FRW universe, expanding space or spacetime?

[waterfall]

If space doesn't expand, the big-bang is not possible. In the FRW model there is some beginning time when there is no space. I think this depends on choice of coordinates. But observations, particularly the CBR, give strong support to the BB theory. If I remember correctly, FTG does not do as well as GR in explaining observations.

If you're looking for a way to quantize gravity using the standard treatments, you'd do better with teleparallel gravity.

Now if cosmological observations prove beyond the shadow of a doubt that space indeed expand. Then spin-2 field over flat spacetime as a priori is falsified. If so. Then all quantum gravity theories that use gravitons in this terms like string theories are falsified. Think of the implications if space indeed expand. What do you think

 

[Dale]

I imagine a manifold as like a map of the Earth with coordinates or latitudes or longitudes.

Actually, the (pseudo-Riemannian) manifold is like the map without the coordinates. The manifold defines ideas of connectedness and neighborhoods (topology), i.e, you can talk about small regions of the manifold near a point in the manifold, and also notions of distances and angles (metric).

One of the key features of manifolds is that if you zoom into a small region near any point it looks like Rn where n is the dimension of the manifold (4 in the case of spacetime). So a good example of a 2D manifold is the surface of a sphere. If you zoom into the surface of a sphere you can see that locally it looks like a 2D plane.

On top of the manifold you can add a coordinate system, called a coordinate chart, but the manifold is a topological and geometrical object which is independent of the coordinate chart used to describe it.

 

[waterfall]

Actually, the (pseudo-Riemannian) manifold is like the map without the coordinates. The manifold defines ideas of connectedness and neighborhoods (topology), i.e, you can talk about small regions of the manifold near a point in the manifold, and also notions of distances and angles (metric).

One of the key features of manifolds is that if you zoom into a small region near any point it looks like Rn where n is the dimension of the manifold (4 in the case of spacetime). So a good example of a 2D manifold is the surface of a sphere. If you zoom into the surface of a sphere you can see that locally it looks like a 2D plane.

On top of the manifold you can add a coordinate system, called a coordinate chart, but the manifold is a topological and geometrical object which is independent of the coordinate chart used to describe it.

Thanks. How come they say that if spacetime is discrete, then there is no manifold. Should a manifold be continuous up to the center of the Planck scale or can it be discontinuous with holes (planck hole) in betweeen?

 

[Mentz114]

Now if cosmological observations prove beyond the shadow of a doubt that space indeed expand. Then spin-2 field over flat spacetime as a priori is falsified. If so. Then all quantum gravity theories that use gravitons in this terms like string theories are falsified. Think of the implications if space indeed expand. What do you think

I certainly wouldn't come to those conclusions on the basis of what I understand. I see no difficulty in the coexistence of gravitons and expanding space.

[I have a memory of someone posting an arXiv paper about the flat spacetime + spin-2 bosons but I can't find the post nor the paper. Does anyone have the reference ?]

 

[Dale]

Thanks. How come they say that if spacetime is discrete, then there is no manifold.

If spacetime is discrete then in small neighborhoods it does not look like R4, and if it does not look like R4 in small neighborhoods then it is not a (4D) manifold.

 

[waterfall]

If spacetime is discrete then in small neighborhoods it does not look like R4, and if it does not look like R4 in small neighborhoods then it is not a (4D) manifold.

You mean Loop Quantum Gravity for example doesn't have a manifold?

 

[waterfall]

I certainly wouldn't come to those conclusions on the basis of what I understand. I see no difficulty in the coexistence of gravitons and expanding space.

[I have a memory of someone posting an arXiv paper about the flat spacetime + spin-2 bosons but I can't find the post nor the paper. Does anyone have the reference ?]

Can you enumerate how exactly the Baryshev approach differs to the Misner, Thorne & Wheeler's? It seems MTW's accept of the coexistence of gravitons and expanding space while the former doesn't. What are their main differences in the formalisms? Isn't it that both are about spin-2 field on flat spacetime? How can they differ when they have this in common?

 

[Dale]

You mean Loop Quantum Gravity for example doesn't have a manifold?

I don't know anything about loop quantum gravity (nor am I very interested in it). But in normal relativistic quantum mechanics spacetime is not discrete, so I would be mildly surprised to learn that it is in LQG. If that is correct then LQG does not have a manifold, although it may approximate one in the classical limit.

 

[Mentz114]

Can you enumerate how exactly the Baryshev approach differs to the Misner, Thorne & Wheeler's? It seems MTW's accept of the coexistence of gravitons and expanding space while the former doesn't. What are their main differences in the formalisms? Isn't it that both are about spin-2 field on flat spacetime? How can they differ when they have this in common?

No, I haven't seen the MTW treatment. FTG is a classical field theory that begins with the Lagrangian which has three terms, one each for the field, one for the matter and crucially one for the interaction between the field and the matter. The exchange boson, if the theory was quantized would be spin-2. All this is done in Minkowski spacetime.

 

[Dale]

Personally waterfall, I think you should learn established physics before attempting to learn speculative physics.

 

[waterfall]

Personally waterfall, I think you should learn established physics before attempting to learn speculative physics.

right now.. the universe is expanding as shown by the supernova lantern techniques. So space expansion is established physics.

What I'd like to understand at this point is how come expanding space is automatically curved space. Can't minkowski space expand? maybe something to do with the submanifolds giving appearance of curvature whenever there is space expansion? Please don't mention the milne model, just directly the issues. Thanks.

 

[Dale]

right now.. the universe is expanding as shown by the supernova lantern techniques. So space expansion is established physics.

Certainly, but all you need for that is GR. Speculative spin-2 fields are not required, and from your frustration in these threads I think they are also not helpful.

What I'd like to understand at this point is how come expanding space is automatically curved space. Can't minkowski space expand? maybe something to do with the submanifolds giving appearance of curvature whenever there is space expansion?

I think that the best way to answer this question is to explain what we mean by saying that spacetime is curved.

First, let's examine 3 key concepts:
1) Spacetime: space and time are combined into one 4D mathematical space where the time dimension is different from the 3 spatial dimensions.
2) Worldlines: the position of a classical point particle over its lifetime is represented by a 1D curve in spacetime.
3) Inertial: the worldline of an inertial particle (a particle which is not acted on by any real force) is a straight line (aka geodesic).

The above 3 concepts are critical for SR and GR, although they even apply to Newtonian physics. The key difference between GR and Newtonian physics in the above is that in GR, due to the equivalence principle, gravity is considered a fictitious force rather than a real force. This means that, in GR, an inertial particle can be experimentally identified simply by attaching an ideal accelerometer: if it reads 0 then the particle is inertial.

Do you follow so far?

 

[waterfall]

Certainly, but all you need for that is GR. Speculative spin-2 fields are not required, and from your frustration in these threads I think they are also not helpful.

I think that the best way to answer this question is to explain what we mean by saying that spacetime is curved.

First, let's examine 3 key concepts:
1) Spacetime: space and time are combined into one 4D mathematical space where the time dimension is different from the 3 spatial dimensions.
2) Worldlines: the position of a classical point particle over its lifetime is represented by a 1D curve in spacetime.
3) Inertial: the worldline of an inertial particle (a particle which is not acted on by any real force) is a straight line (aka geodesic).

The above 3 concepts are critical for SR and GR, although they even apply to Newtonian physics. The key difference between GR and Newtonian physics in the above is that in GR, due to the equivalence principle, gravity is considered a fictitious force rather than a real force. This means that, in GR, an inertial particle can be experimentally identified simply by attaching an ideal accelerometer: if it reads 0 then the particle is inertial.

Do you follow so far?

I understood all of the above concepts from my many books on GR like Relativity Visualized, Relativity Explained and even Taylor's Spacetime Physics. So no problem about those concepts.

My problem is how to visualize expanding space which those books don't cover. Now I understood it thanks to your and others help. There's just this little loose ends about Minkowski. I know it doesn't expand like GR of course bec it is not GR. But can one imagine that the x, y, z coordinates of our 3-space is just getting longer and longer assuming it is not infinite at the start and this is the counterpart of expansion of the 3 coordinates?

Another thing. Perhaps you may know the answer to the following which I've asked for the past 5 days and no one answers it directly. 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.

 

[Vanadium 50]

I understood all of the above concepts from my many books on GR like Relativity Visualized, Relativity Explained and even Taylor's Spacetime Physics. So no problem about those concepts.

I'm afraid you don't. You might think you do, but that's because you don't, and as such, are not in a position to properly evaluate how much you know. The first two books are popularizations, and the third, while a textbook, devotes only 20 pages to the topic, which means that it's a very superficial introduction. (Indeed, one of the authors of that book wrote a textbook on GR which is ~100x longer)

There is more to physics than just getting a bunch of scientific-sounding words together in the right order. After you have taken calculus and a few physics courses, you'll understand that. But until then, I strongly recommend not telling people who actually have studied something that they are wrong when you yourself have only read some popularizations.