collapse
To show that the "decoherence map" (elimination of off-diagonal entries) isn't an isometry on the space of matrices, just consider what this map does with matrices $((a,b),(b,c))$ for different values of $b$. These matrices are clearly very far from each other in the natural metric on the space of matrices, especially if you pick a large $b$. But all these matrices get mapped to $((a,0),(0,b))$ so the distance of the values of the map is zero. ;-)
Oct
17
comment Non-unitarity of wave function collapse
So it makes no sense to ask whether this operation (elimination of off-diag. entries) is an isometry on the Hilbert space itself: it's not a map on the Hilbert space at all, it's a map on the space of density matrices (roughly speaking the tensor product of the Hilbert space and its conjugate copy) only. And on this space, the elimination of the off-diagonal elements is clearly not an isometry, either. So whatever way you look at your statements about the collapse's being an "isometry", they're invalid.
Oct
17
comment Non-unitarity of wave function collapse
Because the text of your answer makes it clear that you actually don't want to pick the "measured outcome" or explain how it is done - you're really trying to explain decoherence and not collapse (which is why your answer has no relevance to the original question which was about the collapse, but let's discuss your answer anyway) - you're talking about decoherence. But decoherence produces a map on the space of density matrices, not on the Hilbert space only.
Oct
17
comment Non-unitarity of wave function collapse
"So what the measurement does in general is kill all off-diagonal components of the density matrix": you wanted to say "So what decoherence does...", right? Your description of what measurement does isn't valid. The measurement, as understood in the incorrect interpretation of QM that you're promoting here, is not only bringing the density matrix to a diagonal form: it also sets to zero all the diagonal entries except for the chosen one.
Oct
17
comment Non-unitarity of wave function collapse
@Lurscher, let me also mention that if you want the post-collapse wave function to be proportional to a delta-function in the position representation, such an outcome would 1) have a very sick normalization because you need $\psi(x)=\sqrt{\delta(x-x_0)}$ for the squared wave function to have the right integral; the square root of a delta function isn't really an element of the Hilbert space; 2) if the wave function is strictly proportional to the delta-function, it carries an infinite average kinetic energy: the momentum is totally undetermined and the expectation value of $p^2$ diverges.
Oct
17
comment Non-unitarity of wave function collapse
Dear @ANKU, I don't know how you proved that the inner product of $C\psi_i$ and $C\psi_j$ is the particular Kronecker-delta. I think that there's no operator that would satisfy your condition for every $\psi_i$, $\psi_j$. Moreover, I don't understand what's the difference between $\psi_j$ and $j$. What you wrote is just very confusing.
Oct
17
comment Non-unitarity of wave function collapse
Dear @lurscher, the fact that the wave function is just a set of numbers to calculate probabilities from, and not a real observable, is an experimentally proven fact, not a matter for beliefs or disbeliefs. By the way, your second statement is also impossible. One can't define a prescription for such a collapse so that it would conserve the norm if we also require the physics to be local: one has to artificially "renormalize" the wave function after the collapse and it's clearly a non-local procedure because it depends on the magnitude of the wave function at other "places".