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Relativity plus quantum mechanics

... Einstein never had a good word for the relativity version of quantum mechanics known as quantum field theory. Its successes did not impress him. Once, in 1912, he said of the quantum theory the more successful it is the sillier it looks. When speaking of successful physical theories, he would, in his later years, quote the example of the old gravitational theory. Had Newton not been successful for more than two centuries? And had his theory not turned out to be incomplete.[41, p 24]

There is no theory that combines quantum mechanics and general relativity. In quantum mechanics the greater the accuracy of a measurement of location the more uncertainty there is a in the measurement of energy. The uncertainty principle applies not just to particles but also to empty space. Over very short intervals phantom or virtual particles can appear. The shorter the time, the more massive the particles can be. At very short intervals, virtual particles will be massive enough to form black holes. One cannot extrapolate simultaneously both quantum mechanics and general relativity to minute distances. The theories explode or diverge.

Quantum field theory combines special relativity and quantum mechanics in a problematic structure. Practical experiments can test the questionable aspects of quantum field theory using Bell's inequality (see Section 8.4). It is only the predictions of quantum field theory and not the mechanism that generates those predictions that are relativistic.

This is possible if probabilities are absolute. For that allows two events to affect each other without being able to determine which is the cause and which is the effect. The direction of the causal arrow is masked by quantum randomness. A mathematical model (like quantum field theory) that creates these predictions has to make a choice and, in making that choice, it violates relativity. Many physicists would not agree with this statement claiming only realistic models have this problem. Such arguments depend on one's philosophical view of quantum randomness. The absolute probabilities claimed for quantum mechanics have no mathematical definition and this leads to philosophical debate (see Section 8.2).

General relativity and quantum mechanics have disjoint experimental domains. General relativity is only observable with massive objects. Quantum effects are only observable with minute particles. Thus these incompatible theories can coexist in a temporary truce. Eventually something has to change.

This has created an unfortunate situation in contemporary foundations research. The hottest research area for extending theoretical physics is combining these theories. The experimental domain in which such combinations could be tested is unreachable with existing and foreseeable technology. The situation is not unlike that in mathematics where fundamental research focuses on properties of large cardinals when no infinite sets let alone large cardinals may exist. Reconciling the two fundamental physical theories is a mathematical exercise that may be devoid of physical content.



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