Quantum Projection Postulate Enigma
Possible interpretations of the Quantum Projection Postulate are considered in view of the history of Quantum Mechanics. However strong are the existing theoretical objections to the strong Projection Postulate, it is suggested that direct experiment is needed in order to reject it for good. In such case the weaker Projection Postulate interpretation is called for, which sees the classical view of a system as its time averaged quantum view. In that case use of the measurement projection as Quantum Computation operation introduces important performance degradation.
As the Quantum Mechanics has been forged in 1924-1927 by genius of Schrodinger, Heisenberg, and Bohr – the measurement was described through the projection postulate (PP) as collapse of the wave function, while wave function itself was interpreted in terms of probabilities of observation.
By the 1929, Quantum Mechanics with Copenhagen Interpretation thereof, appeared
to be satisfactory and settled.
However, as probabilities do imply limits of casual description, Einstein
was still unhappy with the picture.
In 1935, A.Einstein, B.Podolsky and N.Rosen invented a thought experiment, presented in their famous article “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” [1]. Based on their thought experiment, EPR concluded that the quantum state of the second particle of the pair of not interacting particles must depend on the kind of measurement that is performed on the first particle of said pair – if the maximally strong Projection Postulate is being assumed to be true.
Which would imply that QM theory
endorses non-casual casualty and strong non-locality, when two independent
non-interacting particles influence each other, and in the classical limit,
vanishing of Plank’s Constant does not eliminate the said non-locality.
From the point of view of EPR, a theory with such peculiar features contradicts
our basic understanding of the reality, as well as the established principles
of Physical description.
Less than a year later, Margenau has pointed out, that the EPR thought experiment can be reinterpreted in more productive way. It must be considered a proof, that the Quantum-Mechanical Description of Physical Reality was redundant, or rather was limited because of its redundancy. Margenau has identified Projection Postulate as the redundant part.
In QM without Projection Postulate, EPR thought experiment affirms the consistency of physical description, without yielding contradictions, incompleteness, or redundancy. The price of consistency is that we must consider measurement a QM process, which involves both the object measured and the measurement device.
The heated discussion had ensued, which has not resulted in full rejection of the projection postulate, although it was relegated to the superficial status. Projection postulate has become suspect for Physicists, avoided whenever possible, although the reformulation of QM without PP was not fully completed and codified in the textbooks.
Persecution of Jews in Germany and the Second World War, have damaged the scientific school that was largely responsible for decades of remarkable progress of the Physics. Nobody had anymore the authority and insight, necessary for accomplishing the QM reformulation task. The question was left to linger - whether PP is a fundamental assumption of
Quantum Mechanics, or is it just a tentative heuristic rule, which enables us to think in terms of states. For decades it was mostly harmless ambiguity, and over next seventy years nobody has come up with actual experiment that could not be satisfactory explained without projection postulate.
Meanwhile, Computer Science has taken the place of Physics in enabling the leading edge of technological innovation, and Physicists were looking for a comeback. An opportunity presented itself in the shape of idea of Quantum Computation, based on the q-bits instead of bits, as was suggested in general terms in 1982 by Richard Feynman [3].
Since Projection Postulate was formally still in the QM, and since the Computer Scientists were not aware of the subtleties involved, they come to rely on the strong PP in their attempts to expand upon the idea. Pretty soon Quantum Computing and Quantum Cryptography, all based on PP, has become burgeoning branches at intersection of the Computer Science and Physics. However, the practical results in this area until now are rather disappointing, especially compared to spectacular progress achieved by digital computers over the same time period.
We must explain this discrepancy and must correct the course, if needed. In particular, whether we want it or do not want, we must now finish the reevaluation of projection postulate, picking up where this job was left seven decades ago. And the way to do it is to devise and perform the actual experiment corresponding closely to the thought experiment of EPR. This would probably happen 70 years ago, were not Physics been derailed by war. The revaluation should not be delayed anymore, no matter how painful the expected result can be.
An experiment based on the particle scattering could be designed as a close real version of EPR thought experiment. If strong PP were correctly describing the Physics involved, by changing the measured characteristic of the first scattered particle of the pair, we would be able change of results of the fixed measurement that is performed on the second scattered particle of the pair.
If strong PP were confirmed in such direct experiment, the Quantum Computing and Quantum Cryptography, entanglement, and teleportation applications would continue on with stronger confidence in soundness of their foundations. On other hand, if strong PP is overturned and must be dropped, the very foundation of these theories and of their applications must be reconsidered.
From the point of view of Physics, such negative outcome would require a more careful reinterpretation of the Projection Postulate.
The Projection Postulate provides a bridge between the microscopic purely Quantum Mechanics, and the classical macroscopic mechanics that describes large systems’ averages in a statistical way that involves classical probabilities, averages and temperature, along with classical unhindered measurability.
It appears that it must be possible to deduce a Projection Theorem from the Quantum Mechanics, in other words to provide a mathematical proof of the Projection Postulate that also discovers its limitations and its applicability area.
Similar to the way that Statistical Physics is deducible from the classical mechanics by averaging over infinite time, such a proof could probably be obtained by analysis of behavior of averages of the quantum values over time spans much longer than h/kT. [4]
Assuming that the Projection Theorem is provable along the lines suggested, we can see why the Projection Postulate does not say anything about the measurement time. It is indefinite, and the more precisely we want the result to be predicted the longer it is.
In other words, the Projection Postulate is to be interpreted as a rule, yielding average of an observable value over infinite time.
The important consequence of such interpretation would be that it is incorrect to ignore the measurement time in the computing applications that are relying on the measurement projection. The estimates based on the Uncertainty Principle suggest that said measurement time is likely to increase exponentially with size of the problem.
References:
[1] A. Einstein, B. Podolsky and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete”, Phys. Rev. 47, 777 (1935)
[2] H. Margenau, “Quantum-Mechanical Description”, Phys. Rev. 49, 240 (1936)
[3] R. P. Feynman, "Simulating Physics with Computers", International Journal of Theoretical Physics, 21, 467, (1982)
[4] L. D. Landau and E. M. Lifshitz, Statistical Physics, Addison-Wesley (1969)
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