In the past 10 or so years, a combinatoric approach to particle interactions has shown surprisingly good results. Simple algebraic calculations have been able to give answers that requires hundreds of pages of math through the feynman diagram approach.
This is the amplituhedron, led by Nima Arkani-Hamed, here's an article also by quanta magazine about it
In addition to giving exact simple calculations to particle scattering amplitudes, the most important aspect is that it does so in a way that does not require notions of space or time. Leading to the notion that there are more fundamental aspects to reality and space and time may be emergent phenomena.
This is the third formulation I've come across that sounds like this with space and time emerging from particle interactions. The other two are from Stephen Wolfram and Carlo Rovelli. Are the formulations related do you know?
I've struggled to get beyond their popular science descriptions to the actual theories, I find descriptions like the amplituhedron being 'a multidimensional jewel' distracting, if you have any suggestions where to start for a deeper understanding of this one I'd be interested.
Until we get evidence of such a thing, those ideas have little credibility though they are nice thought experiments.
What they're really seeing is that mathematically something can be expressed with less dimensions or degrees of freedom than what you observe in the real world, and then make the conclusion that therefor the dimensions and properties etc. that we observe are some emergent property and not fundamental.
But you can't make this conclusion from the mathematical model.
For example, if I have a finite sized two dimensional plane where each point is associated with some function f(x,y),you can trivially express it as a one dimensional system where all the rows of the plane are sort of unwound onto a single line.
This trick does not work for infinite 2D spaces but there are other ways to remap infinite sized spaces onto finite ones (e.g. via tan).
Yet there's nothing fundamental about this, it's just a mathematical modelling trick.
this trick works for infinite sets of the same cardinality and in fact works continuously for the case you are describing. there is a surjective continuous function fron R to R^n for any n
The biggest clue we have right now is illustrated by last year's nobel prize. Particles in an entangled state can interact instantaneously, disregarding space and time entirely.
It's a common thing to see in theories that try to unify QM with GR because in GR spacetime is dynamic, while in QM it's static. For QM to produce GR, there needs to be some way of generating space and time instead of taking it as an assumption.
You can find quite a few lectures by Nima Arkani-Hamed on YouTube including some on the amplituhedron. But they are mostly not gentle introductions and require some knowledge of physics to follow along. I think this one [1] provides a lot of background and explains the motivation.
I used to follow his lectures, but in the past 3 or 4 years he's become really quiet. I wonder if people stopped inviting him because he always overruns his time limit, or if he's too busy making progress on his theory.
This is the amplituhedron, led by Nima Arkani-Hamed, here's an article also by quanta magazine about it
https://www.quantamagazine.org/physicists-discover-geometry-...
In addition to giving exact simple calculations to particle scattering amplitudes, the most important aspect is that it does so in a way that does not require notions of space or time. Leading to the notion that there are more fundamental aspects to reality and space and time may be emergent phenomena.