Matryoshka World

Thursday, September 16, 2010

Is there a deep relationship between string theory and quantum theory?

ScienceDaily (Sep. 2, 2010) — Researchers describe how to carry out the first experimental test of string theory in a paper published September 2 in Physical Review Letters.

Professor Duff recalled sitting in a conference in Tasmania where a colleague was presenting the mathematical formulae that describe quantum entanglement: "I suddenly recognised his formulae as similar to some I had developed a few years earlier while using string theory to describe black holes. When I returned to the UK I checked my notebooks and confirmed that the maths from these very different areas was indeed identical."

This relationship between the math of string theory and the math of quantum entanglement may allow for direct testing of string theory in the lab, at least to the extent that the relationship pertaining to quantum entanglement is testable.

Here is the link to the Science Daily story

Saturday, September 4, 2010

Born in an infinite universe: a cosmological interpretation of quantum mechanics

This paper argues the Born rule is actually rendered redundant in an infinite universe in which all outcomes are realized.

this paper takes the conclusions of Page from the paper linked in the August 27 post immediately below a step further.
Page argued that Born's Rule would be insufficient in an extremely large universe due to the lack of definite projection operators.
We study the quantum measurement problem in the context of an infinite, statistically uniform space, as could be generated by eternal inlfation. It has recently been argued that when identical copies of a quantum measurement system exist, the standard projection operators and Born rule method for calculating probabilities must be supplemented by estimates of relative frequencies of observers. We argue that an infinite space actually renders the Born rule redundant, by physically realizing all outcomes of a quantummeasurement in different regions, with relative frequencies given by the square of the wave function amplitudes. Our formal argument hinges on properties of what we term the quantum confusion operator, which projects onto the Hilbert subspace where the Born rule fails, and we comment on its relation to the oft-discussed quantum frequency operator. This analysis unifies the classical and quantum levels of parallel universes that have been discussed in the literature, and has implications for several issues in quantum measurement theory. Replacing the standard hypothetical ensemble of measurements repeated ad inifnitum by a concrete decohered spatial collection of experiments carried out in different distant regions of space provides a natural context for a statistical interpretation of quantum mechanics. It also shows how, even for a single measurement, probabilities may be interpreted as relative frequencies in unitary (Everettian) quantum mechanics.

We also argue that after discarding a zero-norm part of the wavefunction, the remainder consists of a superposition of indistinguishable terms, so that arguably “collapse” of the wavefunction is irrelevant, and the “many worlds” of Everett’s interpretation are uniifed into one. Finally, the analysis suggests a “cosmological interpretation” of quantum theory in which the wave function describes the actual spatial collection of identical quantum systems, and quantum uncertainty is attributable to the observer’s inability to self-locate in this collection.