dog days of blogging

Hey, is it true that if you cut the physics blogosphere into two pieces, the two parts will both have equal volume after the cut? If you cut it right?

Nah. The physics blogosphere is two-dimensional. Area is conserved.

two-spheres are so boring.
But surely the physics blogosphere is high entropy-er-information structure - if not a "monster".
So... shouldn't the area grow when operated on, with area conservation a limiting ideal in the classical model?

Of course quantum mechanically it is hot and evaporating, sending information to infinity, possibly faster than it is added.

Question then is whether the physics blogosphere is unitary or does it destroy information.

The bottom half of the decadal physics suit problem is, recently, more studied (see below) than the top (see further below).

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Bottom:

The trousers problem revisited
JournalPramana

PublisherSpringer India
ISSN0304-4289 (Print) 0973-7111 (Online)
IssueVolume 30, Number 4 / April, 1988
CategoryGeneral Relativity
DOI10.1007/BF02846737
Pages279-292
Subject CollectionPhysics and Astronomy
SpringerLink DateFriday, February 29, 2008

PDF (576.1 KB)

General Relativity

The trousers problem revisited

Corinne A Manogue1, 2, 5 Contact Information, Ed Copeland3, 6 and Tevian Dray4, 2, 7
(1) Department of Mathematical Sciences, University of Durham, DH1 3LE Durham, UK
(2) Institute of Mathematical Sciences, 600 113 Madras, India
(3) Blackett Laboratory, Imperial College, SW7 2BZ London, UK
(4) Department of Mathematics, University of York, YO1 5DD York, UK
(5) Present address: Department of Physics, Oregon State University, 97331 Corvallis, OR, USA
(6) Present address: NASA/Fermilab Astrophysics Centre, Fermi National Accelerator Laboratory, 60510 Batavia, IL, USA
(7) Present address: Department of Mathematics, Oregon State University, 97331 Corvallis, OR, USA

Received: 14 December 1987
Abstract Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our results using a more general propagation rule support their conclusion.

Keywords Trousers topology - propagation rules - massless scalar field - energy density

PACS Nos 11.10 - 03.70

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Top:

excerpted from the "Physics of Cognition" thread of
http://god-does-not-play-dice.net/right.html

Suppose you chase somebody on the street (let's call him John), and any time you catch him, he leaves his jacket in your hands. You can't catch John. Just his jackets. You also know that he has a set (or is it strictly a set?) of jackets with different probability-for-catching, and you deeply believe and hope that this set can be normalized, i.e., the sum of probability-for-catching his jackets is unity. This elusive John does not ware any jacket by default (i.e., the concept of "possessed values" finds no place in proper physical reasoning [Ref. 51]). Neither before nor after you catch his "current" jacket. John is simply a Platonic idea.

Does he have a quantum correlate? I hope he does, or else we have to consider the possibility that time does not exist...

On the practical side, the idea about John's jackets suggests that quantum computation [Ref. 5] can not be implemented with any inanimate device, but we can extend our brain to cover the quantum reality of John and to control his jackets, just like we control our body. The phrase "the whole is more than the linear sum of its parts" means that John is not in the Hilbert space. Never been, never will. He has been totally erased from the outset, right from the linear decomposition of his jackets.

To explain this, let's suppose John has two jackets only, their classical projections are denoted by |0> and |1> , and superpositions are [alpha]|0> + [beta]|1> , where [alpha] and [beta] are complex numbers satisfying |alfa|2 + |beta|2 = 1, in line with the normalization procedure. The jackets |0> and |1> represent an orthonormal basis of a two-dimensional Hilbert space. Where is John, then? He has been deleted from the Hilbert space by the normalization procedure. The latter does not refer to the genuine superposed state of the two jackets but to some stripped classical shapes |alfa|2 and |beta|2. With inanimate devices, we can observe stripped classical jackets only. Not John wearing two jackets in a superposed state or entangled state [Ref. 6; Ref. 26; Note 1 ]. Hence we can not employ John to do some "quantum computing" [Ref. 7]. All questions we could ask about what John might be doing "during" the "time" of wearing two superposed jacket(s) are just meaningless -- there are no time operators in quantum mechanics. Even more: time is not an observable [Ref. 8]. Also, there is no such thing as "perfect clock" [Ref. 9].

All I could say at this point is what would be the wrong way of thinking about John's jackets. We can infer from classical physics that reality can be independent from observations: there is a chair behind me, no matter if I see it or not. Reality could also be totally subjective, for instance, if I want to think of a chair, I can evoke it in my imagination. These two extreme cases, objective and subjective reality, are not applicable to John's jackets....

Well, duh.
The Trousers Problem is well know to be hard. Even in summer when it is reducable to the equivalent Shorts Problem.
But who wears jackets in summer?
So clearly the Jacket Problem is trivial.

And why do I now think of this as the Barack Paradox?

Because he's the Pro-Axiom-of-Choice candidate?

John Sidles has just made a fascinating variant of the Anthropic principal: "the quantum state-space of Nature is itself likely to be dynamically Kahlerian." This is over on the "Quantum Computing Since Democritus Lecture 19: Time Travel" thread of Professor Scott Aaronson's blog "Shtetl-Optimized."

I've wondered thus:

In a simple sense, the speedup [by embedding quantum trajectories on a suitably-curved Kahlerian manifold, so that the state-space geometry itself implicitly handles much of the computational complexity of calculating the trajectory, and hence that the resulting codes are tremendously fast] is because of results such as the Lefschetz Theorem (that each double point assigned to an irreducible algebraic curve whose curve genus is nonnegative imposes exactly one condition) which is itself a consequence of the Kahler condition (equivalently: existence of a Kahler metric; existence of a Kahler form, i.e. a real closed nondegenerate two-form, i.e., a symplectic form, satisfying a technical condition with the almost complex structure induced by multiplication by i; existence of a Hermitian metric where the real part is a Kahler metric, and the imaginary part is a Kahler form; or existence of a metric for which the almost complex structure is parallel).

Similarly, the Hodge decomposition of cohomology stems from the Kahler condition for compact manifolds. But exactly why, other than 'neat Math?', should we suspect that "the quantum state-space of Nature is itself likely to be dynamically Kahlerian?"

I like the conjecture very much, but seek more confidence in it.