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A: Is spacetime wholly a mathematical construct and not a real thing?

Bob KnightonTL;DR This is a complicated question and anyone who tells you a definitive answer one way or another is either a philosopher or is trying to sell you something. I justify arguments either way below, and conclude with the AdS/CFT correspondence, in which two theories on two vastly different spacet...

user76284
user76284
I don't see what's problematic about describing the curvature of a Riemannian manifold as "warping/bending/stretching/distorting/etc". That's literally what curvature means.
Bob Knighton
Bob Knighton
That’s what curvature means if you visualize a manifold as being embedded in a higher-dimensional ambient space, “bending” away from an idealized flatness. This is simply not a helpful way to think about it, IMO, and leads to a LOT of confusion/misinterpretation from novice physicists/lay people.
user76284
user76284
The extrinsic perspective isn't necessary. The Ricci scalar, for example, directly measures the distortion in the volume of small balls: en.wikipedia.org/wiki/…. Distortion/warping/bending/stretching/etc. aren't fundamentally extrinsic concepts (though they can sometimes be visualized that way).
Bob Knighton
Bob Knighton
Yes, intrinsic geometric properties can be described as “deformation” from flatness of certain geometric measurements, but the common popular explanation is that spacetime itself is warped/stretched/etc.. My point is that this explanation is highly misleading and often lead people to think of the oversimplified “trampoline” model often showed in popularized explanations.
Furthermore, the action-type sounds of words like bending/stretching/warping leads people to think of space as having curvature, which then evolves in time, which is a very not-relativistic way of looking at things. Instead, spacetime is a single object which doesn’t evolve, it just has curvature (at least classically — who the hell knows what’s happening at the quantum level).
Again, this is just a personal preference in how I teach. I think it’s important to be precise, else people start getting false ideas about trampolines and balls (and especially black holes).
bob
bob
+1 for the final quote!
Draco18s
Draco18s
05:02
@debo.stackoverflow ...and I understood most of it!
elliot svensson
elliot svensson
Now give critical review for this PBS documentary image! en.wikipedia.org/wiki/Big_Bang#/media/…
Bob Knighton
Bob Knighton
@cpburnz Thanks! I typed this on my iPad while getting out of bed this morning, so I wasn't the biggest on spell check.
Joshua Lin
Joshua Lin
I think I have to disagree with the dismissal of fabric as a useful picture of spacetime (or general riemannian manifolds) - the fact that they can be embedded in high enough dimensional space (of course preserving all the structure that we care about) means that it's still a useful picture to keep in mind... sure I can describe everything just by describing their algebraic properties - but pictures are good?
Ixrec
Ixrec
Indeed, any straightforward answer to this requires going beyond physics and into philosophy. If anyone is interested in the philosophy around "is spacetime real?", check out plato.stanford.edu/entries/spacetime-theories
Cort Ammon
Cort Ammon
@user76284 I find terms like "stretch" or "warp" provide an implication that space is supposed to have no curvature, and it is by an external action that they arrive in their final shape. They are terms which induce a curvature. Often this is a valid phrasing, so I can see why it is common, but when discussing very precise questions about whether spacetime is "real," they encourage unintended expectations about what reality should be. Terms like "curvature" do so to a much lesser degree.
jpmc26
jpmc26
05:02
@JoshuaLin How do you draw a 5 dimensional picture?
N. Steinle
N. Steinle
Lovely. Is that last quote also from Gannon's book?
Bob Knighton
Bob Knighton
@N.Steinle Nah, that last quote was just me rambling.
Drunken Code Monkey
Drunken Code Monkey
@BobKnighton I am a layperson, programmer by day, follower of everything science by night, and I have been avidly reading all physics papers and literature I can muster an understanding of for years. I always thought the fabric representation of space time was a nice image but couldn't possibly be right. This answer is the first time I understand well and truly the idea of a manifold, and WHY the fabric analogy is faulty. Thank you so much for this wonderful answer!
Anonymous
While interesting, this is not a real answer -- AdS/CFT just says different spacetimes can lead to the same physics, analogously different co-ordinate systems in relativity can lead to the same physics. That doesn't mean co-ordinates don't "exist". Your claim that this is a difficult question is not correct, it is an easy question, and the answer is "shut up" (or if you prefer, "shut up and calculate").
Joshua Lin
Joshua Lin
@jpmc26 with a little bit of difficulty

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