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THE QUANTUM BOX EXPERIMENT:
In 2007, I had the good fortune of attending the "Quantum Paradox" class that was taught by Drs. Aharonov or Tollaksen at George Mason University. The "Quantum Box Experiment" was related at a class I attended. Although the experiment provides one "proof" that TSQM is "real", the findings have not, to the best of my knowledge, been published. Accordingly, the following reflect my notes, recollection and handout from the class lecture.
Before I go on, you may wish to review an early description of the experiment. (See: http://arxiv.org/abs/quant-ph/0310091v1)
Now, please visualize a set of six boxes arranged in a three by three matrix with the columns labeled from left to right: Box A, B, and C; and rows labeled from bottom to top: time t, t1 and t2. A particle entering the system at the bottom (e.g. at time t) is understood to have a one-third probability of being in Box A, B, or C at all levels, t, t1 and t2. It was my understanding that these probabilities were confirmed through ideal, or von Neumann, measurements taken at each level. However, these confirming measurements were not part of the experiment that I am about to describe.
In the experiment, a very large ensemble of particles was introduced into the experiment and, although ideal measurements were taken at time t2 for Boxes A, B, and C, only the experimental data for those particles found Box A (the post-selection sub-ensemble) were retained for further consideration. The theory behind the experiment is, to my understanding, that the ideal measurement of the sub-ensemble of particles found in Box A at t2 constitutes a boundary condition, which through the propagation of a time-reversed wave, constrains the potential locations and states of the particle to that subset of positions and states that remain possible given both the t (starting) boundary condition and t2 (ending) boundary condition. Mathematically, the theory generates for the selected sub-ensemble a probability of "1" that the particle at time t+1 will be found in Box A and also generates a probability of "1" that the particle at time t1 will be found Box B. This means that if an ideal measurements had been conducted at time t1 and Box A or Box B were, metaphorically speaking, opened, the particle would always be found inside the selected Box with absolute certainty. While this verification cannot be actually performed using ideal measurements, the prediction can be experimentally confirmed using weak measurements where the selected sub-ensemble includes a large number of particles. (See: Non-statistical Weak Measurements http://arxiv.org/abs/quant-ph/0607208; Weak measurements, weak values, and entanglement http://link.aip.org/link/?PSISDG/6573/65730Z/1; Pre-and post-selection, weak values and contextuality http://cat.inist.fr/?aModele=afficheN&cpsidt=18922792; and Robust Weak Measurements on Finite Samples http://arxiv.org/abs/quant-ph/0703038.) The resulting interference pattern that Dr. Tollaksen presented arose from these weak measurements and was proffered as "proof" that TSQM is not just a mathematical model (with explanatory value) but also reflects an underlying reality (that I hope to further explore in future communications).
Noting that the probability of finding the particle in Box A and Box B at t+1 were both "1", you may be wondering about Box C. Here, the mathematics predicts something that seemed astounding (which is probably why the reported findings do not appear to have been published.) Where the subject particles are electrons, TSQM predicts a particle with all of the attributes of a positron - but with a fundamental difference. The particle predicted for Box C must have a negative mass. (Although not discussed by Drs. Aharonov or Tollaksen, it appears that this finding would be necessary under a reasonable extension of the conservation of lepton law.) In any event, this outcome was mathematically demonstrated by Dr. Tollaksen. It was also implicitly confirmed in the Physics Applications class I subsequently attended at George Mason University; where it was shown that the time-reversed evolution of a matter wave was impossible for any particle with a positive mass. Additionally, Dr. Tollaksen indicated that experimental verifications of these negative mass particles had been obtained.