Non-geometric approach to gravity impossible?

[atyy]

The FRW solutions have matter everywhere. In the case where they don't have matter anywhere, we get the Milne universe.

 

[waterfall]

The FRW solutions have matter everywhere. In the case where they don't have matter anywhere, we get the Milne universe.

I know that. But you are not answering my questions for over 4 days already. Well. I'll re words them in the following context.

Curved Spacetime = Flat Spacetime + spin-2 Field
FRW Spacetime = Milne Spacetime + Spin-2 Field

In the first case, the spin-2 field stands for matter and attraction. Without matter. It's

Curved Spacetime = Flat Spacetime meaning there is no curved spacetime and all flat.

Hence without matter. It's FRW Spacetime = Milne Spacetime meaning there is no curvature hence the universe would be a Milne and all flat.

Can't you see the analogy. It's plain logic 101. Where is the flaw? Can't anyone see where I'm coming from or stating? Please address this directly and not discuss others. Maybe you reply will be "Curved spacetime is classical" or others totally irrelevant to my questions!

 

[Mentz114]

Curved Spacetime = Flat Spacetime + spin-2 Field

Not true.

FRW Spacetime = Milne Spacetime + Spin-2 Field

Not true.

The Milne spacetime is the Minkowski spacetime with a weird coordinate transformation which gives an expanding spatial coordinates so that a 'comoving' observer sees all other comoving observers moving away.

The FRW solution is that of non-interacting matter in an expanding or contracting spactime.

You can't add metrics (spacetimes) together.

 

[atyy]

Not true.

Why not? Isn't the only requirement to write the EFEs as a field on flat spacetime that the curved spacetime be coverable by harmonic cooridinates? Weinberg gives the FRW solution in harmonic coordinates in his textbook.

There's a similar viewpoint in http://relativity.livingreviews.org/Articles/lrr-2006-3/index.html Eq 62. "Equation (62) is exact, and depends only on the assumption that spacetime can be covered by harmonic coordinates."

 

[bcrowell]

Here are two other useful sources of information on this:

Feynman Lectures on Gravitation. This has a 1995 foreword by Preskill and Thorne, which describes in considerable detail the ideas behind the argument that the spin-2 theory is equivalent to GR. This suggests that if there are doubts about the validity of this claim of equivalence to GR, those doubts were either not known in 1995 or not taken seriously enough by Preskill and Thorne to be worthy of mention -- in a lengthy foreword to an entire book that is mainly concerned with this topic.

L.Butcher, M.Hobson and A.Lasenby, Phys. Rev D80 084014(2009),
http://arxiv.org/abs/0906.0926

Deser, Gravity from self-interaction redux, 2009, http://arxiv.org/abs/0910.2975

 

[Mentz114]

Ben, thanks for the Deser reference. Now to hear it from the man himself ...

 

[waterfall]

Here are two other useful sources of information on this:

Feynman Lectures on Gravitation. This has a 1995 foreword by Preskill and Thorne, which describes in considerable detail the ideas behind the argument that the spin-2 theory is equivalent to GR. This suggests that if there are doubts about the validity of this claim of equivalence to GR, those doubts were either not known in 1995 or not taken seriously enough by Preskill and Thorne to be worthy of mention -- in a lengthy foreword to an entire book that is mainly concerned with this topic.

L.Butcher, M.Hobson and A.Lasenby, Phys. Rev D80 084014(2009),
http://arxiv.org/abs/0906.0926

Deser, Gravity from self-interaction redux, 2009, http://arxiv.org/abs/0910.2975

hi bcrowel.. I'd been asking something from atyy and for 5 days he isn't answering it directly so I'm so frustrated now and gave up asking him. Now let me ask it to you maybe you understand what I'm talking about. It's just very simple. It's like this.

FRW spacetime is curved, right? Now from the theory that spin-2 field in flat spacetime is equivalent to GR (curved spacetime). Then why can't the FRW spacetime be formulated as spin-2 field in flat spacetime? And how does one do it? Do you turn the FRW spacetime first into flat equivalent which may be the Milne Spacetime and then add spin-2 field? or if you haven't heard of Milne. Just reply using the simple statement how do you turn the FRW spacetime into flat spacetime + spin-2 fields. Thanks.

 

[Mentz114]

Why not? Isn't the only requirement to write the EFEs as a field on flat spacetime that the curved spacetime be coverable by harmonic cooridinates? Weinberg gives the FRW solution in harmonic coordinates in his textbook.

There's a similar viewpoint in http://relativity.livingreviews.org/Articles/lrr-2006-3/index.html Eq 62. "Equation (62) is exact, and depends only on the assumption that spacetime can be covered by harmonic coordinates."

I don't know what "curved spacetime be coverable by harmonic coordinates" means so I can't argue about this.

 

[atyy]

Then why can't the FRW spacetime be formulated as spin-2 field in flat spacetime?

But do we know it can't? I'm not sure, but my understanding is that it can.

 

[waterfall]

But do we know it can't? I'm not sure, but my understanding is that it can.

How? that's what I've asking your for the past 5 days.

 

[atyy]

How? that's what I've asking your for the past 5 days.

I don't know in detail. I can point you to Weinberg's text and you'll have to do some additional work yourself, but I believe it doable from general considerations.

 

[waterfall]

I don't know in detail. I can point you to Weinberg's text and you'll have to do some additional work yourself, but I believe it doable from general considerations.

I think this is how to do it. How does one decompose the FRW spacetime into flat and spin-2 fields. There is already a version of the flat in the Milne Spacetime. Therefore, perhaps one can imagine that our universe is really Flat or Milne Spacetime and spin-2 fields just turn it into FRW. You know that in Milne universe, there is zero energy density, no cosmic microwave background radiation, no matter of any kind. Now when you add the spin-2 fields. It would recreate FRW... hmm.. wait.. I think I see the problem. It seems adding spin-2 field is not enough to produce matter, one has to add matter. Therefore let me go to the original formulation of

Curved Spacetime = Flat Spacetime + Spin-2 Fields

How does one embed matter into the above? We forgot about matter. Is it like this?

Curved Spacetime = Flat Spacetime + Spin-2 Fields + Matter?

When one can do it. One can apply it to the FRW Spacetime.

 

[PAllen]

Ben, thanks for the Deser reference. Now to hear it from the man himself ...

I gave the same Deser link in #75.

 

[Mentz114]

I gave the same Deser link in #75.

Thanks, but I missed it. These threads have grown to unmanageable sizes ...

 

[bcrowell]

These threads have grown to unmanageable sizes ...

And none of us who have been posting have the combination of theory chops and several months of spare time that it's now clear would be needed to do more than skim through some of the literature and note what different experts seem to be claiming.

 

[waterfall]

I don't know in detail. I can point you to Weinberg's text and you'll have to do some additional work yourself, but I believe it doable from general considerations.

Ok. I have the MTW book. What particular pages can I find the answers of how to decompose the FRW Spacetime into flat space equivalent so that I can maybe contribute a future article in Sci.Am and and state that "You know, in FRW universe, it's not really curved, it only appeared curved. We are really living in flat spacetime with spin-2 field giving us the curveness." I'm sure the sci-am editors would love it.

 

[waterfall]

Ok. I have the MTW book. What particular pages can I find the answers of how to decompose the FRW Spacetime into flat space equivalent so that I can maybe contribute a future article in Sci.Am and and state that "You know, in FRW universe, it's not really curved, it only appeared curved. We are really living in flat spacetime with spin-2 field giving us the curveness." I'm sure the sci-am editors would love it.

If I can't find it in MTW.. the simplest I'd use is this:

In Milne universe, there is zero energy density, no cosmic microwave background radiation, no matter of any kind.

When one adds matter and spin-2 fields. Then it becomes FRW Universe with the curveness only as illusion".

I think the above makes sense. Do you agree with it atyy?

 

[PAllen]

If I can't find it in MTW.. the simplest I'd use is this:

In Milne universe, there is zero energy density, no cosmic microwave background radiation, no matter of any kind.

When one adds matter and spin-2 fields. Then it becomes FRW Universe with the curveness only as illusion".

I think the above makes sense. Do you agree with it atyy?

Or you could say the spin 2 field is illusion. The only thing that counts as clearly not subject to interpretation is predictions of observation or experiments. Beyond that, curvature and fields, both, are not observable per se.

 

[waterfall]

If I can't find it in MTW.. the simplest I'd use is this:

In Milne universe, there is zero energy density, no cosmic microwave background radiation, no matter of any kind.

When one adds matter and spin-2 fields. Then it becomes FRW Universe with the curveness only as illusion".

I think the above makes sense. Do you agree with it atyy?

You guys may ask what is the point of all this. The point is this. The mere facts about gravitons makes General Relativity just an effective field theory. Meaning GR is not a priori. What is a priori are gravitons. Note you can't combine gravitons and General Relativity because geometry can't have gravitons. Therefore let's accept the GR we are studying is not really a priori or primary. Perhaps just a classical limit. The true thing are the gravitons and spin-2 fields in flat spacetime. This is the real meat of it.

 

[PAllen]

You guys may ask what is the point of all this. The point is this. The mere facts about gravitons makes General Relativity just an effective field theory. Meaning GR is not a priori. What is a priori are gravitons. Note you can't combine gravitons and General Relativity because geometry can't have gravitons. Therefore let's accept the GR we are studying is not really a priori or primary. Perhaps just a classical limit. The true thing are the gravitons and spin-2 fields in flat spacetime. This is the real meat of it.

Note that no one has observed a graviton, and Tony Rothman has 'nearly proved' that no graviton will ever be detected in the way photons are. Further, in a graviton theory, the flatness of spacetime is inherently unobservable and unrelated to predictions of time or distance measurements.

 

[waterfall]

Note that no one has observed a graviton, and Tony Rothman has 'nearly proved' that no graviton will ever be detected in the way photons are. Further, in a graviton theory, the flatness of spacetime is inherently unobservable and unrelated to predictions of time or distance measurements.

But 97% of Ph.D.s believe in gravitons.. this is precisely what String Theory is about.. gravitons. The 3% are the Loop Quantum Gravity camp which believes geometry or GR is primary, they are just a minority.. so if you believe in the latter.. then you belong to the minority LQG camp.

 

[Passionflower]

But 97% of Ph.D.s believe in gravitons.. this is precisely what String Theory is about.. gravitons. The 3% are the Loop Quantum Gravity camp which believes geometry or GR is primary, they are just a minority.. so if you believe in the latter.. then you belong to the minority LQG camp.

Whether true or not, science is not about believing.

 

[waterfall]

Whether true or not, science is not about believing.

Bottomline is that we need a theory of quantum gravity. Gravitons are good approach becuase of the success of QED, Electroweak, Strong Force which is based on particles and quantum field theory. You can' make a geometry theory out of them. This is why Gravity force needs to follow the path of field approach. This is what makes String Theory so popular. And if you think String Theory has the geometry as a priori and the gravitons are just an excitation of the gravitational wave.. then you are wrong. Gravitons exist in string theory in the sense that when you have gravitons, you have gravity. And for gravitons to exist. You need quantum fields. This makes Geometry as secondary. This is the precise reasons why I want to understand more about spin-2 fields in flat spacetime. Because if they are unlikely on empirical grounds like FRW metric unable to decompose to spin-2 field + flat spacetime. Then we have to go to geometry and LQG may be a way to go or other geometry based theory.

 

[Vanadium 50]

And now we have moved beyond asking questions and into the realm of pushing your viewpoint.