Some researchers have done some work on the constraints on small scale behavior that you get from large scale structure: for instance, just being inside a box limits the number of quantum states available to a particle. A free particle has an infinite number of possible states; a particle in a box only a finite number. "They then realized that if their same bound applies to our entire universe, it resolves the cosmological constant problem. In this scenario, the observable universe is like a very large box. And the number of high-energy particle states it can contain is proportional to the observable universe’s surface area to the three-fourths power, not the universe’s (much larger) volume."
Boundary conditions matter. (I'm not going to go into the "holographic universe" notion that the boundary encodes the contents as a kind of dual to the 4D universe--I'm not persuaded it's a useful exercise.)
If somebody can work quantum gravity into the picture, that'd be very interesting indeed. And no ugly supersymmetry around...
It might be interesting also to think through the limits of the Pauli Exclusion Principle too: if the (e.g.) electrons are separated so far that light hasn't made the trip yet their wavefunction overlap is 0, but once they do...
4 comments:
Epicycles. Both cosmology and quantum mechanics keep getting more complex. Whenever they encounter an anomaly they add exotic new thingies - dark matter, quarks - rather than questioning their assumptions.
Cosmology is certainly getting more complex (e.g. "inflation"), but quantum mechanics is, as far as I can see, either working on applications or trying to pin down the meaning of what it does.
Quantum mechanics is really two separate fields of study. The first, the part that underlies a vast number of very useful phenomena, is a statistical treatment of large numbers of particles (typically > 10^6) and resembles the gas laws. The other, the study of individual particles, is a mystery.
"Nobody understands quantum mechanics." ~ Richard Feynman
With your indulgence, this is the comment I wrote on the article you reference -
Herewith lies the fundamental fallacy of reductionism. By definition, when it is employed you discard information. Its mathematical analog is the differentiation of the calculus of variations. Differentiation's inverse, integration, is not a return ticket. Likewise, a truckload of Scrabble sets might contain the works of Shakespeare - it's just that some assembly is required.
"[T]he atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts." ~ Werner Heisenberg
That you are reading this demands a telos - a raison d'être - to even form the question. The answers are not to be found within the blinders of Physics.
It isn't really statistical in that sense. It is founded on the discovery that at a small enough scale particles can be described as waves--something outside everyday experience--and that those waves have some of the properties of particles too.
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