Wednesday, October 23, 2013
In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the 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.
If you are not familiar with this quotation, it is taken directly from the original EPR paper (See: Can Quantum-Mechanical Description of Physical Reality Be Considered Complete' ? A.EINSTEIN, B.PODOLSKY AND N.ROSEN, Institute for Advanced Study, Princeton, New Jersey (Received March 25, 1935))
There are two distinct errors in the logic to the pre-amble of one of the most famous scientific papers ever written. In the statement, If P then Q, one generally accepts that the premise P implies the conclusion Q. We are making the allusion to the following sentences:
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.
(1) Knowledge is one thing, reality is something else. Even Einstein famously quoted, “Do you really believe that the moon isn't there when nobody looks?” Not knowing the position ( or momentum) of a particle does not deny its existence.
(2) Not being able to measure two things simultaneously does not deny the existence of either thing.
Yet it is this erroneous thinking that leads the EPR to conclude that QM is “incomplete”.
The beauty of the Heisenberg Uncertainty Principle (HUP) is that it conveys quite accurately the wave/particle duality. In classical physics, all things were placed into two different bins: (1) particles - those things that bounce off each other; (2) waves - those things that went through each other, amplitudes interfering constructively/destructively, but then went on their way as if nothing had happened. In the subatomic, reluctantly we found objects that don't fit into this framework - hence the need of a different framework that went under the name of Quantum Mechanics (QM).
But the HUP is at the core of this alternative framework.
Δx Δp ≈ ℏ
If we measure a particle, Δx → 0 then Δp →∞, we don’t know where the particle is going.
If we measure with certainty its momentum Δp → 0 then Δx →∞, which is what a wave is.
The best picture we get from QM of these objects is a wave packet for which there is some uncertainty in both the position and momentum.
Quantum Field Theory (QFT)
This is borne out by QFT, in which the theory gives predominance to fields, and particles are regarded as excited states of the fields. To make the theory work, particles are conceived as things being surrounded by a cloud of particles/anti-particles, sometimes interacting with themselves, sometimes with other fields or particles, and sometimes even with the quantum fluctuations of the vacuum. Indeed, these are complicated objects.
Historically speaking, the word “incomplete” as used in the EPR paper was technically correct, but it was interpreted incorrectly. If QFT is the house, then QM is the basement. It is the foundation on which QFT was built. However, there were those persuaded by the EPR paper who were drawn to conclude that QM gave the wrong description of reality and an alternative, new theory had to be developed. These attempts may have been brave but led to nowhere. In the meantime, QFT was being built (1930-1970’s), which would complete the house. The irony is that this was accomplished by incorporating into QFT, Special Relativity – Einstein’s own theory that had stunned the world in 1905.