It is not actually a paradox. In 1935, the orthodoxy view of quantum mechanics was that, because of Heisenberg’s Uncertainty Relations, a quantum system can’t have a position and a momentum at the same time. That wasn’t (still isn’t) an unreasonable view, but it doesn’t simply follow from the uncertainty relations.

All quantum mechanical phenomena deal with random events which are a fundamental part of nature. This is what bothered Einstein. He hoped to find a deeper theory to explain this randomness that must be generated by some deeper mechanism, he thought. Einstein was a strong realist: the Moon exists also when no one is looking at the sky. The mathematics of quantum mechanics on the other hand don't need this very strong form of realism. In subatomic processes particles can have an indefinite state that only gets real when interacting with macroscopic systems. As if the moon is always in a combination of a full moon, waxing moon, waning moon etc and only gets is real state when an Earthling or alien is watching the sky. The subatomic quantum "reality", which can be tested in any physics lab, just can't be the whole story according to Einstein. "Sure," he could have said, "photons, electrons do behave according to these quantum laws but deep inside there are more fundamental laws that are as real and definitive as the Moon in the sky".

Enter Einstein, Podolsky and Rosen, who offered an argument intended to show that if quantum mechanics is correct as far as it goes, then quantum systems can have simultaneous positions and momenta, even though quantum theory doesn’t give us any way to represent that. The conclusion that EPR drew: quantum mechanics is incomplete; there are “elements of reality,” to use their phrase, that quantum theory doesn’t include in its mathematical picture.

EPR’s argument is interesting. They described a case that quantum theory clearly allows, in which by measuring position on his particle, a scientist, call her Alice, can predict the position of her co-experimenter Bob’s particle, even though she is far away from Bob. Alternatively, if she chooses instead to measure the momentum of her particle, she can predict Bob’s momentum. She can’t do both; there’s no way to measure the position of a particle without losing momentum information, and vice-versa. But she can choose to know Bob’s particle’s position or momentum as she wishes.

EPR make a crucial assumption: by simply measuring her particle, Alice doesn’t disturb or influence Bob’s, which, after all, may be far away and shielded from influences in whatever way you like. So they ask: what would explain the fact that Alice can pull off this trick? Their answer: Bob’s particle must already have had a position, correlated with the position of her particle. Likewise, Bob’s particle must have already had a momentum, correlated with the momentum of Alice’s particle.

As EPR saw it, there’s no paradox here at all. They took their argument to be scientific common-sense reasoning, applied to a certain kind of quantum case. Their goal was simply to show that quantum theory leaves out information that a better theory would find a way to include.

The story doesn’t end there. Thirty years later, John Bell realized that if EPR were right, there’s a kind of experiment that would turn out one way. If they were wrong, it would turn out differently. In particular, the EPR point of view would predict something different from quantum mechanics, and so if EPR were right, quantum theory wouldn’t be incomplete; it would be wrong.

In the intervening fifty-plus years, the experimentalists have done their work: EPR got it wrong. Ever since, the debate about exactly what this tells us about quantum reality has raged on with no end in sight. In spite of the philosophical disagreement, however, understanding the physical implications of the EPR argument and the experiments that defeat it has given us surprising and fascinating results, including the prospect of quantum computers and of uncrackably secure communication. This isn’t what EPR had in mind, but then if we knew how science was going to turn out, we wouldn’t need to bother doing it.

**Note :**

*Some people will tell you that the experiments have proved the existence of what Einstein derisively called “spooky action at a distance.” That’s certainly one interpretation. But it’s not the only one, in spite of what the headlines show.*

**Relation with the Reality**

EPR and reality is an interesting subject for a lecture but can indeed be problematic to give a lecture when you don't have a physics background. The paradox goes to the heart of interpretation of quantum mechanics which is a very subtle subject.

Einstein was one of the founders of quantum physics and spend most of his career in its study. The EPR paradox is not a critique given by Einstein to prove quantum mechanics wrong. Einstein strongly believed the theory to be correct. But, he was not at ease with some of the interpretations and tried to the day of his death to find a deeper theory solving interpretation problems in the laws of quantum mechanics.

Now let us give an overview of quantum phenomena that guided physics in the late 19th century and early 20th century to the development of a new mechanics:

- Radioactivity - particularly the notion of half-life and randomness (you can't know the exact moment a radioactive atom decays)
- Particle-wave duality and the double slit experiment - mostly the notion how the interference pattern is a statistical result (you can't view the interference pattern of a single photon, you need many repeated experiments)
- EPR paradox

All quantum mechanical phenomena deal with random events which are a fundamental part of nature. This is what bothered Einstein. He hoped to find a deeper theory to explain this randomness that must be generated by some deeper mechanism, he thought. Einstein was a strong realist: the Moon exists also when no one is looking at the sky. The mathematics of quantum mechanics on the other hand don't need this very strong form of realism. In subatomic processes particles can have an indefinite state that only gets real when interacting with macroscopic systems. As if the moon is always in a combination of a full moon, waxing moon, waning moon etc and only gets is real state when an Earthling or alien is watching the sky. The subatomic quantum "reality", which can be tested in any physics lab, just can't be the whole story according to Einstein. "Sure," he could have said, "photons, electrons do behave according to these quantum laws but deep inside there are more fundamental laws that are as real and definitive as the Moon in the sky".

The EPR paradox is a thought experiment that directly follows from the laws of quantum physics. It is possible to create a composite system of particles where you know everything about the system at a whole but nothing about the parts. Einstein tries in this argument to "prove" (this is in quotes because he doesn't prove but tries to convince us) that quantum mechanics can't be complete. He creates a quantum thought experiment in which a composite system of particles needs to maintain their statistics over great distances without being able to communicate to eachother. As if I would say to two architects "build me a house" and both of them go on a journey to two planets far apart. By magic, when one of them builds the roof the other one builds the basement and vice versa. None of them can communicate with each other and both of them always manage to build together but far apart the missing parts of a complete house. This is what quantum mechanics tells us about subatomic processes and what can actually be measured in a lab. This not an Einsteinian magic trick but real events. Einstein says: "this proves quantum mechanics can't possibly tell the whole story; there must be something happening at a more deeper level to explain this". In the late 60-s Bell proved a theorem that Einsteins "deeper level" doesn't come without a cost. Even if there is a deeper hidden theory than explain all these phenomena, it must require faster than light communication (which disproves Einsteins theory of relativity). In a stronger interpretation it even disproved the existence of an objective reality. We could live in a world were every action is predetermined and no free will is possible. An architect (every architect) can't possible do anything else than follow the exact script of the universe: if one build a roof then the other must build the basement even if they don't know of the others actions. All creativity is just an illusion. We live as robots in a mechanical super deterministic universe. We still now do not know the exact answer, but the very simple deeper truth that Einstein tried to find might be very complex after all.

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