EPR paradox
- Pedro
- Jul 12, 2020
- 5 min read
Albert Einstein repudiated quantum mechanics because of its probabilistic and random character. Einstein, along with other physicists with a more "conservative" view of science, were convinced that the universe had a deterministic character. But what does a "deterministic universe" imply? The imposition of a deterministic cosmos implies that it must present phenomena that can be entirely predictable, that is, everything in the universe can be known with absolute precision. In a deterministic cosmos, it would be possible, in an ideal scenario, to know all the future dynamics of the universe if we knew the initial positions and conditions of the particles at the beginning of time. The unpredictability of quantum theory, however, took this "power" away from the reach of human knowledge. It is impossible to know fundamentally the universe because nature itself imposes limits impossible to be broken, and the principle of uncertainty of Heisenberg is a perfect example of such limitation.
In his attempts to disprove quantum mechanics, Albert Einstein, together with physicists Boris and Nathan Rosen, launched a mental experiment whose purpose was to expose the lack of logic of the quantum theory, especially referring to the main interpretation of quantum mechanics: the Copenhagen interpretation. The mental experiment involved the concept of entangled particles, that is, particles with intrinsically bound states. Entangled particles are described such that it is not possible to describe the state of one without the other (mathematically that means we can't factor out a term involving a single particle). Entangled particles are so deeply connected that the bond is maintained regardless of the distance they are separated. The mathematical representation of an entangled state of photons is shown in photo 2. Let's consider two entangled electrons. If a measurement in the spin, say on the z-axis, is made on one of the particles, and we find out it is pointing to +z, the other must have a spin in the opposite direction, -z. This is true even for arbitrarily large distances. Einstein and his colleagues explained that quantum mechanics had to be wrong because of the bizarre, and seemingly illogical, fact that particles could influence each other instantly, regardless of the distance considered. In this sense, there appeared to be a violation in respecto to relativity, which states that nothing can travel faster than light. When we measured the spin of a particle, which, according to quantum mechanics, was in an superposition of all possible orientations, we forced the other particle, which was also in superposition condition, to a specific state, which is the inverse of what was obtained in the measurement of the first particle (as described for the example of electrons). In short, the flaw pointed out by Einstein and his colleagues was that quantum mechanics predicted that particles could have effects on each other instantly. This mental experiment became known as the "EPR paradox", referencing the initials of Einstein, Podolsky and Rosen.
For a counterposition, Einstein suggested an explanation that became known as "hidden variable theory". In this theory the famous scientist claimed that the reason behind nature's apparent randomness was due to a series of variables/properties that particles had, these being unknown to us. It would be as if the particles had characteristics "hidden under the cloths". These "extra" properties, if determined, would bring out predictability in nature, restoring determinism. Einstein argued in his explanations that each particle carries, locally (with it), all its well-defined properties since the moment of its creation. In this sense, there is no state of quantum superposition because since its creation, the particle would have, for example, the direction of its spin defined, regardless of the measurement act(s). The explanation seemed reasonable, but something fundamental was missing: an experimental confirmation. An idea in science is not true until an experiment-or series of experiments confirms it. With the need for the formulation of such an experiment, the scientist John Stewart Bell proposed an experiment involving the polarization of entangled photons and, if true, the theory of hidden variables should obey a series of inequalities called "Bell inequalities". However, Einstein's proposal did not agree with the experiment and, therefore, was incorrect. Bell's inequalities eventually disproved the hidden variables and not quantum mechanics, whose calculations, based on probabilistic (nondeterministic) concepts, provided answers that agreed with several experiments, including the issue of the polarization of entangled photons.
Therefore, in the end, it was concluded that in fact the version of quantum mechanics was the most correct and that particles have their properties "compromised" by randomness and may have influence on each other instantaneously.
Although the theory of hidden variables is not correct, there was still a question to be considered: how to solve the apparent violation of relativity? Not even quantum mechanics has a "free pass" to disobey it. In reality there is no "teleportation" of matter, so in this sense, there is no violation regarding the theory of relativity. But would the information (like the spin) be "delivered" to another particle instantly? Can we communicate faster than light (again violating relativity)? The answer, depending on the point of view, is a "no". Although one particle is actually able to influence the other even at arbitrarily large distances away, no information can be extracted effectively. Let us consider two observers, Anakin and Obi Wan, at opposite ends of a galaxy, each with an electron, and these are entangled. If Anakin measures the spin of its electron, a single state will be "chosen" from the options provided by the superposition state. The only fact known to Obi Wan is that the spin of his particle will be opposite to Anakin's, but he won't know what it is unless he performs the measurement on his particle himself (which would be analogous to Anakin's initial condition). Obi Wan therefore failed to obtain any information from Anakin's action. The only "information" obtained is that, given the random result of the Anakin measurement, the Obi Wan measurement will be the "opposite random", which in itself does not constitute a valid form of information. The only way to obtain the information would be if both observers met and directly compared their obtained results. Thus, again, quantum mechanics preserves the principles found in relativity.
Although communication faster than light is not possible, entangled particles brings incredible applications in engineering, such as the development of quantum computers, these being exponentially more efficient than traditional ones and the so-called quantum encryption, a form of encryption in which it is impossible for an "intruder" to intercept the sending of information without exposing himself, i.e. 100% efficient encryption.
Reference material: Quantum mechanics for scientists and engineers SE02 (David A.B. Miller)
The universe in a nutshell (Stephen Hawking)
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