title

Bell's Theorem: The Quantum Venn Diagram Paradox

description

Featuring 3Blue1Brown
Watch the 2nd video on 3Blue1Brown here: https://www.youtube.com/watch?v=MzRCDLre1b4
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This video is about Bell's Theorem, one of the most fascinating results in 20th century physics. Even though Albert Einstein (together with collaborators in the EPR Paradox paper) wanted to show that quantum mechanics must be incomplete because it was nonlocal (he didn't like "spooky action at a distance"), John Bell managed to prove that any local real hidden variable theory would have to satisfy certain simple statistical properties that quantum mechanical experiments (and the theory that describes them) violate. Since then, GHZ and others have managed to extend the theoretical work, and Alain Aspect performed the first Bell test experiment in the late 1980s.
Thanks to Vince Rubinetti for the music: https://soundcloud.com/vincerubinetti/one-two-zeta
And thanks to Evan Miyazono, Aatish Bhatia, and Jasper Palfree for discussions and camaraderie during some of the inception of this video.
REFERENCES:
John Bell's Original Paper: http://inspirehep.net/record/31657/files/vol1p195-200_001.pdf
Quantum Theory and Reality: https://www.scientificamerican.com/media/pdf/197911_0158.pdf
"What Bell Did" By Tim Maudlin: https://arxiv.org/pdf/1408.1826
Bell's Theorem on Wikipedia: https://en.wikipedia.org/wiki/Bell%27s_theorem
2015 experimental confirmation that QM violates Bell's theorem: https://arxiv.org/pdf/1508.05949.pdf
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.250402
Bell's Theorem without Inequalities (GHZ): http://dx.doi.org/10.1119/1.16243
Kochen-Specker Theorem: https://en.wikipedia.org/wiki/Kochenâ€“Specker_theorem
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Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!
Created by Henry Reich

detail

{'title': "Bell's Theorem: The Quantum Venn Diagram Paradox", 'heatmap': [{'end': 907.828, 'start': 893.919, 'weight': 1}], 'summary': 'Explores quantum behavior of light passing through polarizing filters, challenges assumptions about light behavior, discusses quantum state representation and polarization of photons, and highlights violations of bell inequalities, challenging notions of realism and locality in quantum mechanics.', 'chapters': [{'end': 110.488, 'segs': [{'end': 30.341, 'src': 'embed', 'start': 2.253, 'weight': 0, 'content': [{'end': 5.856, 'text': 'If you have polarized sunglasses, you have a quantum measurement device.', 'start': 2.253, 'duration': 3.603}, {'end': 11.722, 'text': "Each of these pieces of glass is what's called a polarizing filter, which means when a photon of light reaches the glass,", 'start': 6.177, 'duration': 5.545}, {'end': 13.303, 'text': "it either passes through or it doesn't.", 'start': 11.722, 'duration': 1.581}, {'end': 19.789, 'text': 'And whether or not it passes through is effectively a measurement of whether or not that photon is polarized in a given direction.', 'start': 13.723, 'duration': 6.066}, {'end': 20.49, 'text': 'Try this.', 'start': 20.109, 'duration': 0.381}, {'end': 24.474, 'text': 'Find yourself several sets of polarized sunglasses or old photographic filters.', 'start': 20.85, 'duration': 3.624}, {'end': 30.341, 'text': 'Look through one set of sunglasses at some light source, like a lamp, then hold a second polarizing filter between you and the light.', 'start': 24.734, 'duration': 5.607}], 'summary': 'Polarized sunglasses act as a quantum measurement device, determining the polarization of light.', 'duration': 28.088, 'max_score': 2.253, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs2253.jpg'}, {'end': 81.393, 'src': 'embed', 'start': 55.228, 'weight': 1, 'content': [{'end': 61.289, 'text': 'But if you take a third filter and orient it 45 degrees off from that first one and then you put it in between the two,', 'start': 55.228, 'duration': 6.061}, {'end': 62.869, 'text': 'the lamp actually looks brighter.', 'start': 61.289, 'duration': 1.58}, {'end': 65.45, 'text': 'This is not the middle filter generating more light.', 'start': 63.23, 'duration': 2.22}, {'end': 69.951, 'text': 'Somehow, introducing another filter actually lets more light through.', 'start': 65.83, 'duration': 4.121}, {'end': 75.912, 'text': 'With perfect filters, if you keep adding more and more in between at in-between angles, this trend actually continues.', 'start': 70.271, 'duration': 5.641}, {'end': 76.792, 'text': 'More light.', 'start': 76.212, 'duration': 0.58}, {'end': 81.393, 'text': "This feels super weird, but it's not just weird that more light comes through.", 'start': 77.192, 'duration': 4.201}], 'summary': 'Introducing a third filter at a 45-degree angle between two filters allows more light through, with the trend continuing as more filters are added.', 'duration': 26.165, 'max_score': 55.228, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs55228.jpg'}], 'start': 2.253, 'title': 'Quantum light behavior', 'summary': 'Delves into the quantum behavior of light passing through polarizing filters, revealing how specific filter orientations can paradoxically allow more light to pass through, challenging fundamental assumptions about light behavior.', 'chapters': [{'end': 110.488, 'start': 2.253, 'title': 'Quantum measurement with polarized sunglasses', 'summary': 'Discusses the quantum behavior of light passing through polarizing filters, demonstrating how a series of filters at specific orientations can paradoxically allow more light to pass through, challenging fundamental assumptions about the behavior of light.', 'duration': 108.235, 'highlights': ['Polarized sunglasses act as quantum measurement devices, with each piece of glass functioning as a polarizing filter, allowing or blocking the passage of photons based on their polarization. The concept of polarizing filters in sunglasses being quantum measurement devices is highlighted, demonstrating their function in allowing or blocking photons based on their polarization.', 'The introduction of a third filter oriented at 45 degrees between two existing filters paradoxically results in the light appearing brighter, contrary to the expected behavior of filters simply blocking light. The counterintuitive effect of adding an additional filter at a specific angle leading to more light passing through challenges conventional understanding of filter behavior, demonstrating a quantum phenomenon.', 'The phenomenon of more light passing through as additional filters are introduced at in-between angles presents quantifiably impossibly high results, leading to a deeper questioning of fundamental assumptions about the behavior of light. The quantifiably impossibly high results of more light passing through as additional filters are introduced at specific angles prompts a reevaluation of fundamental assumptions about light behavior, indicating a paradigm shift in understanding.']}], 'duration': 108.235, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs2253.jpg', 'highlights': ['Polarized sunglasses act as quantum measurement devices, allowing or blocking photons based on their polarization.', 'The introduction of a third filter at 45 degrees paradoxically results in brighter light, challenging conventional understanding.', 'More light passing through as additional filters are introduced at in-between angles presents quantifiably impossibly high results, prompting a reevaluation of fundamental assumptions.']}, {'end': 481.659, 'segs': [{'end': 159.809, 'src': 'embed', 'start': 127.594, 'weight': 1, 'content': [{'end': 129.854, 'text': 'Waves in a thing called the electromagnetic field.', 'start': 127.594, 'duration': 2.26}, {'end': 133.495, 'text': 'And polarization just means the direction in which that wave is wiggling.', 'start': 130.054, 'duration': 3.441}, {'end': 144.938, 'text': 'Polarizing filters absorb this wiggling energy along one direction so that the wave coming out on the other side is wiggling purely in the direction perpendicular to the one where the energy absorption is happening.', 'start': 133.715, 'duration': 11.223}, {'end': 153.124, 'text': 'But unlike a water wave or a sound wave, photons are quantum objects, and as such, they either pass through the polarizer completely or not at all.', 'start': 145.498, 'duration': 7.626}, {'end': 159.809, 'text': "And this is apparently probabilistic, like how we don't know whether or not Schrodinger's cat will be alive or dead until we look into the box.", 'start': 153.584, 'duration': 6.225}], 'summary': 'Electromagnetic waves polarize, photons pass through polarizers probabilistically.', 'duration': 32.215, 'max_score': 127.594, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs127594.jpg'}, {'end': 200.958, 'src': 'embed', 'start': 163.211, 'weight': 0, 'content': [{'end': 168.315, 'text': "it's tempting to imagine that a probabilistic event like this might have some deeper cause that we just don't know yet.", 'start': 163.211, 'duration': 5.104}, {'end': 175.223, 'text': "that there's some hidden variable describing the photon's state that would tell us with certainty whether it should pass through a given filter or not.", 'start': 168.775, 'duration': 6.448}, {'end': 180.309, 'text': 'And maybe that variable is just too subtle for us to probe without deeper theories and better measuring devices.', 'start': 175.764, 'duration': 4.545}, {'end': 184.074, 'text': "Or maybe it's somehow fundamentally unknowable, but still there.", 'start': 180.81, 'duration': 3.264}, {'end': 189.226, 'text': 'The possibility of such a hidden variable seems beyond the scope of experiment.', 'start': 185.663, 'duration': 3.563}, {'end': 196.554, 'text': 'I mean, what measurements could possibly probe at a deeper explanation that might or might not exist? And yet, we can do just that.', 'start': 189.507, 'duration': 7.047}, {'end': 198.956, 'text': 'With sunglasses and polarization of light.', 'start': 196.814, 'duration': 2.142}, {'end': 200.958, 'text': "Let's go ahead and lay down some numbers here.", 'start': 199.456, 'duration': 1.502}], 'summary': 'Discussing the possibility of hidden variables in probabilistic events and the use of sunglasses and polarization of light to probe deeper explanations.', 'duration': 37.747, 'max_score': 163.211, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs163211.jpg'}, {'end': 341.883, 'src': 'embed', 'start': 313.049, 'weight': 2, 'content': [{'end': 320.193, 'text': "In fact, these numbers suggest that it's impossible for there to be some hidden variable determining each photon's state with respect to each filter.", 'start': 313.049, 'duration': 7.144}, {'end': 326.376, 'text': "In other words, it suggests that it's not even possible for these photons to have some definite answer to the three questions.", 'start': 320.373, 'duration': 6.003}, {'end': 332.259, 'text': 'would it pass through A, would it pass through B and would it pass through C before those measurements are actually made?', 'start': 326.376, 'duration': 5.883}, {'end': 334.52, 'text': "What we'll do here is a proof by contradiction.", 'start': 332.579, 'duration': 1.941}, {'end': 341.883, 'text': 'Imagine 100 photons who do have some hidden variable which, through whatever crazy underlying mechanism you might imagine,', 'start': 334.86, 'duration': 7.023}], 'summary': 'Quantum theory suggests photons have no hidden variable determining their state with respect to filters, as proven by a proof by contradiction.', 'duration': 28.834, 'max_score': 313.049, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs313049.jpg'}], 'start': 110.668, 'title': 'Quantum photon polarization', 'summary': "Focuses on quantum state representation and polarization of photons, explaining the math used to represent quantum states and discussing the probabilistic nature of photon polarization. it emphasizes the experimental results challenging the concept of hidden variables and suggesting the impossibility of determining a photon's state prior to measurement.", 'chapters': [{'end': 144.938, 'start': 110.668, 'title': 'Quantum state representation and polarization of photons', 'summary': 'Explains the math used to represent quantum states like photon polarization, emphasizing that photons are waves in the electromagnetic field and polarization refers to the direction of wave wiggling, with polarizing filters absorbing energy along one direction to allow wave wiggling purely in the perpendicular direction.', 'duration': 34.27, 'highlights': ['Photons are waves in the electromagnetic field, and polarization signifies the direction in which the wave is wiggling.', 'Polarizing filters absorb wiggling energy along one direction, allowing the wave coming out on the other side to wiggle purely in the direction perpendicular to the absorbed energy.']}, {'end': 481.659, 'start': 145.498, 'title': 'Quantum photon polarization', 'summary': "Discusses the probabilistic nature of photon polarization and its implications, showcasing experimental results where photons exhibit unexpected behavior when passing through polarizing filters, challenging the concept of hidden variables and suggesting the impossibility of determining a photon's state prior to measurement.", 'duration': 336.161, 'highlights': ['Experiments show that when light passes through polarizing filters oriented at specific angles, the probabilities of photons passing through or getting blocked exhibit surprising numerical values, such as 0%, 50%, and 85%, challenging the intuitive expectations based on filter angles and highlighting the non-deterministic nature of photon polarization.', "The experimental results suggest that it's impossible for hidden variables to determine each photon's state with respect to different filters, indicating that photons may not possess a definite answer to whether they would pass through a filter or not before measurements are made, leading to the concept of 'proof by contradiction' to demonstrate the implausibility of hidden variables influencing photon behavior.", 'The detailed analysis using a Venn diagram further illustrates the contradiction between the expected behavior of photons based on hidden variables and the actual experimental outcomes, showcasing the incompatibility of the predicted and observed results, ultimately challenging the notion of deterministic photon behavior and hidden variables in quantum mechanics.']}], 'duration': 370.991, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs110668.jpg', 'highlights': ['Experiments challenge intuitive expectations of photon polarization probabilities.', 'Polarizing filters absorb energy along one direction, allowing the wave to wiggle purely in the perpendicular direction.', 'Experimental results suggest the impossibility of hidden variables determining photon states with respect to different filters.', 'Photon behavior contradicts the expected outcomes based on hidden variables, challenging deterministic behavior in quantum mechanics.']}, {'end': 1053.782, 'segs': [{'end': 511.594, 'src': 'embed', 'start': 481.659, 'weight': 3, 'content': [{'end': 483.299, 'text': "even when we don't make that measurement.", 'start': 481.659, 'duration': 1.64}, {'end': 486.28, 'text': 'And this is what gives us a numerical contradiction.', 'start': 483.899, 'duration': 2.381}, {'end': 490.761, 'text': 'For comparison, think of any other non-quantum questions that you might ask.', 'start': 486.64, 'duration': 4.121}, {'end': 496.763, 'text': 'Like, take 100 people and ask them if they like minute physics, if they have a beard, and if they wear glasses.', 'start': 491.261, 'duration': 5.502}, {'end': 503.048, 'text': "Well, obviously everyone likes minute physics, but then among those, take the number that don't have a beard,", 'start': 497.603, 'duration': 5.445}, {'end': 505.83, 'text': 'plus the number who do have a beard but not glasses.', 'start': 503.048, 'duration': 2.782}, {'end': 509.753, 'text': "Now that should be greater than or equal to the number who don't have glasses.", 'start': 506.45, 'duration': 3.303}, {'end': 511.594, 'text': 'One is just a superset of the other.', 'start': 510.093, 'duration': 1.501}], 'summary': 'Quantum measurement leads to numerical contradiction, illustrated with a non-quantum example.', 'duration': 29.935, 'max_score': 481.659, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs481659.jpg'}, {'end': 794.309, 'src': 'embed', 'start': 764.372, 'weight': 0, 'content': [{'end': 768.174, 'text': "The contradictions in this experiment show it can't be locally real, period.", 'start': 764.372, 'duration': 3.802}, {'end': 772.457, 'text': "What we've described here is one example of what's called a Bell inequality.", 'start': 768.695, 'duration': 3.762}, {'end': 780.361, 'text': "It's a simple counting relationship that must be obeyed by any set of questions with definite answers, but which quantum states seem to disobey.", 'start': 772.737, 'duration': 7.624}, {'end': 787.565, 'text': 'In fact, the math of quantum theory predicts that entangled quantum states should violate Bell inequalities in exactly this way.', 'start': 780.661, 'duration': 6.904}, {'end': 794.309, 'text': 'John Bell originally put out the inequalities and the observation that quantum mechanics would violate them in 1964.', 'start': 787.765, 'duration': 6.544}], 'summary': 'Experiment shows quantum states violate bell inequalities, as predicted by quantum theory.', 'duration': 29.937, 'max_score': 764.372, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs764372.jpg'}, {'end': 835.893, 'src': 'embed', 'start': 811.556, 'weight': 1, 'content': [{'end': 818.138, 'text': "There have also been numerous theoretical developments in the intervening years, strengthening Bell's and other similar results, that is,", 'start': 811.556, 'duration': 6.582}, {'end': 820.599, 'text': 'strengthening the case against local realism.', 'start': 818.138, 'duration': 2.461}, {'end': 822.701, 'text': "In the end, here's what I find crazy.", 'start': 820.979, 'duration': 1.722}, {'end': 829.427, 'text': "Bell's theorem is an incredibly deep result upending what we know about how our universe works, that humanity has only just recently come to know.", 'start': 823.141, 'duration': 6.286}, {'end': 835.893, 'text': 'And yet the math at its heart is a simple counting argument, and the underlying physical principles can be seen in action with a cheap home demo.', 'start': 829.687, 'duration': 6.206}], 'summary': "Bell's theorem challenges local realism using simple math and observable principles.", 'duration': 24.337, 'max_score': 811.556, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs811556.jpg'}, {'end': 923.921, 'src': 'heatmap', 'start': 893.919, 'weight': 1, 'content': [{'end': 899.603, 'text': "I think it took long because Bell's theorem in particular, there's like a thousand different ways you can go about it right?", 'start': 893.919, 'duration': 5.684}, {'end': 901.424, 'text': "I don't know about the other topics you do,", 'start': 900.023, 'duration': 1.401}, {'end': 907.828, 'text': "but usually there's like a handful of approaches you can take and you kind of choose one you talk with someone about it and you go down that path.", 'start': 901.424, 'duration': 6.404}, {'end': 910.11, 'text': "Typically Bell's theorem is arrived at,", 'start': 907.848, 'duration': 2.262}, {'end': 917.435, 'text': 'and the way it was historically arrived at is thinking about this kind of spooky action at a distance due to entanglement and measurements on entangled particles.', 'start': 910.11, 'duration': 7.325}, {'end': 923.921, 'text': "And we came at it a totally different direction, which I have never seen before, and hopefully people won't be horribly angry with us for doing.", 'start': 917.796, 'duration': 6.125}], 'summary': "The discussion explores a unique approach to bell's theorem, deviating from traditional methods, and aims to avoid criticism.", 'duration': 30.002, 'max_score': 893.919, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs893919.jpg'}], 'start': 481.659, 'title': "Quantum state contradiction and bell's theorem", 'summary': "Discusses a numerical contradiction in quantum questions, comparing with non-quantum questions and highlighting the violation of a certain inequality in quantum states. it also explores the concept of quantum entanglement and bell's theorem, featuring an experiment with entangled photons and polarizing filters, demonstrating violations of bell inequalities, and challenging the notions of realism and locality in quantum mechanics.", 'chapters': [{'end': 524.225, 'start': 481.659, 'title': 'Quantum state contradiction', 'summary': 'Discusses a numerical contradiction in quantum questions, using a comparison with non-quantum questions and highlighting the violation of a certain inequality in quantum states.', 'duration': 42.566, 'highlights': ['Some questions about quantum states seem to violate the inequality that one would expect, which contradicts the premise that these questions could have definite answers even when the measurements are not made.', 'Comparing the violation of inequality in quantum questions to non-quantum questions, such as the scenario of liking MinutePhysics, having a beard, and wearing glasses, illustrates the contradiction in quantum states.', 'Using the comparison of taking 100 people and asking about their preferences and attributes, an inequality is highlighted where the sum of people not having a beard and those with a beard but no glasses should be greater than or equal to the number of people without glasses.']}, {'end': 1053.782, 'start': 525.246, 'title': "Quantum entanglement and bell's theorem", 'summary': "Discusses the concept of quantum entanglement and bell's theorem, highlighting the experiment with entangled photons and polarizing filters, which demonstrated violations of bell inequalities, challenging the notions of realism and locality in quantum mechanics.", 'duration': 528.536, 'highlights': ['Entangled photons experiment demonstrated violations of Bell inequalities, challenging the notions of realism and locality in quantum mechanics. The experiment with entangled photons and polarizing filters demonstrated violations of Bell inequalities, challenging the notions of realism and locality in quantum mechanics.', 'The experiment revealed that quantum entanglement cannot be explained by hidden variable theories, as it would require faster-than-light influence between particles. The experiment revealed that quantum entanglement cannot be explained by hidden variable theories, as it would require faster-than-light influence between particles.', "Bell's Theorem upends our understanding of the universe and has been experimentally verified, with the first loophole-free test conducted in 2015. Bell's Theorem upends our understanding of the universe and has been experimentally verified, with the first loophole-free test conducted in 2015.", "The experiment with entangled photons and polarizing filters provides a simple way to demonstrate the underlying physical principles of Bell's Theorem. The experiment with entangled photons and polarizing filters provides a simple way to demonstrate the underlying physical principles of Bell's Theorem."]}], 'duration': 572.123, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/zcqZHYo7ONs/pics/zcqZHYo7ONs481659.jpg', 'highlights': ['The experiment with entangled photons and polarizing filters demonstrated violations of Bell inequalities, challenging the notions of realism and locality in quantum mechanics.', "Bell's Theorem upends our understanding of the universe and has been experimentally verified, with the first loophole-free test conducted in 2015.", 'Some questions about quantum states seem to violate the inequality that one would expect, which contradicts the premise that these questions could have definite answers even when the measurements are not made.', 'Comparing the violation of inequality in quantum questions to non-quantum questions, such as the scenario of liking MinutePhysics, having a beard, and wearing glasses, illustrates the contradiction in quantum states.']}], 'highlights': ['The experiment with entangled photons and polarizing filters demonstrated violations of Bell inequalities, challenging the notions of realism and locality in quantum mechanics.', "Bell's Theorem upends our understanding of the universe and has been experimentally verified, with the first loophole-free test conducted in 2015.", 'Comparing the violation of inequality in quantum questions to non-quantum questions, such as the scenario of liking MinutePhysics, having a beard, and wearing glasses, illustrates the contradiction in quantum states.', 'Some questions about quantum states seem to violate the inequality that one would expect, which contradicts the premise that these questions could have definite answers even when the measurements are not made.', 'Photon behavior contradicts the expected outcomes based on hidden variables, challenging deterministic behavior in quantum mechanics.', 'Experiments challenge intuitive expectations of photon polarization probabilities.', 'Polarizing filters absorb energy along one direction, allowing the wave to wiggle purely in the perpendicular direction.', 'The introduction of a third filter at 45 degrees paradoxically results in brighter light, challenging conventional understanding.', 'Polarized sunglasses act as quantum measurement devices, allowing or blocking photons based on their polarization.', 'More light passing through as additional filters are introduced at in-between angles presents quantifiably impossibly high results, prompting a reevaluation of fundamental assumptions.']}