then one must deny (2), (1) must be true and thus quantum mechanics is incomplete. 18
possibility of predicting it with certainty, without disturbing the system. 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. Then either (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. 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. One is thus led to conclude that the description of reality as given by a wave function is not complete. 16 The original paper considered momentum and position but in a more modern context 17 it is demonstrated with spin, which is also governed by the Heisenberg uncertainty principle. Say two particles were entangled and are now separated into two different labs. If one were to observe in one lab that the spin of the particle is ÂupÊ, it can be stated with absolute certainty that the spin of the other particle is then ÂdownÊ. However, the Copenhagen interpretation states that spin is not attributable to either particle until the measurement is made and the particle ÂobservedÊ, so the observation of one instantaneously affects the other. This would require a ÂsignalÊ exceeding the speed of light and thus the paradox is born. It was concluded in the paper since both (1) and (2) cannot both be false and if one denies (1) 16 Einstein, Albert, Boris Podolsky, and Nathan Rosen. ÂCan quantum-mechanical description of physical reality be considered complete?Ê . Physical Review 47, No. 10 (1935): p. 777. 17 There seems to be many shortcomings in the original paper which Einstein himself claimed to regret. They are summarised in the Stanford Encyclopaedia of Philosophy : http://plato.stanford.edu/entries/qt-epr/
It was after a discussion with a university professor of the Philosophy of Physics that I became aware of a way to circumvent the predicament presented by the quantum mechanics referred to as Âhidden variablesÊ. There have been many attempts to rule out such variables, the most famous of which is BellÊs Theorem. It shows that in order for there to be an objective reality, and for the result of a particle measured at A to be independent from the result at B, there can be no local, determinate hidden-variables that can agree with all the predictions of quantum mechanics. Thus in his paper On the Einstein Podolsky Rosen Paradox , Bell prompts us to either give up realism or locality. The resulting theories would therefore significantly stray from what Einstein would have preferred. With the Copenhagen interpretation, defined trajectories of particles and causality of events are effectively ruled out. There is also the issue of what is known as the Âmeasurement problemÊ as is summed up by David Albert as ÂThe dynamics and the postulate of collapse are flatly in contradiction with one another ... the postulate of collapse seems to be right about what happens when we make measurements, and the dynamics seems to be bizarrely wrong about what happens when we make measurements, and yet the dynamics seems to be right about what happens whenever we aren't making measurements.Ê 19 An alternative interpretation of quantum mechanics is offered by David Bohm. Bohmian mechanics can be described as Âa completely deterministic theory in which particles have actual, objectively existing trajectories at all times and they interact via
18 This is all based on the assumption of locality and thus such instantaneous action cannot occur. 19 Albert, D. Quantum Mechanics and Experience , Cambridge, MA: Harvard University Press, 1992, p. 79.
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