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Someone claiming to have studied physics is telling me that spacetime is all that exists and that this fact is the basis of modern physics. When I said matter/energy also exists in its various forms, he said that energy is merely spacetime "waving/vibrating/acting", else what did I think was doing the waving: magical fairy dust? and has presented the following Einstein quote to support his claim:

"When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter."

Does Einstein's quote support what he's saying, that space-time is all that exists, and that matter/energy is spacetime waving?

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You should stop listening to this person; the way you phrase what he's saying, at leadst, makes him seem like a crackpot. –  Dimensio1n0 Sep 16 '13 at 13:19
    
@DImension10 Isn't it correct from string theory point of view where "spacetime fields" $X^{\mu}$ (along with fermions $\Psi^{\mu}$ which too can be thought of as anticommuting extension of spacetime) are the basic constituent of matter? –  user10001 Sep 16 '13 at 13:59
    
@user10001: Sure, I was talking about the fact that this "someone" (who said this to the OP) is a crackpot, as he's only blabbering philosophical spacetime. –  Dimensio1n0 Sep 16 '13 at 14:04
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I think some of the strong negative comments on this question are not warranted. I don't know the source of the Einstein quote, but it's possible he might have been referring to the Kaluza-Klein theory, which, although since disproved, was a theory much like what you describe. –  Nathaniel Sep 16 '13 at 14:54
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The similar quote in Prathyush's comment is from a 1950 piece that Einstein wrote for Scientific American. You can find copies online by googling for its title, "On the generalized theory of gravitation." The article presents a lot of complex ideas and is not something that can be reduced to a sound bite. A modern reader can immediately tell that it's extremely out of date. Examples: (1) He presents the distinction between SR and GR in terms of accelerated frames. (2) He thinks GR is consistent with Mach's principle. (3) He's focused on classical unified theories. –  Ben Crowell Sep 16 '13 at 20:14
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2 Answers

When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter.

This reads to me as a statement of Mach's principle, probably from very early in the history of GR. Einstein originally thought that GR would embody Mach's principle. He was wrong, but it took decades for this to become completely clarified. For a longer discussion of Mach's principle, see this question: Is Mach's Principle Wrong?

As a counterexample to Einstein's claim, gravitational waves carry energy, and they exist independently of matter. (They don't even need to be generated by matter -- it's very reasonable to expect the existence of gravitational waves as a result of the Big Bang, and in fact in a maximum-entropy Big Bang, almost all the energy and entropy would have been in that form.) For precisely this reason, Einstein didn't want to believe that gravitational waves were real or detectable. He published an erroneous paper claiming that they were just a coordinate effect, and he never admitted later that the paper was wrong.

Even very early on in the history of GR, Einstein was dismayed by the existence of the Schwarzschild solution as an exact solution of the field equations. He didn't like it on Machian grounds, since it described a gravitational field surrounding a single pointlike object, but based on Mach's principle such a thing should have no physical meaning unless there were two objects interacting.

When I said matter/energy also exists in its various forms, he said that energy is merely spacetime "waving/vibrating/acting",

This is conceivable, but is considered unlikely. See the WP article on geons. As a simple counterargument, if spacetime is "waving," then we're talking about a gravitational wave. But gravitational waves carry no electric charge.

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Of course, there's a version of Mach's principle, where you could argue that the inertia in the Schwarzschild spacetime is set by the asymptotic flatness of the solution, as is also the case inside a spinning thin shell of mass. The problem with Mach's principle is that it's vague enough that it can never really be true or false (or at least, you can motivate a "Mach's principle" that is inspired enough by GR that it is consistent). I wish people would stop teaching it, irrespecitvely. It's more misleading than it is instructive. –  Jerry Schirmer Sep 16 '13 at 22:48
    
@JerrySchirmer: Of course, there's a version of Mach's principle, where you could argue that the inertia in the Schwarzschild spacetime is set by the asymptotic flatness of the solution I've never seen Mach's principle formulated in this way, and it doesn't seem reasonable to me. Mach's principle has to do with distant matter, not with asymptotic properties of empty space. I really don't think this is controversial. Re vagueness, I disagree, for the admittedly more subjective reasons given in my answer to physics.stackexchange.com/questions/5483/… . –  Ben Crowell Sep 17 '13 at 3:48
    
I get what you're saying, but I don't see why 'the distant stars' couldn't just as easily be interpreted to mean 'the sphere at infinity' in a modern sense. It's just a different interpretation of the same basic idea, and I've seen John Archibald Wheeler write it down this way before.. –  Jerry Schirmer Sep 17 '13 at 4:11
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I don't think Einstein is anything about space time dynamics containing the description of matter and their properties. Or even about Gravitational waves existing independently without any matter being present.

I think he is saying something very different all together( and I could be wrong).

Space time is defined through how events co-ordinate, and an event by its definition implies that it is a material interaction. So any perception of space time and its properties implicitly contains within the limitation that we have to use matter and its properties to probe it. Thus spacetime is meaningless if it is seen to exist separately from the material whose behavior it describes.

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