Aside

Who cares about…

Update (18 March 2012):

Copy of my comment submitted to Calder’s blog post on Quantum Computing:

“If you’re not sure whether an electron in an atom is in one possible energy state, or in the next higher energy state permitted by the physical laws, then it can be considered to be both states at once.”

Thanks for this article. The quantum computing idea depends on intrinsic indeterminism, the single wavefunction of Schrodinger’s equation. This gives a spread of probabilities for the energy state, until the wavefunction is “collapsed” by an actual measurement.

The quantum computing question is whether the single wavefunction (1st quantization quantum mechanics) mathematical model is an accurate, experimentally justified model. It’s non-relativistic, and in 1929 Dirac showed that the Hamiltonian in Schroedinger’s equation needs to be replaced by an SU(2) spinor to make it relativistic, which quantizes the field.

This is Feynman’s path integral (2nd quantization, or QFT), where there is no single wavefunction amplitude. Instead, each path has a separate wavefunction amplitude, and apparent indeterminist is just multipath interference from the virtual particles (similar to multipath interference of old HF radio waves due to partial reflection by different charged layers in the ionosphere). Feynman explains this fact clearly in his 1985 book QED, stating that Heisenberg’s uncertainty principle is unnecessary. All indeterminism is multipath interference, a physical mechanism. So if Feynman is right, there is no real mathematical magic, and the 1st quantization single wavefunction states at the heart of quantum computing research are a delusion.

The Majorana fermions news is very interesting, but again is a spin story. The “pair of Majorana fermions” described in the paper referenced by the Nature article (R. M. Lutchyn et al. http://arxiv.org/abs/1002.4033; 2010) is simply an electron and a semi-conductor “hole” at the interface between a superconductor and a semiconducting nanowire. The hole behaves as a fermion, and is electrically like a positron. So this Majorana pair is electrically neutral, and with entangled wavefunctions would prove useful for quantum computing.

But according to Feynman, the only entangled wavefunctions are from the 1st quantization non-relativistic model. Aspect’s experiments alleging quantum entanglement, and others, are fully explained by Feynman’s 2nd quantization multipath interference mechanism in path integrals, which simply isn’t included in Bell’s equality (a statistical test of 1st quantization). There is no discrimination between 1st and 2nd quantization in these experiments. Experimental spin correlation is assumed to be the entanglement of single wavefunctions. They simply ignore the path integral’s multipath interference mechanism. The use of statistical hypothesis testing is fiddled with a false selection of explanations: it is assumed that the experiments are a test of whether 1st quantization is right or wrong. Of course, under this assumption, it appears correct.

A more scientific version of Bell’s inequality would include a third possibility, namely Feynman’s path integral where all indeterminism is due to multipath interference, so there are no single wavefunctions to begin with. Supposed pairs of spin-correlated particles actually follow all paths, most of which cancel one another. There is no single wavefunction; instead, Aspect’s two apparently correlated wavefunctions (one for each detected particle) are each the sum of wavefunction amplitudes for all the virtual paths taken. This provides the physical mechanism for what is actually taking place.