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{{short description|Series of public disputes between physicists Niels Bohr and Albert Einstein}} | |||
] with ] at ]'s home in Leiden (December 1925)]] | |||
] (left) with ] (right) at ]'s home in ] (December 1925)]] | |||
The '''Bohr–Einstein debates''' were a series of public disputes about ] between ] and ]. Their debates are remembered because of their importance to the ], insofar as the disagreements—and the outcome of Bohr's version of quantum mechanics becoming the prevalent view—form the root of the modern understanding of physics.<ref>{{Cite web|title=Learn about Niels Bohr and the difference of opinion between Bohr and Albert Einstein on quantum mechanics|url=https://www.britannica.com/video/186823/Abraham-Pais-authorities-Niels-Bohr-Paul-Davies}}</ref> Most of Bohr's version of the events held in the ] in 1927 and other places was first written by Bohr decades later in an article titled, "Discussions with Einstein on Epistemological Problems in Atomic Physics".<ref>{{Cite web|title=Revisiting the Einstein-Bohr Dialogue |url=https://www3.nd.edu/~dhoward1/Revisiting%20the%20Einstein-Bohr%20Dialogue.pdf}}</ref><ref name='Bohr1949'>{{cite web | url = http://www.marxists.org/reference/subject/philosophy/works/dk/bohr.htm | title = Discussions with Einstein on Epistemological Problems in Atomic Physics | access-date = 2010-08-30 | last = Bohr N | work = The Value of Knowledge: A Miniature Library of Philosophy | publisher = ]}} From Albert Einstein: Philosopher-Scientist (1949), publ. Cambridge University Press, 1949. Niels Bohr's report of conversations with Einstein.</ref> Based on the article, the philosophical issue of the debate was whether Bohr's ] of quantum mechanics, which centered on his belief of ], was valid in explaining nature.<ref>{{Cite book|last=Marage|first=Pierre|title=The Solvay Councils and the Birth of Modern Physics|chapter=The Debate between Einstein and Bohr, or How to Interpret Quantum Mechanics|year=1999|pages=161–174|doi=10.1007/978-3-0348-7703-9_10|isbn=978-3-0348-7705-3|chapter-url=https://link.springer.com/chapter/10.1007/978-3-0348-7703-9_10}}</ref> Despite their differences of opinion and the succeeding discoveries that helped solidify quantum mechanics, Bohr and Einstein maintained a mutual admiration that was to last the rest of their lives.<ref name='González'>{{cite web | url = http://dipc.ehu.es/digitalak/orriak/english/quantumdilema.html | title = Albert Einstein | access-date = 2010-08-30 | author = González AM | publisher = Donostia International Physics Center | archive-date = 2015-05-02 | archive-url = https://web.archive.org/web/20150502121313/http://dipc.ehu.es/digitalak/orriak/english/quantumdilema.html | url-status = dead }}</ref><ref>{{Cite book|title=The Einstein-Podolsky-Rosen Argument in Quantum Theory|year=2020 |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/entries/qt-epr/}}</ref> | |||
The '''Bohr-Einstein debates''' is a popular name given to what was actually a series of ] challenges presented by ] against what has come to be called the ''standard'' or ] of ]. Since Einstein's closest friend and primary interlocutor in the "school" of Copenhagen was the physicist ], and it was Bohr who provided answers to most of the challenges presented by Einstein, what was actually a friendly and fruitful series of exchanges of ideas, has taken on the label of a "debate". | |||
Although Bohr and Einstein disagreed, they were great friends all their lives and enjoyed using each other as a foil.<ref>Louisa Gilder, The Age of Entanglement, chap. 5, 2008. “ “Not often in my life has a person, by his mere presence, given me such joy as you did,” wrote Einstein in 1920, in that first letter to Bohr. “I now understand why Ehrenfest loves you so. I am now studying your great papers and in doing so—especially when I get stuck somewhere—I have the pleasure of seeing your youthful face before me, smiling and explaining. I have learned much from you, especially also about your attitude regarding scientific matters.” (“What is so marvellously attractive about Bohr as a scientific thinker,” Einstein wrote not long afterward, “is his rare blend of boldness and caution; seldom has anyone possessed such an intuitive grasp of hidden things combined with such a strong critical sense.”) Somewhat awed, Bohr wrote in reply, “To me it was one of the greatest experiences ever to meet you and talk with you…. You cannot know how great a stimulus it was for me to have the long-hoped-for opportunity to hear of your views on the questions that have occupied me. I shall never forget our talks on the way from Dahlem to your home.”</ref> | |||
Einstein's position with respect to quantum mechanics is infinitely more subtle and open-minded than it has often been portrayed in technical manuals and popular science articles. This will become clearer during the course of the discussion. Be that as it may, his constant and powerful criticisms of the quantum "orthodoxy” compelled the defenders of that orthodoxy to sharpen and refine their understanding of the philosophical and scientific implications of their own theory. | |||
==Pre-revolutionary debates== | |||
Einstein's natural reference point, as mentioned above, was always Niels Bohr, as the person who, more than other members of the School of Copenhagen, was animated by a particular interest for the philosophical and epistemological aspects of the theory and drew inspiration from the surprising aspects of the microscopic world in order to present daring hypotheses about reality and about knowledge, such as his idea of ]. These two giants of scientific thought nurtured a profound respect for each other and they were both extremely attentive to the acute and penetrating observations of the other. The debate is not only of historical interest: as we will see Einstein's attacks often provoked reactions on the part of Bohr which called into question the crucial elements of the formalization of QM and of its interpretation. This articulated process, in which many other important scientists, from ] and ] to ] and from ] to ], took part, brought more and more detailed attention on certain particularly problematic points of the theory. | |||
Einstein was the first physicist to say that ]'s discovery of the energy quanta would require a rewriting of the laws of ]. To support his point, in 1905 Einstein proposed that light sometimes acts as a particle which he called a light ] (see ] and ]). Bohr was one of the most vocal opponents of the photon idea and did not openly embrace it until 1925.<ref name="Pais"/> The photon appealed to Einstein because he saw it as a physical reality (although a confusing one) behind the numbers presented by Planck mathematically in 1900. Bohr disliked it because it made the choice of mathematical solution arbitrary. Bohr did not like a scientist having to choose between equations.<ref name="Bolles">Bolles</ref> This disagreement was perhaps the first real Bohr-Einstein debate. Einstein had proposed the photon in 1905, and ] provided experiment in 1922 with his ], but Bohr refused to believe the photon existed even then. Bohr continued to dispute the existence of the quantum of light (photon) and along with ] and ] elaborated the ] in 1924. However, after the 1925 ], BKS was proved to be wrong and Einstein's hypothesis was proven to be correct.<ref>Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.5.</ref> | |||
==The quantum revolution== | |||
==First stage== | |||
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. ]'s ] in 1925 reinterpreted ] in terms of matrix-like operators, removing the Newtonian elements of space and time from any underlying reality. In parallel, ] redeveloped quantum theory in terms of a wave mechanics formulation, leading to the ]. However, when Schrödinger sent a preprint of his new equation to Einstein, Einstein wrote back hailing his equation as a decisive advance of “true genius.”<ref>Kumar, Manjit. | |||
As mentioned above, Einstein's position underwent significant modifications over the course of the years. In the first stage, Einstein refuses to accept quantum indeterminism and seeks to demonstrate that the ] can be violated, suggesting ingenious '']'' which should permit the simultaneous and arbitrarily 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. | |||
Quantum: Einstein, Bohr, and the great debate about the nature | |||
of reality / Manjit Kumar.—1st American Edition, “Schrödinger received a letter from Einstein, who told him ‘the idea of your work springs from true genius’.21 ‘Your approval and Planck’s mean more to me than that of half the world’, Schrödinger wrote back.22 Einstein was convinced that Schrödinger had made a decisive advance, ‘just as I am convinced that the Heisenberg-Born method is misleading’.“</ref> Then in 1926 when ], collaborating with Heisenberg, proposed that mechanics were to be understood as a probability without any causal explanation. | |||
Both Einstein and Schrödinger rejected ] with its renunciation of ] which had been a key feature of science previous to old quantum theory and was still a feature of ].<ref>Kumar, Manjit. | |||
The first serious attack by Einstein on the "orthodox" conception took place during the ''Fifth Conference of Physics'' at the ''Solvay Institute'' in 1927. Einstein pointed out how it was possible to take advantage of the (universally accepted) laws of conservation of energy and of impulse (]) in order to obtain information on the state of a particle in a process of ] which, according to the principle of indeterminacy or that of ], should not be accessible. | |||
Quantum: Einstein, Bohr, and the great debate about the nature | |||
of reality / Manjit Kumar.—1st American ed.</ref> In a 1926 letter to Max Born, Einstein wrote:<ref>{{Cite book |last=Einstein |first=Albert |date=1969 |title=Albert Einstein, Hedwig und Max Born: Briefwechsel 1916–1955 |publisher=Nymphenburger Verlagshandlung |location=Munich |language=de |isbn=978-3-88682-005-4 }}</ref> | |||
{{Quote2|quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the “old one”. I, at any rate, am convinced that He is not playing at dice.}} | |||
] | |||
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 first, even Heisenberg had heated disputes with Bohr that his ] was not compatible with the Schrödinger's wave mechanics.<ref>Kumar, Manjit. | |||
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 ] 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 | |||
Quantum: Einstein, Bohr, and the great debate about the nature | |||
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. | |||
of reality / Manjit Kumar.—1st American ed. “Heisenberg was totally committed to particles, quantum jumps, and discontinuity. For him the particle aspect was dominant in wave-particle duality. He was not prepared to make room to accommodate anything remotely linked to Schrödinger’s interpretation. To Heisenberg’s horror, Bohr wanted to ‘play with both schemes’.”</ref> And Bohr was at first opposed to Heisenberg's ].<ref>Kumar, Manjit. | |||
Quantum: Einstein, Bohr, and the great debate about the nature | |||
of reality / Manjit Kumar.—1st American ed. “He was furious and Bohr upset at the reaction of his young protégé. Living next to door to each other and with their offices on the ground floor of the institute separated only by a staircase, Bohr and Heisenberg did well to avoid one another for a few days before meeting again to discuss the uncertainty paper. Bohr hoped that, having had time to cool down, Heisenberg would see reason and rewrite it. He refused. ‘Bohr tried to explain that it was not right and I shouldn’t publish the paper’, Heisenberg said later.57 ‘I remember that it ended by my breaking out in tears because I just couldn’t stand this pressure from Bohr.’58 ”</ref> But by the ] Heisenberg and Born concluded 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.<ref name="Bolles" /> | |||
Einstein's refusal to accept the revolution as complete reflected his desire to see developed a model for the underlying causes from which these apparent random statistical methods resulted. He did not reject the idea that positions in space-time could never be completely known but did not want to allow the uncertainty principle to necessitate a seemingly random, non-deterministic mechanism by which the laws of physics operated. Einstein himself was a statistical thinker but denied that no more needed to be discovered or clarified.<ref name="Bolles" /> Einstein worked the rest of his life to discover a new theory that would make sense of quantum mechanics and return causality to science, what many now call the ].<ref>BBC TV Documentary, September 17, 2014. “But Einstein had a trick up his sleeve. He had already begun a piece of work that he believed would ultimately replace quantum mechanics. It would become later known as his theory of everything – it was his attempt to extend general relativity and unite the known forces in the universe. By completing this theory of everything Einstein hoped he would rid physics of the unpredictability at the heart of quantum mechanics and show that the world was predictable – described by beautiful, elegant mathematics. Just the way he believed God would make the universe. He would show that the way the quantum mechanics community interpreted the world was just plain wrong. It was a project that he would work on for the next 30 years, until the final day of his life.“ https://www.bbc.co.uk/sn/tvradio/programmes/horizon/einstein_symphony_prog_summary.shtml</ref> 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 that assigns properties only as result of measurements.<ref name="Baggott">{{Cite book |last=Baggott |first=J. E. |title=The quantum story: a history in 40 moments |date=2013 |publisher=Oxford Univ. Press |isbn=978-0-19-965597-7 |edition=Impression: 3 |location=Oxford}}</ref>{{rp|104}} | |||
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 than can cause a deflection from the original direction of propagation, by the law of ] 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. | |||
==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 uncertainty principle could be violated, suggesting ingenious ] 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 main source and substance for these thought experiments is solely from Bohr's account twenty years later.)<ref>{{Cite book|last1=Bacciagaluppi|first1=Guido|url=https://books.google.com/books?id=EAPX3JfQAgIC|title=Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference|last2=Valentini|first2=Antony|date=2009-10-22|publisher=Cambridge University Press|isbn=978-0-521-81421-8|pages=408|language=en}} p.272. (This book contains a translation of the entire authorized proceedings of the 1927 Solvay conference from the original transcripts.)</ref><ref>Jammer, M. (1974) The Philosophy of Quantum Mechanics, New York, John Wiley and Sons, p.120.</ref> Bohr admits: “As regards the account of the conversations I am of course aware that I am relying only on my own memory, just as I am prepared for the possibility that many features of the development of quantum theory, in which Einstein has played so large a part, may appear to himself in a different light.”<ref>Niels Bohr, Original transcript of account of debates by Bohr in 1949, University Institute for Theoretical Physics, Copenhagen Denmark, originally published in “Albert Einstein: Philosopher Scientist, P.A. Schilpp, e., p. 241, The Library of Living Philosophers, Evanston, 1949.</ref> | |||
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. | |||
=== Einstein's argument === | |||
] | |||
The first serious attack by Einstein on the "orthodox" conception took place during the Fifth Solvay International Conference on "] and ]" in 1927. Einstein pointed out how it was possible to take advantage of the (universally accepted) laws of ] and of impulse (]) in order to obtain information on the state of a particle in a process of ] which, according to the principle of indeterminacy or that of complementarity, should not be accessible. | |||
This argument is correct and convincing. Nevertheless 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 ]. | |||
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 (here aligned vertically) propagates in the direction ''z'' and encounters a screen ''S''<sub>1</sub> with a narrow (relative 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 ''S''<sub>2</sub> with two slits. The successive propagation of the wave results in the formation of the interference figure on the final screen ''F''. | |||
===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 angular 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 preparation 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 <math> \triangle t </math>. Beyond the slit, there will be a wave of limited spatial extension which continues to propagate toward the right. | |||
At the passage through the two slits of the second screen ''S''<sub>2</sub>, the wave aspects of the process become essential. In fact, it is precisely the interference between the two terms of the ] corresponding to states in which the particle is localized in one of the two slits which produces zones of constructive and destructive interference (in which the wave function is nullified). It is also important to note that any experiment designed to evidence the "]" aspects of the process at the passage of the screen ''S''<sub>2</sub> (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. | |||
A perfectly monochromatic wave (such as a note which cannot be divided into harmonics) is infinitely spatially extended. In order to have a wave which is limited in spatial extension (which is technically called a ]), several waves of different frequencies must be superimposed and distributed continuously within a certain interval of frequencies around an average value, such as <math> \nu_0; </math>. | |||
It then happens that at a certain instant, there exists a spatial region (which translates with 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 ]s of the various fields, in any specified point, are distributed casually and destructive interference is produced. The region in which the wave is non-zero is therefore spatially limited. It is easy to demonstrate that if the wave has a spatial extension equal to <math> \triangle x </math> (which means, in our example, that the shutter has remained open for a time <math> \triangle t = \triangle x/v </math> 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 <math> \triangle \nu </math> which satisfies the relation: | |||
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 ''S''<sub>1</sub>, 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 large 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), whether the particle in question has been deviated toward the bottom or top, and therefore through which slit in ''S''<sub>2</sub> 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. | |||
:<center><math> \triangle \nu \ge 1/\triangle t </math> | |||
</center> | |||
This thought experiment was begun in a simpler form during the general discussion portion of the actual proceedings during the 1927 Solvay conference. In those official proceedings, Bohr's reply is recorded as: “I feel myself in a very difficult position because I don’t understand precisely the point that Einstein is trying to make.”<ref>{{Cite book|last1=Bacciagaluppi|first1=Guido|url=https://books.google.com/books?id=EAPX3JfQAgIC|title=Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference|last2=Valentini|first2=Antony|date=2009-10-22|publisher=Cambridge University Press|isbn=978-0-521-81421-8|pages=408|language=en}}</ref> Einstein had explained, “it could happen that the same elementary process produces an action in two or several places on the screen. But the interpretation, according to which psi squared expresses the probability that this particular particle is found at a given point, assumes an entirely peculiar mechanism of action at a distance.”<ref>{{Cite book|last1=Bacciagaluppi|first1=Guido|url=https://books.google.com/books?id=EAPX3JfQAgIC|title=Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference|last2=Valentini|first2=Antony|date=2009-10-22|publisher=Cambridge University Press|isbn=978-0-521-81421-8|pages=408|language=en}} General Discussion, p. 487.</ref> It is clear from this that Einstein was referring to separability (in particular, and most importantly local causality, i.e. locality), not indeterminacy. In fact, ] wrote a letter to Bohr stating that the 1927 thought experiments of Einstein had nothing to do with the uncertainty principle, as Einstein had already accepted these “and for a long time never doubted.”<ref>Letter Ehrenfest wrote to Bohr after visiting Einstein dated 9 July 1931. Howard, D. (1990), Nicht sein kann was nicht sein darf, or the Prehistory of EPR. Pp. 98,99.</ref> | |||
Remembering that in the universal relation of Planck, frequency and energy are proportional: | |||
=== Bohr's response === | |||
:<center><math> E = h\nu \,</math></center> | |||
Bohr evidently misunderstood Einstein's argument about the quantum mechanical violation of relativistic causality (locality) and instead focused on the consistency of quantum indeterminacy. Bohr's response was to illustrate Einstein's idea more clearly using the diagram in Figure C. (Figure C shows a fixed screen S<sub>1</sub> that is bolted down. Then try to imagine one that can slide up or down along a rod instead of a fixed bolt.) 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 the interference is destructive. 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 S<sub>1</sub>, 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 ''S''<sub>2</sub> has destroyed the possibility of interference in ''F'', which depends crucially on the wave aspects. | |||
] | |||
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."{{citation needed|date=March 2014}} 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.''{{citation needed|date=March 2014}} | |||
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 ''S''<sub>1</sub>) obeys quantum laws. On the other hand, Bohr consistently held 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 ]. | |||
However, Bohr in his article refuting the ], states “there is no question of a mechanical disturbance of the system under investigation.”<ref>Bohr, Niels (1935), ‘Can quantum-Mechanical Description of Physical Reality Be Considered Complete?’, Physical Review, 48, 696–702. Reprinted in Wheeler and Zurek (1983), 145–151</ref> Heisenberg quotes Bohr as saying, “I find all such assertions as ‘observation introduces uncertainty into the phenomenon’ inaccurate and misleading.”<ref>Heisenberg, Werner (1971), Physics and Beyond: Encounters and Conversations (London: George Allen and Unwin) p. 105.</ref> Manjit Kumar's book on the Bohr–Einstein debates finds these assertions by Bohr contrary to his arguments.<ref>Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality—1st American ed., 2008. Chap.13.</ref> Others, such as the physicist ], did find Bohr's argument convincing.<ref>Rosenfeld, Léon. "Komplementaritetssynspunktet konsolideres og udbygges", in Stefan Rozental (ed.), Niels Bohr, 1964, pp. 109-131.</ref> | |||
===Uncertainty principle 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 <math> \Delta t </math>. 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 ]), several waves of different frequencies must be superimposed and distributed continuously within a certain interval of frequencies around an average value, such as <math> \nu_0 </math>. | |||
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 ]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 <math> \Delta x </math> (which means, in our example, that the shutter has remained open for a time <math> \Delta t = \Delta x/v </math> 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 <math> \Delta \nu </math> which satisfies the relation: | |||
: <math> \Delta \nu \ge \frac{1}{\Delta t}. </math> | |||
Remembering that in the ], frequency and energy are proportional: | |||
: <math> E = h\nu \,</math> | |||
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: | 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: | ||
: |
: <math> \Delta E = h\,\Delta\nu \ge \frac{h}{\Delta t}. </math> | ||
From this it follows immediately that: | From this it follows immediately that: | ||
: |
: <math> \Delta E \, \Delta t \ge h </math> | ||
which is the relation of indeterminacy between time and energy. | which is the relation of indeterminacy between time and energy. | ||
===Einstein's second |
===Einstein's second criticism=== | ||
] | |||
At the sixth Congress of Solvay in 1930, the indeterminacy relation just discussed was Einstein's target of attack. 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 (figure E) 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 temporal interval <math> \triangle t </math> 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 an adequate precision the energy that the photon has brought with it. At this point, Einstein turns to the celebrated relation between mass and energy of special relativity: <math> E=mc^2 \,</math>. 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 weight multiplied by <math> c^2 \,</math> | |||
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''', or '''Einstein's light 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 <math> \Delta t </math> 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 ] of ]: <math> E=mc^2 </math>. 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 <math> c^2 </math> | |||
will provide precise knowledge of the energy emitted. | will provide precise knowledge of the energy emitted. | ||
Moreover, the clock will indicate the precise time at which the event of the |
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 <math> \Delta E </math> as accurate as one desires. Therefore, the product <math> \Delta E \Delta t </math> can be rendered less than what is implied by the principle of indeterminacy. | ||
]'s make-believe experimental apparatus for validating the ] at the ] in ]]] | |||
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, 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 idea, like all of those advanced by Einstein, 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. ], a scientist who had participated in the Congress, described the event several years later: | |||
===Bohr's triumph=== | |||
:''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, together with the time dilation of special relativity, and a consequence of these—the ]. 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 the weight of the box, a pointer would have to be attached to the box which corresponded with the index on a scale. After the release of a photon, a mass <math>m</math> could be added to the box to restore it to its original position and this would allow us to determine the energy <math>E = mc^2</math> that was lost when the photon left. The box is immersed in a gravitational field of strength <math>g</math>, and the gravitational redshift affects the speed of the clock, yielding uncertainty <math> \Delta t </math> in the time <math>t</math> required for the pointer to return to its original position. Bohr gave the following calculation establishing the uncertainty relation <math> \Delta E \Delta t \ge h </math>. | |||
Let the uncertainty in the mass <math>m</math> be denoted by <math>\Delta m</math>. Let the error in the position of the pointer be <math>\Delta q</math>. Adding the load <math>m</math> to the box imparts a momentum <math>p</math> that we can measure with an accuracy <math>\Delta p</math>, where <math>\Delta p \Delta q</math> ≈ <math>h</math>. Clearly <math>\Delta p \le tg\Delta m</math>, and therefore <math>tg\Delta m\Delta q \ge h</math>. By the redshift formula (which follows from the principle of equivalence and the time dilation), the uncertainty in the time <math>t</math> is <math>\Delta t = c^{-2} gt\Delta q</math>, and <math>\Delta E = c^2\Delta m</math>, and so <math>\Delta E \Delta t = c^2\Delta m \Delta t \ge h</math>. We have therefore proven the claimed <math>\Delta E\Delta t \ge h</math>.<ref name=Pais>Abraham Pais, '']'', Oxford University Press, p.447-8, 1982</ref><ref>Niels Bohr in ''Albert Einstein: Philosopher-Scientist'' (P.Schilpp, Editor), p.199. Tudor, New York, 1949</ref> | |||
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 <math> \triangle t </math>. A precise evaluation of this effect leads to the conclusion that the relation <math> \triangle E \triangle t \ge h, </math>, cannot be violated. | |||
More recent analyses of the photon box debate questions Bohr's understanding of Einstein's thought experiment, referring instead to a prelude to the EPR paper, focusing on inseparability rather than indeterminism being at issue.<ref>Don Howard, "Nicht Sein Kann Was Nicht Sein Darf, or The Prehistory of EPR, 1909–1935: Einstein's Early Worries About The Quantum Mechanics of Composite Systems", ''Sixty-Two Years of Uncertainty'', edited by A. I. Miller, Plenum Press, New York, 1990.</ref><ref>Bacciagaluppi, Guido and Anthony Valentini (2006), "Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference", arXiv:quant-ph/0609184v1, 24 September. Cambridge University Press in December 2008. Quoted p.274.</ref> | |||
==Second stage== | |||
==Post-revolution: Second stage== | |||
{{Main|Hidden variable theories}} | {{Main|Hidden variable theories}} | ||
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. |
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. Einstein rejects the probabilistic interpretation of Born and insists that quantum probabilities are ] and not ] 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. | :''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.''{{citation needed|date=March 2014}} | ||
These thoughts of Einstein would set off a line of research into ], such as the ], 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 ]; this fact was demonstrated by ] with the formulation of ] in 1964.<ref name=Bell1964>{{cite journal | last1 = Bell | first1 = J. S. | author-link = John Stewart Bell | year = 1964 | title = On the Einstein Podolsky Rosen Paradox | url = https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf | journal = ] | volume = 1 | issue = 3| pages = 195–200 | doi = 10.1103/PhysicsPhysiqueFizika.1.195 | doi-access = free }}</ref> Although, the Bell inequality ruled out local hidden variable theories, Bohm's theory was not ruled out. A 2007 experiment ruled out a large class of non-Bohmian non-local hidden variable theories, though not Bohmian mechanics itself.<ref>{{cite journal |doi=10.1038/nature05677 |title=An experimental test of non-local realism |year=2007 |last1=Gröblacher |first1=Simon |last2=Paterek |first2=Tomasz |last3=Kaltenbaek |first3=Rainer |last4=Brukner |first4=Časlav |last5=Żukowski |first5=Marek |last6=Aspelmeyer |first6=Markus |last7=Zeilinger |first7=Anton |journal=Nature |volume=446 |issue=7138 |pages=871–5 |pmid=17443179|bibcode = 2007Natur.446..871G | arxiv= 0704.2529 |s2cid=4412358 }}</ref> | |||
These thoughts of Einstein’s would set off a line of research into so-called ], such as the one formulated by ], in an attempt to complete the edifice of quantum theory. The impossibility of completing the theory of quantum mechanics was definitively demonstrated by ] with the formulation of ] in 1964. | |||
==Post-revolution: Third stage== | |||
{{Main|Photon entanglement}} | |||
==Third stage== | |||
{{Supplement|Photon entanglement}} | |||
===The argument of EPR=== | ===The argument of EPR=== | ||
] | |||
In 1935 Einstein, ] and ] developed an argument, published in the magazine ''Physics Review'' with the title ''Is the quantum description of physical reality complete?'', based on an entangled state of two particles (a similar argument can be found in the ]). Before coming to this argument, it is necessary to formulate another hypothesis that comes out of Einstein's work in relativity: the idea of non-locality. ''The elements of physical reality which are objectively possessed cannot be influenced instantaneously at a distance.'' | |||
{{see also|EPR paradox}} | |||
In 1935 Einstein, ] and ] 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 ]. ''The elements of physical reality which are objectively possessed cannot be influenced instantaneously at a distance.'' | |||
] picked up the EPR argument in 1951. In his textbook ''Quantum Theory,'' he reformulated it in terms of an ], which can be summarized as follows: | |||
The argument of EPR 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 <math> \left|\Psi\right\rang </math> described |
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 <math> \left|\Psi\right\rang </math> described below: | ||
:<math> \left|\Psi,t\right\rang = |
:<math> \left|\Psi,t\right\rang = \frac1{\sqrt{2}}\left|1,V\right\rang \left|2,V\right\rang + \frac1{\sqrt{2}}\left|1,H\right\rang \left|2,H\right\rang. </math> | ||
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 |
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 | ||
: |
: <math>\left|\Psi,t+dt\right\rang = \left|1,V\right\rang \left|2,V\right\rang. </math> | ||
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, can predict with certainty that photon ''2'' will pass a test of vertical polarization. |
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 |
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. | 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 |
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=== | ||
Bohr's response to this |
Bohr's response to this 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.<ref>{{Cite journal |doi = 10.1103/PhysRev.48.696|title = Can Quantum-Mechanical Description of Physical Reality be Considered Complete?|journal = Physical Review|volume = 48|issue = 8|pages = 696–702|year = 1935|last1 = Bohr|first1 = N.|bibcode = 1935PhRv...48..696B|doi-access = free}}</ref> The crucial point of Bohr's answer is distilled in a passage which he later had republished in ]'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''. | ||
Bohr's presentation of his argument was hard to follow for many of the scientists (although his views were generally accepted). Rosenfeld, who had worked closely with Bohr for many years, later explains Bohr's argument in a way that is perhaps more accessible:<ref>Rosenfeld, Léon. "Komplementaritetssynspunktet konsolideres og udbygges", in Stefan Rozental (ed.), Niels Bohr, 1964, p. 125.</ref> | |||
As John Bell 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 non-locality, the argument of EPR obviously collapses immediately. But the fact that non-locality is intrinsic to the quantum universe was demonstrated thirty years later by Bell, so this seems extremely unlikely. | |||
:''In the case of the two particles, it is true that the measurement carried out on the first particle does not cause any direct physical disturbance of the second; but the measurement decisively affects the nature of verifiable predictions we will be able to make about this second particle. (...) s long as we do not carry out any measurement (...) we have no control at all over this correlation . If we really want the system to be subject to study and communication, we must carry out some measurement. If we now observe the position of the first particle, the correlation between the positions of the particles can be used to give us information about where the second particle is, but we have no way of making use of the correlation between the pulses of the particles (...). If we observe the momentum of the first particle, it is just the opposite. We retain control over the momentum correlation, but lose it over the position correlation. The two different measurements define two complementary phenomena that can never be reconciled into a single description of the given two-particle system''. | |||
In any case, very few among the illustrious protagonists of the debate on the foundations of quantum theory were able to grasp the true sense of the profound analysis of Einstein. Pauli dismissed it with a few words and Born completely misinterpreted it. But Einstein's defeat (and it really was a defeat) represents one of the highest points of scientific research in the first half of the twentieth century because it called attention to an element of reality, ], which is absolutely central to our modern understanding of the physical world. | |||
===Confirmatory experiments=== | |||
==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 macroscopic 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 a growing number of critics | |||
Years after the exposition of Einstein via his EPR experiment, many physicists started performing experiments to show that Einstein's view of a spooky action in a distance is indeed consistent with the laws of physics. The first experiment to definitively prove that this was the case was in 1949, when physicists ] and her colleague Irving Shaknov showcased this theory in real time using photons.<ref>{{Cite journal|last=Nordén|first=Bengt|title=Quantum entanglement: facts and fiction – how wrong was Einstein after all?|journal=Quarterly Reviews of Biophysics |url=https://www.cambridge.org/core/services/aop-cambridge-core/content/view/0F80EA03E4D8CAB4F8DD5C7AEB9F07B3/S0033583516000111a.pdf/quantum_entanglement_facts_and_fiction_how_wrong_was_einstein_after_all.pdf|date=2016-01-28|volume=49 |pages=e17 |doi=10.1017/S0033583516000111 |pmid=27659445 |s2cid=13919757 }}</ref> Their work was published in the new year of the succeeding decade.<ref>{{cite journal | |||
who, like Einstein, believe that it has failed to provide a sensible and acceptable representation of reality (see ]). | |||
|last1=Wu |first1=C. S. | |||
|last2=Shaknov |first2=I. | |||
|year=1950 | |||
|title=The Angular Correlation of Scattered Annihilation Radiation | |||
|journal=] | |||
|volume=77 |issue= 1|pages=136 | |||
|bibcode=1950PhRv...77..136W | |||
|doi=10.1103/PhysRev.77.136 | |||
}}</ref> | |||
Later in 1975, ] proposed in an article, an experiment meticulous enough to be irrefutable: ''Proposed experiment to test the non-separability of quantum mechanics''.<ref>{{cite book |last1=Nikseresht |first1=Iraj |title=La physique quantique : origines, interprétations et critiques |date=2005 |publisher=Ellipses |location=Paris |isbn=978-2-7298-2366-5 |page=235 |language=French}}</ref><ref>{{cite journal |last1=Aspect |first1=Alain |title=Proposed experiment to test the nonseparability of quantum mechanics |journal=Physical Review D |date=15 October 1976 |volume=14 |issue=8 |pages=1944–1951 |doi=10.1103/PhysRevD.14.1944|bibcode=1976PhRvD..14.1944A |doi-access=free }}</ref> This led Aspect, together with his assistant Gérard Roger, and ] and {{ill|Philippe Grangier|fr}} (two young physics students at the time) to set up ] between 1980 and 1982 that further established quantum entanglement. Finally in 1998, the Geneva experiment tested the correlation between two detectors set 30 kilometres apart, virtually across the whole city, using the Swiss optical fibre telecommunication network. The distance gave the necessary time to commute the angles of the polarizers. It was therefore possible to have a completely random electrical shunting. Furthermore, the two distant polarizers were entirely independent. The measurements were recorded on each side, and compared after each experiment by dating each measurement using an atomic clock. The experiment once again verified entanglement under the strictest and most ideal conditions possible. If Aspect's experiment implied that a hypothetical coordination signal travel twice as fast as ''c'', Geneva's reached 10 million times ''c''.<ref>{{cite journal |last1=Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, ] |s2cid=29855302 |title=Violation of Bell's inequality under strict Einstein locality conditions |journal=Phys. Rev. Lett. |date=1998 |volume=81 |issue=23 |pages=5039–5043 |doi=10.1103/PhysRevLett.81.5039 |arxiv=quant-ph/9810080 |bibcode=1998PhRvL..81.5039W }}</ref><ref>{{Cite web|last=Berardelli|first=Phil|title=Quantum Physics Gets "Spooky"|url=https://www.science.org/content/article/quantum-physics-gets-spooky|date=August 2008|access-date=2020-09-08}}</ref> | |||
== See also == | |||
==Post-revolution: Fourth stage== | |||
* ] | |||
In his last writing on the topic{{Citation needed|date=April 2012}}, 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. Since the early days of quantum theory the assumption of locality and Lorentz invariance guided his thoughts and led to his determination that if we demand strict locality then hidden variables are naturally implied apropos EPR. Bell, starting from this EPR logic (which is widely misunderstood or forgotten) showed that local hidden variables imply a conflict with experiment. Ultimately what was at stake for Einstein was the assumption that physical reality be universally local. Although the ] in the field agree that Einstein was wrong, the current understanding is still not complete (see ]).<ref>{{cite book|last1=Bishop|first1=Robert C.|editor1-first=Robert|editor1-last=Kane|title=The Oxford Handbook of Free Will|access-date=2013-02-04|edition=Second|year=2011|publisher=Oxford University Press|location=Oxford, New York|isbn=978-0-19-539969-1|page=90|chapter=Chaos, Indeterminism, and Free Will|chapter-url=https://books.google.com/books?id=kzcFDsWg0GEC&pg=PA90 |quote=The key question is whether to understand the nature of this probability as epistemic or ontic. Along epistemic lines, one possibility is that there is some additional factor (i.e., a hidden mechanism) such that once we discover and understand this factor, we would be able to predict the observed behavior of the quantum stoplight with certainty (physicists call this approach a "hidden variable theory"; see, e.g., Bell 1987, 1-13, 29-39; Bohm 1952a, 1952b; Bohm and Hiley 1993; Bub 1997, 40-114, Holland 1993; see also the preceding essay in this volume by Hodgson). Or perhaps there is an interaction with the broader environment (e.g., neighboring buildings, trees) that we have not taken into account in our observations that explains how these probabilities arise (physicists call this approach decoherence or consistent histories<sup>15</sup>). Under either of these approaches, we would interpret the observed indeterminism in the behavior of stoplights as an expression of our ignorance about the actual workings. Under an ignorance interpretation, indeterminism would not be a fundamental feature of quantum stoplights, but merely epistemic in nature due to our lack of knowledge about the system. Quantum stoplights would turn to be deterministic after all.}}</ref><ref>{{cite book|last1=Baggott|first1=Jim E.|title=Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory|access-date=2013-02-04|year=2004|publisher=Oxford University Press|location=Oxford, New York|isbn=0-19-852536-2|page=203|chapter=Complementarity and Entanglement|chapter-url=https://books.google.com/books?id=uVdjwsqrgz8C&pg=PA203 |quote=So, was Einstein wrong? In the sense that the EPR paper argued in favour of an objective reality for each quantum particle in an entangled pair independent of the other and of the measuring device, the answer must be yes. But if we take a wider view and ask instead if Einstein was wrong to hold to the realist's belief that the physics of the universe should be objective and deterministic, we must acknowledge that we cannot answer such a question. It is in the nature of theoretical science that there can be no such thing as certainty. A theory is only 'true' for as long as the majority of the scientific community maintain a consensus view that the theory is the one best able to explain the observations. And the story of quantum theory is not over yet.}}</ref> | |||
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== References == | |||
{{Reflist|colwidth=30em}} | |||
== Further reading == | |||
* Boniolo, G., (1997) ''Filosofia della Fisica'', Mondadori, Milan. | |||
* Bolles, Edmund Blair (2004) ''Einstein Defiant'', Joseph Henry Press, Washington, D.C. | |||
* Born, M. (1973) ''The Born Einstein Letters'', Walker and Company, New York, 1971. | |||
* Ghirardi, Giancarlo, (1997) ''Un'Occhiata alle Carte di Dio'', Il Saggiatore, Milan. | |||
* Schilpp, P.A., (1958) ''Albert Einstein: Philosopher-Scientist'', Northwestern University and Southern Illinois University, Open Court, 1951. | |||
{{Einstein}} | |||
==References== | |||
{{History of physics}} | |||
*Boniolo, G., (1997) ''Filosofia della Fisica'', Mondadori, Milan. | |||
*Born, M. (1973) ''The Born Einstein Letters'', Walker and Company, New York, 1971. | |||
*Ghirardi, Giancarlo, (1997) ''Un Occhiata alle Carte di Dio'', Il Saggiatore, Milan. | |||
*Pais, A., (1986) ''Subtle is the Lord... The Science and Life of Albert Einstein'', Oxford University Press, Oxford, 1982. | |||
*Shilpp, P.A., (1958) ''Albert Einstein: Philosopher-Scientist'', Northwestern University and Southern Illinois University, Open Court, 1951. | |||
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Latest revision as of 03:08, 11 December 2024
Series of public disputes between physicists Niels Bohr and Albert EinsteinThe Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr. Their debates are remembered because of their importance to the philosophy of science, insofar as the disagreements—and the outcome of Bohr's version of quantum mechanics becoming the prevalent view—form the root of the modern understanding of physics. Most of Bohr's version of the events held in the Solvay Conference in 1927 and other places was first written by Bohr decades later in an article titled, "Discussions with Einstein on Epistemological Problems in Atomic Physics". Based on the article, the philosophical issue of the debate was whether Bohr's Copenhagen interpretation of quantum mechanics, which centered on his belief of complementarity, was valid in explaining nature. Despite their differences of opinion and the succeeding discoveries that helped solidify quantum mechanics, Bohr and Einstein maintained a mutual admiration that was to last the rest of their lives.
Although Bohr and Einstein disagreed, they were great friends all their lives and enjoyed using each other as a foil.
Pre-revolutionary debates
Einstein was the first physicist to say that Max Planck's discovery of the energy quanta would require a rewriting of the laws of physics. To support his point, in 1905 Einstein proposed that light sometimes acts as a particle which he called a light quantum (see photon and wave–particle duality). Bohr was one of the most vocal opponents of the photon idea and did not openly embrace it until 1925. The photon appealed to Einstein because he saw it as a physical reality (although a confusing one) behind the numbers presented by Planck mathematically in 1900. Bohr disliked it because it made the choice of mathematical solution arbitrary. Bohr did not like a scientist having to choose between equations. This disagreement was perhaps the first real Bohr-Einstein debate. Einstein had proposed the photon in 1905, and Arthur Compton provided experiment in 1922 with his Compton effect, but Bohr refused to believe the photon existed even then. Bohr continued to dispute the existence of the quantum of light (photon) and along with Hans Kramers and John C. Slater elaborated the BKS theory in 1924. However, after the 1925 Bothe–Geiger coincidence experiment, BKS was proved to be wrong and Einstein's hypothesis was proven to be correct.
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. Werner Heisenberg's Umdeutung paper in 1925 reinterpreted old quantum theory in terms of matrix-like operators, removing the Newtonian elements of space and time from any underlying reality. In parallel, Erwin Schrödinger redeveloped quantum theory in terms of a wave mechanics formulation, leading to the Schrödinger equation. However, when Schrödinger sent a preprint of his new equation to Einstein, Einstein wrote back hailing his equation as a decisive advance of “true genius.” Then in 1926 when Max Born, collaborating with Heisenberg, proposed that mechanics were to be understood as a probability without any causal explanation.
Both Einstein and Schrödinger rejected Born's interpretation with its renunciation of causality which had been a key feature of science previous to old quantum theory and was still a feature of general relativity. In a 1926 letter to Max Born, Einstein wrote:
quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the “old one”. I, at any rate, am convinced that He is not playing at dice.
At first, even Heisenberg had heated disputes with Bohr that his matrix mechanics was not compatible with the Schrödinger's wave mechanics. And Bohr was at first opposed to Heisenberg's uncertainty principle. But by the Fifth Solvay Conference held in October 1927 Heisenberg and Born concluded 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 desire to see developed a model for the underlying causes from which these apparent random statistical methods resulted. He did not reject the idea that positions in space-time could never be completely known but did not want to allow the uncertainty principle to necessitate a seemingly random, non-deterministic mechanism by which the laws of physics operated. Einstein himself was a statistical thinker but denied that no more needed to be discovered or clarified. Einstein worked the rest of his life to discover a new theory that would make sense of quantum mechanics and return causality to science, what many now call the theory of everything. 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 that assigns properties only as result of measurements.
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 uncertainty principle could be violated, suggesting ingenious thought experiments 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 main source and substance for these thought experiments is solely from Bohr's account twenty years later.) Bohr admits: “As regards the account of the conversations I am of course aware that I am relying only on my own memory, just as I am prepared for the possibility that many features of the development of quantum theory, in which Einstein has played so large a part, may appear to himself in a different light.”
Einstein's argument
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 and of impulse (momentum) 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, 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 (here aligned vertically) propagates in the direction z and encounters a screen S1 with a narrow (relative 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 with 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 corresponding to states in which the particle is localized in one of the two slits which produces zones of constructive and 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 large 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), whether the particle in question has been deviated toward the bottom or top, and therefore through 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.
This thought experiment was begun in a simpler form during the general discussion portion of the actual proceedings during the 1927 Solvay conference. In those official proceedings, Bohr's reply is recorded as: “I feel myself in a very difficult position because I don’t understand precisely the point that Einstein is trying to make.” Einstein had explained, “it could happen that the same elementary process produces an action in two or several places on the screen. But the interpretation, according to which psi squared expresses the probability that this particular particle is found at a given point, assumes an entirely peculiar mechanism of action at a distance.” It is clear from this that Einstein was referring to separability (in particular, and most importantly local causality, i.e. locality), not indeterminacy. In fact, Paul Ehrenfest wrote a letter to Bohr stating that the 1927 thought experiments of Einstein had nothing to do with the uncertainty principle, as Einstein had already accepted these “and for a long time never doubted.”
Bohr's response
Bohr evidently misunderstood Einstein's argument about the quantum mechanical violation of relativistic causality (locality) and instead focused on the consistency of quantum indeterminacy. Bohr's response was to illustrate Einstein's idea more clearly using the diagram in Figure C. (Figure C shows a fixed screen S1 that is bolted down. Then try to imagine one that can slide up or down along a rod instead of a fixed bolt.) 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 the interference is destructive. 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.
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 held 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.
However, Bohr in his article refuting the EPR paper, states “there is no question of a mechanical disturbance of the system under investigation.” Heisenberg quotes Bohr as saying, “I find all such assertions as ‘observation introduces uncertainty into the phenomenon’ inaccurate and misleading.” Manjit Kumar's book on the Bohr–Einstein debates finds these assertions by Bohr contrary to his arguments. Others, such as the physicist Leon Rosenfeld, did find Bohr's argument convincing.
Uncertainty principle 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), 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 phases 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 Planck relation, 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, or Einstein's light 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 mass–energy equivalence 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, 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.
Bohr's triumph
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, together with the time dilation of special relativity, and a consequence of these—the gravitational redshift. 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 the weight of the box, a pointer would have to be attached to the box which corresponded with the index on a scale. After the release of a photon, a mass could be added to the box to restore it to its original position and this would allow us to determine the energy that was lost when the photon left. The box is immersed in a gravitational field of strength , and the gravitational redshift affects the speed of the clock, yielding uncertainty in the time required for the pointer to return to its original position. Bohr gave the following calculation establishing the uncertainty relation .
Let the uncertainty in the mass be denoted by . Let the error in the position of the pointer be . Adding the load to the box imparts a momentum that we can measure with an accuracy , where ≈ . Clearly , and therefore . By the redshift formula (which follows from the principle of equivalence and the time dilation), the uncertainty in the time is , and , and so . We have therefore proven the claimed .
More recent analyses of the photon box debate questions Bohr's understanding of Einstein's thought experiment, referring instead to a prelude to the EPR paper, focusing on inseparability rather than indeterminism being at issue.
Post-revolution: Second stage
Main article: Hidden variable theoriesThe 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. Einstein rejects the probabilistic interpretation of Born and insists that quantum probabilities are epistemic and not ontological 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 would set off a line of research into hidden variable theories, such as the Bohm interpretation, 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; this fact was demonstrated by John Stewart Bell with the formulation of Bell's inequality in 1964. Although, the Bell inequality ruled out local hidden variable theories, Bohm's theory was not ruled out. A 2007 experiment ruled out a large class of non-Bohmian non-local hidden variable theories, though not Bohmian mechanics itself.
Post-revolution: Third stage
Main article: Photon entanglementThe argument of EPR
See also: EPR paradoxIn 1935 Einstein, Boris Podolsky and Nathan Rosen 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. The elements of physical reality which are objectively possessed cannot be influenced instantaneously at a distance.
David Bohm picked up the EPR argument in 1951. In his textbook Quantum Theory, he reformulated it 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 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'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.
Bohr's presentation of his argument was hard to follow for many of the scientists (although his views were generally accepted). Rosenfeld, who had worked closely with Bohr for many years, later explains Bohr's argument in a way that is perhaps more accessible:
- In the case of the two particles, it is true that the measurement carried out on the first particle does not cause any direct physical disturbance of the second; but the measurement decisively affects the nature of verifiable predictions we will be able to make about this second particle. (...) s long as we do not carry out any measurement (...) we have no control at all over this correlation . If we really want the system to be subject to study and communication, we must carry out some measurement. If we now observe the position of the first particle, the correlation between the positions of the particles can be used to give us information about where the second particle is, but we have no way of making use of the correlation between the pulses of the particles (...). If we observe the momentum of the first particle, it is just the opposite. We retain control over the momentum correlation, but lose it over the position correlation. The two different measurements define two complementary phenomena that can never be reconciled into a single description of the given two-particle system.
Confirmatory experiments
Years after the exposition of Einstein via his EPR experiment, many physicists started performing experiments to show that Einstein's view of a spooky action in a distance is indeed consistent with the laws of physics. The first experiment to definitively prove that this was the case was in 1949, when physicists Chien-Shiung Wu and her colleague Irving Shaknov showcased this theory in real time using photons. Their work was published in the new year of the succeeding decade.
Later in 1975, Alain Aspect proposed in an article, an experiment meticulous enough to be irrefutable: Proposed experiment to test the non-separability of quantum mechanics. This led Aspect, together with his assistant Gérard Roger, and Jean Dalibard and Philippe Grangier [fr] (two young physics students at the time) to set up several increasingly complex experiments between 1980 and 1982 that further established quantum entanglement. Finally in 1998, the Geneva experiment tested the correlation between two detectors set 30 kilometres apart, virtually across the whole city, using the Swiss optical fibre telecommunication network. The distance gave the necessary time to commute the angles of the polarizers. It was therefore possible to have a completely random electrical shunting. Furthermore, the two distant polarizers were entirely independent. The measurements were recorded on each side, and compared after each experiment by dating each measurement using an atomic clock. The experiment once again verified entanglement under the strictest and most ideal conditions possible. If Aspect's experiment implied that a hypothetical coordination signal travel twice as fast as c, Geneva's reached 10 million times c.
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. Since the early days of quantum theory the assumption of locality and Lorentz invariance guided his thoughts and led to his determination that if we demand strict locality then hidden variables are naturally implied apropos EPR. Bell, starting from this EPR logic (which is widely misunderstood or forgotten) showed that local hidden variables imply a conflict with experiment. Ultimately what was at stake for Einstein was the assumption that physical reality be universally local. Although the majority of experts in the field agree that Einstein was wrong, the current understanding is still not complete (see Interpretation of quantum mechanics).
See also
- Bell test experiments
- Bell's theorem
- Complementarity
- Copenhagen interpretation
- Double-slit experiment
- Einstein's thought experiments
- Invariant set postulate
- Quantum eraser
- Schrödinger's cat
- Uncertainty principle
- Wheeler's delayed choice experiment
- Superdeterminism
References
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- Louisa Gilder, The Age of Entanglement, chap. 5, 2008. “ “Not often in my life has a person, by his mere presence, given me such joy as you did,” wrote Einstein in 1920, in that first letter to Bohr. “I now understand why Ehrenfest loves you so. I am now studying your great papers and in doing so—especially when I get stuck somewhere—I have the pleasure of seeing your youthful face before me, smiling and explaining. I have learned much from you, especially also about your attitude regarding scientific matters.” (“What is so marvellously attractive about Bohr as a scientific thinker,” Einstein wrote not long afterward, “is his rare blend of boldness and caution; seldom has anyone possessed such an intuitive grasp of hidden things combined with such a strong critical sense.”) Somewhat awed, Bohr wrote in reply, “To me it was one of the greatest experiences ever to meet you and talk with you…. You cannot know how great a stimulus it was for me to have the long-hoped-for opportunity to hear of your views on the questions that have occupied me. I shall never forget our talks on the way from Dahlem to your home.”
- ^ Abraham Pais, Subtle is the Lord: The Science and the Life of Albert Einstein, Oxford University Press, p.447-8, 1982
- ^ Bolles
- Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.5.
- Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American Edition, “Schrödinger received a letter from Einstein, who told him ‘the idea of your work springs from true genius’.21 ‘Your approval and Planck’s mean more to me than that of half the world’, Schrödinger wrote back.22 Einstein was convinced that Schrödinger had made a decisive advance, ‘just as I am convinced that the Heisenberg-Born method is misleading’.“
- Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed.
- Einstein, Albert (1969). Albert Einstein, Hedwig und Max Born: Briefwechsel 1916–1955 (in German). Munich: Nymphenburger Verlagshandlung. ISBN 978-3-88682-005-4.
- Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed. “Heisenberg was totally committed to particles, quantum jumps, and discontinuity. For him the particle aspect was dominant in wave-particle duality. He was not prepared to make room to accommodate anything remotely linked to Schrödinger’s interpretation. To Heisenberg’s horror, Bohr wanted to ‘play with both schemes’.”
- Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed. “He was furious and Bohr upset at the reaction of his young protégé. Living next to door to each other and with their offices on the ground floor of the institute separated only by a staircase, Bohr and Heisenberg did well to avoid one another for a few days before meeting again to discuss the uncertainty paper. Bohr hoped that, having had time to cool down, Heisenberg would see reason and rewrite it. He refused. ‘Bohr tried to explain that it was not right and I shouldn’t publish the paper’, Heisenberg said later.57 ‘I remember that it ended by my breaking out in tears because I just couldn’t stand this pressure from Bohr.’58 ”
- BBC TV Documentary, September 17, 2014. “But Einstein had a trick up his sleeve. He had already begun a piece of work that he believed would ultimately replace quantum mechanics. It would become later known as his theory of everything – it was his attempt to extend general relativity and unite the known forces in the universe. By completing this theory of everything Einstein hoped he would rid physics of the unpredictability at the heart of quantum mechanics and show that the world was predictable – described by beautiful, elegant mathematics. Just the way he believed God would make the universe. He would show that the way the quantum mechanics community interpreted the world was just plain wrong. It was a project that he would work on for the next 30 years, until the final day of his life.“ https://www.bbc.co.uk/sn/tvradio/programmes/horizon/einstein_symphony_prog_summary.shtml
- Baggott, J. E. (2013). The quantum story: a history in 40 moments (Impression: 3 ed.). Oxford: Oxford Univ. Press. ISBN 978-0-19-965597-7.
- Bacciagaluppi, Guido; Valentini, Antony (2009-10-22). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press. p. 408. ISBN 978-0-521-81421-8. p.272. (This book contains a translation of the entire authorized proceedings of the 1927 Solvay conference from the original transcripts.)
- Jammer, M. (1974) The Philosophy of Quantum Mechanics, New York, John Wiley and Sons, p.120.
- Niels Bohr, Original transcript of account of debates by Bohr in 1949, University Institute for Theoretical Physics, Copenhagen Denmark, originally published in “Albert Einstein: Philosopher Scientist, P.A. Schilpp, e., p. 241, The Library of Living Philosophers, Evanston, 1949.
- Bacciagaluppi, Guido; Valentini, Antony (2009-10-22). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press. p. 408. ISBN 978-0-521-81421-8.
- Bacciagaluppi, Guido; Valentini, Antony (2009-10-22). Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference. Cambridge University Press. p. 408. ISBN 978-0-521-81421-8. General Discussion, p. 487.
- Letter Ehrenfest wrote to Bohr after visiting Einstein dated 9 July 1931. Howard, D. (1990), Nicht sein kann was nicht sein darf, or the Prehistory of EPR. Pp. 98,99.
- Bohr, Niels (1935), ‘Can quantum-Mechanical Description of Physical Reality Be Considered Complete?’, Physical Review, 48, 696–702. Reprinted in Wheeler and Zurek (1983), 145–151
- Heisenberg, Werner (1971), Physics and Beyond: Encounters and Conversations (London: George Allen and Unwin) p. 105.
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- Niels Bohr in Albert Einstein: Philosopher-Scientist (P.Schilpp, Editor), p.199. Tudor, New York, 1949
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: CS1 maint: multiple names: authors list (link) - Berardelli, Phil (August 2008). "Quantum Physics Gets "Spooky"". Retrieved 2020-09-08.
- Bishop, Robert C. (2011). "Chaos, Indeterminism, and Free Will". In Kane, Robert (ed.). The Oxford Handbook of Free Will (Second ed.). Oxford, New York: Oxford University Press. p. 90. ISBN 978-0-19-539969-1. Retrieved 2013-02-04.
The key question is whether to understand the nature of this probability as epistemic or ontic. Along epistemic lines, one possibility is that there is some additional factor (i.e., a hidden mechanism) such that once we discover and understand this factor, we would be able to predict the observed behavior of the quantum stoplight with certainty (physicists call this approach a "hidden variable theory"; see, e.g., Bell 1987, 1-13, 29-39; Bohm 1952a, 1952b; Bohm and Hiley 1993; Bub 1997, 40-114, Holland 1993; see also the preceding essay in this volume by Hodgson). Or perhaps there is an interaction with the broader environment (e.g., neighboring buildings, trees) that we have not taken into account in our observations that explains how these probabilities arise (physicists call this approach decoherence or consistent histories). Under either of these approaches, we would interpret the observed indeterminism in the behavior of stoplights as an expression of our ignorance about the actual workings. Under an ignorance interpretation, indeterminism would not be a fundamental feature of quantum stoplights, but merely epistemic in nature due to our lack of knowledge about the system. Quantum stoplights would turn to be deterministic after all.
- Baggott, Jim E. (2004). "Complementarity and Entanglement". Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory. Oxford, New York: Oxford University Press. p. 203. ISBN 0-19-852536-2. Retrieved 2013-02-04.
So, was Einstein wrong? In the sense that the EPR paper argued in favour of an objective reality for each quantum particle in an entangled pair independent of the other and of the measuring device, the answer must be yes. But if we take a wider view and ask instead if Einstein was wrong to hold to the realist's belief that the physics of the universe should be objective and deterministic, we must acknowledge that we cannot answer such a question. It is in the nature of theoretical science that there can be no such thing as certainty. A theory is only 'true' for as long as the majority of the scientific community maintain a consensus view that the theory is the one best able to explain the observations. And the story of quantum theory is not over yet.
Further reading
- Boniolo, G., (1997) Filosofia della Fisica, Mondadori, Milan.
- Bolles, Edmund Blair (2004) Einstein Defiant, Joseph Henry Press, Washington, D.C.
- Born, M. (1973) The Born Einstein Letters, Walker and Company, New York, 1971.
- Ghirardi, Giancarlo, (1997) Un'Occhiata alle Carte di Dio, Il Saggiatore, Milan.
- Schilpp, P.A., (1958) Albert Einstein: Philosopher-Scientist, Northwestern University and Southern Illinois University, Open Court, 1951.
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