Mar 6, 2019 04:08 AM
https://www.quantamagazine.org/the-unive...-20190305/
EXCERPT: . . . John Stewart Bell came up with “nonlocal” games, which require players to be at a distance from each other with no way to communicate. Each player answers a question. The players win or lose based on the compatibility of their answers. One such game is the magic square game. [...] In the magic square game, and other games like it, there doesn’t seem to be a way for the players to win 100 percent of the time. And indeed, in a world completely explained by classical physics, 89 percent is the best Alice and Bob could do. But quantum mechanics — specifically, the bizarre quantum phenomenon of “entanglement” — allows Alice and Bob to do better.
In quantum mechanics [...] When two particles are entangled ... This relationship between the two ... holds when they’re right next to each other and when they’re light-years apart: Even at that distance, if you measure the position of one electron, the position of the other becomes instantly determined, even though no causal event has passed between them. The phenomenon seems preposterous because there’s nothing about our non-quantum-scale experience to suggest such a thing is possible....
To implement a quantum strategy in the magic square game, Alice and Bob each take one of a pair of entangled particles. To determine which numbers to write down, they measure properties of their particles — almost as if they were rolling correlated dice to guide their choice of answers. What Bell calculated, and what many subsequent experiments have shown, is that by exploiting the strange quantum correlations found in entanglement, players of games like the magic square game can coordinate their answers with greater exactness and win the game more than 89 percent of the time.
Bell came up with nonlocal games as a way to show that entanglement was real, and that our classical view of the world was incomplete — a conclusion that was very much up for grabs in Bell’s time. “Bell came up with this experiment you could do in a laboratory,” Cleve said. If you recorded higher-than-expected success rates in these experimental games, you’d know the players had to be exploiting some feature of the physical world not explained by classical physics.
What William Slofstra and others have done since then is similar in strategy, but different in scope. They’ve shown that not only do Bell’s games imply the reality of entanglement, but some games have the power to imply a whole lot more — like whether there is any limit to the number of configurations the universe can take.
[...] Slofstra’s result came as a shock. Eleven days after his paper appeared, the computer scientist Scott Aaronson wrote that Slofstra’s result touches “on a question of almost metaphysical significance: namely, what sorts of experimental evidence could possibly bear on whether the universe was discrete or continuous?”
Aaronson was referring to the different states the universe can take — where a state is a particular configuration of all the matter within it. Every physical system has its own state space, which is an index of all the different states it can take. Researchers talk about a state space as having a certain number of dimensions, reflecting the number of independent characteristics you can adjust in the underlying system.
A deep question about the physical world is whether there’s a limit to the size of the state space of the universe (or of any physical system). If there is a limit, it means that no matter how large and complicated your physical system is, there are still only so many ways it can be configured. “The question is whether physics allows there to be physical systems that have an infinite number of properties that are independent of each other that you could in principle observe,” said Thomas Vidick, a computer scientist at the California Institute of Technology.
The field of physics is undecided on this point. In fact, it maintains two contradictory views. On the one hand, students in an introductory quantum mechanics course are taught to think in terms of infinite-dimensional state spaces. [...] But perhaps the idea of infinite-dimensional state spaces is nonsense. In the 1970s, the physicists Jacob Bekenstein and Stephen Hawking calculated that a black hole is the most complicated physical system in the universe, yet even its state can be specified by a huge but finite number of parameters ...
These competing perspectives on state spaces reflect fundamentally different views about the nature of physical reality. If state spaces are truly finite-dimensional, this means that at the smallest scale, nature is pixelated. But if electrons require infinite-dimensional state spaces, physical reality is fundamentally continuous — an unbroken sheet even at the finest resolution.
So which is it? Physics hasn’t devised an answer, but games like Slofstra’s could, in principle, provide one....
MORE (details): https://www.quantamagazine.org/the-unive...-20190305/
EXCERPT: . . . John Stewart Bell came up with “nonlocal” games, which require players to be at a distance from each other with no way to communicate. Each player answers a question. The players win or lose based on the compatibility of their answers. One such game is the magic square game. [...] In the magic square game, and other games like it, there doesn’t seem to be a way for the players to win 100 percent of the time. And indeed, in a world completely explained by classical physics, 89 percent is the best Alice and Bob could do. But quantum mechanics — specifically, the bizarre quantum phenomenon of “entanglement” — allows Alice and Bob to do better.
In quantum mechanics [...] When two particles are entangled ... This relationship between the two ... holds when they’re right next to each other and when they’re light-years apart: Even at that distance, if you measure the position of one electron, the position of the other becomes instantly determined, even though no causal event has passed between them. The phenomenon seems preposterous because there’s nothing about our non-quantum-scale experience to suggest such a thing is possible....
To implement a quantum strategy in the magic square game, Alice and Bob each take one of a pair of entangled particles. To determine which numbers to write down, they measure properties of their particles — almost as if they were rolling correlated dice to guide their choice of answers. What Bell calculated, and what many subsequent experiments have shown, is that by exploiting the strange quantum correlations found in entanglement, players of games like the magic square game can coordinate their answers with greater exactness and win the game more than 89 percent of the time.
Bell came up with nonlocal games as a way to show that entanglement was real, and that our classical view of the world was incomplete — a conclusion that was very much up for grabs in Bell’s time. “Bell came up with this experiment you could do in a laboratory,” Cleve said. If you recorded higher-than-expected success rates in these experimental games, you’d know the players had to be exploiting some feature of the physical world not explained by classical physics.
What William Slofstra and others have done since then is similar in strategy, but different in scope. They’ve shown that not only do Bell’s games imply the reality of entanglement, but some games have the power to imply a whole lot more — like whether there is any limit to the number of configurations the universe can take.
[...] Slofstra’s result came as a shock. Eleven days after his paper appeared, the computer scientist Scott Aaronson wrote that Slofstra’s result touches “on a question of almost metaphysical significance: namely, what sorts of experimental evidence could possibly bear on whether the universe was discrete or continuous?”
Aaronson was referring to the different states the universe can take — where a state is a particular configuration of all the matter within it. Every physical system has its own state space, which is an index of all the different states it can take. Researchers talk about a state space as having a certain number of dimensions, reflecting the number of independent characteristics you can adjust in the underlying system.
A deep question about the physical world is whether there’s a limit to the size of the state space of the universe (or of any physical system). If there is a limit, it means that no matter how large and complicated your physical system is, there are still only so many ways it can be configured. “The question is whether physics allows there to be physical systems that have an infinite number of properties that are independent of each other that you could in principle observe,” said Thomas Vidick, a computer scientist at the California Institute of Technology.
The field of physics is undecided on this point. In fact, it maintains two contradictory views. On the one hand, students in an introductory quantum mechanics course are taught to think in terms of infinite-dimensional state spaces. [...] But perhaps the idea of infinite-dimensional state spaces is nonsense. In the 1970s, the physicists Jacob Bekenstein and Stephen Hawking calculated that a black hole is the most complicated physical system in the universe, yet even its state can be specified by a huge but finite number of parameters ...
These competing perspectives on state spaces reflect fundamentally different views about the nature of physical reality. If state spaces are truly finite-dimensional, this means that at the smallest scale, nature is pixelated. But if electrons require infinite-dimensional state spaces, physical reality is fundamentally continuous — an unbroken sheet even at the finest resolution.
So which is it? Physics hasn’t devised an answer, but games like Slofstra’s could, in principle, provide one....
MORE (details): https://www.quantamagazine.org/the-unive...-20190305/
