Fubini said:
What is the accepted view of spacetime?
Do we think we really live in a four-dimensional spacetime, or is it accepted that we live in a three-dimensional space but where four-dimensional spacetime is the correct way to model causality?
jtbell said:
What is the difference (in experimental terms) between four-dimensional spacetime being "real" versus being a "model"?
I like JT's answer. If operationally there is no difference then in some sense you can't ask Fubini's question. Except as an aesthetic or mathematical stylistic question. Which way is NICER to model the universe?
Is it nicer or more elegant to think of it as spatialgeometry+matter that is wiggling and waggling and dynamically changing according to some rules.
Or is it nicer to picture it as an eternal crystal.
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But people who do research in quantum gravity
do ask this kind of question. Even if it is slippery, and has problems of operational definition as JT points out, they keep asking this type of question.
A good paper to read, for perspective, is November 2007 by Renate Loll.
http://arxiv.org/abs/0711.0273
The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
A classical spacetime is a PATH from a beginning spatialgeometry to a final spatialgeomtry-----like the classic trajectory of a particle from startposition to endposition.
But we cannot say that the classic trajectory EXISTS. We can only observe the particle at various places where we observe it. We cannot say what it did in between.
So there is the FEYNMAN PATHINTEGRAL, an amplitude-weighted sum over histories, to handle that.
So by analogy
we cannot say that the classic 4D spacetime exists because there is really just an amplitude-weighted sum of different ways the universe can evolve from some initial geometry to some final geometry.
Bohr said physics is not concerned with what exists, physics concerns what we can say about nature. Or something like that. We cannot say a 4D spacetime exists because that would be a classic trajectory in a realm of geometries and classic trajectories do not exist, they are just useful idealization.
OK. I don't say Loll is right or wrong. I just say that right now Loll is philosophically at the forefront of Quantum Geometry and Gravity. To understand Fubini's question you have to at least look at Loll's paper and see what it says. Gravity is geometry. Quantum gravity is quantum geometry. Quantum is more realistic. There are only a handful of people. You have to look if you want to address the question.
Loll's team at Utrecht does computer simulations where they have small universes come into existence in the computer, and grow (according to quantum version of Einstein rule) and then shrink down and disappear.
Each spacetime is a path from a minimal state back to a minimal state. they can study each spacetime individually and measure things about it
they can also take weighted averages and correlations and study that stuff.
Another person who considers Fubini's question in a careful way, and has insightful things to say on the subject is Carlo Rovelli. Google the name, go to his website, read chapter one of the free version of his book.
