The Flaws of General Relativity: Is Space Really Constant and Defined?

[Ikoro]

Why is that general relativity does not define what space is. It just says when there is a stress-energy tensor in space it creates an einstein curvature and to mathematically balance it adds the cosmological constant. Space has to be defined for the equation to make complete sense given the fact that space is expanding. So how is it that something we cannot see is expanding and yet the gravitational curvature is still constant on earth(even though space is stretching out). Does that make you wonder whether Einstein got the equations backward.

 

[Vanadium 50]

Why is it GR's (or any theory's) responsibility to tell us what anything "is"? It tells us how things behave - particularly how curvature depends on stress-energy. What things "really are" is the realm of philosophy.

Let me remind everyone that this thread should not move into the realm of personal theories.

 

[bcrowell]

I would tend to agree with Vanadium 50's philosophical tack on whether GR should be able to say what space "is." It would be cool if some deeper theory, such as loop quantum gravity, could explain spacetime as emerging from something more basic via some definite mechanism. But just as every mathematical theory has to start from some axioms, every physical theory is going to have some things that it can't explain.

So how is it that something we cannot see is expanding and yet the gravitational curvature is still constant on earth(even though space is stretching out).

For a discussion of this, see http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.2 , subsection 8.2.5.

 

[atyy]

Why is that general relativity does not define what space is. It just says when there is a stress-energy tensor in space it creates an einstein curvature and to mathematically balance it adds the cosmological constant. Space has to be defined for the equation to make complete sense given the fact that space is expanding. So how is it that something we cannot see is expanding and yet the gravitational curvature is still constant on earth(even though space is stretching out). Does that make you wonder whether Einstein got the equations backward.

No you have it backward - the incompleteness of G=T is that it does not say what matter is!

 

[atyy]

For a discussion of this, see http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.2 , subsection 8.2.5.

FRW is not flat spacetime in general, but I think there is a particular solution in the FRW family that is flat spacetime.

George Jones gives the coordinate transformations somewhere here https://www.physicsforums.com/showthread.php?t=234224

 

[bcrowell]

FRW is not flat spacetime in general, but I think there is a particular solution in the FRW family that is flat spacetime.

George Jones gives the coordinate transformations somewhere here https://www.physicsforums.com/showthread.php?t=234224

The thread you linked to is very interesting, but I think I'm missing something. Is there a link between this and the quote from my #3? I don't see the connection. I don't think anyone in the present thread has said anything about flat spacetime, or about spatial flatness, which is what the thread you linked to seems to be about.

 

[atyy]

The thread you linked to is very interesting, but I think I'm missing something. Is there a link between this and the quote from my #3? I don't see the connection. I don't think anyone in the present thread has said anything about flat spacetime, or about spatial flatness, which is what the thread you linked to seems to be about.

It was just a side comment on "Since the Einstein tensor is nonzero for an FRW metric, and zero for a flat-space metric, the claim is false.", but I see you actually addressed this in 8.2.4.

 

[bcrowell]

It was just a side comment on "Since the Einstein tensor is nonzero for an FRW metric, and zero for a flat-space metric, the claim is false.", but I see you actually addressed this in 8.2.4.

Ah, I see. Thanks for the correction! It should just say "flat," not "flat-space."

 

[Troponin]

Why is that general relativity does not define what space is. It just says when there is a stress-energy tensor in space it creates an einstein curvature and to mathematically balance it adds the cosmological constant. Space has to be defined for the equation to make complete sense

That sounds more like a personal philosophy. I don't need a worded definition for space in order for it to be complete. I'd actually prefer that it be defined by the mathematics so as to avoid the semantics and possible ambiguity of defining it with words as well.

Does that make you wonder whether Einstein got the equations backward.

What do you mean by this? By "backwards," do you mean that instead of mass (energy) causing the geometry of space, the theory should have been formulated such that the geometry of space causes the gravity?

People have addressed this lack of symmetry between "gravity causes geometry" but "geometry doesn't cause gravity." I don't have any of them referenced off the top of my head, but I know I've come across papers on the subject.

 

[Ikoro]

After a long time i have come to a conclusion since the stress tensor= F/A then it is a logical way to go about the equation. So I do now believe that Einstein does give a full depth. where my question now makes a standing is in one of my forums: Cosmological Constant. because if we can explain the higgs field we may well be able to explain the vacuum as a hole.

 

[Phrak]

No you have it backward - the incompleteness of G=T is that it does not say what matter is!

This thread is a month old, but if you are still monitoring atty, I disagree to an extent. An equation can say two things. It can be an equivalence or an equality. Taken as an equality, mass-energy-momentum density is the curvature of space; they are one and the same thing. I prefer this until shown otherwise.

 

[Dale]

FWIW, space is the thing measured by a rod IMO. Space is well-defined.

 

[Naty1]

Why is that general relativity does not define what space is.

take your pick:
(a) Einstein wasn't interested ,
(b) It is not important to Einstein's formulation,
(c) Einstein realized he would not be able to do that,
(d) Einstein saved that for his Grand Unification efforts,
(e) nobody is smart enough to know yet.
(f) Crowells' comment:

every physical theory is going to have some things that it can't explain.

[You solve what you can.]

I don't buy Vanadium's:

What things "really are" is the realm of philosophy.

It's worth noting that supposed "failing" of GR is not what interests most scientists but rather it's small scale weaknesses...

 

[kamenjar]

I think that Mach thought that space "is" a field that all matter in the universe exerts on us.
I read somewhere an interesting example...

If were spacewalking and someone was to start to spin you in space, even if you were blindfolded, you would know that you were spinning because you would feel it.

If you were dropped into "no space", where there aren't any stars, you would feel nothing and you would feel no spinning because there would be no objects to move against.

It doesn't define what space is, but it is something that maybe helps understand it better.

 

[Naty1]

What Ernest "thought" and what's "actual" are two different things:

If you were dropped into "no space", where there aren't any stars, you would feel nothing and you would feel no spinning because there would be no objects to move against.

did have some poeple confused for a while... but it violates Einstein's equivalence principle...

 

[Garth]

FWIW, space is the thing measured by a rod IMO. Space is well-defined.

The problem with that is that we don't have rods that extend to the nearest heavenly body, the Moon, let alone the depths of space.

In practice we use light and other forms of electromagnetic radiation, and perhaps in the future, gravitational radiation, to observe and measure 'space'.

Garth