Now that we have a few more concepts under our belts, I would like to go back and revisit in some more detail just what John Bell proved in 1964 about entangled states. He considered a simple quantum situation like the entangled ions in Alice and Bob’s pocket watches and then set about to compare the predictions of quantum theory for such a setup to the predictions of a classical hidden variable theory that had all of Einstein’s constraints: reality, locality, and certainty. Remember-there was already the Bohm hidden variable theory, well known in 1964, which did predict the same outcome as quantum theory, but this Bohm theory doesn’t count because it violates Einstein’s locality condition. (Einstein thumbs his nose at the Bohmians.) Bell’s goal was to see if he could construct a local classical hidden variable theory that would agree with all the predictions of quantum theory and satisfy Einstein’s three conditions. If such a hidden variable theory could be found, then it would be tempting to just replace quantum theory with that hidden variable theory and all the spookiness would just disappear. But in order for this project to succeed, the classical hidden variable theory had to obey all three of Einstein’s reality, locality, and certainty conditions and reproduce all the predictions of quantum theory. at was just too tall of an order to ask of any local hidden variable theory, Bell discovered. Something, somewhere, had to give.
Now that we have a few more concepts under our belts, I would like to go back and revisit in some more detail just what John Bell proved in 1964 about entangled states. He considered a simple quantum situation like the entangled ions in Alice and Bob’s pocket watches and then set about to compare the predictions of quantum theory for such a setup to the predictions of a classical hidden variable theory that had all of Einstein’s constraints: reality, locality, and certainty. Remember-there was already the Bohm hidden variable theory, well known in 1964, which did predict the same outcome as quantum theory, but this Bohm theory doesn’t count because it violates Einstein’s locality condition. (Einstein thumbs his nose at the Bohmians.) Bell’s goal was to see if he could construct a local classical hidden variable theory that would agree with all the predictions of quantum theory and satisfy Einstein’s three conditions. If such a hidden variable theory could be found, then it would be tempting to just replace quantum theory with that hidden variable theory and all the spookiness would just disappear. But in order for this project to succeed, the classical hidden variable theory had to obey all three of Einstein’s reality, locality, and certainty conditions and reproduce all the predictions of quantum theory. at was just too tall of an order to ask of any local hidden variable theory, Bell discovered. Something, somewhere, had to give.
Prologue A memorial conference for John Bell, open to the public, was held at Rutgers University around 20 years ago. I gave a short talk there on Bell's views about David Bohm's “hidden variables” formulation of quantum mechanics, a version of quantum mechanics often called the de Broglie–Bohm theory or Bohmian mechanics. This theory was in fact discovered by Louis de Broglie in 1927. In 1952, it was rediscovered and developed by Bohm, who was the first to appreciate its connection to the predictions of standard quantum mechanics. I did not publish the talk. I have decided that it would be appropriate to publish a very lightly edited version of it here, in this volume devoted to the work of Bell on the foundation of quantum mechanics. One reason for doing so is that the connection between Bell and Bohm continues to be somewhat underplayed, with the strength of his advocacy of Bohmian mechanics not properly appreciated. For example, about half of the papers in Bell's collected works on the foundations of quantum mechanics deal with Bohmian mechanics. But in his fine introduction to the revised edition of this great book [1], Alain Aspect mentions this theory in only a single sentence, and parenthetically at that. For several decades after Bell proved his nonlocality theorem, based in part on Bell's inequality, it was widely claimed that Bell had shown that hidden variables – and Bohmian mechanics in particular – were impossible, that they were incompatible with the predictions of quantum mechanics. For example, the great physicist Eugene Wigner, who, unlike most of his contemporaries, was profoundly concerned with the conceptual foundations of quantum mechanics and usually wrote on the subject with great clarity and insight, has written that This [hidden variables] is an interesting idea and even though few of us were ready to accept it, it must be admitted that the truly telling argument against it was produced as late as 1965, by J. S. Bell … This appears to give a convincing argument against the hidden variables theory.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.
By 1935, the Copenhagen interpretation had become the orthodoxy. Einstein needed to find a situation in which it is possible in principle to acquire knowledge of the state of a quantum system without disturbing it in any way. Working with two young theorists, Boris Podolsky and Nathan Rosen, Einstein devised an extraordinarily cunning challenge based on entangled particles. We can discover the state of one particle with certainty by making measurements on its entangled partner. All we have to assume is that the particles are local: any measurement we make on one in no way affects or disturbs the other. Through the work of David Bohm and John Bell, the challenge posed by EPR became accessible to experiment, and Bell devised a simple test for all locally realistic theories. All the experiments performed to date suggest that the standard quantum formalism is correct: in any realistic interpretation, quantum particles are non-local.
Quantum mechanics makes surprising predictions that defy our classical understanding of the world.Experiments done on entangled particles-particles with linked properties-prove that actions on one particle can affect the other one no matter the distance.In response, physicists came up with local hidden variable theories in an attempt to understand this quantum phenomena through a classical lens.John Bell formulated a way to test whether nature is dictated by local hidden variable theories or quantum mechanics, and since then it has been the goal of numerous physicists to experimentally test the theorem and improve upon the results.This paper describes the history of these experiments, their pros and cons, their advancements, and the potential applications that they will enable.
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimatly doomed in 1964 with the work of Bell Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities and pseudo-telepathy. A discussion of the similarities and differences will follow. 1