Is True Time the Key to Understanding Light Speed and Relativity?

[Idjot]

When thinking of the SLS (surface of last scattering) as the source of the CMB; remember it is not a physical surface of something.
It is a matter of the universe as it aged from the Big Bang less than 0.4 G-Years became transparent basically everywhere. From the view of the Local Matter then from which we are made now the light at some distant radius from it could not be seen until it traveled that distance plus the distance we covered in moving away from it (Hubble expansion); That defines a set source distance or “surface” for what we see today as CBR.
CBR from a closer radius has already passed us by, and from a greater radius will not be seen by us until sometime in the future.

The point is:
from our view about 14 G-Years later, and the Big Bang being a single event, and all SLS light from all areas or radiuses starting out at less than 0.4 G-Years from the Big Bang - we can define SLS light as having an “Absolute” Simultaneous start time.

Thank you!

 

[atyy]

While we're on the subject of nonstandard definitions, I can't help thinking of this guy's definition of SLS as the "surface of last screaming". http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver7_2.html

 

[Idjot]

While we're on the subject of nonstandard definitions, I can't help thinking of this guy's definition of SLS as the "surface of last screaming". http://nedwww.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver7_2.html

Thank you too!

 

[RandallB]

Feel free to argue how a big bang singularity is an event in GR.

I do not think it is.

Personally I don’t believe the idea of a singularity, naked or otherwise Big Bang or Black-Holes, although it is favored speculation.
Plus I don’t think anyone even speculates as to how to apply GR to whatever was there before or even a couple minutes after the Big Bang began.

But there is a wide agreement on much of what happened after the Big Bang as a single event.
For most the timing of when the universe became transparent is 370,000 to 380,000 years after the Big Bang whatever that event might have been.
Most of direct measure of the age of the universe as 13.7 Billion years, nearly 14 G-Years, comes from measuring the that SLS or CBR.
And on a scale of 14 G-Years compared to 0.0004 G-years the SLS or CBR source is effectively simultaneous with the Big Bang itself.
IMO all SLS observations should be considered as coming from simultaneous SLS source events.

I don’t think Astrophysics can make most of its claims about expansion and large distance measurements without taking the Big Bang and its aftermath within just a short Million years as being a single simultaneous event.

 

[Dale]

In reality I only think it's a bit stubborn to deny the usefulness of using CMBR as a universal frame

Please, don't misunderstand me. I am not denying its usefulness (at least for cosmology) as a convention. However your thread was about it as "true" time, not just its usefulness.

Using the CMBR as a universal reference frame would be akin to the international date line, or the fact that red lights mean "stop", or right handed coordinate systems. All of those are very useful conventions, but nothing would be fundamentally different if we had chosen and agreed upon different conventions.

If you had started your posts simply talking about the usefulness of the CMBR frame nobody would have objected. That is not what I was denying.

 

[RandallB]

Using the CMBR as a universal reference frame would be akin to the international date line, or the fact that red lights mean "stop", or right handed coordinate systems. All of those are very useful conventions, but nothing would be fundamentally different if we had chosen and agreed upon different conventions.

I have to disagree,
picking a place for the dateline is an arbitrary choice we make from our POV to establish a useful convention. What other arbitrary choice can we make to serve as an equivalent but different perspective than what we get from the CBR? IMO there is nothing arbitrary about the CBR, it is a fact presented to us by nature. And if we are to believe our interpretation of nature as our universe having a single beginning with what we define as the Big Bang and the CBR as coming from the resulting SLS, it gives us as far as I know the only know instance of simultaneous events we can see form our local view that is “outside the box” of the SR- simultaneity rule.

That does not automatically say it will resolve to something as “Absolute” or “Universal”. But IMO it rates more than just thinking it was some arbitrary reference choice that we somehow had a hand in picking.

 

[Dale]

I have to disagree,
picking a place for the dateline is an arbitrary choice we make from our POV to establish a useful convention. What other arbitrary choice can we make to serve as an equivalent but different perspective than what we get from the CBR? IMO there is nothing arbitrary about the CBR, it is a fact presented to us by nature. And if we are to believe our interpretation of nature as our universe having a single beginning with what we define as the Big Bang and the CBR as coming from the resulting SLS, it gives us as far as I know the only know instance of simultaneous events we can see form our local view that is “outside the box” of the SR- simultaneity rule.

That does not automatically say it will resolve to something as “Absolute” or “Universal”. But IMO it rates more than just thinking it was some arbitrary reference choice that we somehow had a hand in picking.

Do you think that any of the laws of physics will be different in the CMBR frame than in any other frame? If not then it is an arbitrary convention.

Certainly, if you live near a mountain or some other prominent geographical feature it would be convenient to measure coordinates relative to that feature which is as you say "presented to us by nature". But that does not make any other choice less valid, nor does it make that choice any more fundamental. For the purposes of defining distances and times the CMBR is the cosomlogical equivalent of an easily identifiable landmark.

Defining the CMBR as "at rest" is every bit as arbitrary as defining the solar system, our local group, or some other object "presented to us by nature" to be at rest. Or as arbitrary as defining any of those things to be moving at some specific velocity.

 

[RandallB]

Do you think that any of the laws of physics will be different in the CMBR frame than in any other frame? If not then it is an arbitrary convention.

Certainly, if you live near a mountain or some other prominent geographical feature it would be convenient to measure coordinates relative to that feature which is as you say "presented to us by nature". But that does not make any other choice less valid, nor does it make that choice any more fundamental. For the purposes of defining distances and times the CMBR is the cosomlogical equivalent of an easily identifiable landmark.

Defining the CMBR as "at rest" is every bit as arbitrary as defining the solar system, our local group, or some other object "presented to us by nature" to be at rest. Or as arbitrary as defining any of those things to be moving at some specific velocity.

I do not think how we understand Physics and the Laws that define it is “Complete” (if they were we would have unification forces and QM & GR). So, yes I think CBR might yet be a part of changes some of what we think we know. What and how exactly some law may change is speculation at this level, it is just my opinion the CBR could contribute more to helping complete our understanding of physics.

I understand picking one mountain as a reference point over a second, third, or other mountain option certainly cannot be thought of as a fundamental reference point.
But certainly, Astrophysics seems to regard the CBR as fundamental, and I’ve yet to see anyone point out a second option for the fundamental reference CBR provides them. Thus I find no grounds to support claiming their using it as fundamental was in fact an arbitrary choice.

Unless you include a completely different interpretation of, or completely reject, how they interpret the Big Bang; I don’t see where you can justify these fundamental assumptions of Astrophysics as being arbitrary.
But, you are entitled to your opinion. We just have differences here.

 

[Dale]

Is GR not the fundamental theory accepted by the Astrophysics/Cosmology community? If so then you are incorrect to claim that they regard the reference frame of the CMBR as fundamental. According to GR the rest frame of the CMBR is no different than a reference frame where it is moving at some arbitrary velocity.

 

[RandallB]

Is GR not the fundamental theory accepted by the Astrophysics/Cosmology community? If so then you are incorrect to claim that they regard the reference frame of the CMBR as fundamental. According to GR the rest frame of the CMBR is no different than a reference frame where it is moving at some arbitrary velocity.

I would not call GR exclusively “THE FUNDAMENTAL THEORY” of Astrophysics/Cosmology. Just one of the fundamental theories Astrophysics/Cosmology uses. Much of the conclusions drawn by them depends on the chemistry in space which is based on the Standard Model and therefore the fundamental theory of QM. Meaning it accepts working with two theories that are fundamentally incompatible.

Now a significant part of what the Astrophysics/Cosmology community tells us about the history of our reality, especially as it relates to the sequence of events following the Big Bang up to when stars first began to form, is fundamentally based on the Big Bang including how that unique point of view cannot be replace by any arbitrarily chosen frame of reference.
To the extent that means they may well be working with three fundamental theories (by adding Big Bang CMR as something new) each in some respect incompatible with the others that is OK by me.

IMO your opinion requires rejecting the proposed reactions, interactions and formation of fundamental particles like quarks proceeding to the formation neutrons, protons, etc as not plausible.
Although that theory of fundamental particle and force development may not by 100% on the mark and complete; I consider to be largely correct and take to be very plausible. Thus I cannot reject the Big Bang or the uniqueness of a fundamental SLS benchmark as used in Astrophysics/Cosmology.

That remains my opinion. To the extend you can minimize the value of the Big Bang and the early history implied by it we just have different opinions. I only ask you give mine sincere consideration before rejecting it. However, unless you have something additional to offer to support it, I cannot adopt yours.

 

[Idjot]

I would not call GR exclusively “THE FUNDAMENTAL THEORY” of Astrophysics/Cosmology. Just one of the fundamental theories Astrophysics/Cosmology uses. Much of the conclusions drawn by them depends on the chemistry in space which is based on the Standard Model and therefore the fundamental theory of QM. Meaning it accepts working with two theories that are fundamentally incompatible.

Now a significant part of what the Astrophysics/Cosmology community tells us about the history of our reality, especially as it relates to the sequence of events following the Big Bang up to when stars first began to form, is fundamentally based on the Big Bang including how that unique point of view cannot be replace by any arbitrarily chosen frame of reference.
To the extent that means they may well be working with three fundamental theories (by adding Big Bang CMR as something new) each in some respect incompatible with the others that is OK by me.

IMO your opinion requires rejecting the proposed reactions, interactions and formation of fundamental particles like quarks proceeding to the formation neutrons, protons, etc as not plausible.
Although that theory of fundamental particle and force development may not by 100% on the mark and complete; I consider to be largely correct and take to be very plausible. Thus I cannot reject the Big Bang or the uniqueness of a fundamental SLS benchmark as used in Astrophysics/Cosmology.

That remains my opinion. To the extend you can minimize the value of the Big Bang and the early history implied by it we just have different opinions. I only ask you give mine sincere consideration before rejecting it. However, unless you have something additional to offer to support it, I cannot adopt yours.

Please keep arguing! I'm learning as you reply to him! Haha Thanks.

 

[russ_watters]

But certainly, Astrophysics seems to regard the CBR as fundamental, and I’ve yet to see anyone point out a second option for the fundamental reference CBR provides them.

Could you explain what you mean by "fundamental" in this context?

Heck, is the CMB even really a reference frame? It is a reference for zeroing a velocity, but it has no intrinsic xyz coordinate reference, unlike the prime meridian, which is one axis of a two-axis coordinate system and stationary.

And the date line may be completely arbitrary, but the equator is not. The equator (and the poles) couldn't be arbitrarily located anywhere else. Does that have implications for your usage of the word "fundamental"?

 

[Dale]

I would not call GR exclusively “THE FUNDAMENTAL THEORY” of Astrophysics/Cosmology. Just one of the fundamental theories Astrophysics/Cosmology uses. Much of the conclusions drawn by them depends on the chemistry in space which is based on the Standard Model and therefore the fundamental theory of QM. Meaning it accepts working with two theories that are fundamentally incompatible.

The principle of relativity is an integral part of both theories (GR and the SM). So I don't understand how you can make the leap from GR and the SM are fundamentally incompatible to the conclusion that one of the things that they do agree on is wrong. Neither of these two fundamental theories of astrophysics/cosmology support your claim that the rest frame of the CMBR would be anything more than a convenience.

The topic of this thread is simply whether the rest frame of the CMBR represents a "true" time or if it would merely be a convenient convention. Accepting the premise that it is anything other than a convenience is a rejection of the principle of relativity, which is certainly not supported by the theories used by the astrophysics community.

IMO your opinion requires rejecting the proposed reactions, interactions and formation of fundamental particles like quarks proceeding to the formation neutrons, protons, etc as not plausible.

I don't know how you conclude that I reject the Big Bang or any of the fundamental particles. You are way off-base here.

 

[RandallB]

The principle of relativity is an integral part of both theories (GR and the SM).

I don’t understand this sentence, it offers nothing to this debate. It seems to say SM is a relativity theory but still calls it one of “both theories”. SM is fundamentally a QM theory that to the best that a QM theory can, it tries to respect the principle of relativity. But I know of no one that considers SR/GR and SM/QM as compatible, they are two independent view with fundamentally incompatible ideas of how gravity works. If we are not on the same page here then there we are having an argument (seems to delight Idgot) and I am not interested in dealing with augmentative rhetoric so let's try to this a rational debate.

… how you can make the leap from GR and the SM are fundamentally incompatible to the conclusion that one of the things that they do agree on is wrong. Neither of these two fundamental theories of astrophysics/cosmology support your claim that the rest frame of the CMBR would be anything more than a convenience.

You are repeating my point here. As we both say nether SR/GR or SM/QM can directly support or define the idea that the Big Bang and nearby events to it can be taken as a single simultaneous event relative to our view 14 Billion years later. And yet Astrophysics/Cosmology takes as a fundamental truth that the SLS events are simultaneous much like 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 topic of this thread is simply whether the rest frame of the CMBR represents a "true" time or if it would merely be a convenient convention. Accepting the premise that it is anything other than a convenience is a rejection of the principle of relativity, which is certainly not supported by the theories used by the astrophysics community.
I don't know how you conclude that I reject the Big Bang or any of the fundamental particles. You are way off-base here.

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.

I understand the OP, what we a debating is your assertion that the OP idea should not even be considered because the astrophysics community use of the SLS was an “arbitrary choice”. My point is that astrophysics/cosmology use of SLS is not arbitrary but recognizes it as a fundamental thing that allows them to build the early history of how fundamental particles were made.

Now if all we have left is an argument about which opinion is better than this discussion was done a few posts ago – we have different opinions and I have no interest in arguing about it, that’s non-productive.

But if you have a debatably point that you think can change my opinion I’m willing to continue as a debate, but not an argument. For that you need to answer my question from post 56 :

“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.

How or IF that might impact on ideas about “Absolute” or “Universal” time is a topic for Journal Papers. But I cannot deny anyone in astrophysics the right to consider it.

 

[Aether]

My point is that astrophysics/cosmology use of SLS is not arbitrary but recognizes it as a fundamental thing that allows them to build the early history of how fundamental particles were made.

The SLS is calculated using GR (FLRW metric + GR --> Friedmann equations, Friedmann equations + CMBR --> SLS). How would you know that there was an SLS without GR?

 

[Idjot]

The SLS is calculated using GR (FLRW metric + GR --> Friedmann equations, Friedmann equations + CMBR --> SLS). How would you know that there was an SLS without GR?

1. You use a shovel to unearth a buried rock.
2. You use a wet saw to cut that rock into pieces.
3. You use a microscope to study the pieces.

Maybe GR was the shovel here.

 

[JesseM]

I don’t understand this sentence, it offers nothing to this debate. It seems to say SM is a relativity theory but still calls it one of “both theories”. SM is fundamentally a QM theory that to the best that a QM theory can, it tries to respect the principle of relativity. But I know of no one that considers SR/GR and SM/QM as compatible

Everyone recognizes that SM/QM are fundamentally not compatible with GR (one reason is that in quantum theories, the Planck scale should be associated with large energy fluctuations which in GR would themselves contribute significantly to the curvature of spacetime on those scales, but existing quantum theories assume a fixed background spacetime--see http://64.233.169.104/search?q=cache:96vSRqNGD6AJ:hyperphysics.phy-astr.gsu.edu/Hbase/quantum/string.html+%22conflict+between+the+uncertainty+principle+and+general+relativity%22&hl=en&ct=clnk&cd=1&gl=us for a discussion). However, the Standard Model and quantum field theories in general are both compatible with SR (which does not assume energy curves spacetime) because they are Lorentz-invariant theories. So, an absolute definition of simultaneity is every bit as incompatible with the Standard Model as it is with SR.

And yet Astrophysics/Cosmology takes as a fundamental truth that the SLS events are simultaneous much like as Russ puts it

No it doesn't. Where did you get the idea that cosmologists could not analyze the surface of last scattering in a coordinate system where different points on the surface are non-simultaneous? I'm sure it is most convenient to use a coordinate system where all points on this surface are assigned the same time-coordinate, but there are no fundamental physical considerations that forbid you from using other coordinate systems.

 

[RandallB]

The SLS is calculated using GR (FLRW metric + GR --> Friedmann equations, Friedmann equations + CMBR --> SLS). How would you know that there was an SLS without GR?

I don’t see your point. - - Did you think I’d denied SR/GR was used by astrophysics?
I think I was clear that they use both SR/GR and SM/QM.

My contention is that they are successfully using not only those two theories while they are technically incompatible (yet to be unified on the gravity issue) with each other. And my main point is that astrophysics use of SLS is not an arbitrary selection of a reference point. But that they fundamentally recognize the Big Bang and the SLS as we observe it as effectively from our POV sourced from simultaneous events. And they depend upon using all three things without allowing anyone of them to invalidate either of the other two.

I suppose I should acknowledge they did not need modern CBR observations to develop this mixed view of reality. The Hubble expansion model modified how they applied GR (with was approved of by Einstein) that lead to the development of the big Bang Bang idea before the SLS was indentified. Prior to the SLS and CRB they were using the distant star background in much the same way they now define SLS.

And again:
I already asked what arbitrary selection of a reference point differing from a fundamental use of all SLS points coming from simultaneous events, would allow astrophysics to define the early Timeline of Cosmology as they have.

No one has provided one yet.
So the rest is just argumentative rhetoric, that will not change my opinion.
It is a legit question so unless someone cares to address it seriously I choose not to continue this further – it can only turn to pointless arguments and IMO that is not the purpose of PF.

 

[JesseM]

But that they fundamentally recognize the Big Bang and the SLS as we observe it as effectively from our POV sourced from simultaneous events. And they depend upon using all three things without allowing anyone of them to invalidate either of the other two.

Totally wrong. Again, GR allows you to use any coordinate system and still get the same predictions about all empirical observations like how the CMBR will look from our perspective--nothing would stop you from using a coordinate system where different points on the surface of last scattering were non-simultaneous, it wouldn't have any effect on predictions about how the CMBR looks.

 

[Aether]

I don’t see your point. - - Did you think I’d denied SR/GR was used by astrophysics?

Do you want to consider the SLS as being outside of the context of GR? How would you know that there was an SLS without GR?

And again:
I already asked what arbitrary selection of a reference point differing from a fundamental use of all SLS points coming from simultaneous events, would allow astrophysics to define the early Timeline of Cosmology as they have. No one has provided one yet.

The definition of simultaneity in the FLRW metric, which comes from assuming that the universe is spatially homogeneous, is the only justification that I know of for taking all SLS points to be simultaneous. Do you know of another justification? 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.

So the rest is just argumentative rhetoric, that will not change my opinion.
It is a legit question so unless someone cares to address it seriously I choose not to continue this further – it can only turn to pointless arguments and IMO that is not the purpose of PF.

Can you show how to find/detect/model/describe the SLS without first assuming that the universe is spatially homogeneous? It isn't just argumentative rhetoric to point out that the concept of an (symmetric) SLS is based mathematically on a certain definition of simultaneity, and that you're limited by that definition unless you can describe the SLS without making that assumption.

 

[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.