The 2022 Physics Nobel Prize - Spooky Action at a Distance prevails over classical physics and Einstein's objections.

Bell's inequality violated in favour of quantum mechanics. Alain Aspect, John Clauser and Anton Zeilinger awarded

Introduction

The Nobel Prize of 2022 in Physics honours initiatives to remove quantum strangeness from philosophical debates and put it on experimental exhibit for all to observe. Alain Aspect (France), John Clauser (USA), and Anton Zeilinger (Austria), all shown a knowledge of entanglement, which is a quantum link between two particles that may exist across great distances, and they all received the Nobel prize. Clauser and Aspect conducted some of first "Bell tests" with entangled photons, confirming quantum mechanics predictions and disproving several competing theories which was based on classical physics. Zeilinger demonstrated entanglement control strategies that can be employed in quantum computing, quantum cryptography, and other quantum information technologies using some of those Bell-test procedures. Their research findings cleared the path for future quantum information-based technology.

Quantum mechanics has already had incredible success since its conception in predicting the results of tests. However, the theory assumes that aspects of a particle's properties are intrinsically unpredictable, which alarmed many physicists, including Albert Einstein. In 1935, he and his colleagues articulated a paradox in which they stated their concern [1].

Einstein- Podolsky-Rosen (EPR)

The Gedanken-Experiment of Einstein- Podolsky-Rosen (EPR) was particularly overlooked in terms of its significance in 1935. For approximately 30 years, it was completely ignored and thought to be useless [2].  "The EPR article was the single slip Einstein made!" Abraham Pais had just released the blockbuster "Subtle is the Lord: The Science and the Life of Albert Einstein" [3]. How terribly inaccurate some predictions and judgements in the world of physics can be! When John Bell had time to reflect about the Einstein-Podolsky-Rosen example in 1964 while on leave in the US, he prepared the paper "On the Einstein Podolsky-Rosen Paradox" [4], which included Bell's inequality.

 In general, Bell inequality is discrepancy between the expectation values of two parties' joint measurements, Alice and Bob in this instance. This discrepancy must be fulfilled by all local realistic theories, but quantum physics deviates from this requirement. The Bell's Theorem is stated as "local realistic theories are incompatible with quantum physics" and is based on Bell inequalities. Bell's work did not spark any curiosity for an exceptionally long time.

Bell's work demonstrated how to resolve the quantum versus classical viewpoint conflict, but his suggested experiment made assumptions about detector capabilities that were not realistic. In 1969, Clauser and his colleagues at Columbia University proposed a redesigned version utilising photons and polarizers [5]. That experiment was successfully carried out three years later by Clauser and Stuart Freedman, both of whom were affiliated with the University of California, Berkeley [6].

Bell's inequality tested

 In the Freedman-Clauser experiment, excited calcium atoms' entangled photons were utilised. Two different polarizers that were placed at specific orientations in relation to one another received the photons. Both photons passed through these polarizers at a rate that was consistent with predictions made by quantum physics.

Theoretically, Freedman and Clauser demonstrated that when Alice and Bob's polarizers are offset from one another by 22.5° or 67.5°, quantum mechanics predictions vary sharply from hidden variable predictions. After gathering 200 hours of data, the researchers discovered that the coincidence rates broke a revised version of Bell's inequality, representing validity of quantum mechanics (QM).

John Clauser

John Clauser did postdoc from Columbia University, was the first to show interest in the topic in the late 1960s. He was fascinated and motivated to provide support when he read Bell's inequality work and discovered that it had a boundary for all unseen variable theories, which he accepted as true. He decided to do the experiment as a result. The importance of these kinds of experiments, nevertheless, was not understood at that time. Richard Feynman abruptly threw Clauser out of his office when they met at Caltech to debate an EPR experimental configuration to test quantum mechanical predictions, saying[7]: "Well, when you have found an error in quantum-experimental theory's predictions, come back then, and we can discuss your problem with it." Fortunately, Clauser didn't waver and was committed to seeing the trial through. He sent letters to John Bell, Louis de Broglie, and David Bohm, all of whom were regarded as realists, asking for counsel or moral support. Let me quote Bell's response: [7]“In view of the general success of quantum mechanics it is very hard for me to doubt the outcome of such experiments. However, I would prefer these experiments, to have been done. Moreover, there is always the slim chance of an unexpected result, which would shake the world!”

Clauser, a member of the 1960s' rebellious Hippie movement [8], undoubtedly "wanted to shake the world", and in 1969 he submitted an abstract to the American Physical Society's Spring Meeting recommending an experiment. After that, Abner Shimony invited him and revealed that he and Michael Horne, one of his students, had very similar thoughts. As a result, they came together and wrote the renowned CHSH paper [8] with Richard Holt, a PhD candidate doing research with Francis Pipkin from Harvard. In this publication, they presented an inequality that was well suited to experiments. Along with Stuart Freedman, a doctoral student at Berkeley who earned his PhD degree for this experiment, Clauser eventually carried out experiment in 1972.

A pair of photons released in atomic radiative force will be appropriate for  test of Bell inequality, as stated in the CHSH study[8]. Clauser and Freedman decided to use excited calcium atoms that were being pushed by lasers since they were emitting the needed photon pairs. At the time, the signals were so faint that a measurement would only endure for roughly 200 hours. A highly useful inequality that Freedman derived was used for comparison with theory. The experiment's conclusion is well recognized as they gained a pure breach of the Bell inequality that was closely related to quantum mechanics. The consequence of subsequent trials supported this conclusion. At the time, conducting this experiment was a truly heroic feat because all the necessary tools—including the laser—were homemade. Clauser was also only able to work on the experiment because Charles H. Townes, who was interested in Clauser's theories, gave him a job that would split his time between Clauser's project and Townes' radio astronomy. Clauser was regrettably unable to pursue a career in academia as a result of this experiment. But the fact that he has now received the Nobel Prize can be considered as atonement.

Alain Aspect

Young French physicist Alain Aspect was so inspired by Bell's inequality article that he chose to make it the focus of his thesis work. He went to see John Bell at CERN to talk about his idea. Alain later informed that John's initial inquiry to him was, "Do you have a permanent position?" Bell was terrified that Aspect's career would be destroyed. The conversation couldn't start unless Aspect responded in the positive to that question. Aspect wanted the setup to have variable analysers. Early in the 1980s, Aspect and his colleagues conducted a large number of tests [9], with the end result being that each experiment dramatically violated the Bell inequalities that were being employed. Aspect's third experiment came near to addressing the locality gap, but it was too difficult to conclude that it had due to the quasi-randomness of the changing polarizers. Another loophole, known as the "detector-efficiency loophole" or the "fair-sampling loophole," resulted from statistic that, because we were unable to distinguish all photon pairs, a sample used in the statistical calculations to make comparisons the results of the experiments with Bell's inequalities could theoretically be biased. In fact, it was able to replicate experimental findings deviating from local realist presumptions using detectors from the early Bell's theorem experiments. The freedom of choice is the name given to the third loophole. Now that the Nobel Prize has been given out, this has been acknowledged. 

Anton Zeilinger

The physics world first became aware of the significance and effects of such Bell-type experiments in the 1990s, following Aspect's investigations. Bell inequalities and quantum entanglement, at the centre of quantum theory, communication, and computation, are attracting more and more attention. Finally, there occurred a shift in public opinion on underlying principles of quantum mechanics. At same time, technological advancements in electronics and lasers were also being made. The development of recent source for producing two entangled photons—specifically, impulsive parametric down transfer—was crucial. Here, a laser was used to pump a nonlinear crystal, and pump photon split into two photons which travelled along two distinct cones. The photons were horizontally polarised on one cone and vertically polarised on the other. They became knotted in the area of overlap. Anton Zeilinger and his team conducted their renowned tests using such an EPR source. Not only in quantum physics and quantum information, but also in teaching and scientific management, his efforts are significant and influential in a wide range of fields. Zeilinger, also known as "Mr Beam," helped make science more accessible to the general public. Zeilinger is the epitome of a Renaissance Academic because of all of this as well as his love of philosophy and art.

Curiosity has always been Zeilinger's primary motivation for studying physics. His interest has always been centred in curiosity, even in experiments which have made applications conceivable. Particularly noteworthy is the bravery he displayed when, around 1990, he changed his field of expertise from neutron to photon physics and accepted a position as a professor at University of Innsbruck. There were obviously significant risks involved in this. But because of his magnetic personality and uncanny sense of physics, Zeilinger attracted a group of exceptionally gifted students around himself, with whom he conducted fascinating experiments. Zeilinger moved from Innsbruck to the University of Vienna in 1999 with his entire team, where he was appointed Professor of Experimental Physics. His breakthrough was the well-known experiment "Wave-particle duality of C60 molecules," which used large molecules like fullerenes to illustrate the effects of quantum mechanical interference [10]. It paved the way for subsequent studies into interfering with much larger molecules, under the direction of Markus Arndt.

Another incredible quantum property was entanglement switching, which Anton and his associates had already discovered in 1993. Actually, it is an entangled state that was teleported. To put it more specifically, when two pairs of entangled photons are measured for their Bell states, the other two photons in each pair are instantly brought into the same entangled Bell state. In 1998, Zeilinger's team experimentally implemented it [11].

Testing Bell inequalities became increasingly popular in the late 1990s. At Geneva, Nicolas Gisin's team used energy-time entangled photon pairs in photosensitive fibres to set a record. They were successful in separating their spectators Alice and Bob by more than 10 kilometres, and they were able to demonstrate that this distance had almost no impact on the photons' ability to entangle. A vast array of experiments exploring an entanglement of particles across long distances were conducted in new millennium by Bell inequalities. The main goal was to eventually be able to set up world network in space [12].

Experimental Results

The well-known paper (EPR) by Einstein, Podolsky, and Rosen was published in 1935, and it revealed the inadequacy of quantum theory. The scientists argued that if quantum theory was accurate, it would contradict common sense in the way that was revolting to a human mind that was more oriented towards classical thought. Bohr's response was an confirmation of the reality that quantum theory does exactly that rather than a denial of their reasoning.

They were concerned with the theory's completeness and stated that "Every aspect of the Physical Reality must have a counterpart in the Physical Theory" is a requirement for a complete theory. They did not claim to be capable of defining "Physical Reality," as it is used in this context. Instead, they listed what they believed to be the very minimum characteristics that a part of physical reality ought to possess. This presumption, which seems so essential and clear, is what quantum theory disproves. They suggested that "there exists an element of physical reality corresponding to this physical quantity if, without in any way altering a system, we can predict with certainty (i.e., a probability equal to unity) the value of a physical quantity." They provided one good example, but mostly discussion that followed put different example provided by Bohm [2].

Consider a system having spin-0 that splits into two (½) spin particles. The wave function would be such that particle 2 will have spin down (↓) if particle 1 has spin up (↑), and vice versa. To maintain momentum, the two particles will separate in different directions. If particle 1, which is distant from decay point, has spin up, so it is certain that particle 2, which is not here, has down spin. The down spin property must be a component of basic reality, according to the EPR argument, as one hasn't interfered with particle 2 in any way. Being down spin is therefore a characteristic of the particle itself and cannot have been caused by any measurement we took on particle 1. The spin must be down when it left the decay point, the point of interaction.

Quantum mechanics refutes this obvious point. It asserts that until the spin of 1^st particle is considered, the spin of 2^nd particle is unknown since it is theoretically possible to experience interference between the possible states because up until that point, it was in a superposition of up and down states. This was the main topic of contention between Einstein and Bohr, although it wasn't believed that the two points of view differed experimentally until 1965.  Only then Bell demonstrate his theorem, which states that if one conducts spin measurements in any direction, the assumption that the spin is genuine severely limits the correlations that could potentially exist between the particles. Since then, several investigations have verified the findings of quantum theory [13].

It is intriguing that findings of Bell do not take account of the scenario, which is directly addressed by the EPR argument, in which a measurement of 1 particle permits one to predict with absolute confidence what would happen to another particle. In this scenario, one particle's spin is measured, followed by measurements of other particle either in same direction or in opposite direction. This instance not only produce measurement certainty, but someone could also attain a classical system model that produces the same outcome. Quantum theory only produces outcomes that differ from the classical ones in general scenario of a random angle between particles, where one lacks certainty. For example, using the wave function above, if particle 1's spin is measured in one direction (n), while particle 2's spin is measured in different direction (l), then expected value of quantum mechanical correlation between two particles will be,

E (n · l) = 〈ψ| (σ · n) (σ · l) |ψ〉 = -cos (n · l),

and this changes to cos (α – β) when particles are travelling in the ± z direction. On the other hand, n and l are at angles α and β and to the x-y plane. These cases—where the measurement orientations diverge by 0° or 180°—provide examples of situations in which a firm forecast is attainable. This situation, where an element of fact exists by means of complete expectedness, in accordance with EPR requirement, is known as the "super-classical" case.

Bell supposed that spin of particles was determined at moment they divided in order to build a model for association in case of a deterministic and local theory. He gave an outcome a value of 1 because there are only two potential values for the calculation of spin in a certain direction. Hence, he provided a value,

Aλ (n) · Bλ (l),

Here both A and B may have values only l, which in this case were controlled by some internal, hidden variable. He did this by measuring the spin of both particles, one along n and the other along l. The product's main restriction was that, as previously said, if l = n, one got

Aλ (n) · Bλ (n) = -1,                             Aλ (n) · Bλ (-n) = +1.

Finally, the measurement's expected value represented the sum of all possibilities λ.

E (n, l) = ∫ dλ ρ(λ) Aλ (n) Bλ (l)

He could calculate the inequality,

|E (n, l) – E (n, k) | ≤ 1+ E (l, k)

since the probabilities are factorable (l, k). The quantum mechanical conclusion for most angles eliminates this inequality. But regrettably, when l = ±n, it provides zero information. One can create a straightforward predictable model to describe the outcome in super-classical scenario, where one could create a certain statement but there, the Bell inequality above provides no information. However, the Bell inequality demonstrates that this is not feasible for general angles [13].

The issue "Can one always discover a classical model for superclassical case?" arises naturally as a result. From the perspective of Bell's inequality, which is least fascinating case, but from the perspective of reality, it is the most intriguing. In other words, Bell's theorem provides a definitive response to the question of whether it is possible to create a classical, localized, deterministic model that can replicate the general conclusions of quantum theory. But it doesn't address whether one can create such a model in the unique situation where precise predictions are possible, or the EPR scenario. This question also has a negative response. Yet, a more complex model than two-body decay described above is required to provide an answer. We have created a straightforward modification of the Bohm model that places more limitations on the potential outcomes for different particles. So, the limit is so severe that even in super-classical example, a deterministic, local model cannot be created, and inequalities are not even necessary. One can demonstrate that it is impossible to build such a model for any given value of hidden variable [14].

Conclusion

Recent Bell inequality experiments had a considerable influence on how we perceive reality.  In contrast to "naive" realism, objects have no qualities prior to observation, and the order of observations is not important. Bell's Theorem also implies that nature is not local. All of these "philosophical" experiments also resulted in very useful applications, such as quantum information science, a growing area of study today.

Thus, we arrive at the conclusion that even in easier case where one could make certain estimates in EPR sense, one cannot do so with such a model. Furthermore, we also conclude that there is no way to construct a classical, deterministic, local theory that replicates quantum theory in general. To demonstrate this, one must move away from Bell theorem. Another final conclusion is that, with the proper 4-particle system, all that needs to be done to demonstrate that quantum theory is valid experimentally is to show that it cannot be reproduced classically. This means that it will be much simpler to refute the classical explanations that are frequently offered to account for the outcomes of 2-particle experiments that confirm quantum theory.

References

[1]          J.-W. Pan, D. Bouwmeester, M. Daniell,H. Weinfurter, and A. Zeilinger, "Experimental test of quantum nonlocalityin three-photon Greenberger–Horne–Zeilinger entanglement," Nature, vol. 403, no. 6769, pp. 515-519,2000.

[2]          A. Einstein, B. Podolsky, and N.Rosen, "Can quantum-mechanical description of physical reality beconsidered complete?," Physicalreview, vol. 47, no. 10, p. 777, 1935.

[3]          A. Pais, "Subtle is the Lord…‘:The Science and the Life of Albert Einstein. New York, NY: Oxford UniversityPress," 1982.

[4]          J. S. Bell, "On the einsteinpodolsky rosen paradox," PhysicsPhysique Fizika, vol. 1, no. 3, p. 195, 1964.

[5]          J. F. Clauser, M. A. Horne, A.Shimony, and R. A. Holt, "Proposed experiment to test localhidden-variable theories," Physicalreview letters, vol. 23, no. 15, p. 880, 1969.

[6]          S. J. Freedman and J. F. Clauser,"Experimental test of local hidden-variable theories," Physical Review Letters, vol. 28, no.14, p. 938, 1972.

[7]          R. A. Bertlmann, A. Zeilinger, and J.F. Clauser, "Early History of Bell’s Theorem," Quantum [Un] speakables: From Bell to Quantum Information, pp.61-98, 2002.

[8]          J. F. Clauser, M. A. Horne, A.Shimony, and R. A. Holt, "Proposed Experiment to Test Local Hidden Variable Theories," Physical ReviewLetters, vol. 24, no. 10, p. 549, 1970.

[9]          A. Aspect, J. Dalibard, and G. Roger,"Experimental test of Bell's inequalities using time-varyinganalyzers," Physical review letters,vol. 49, no. 25, p. 1804, 1982.

[10]        M. Arndt, O. Nairz, J. Vos-Andreae, C.Keller, G. Van der Zouw, and A. Zeilinger, "Wave–particle duality of C60molecules," nature, vol. 401,no. 6754, pp. 680-682, 1999.

[11]        J.-W. Pan, D. Bouwmeester, H.Weinfurter, and A. Zeilinger, "Experimental entanglement swapping:entangling photons that never interacted," Physical review letters, vol. 80, no. 18, p. 3891, 1998.

[12]        W. Tittel, J. Brendel, H. Zbinden, andN. Gisin, "Violation of Bell inequalities by photons more than 10 kmapart," Physical review letters, vol.81, no. 17, p. 3563, 1998.

[13]        D. M. Greenberger, M. A. Horne, and A.Zeilinger, "Going beyond Bell’s theorem," Bell’s theorem, quantum theory and conceptions of the universe, pp.69-72, 1989.

[14]        A. Drezet and B.Stock, "A causal and continuous interpretation of the quantum theory:About an original manuscript by David Bohm sent to Louis de Broglie in1951," arXiv preprintarXiv:2103.00576, 2021.