"The Einstein-Podolsky-Rosen paradox, by itself, makes manifest the need for a radical restructuring of our ideas about the nature of physical reality."Logical gap "… and then a miracle occurs." Stapp says this is not the case for Heisenberg/James theory of mind/matter physics.
EPR There are strong instantaneous connections over large distances at the quantum level of reality. Two experimenters perform independent measurements on the same extended system at the same time in two well-separated regions of space. Each experimenter can freely choose and then immediately perform --one of two alternative possible measurements on the large system. So we have a pair of measurements one by each experimenter. We have four possible pairs.
Quantum mechanics allows an extended system with the following features. The two alternative measurements are of "color" and "size". Color can be "black" or "white". Size can be "large" or "small".
Quantum mechanics makes four true assertions about this system.
1. Measure size in region 1 with outcome "large". Measure color in region 2. The outcome is certain to be "white". That is, the conditional probability P(1large|2 white) = 1.
2. Measure color in region 2 with outcome "white", then if color is measured in region 1 the outcome is "black" with 100% probability. So, P(1black|2 white) = 1.
3. Measure color in region 1 with outcome "black", then if size is measured in region 2 the outcome is "small" with 100% probability. So, P(1 black|2 small) = 1
4. Measure "size" in both regions, the joint probability that both outcomes are "large" are approximately 1/16. So, P(1 large|2 large) = 1/16.
Assume locality i.e., there is no faster-than-light action at a distance.
Conclusion A. Suppose "size" is measured in region 1 and the outcome there is "large". Then if "color" instead of "size" had been measured in region 1, the outcome there would necessarily have been "black".
Proof of A: Suppose size is measure in 1 with outcome large. Suppose color is measure in region 2 to get white according to prediction 1 above. Given this white in region 2 and locality. So imagine color instead of size measure in region 1. Then according to prediction 2 we must have black in region 1. So we have both large and black in region 1. But by locality it does not matter what measurement was done in region 2. Hence the connection established between results in region 1 cannot be disturbed by changing what we do in region 2. So we have both black and large simultaneously in region 1 and we have violated the Heisenberg uncertainty principle.
Next combine A with prediction 3 to get small in region 2 with 100% probability assuming locality. This violates prediction 4. P.8
"Thus the predictions of quantum theory are logically incompatible with the assertion that the outcome of any measurement performed on one part of a quantum system must be independent of which measurement is performed simultaneously on a faraway part: large quantum systems seem to behave.. as if they were instantaneously linked-up wholes. The entire argument refers only to large visible objects."
This is the paper that launched the really new "New Physics" (i.e., Post-Modern Physics):
"Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"
by Albert Einstein and his students Boris Podolsky and Nathan Rosen (i.e., EPR) published in Physical Review, Vol 47, May 15, 1935.
As the subject is confusing and controversial, let's see what the Old Man really said by going to the original source.
First look at the abstract A. Let's break apart the different ideas.
Key technical terms are "complete", "element of reality" and "without disturbing the system".
A1 "In a complete theory there is an element corresponding to each element of reality."
What does this sentence mean? The idea is that on the one hand there is an objective reality. The word "objective" means independent of the observer's consciousness and any measuring apparatus that probes the system of interest. Einstein never wavered in his faith in such an objective reality. Bohr was ready to renounce it completely. Wigner, London and von Neumann all required the observer's consciousness to collapse the wave function in Bohr's "Smoky Dragon" Copenhagen interpretation. Bohm's nonlocal hidden variable theory does not require consciousness to play a role in quantum measurement. Bohm's theory is objective in Einstein's sense, but it is not local on the level of individual quantum systems. It is statistically local for ensembles of quantum systems in the absence of back-reaction of the hidden variable on the wavefunction.
So objective reality intrinsically breaks apart into a set of elements. The atomic terms of any correct theory must be in one-to-one correspondence with these elements in order to be complete. Our minds, being part of this reality, are naturally "hard-wired" to be able to perceive these objective elements of reality as soon as culture advances sufficiently.
A2 "A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system."
First notice that A2 is "sufficient". It is not "necessary" nor is it "necessary and sufficient". By sufficient, EPR mean that it is enough. A2 is impeccable and has not been overthrown by any experiment. What has been overthrown is the subsidiary condition "without disturbing the system".
A3 "In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other."
This is one way of stating the Heisenberg uncertainty relation in terms of Bohr's Copenhagen interpretation with no hidden variables. It is implicitly assumed that the wave function is a complete description of individual quantum systems.
EPR then make a logical transformation of the set {A1,A2 A3} to A4 when they next assert:
A4 "Then eitherLet's analyse the meaning of A4 further. First suppose (1) is true and (2) is false. That is, we have incompleteness, and we have simultaneous reality of two elements that correspond to non-commuting incompatible Hermitian operators on Hilbert space. Bohm's hidden variable model of quantum mechanics is precisely this situation. The actual "hidden variable" particle, in an individual case, has a definite trajectory with both a precise position and a precise velocity given by the gradient of the phase of the wave function. Nevertheless, measurements on ensembles of such particles will show that the product of standard deviations for the non-commuting operators obey the Heisenberg relations. The problem with Bohm's theory for Einstein was that Bohm's theory is strongly nonlocal on the individual level.(1) the description of reality given by the wave function in quantum mechanics is not complete
or
(2) these two quantities cannot have simultaneous reality.
On the other hand, suppose (1) is false. That is, suppose, as Bohr assumes, that the description of reality given by the wave function is complete. Also suppose (2) is true. Indeed, (1) false and (2) true is precisely what Bohr's Copenhagen interpretation asserts.
However, and here is the essential point of the whole EPR paper, use of A2 (the sufficient criterion for an element of reality) together with the assumption of "locality", or, more precisely, "relativistic causality", shows the logical implication "if (1) is false then (2) is also false". That is,
A5 "Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false."
That is, if the wave function is a complete description of reality and if relativistic causality is true, then two incompatible quantities have simultaneous reality.
EPR then argue that experiment forces us to conclude that (2) is true. Therefore, the logic of implication demands that (1) is true. Thus, EPR's final conclusion is
A6 "One is thus led to conclude that the description of reality as given by a wave function is not complete."
Remember, Einstein needs to assume locality (i.e., special relativistic causality that there are no faster-than-light influences over spacelike separations between two events in flat spacetime) to come to his conclusion that the wave function is not a complete description of quantum reality. If one renounces locality one can keep the Copenhagen intepretation that the wavefunction is a complete description even on the individual level. That is, Bohr's theory must renounce locality in order to have completeness. But then as Aharonov showed it is not possible to have a consistent theory of collapse of the quantum state in special relativity. Bohm's theory renounces both locality and completeness. But Bohm's theory violates relativity at the individual level though not at the statistical level. No theory today is adequate to combine both special relativity and quantum theory.