# EPR paradox

The **Einstein–Podolsky–Rosen paradox** or **EPR paradox** of 1935 is an influential thought experiment in quantum mechanics with which Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen ("EPR") claimed to demonstrate that the wave function does not provide a complete description of physical reality, and hence that the Copenhagen interpretation is unsatisfactory; resolutions of the paradox have important implications for the interpretation of quantum mechanics. The essence of the paradox is that particles can interact in such a way that it is possible to measure both their position and their momentum more accurately than Heisenberg's uncertainty principle allows, unless measuring one particle instantaneously affects the other to prevent this accuracy, which would involve information being transmitted faster than light as forbidden by the theory of relativity.

## Contents

## "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" (1935)[edit]

A. Einstein, B. Podolsky and N. Rosen, *Physical Review* (May 15, 1935) Vol. 47

- In a complete theory there is an element corresponding to each element in 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 the wave function is not complete.
- abstract

- The elements of the physical reality cannot be determined by
*a priori*philosophical considerations, but must be found by an appeal to results of experiments and measurements. ...We shall be satisfied with the following criterion...*If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, there exists an element of physical reality corresponding to this physical quantity*. It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way...

- The usual conclusion... in quantum mechanics is that when the momentum of a particle is known, its coordinate has no physical reality.

More generally, it is shown in quantum mechanics that, if the operators corresponding to two physical quantities... do not commute... then the precise knowledge of one of them precludes such knowledge of the other. Furthermore, any attempt to determine the latter experimentally will alter the state of the system in such a way as to destroy the knowledge of the first.

From this follows that either (1)*the quantum mechanical description of reality given by the wave function is not complete*or (2)*when the operators corresponding to the two physical quantities do not commute the two quantities cannot have simultaneous reality*.

- In quantum mechanics it is usually assumed that the wave function
*does*contain a complete description of the physical reality of the system in the state to which it corresponds. ...We shall show, however, that this assumption, together with the criterion of reality given above, leads to a contradiction.

- As a consequence of two different measurements performed upon the first system, the second system may be left in states with two different wave functions. On the other hand, since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system. ...Thus,
*it is possible to assign two different wave functions... to the same reality*.

- Starting then with the assumption that the wave function does give a complete description of reality, we arrive to the conclusion that two physical quantities, with noncommuting operators, can have simultaneous reality. Thus the negation of (1) leads to the negation of the only other alternative (2). We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

- One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. Indeed, one would not arrive at our conclusion if one insisted that two or more physical realities can be regarded as simultaneous elements of reality
*only when they can be simultaneously measured or predicted*. On this point of view, since either one or the other, but not both simultaneously... can be predicted, they are not simultaneously real. ...No reasonable definition of reality could be expected to permit this.

- While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.

## Quotes about EPR paradox[edit]

- We know something about Einstein's genius we didn't know before.
- David Z. Albert, regarding the 1935 EPR paper, quoted in Dennis Overbye, "Quantum Trickery: Testing Einstein's Strangest Theory",
*The New York Times*(Dec. 27, 2005)

- David Z. Albert, regarding the 1935 EPR paper, quoted in Dennis Overbye, "Quantum Trickery: Testing Einstein's Strangest Theory",

- While Einstein's belief in an objective reality is similar to that of Weinberg and Sokal, his arguments for his conception of reality are not. In fact, Einstein was no "naive realist," despite such caricaturing of his stand by the Copenhagen orthodoxy. He ridiculed the "correspondence" view of reality that many scientists accept uncritically. Einstein fully realized that the world is not presented to us twice-first as it is, and second, as it is theoretically described-so we can compare our theoretical "copy" with the "real thing." The world is given to us only once - through our best scientific theories. So Einstein deemed it necessary to ground his concept of objective reality in the invariant characteristics of our best scientific theories.
- Mara Beller, "The Sokal Hoax: At Whom Are We Laughing?",
*Physics Today*(September, 1998)

- Mara Beller, "The Sokal Hoax: At Whom Are We Laughing?",

- It deals with an imaginary experiment, but like so many other works of the imagination this one has surpassed the intentions of its creators. In the first place, it is unlikely that they thought that the experiment they were proposing, or any facsimile, would ever be carried out. This, thanks largely to the work inspired by Bell, has now happened. Indeed, our physics journals are now resplendent with new and ever more ingenious versions of the Einstein-Podolsky-Rosen experiment, along with increasingly accurate experimental results. In the second place, and this is also an aftermath of Bell’s work, the Einstein-Podolsky-Rosen experiment has made its way into much of the popular folklore about the quantum theory. (It is usually referred to in the literature, familiarly, as the EPR experiment.)
- Jeremy Bernstein,
*Quantum Profiles*(1991), John Stewart Bell: Quantum Engineer

- Jeremy Bernstein,

- Due to the lucidity and apparently incontestable character of the argument, the paper of Einstein, Podolsky and Rosen created a stir among physicists and has played a large role in general philosophical discussion. Certainly the issue is of a very subtle character and suited to emphasize how far, in quantum theory, we are beyond the reach of pictorial visualization.
- Niels Bohr, "Discussion with Einstein on Epistemological Problems in Atomic Physics", published in
*Albert Einstein: Philosopher-Scientist*(1949)

- Niels Bohr, "Discussion with Einstein on Epistemological Problems in Atomic Physics", published in

- If Monod and Weinberg are truly speaking for the twentieth century, then I prefer the eighteenth. But in fact Monod and Weinberg, both of them first-rate scientists and leaders of research in their specialties, are expressing a point of view which does not take into account the subtleties and ambiguities of twentieth-century physics. The roots of their philosophical attitudes lie in the nineteenth century, not in the twentieth. The taboo against mixing knowledge with values arose during the nineteenth century out of the great battle between the evolutionary biologists led by Thomas Huxley and the churchmen led by Bishop Wilberforce. Huxley won the battle, but a hundred years later Monod and Weinberg were still fighting the ghost of Bishop Wilberforce.… For the biologists, every step down in size was a step toward increasingly simple and mechanical behavior. A bacterium is more mechanical than a frog, and a DNA molecule is more mechanical than a bacterium. But twentieth-century physics has shown that further reductions in size have an opposite effect. If we divide a DNA molecule into its component atoms, the atoms behave less mechanically than the molecule...

... If we divide an atom into nucleus and electrons, the electrons are less mechanical than the atom. There is a famous experiment, originally suggested by Einstein, Podolsky and Rosen in 1935 as a thought experiment to illustrate the difficulties of quantum theory, which demonstrates that the notion of an electron existing in an objective state independent of the experimenter is untenable. The experiment has been done in various ways with various kinds of particles, and the results show clearly that the state of a particle has a meaning only when a precise procedure for observing the state is prescribed. Among physicists there are many different philosophical viewpoints, and many different ways of interpreting the role of the observer in the description of subatomic processes. But all physicists agree with the experimental facts which make it hopeless to look for a description independent of the mode of observation. When we are dealing with things as small as atoms and electrons, the observer or experimenter cannot be excluded from the description of nature. In this domain, Monod's dogma, "The cornerstone of the scientific method is the postulate that nature is objective," turns out to be untrue. … We are saying only that if as physicists we try to observe in the finest detail the behavior of a single molecule, the meaning of the words "chance" and "mechanical" will depend upon the way we make our observations. The laws of subatomic physics cannot even be formulated without some reference to the observer. "Chance" cannot be defined except as a measure of the observer's ignorance of the future. The laws leave a place for mind in the description of every molecule.- Freeman Dyson,
*Disturbing the Universe*(1979), p. 246-249

- Freeman Dyson,

- Quantum key distribution as described above was the product of my graduate infatuation with quantum theory. It all happened back in Oxford in the late 1980s and early 1990s. I do not remember exactly what prompted me to visit the Clarendon Laboratory library one rainy day, browse the dusty shelves and pick up the original Einstein, Podolsky and Rosen paper for casual reading. However, I do remember this one sentence in the paper that drew my attention: "...If, without in any way disturbing a system, we can predict with certainty ... the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity." This is a definition of perfect eavesdropping! I guess I was lucky to read it in this particular way. The rest was just about rephrasing the subject in cryptographic terms.
- Artur Ekert, "Cracking codes, part II" (May 1, 2005)

- Many years ago David Bohm proposed replacing the hypothetical "completeness" experiment of Einstein, Podolsky, and Rosen...by a modified and more practical version. Bohm's experiment (called the EPRB...) involves the decay of a particle into two photons... the photons travel in opposite directions, have equal energy, and have identical polarizations. ...John Bell revealed that the EPRB... could be used to distinguish quantum mechanics from hypothetical hidden variable theories. Bell's theorem (also called Bell's inequalities) concerns a particular quantity that specifies the correlation between the polarizations of the two photons.
- Murray Gell-Mann,
*The Quark and the Jaguar*(1994)

- Murray Gell-Mann,

**The principal distortion disseminated ... is the implication, or even the explicit claim, that measuring the polarization, circular or plane, of one of the photons somehow affects the other photon. In fact, the measurement does not cause any physical effect to propagate from one photon to the other.**...If on one branch of history, the plane polarization of one photon is measured and thereby specified with certainty, then on the same branch of history the circular polarization of the other photon is also specified with certainty. On a different branch of history the circular polarization of one of the photons may be measured, in which case the circular polarization of both photons is specified with certainty. On each branch, the situation is like that of Bertlmann's socks, described by John Bell... Bertlmann... always wears one pink and one green sock. If you see just one... you know immediately the other... Yet no signal is propogated... Likewise no signal passes from one photon to the other in the experiment that confirms quantum mechanics. No action at a distance takes place.- Murray Gell-Mann,
*The Quark and the Jaguar*(1994)

- Murray Gell-Mann,

**The false report that measuring one of the photons immediately affects the other leads to all sorts of unfortunate conclusions.**...the alleged effect... would violate the requirement of relativity theory that no signal... can travel faster than the speed of light. If it were to do so, it would appear to observers in some states of motion that the signal were traveling backward in time.- Murray Gell-Mann,
*The Quark and the Jaguar*(1994)

- Murray Gell-Mann,

- The intent of the Einstein-Podolsky-Rosen paper was to show that quantum mechanics... could not be the final word regarding the physics of the microcosmos. ...they wanted to show that every particle does possess a definite position and a definite velocity at any given instant of time, and thus they wanted to conclude that the uncertainty principle reveals a fundamental limitation of the quantum mechanical approach. ...quantum mechanics provides only a partial description of the universe. ...an incomplete theory of physical reality and, perhaps, merely a stepping-stone toward a deeper framework waiting to be discovered.
- Brian Greene,
*The Fabric of the Cosmos: Space, Time, and the Texture of Reality*(2007)

- Brian Greene,

- Einstein had drawn attention to nonlocality in 1935 in an effort to show that quantum mechanics must be flawed. ...Einstein proposed a thought experiment—now called the EPR experiment—involving two particles that spring from a common source and fly in opposite directions.

According to the standard model of quantum mechanics, neither particle has a definite position or momentum before it is measured; but by measuring the momentum of one particle, the physicist instantaneously forces the other particle to assume a fixed position... Deriding this effect as "spooky action at a distance," Einstein argued that it violated both common sense and his own theory of special relativity, which prohibits the propagation of effects faster than the speed of light; quantum mechanics must therefore be an incomplete theory. In 1980, however, a group of French physicists carried out a version of the EPR experiment and showed that it did indeed give rise to spooky action. (The reason that the experiment does not violate special relativity is that one cannot exploit nonlocality to transmit information.)- John Horgan,
*The End of Science*(1996)

- John Horgan,

- The only part of this article that will ultimately survive, I believe, is this last phrase, which so poignantly summarizes Einstein's views on quantum mechanics in his later years. The content of this paper has been referred to on occasion as the Einstein-Podolsky-Rosen paradox. It should be stressed that this paper contains neither a paradox nor any flaw of logic. It simply concludes that objective reality is incompatible with the assumption that quantum mechanics is complete. This conclusion has not affected subsequent developments in physics, and it is doubtful that it ever will. [...] Experimentalists have actively participated, as well. A number of experimental tests of quantum mechanics in general and also of the predictions of specific alternative schemes have been made. This has not led to any surprises.
- Abraham Pais,
*Subtle is the Lord...*(1982), 25. Einstein's Response to the New Dynamics

- Abraham Pais,

- Finally, in that period the 'EPR paper' appeared, a collaboration with Nathan Rosen and Boris Podolsky which deals with the foundations of quantum mechanics. There are a number of physicists who consider this a fundamental contribution to that subject. I am not one of those.
- Abraham Pais,
*Einstein Lived Here*(1994), 11. Einstein and the press

- Abraham Pais,

- This onslaught came down upon us as a bolt from the blue. Its effect on Bohr was remarkable... as soon as Bohr had heard my report of Einstein’s argument, everything else was abandoned: we have to clear up such a misunderstanding at once. We should reply by taking up the same example and showing the right way to speak about it. In great excitement, Bohr immediately started dictating to me the outline of such a reply. Very soon, however, he became hesitant. ‘No, this won’t do, we must try all over again... we must make it quite clear...’ So it went on for a while, with growing wonder at the unexpected subtlety of the argument.
- Léon Rosenfeld,
*Niels Bohr in the Thirties in Niels Bohr, his life and work as seen by his friends and colleagues*(ed. S. Rozental), 1967

- Léon Rosenfeld,

- Aage Bohr expressed the same point to me the last time I talked to him. He just couldn’t understand why there were all these conferences—conference after conference—on EPR, when it is just the way it works. It is just exactly the wrong thing to be asking about. There is a conference coming up in Finland in August with some people I’d love to talk to, but I’ve written them to say that I’m not going. If you keep trying to pull apples off the apple tree, after a while it doesn’t do. I hope that I am not being too propagandistic in speaking of the idea that when we see it all it will be so simple we’ll all say, ‘How stupid we’ve been all this time!’ We’ve got to look for the right word, the right image. So you try one word for a day, for a week, for a month, or for a year, and then you give it up and try another one.
- John Wheeler, quoted in Jeremy Bernstein,
*Quantum Profiles*(1991), John Wheeler: Retarded Learner

- John Wheeler, quoted in Jeremy Bernstein,

- In conclusion, although Einstein, Podolsky, and Rosen presented a picture of the world that was disproven experimentally, I would still regard them as having won a moral victory: The then-common interpretation of quantum mechanics did indeed have a one person measuring at A, seeing a single outcome, and then making a certain prediction about a unique outcome at B; and this is indeed incompatible with relativity, and wrong. Though people are still arguing about that.
- Eliezer Yudkowsky, "Bell's Theorem: No EPR "Reality" " (04 May 2008)