Resolving the problem of time:
In Einstein’s theory of general relativity, gravity arises when a massive object distorts the fabric of spacetime the way a ball sinks into a piece of stretched cloth. Solving Einstein’s equations by using quantities that apply across all space and time coordinates could enable physicists to eventually find their ‘white whale’: a quantum theory of gravity. In a new article in EPJ H: Historical Perspectives on Contemporary Physics, Donald Salisbury from Austin College in Sherman, USA, explains how Peter Bergmann and Arthur Komar first proposed a way to get one step closer to this goal by using Hamilton-Jacobi techniques. These arose in the study of particle motion in order to obtain the complete set of solutions from a single function of particle position and constants of the motion.
Three of the four fundamental forces – strong, weak, and electromagnetic – hold under both the ordinary world of our everyday experience, modelled by classical physics, and the spooky world of quantum physics. Problems arise, though, when trying to apply to the fourth force, gravity, to the quantum world. In the 1960s and 1970s, Peter Bergmann of Syracuse University, New York and his associates recognised that in order to someday reconcile Einstein’s theory of general relativity with the quantum world, they needed to find quantities for determining events in space and time that applied across all frames of reference. They succeeded in doing this by using the Hamilton-Jacobi techniques.
This is in contrast to other researchers’ approaches, including that of John Wheeler and Bryce DeWitt, who thought it only essential to find quantities of space that applied across all frames of reference. By excluding time, their solutions result in ambiguities in the way time develops, which are known as the problem of time.
Salisbury concludes that because the approach taken by Bergmann and associates resolves the ambiguity in the way time develops, their approach deserves more recognition by those exploring an eventual theory of quantum gravity.
D. Salisbury. A History of observables and Hamilton-Jacobi approaches to general relativity EPJ H 47, 7 (2022). https://doi.org/10.1140/epjh/s13129-022-00039-8
(Score: 2) by hendrikboom on Saturday August 13 2022, @03:12PM (3 children)
Very interesting stuff. Unfortunately I'm discovering that my knowledge of even classical mechanics is too rusty. The summary of Cartan's work in page 4 leaves me somewhat lost. Unfortunately I don't have access to the book from 1922 in which Cartan presented it.
It'll take me a while to digest this, too.
(Score: 2) by hubie on Saturday August 13 2022, @05:21PM (2 children)
I can find Cartan's book [archive.org], but I sure can't read the French. :)
The note said that Cartan's approach was described in Yourgrau and Mandelstam (1968), which fortunately is available from archive as well [archive.org].
(Score: 2) by hendrikboom on Sunday August 14 2022, @11:06PM (1 child)
Haven't been able to get Yourgrau and Mandelstam from archive, though it is apparently avaiable on some kind of loan basis, or for purchase. Attempts to download the encrypted versions led nowhere. I have got Cartan's book as a pdf, and I might even be able to read it.
Thank you for the links.
(Score: 3, Interesting) by hubie on Sunday August 14 2022, @11:41PM
No problem. To borrow a book from archive, you need to register an account. I didn't try checking that book out, but I've done that with other books. If you do have an account and it isn't working, then there is probably some other issue. I think they went to the book loan model for books in copyright because of pressure from the publishing industry.