Nick's Theorem as a Coin Guessing Game

In the late Sixties, Aberdeen Proving Ground physicist Evan Harris Walker published a novel theory of consciousness in which an immaterial mind occupies a physical brain by taking advantage of quantum uncertainty in the neural synapses. According to Walker we operate our bodies by a sort of quantum psychokinesis (PK) in the brain. Later Walker extended his mind model to explain external PK on rolling dice which he modeled as an unstable mechanical system in which small quantum uncertainties are amplified by the chaotic nature of tumbling cubes. In 1977 Walker and I published a paper together in John White and Stanley Krippner's book Future Science originally entitled "Calculating the Push of a Wish" which popularized this quantum PK model.

A week ago I discovered a mathematical proof that strongly constrains local psychic powers and is relevant to the late E. H. Walker's hypothesis (he died in 2006) that consciousness and its paranormal extensions cannot arise in a classical world and are fundamentally quantum-mechanical phenomena.

Nick's Theorem concerns an observer BOB trying to guess the outcome of an instrument that measures the polarization of light via a beam splitter whose outcome is either a Vertical or Horizontally Polarized photon. The photons impinge on the detector at a rate of 1 photon per minute so BOB has plenty of time to make his choice. BOB's task is always the same--to guess whether the next photon will be an H or a V. But the photons he has to guess are packaged in two distinctively different ways--Situation #1 corresponding to CLASSICAL IGNORANCE and Situation #2 corresponding to QUANTUM IGNORANCE.

In Situation #1, the state of the photons are definite but unknown (classical ignorance). In Situation #2, the state of the photons are in a quantum superposition of H and V and whether this superposition will register H or V upon measurement is considered "quantum random". The outcome of such a measurement event is "causeless", a happening that is so uncertain "that not even God knows the outcome."

We assume that BOB possesses LOCAL PSYCHIC POWERS and can reliably guess the outcome of the polarization meter (H or V) with a score P better than chance. We then examine the question of whether it is easier for BOB to exert his psychic powers in a situation of classical ignorance (score = P(C)) or in a situation of quantum ignorance (score = P(Q)).

Instead of photons we will imagine that BOB is presented each minute with A COIN IN AN ENVELOPE. These are unusual coins--their faces are the same on both sides--both sides HEADS or BOTH sides tails. They are a kind of coin that tricksters use to astonish or dupe. We may imagine they were minted by Sir Isaac Newton in the Tower of London.

In the situation of classical ignorance a single coin is in each envelope. It is either a HEAD coin or a TAIL coin and the condition of the coin is the same before and after opening the envelope. BOB's score at guessing a classically unknown coin is P(C).

In the situation of quantum ignorance BOB's envelope contains a quantum superposition of HEAD coin and TAIL coin with "mutual phase" of zero degrees (+ sign) or 180 degrees (- sign). In the quantum picture all matter has a wavelike quality and waves possess a property called phase. We don't completely understand what the "phase of a coin" might actually mean in reality but in graphical representations of quantum systems such as Dean Dauger's Atom in a Box the phase is represented by a position on the Color Wheel. Matter with the same phase has the same color; matter with opposite phase has the complementary color. The superposed coins pictured above are colored according to this convention. We may imagine that these quantum coins were minted by Werner Heisenberg in Copenhagen. When BOB opens an envelope containing a Heisenberg coin, it instantly changes into either a HEAD coin or a TAIL coin in a completely uncertain manner. BOB's score at guessing a quantum unknown coin is P(Q).

Now if consciousness, both conventional and "psychic", is purely quantum mechanical (as Walker and others have surmised) we might expect that BOB's score for predicting the state of a classical Newton coin would be zero. And that his score for predicting the state of quantum Heisenberg coins would be significant because Heisenberg coins are as quantum as it is possible to be. The outcome of a measurement on a Heisenberg coin is absolutely uncertain, precisely 50/50 random for HEADS or for TAILS.

Thus quantum models of consciousness would seem to favor the conclusion that P(Q) must be greater than P(C).

However Nick's Theorem proves that P(Q) must equal P(C). The reason? If these two scores were not equal, then BOB could use his local psychic powers to communicate faster than light.

Therefore if Einstein's speed limit is valid, quantum ignorance and classical ignorance must be equally accessible to psychic investigation--a coin minted by Newton precisely as easy to guess as a coin minted by Heisenberg. I believe this simple and unanticipated result is one of the few instances where mathematical reasoning has been used to derive fundamental constraints on the powers of mind.