ABSTRACT: Using Heisenberg's Uncertainty Principle and Einstein's light-speed restriction, I derive a simple and unanticipated limitation on local psychic powers. I believe this proof represents one of the few instances where math and physics have been applied to quantify the powers of the human mind.
Some of the most important truths in physics are expressed as impossibility theorems--fundamental "thou shalt nots" that set basic limits on what can and cannot happen in the world. I've published a list of 8 of these physics "thou shalt nots" as Reality is When Nature Says NO. They include the first and second laws of thermodynamics, Einstein's light-speed limits on energy and information transfer and Heisenberg's Uncertainty Principle.
1. Fundamental Limitation on Heat Engine Efficiency
Useful on their own, these laws can also be used as postulates to derive other laws. For example the first and second laws of thermodynamics can be used to derive the Maximum Efficiency E of a heat engine operating between two reservoirs at two different temperatures T(1) and T(2).
Let T(1) be greater than T(2) so that a quantity of heat energy Q flows from hot T(1) to cold T(2). What fraction of that heat that can be converted to work W defines the efficiency of a heat engine operating between T(1) and T(2). E is defined as W/Q. If the heat Q can be completely converted to work, E = 1.
The first law of thermodynamics expresses conservation of energy and requires that of the total heat Q that flows from T(1), W ends up as work and Q - W is deposited in reservoir T(2).
The second law of thermodynamics requires that for a closed system a quantity S called entropy must always increase where entropy for thermal systems is defined as S = Q/T. Thus in this situation the entropy loss S(1) of T(1) is Q/T(1) and the entropy gain S(2) of T(2) is (Q-W) / T(2).
Since entropy must always increase, the most efficient heat engine will be that for which the entropy increase approaches zero. This is achieved when the entropy loss at T(1) is equal to the entropy gain at T(2).
Setting S(1) = S(2) we derive the maximum efficiency E(MAX):
E(MAX) = (T(1) - T(2)) / T(1)
This is one of the most fundamental results in thermodynamics and sets basic limits on the output of heat engines, including for instance all automotive internal combustion engines. Note that the greater the difference in temperature between "firebox" T(1) and "exhaust" T(2), the greater the possible efficiency of converting heat to work. Note also that 100% efficiency can only be achieved if the exhaust temperature T(2) is equal to absolute zero.
This simple proof familiar to all students of thermodynamics is an example of the power of the "thou shalt not" laws and is more than 150 years old. The following proof of the limits of psychic power is brand new.
2. Fundamental Limitation on Local Psychic Powers
For my primal "thou shalt nots" I will use the Heisenberg Uncertainty Principle and Einstein's prohibition against faster-than-light signaling.
Light can be polarized and measured in a number of different ways, some of which come under the constraint of the Uncertainty Principle because they involve attempting to simultaneously measure two complementary observables.
The best possible polarization measurement involves a Beam Splitter (BS) that divides the light into two beams--a beam of photons all polarized in one direction (say Horizontal (H)) and a beam of photons all polarized in the orthogonal direction (say Vertical (V)). No better measurement of polarization is possible.
Instead of measuring the proportion of H and V photons in a beam we can tilt the Beam Splitter (BS) by 45 degrees and measure the proportions of Diagonal (D) photons and Slant (S) photons.
The relationship between H/V light (call it Upright Light) and the D/S light (Skew Light) is given (unnormalized) by:
H = D + S
V = D - S
The two kinds of light (Upright Light and Skew Light) are complementary properties of the light beam. According to Heisenberg, measuring one kind of light implies an uncertainty in the value of the other kind of light. And at this basic level of single photon measurement this uncertainty is total. Accurately measuring Upright (H/V) Light means complete uncertainty as to the nature of Skew (D/S) Light.
In particular, as indicated by the above equations, an H photon consists of an equal quantum superposition of D and S photons, so if a photon has been measured to be in the H state, it is completely uncertain what it will do when measured by a Skew beam splitter. There is a 50/50 chance that it will register as a D photon or as an S photon. Furthermore this uncertainty is considered a fundamental property of nature, sometimes expressed as: Not even God knows which way this H photon will go (into the D channel or into the S channel).
Next we imagine an EPR Source OO which produces a series of polarization-entangled photon pairs A and B which travel in opposite directions. The A photon goes to ALICE who possesses a polarized Beam Splitter (BSA) which she can set to detect either Upright (H/V) or Skew (D/S) photons. The B photon goes to BOB who possesses a polarized Beam Splitter (BSB) which he sets to always measure Upright (H/V) Light.
For convenience, the OO Source is assumed to regularly produce one photon pair per minute so that both ALICE and BOB can anticipate when their detectors will be triggered as well as having adequate time to perform their roles in the experiment.
The OO Light Source has the property that whenever both ALICE and BOB set their polarizers to UPRIGHT (H/V) both detectors indicate the SAME POLARIZATION for each photon pair. For example, when observing photon pair #299, if ALICE's UPRIGHT detector registers H, then for this same photon pair BOB's UPRIGHT detector will with 100% certainty also register H.
On the other hand, when ALICE sets her detector to the SKEW position and measures, say D, then no one knows what BOB's UPRIGHT detector will indicate. When ALICE registers D, it is completely QUANTUM UNCERTAIN whether BOB's UPRIGHT detector will register an H or a V.
Now let's suppose that BOB possesses LOCAL PSYCHIC POWERS. Which means that he can "guess" with odds better than chance what the outcome of his detector will be before he actually measures it. We define BOB's psychic power P as:
P = (Number Guessed Right - Number Guessed Wrong) / (NGR+NGW)
Since the output of BOB's UPRIGHT detector is always 50/50 random for the photon to be in the H or the V channel, if BOB's psychic powers are nil, the quantity P will on the average be equal to ZERO. There will be fluctuations in P which are well described by the theory of random processes. This means that after a sufficient number of observations we can with a certain level of confidence decide whether BOB has psychic powers and can even QUANTIFY THESE PSYCHIC POWERS by how strongly P RELIABLY AND ROBUSTLY differs from ZERO.
Note that, like the heat engine efficiency E, BOB's psychic powers P can vary over a range from ZERO (no psychic powers) to ONE (maximum psychic powers).
The purpose of this essay is to derive a constraint on the value of P.
Situation #1. ALICE sets her Beam Splitter A to UPRIGHT and generates a local sequence of H and V photons. The EPR set up guarantees that when BOB measures the corresponding photons (using his UPRIGHT detector) he will get the same sequence as ALICE. Thus the value that BOB will measure (and which he will try to guess thru psychic powers) already exists in advance. It is as fixed as the value of a coin (heads or tails) hidden under a saucer. For BOB this situation is an example of CLASSICAL IGNORANCE in which a value exists known to others, but not to you. BOB's psychic powers when confronted with classical ignorance will be called P(C).
Situation #2. ALICE sets her Beam Splitter A to SKEW and generates a local sequence of D and S photons. The EPR set up guarantees that an identical sequence of D and S photons will impact BOB's detector. But BOB's detector is always set on UPRIGHT. And UPRIGHT is an observable that's complementary to SKEW. So when a D photon hits BOB's UPRIGHT detector, IT IS COMPLETELY UNCERTAIN whether it will emerge as an H or as a V photon. This situation is an example of QUANTUM IGNORANCE and BOB's psychic powers when confronted with purely quantum uncertainty will be called P(Q).
The question now arises: Are psychic powers more effective in discovering knowledge that is hidden by classical ignorance or by quantum ignorance? Or in other words is it easier for BOB to get big P(C) scores or big P(Q) scores?
Since we know absolutely nothing about how psychic powers operate we can only speculate here.
Classical Psi is easier: One might argue that the P(C) score is easier for BOB to increase because he is trying to guess the value of something that actually exists rather than trying to guess at the value of something "that not even God knows".
Quantum Psi is easier: Here one might argue that the P(Q) score is easier to increase because the mind might be a quantum thing and hence might possess a more natural affinity for quantum-uncertain targets. Also if there is any merit to the vague "you create your own reality" hypothesis, BOB might be able to PK (psychokinesiate) a quantum target and make of it what he desires which he certainly could not easily do with a fixed classical target as in situation #1.
Now suppose BOB has robust and measurable psychic powers and furthermore his P(C) score is different from his P(Q) score.
Armed with this information (a difference between P(C) and P(Q)) BOB would be able to discern AT A DISTANCE how ALICE has set her detectors. But ALICE could be located half-way across the galaxy and if BOB can ascertain her detector setting she could then send him messages coded in these sequences FASTER THAN LIGHT.
But one of the strongest physics "thou shalt nots" is Einstein's prohibition against faster-than-light signaling.
Therefore P(C) must equal P(Q).
This is the promised new fundamental restriction on psychic powers. If the laws of physics are valid, the power to psychically uncover quantum ignorance must be precisely equal to the power to psychically uncover classical ignorance.
3. Fundamental Limitation on Conscious Wavefunction Collapse
One of the most fundamental problems in physics is the Quantum Reality Question. In my book Quantum Reality I discuss eight candidate realities including the proposal that consciousness collapses the wavefunction—thus turning the quantum world of airy possibilities into solid realities. The notion that this world is a mental construct is usually associated with Bishop Berkeley but has been given new life by the Hungarian polymath John von Neumann who concluded reluctantly that the only LOGICAL solution to the quantum measurement problem was that consciousness brings the world into existence.
One imaginative proposal to experimentally test the conscious creation hypothesis was carried out first by Abner Shimony and his students at Boston University and later by Dick Bierman at the University of Amsterdam. Shimony and Bierman reason that just as in a chess game where there is a profound subjective difference between the moves you make on the board and the moves that your opponent makes, so likewise one might expect there to be a different feeling (or perhaps a different physiological response) to a situation where you yourself collapse the wavefunction and a situation where the wavefunction is collapsed by someone else. I describe Shimony's Boston Experiment in Elemental Mind and Bierman describes his own work in Ref #4. In neither of this experiments was the observer able to reliably ascertain a difference between self-collapse and other-collapse of the wavefunction. However the quantum system used by both Shimony and Bierman was radioactive decay which because there are not many variables to manipulate may not be the optimum case for studying subjective collapse.
A better physical system might be the EPR case in which distant observer ALICE can present BOB with two separate situations: #1 where ALICE has already collapsed the photon wavefunction into an eigenstate of BOB's observable; #2 where ALICE has left the photon wavefunction in a superposition
of H and V states which BOB himself must collapse.
The fundamental question proposed by the VSB group (von Neumann, Shimony, Bierman) is whether BOB can subjectively distinguish between other-collapse and self-collapse of the photon wavefunction.
By the same reasoning that forbids BOB's LOCAL PSYCHIC POWERS from discerning a difference between Situation #1 and Situation #2 we can also conclude that if the laws of physics are valid (in particular Einstein's prohibition against FTL signaling), then BOB will never be able to discern a subjective difference between other-collapse and self-collapse of the photon wavefunction. Thus a second piece of knowledge follows from “Nick's theorem”
No subjective difference between self-collapse and other-collapse of wavefunction.
It looks as though no local powers of mind whether explicitly psychic or subjective feelings associated with wavefunction collapse can make the crucial distinction between two seemingly different physical situations—the collapse of an eigenstate (CLASSICAL IGNORANCE) and the collapse of a superposition (QUANTUM IGNORANCE). But since these two situations seem to be physically different, is it not possible that some clever physical measurement device having nothing to do with powers of mind can be deployed that displays a physical difference between the collapse of an eigenstate and the collapse of a superposition? But by the previous reasoning a purely mechanical measuring device having this property is also forbidden.
No physical device can detect a difference between collapse of an eigenstate and collapse of a superposition.
Conclusion: Nick's theorem imposes strict limits on 1. local psychic powers, 2. on subjective collapse models of reality and 3. on the performance of conventional measurement devices.
Boulder Creek, CA
October 9, 2009
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REFERENCES
1. Nick Herbert, Reality is When Nature Says NO
2. Nick Herbert, Quantum Reality: Beyond the New Physics, Anchor 1985
3. Nick Herbert, Elemental Mind: Human Consciousness and the New Physics, Dutton 1993
4. Dick Bierman & Stephen Whitmarsh, Consciousness and Quantum Physics: Empirical Research on the Subjective Reduction of the State Vector, Springer Verlag 2006
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