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Finding 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

Finding 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.

adastra22 4y ago
Is t the problem of quantum gravity related? Does this being us closer to a grand unified theory?
- once_inc 4y ago
  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.
  - hilbert42 4y ago
    "…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.
- pa7x1 4y ago
  It's related in the sense that the vanilla attempts to quantize gravity lead to infinities as described in the article. But the nature of these infinities is more troubling in the case of quantum gravity than those found in the rest of the theories that compose the Standard Model. Infinities appear very early in the series expansion of quantized gravity, at second order of the series expansion for the free theory. And the techniques developed by physicists to deal with them ( https://en.wikipedia.org/wiki/Renormalization https://en.wikipedia.org/wiki/Renormalization ) do not work at all. It's possible that the mathematical techniques being developed here only work for renormalizable theories. In which case they wouldn't work at all for Quantum Gravity. This would likely signal that there is something else missing that is needed to build a quantum theory of gravity.
  - hilbert42 4y ago
    I recall reading a book on String Theory in the late 1990s edited by Ed Witten where he mentions the problems with physics and the limits of mathematical techniques. It's long ago so I can't paraphrase his words accurately but he did so with such eloquence that I've long remembered the fact. He pitched the problem in terms of both existing physics and of new '21st Century' ideas inklings of which had somehow trickled down into the 20th Century and that physicists needed new mathematics to deal with them (I hope I've not mangled his words too much). Nevertheless, I'm still in awe of Schwinger, Feynman et al who actually made renormalization work despite—according to Feynman—it being a 'dippy process'. These guys were truly physics and mathematics 'magicians'.
    - mindcrime 4y ago
      He pitched the problem in terms of both existing physics and of new '21st Century' ideas inklings of which had somehow trickled down into the 20th Century and that physicists needed new mathematics to deal with them (I hope I've not mangled his words too much). It has definitely been said that "String theory is part of 21st-century physics that fell by chance into the 20th century.". I can recall seeing variations of that quote in a few different books over the years. Interestingly though, a quick Google search (maybe I should have asked ChatGPT?) shows attributions to both Witten and Daniele Amati. So I'm not sure who said that particular bit first.
      - hilbert42 4y ago
        Not surprised, it's a memorable quote. Some months ago, I mentioned the book to the colleague who originally loaned it to me with the view of borrowing it again but he no longer has it. I then did a quick search and couldn't place it. This has spurred me to look again, perhaps starting with GPT.

adastra22 4y ago

Is t the problem of quantum gravity related? Does this being us closer to a grand unified theory?

once_inc 4y ago
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.
- hilbert42 4y ago
  "…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.
pa7x1 4y ago
It's related in the sense that the vanilla attempts to quantize gravity lead to infinities as described in the article. But the nature of these infinities is more troubling in the case of quantum gravity than those found in the rest of the theories that compose the Standard Model. Infinities appear very early in the series expansion of quantized gravity, at second order of the series expansion for the free theory. And the techniques developed by physicists to deal with them ( https://en.wikipedia.org/wiki/Renormalization https://en.wikipedia.org/wiki/Renormalization ) do not work at all. It's possible that the mathematical techniques being developed here only work for renormalizable theories. In which case they wouldn't work at all for Quantum Gravity. This would likely signal that there is something else missing that is needed to build a quantum theory of gravity.
- hilbert42 4y ago
  I recall reading a book on String Theory in the late 1990s edited by Ed Witten where he mentions the problems with physics and the limits of mathematical techniques. It's long ago so I can't paraphrase his words accurately but he did so with such eloquence that I've long remembered the fact. He pitched the problem in terms of both existing physics and of new '21st Century' ideas inklings of which had somehow trickled down into the 20th Century and that physicists needed new mathematics to deal with them (I hope I've not mangled his words too much). Nevertheless, I'm still in awe of Schwinger, Feynman et al who actually made renormalization work despite—according to Feynman—it being a 'dippy process'. These guys were truly physics and mathematics 'magicians'.
  - mindcrime 4y ago
    He pitched the problem in terms of both existing physics and of new '21st Century' ideas inklings of which had somehow trickled down into the 20th Century and that physicists needed new mathematics to deal with them (I hope I've not mangled his words too much). It has definitely been said that "String theory is part of 21st-century physics that fell by chance into the 20th century.". I can recall seeing variations of that quote in a few different books over the years. Interestingly though, a quick Google search (maybe I should have asked ChatGPT?) shows attributions to both Witten and Daniele Amati. So I'm not sure who said that particular bit first.
    - hilbert42 4y ago
      Not surprised, it's a memorable quote. Some months ago, I mentioned the book to the colleague who originally loaned it to me with the view of borrowing it again but he no longer has it. I then did a quick search and couldn't place it. This has spurred me to look again, perhaps starting with GPT.