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Quantum Entanglement - Giray Alkın Erdinç '25 & Batu Çalıyurt '25

In 2022, The Nobel prize in physics is awarded to Alain Aspect, John F. Clauser and Anton Zeilinger for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science. Their work was a result of a long-lasting discussion and their experiments on quantum entanglement have actually shown the extraordinary nature of quantum once again.


In quantum physics, it has always been a matter of discussion whether the universe is guided by a pair of dice. At the core of quantum mechanics lies the uncertainty principle of Heisenberg and the wave-particle duality. According to the uncertainty principle, specific traits of a particle at an instant cannot be known simultaneously. For example, both the position and momentum of a particle cannot be determined at the same time. As Heisenberg remarks, "At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position." This means that the more accurate the determination of a quantity, the less accurate the determination of the other. Additionally, as shown in the double slit experiment, when electrons are not observed, they behave like waves. However, when a detector is placed in various complicated setups, electrons somehow behave like particles. These ambiguous situations, which shatter the deterministic classical physics, lead scientists to many interpretations, the most common ones being: The Copenhagen Interpretation, the Hidden Variables Hypothesis, and the Many Worlds Hypothesis.


The Copenhagen Interpretation mainly states that the wave function, which projects the situations of the quantum world in probabilities, is the right way to describe quantum mechanics, and there is nothing beyond possibilities. If two properties are connected by an uncertainty principle, then what we can know is limited to the principle, and what we know depends on the measurement we do. A photon is either a particle or a wave, depending on the observer's wish. Niels Bohr was one of the pioneers of this interpretation during the 1920s, which caused a conflict between him and Einstein, who opposed the probabilistic structure of quantum mechanics. Consequently, Einstein, Podolsky, and Rosen claimed that quantum mechanics was actually an incomplete theory. They formulated a thought experiment, known as the EPR paradox, to demonstrate that our knowledge may go beyond possibilities.


Think about two particles that interact and then are separated towards opposite directions. When you determine the position of one, you can determine the position of the other. Thus, by determining the position of particle A, you can determine the position of particle B. Then, if you measure the momentum of particle B, you can find the momentum of particle A. This way, you may have information about both position and momentum, which means that quantum mechanics is an incomplete theory and is only a piece of a higher reality. Additionally, according to the Copenhagen Interpretation, two entangled particles would be a piece of non-local reality, which means that they could communicate faster than the speed of light (instantaneously) regardless of the distance and any local variables between them. However, this idea contradicts the theory of special relativity, which states that nothing can travel faster than the speed of light. Therefore, Einstein famously described this instant signal between the particles as "spooky action at a distance."


The thought experiment was later reformed by David Bohm, who built up the hidden variable theory, supposing from a deterministic perspective that there are some hidden variables at work which define the states of the particles, instead of a non-local reality. Bohm replaced momentum and position in EPR with the spin of the particles, changing the conditions. As a response to the hidden variable theories, which were getting popular, in 1966, John Stewart Bell published a paper called "On The Problem of Hidden Variables in Quantum Mechanics." The problem with EPR is their supposition of pre-determined states and ignorance of the causal effect of the intervention of an observer. As has been demonstrated in the double-slit experiment, the observer does not stand outside the experiment; they are a part of the experiment. Additionally, as mathematically demonstrated by Bell, theories, including some predetermined values, do not match with the quantum measurements when three dimensions are taken into account. Most importantly, Bell proposed the idea of switching the axis to measure the spin (not only up and down, but also in the x-axis). If particles had some predetermined spin values, then the change of axis would have no impact on the result, but if spin values were affected by the axis shift, then this would mean that there were no already-determined values.


Quantum Entanglement and The Nobel Prize


Quantum entanglement happens when two particles are in the same quantum state. Bell’s example can be used to express the situation better. In his story, Professor Bertlmann always wears socks in unmatched colors (i.e. if one of them is blue, the other one is pink). Therefore, under normal circumstances when Alice saw one of the socks, Bob could know the color of the other without any observation. This real life situation carries deterministic, real and local (independent of the measurement) features. However, when Bertlmann wears quantum socks, the matter quite changes. The socks now do not have specific colors till an observation is made. Thus, the color of the other sock depends on the observation, so this quantum situation is indeterministic, unreal (no predetermined color) and nonlocal. . However, still, it was very difficult to be completely sure that the socks did not have pre-determined states.


This was the point when experiments were made. Firstly, in 1972, Clauser conducted an experiment, using polarized photons. Despite his claim before the experiment that his results would prove Einstein right, the results sided with Bell’s predictions. After Clauser, Alain Aspect designed an experiment for which he used an extremely complicated setup with lenses which would randomly change during the billionths of a second. His data were indicating the validity of Bell’s idea again. Finally, in 2017, Zeilinger led a team who used the “colors of photons emitted from distant stars hundreds of years ago” as their experiment settings to avoid any kind of loophole and claim of determinism. The results were proving Einstein wrong again. And in 2022, these three scientists - Clauser, Aspect and Zeilinger - were awarded the Nobel Prize for Physics. There are still some claims about the loopholes in the experiments, the most famous objection being superdeterminism. There are different versions of superdeterminism, but the general idea is a hidden factor that shapes the results (i.e. A secret force which leads the strings of the particles). Or with another formulation of the problem, if everything is already determined at the instance of Big-Bang, it becomes impossible to talk about any kind of randomness or uncertainty, everything would develop according to superdeterminism.


Quantum entanglement, seemingly, promises a significant change in quantum computing. Despite the little information we have about its capacity, entanglement may enhance quantum cryptography, providing the possibility for completely secure communication. Furthermore, through quantum teleportation, quantum information such as electrons and photons can be transferred between systems with significantly less energy.


Quantum mechanics has sharply shaken the foundations of classical physics, and many scientists from Einstein to Bell played an important role in its development process. As quantum entanglement demonstrates, and based on our current knowledge, in spite of how difficult it is to accept the idea, it seems like there are some dice on the table.


Bibliography

The nobel prize in physics 2022. NobelPrize.org. (2022, October 4). Retrieved December 14, 2022, from https://www.nobelprize.org/prizes/physics/2022/press-release/


Copenhagen interpretation. University of Oregon Education. (n.d.). Retrieved December 14, 2022, from http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec15.html


Fine, A. (2017, October 31). The einstein-podolsky-rosen argument in quantum theory. Stanford Encyclopedia of Philosophy. Retrieved December 14, 2022, from https://plato.stanford.edu/entries/qt-epr/


T&T Clark. (1999). God, humanity and the cosmos topic: The hidden-variable theory of David Bohm. Counter Balance. Retrieved December 14, 2022, from https://counterbalance.org/ghc-obs/hidvar-frame.html


Goldstein, S., Norsen, T., Tausk, D. V., & Zanghi, N. (2011). Bell's theorem. Scholarpedia. Retrieved December 14, 2022, from http://www.scholarpedia.org/article/Bell%27s_theorem


Blanton, J. (1996). Does Bell's inequality rule out local theories of quantum mechanics? The EPR Paradox and Bell's Inequality. Retrieved December 14, 2022, from https://math.ucr.edu/home/baez/physics/Quantum/bells_inequality.html


Garisto, D. (2022, November 22). What is quantum entanglement? IEEE Spectrum. Retrieved December 14, 2022, from https://spectrum.ieee.org/what-is-quantum-entanglement


Wood, C. (2022, October 6). Pioneering quantum physicists win Nobel prize in physics. Quanta Magazine. Retrieved December 14, 2022, from https://www.quantamagazine.org/pioneering-quantum-physicists-win-nobel-prize-in-physics-20221004/


What is quantum nonlocality? illustrated. Quantum Physics Lady. (2020, May 8). Retrieved December 14, 2022, from http://www.quantumphysicslady.org/glossary/quantum-nonlocality/


Dilmagani, C. (2021, April 11). Quantum Entanglement: What is it & why is it important? AIMultiple. Retrieved December 14, 2022, from https://research.aimultiple.com/quantum-computing-entanglement/

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