<Picture 1 ; Dice>
In the last post, we discussed about Quantum Mechanics and Probability. In quantum mechanics, there is uncertainty principle. It shows that it is impossible to know the exact position and momentum at the same time. The only one we know is the probability. According to the principle, Erwin Schrodinger devised a thought experiment called 'Schrodinger's Cat.' At first, It was devised to criticise the probabilistic interpretation of Quantum mechanics. But it become the most famous interpretation, Copenhagen Interpretation. Einstein, however, didn't like this weird interpretation. He said that God does not play the dice. So, today we're gonna talk about his argument against quantum mechanics, EPR Paradox.
1. EPR Paradox and its Setting
<Picture 2 ; Einstien, Podolsky and Rosen>
In 1935, Albert Einstein co-authored a paper with his two postdoctoral research associates, Boris Podolsky and Nathan Rosen. The article was entitled "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?". The paper is also known as 'EPR Paradox' because of initial letters of its authors' name. It created a lot of debates over the interpretation of Quantum Mechanics and it continues today.
The EPR text started with showing two proposition. The first proposition(1) is that the description of quantum mechanics is incomplete and the other one(2) is that the incompatible quantities(e.g. position and momentum) cannot have simultaneous reality. They asserts that either (1) or (2). But according to the copenhagen interpretation, if (1) is false then (2) is false. So, they concluded that it is contradiction. According to their conclusion, Copenhagen Interpretation has to abandon the completeness of the description for quantum mechanics or the physical reality of two quantities.
2. Separability and Locality
<Picture 3 ; The Setting of a Thought Experiment in The Text>
In the paper, they sketched a thought experiment. In the experiment, two quantum systems interact in such a way that two conservation laws hold following their interaction. One is the conservation of relative position. If we imagine the systems located along the x-axis, then if one of the systems (we can call it A) were found at position q along the axis at a certain time, the other system (call it B) would be found then a fixed distance d away, say at q′ = q − d, where we may suppose that the distance d between q and q′ is substantial. The other conservation law is that the total linear momentum (along that same axis) is always zero. So when the momentum of A system along the x-axis is determined to be p, the momentum of B system would be found to be −p.
On the setting of experiment, they made two critical assumptions. The first one is the separability. The separability is that when the measurement is performed on A system there is some reality that pertains to B system alone. The second one is the locality. The locality supposes that no real change can take place in B system as a consequence of a measurement made on A system. This idea originated in the theory of relativity. According to the relativity, nothing can move faster than light. So, Einstein thought that if B system is extremely far away from the A system then there should be no change in B system caused by A system's change.
3. Conclusion and Bohr's response
<Picture 4 ; Einstein and Niels Bohr>
In summary, the argument in the EPR text show that if two quantum system satisfy the separability and locality then the description provided by quantum mechanics is incomplete.
Copenhagen Interpretation gives probabilistic view over quantum mechanics. But Einstein had a deterministic view and he wrote the paper with his associates to refute the probabilistic interpretation. He left a very famous word about it.
"God does not play the dice with the universe"
Of course, he didn't believe in god. In his aphorism, "God" means the physical laws in metaphorically. Bohr, one of the main supporter of Copenhagen Interpretation, didn't ignore the argument of Einstein. In the next post, we're gonna talk about the Bohr's Response about it. Thank you for reading it.
Bibiology
Einstein, A., B. Podolsky, and N. Rosen, 1935, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, Physical Review, 47: 777–780
http://plato.stanford.edu/entries/qt-epr/
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