Amplituhedron - the shape of particle interaction

[Pigeon]

This might be quite a large find.

The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression.

Beyond making calculations easier or possibly leading the way to quantum gravity, the discovery of the amplituhedron could cause an even more profound shift, Arkani-Hamed said. That is, giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry.

“In a sense, we would see that change arises from the structure of the object,” he said. “But it’s not from the object changing. The object is basically timeless.”

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[Royal]

The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry.

I need more scientific understanding for this sentence.

Parke and Taylor guessed a simple one-term expression for the amplitude. It was, the computer verified, equivalent to the 9-page formula. In other words, the traditional machinery of quantum field theory, involving hundreds of Feynman diagrams worth thousands of mathematical terms, was obfuscating something much simpler. As Bourjaily put it: “Why are you summing up millions of things when the answer is just one function?”

There was an ancient mathematician or philosopher that tried to come up with a geometric object to explain all matter but failed. Looks like he was on to the same thing.

Recently, a strange duality has been found between string theory and quantum field theory, indicating that the former (which includes gravity) is mathematically equivalent to the latter (which does not) when the two theories describe the same event as if it is taking place in different numbers of dimensions.

The strange duality discussed here:
viewtopic.php?f=18&t=3033

No one knows quite what to make of this discovery. But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway.

Would you know how to explain this last sentence?

[Pigeon]

No one knows quite what to make of this discovery. But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway.

Time would be a result of the shape and interactions, not some part of the underlying existence.

That is the very nature of the relativity of time - it is relative to matter and the energy acting upon it. Imagine if suddenly all matter ceased to be acted upon by energy - everything "froze" in an immutable and incessant state. The notion of time in our dimensional universe would cease to be meaningful. Likewise, if matter and energy never existed in some theoretical void, time would not exist (relatively) in that void either. We, as humans living within the constraints of our own time-space continuum, innately assume that same single continuum pertains everywhere and all at once. But it doesn't - as difficult as it may be to conceptualize that while imprisoned within the bounds of our continuum.

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