Bohr-Einstein debates

Bohr-Einstein debates

Overview
The Bohr–Einstein debates were a series of public disputes about quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 between Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 and Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

, who were two of its founders. Their debates are remembered because of their importance to the philosophy of science
Philosophy of science
The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...

. An account of them has been written by Bohr in an article titled "Discussions with Einstein
on Epistemological Problems in Atomic Physics". Despite their differences of opinion regarding quantum mechanics, Bohr and Einstein had a mutual admiration that was to last the rest of their lives.

Einstein was the first physicist to say that Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

's discovery of the quantum (h) would require a rewriting of physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

.
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Encyclopedia
The Bohr–Einstein debates were a series of public disputes about quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 between Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

 and Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...

, who were two of its founders. Their debates are remembered because of their importance to the philosophy of science
Philosophy of science
The philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...

. An account of them has been written by Bohr in an article titled "Discussions with Einstein
on Epistemological Problems in Atomic Physics". Despite their differences of opinion regarding quantum mechanics, Bohr and Einstein had a mutual admiration that was to last the rest of their lives.

Pre-revolutionary debates


Einstein was the first physicist to say that Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

's discovery of the quantum (h) would require a rewriting of physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

. As though to prove his point, in 1905 he proposed that light sometimes acts as a particle
Wave–particle duality
Wave–particle duality postulates that all particles exhibit both wave and particle properties. A central concept of quantum mechanics, this duality addresses the inability of classical concepts like "particle" and "wave" to fully describe the behavior of quantum-scale objects...

 which he called a light quantum (now called the photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

). Bohr was one of the most vocal opponents of the photon idea and did not openly embrace it until 1925. His later ability to work creatively with an idea he had so long resisted is quite unusual in the history of science. The photon appealed to Einstein because he saw it as a physical reality (although a confusing one) behind the numbers. Bohr disliked it because it made the choice of mathematical solution arbitrary. He did not like that a scientist had to choose between equations.

1913 brought the Bohr model of the hydrogen atom
Bohr model
In atomic physics, the Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with electrostatic forces providing attraction,...

 which made use of the quantum to explain the atomic spectrum. Einstein was at first dubious, but quickly changed his mind and embraced it. He tolerated Bohr's model despite the fact that its underlying reality could not be pictured in detail because he considered it a work in progress.

The quantum revolution


The quantum revolution of the mid-1920s occurred under the direction of both Einstein and Bohr, and their post-revolutionary debates were about making sense of the change. The shocks for Einstein began in 1925 when Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

 introduced matrix equations that removed the Newtonian elements of space and time from any underlying reality. The next shock came in 1926 when Max Born
Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...

 proposed that the mechanics was to be understood as a probability without any causal explanation.

Einstein rejected this interpretation. In a 1926 letter to Max Born
Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...

, Einstein wrote: "I, at any rate, am convinced that He [God] does not throw dice."

Finally, in late 1927, Heisenberg and Born declared at the Solvay Conference that the revolution was over and nothing further was needed. It was at that last stage that Einstein's skepticism turned to dismay. He believed that much had been accomplished, but the reasons for the mechanics still needed to be understood.

Einstein's refusal to accept the revolution as complete reflected his rejection of the idea that positions in space-time could never be completely known and by the way quantum probabilities did not reflect any underlying causes. He did not reject the statistics or probabilities on their own and Einstein himself was a great statistical thinker. It was the lack of any reason for an event that Einstein rejected. Bohr, meanwhile, was dismayed by none of the elements that troubled Einstein. He made his own peace with the contradictions by proposing a Principle of Complementarity
Complementarity (physics)
In physics, complementarity is a basic principle of quantum theory proposed by Niels Bohr, closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality...

 that emphasized the role of the observer over the observed.

Post-Revolution: First stage


As mentioned above, Einstein's position underwent significant modifications over the course of the years. In the first stage, Einstein refused to accept quantum indeterminism and sought to demonstrate that the principle of indeterminacy could be violated, suggesting ingenious thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

s which should permit the accurate determination of incompatible variables, such as position and velocity, or to explicitly reveal simultaneously the wave and the particle aspects of the same process.

The first serious attack by Einstein on the "orthodox" conception took place during the Fifth Solvay International Conference on Electrons and Photons in 1927. Einstein pointed out how it was possible to take advantage of the (universally accepted) laws of conservation of energy
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

 and of impulse (momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

) in order to obtain information on the state of a particle in a process of interference which, according to the principle of indeterminacy or that of complementarity
Complementarity (physics)
In physics, complementarity is a basic principle of quantum theory proposed by Niels Bohr, closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality...

, should not be accessible.


In order to follow his argumentation and to evaluate Bohr's response, it is convenient to refer to the experimental apparatus illustrated in figure A. A beam of light perpendicular to the X axis which propagates in the direction z encounters a screen S1 which presents a narrow (with respect to the wavelength of the ray) slit. After having passed through the slit, the wave function diffracts with an angular opening that causes it to encounter a second screen S2 which presents two slits. The successive propagation of the wave results in the formation of the interference figure on the final screen F.

At the passage through the two slits of the second screen S2, the wave aspects of the process become essential. In fact, it is precisely the interference between the two terms of the quantum superposition
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...

 corresponding to states in which the particle is localized in one of the two slits which implies that the particle is "guided" preferably into the zones of
constructive interference and cannot end up in a point in the zones of destructive interference (in which the wave function is nullified). It is also important to note that any experiment designed to evidence the "corpuscular" aspects of the process at the passage of the screen S2 (which, in this case, reduces to the determination of which slit the particle has passed through) inevitably destroys the wave aspects, implies the disappearance of the interference figure and the emergence of two concentrated spots of diffraction which confirm our knowledge of the trajectory followed by the particle.

At this point Einstein brings into play the first screen as well and argues as follows: since the incident particles have velocities (practically) perpendicular to the screen S1, and since it is only the interaction with this screen that can cause a deflection from the original direction of propagation, by the law of conservation of impulse which implies that the sum of the impulses of two systems which interact is conserved, if the incident particle is deviated toward the top, the screen will recoil toward the bottom and vice-versa. In realistic conditions the mass of the screen is so heavy that it will remain stationary, but, in principle, it is possible to measure even an infinitesimal recoil. If we imagine taking the measurement of the impulse of the screen in the direction X after every single particle has passed, we can know, from the fact that the screen will be found recoiled toward the top (bottom), if the particle in question has been deviated toward the bottom (top) and therefore we can know from which slit in S2 the particle has passed. But since the determination of the direction of the recoil of the screen after the particle has passed cannot influence the successive development of the process, we will still have an interference figure on the screen F. The interference takes place precisely because the state of the system is the superposition of two states whose wave functions are non-zero only near one of the two slits. On the other hand, if every particle passes through only the slit b or the slit c, then the set of systems is the statistical mixture of the two states, which means that interference is not possible. If Einstein is correct, then there is a violation of the principle of indeterminacy.


Bohr's response was to illustrate Einstein's idea more clearly via the diagrams in Figures B and C.
Bohr observes that extremely precise knowledge of any (potential) vertical motion of the screen is an essential presupposition in Einstein's argument. In fact, if its velocity in the direction X before the passage of the particle is not known with a precision substantially greater than that induced by the recoil (that is, if it were already moving vertically with an unknown and greater velocity than that which it derives as a consequence of the contact with the particle), then the determination of its motion after the passage of the particle would not give the information we seek. However, Bohr continues, an extremely precise determination of the velocity of the screen, when one applies the principle of indeterminacy, implies an inevitable imprecision of its position in the direction X. Before the process even begins, the screen would therefore occupy an indeterminate position at least to a certain extent (defined by the formalism). Now consider, for example, the point d in figure A, where there is destructive interference. It's obvious that any displacement of the first screen would make the lengths of the two paths, a-b-d and a-c-d, different from those indicated in the figure. If the difference between the two paths varies by half a wavelength, at point d there will be constructive rather than destructive interference. The ideal experiment must average over all the possible positions of the screen S1, and, for every position, there corresponds, for a certain fixed point F, a different type of interference, from the perfectly destructive to the perfectly constructive. The effect of this averaging is that the pattern of interference on the screen F will be uniformly grey. Once more, our attempt to evidence the corpuscular aspects in S2 has destroyed the possibility of interference in F which depends crucially on the wave aspects.
It should be noted that, as Bohr recognized, for the understanding of this phenomenon "it is decisive that, contrary to genuine instruments of measurement, these bodies along with the particles would constitute, in the case under examination, the system
to which the quantum-mechanical formalism must apply. With respect to the precision of the conditions under which one can correctly apply the formalism, it is essential to include the entire experimental apparatus. In fact, the introduction of any new apparatus, such as a mirror, in the path of a particle could introduce new effects of interference which influence essentially the predictions about the results which will be registered at the end." Further along, Bohr attempts to resolve this ambiguity concerning which parts of the system should be considered macroscopic and which not:
In particular, it must be very clear that...the unambiguous use of spatiotemporal concepts in the description of atomic phenomena must be limited to the registration of observations which refer to images on a photographic lens or to analogous practically irreversible effects of amplification such as the formation of a drop of water around an ion in a dark room.


Bohr's argument about the impossibility of using the apparatus proposed by Einstein to violate the principle of indeterminacy depends crucially on the fact that a macroscopic system (the screen S1) obeys quantum laws. On the other hand, Bohr consistently asserted that, in order to illustrate the microscopic aspects of reality it is necessary to set off a process of amplification which involves macroscopic apparatuses, whose fundamental characteristic is that of obeying classical laws and which can be described in classical terms. This ambiguity would later come back in the form of what is still called today the measurement problem
Measurement problem
The measurement problem in quantum mechanics is the unresolved problem of how wavefunction collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer...

.

The principle of indeterminacy applied to time and energy



In many textbook examples and popular discussions of quantum mechanics, the principle of indeterminacy is explained by reference to the pair of variables position and velocity (or momentum). It is important to note that the wave nature of physical processes implies that there must exist another relation of indeterminacy: that between time and energy. In order to comprehend this relation, it is convenient to refer to the experiment illustrated in
Figure D, which results in the propagation of a wave which is limited in spatial extension. Assume that, as illustrated in the figure, a ray which is extremely extended longitudinally is propagated toward a screen with a slit furnished with a shutter which remains open only for a very brief interval of time . Beyond the slit, there will be a wave of limited spatial extension which continues to propagate toward the right.

A perfectly monochromatic wave (such as a musical note which cannot be divided into harmonics) has infinite spatial extent. In order to have a wave which is limited in spatial extension (which is technically called a wave packet
Wave packet
In physics, a wave packet is a short "burst" or "envelope" of wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere...

), several waves of different frequencies must be superimposed and distributed continuously within a certain interval of frequencies around an average value, such as .
It then happens that at a certain instant, there exists a spatial region (which moves over time) in which the contributions of the various fields of the superposition add up constructively. Nonetheless, according to a precise mathematical theorem, as we move far away from this region, the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

s of the various fields, at any specified point, are distributed causally and destructive interference is produced. The region in which the wave has non-zero amplitude is therefore spatially limited. It is easy to demonstrate that, if the wave has a spatial extension equal to (which means, in our example, that the shutter has remained open for a time where v is the velocity of the wave), then the wave contains (or is a superposition of) various monochromatic waves whose frequencies cover an interval which satisfies the relation:


Remembering that in the universal relation of Planck, frequency and energy are proportional:


it follows immediately from the preceding inequality that the particle associated with the wave should possess an energy which is not perfectly defined (since different frequencies are involved in the superposition) and consequently there is indeterminacy in energy:


From this it follows immediately that:


which is the relation of indeterminacy between time and energy.

Einstein's second criticism


At the sixth Congress of Solvay in 1930, the indeterminacy relation just discussed was Einstein's target of criticism. His idea contemplates the existence of an experimental apparatus which was subsequently designed by Bohr in such a way as to emphasize the essential elements and the key points which he would use in his response.

Einstein considers a box (called Einstein's box; see figure) containing electromagnetic radiation and a clock which controls the opening of a shutter which covers a hole made in one of the walls of the box. The shutter uncovers the hole for a time which can be chosen arbitrarily. During the opening, we are to suppose that a photon, from among those inside the box, escapes through the hole. In this way a wave of limited spatial extension has been created, following the explanation given above. In order to challenge the indeterminacy relation between time and energy, it is necessary to find a way to determine with adequate precision the energy that the photon has brought with it. At this point, Einstein turns to his celebrated relation between mass and energy of special relativity: . From this it follows that knowledge of the mass of an object provides a precise indication about its energy. The argument is therefore very simple: if one weighs the box before and after the opening of the shutter and if a certain amount of energy has escaped from the box, the box will be lighter. The variation in mass multiplied by
will provide precise knowledge of the energy emitted.
Moreover, the clock will indicate the precise time at which the event of the particle’s emission took place. Since, in principle, the mass of the box can be determined to an arbitrary degree of accuracy, the energy emitted can be determined with a precision as accurate as one desires. Therefore, the product can be rendered less than what is implied by the principle of indeterminacy.

The idea is particularly acute and the argument seemed unassailable. It's important to consider the impact of all of these exchanges on the people involved at the time. Leon Rosenfeld
Léon Rosenfeld
Léon Rosenfeld was a Belgian physicist. He obtained a PhD at the University of Liège in 1926, and he was a collaborator of the physicist Niels Bohr. He did early work in quantum electrodynamics that predates by two decades the work by Dirac and Bergmann. He coined the name lepton...

, a scientist who had participated in the Congress, described the event several years later:
It was a real shock for Bohr...who, at first, could not think of a solution. For the entire evening he was extremely agitated, and he continued passing from one scientist to another, seeking to persuade them that it could not be the case, that it would have been the end of physics if Einstein were right; but he couldn't come up with any way to resolve the paradox. I will never forget the image of the two antagonists as they left the club: Einstein, with his tall and commanding figure, who walked tranquilly, with a mildly ironic smile, and Bohr who trotted along beside him, full of excitement...The morning after saw the triumph of Bohr.


The "triumph of Bohr" consisted in his demonstrating, once again, that Einstein's subtle argument was not conclusive, but even more so in the way that he arrived at this conclusion by appealing precisely to one of the great ideas of Einstein: the principle of equivalence between gravitational mass and inertial mass. Bohr showed that, in order for Einstein's experiment to function, the box would have to be suspended on a spring in the middle of a gravitational field. In order to obtain a measurement of weight, a pointer would have to be attached to the box which corresponded with the index on a scale. After the release of a photon, weights could be added to the box to restore it to its original position and this would allow us to determine the weight. But in order to return the box to its original position, the box itself would have to be measured. The inevitable uncertainty of the position of the box translates into an uncertainty in the position of the pointer and of the determination of weight and therefore of energy. On the other hand, since the system is immersed in a gravitational field which varies with the position, according to the principle of equivalence the uncertainty in the position of the clock implies an uncertainty with respect to its measurement of time and therefore of the value of the interval . A precise evaluation of this effect leads to the conclusion that the relation cannot be violated.

Post-Revolution: Second stage



The second phase of Einstein's "debate" with Bohr and the orthodox interpretation is characterized by an acceptance of the fact that it is, as a practical matter, impossible to simultaneously determine the values of certain incompatible quantities, but the rejection that this implies that these quantities do not actually have precise values. He rejects the probabilistic interpretation of Born
Max Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...

 and insists that quantum probabilities are epistemic and not ontological
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...

 in nature. As a consequence, the theory must be incomplete in some way. He recognizes the great value of the theory, but suggests that it "does not tell the whole story," and, while providing an appropriate description at a certain level, it gives no information on the more fundamental underlying level:
I have the greatest consideration for the goals which are pursued by the physicists of the latest generation which go under the name of quantum mechanics, and I believe that this theory represents a profound level of truth, but I also believe that the restriction to laws of a statistical nature will turn out to be transitory....Without doubt quantum mechanics has grasped an important fragment of the truth and will be a paragon for all future fundamental theories, for the fact that it must be deducible as a limiting case from such foundations, just as electrostatics is deducible from Maxwell's equations of the electromagnetic field or as thermodynamics is deducible from statistical mechanics.


These thoughts of Einstein’s would set off a line of research into so-called hidden variable theories
Hidden variable theory
Historically, in physics, hidden variable theories were espoused by some physicists who argued that quantum mechanics is incomplete. These theories argue against the orthodox interpretation of quantum mechanics, which is the Copenhagen Interpretation...

, such as the Bohm interpretation
Bohm interpretation
The de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...

, in an attempt to complete the edifice of quantum theory. If quantum mechanics can be made complete in Einstein's sense, it cannot be done locally
Principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. Experiments have shown that quantum mechanically entangled particles must violate either the principle of locality or the form of philosophical realism known as counterfactual...

; this fact was demonstrated by John Stewart Bell
John Stewart Bell
John Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...

 with the formulation of Bell's inequality in 1964; however, should we live in a superdeterminist
Superdeterminism
In the context of quantum mechanics, superdeterminism is a term that has been used to describe a hypothetical class of theories which evade Bell's theorem by virtue of being completely deterministic. Bell's theorem depends on the assumption of counterfactual definiteness, which technically does...

 universe, that demonstration would not be valid, as admitted by Bell himself.

The argument of EPR




In 1935 Einstein, Boris Podolsky
Boris Podolsky
Boris Yakovlevich Podolsky , was an American physicist of Russian Jewish descent.-Education:In 1896, Boris Podolsky was born into a poor Jewish family in Taganrog, in what was then the Russian Empire, and he moved to the United States in 1913...

 and Nathan Rosen
Nathan Rosen
Nathan Rosen was an American-Israeli physicist noted for his study on the structure of the hydrogen molecule and his work with Albert Einstein and Boris Podolsky on entangled wave functions and the EPR paradox.-Background:Nathan Rosen was born into a Jewish family in Brooklyn, New York...

 developed an argument, published in the magazine Physical Review with the title Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?, based on an entangled state of two systems. Before coming to this argument, it is necessary to formulate another hypothesis that comes out of Einstein's work in relativity: the principle of locality
Principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. Experiments have shown that quantum mechanically entangled particles must violate either the principle of locality or the form of philosophical realism known as counterfactual...

. The elements of physical reality which are objectively possessed cannot be influenced instantaneously at a distance.

The argument of EPR was in 1957 picked up by David Bohm
David Bohm
David Joseph Bohm FRS was an American-born British quantum physicist who contributed to theoretical physics, philosophy, neuropsychology, and the Manhattan Project.-Youth and college:...

 and Yakir Aharonov
Yakir Aharonov
Yakir Aharonov is an Israeli physicist specializing in quantum physics. He is a Professor of Theoretical Physics and the James J. Farley Professor of Natural Philosophy at Chapman University in California. He is also a distinguished professor in Perimeter Institute.He also serves as a professor...

 in a paper published in Physical Review with the title Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky. The authors re-formulated the argument in terms of an entangled state of two particles, which can be summarized as follows:

1) Consider a system of two photons which at time t are located, respectively, in the spatially distant regions A and B and which are also in the entangled state of polarization described below:


2) At time t the photon in region A is tested for vertical polarization. Suppose that the result of the measurement is that the photon passes through the filter. According to the reduction of the wave packet, the result is that, at time t+dt, the system becomes:


3) At this point, the observer in A who carried out the first measurement on photon 1, without doing anything else that could disturb the system or the other photon ("assumption (R)," below), can predict with certainty that photon 2 will pass a test of vertical polarization. It follows that photon 2 possesses an element of physical reality: that of having a vertical polarization.

4) According to the assumption of locality, it cannot have been the action carried out in A which created this element of reality for photon 2. Therefore, we must conclude that the photon possessed the property of being able to pass the vertical polarization test before and independently of the measurement of photon 1.

5) At time t, the observer in A could have decided to carry out a test of polarization at 45°, obtaining a certain result, for example, that the photon passes the test. In that case, he could have concluded that photon 2 turned out to be polarized at 45°. Alternatively, if the photon did not pass the test, he could have concluded that photon 2 turned out to be polarized at 135°. Combining one of these alternatives with the conclusion reached in 4, it seems that photon 2, before the measurement took place, possessed both the property of being able to pass with certainty a test of vertical polarization and the property of being able to pass with certainty a test of polarization at either 45° or 135°. These properties are incompatible according to the formalism.

6) Since natural and obvious requirements have forced the conclusion that photon 2 simultaneously possesses incompatible properties, this means that, even if it is not possible to determine these properties simultaneously and with arbitrary precision, they are nevertheless possessed objectively by the system. But quantum mechanics denies this possibility and it is therefore an incomplete theory.

Bohr's response


Bohr's response to this fascinating and elegant argument was published, five months later than the original publication of EPR, in the same magazine Physical Review and with exactly the same title as the original. The crucial point of Bohr's answer is distilled in a passage which he later had republished in Paul Arthur Schilpp
Paul Arthur Schilpp
Paul Arthur Schilpp was an American educator.He was born in Germany and immigrated to the United States prior to World War I...

's book Albert Einstein, scientist-philosopher in honor of the seventieth birthday of Einstein. Bohr attacks assumption (R) of EPR by stating:
the statement of the criterion in question is ambiguous with regard to the expression "without disturbing the system in any way". Naturally, in this case no mechanical disturbance of the system under examination can take place in the crucial stage of the process of measurement. But even in this stage there arises the essential problem of an influence on the precise conditions which define the possible types of prediction which regard the subsequent behaviour of the system...their arguments do not justify their conclusion that the quantum description turns out to be essentially incomplete...This description can be characterized as a rational use of the possibilities of an unambiguous interpretation of the process of measurement compatible with the finite and uncontrollable interaction between the object and the instrument of measurement in the context of quantum theory.


As John Bell
John Stewart Bell
John Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...

 later pointed out, this passage is almost unintelligible. What does Bohr mean, Bell asks, by the specification "mechanical" that is used to refer to the "disturbances" that Bohr maintains should not be taken into consideration? What is meant by the expression "an influence on the precise conditions" if not that different measurements in A provide different information on the system in B? This fact is not only admitted but is an essential part of the argument of EPR. Lastly, what could Bohr have meant by the expression "uncontrollable interaction between the object and the measuring apparatus", considering that the central point of the argument of EPR is the hypothesis that, if one accepts locality, only the part of the system in A can be disturbed by the process of measurement and that, notwithstanding this fact, this process provides precise information on the part of the system in B? Is Bohr already contemplating the possibility of "spooky action at a distance?" If so, why not declare it explicitly? If one abandons the assumption of locality, the argument of EPR obviously collapses immediately.

The debates represent one of the highest points of scientific research in the first half of the twentieth century because it called attention to an element of quantum theory, quantum non-locality
Quantum nonlocality
Quantum nonlocality is the phenomenon by which measurements made at a microscopic level necessarily refute one or more notions that are regarded as intuitively true in classical mechanics...

, which is absolutely central to our modern understanding of the physical world.

Post-Revolution: Fourth stage


In his last writing on the topic, Einstein further refined his position, making it completely clear that what really disturbed him about the quantum theory was the problem of the total renunciation of all minimal standards of realism, even at the microscopic level, that the acceptance of the completeness of the theory implied. Although the majority of experts in the field seem to accept the Copenhagen interpretation, there are critics
who, like Einstein, believe that it has failed to provide a sensible and acceptable representation of reality (see Interpretation of quantum mechanics
Interpretation of quantum mechanics
An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations...

).

See also

  • Afshar's experiment
    Afshar experiment
    The Afshar experiment is an optical experiment, devised and carried out by Shahriar Afshar in 2001, which investigates the principle of complementarity in quantum mechanics...

  • Bell test experiments
    Bell test experiments
    The Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...

  • Bell's theorem
    Bell's theorem
    In theoretical physics, Bell's theorem is a no-go theorem, loosely stating that:The theorem has great importance for physics and the philosophy of science, as it implies that quantum physics must necessarily violate either the principle of locality or counterfactual definiteness...

  • Complementarity
    Complementarity (physics)
    In physics, complementarity is a basic principle of quantum theory proposed by Niels Bohr, closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality...

  • Copenhagen interpretation
    Copenhagen interpretation
    The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...

  • Double-slit experiment
    Double-slit experiment
    The double-slit experiment, sometimes called Young's experiment, is a demonstration that matter and energy can display characteristics of both waves and particles...

  • Quantum eraser
  • Schrödinger's cat
    Schrödinger's cat
    Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...

  • Uncertainty principle
    Uncertainty principle
    In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

  • Wheeler's delayed choice experiment
    Wheeler's delayed choice experiment
    Wheeler's delayed choice experiment is a thought experiment proposed by John Archibald Wheeler in 1978, and later confirmed. Wheeler proposed a variation of the famous double-slit experiment of quantum physics, one in which the method of detection can be changed after the photon passes the double...

  • Many-world's interpretation