A The "no metric, no nothing" view

[jake jot]

All normal relativists already adapted the point of view of "no metric, no thing"? Who are the relativists who don't?

John Stachel who wrote the book Einstein from B to Z is a veteran 90 year old relativist.

Einstein from 'B' to 'Z' - John Stachel - Google Books

Even relativists have not yet fully adopted the point of view, "no metric, no nothing". If you look at the way the general theory of relativity is formulated mathematically in even the most careful treatises, for example, you see this clearly. They start out by introducing a global manifold (the points of which are usually identified forthwith with events - I have already discussed that problem), and then put such structures on this manifold as the metric tensor field. Is that the way that anyone of us actually goes about solving the field equations of general relativity? Of course not. One first solves them on a generic patch, and then one tries to maximally extend the local solution (using some criteria for acceptable extensions) from that patch to a global manifold, which is not known ahead of time. Before solving the field equations, one generally doesn't know the global manifold on which the solution will turn out to be maximally extended. So we are pulling a swindle when we tell students, as our definitions imply, that you first pick the manifold and then solve the field equations on it."

Which textbooks are described as "introducing a global manifold (the points of which are usually identified forthwith with events - I have already discussed that problem), and then put such structures on this manifold as the metric tensor field."?

Who are the lecturers who "we are pulling a swindle when we tell students, as our definitions imply, that you first pick the manifold and then solve the field equations on it.". Why is our current GR not like this? What versions of GR are like this?

 

[Dale]

@jake jot why are you trying to study general relativity before studying Newton’s laws? This is doomed to be an unproductive discussion.

I have never heard of the “no metric no nothing” view. I cannot say if it is commonly held or not, only that it is not commonly known by that name.

 

[PeterDonis]

@jake jot I have responded to your post about this same issue in your other thread:

https://www.physicsforums.com/threads/general-relativistic-quantum-theory.997756/post-6441184

Please go read my response there. And it is not good forum etiquette to start a new thread about a question you already asked in another thread (and got a response to) without any link or other connection to that other thread.

If, after reading my response in the other thread, you decide you want to discuss this topic further purely as a relativity question, separate from the QM/quantum gravity question being discussed in the other thread, let me know by PM and I will try to separate out the two discussions. (But please consider carefully that, while you labeled this thread "A", I am not convinced you actually have the background in relativity to understand an "A" level discussion of this topic.) In the meantime, this thread is closed.