Cosmologic philosophy: twistors and spinors (Introduction)

by David Turell , Sunday, February 11, 2024, 20:01 (286 days ago) @ David Turell

Starts with Penrose:

https://www.newscientist.com/article/mg26134773-000-why-physicists-are-rethinking-the-r...

"The twistor was first dreamed up in the late 1960s by the University of Oxford mathematician Roger Penrose. He saw it as a tool that might help unite quantum theory with gravity. Twistor theory essentially seeks to encode the universe’s events – a particle collision, say – as twistors, whose interactions give us the physics we observe. But twistors can be broken down, mathematically speaking, into yet more geometrical objects called spinors. These come in two varieties, referred to as left and right-handed spinors.

"Woit is using spinors and twistors to create what he hopes are the foundations of a theory of everything. He describes space and time using vectors, which are mathematical instructions for how to move between two points in space and time – that are the product of two spinors. “The conventional thing to do has been to say that space-time vectors are products of a right-handed and a left-handed spinor,” says Woit. But he claims he has now worked out how to create space-time from two copies of the right-handed spinors.

"The beauty of it, says Woit, is that this “right-handed space-time” leaves the left-handed spinors free to create particle physics. In quantum field theory, spinors are used to describe fermions, the particles of ordinary matter. So Woit’s insights into spinor geometry might lead to laws describing the holy trinity of space, time and matter.

"The idea has got Woit excited. He has spent most of his career looking at other ideas, thinking they will go somewhere, and being disappointed. “But the more I looked at twistor theory, the more it didn’t fall apart,” he says. “Not only that, I keep discovering new ways in which it actually works.”

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"Berman agrees there is scope for improvement, but feels string theory is still the best candidate. “I just don’t see anything else with that level of complexity and achievement,” he says. But he adds that there is room for other approaches and we should encourage them: “We certainly shouldn’t throw stones at each other.”

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"Loll’s framework gets a good bit more sophisticated. Use not one sheet of space-time, but an ensemble of many layers, and she can recreate some features of quantum theory, which is encouraging. And, even if it is early days for the idea, Loll reckons there will be ways to probe it with real experiments connected to the radiation left over after the big bang. “We are getting towards observables that could conceivably have left some imprint in the cosmic microwave background radiation.”

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"The pair [Grimstrup and Aastrup] start with their configuration space, which is a description of space-time. But as they analysed the mathematics, they found the mathematical signatures of fermions encoded within the geometry. “What we are doing is simply considering the geometry of that space,” says Grimstrup. “By doing this, we relatively easily obtain the basic building blocks of both general relativity and quantum field theory. So the ‘stuff’ is there, but not as a part of the foundation.”

"Perhaps even more exciting is the fact that something akin to Einstein’s vision of gravity appears too. “Gravity plays no role in our construction in its initial form: gravity in this construction is emergent,” says Grimstrup. It isn’t yet clear whether this is actually general relativity. “We see promising signs, but we need to check a few things before we can say that with certainty.”

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"It is speculation at this point. That said, when Woit – who has long been known as an arch cynic – is excited about the search for a theory of everything again, maybe all bets are off. Playing with twistors has changed him, he says. “I’ve spent most of my life saying that I don’t have a convincing idea and I don’t know anyone who does. But now I’m sending people emails saying: ‘Oh, I have this great idea’.”

"Woit says it with a grin, acknowledging the hubris of thinking that maybe, after so many millennia, we might finally have cracked the universe open. “Of course, it may be that there’s something wrong with me,” he says. “Maybe I’ve just gotten old and just lost my way.'”

Comment: next Einstein needed. All this activity tells us the very old string theory is dying. These theories are too difficult for lay people to understand. Space-time is not really difficult. That tells us the next theory should reach a simple point.