True Time & True c: Exploring Light Speed & Relativity

[Aether]

We could easily change the FLRW metric around, compute modified versions of the Friedmann equations, and then show the SLS as something that looks quite different; no problem. The real questions are "what are dark matter and dark energy?", which are both required to project the CMBR back onto a SLS.

For example, what if we wanted to simply get rid of "dark energy" and/or "dark matter" by modifying the FLRW metric to re-define its standard simultaneity in such a way that the CMBR projects onto a simultaneous big bang at t=0, but not onto a spatially homogeneous universe at t=370,000 years? The SLS would no longer be spherically symmetric then, but dark matter and/or dark energy would be gone.

 

[JesseM]

For example, what if we wanted to simply get rid of "dark energy" and/or "dark matter" by modifying the FLRW metric to re-define its standard simultaneity in such a way that the CMBR projects onto a simultaneous big bang at t=0, but not onto a spatially homogeneous universe at t=370,000 years? The SLS would no longer be spherically symmetric then, but dark matter and/or dark energy would be gone.

What do you mean when you say the SLS is "spherically symmetric"? In terms of the FLRW model of the universe the SLS occupies all of space at a particular moment (according to the definition of simultaneity in the standard coordinate system where each surface of simultaneity is spatially homogenous)...are you just talking about the visual sphere with the Earth at the center and the CMBR as the outer surface (and objects being older the farther you go from the center) which constitutes the "observable universe"? If so, aren't visual appearances independent of your choice of coordinate system, since they are a consequence of how the worldlines of photons intersect our own worldline?

Also, what did you mean earlier when you said dark matter and dark energy "are both required to project the CMBR back onto a SLS"? Dark matter and dark energy are needed to explain the particular rate of expansion at different times as measured in the pattern of redshifts of distant objects, but the original FLRW model was invented before the idea of dark matter or dark energy and the idea of a "surface of last scattering" was around then too, it only depends on the idea that there was a moment when the temperature of the universe became low enough that free electrons were captured by protons to form hydrogen atoms.

 

[Dale]

Hi RandallB,

Sorry about the delay in my response. I think we may be having a simple miscommunication here. I will answer your question below, but I wanted to put what I think is the source of the miscommunication at the top.

My intent in this thread is simple: to argue in favor of the principle of relativity. If the principle of relativity applies to the CMBR rest frame then its time coordinate would only be "true" or "universal" by convention. From your comments I cannot tell if you believe that the principle of relativity applies to the rest frame of the CMBR. If you do then we simply have a miscommunication somewhere, if you do not then we have a genuine disagreement.

So, do you accept the principle of relativity in general, and specifically do you believe that it applies to the CMBR rest frame?

as Russ puts it, the equator or pole locations have a fundamental truth about where they are located and cannot be arbitrarily positioned anywhere on a spinning globe.

The axis of rotation of the Earth is a physical feature of the earth, but the choice to use that axis as the z-axis of a spherical coordinate system is a completely arbitrary choice. We could just as well define lattitude and longitude by magnetic north rather than true north. In such a coordinate system expressions for the position of the sun in the sky would be more complicated, but expressions for the direction of compass needles would be simplified. Using each set of coordinates you would obtain the same predictions for the results of any physical experiment.

I didn’t say your claim would lead to rejecting the existence of any fundamental particles, I said it would reject how the astrophysics community explains they were created.

That is quite possible. Standard explanations are generally in terms of the conventions which are accepted by that community and which aid communication and understanding within the community. That is not to say that the explanation is incorrect in any way or that the conventions are in any way unreasonable, but it is simply a recognition of the conventions for what they are.

“What other arbitrary choice can we make to serve as an equivalent but different perspective than what we get from the CBR?”
Include with that how this alternate “mountain” choice can be used by astrophysics/cosmology to build a new description that is:
A) Still identical to the currently defined Big Bang history.
or
B) Builds an alternative to the Big Bang and the history of particle creation it defines that is considered by anyone to be viable.

Unless there are such addition choices the way astrophysics/cosmology uses CBR & SLS is “Fundamental” and that is the extent of my point.

Under the principle of relativity any other coordinate system would be just as valid, e.g. a coordinate system where the CMBR is moving at 600 km/s (and our local group is at rest). In order to ensure that the new coordinate system makes the same predictions, you can simply take the standard metric (FLRW?), do a change of variables so that our local group is at rest and the CMBR is moving, and thus obtain a new coordinate system and a new metric describing the same spacetime. This coordinate system would be every bit as valid a description of the universe as the conventional one, and they would agree on all observations, but in the new system the CMBR would not be at rest.

 

[Aether]

What do you mean when you say the SLS is "spherically symmetric"? In terms of the FLRW model of the universe the SLS occupies all of space at a particular moment (according to the definition of simultaneity in the standard coordinate system where each surface of simultaneity is spatially homogenous)...are you just talking about the visual sphere with the Earth at the center and the CMBR as the outer surface (and objects being older the farther you go from the center) which constitutes the "observable universe"? If so, aren't visual appearances independent of your choice of coordinate system, since they are a consequence of how the worldlines of photons intersect our own worldline?

I mean that a hypersphere of homogeneity is spherically symmetric.

Also, what did you mean earlier when you said dark matter and dark energy "are both required to project the CMBR back onto a SLS"?

To actually project the CMBR anisotropies back onto a SLS, you need to model the expansion history of the universe. The SLS is just one point on that timeline. Dark matter and dark energy are required to generate an expansion history for an FLRW/Friedmann universe that is consistent with the CMBR anisotropies.

Dark matter and dark energy are needed to explain the particular rate of expansion at different times as measured in the pattern of redshifts of distant objects, but the original FLRW model was invented before the idea of dark matter or dark energy and the idea of a "surface of last scattering" was around then too, it only depends on the idea that there was a moment when the temperature of the universe became low enough that free electrons were captured by protons to form hydrogen atoms.

To actually find an expansion history for an FLRW/Friedmann universe that is consistent with the CMBR anisotropies, dark matter and dark energy is required. This is usually done using the Friedmann equations, and the dark matter and dark energy denity are just parameters added in addition to normal matter density.

If, for example, we were to modify the Friedmann equations as needed to generate the same expansion history without dark matter and/or dark energy, then maybe we could reverse the GR procedures that are used to get the Friedmann equations from the FLRW metric, and show a metric that is consistent with the CMBR anisotropies without dark energy and/or dark matter. At least that may serve as a good example of why the standard simultaneity of the FLRW metric and SLS are not fundamental physical things.

 

[JesseM]

I mean that a hypersphere of homogeneity is spherically symmetric.

So you're specifically referring to a spatially finite universe with positive curvature? The evidence suggests the spatial curvature is very close to flat, although I think it's possible space could have very slight positive curvature, too small to be seen with current observations.

To actually project the CMBR anisotropies back onto a SLS, you need to model the expansion history of the universe. The SLS is just one point on that timeline. Dark matter and dark energy are required to generate an expansion history for an FLRW/Friedmann universe that is consistent with the CMBR anisotropies.

OK, that makes sense--I was confused because you didn't specify that you were talking about the observed CMBR anisotropies, as opposed to just the existence of the CMBR in general.

 

[Aether]

So you're specifically referring to a spatially finite universe with positive curvature?

No, I am specifically referring to FLRW space at any given time.

The evidence suggests the spatial curvature is very close to flat, although I think it's possible space could have very slight positive curvature, too small to be seen with current observations.

I do not mean to imply that there is spatial curvature necessarily. I am only trying to show an alternative to standard FLRW space at any given time.

 

[JesseM]

No, I am specifically referring to FLRW space at any given time.

But then why did you refer to a hypersphere? In a spatially flat universe, using the standard choice of coordinate system a hypersurface of simultaneity would be be an infinite hyperplane (i.e. infinite 3D Euclidean space), and in a universe with negative curvature it'd be an infinite hyperbolic space. Either way, the SLS would fill all of space in a hypersurface of simultaneity, it wouldn't be a finite hypersphere.

 

[Aether]

But then why did you refer to a hypersphere? In a spatially flat universe, using the standard choice of coordinate system a hypersurface of simultaneity would be an infinite hyperplane (i.e. infinite 3D Euclidean space)...the SLS would fill all of space in a hypersurface of simultaneity, it wouldn't be a finite hypersphere.

We can only see out to our own particle horizon which currently has a radius of about $$\eta_0 \cdot c = 46 Glyr$$. It is the difference between this distance and about $$t_0 \cdot c = 13.7 Glyr$$ which is accounted for in the computation of expansion histories by means of inserting dark energy and dark matter into the Friedmann equations. This may imply the use of a slightly different choice, though still a standard choice, of coordinate system than "the" standard choice that you are thinking of. Nevertheless, what I am referring to as hyperspheres are spacelike slices of the observable universe which have a comoving radius of $$\eta \cdot c$$. These are not infinite hyperplanes, though I suppose that they might be considered as the observable piece of an infinite hyperplane.

 

[Aether]

...are you just talking about the visual sphere with the Earth at the center and the CMBR as the outer surface (and objects being older the farther you go from the center) which constitutes the "observable universe"?

Yes, except that when we generate an expansion history it is well defined almost all the way down to t=0 (the SLS is at around t=370,000 years).

If so, aren't visual appearances independent of your choice of coordinate system, since they are a consequence of how the worldlines of photons intersect our own worldline?

Yes, but how we parameterize the Friedmann equations in order to generate an expansion history that is consistent with visual appearances today, an SLS at t=370,000 years, nucleosynthesis at t<a few minutes, and a big bang at t=0 is not independent of our choice of coordinate system.