The Born rule is that the probability of observing a particular outcome happening is
Where A is the value from the particular column of the out vector. Since probabilities add up to one we require both the input and the output vectors to sum to a value with modulus one. That is also why the transformation matrix is unitary, the total of the probabilties has to be conserved.
This is all standard QM, what Henry Stapp claims in his recent paper, is that human observation can effect which outcome actually occurs. Not only that but its chooses in outcome that is happier for the observer than normal. Its as if you run a schroedigers cat experiment with an atom has a fifty percent chance of decaying in the period, but when the cat is in the box, it stays alive more often that not. Well Barry likes happy cats, but doesn't believe much in magic.
How can such a deviation from the QM occur? Henry claims retro-causual influence, i.e. the ability of a future mind to occasionally or at-will? Send information backwards in time. This sounds like pseudo-science but Herny Stapps credentials are very good, PhD, Post doctored under no less than Wolfgang Pauli, capable of a extremal complex proofs in quantum electrodynamics.
The experiment Henry refers to was a psychological experiment run in Zurich and since Henry did not go into much details of the actual experiment, the statistics are probably flawed. Remember the rule, exceptional claims require exceptionally strong evidence to prove them.
Henry's model of the universe, if i understand his description correctly contains a crystallized past with definite events at particular times and places, with any possible future, and the whole system is evolving in meta-time. A simulation of his view point, might be having a classical computer recording the outputs from a quantum computer calculating all the possible futures, when the quantum computer gets to the simulation time t, the classical computer records one event from all the possibilties. Usually that event is choosen at random by the Born rule. What Henry claims is also claiming is that occasionally the choose is made in a ways that better for human than at random, by retrocausal (backwards in time) signals from deeper in the simulated future. Of course humans try to predict the future and avoid the worse outcomes in the now. But does some extra influence alter which events are actualised at the time of actualisation. I remain doubtful but at the same time hopeful.
Could in the future humanity build a machine that sends signals backwards in time, from near disasterous events, and prevent them from happening. Perphaps, usualling the Feynman Wheeler absorber theory which allows signals to travel in both directions in time. It is only the law of increasing entropy that leads to signal propagating forward in time. What happens if you bounced a radio-wave off a region of space that happened to have decreasing entropy at the time of reception of the signal. In that condition a signal backwards in time might be sent.
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