‘Alien calculus’ could save particle physics from infinities
quantamagazine.org
‘Alien calculus’ could save particle physics from infinities
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Re: ‘Alien calculus’ could save particle physics from infinities
#2Finding a way around the problem of infinities in perturbative quantum theory/QFT would not only put the science on a more sound mathematical footing but would also greatly benefit it in other ways. It seems to me that with a rigorous mathematical foundation it's likely phenomena will emerge that would never have been obvious without it. We can only hope the 'discovery' of Écalle's work leads us along that path.
Re: ‘Alien calculus’ could save particle physics from infinities
#3Écalle's own summary can be found here: https://www.imo.universite-paris-saclay.fr/~jean.ecalle/fich...
Re: ‘Alien calculus’ could save particle physics from infinities
#4Écalle's own summary can be found here: https://www.imo.universite-paris-saclay.fr/~jean.ecalle/fich...
I am not a scientist, is this Alien calculus akin (somehow) to a derivative?
Re: ‘Alien calculus’ could save particle physics from infinities
#5Finding a way around the problem of infinities in perturbative quantum theory/QFT would not only put the science on a more sound mathematical footing but would also greatly benefit it in other ways. It seems to me that with a rigorous mathematical foundation it's likely phenomena will emerge that would never have been obvious without it. We can only hope the 'discovery' of Écalle's work leads us along that path.
Is t the problem of quantum gravity related? Does this being us closer to a grand unified theory?
Re: ‘Alien calculus’ could save particle physics from infinities
#6Écalle's own summary can be found here: https://www.imo.universite-paris-saclay.fr/~jean.ecalle/fich...
I am not a scientist, is this Alien calculus akin (somehow) to a derivative?
The capital delta acts like a "normal" derivative if you want to say so. In eq. 4, you can see the product rule which is one of the most defining features for any sort of calculus. However, I must admit that this summary will take me a lot of time to digest...
Re: ‘Alien calculus’ could save particle physics from infinities
#7> Tunneling is one of many nonperturbative phenomena in quantum physics, but nonperturbative effects are everywhere: The branching growth of snowflakes, the flow of a liquid through a pipe with holes, the orbits of planets in a solar system, the rippling of waves trapped between round islands, and countless other physical phenomena are nonperturbative.
This is beautiful. Any examples of using Écalle's method to solve three-body problem?
Re: ‘Alien calculus’ could save particle physics from infinities
#8Finding a way around the problem of infinities in perturbative quantum theory/QFT would not only put the science on a more sound mathematical footing but would also greatly benefit it in other ways. It seems to me that with a rigorous mathematical foundation it's likely phenomena will emerge that would never have been obvious without it. We can only hope the 'discovery' of Écalle's work leads us along that path.
Is t the problem of quantum gravity related? Does this being us closer to a grand unified theory?
A better understanding of Quantum Physics, or Physics in general will always bring us closer to either finding a grand unified theory, or being able to mathematically exclude the possibility of it.
Re: ‘Alien calculus’ could save particle physics from infinities
#9I really appreciate how writers at Quanta turn extremely complex and dry topics into a pleasurable read by mixing simple analogies with history. I really admire the skill it takes to break down these topics and make them fascinating for someone with no understanding of them, such as me.
Re: ‘Alien calculus’ could save particle physics from infinities
#10Earlier quoted context omitted.
Is t the problem of quantum gravity related? Does this being us closer to a grand unified theory?
A better understanding of Quantum Physics, or Physics in general will always bring us closer to either finding a grand unified theory, or being able to mathematically exclude the possibility of it.
"…or being able to mathematically exclude the possibility of it."
Good point, with the expense of even larger colliders, or where experimentation remains impossible resorting to mathematics is likely the only option.