- #1
Cerenkov
- 274
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Hello.
I have some questions concerning this extract from, 'The Nature of Space and Time' the Isaac Newton Institute series of Lectures and debate between Stephen Hawking and Roger Penrose in 1994, published by Princeton University Press in 1996. I have crudely reproduced fig 4.1, using MS Paint.
Chapter 4. Quantum Theory and Spacetime. R. Penrose.
"The great physical theories of the twentieth century have been quantum theory (QT), special relativity (SR), general relativity (GR), and quantum field theory (QFT). These theories are not independent of each other: general relativity was built on special relativity, and quantum field theory has special relativity and quantum theory as inputs (see fig. 4.1)."
"Although these four theories have been remarkably successful, they are not without their problems. QFT has the problem that whenever you calculate the amplitude for a multiply-connected Feynman diagram, the answer is infinity. These infinities must be subtracted away or scaled away as part of the process of renormalization of the theory. GR predicts the existence of spacetime singularities."
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Penrose then goes on to briefly describe how it was hoped that QFT might “smear” out the singularities of GR in some way. He also writes that the divergence problems of QFT could be solved in part by an ultraviolet cutoff from GR.
Now to my questions.
1.
As well as renormalization, what other techniques are used in physics to eliminate or minimize infinities?
2.
Besides the infinities mentioned here where else in physics do infinities occur?
3.
Was Planck's solution to the Ultraviolet Catastrophe an example of how an infinity was 'tamed'?
4.
Is this the kind of 'taming' Penrose refers to when he talks about... 'an ultraviolet cutoff from GR'?
5.
I Googled 'taming infinities' and this link came up.
https://warwick.ac.uk/fac/sci/maths...2014/statmech/adk/abstracts/martin-taming.pdf
Relevant much?
6.
(Going out on a limb now, so please be gentle. My level of understanding is Basic, with a capital B.)
If I read this Wiki page right... https://en.wikipedia.org/wiki/Semiclassical_gravity ...should combine GR and QFT. Which might be illustrated in an extension of figure 4.1 by two lines emanating from the GR and QFT boxes, converging on a new box entitled, Semiclassical Gravity. Like this. Am I even warm?
7.
If so, won't the fundamental problems of each - singularities for GR and infinities for QFT - rear their ugly heads in Semiclassical gravity too?
Any help given at my Basic level would be greatly appreciated.
Thank you.
Cerenkov.
I have some questions concerning this extract from, 'The Nature of Space and Time' the Isaac Newton Institute series of Lectures and debate between Stephen Hawking and Roger Penrose in 1994, published by Princeton University Press in 1996. I have crudely reproduced fig 4.1, using MS Paint.
Chapter 4. Quantum Theory and Spacetime. R. Penrose.
"The great physical theories of the twentieth century have been quantum theory (QT), special relativity (SR), general relativity (GR), and quantum field theory (QFT). These theories are not independent of each other: general relativity was built on special relativity, and quantum field theory has special relativity and quantum theory as inputs (see fig. 4.1)."
"Although these four theories have been remarkably successful, they are not without their problems. QFT has the problem that whenever you calculate the amplitude for a multiply-connected Feynman diagram, the answer is infinity. These infinities must be subtracted away or scaled away as part of the process of renormalization of the theory. GR predicts the existence of spacetime singularities."
--------------------------------------------------------------------
Penrose then goes on to briefly describe how it was hoped that QFT might “smear” out the singularities of GR in some way. He also writes that the divergence problems of QFT could be solved in part by an ultraviolet cutoff from GR.
Now to my questions.
1.
As well as renormalization, what other techniques are used in physics to eliminate or minimize infinities?
2.
Besides the infinities mentioned here where else in physics do infinities occur?
3.
Was Planck's solution to the Ultraviolet Catastrophe an example of how an infinity was 'tamed'?
4.
Is this the kind of 'taming' Penrose refers to when he talks about... 'an ultraviolet cutoff from GR'?
5.
I Googled 'taming infinities' and this link came up.
https://warwick.ac.uk/fac/sci/maths...2014/statmech/adk/abstracts/martin-taming.pdf
Relevant much?
6.
(Going out on a limb now, so please be gentle. My level of understanding is Basic, with a capital B.)
If I read this Wiki page right... https://en.wikipedia.org/wiki/Semiclassical_gravity ...should combine GR and QFT. Which might be illustrated in an extension of figure 4.1 by two lines emanating from the GR and QFT boxes, converging on a new box entitled, Semiclassical Gravity. Like this. Am I even warm?
7.
If so, won't the fundamental problems of each - singularities for GR and infinities for QFT - rear their ugly heads in Semiclassical gravity too?
Any help given at my Basic level would be greatly appreciated.
Thank you.
Cerenkov.