Cont: Why James Webb Telescope rewrites/doesn't the laws of Physics/Redshifts (2)

Mike Helland · Jun 26, 2023

hecd2 said:
Don’t want to take my word for it? Try a standard textbook, for example Ciufolini and Wheeler Gravitation and inertia. Turn to section 4.2 on pages 193 - 220. First the metric is formally derived by applying the formalism of the Lie derivative of a tensor field with respect to a vector field. The derivation proceeds to define the homogeneity and isotropy of the manifold in terms of an isometry group of the Killing vector fields. Once the familiar metric is formally and rigorously derived, it can be formally shown that the origin can be translated freely anywhere and the metric has the same form with the new coordinates as it had with the original ones. The expression for the Gaussian curvature is derived and from that the Ricci curvature and the Einstein curvature tensor, to show formally that the curvature is constant over the manifold. Ciufolini and Wheeler then go on to formally derive the distance versus redshift relationship. The dynamics of the model - ie how it evolves over time. This is all perfectly compatible with, and indeed derived from the concepts of general relativity.

So the authors claiming g_tt=1 violates the equivalence principle are wrong. You could be right. I don't trust you though, so there's that.

hecd2 · Jun 26, 2023

Mike Helland said:
So the authors claiming g_tt=1 violates the equivalence principle are wrong. You could be right. I don't trust you though, so there's that.

Can you explain exactly and mathematically how the FLRW metric is incompatible with general relativity?

I don't care in the slightest whether you trust me. You don't have to trust me - just read and understand (I realise the latter is impossible for you) the standard text books and stop cherry picking and/or misunderstanding your experts.

W.D.Clinger · Jun 26, 2023

Mike Helland said:
So the authors claiming g_tt=1 violates the equivalence principle are wrong. You could be right. I don't trust you though, so there's that.

Those are the same authors who say

And yet, in ΛCDM the time-time component of the metric, g_tt, is set at 1 at all times and stages of cosmic evolution, even under conditions where it may not be mathematically robust to do so.

That's quite a silly thing for those authors to say, because g_tt = − c² in this familiar metric form:

ds² = − c² dt² + dx² + dy² + dz²

What this shows is that those authors were speaking imprecisely. Everyone who knows what they're talking about is aware that the numerical value of g_tt depends on the coordinate system you prefer. In particular, as that metric form shows, its value depends on the units you prefer to use.

The authors who said that silly thing would agree with what I just said, and would hasten to explain what they really meant when they wrote those silly words.

It's safe to assume the author and sole proponent of Helland physics can't explain what those authors really meant when they wrote those silly words.

Mike Helland · Jun 26, 2023

W.D.Clinger said:
Those are the same authors who say

And yet, in ΛCDM the time-time component of the metric, g_tt, is set at 1 at all times and stages of cosmic evolution, even under conditions where it may not be mathematically robust to do so.
That's quite a silly thing for those authors to say, because g_tt = − c² in this familiar metric form:

ds² = − c² dt² + dx² + dy² + dz²
What this shows is that those authors were speaking imprecisely. Everyone who knows what they're talking about is aware that the numerical value of g_tt depends on the coordinate system you prefer. In particular, as that metric form shows, its value depends on the units you prefer to use.

The authors who said that silly thing would agree with what I just said, and would hasten to explain what they really meant when they wrote those silly words.

It's safe to assume the author and sole proponent of Helland physics can't explain what those authors really meant when they wrote those silly words.

There's a non zero chance you're the one being silly.

Mike Helland · Jun 26, 2023

hecd2 said:
Can you explain exactly and mathematically how the FLRW metric is incompatible with general relativity?

I don't care in the slightest whether you trust me. You don't have to trust me - just read and understand (I realise the latter is impossible for you) the standard text books and stop cherry picking and/or misunderstanding your experts.

The point made was that cosmic time isn't entirely relative and breaks the equivalence principle.

Are you disputing that?

hecd2 · Jun 26, 2023

Mike Helland said:
The point made was that cosmic time isn't entirely relative and breaks the equivalence principle.

Are you disputing that?

Yes, unless you can show me mathematically how it does so.

hecd2 · Jun 26, 2023

W.D.Clinger · Jun 26, 2023

correction

Correcting the highlighted word:

W.D.Clinger said:
Lemaître (the L) didn't publish until 1927 (and wrote in Dutch, so his contributions weren't generally recognized until several years later),

That paper was written in French (not Dutch), but was published in an obscure Belgian (not Dutch) journal. In 1931, after Arthur Eddington had described it as a "brilliant solution", part of the paper was translated into English and Lemaître, building on that paper, proposed a "Primeval Atom", which is now more commonly known as the Big Bang.

ETA: Not long before Lemaître's death, he learned that cosmic background radiation from that "Primeval Atom" had been detected.

Mike Helland · Jun 26, 2023

hecd2 said:
Yes, unless you can show me mathematically how it does so.

Oh, so like when I said H₀ is km/s/Mpc, and you said its in inverse seconds. And when I said it's in inverse seconds you said it's in km/s/Mpc?

Yeah. That's probably a fun game for you. Not playing.

hecd2 · Jun 26, 2023

Mike Helland said:
Oh, so like when I said H₀ is km/s/Mpc, and you said its in inverse seconds. And when I said it's in inverse seconds you said it's in km/s/Mpc?

Yeah. That's probably a fun game for you. Not playing.

Suit yourself. We all know that you don’t understand what you are parroting.

Also the fact that you still don’t understand the difference between dimensions and units, and you still don’t understand that there was no contradiction between the two statements is because you haven’t a clue about any of this stuff.

You can carry in talking to yourself now.

Mike Helland · Jun 26, 2023

hecd2 said:
Suit yourself. We all know that you don’t understand what you are parroting.

Also the fact that you still don’t understand the difference between dimensions and units, and you still don’t understand that there was no contradiction between the two statements is because you haven’t a clue about any of this stuff.

You can carry in talking to yourself now.

You're the one who said (in one post) that it had dimensions and units of inverse seconds.

Melia's argument that LCDM is incompatible with with the Einstein equivalence principle is based on the change of dominating ingredient throughout the history of the universe. In times when it's accelerating and times when its decelerating, I think he's suggesting that the non-free fall and the free fall associated with each can't both be described g_tt=1 (or -c² if you prefer).

That of course wouldn't apply to a pure cosmological constant FLRW model such as de Sitter space.

However, Willem de Sitter said that g_tt=1 is fundamentally at odds with relativity itself.

Here is a quote from one of his papers I already mentioned:

The system A satisfies the "material postulate of relativity of inertia," but it restricts the admissible transformation to those for which at infinity t' = t, and thus introduces a quasi-absolute time, as has been explained in art. 2.

The second article referenced in that paper is this:

https://ui.adsabs.harvard.edu/link_gateway/1917KNAB...19.1217D/PUB_PDF

On the relativity of inertia. Remarks concerning Einstein's latest hypothesis

Also by de Sitter in 1917.

p. 8

If the postulate is applied to the four-dimensional world, and to all transformations, then the system B is the only one that satisfies. We thus find that in the system A the time has a separate position. That this must be so, is evident a priori. For speaking of the three-dimensional world, if not equivalent to introducing an absolute time, at least implies the hypothesis that at each point of the four-dimensional space there is one definite coordinate x₄ which is preferable to all others to be used as "time", and that at all points and always this one coordinate is actually chosen as time. Such a fundamental difference between the time and the space-coordinates seems to be somewhat contradictory to the complete symmetry of the field-equations and the equations of motion (equations of the geodetic line) with respect to the four variables.

p. 10

On the other hand we have the "mathematical postulate" of the relativity of inertia, i. e. the postulate that the http://latex.codecogs.com/gif.latex?g_{\mu\nu} shall be invariant at infinity. This postulate, which, as has already been pointed out above, has no real physical meaning, makes no mention of matter. It can be satisfied by choosing the system B, without a world-matter, and with complete relativity of the time. But here also we need the constant λ. The introduction of this constant can only be avoided by abandoning the postulate of the relativity of inertia all together.

This world-matter is described on page 3-4:

Moreover it is found necessary to suppose the whole three-dimensional space to be filled with matter, of which the total mass is so enormously great, that compared with it all matter known to us is utterly negligible. This hypothetical matter I will call the "world-matter".

hecd2 · Jun 26, 2023

Mike Helland said:
You're the one who said (in one post) that it had dimensions and units of inverse seconds.

Indeed I did, and I have already said that that was a sloppy statement and corrected it. What I should have said was that, as defined by the relationship H=ȧ/a, H has dimensions of T^-1 and units of s^-1. That is not inconsistent with the statement that as normally understood in cosmology H is given in units of km s^-1Mpc^-1, which is is an expansion rate or speed per unit distance. I have already also stated several times that you can quote in H in any units you like provided they have a dimension of T^-1, but if you change the units then the numerical value will change.

Melia's argument that LCDM is incompatible with with the Einstein equivalence principle is based on the change of dominating ingredient throughout the history of the universe. In times when it's accelerating and times when its decelerating, I think he's suggesting that the non-free fall and the free fall associated with each can't both be described g_tt=1 (or -c² if you prefer).

Melia is a highly respected astrophysicist, who has a cosmological theory of his own, and so he is naturally going to emphasise things that he thinks supports his model. But his model is highly controversial and his arguments are not accepted by the vast majority of the cosmology community. You are in no position to arbitrate between them, especially as you misunderstand his argument and you are only able to reproduce it third hand via the handwaving of a journalist. As far as I can tell from that handwaving description, his argument is that FRLW would not rigorously describe a universe with time varying lambda, and this is rather self-evident, but lambda is constant in vanilla LCDM.

You haven't begun to explain why any of this leads one to conclude that LCDM is incompatible with the Einstein equivalence principle. Can you state in your own words the logic that might lead one to that conclusion?

Can you state why you think that galaxies are not moving on geodesics in de Sitter space?

That of course wouldn't apply to a pure cosmological constant FLRW model such as de Sitter space.

Why "of course"?

However, Willem de Sitter said that g_tt=1 is fundamentally at odds with relativity itself.

Here is a quote from one of his papers I already mentioned:

The second article referenced in that paper is this:

https://ui.adsabs.harvard.edu/link_gateway/1917KNAB...19.1217D/PUB_PDF

On the relativity of inertia. Remarks concerning Einstein's latest hypothesis

Also by de Sitter in 1917.

This world-matter is described on page 3-4:

I regard de Sitter's 1917 paper as of historical interest only. It was written very soon after Einstein's 1917 paper setting out general relativity, and it begins to explore, in a rather confused way, consequences of GR that are much better understood today.

W.D.Clinger · Jun 26, 2023

Mike Helland said:
However, Willem de Sitter said that g_tt=1 is fundamentally at odds with relativity itself.

Amusingly, that is what Mike Helland concludes from a 1917 paper in which de Sitter explicitly acknowledges two exact solutions (Einstein's static universe and Minkowski spacetime) for which g_tt = c² holds everywhere.

hecd2 said:
I regard de Sitter's 1917 paper as of historical interest only. It was written very soon after Einstein's 1917 paper setting out general relativity, and it begins to explore, in a rather confused way, consequences of GR that are much better understood today.

Indeed.

In 1917, Einstein and de Sitter were borderline obsessed with the problem of reconciling the theory of general relativity with Mach's principle. They weren't yet completely free of the Newtonian legacy that led them to think of the coordinate-dependent components g_μν as components of a gravitational field, and they were also limited by their understanding of absolute differential calculus, a branch of mathematics that was still evolving into modern differential geometry. That is why de Sitter's 1917 papers take g_μν = 0 at infinity (where they assumed there is no matter) as a boundary condition. With the modern understanding of pseudo-Riemannian manifolds, g_μν = 0 is forbidden because the metric tensor must be non-degenerate. In effect, de Sitter was actually trying to build a coordinate singularity into his coordinate systems. This was of course several years before those pioneering relativists understood the distinction between coordinate singularities and genuine singularities.

Their thinking evolved. In 1932, Einstein and de Sitter co-authored a two-page paper describing an FLRW model that came to be known as the Einstein-de Sitter universe. Their equation (1) is the standard FLRW metric form for an expanding universe with flat space, for which g_tt = c² everywhere. For the next sixty years, that Einstein-de Sitter model reigned as one of the leading models of the universe, until it was dethroned in the 1990s by accumulation of new data and the Nobel-prize-winning research of James Peebles.

It is therefore quite amusing that Mike Helland rejects the FLRW metric form of Einstein and de Sitter's equation (1), and continues to insist that FLRW models are incompatible with relativity, ignoring derivations of the FLRW models directly from the field equations as found in standard textbooks and even within the archives of this forum.

Mike Helland · Jun 26, 2023

hecd2 said:
Melia is a highly respected astrophysicist, who has a cosmological theory of his own, and so he is naturally going to emphasise things that he thinks supports his model.

Makes sense. As I noted, his cosmology's equation for luminosity distance is the same as mine, so they are equal fits to the supernovae data.

As far as I can tell from that handwaving description, his argument is that FRLW would not rigorously describe a universe with time varying lambda, and this is rather self-evident, but lambda is constant in vanilla LCDM.

I don't think he's suggesting a time varying lambda. He's just referring to the standard idea that our universe is changing from a matter dominated one, to a dark energy one, which means objects that were in free fall will change to not be in free fall.

"While this simplifies the metric coefficients greatly, it ignores the important fact that the metric coefficients depend on the chosen stress-energy tensor, which changes as the universe evolves through phases of deceleration (when matter and radiation dominate) and acceleration (when dominated by inflation and dark energy)."

Why "of course"?

Because in a dark energy only universe, there is only the acceleration phase, and never the free fall phase.

theprestige · Jun 26, 2023

W.D.Clinger said:
Their thinking evolved.

Mike Helland don't think theoretical physics be like it is, but it do.

Mike Helland · Jun 26, 2023

W.D.Clinger said:
Their thinking evolved. In 1932, Einstein and de Sitter co-authored a two-page paper describing an FLRW model that came to be known as the Einstein-de Sitter universe. Their equation (1) is the standard FLRW metric form for an expanding universe with flat space, for which g_tt = c² everywhere. For the next sixty years, that Einstein-de Sitter model reigned as one of the leading models of the universe, until it was dethroned in the 1990s by accumulation of new data and the Nobel-prize-winning research of James Peebles.

It is therefore quite amusing that Mike Helland rejects the FLRW metric form of Einstein and de Sitter's equation (1), and continues to insist that FLRW models are incompatible with relativity, ignoring derivations of the FLRW models directly from the field equations as found in standard textbooks and even within the archives of this forum.

If you accept the expansion of the universe, and you accept that it rewinds back to a singularity, then a cosmic time is a simple, convenient, and "natural" choice of coordinates.

You also are admitting a time coordinate that is not completely relative.

It seems your argument is that since this is how GR is applied in cosmology, it is therefore compatible with GR.

That is to say, canonically, FLRW is compatible with GR. It is because we say it is.

But cosmic time is not completely relative.

The derivations of FLRW all have in common that you deliberately choose a time coordinate that's not entirely relative. That might be how GR is used. But that doesn't get around the fact that you've abandoned what de Sitter calls the "mathematical postulate of the relativity of inertia."

Ziggurat · Jun 26, 2023

Mike Helland said:
But cosmic time is not completely relative.

What exactly do you even mean by this?

Mike Helland · Jun 26, 2023

Ziggurat said:
What exactly do you even mean by this?

de Sitter:

if not equivalent to introducing an absolute time, at least implies the hypothesis that at each point of the four-dimensional space there is one definite coordinate x4 which is preferable to all others to be used as "time", and that at all points and always this one coordinate is actually chosen as time.

He's basically saying that even if you deny the chosen time coordinate is a duck, it quacks like one. That maybe cosmic time isn't absolute, but it's not very relative.

That's system A.

He says that his system B is "entirely relative" and "completely relative" at various points.

It can be satisfied by choosing the system B, without a world-matter, and with complete relativity of the time.

And:

The system A satisfies the "material postulate of relativity of inertia," but it restricts the admissible transformation to those for which at infinity t' = t, and thus introduces a quasi-absolute time, as has been explained in art. 2. In B and C the time is entirely relative

art. 2 in that sentence refers to the article where the two preceding quotes come from.

hecd2 · Jun 26, 2023

Mike Helland said:
Makes sense. As I noted, his cosmology's equation for luminosity distance is the same as mine, so they are equal fits to the supernovae data.

He knows what he’s talking about and is able to fully make his arguments in mathematical terms. You, not at all. Don’t even dream of thinking your silly ideas are in any way equivalent to his.

I don't think he's suggesting a time varying lambda. He's just referring to the standard idea that our universe is changing from a matter dominated one, to a dark energy one, which means objects that were in free fall will change to not be in free fall.

What does this even mean? Are you suggesting that the galaxies are not following geodesics. Can you show me that mathematically, or are you just being a parrot as usual?

"While this simplifies the metric coefficients greatly, it ignores the important fact that the metric coefficients depend on the chosen stress-energy tensor, which changes as the universe evolves through phases of deceleration (when matter and radiation dominate) and acceleration (when dominated by inflation and dark energy)."

Well, duh. I would be very surprised if that is what he’s saying. That would be like saying the laws governing the acceleration of a mass by a spring force are wrong because the spring force changes as the spring expands. You don’t think cosmologists understand and take into account that the stress energy tensor varies across different epochs of universal evolution?

Because in a dark energy only universe, there is only the acceleration phase, and never the free fall phase.

You don’t think that the galaxies are following geodesics in an expanding universe, in other words in free-fall? Can you mathematically distinguish between this so-called free-fall and some other state? Do you think that there is measurable force on celestial bodies predicted in the dark matter dominated epoch? I think someone is misunderstanding what he is reading.

hecd2 · Jun 26, 2023

Mike Helland said:
If you accept the expansion of the universe, and you accept that it rewinds back to a singularity, then a cosmic time is a simple, convenient, and "natural" choice of coordinates.

You also are admitting a time coordinate that is not completely relative.

It seems your argument is that since this is how GR is applied in cosmology, it is therefore compatible with GR.

That is to say, canonically, FLRW is compatible with GR. It is because we say it is.

But cosmic time is not completely relative.

The derivations of FLRW all have in common that you deliberately choose a time coordinate that's not entirely relative. That might be how GR is used. But that doesn't get around the fact that you've abandoned what de Sitter calls the "mathematical postulate of the relativity of inertia."

You seem to be ignoring the fact that FLRW models are derived from GR, and that both Einstein and de Sitter had no problem in proposing a flat expanding metric (which is an FLRW metric) in that 1930s paper WDC referenced. It’s clear that their thinking evolved and you’re quote mining an earlier and flawed interpretation, because that’s just what crackpots do. This is the very definition of quote mining - using quotes from authorities which appear to support you pov, either taken out of context or subsequently abandoned, and where the authority would certainly not agree with the crackpot’s proposition. Just like a YEC, and not for the first time.

What do you actually mean by the statement that “cosmic time is not relative”. Could you define what you mean precisely?

ETA: or perhaps you think that by the early 1930s de Sitter and Einstein were geriatric drooling idiots.

hecd2 · Jun 26, 2023

And while we’re about it could you do the converse and explain what a relative time would be in a homogeneous and isotropic universe?

Ziggurat · Jun 26, 2023

Mike Helland said:
He's basically saying that even if you deny the chosen time coordinate is a duck, it quacks like one. That maybe cosmic time isn't absolute, but it's not very relative.

So what? Relativity requires that the laws of physics be invariant. It does not require that the universe itself be invariant, and it obviously cannot be. A reference frame where mass is on average stationary is unique, and can be differentiated from reference frames where mass is on average not stationary. This is unavoidable, but it is not the problem you imagine it to be.

He says that his system B is "entirely relative" and "completely relative" at various points.

If you make a model universe without any matter in it, yes, that universe can be invariant. It also cannot describe our universe, which obviously has mass in it.

Mike Helland · Jun 26, 2023

hecd2 said:
I would be very surprised if that is what he’s saying. That would be like saying the laws governing the acceleration of a mass by a spring force are wrong because the spring force changes as the spring expands. You don’t think cosmologists understand and take into account that the stress energy tensor varies across different epochs of universal evolution?

You don’t think that the galaxies are following geodesics in an expanding universe, in other words in free-fall? Can you mathematically distinguish between this so-called free-fall and some other state? Do you think that there is measurable force on celestial bodies predicted in the dark matter dominated epoch? I think someone is misunderstanding what he is reading.

Well, you can read it yourself, and you tell me. I don't see where a time varying cosmological constant is proposed tho:

And yet, in ΛCDM the time-time component of the metric, g_tt, is set at 1 at all times and stages of cosmic evolution, even under conditions where it may not be mathematically robust to do so. Given that the Hubble flow – the motion of galaxies due to the universe’s expansion – is not inertial in ΛCDM, i.e., the galaxies don’t experience “freefall,” why should we be comfortable applying free-fall conditions during phases of accelerated expansion? Melia then goes on to prove that when the universe accelerates, an observer must see their time being dilated relative to local free-falling frames, so that g_tt can by no means be 1. And yet, because the condition g_tt = 1 is always imposed, we arrive at an inherent inconsistency: ΛCDM is inconsistent with Einstein’s equivalence principle.

https://new-ground.com/en/articles/...dard-model-of-cosmology/new-ground.2023.77033

As for his cosmology and my idea, of course they are not the same. But they have the same luminosity distance equation, which he argues is a better fit to the data along a different line of reasoning, involving the "cosmic distance duality relation":

https://arxiv.org/pdf/1804.09906.pdf

Mike Helland · Jun 26, 2023

Mike Helland said:
He's basically saying that even if you deny the chosen time coordinate is a duck, it quacks like one. That maybe cosmic time isn't absolute, but it's not very relative.

Ziggurat said:
So what?

So cosmic time isn't entirely relative. That's what you asked.

I'm not fond of the term "gaslighting", but that seems to be your MO.

Mike Helland · Jun 26, 2023

hecd2 said:
And while we’re about it could you do the converse and explain what a relative time would be in a homogeneous and isotropic universe?

Wouldn't it be this:

http://latex.codecogs.com/gif.latex?ds^2 = -\left(1-\frac{r^2}{\alpha^2}\right)dt^2 + \left(1-\frac{r^2}{\alpha^2}\right)^{-1}dr^2 + r^2 d\Omega_{2}^2.

?

I think this covers a part of the manifold centered on an observer.

So to the observer, I think you will argue it wouldn't be exactly homogeneous. But it's inhomogeneous in the same way our observation of the universe is inhomogeneous: the farther we look out, the more time dilation and redshift we see.

Ziggurat · Jun 26, 2023

Mike Helland said:
So cosmic time isn't entirely relative.

Again, so what?

Why is that a problem?

I'm not fond of the term "gaslighting", but that seems to be your MO.

I'm not gaslighting you at all. Rather, you're clueless about physics, and don't understand why relativity matters and what it all means. That's not my fault. At this point, after years of you failing to educate yourself, it's entirely yours.

Mike Helland · Jun 26, 2023

Ziggurat said:
Again, so what?

Why is that a problem?

The argument was time isn't completely relative.

I didn't say that's a problem.

That's just how it is. de Sitter's system B has a completely relative time.

If you want to use a quasi-absolute time because it's simple and convenient, be my guest.

hecd2 · Jun 26, 2023

Mike Helland said:
Wouldn't it be this:

http://latex.codecogs.com/gif.latex?ds^2 = -\left(1-\frac{r^2}{\alpha^2}\right)dt^2 + \left(1-\frac{r^2}{\alpha^2}\right)^{-1}dr^2 + r^2 d\Omega_{2}^2.

?

I think this covers a part of the manifold centered on an observer.

So to the observer, I think you will argue it wouldn't be exactly homogeneous. But it's inhomogeneous in the same way our observation of the universe is inhomogeneous: the farther we look out, the more time dilation and redshift we see.

That’s the Schwarzschild metric which describes the effect of gravity outside a spherically symmmetric central mass, so it’s obviously not homogeneous and is completely inappropriate for cosmology.

Ziggurat · Jun 26, 2023

Mike Helland said:
The argument was time isn't completely relative.

That's not an answer to my question. You still haven't said why it matters whether or not there's a non-relative time.

That's just how it is. de Sitter's system B has a completely relative time.

Why does that matter? Do you think that's a reason to prefer B to A? Because it's not.

Mike Helland · Jun 26, 2023

hecd2 said:
That’s the Schwarzschild metric which describes the effect of gravity outside a spherically symmmetric central mass, so it’s obviously not homogeneous and is completely inappropriate for cosmology.

Yeah. I see that.

Although in the Schwarz metric, r > r_s and there is mass present.

In this case r < a.

That equation is from:

https://physics.stackexchange.com/q...bble-redshift-be-interpreted-as-time-dilation

http://latex.codecogs.com/gif.latex?ds^2 = -\left(1-\frac{r^2}{\alpha^2}\right)dt^2 + \left(1-\frac{r^2}{\alpha^2}\right)^{-1}dr^2 + r^2 d\Omega_{2}^2

This is a static universe (not just 'more or less'). We see that at r=α the metric has a cosmological horizon. The region r<α contains the operationally meaningful portion of the de Sitter space, which can be probed by a single observer located at origin.

W. de Sitter's line element (8B) is:

http://latex.codecogs.com/gif.latex?ds^2 = -dr^2-R^2\sin^2\frac{r}{R}[d\psi^2+\sin^2\psi d\theta^2]+\cos^2\frac{r}{R}c^2dt^2

I suppose through trigonometry they're equivalent? Haven't fully worked that part out yet.

theprestige · Jun 26, 2023

Mike Helland said:
I'm not fond of the term "gaslighting", but that seems to be your MO.

We can add gaslighting to the list of concepts you don't understand.

Mike Helland · Jun 26, 2023

Ziggurat said:
That's not an answer to my question. You still haven't said why it matters whether or not there's a non-relative time.

Why does that matter? Do you think that's a reason to prefer B to A? Because it's not.

If you're comfortable making a special exception for non-relative time in FLRW, that's cool.

I'm just pointing out, that de Sitter pointed out that in system B, time is completely relative.

If you set aside cosmology, the story of the universe's beginning and such, and look at the rest of physics, where experiments take place, non-relative time isn't necessary.

If alien's ever showed up for dinner, and started going through our science textbooks, they would probably look at the laws of motion, gravity, electromagnetism, chemistry, GR, QM, and say "well, it looks like you're coming along."

But when we get to cosmology, and tell them how old the universe is, are they going to be like "yeah, dude, 13.8 billion years!" Or will they be like "wut?"

You could throw cosmology out in its entirety and it would have no affect on any other field of physics, the ones where controlled experiments take place. The one's that are useful.

We make a special exception for the quasi-absolute cosmic time because it feels natural in a universe that has a beginning of time.

I get that the description of the universe at large is a majorly active area in physics. I would suppose the combination of the human need for a creation story and the lack of any real controlled experiments is what promotes the robust amount of theories and interpretations.

At some point, though, as interesting as all this is, one has to ask, is any of it real?

Did galaxies appear a few hundred million years after the beginning of time fully formed?

Maybe this cosmic time is not only unnecessary, but straight up wrong.

Ziggurat · Jun 26, 2023

Mike Helland said:
If you're comfortable making a special exception for non-relative time in FLRW, that's cool.

What exception do you imagine is required? I don't think you actually know what you're talking about.

I'm just pointing out, that de Sitter pointed out that in system B, time is completely relative.

Again, so what? System B does not describe our universe. It's an interesting thought experiment, but it's not physically relevant.

If you set aside cosmology, the story of the universe's beginning and such, and look at the rest of physics, where experiments take place, non-relative time isn't necessary.

It's not necessary in cosmology either. It's convenient. And it's only observable on a universe scale, which we can't do experiments on.

We make a special exception for the quasi-absolute cosmic time because it feels natural in a universe that has a beginning of time.

Exception to what?

At some point, though, as interesting as all this is, one has to ask, is any of it real?

That's where knowing some actual physics and math might be useful.

Too bad you don't.

Maybe this cosmic time is not only unnecessary, but straight up wrong.

Nope, it's not going to be wrong. In any universe with mass, you're going to have a unique reference frame where mass is on average locally stationary. That's unavoidable. The only way out is a universe with no mass, but that's obviously not our universe.

You don't understand what you're talking about. You never have.

Mike Helland · Jun 26, 2023

Ziggurat said:
What exception do you imagine is required?

An exception to time being relative.

Ziggurat · Jun 27, 2023

Mike Helland said:
An exception to time being relative.

I don't think you actually know what this means.

Mike Helland · Jun 27, 2023

Mike Helland said:
As for his cosmology and my idea, of course they are not the same. But they have the same luminosity distance equation, which he argues is a better fit to the data along a different line of reasoning, involving the "cosmic distance duality relation":

https://arxiv.org/pdf/1804.09906.pdf

Interesting new paper:

https://iopscience.iop.org/article/10.3847/2041-8213/acdb49

Distance Duality Test: The Evolution of Radio Sources Mimics a Nonexpanding Universe

Distance duality relation (DDR) marks a fundamental difference between expanding and nonexpanding universes, as an expanding metric causes angular diameter distance smaller than luminosity distance by an extra factor of (1 + z). Here we report a test of this relation using two independent samples of ultracompact radio sources observed at 2.29 GHz and 5.0 GHz. The test with radio sources involves only geometry, so it is independent of cosmological models. Since the observed radio luminosities systematically increase with redshift, we do not assume a constant source size. Instead, we start with assuming the intensive property, luminosity density, does not evolve with redshift and then infer its evolution from the resultant DDR. We make the same assumption for both samples, and find it results in the same angular size–redshift relation. Interestingly, the resultant DDR is fully consistent with a nonexpanding universe. Imposing the DDR predicted by the expanding universe, we infer the radio luminosity density evolves as ρL ∝ (1 + z)3. However, the perfect agreement with a nonexpanding universe under the assumption of constant luminosity densities poses a conspiracy and fine-tuning problem: the size and luminosity density of ultracompact radio sources evolve in the way that precisely mimics a nonexpanding universe.

W.D.Clinger · Jun 27, 2023

Abstract

In 1917, Willem de SItter published the first description of an FLRW model for a universe that is expanding at an exponential rate. That FLRW model has come to be known as de Sitter space.

In 1917, it was philosophically fashionable to assume the universe in which we live is static, so de Sitter described the space using a particular set of static coordinates. Those static coordinates present a misleading impression of the space, because the metric form of de Sitter's equation (8B) is not spatially homogeneous: the g_tt component of the metric tensor depends upon one of the spatial coordinates.

The author and sole proponent of Helland physics has been citing and quoting two different metric forms for de Sitter space, without understanding how those two metric forms assume two distinct systems of static coordinates.

He has also been failing to understand that the metric tensor described by those two metric forms is an FLRW metric. The homogeneity and isotropy of de Sitter space becomes obvious when that metric is written as an FLRW metric form.

Warning

What follows is mostly first year calculus. The author and sole proponent of Helland physics won't understand it, but scientifically literate readers who have been reading this thread for laughs might enjoy it.

Mike Helland said:
What I've read since then also casts doubts on your coordinate system claims.

http://www.bourbaphy.fr/moschella.pdf

....snip....

Ok, as for choosing time coordinates, the "de Sitter tour" goes on:

[qimg]http://www.internationalskeptics.com/forums/imagehosting/thum_762186490b4c275093.png[/qimg]
(click thumbnail to read the caption)

A couple other sources say similar things:

https://astro.uchicago.edu/~kent/fnal/effect.html

https://physics.stackexchange.com/q...bble-redshift-be-interpreted-as-time-dilation

And here's de Sitter's 1917 paper:

So I guess as far as the map territory stuff goes, choosing how to make your time coordinate seems like a normal thing to do.

And de Sitter's original version, seems to give a time dilated past, when the appropriate part of the manifold is covered, which in this case should be less than or equal to zero but greater than -1. This represents the present and the past.

As for the sentence I highlighted: Yes, the theory of relativity allows you to select a coordinate system you prefer to use. That's why it's called the theory of relativity.

As this thread and its predecessor have demonstrated again and again, some coordinate systems are less misleading than others. Although all admissible coordinate systems can be used to reason correctly about the physics, a poor choice of coordinate system makes the physics considerably harder to understand. If your knowledge of general relativity and cosmology is marginal to begin with, so you struggle to understand even the best choices of coordinate system, then a poor choice of coordinate system is going to make the physics even harder for you to understand, to such an extent that you will almost certainly make mistakes.

Which explains why individuals whose hobby horses require them to make such mistakes are especially likely to prefer a poor choice of coordinate system.

For example:

Mike Helland said:
It kind of looks like de Sitter's 1917 model with closed static spatial coordinates might have been a better fit all along.

hecd2 said:
And while we’re about it could you do the converse and explain what a relative time would be in a homogeneous and isotropic universe?

Mike Helland said:
Wouldn't it be this:

http://latex.codecogs.com/gif.latex?ds^2 = -\left(1-\frac{r^2}{\alpha^2}\right)dt^2 + \left(1-\frac{r^2}{\alpha^2}\right)^{-1}dr^2 + r^2 d\Omega_{2}^2.

?

I think this covers a part of the manifold centered on an observer.

hecd2 said:
That’s the Schwarzschild metric which describes the effect of gravity outside a spherically symmmetric central mass, so it’s obviously not homogeneous and is completely inappropriate for cosmology.

No, that is not the Schwarzschild metric. It is a metric form for de Sitter space, expressed using a certain set of static coordinates that (misleadingly) makes the space appear to be inhomogeneous: the g_tt component depends upon the spatial coordinate r.

Because de Sitter space really is homogeneous and isotropic, and that particular choice of coordinates really does make the progress of time depend on one's spatial location, Mike Helland actually gave a fairly good answer to hecd2's challenge.

But Mike Helland came up with that metric form via his usual cargo cult process of searching the web for something he can misinterpret as support for his mistakes. He doesn't understand how that particular coordinate system and that particular metric form are related to the coordinate system and metric form in de Sitter's paper from 1917:

Mike Helland said:
That equation is from:

https://physics.stackexchange.com/q...bble-redshift-be-interpreted-as-time-dilation

W. de Sitter's line element (8B) is:

http://latex.codecogs.com/gif.latex?ds^2 = -dr^2-R^2\sin^2\frac{r}{R}[d\psi^2+\sin^2\psi d\theta^2]+\cos^2\frac{r}{R}c^2dt^2

I suppose through trigonometry they're equivalent? Haven't fully worked that part out yet.

I can help with that.

Theorem

All four of the following metric forms describe exactly the same metric tensor, which is the metric tensor of de Sitter space:

http://latex.codecogs.com/gif.latex?ds^2 = -dr^2-R^2\sin^2\frac{r}{R}[d\psi^2+\sin^2\psi d\theta^2]+\cos^2\frac{r}{R}c^2dt^2
http://latex.codecogs.com/gif.latex?ds^2 = -\left(1-\frac{r^2}{\alpha^2}\right)dt^2 + \left(1-\frac{r^2}{\alpha^2}\right)^{-1}dr^2 + r^2 d\Omega_{2}^2.
http://latex.codecogs.com/gif.latex?ds^2 = -dt^2 + \alpha^2 \cosh^2(t / \alpha) d\Omega_{3}^2
http://latex.codecogs.com/gif.latex?ds^2 = - dt^2 + \left(e^{(t / \alpha)}\right)^2 [dx^2 + dy^2 + dz^2]

Metric form 1 is expressed using de Sitter's static coordinates from his 1917 paper, and is equation (8B) of that paper. Its sign convention is (− − − +). The g_tt component depends on the spatial coordinate r, so these static coordinates obscure the homogeneity and isotropy of the model.

Metric form 2 is expressed using a different set of static coordinates, a different sign convention (− + + +), and the abbreviation

http://latex.codecogs.com/gif.latex?d\Omega_{2}^2 = d\psi^2+\sin^2\psi d\theta^2

Once again, the g_tt component depends on the spatial coordinate r, so this second set of static coordinates also obscures the homogeneity and isotropy of the model.

Metric form 3 is expressed using spherical spatial coordinates in which the homogeneity and isotropy of the model become evident.

Metric form 4 is expressed using Cartesian spatial coordinates and the (− + + +) sign convention. Once again, the homogeneity and isotropy of the model are evident.

Metric forms 3 and 4 are instances of the familiar FLRW metric form. With metric form 3, the spatial slices are hyperspherical, with constant positive curvature. With metric form 4, the spatial slices are flat (Euclidean), with zero curvature. How can they be describing the same metric tensor?

The Ricci and Riemann curvature tensors are invariants, independent of the coordinate system you choose to use, but their numerical components depend on that coordinate system. Furthermore, they are defined on the 4-dimensional spacetime manifold. In relativity, the division of 4-dimensional spacetime into one time dimension and 3 spatial dimensions is not absolute. (That's part of why we call it the theory of relativity.) In some cases, that limited choice of what counts as time and what counts as space allows your choice of coordinate system to push curvature into spatial dimensions if you so desire, or into the time dimension if that is what you prefer.

I will now sketch a proof that metric form 1 (de Sitter's equation (8B) from 1917) describes the same metric tensor as metric form 2. (Mike Helland guessed that their equivalence could be proved using trigonometry, but he guessed wrong.) Their equivalence is proved by a change of variables, just as in my proofs that the (revised) Helland metric form and the TDP metric form are nothing more than obfuscations of the familiar Minkowski metric.

Sketch of proof

Rewrite de Sitter's equation (8B) to use the (− + + +) sign convention.

Rename de Sitter's R to α (alpha).

Define a new variable u by

http://latex.codecogs.com/gif.latex?u \equiv \alpha \sin \frac{r}{\alpha} = R \sin \frac{r}{R}

Then

cos² (r/R) = 1 − sin² (r/R) = 1 − (u²/α²)

and

du² = (cos² (r/R)) dr² = (1 − (u² / α²))

so

dr² = (1 − (u² / α²))⁻¹ du²

Use those equations to replace R and r and dr by expressions involving α, u, and du.

That gives you a metric form that is the same as metric form 2 except it is expressed in terms of u and du instead of r and dr. Simply rename u to r, and you get metric form 2.

To prove the rest of the theorem, I'm going to let Wikipedia do the work.

Metric form 2 is the metric form of Wikipedia's static coordinates for de Sitter space. Wikipedia gives equations that define another set of coordinates x_i in terms of those static coordinates. (Wikipedia's presentation actually starts with the x_i coordinates and defines the static coordinates in terms of those x_i, but we can go in the other direction.)

Metric form 3 is obtained from metric form 2 via transformation to Wikipedia's closed slicing coordinates, which are defined (implicitly) by equations that have the x_i on the left hand side.

Metric form 4 is obtained from metric form 2 via transformation to Wikipedia's flat slicing coordinates, which are also defined (implicitly) by equations that have the x_i on the left hand side.

Metric form 4 is the metric form that makes it easiest to see that de Sitter space describes a universe that is expanding at an exponentially increasing rate. It is also the metric form that makes it easiest to see that the relationship between redshift and distance in a de Sitter universe coincides with the relationship postulated by Helland physics, for an allegedly non-expanding universe (with absolutely no attempt to explain how a non-expanding universe could possibly give rise to the same cosmological redshift as the exponentially expanding de Sitter universe).

W.D.Clinger · Jun 27, 2023

Mike Helland said:
Interesting new paper:

https://iopscience.iop.org/article/10.3847/2041-8213/acdb49

Distance Duality Test: The Evolution of Radio Sources Mimics a Nonexpanding Universe

I have a couple of questions about that paper.

In section 4, the paragraph bracketed by equations (10) and (11) makes three references to proper distance. Consulting a Wikipedia article for definitions of the various distance measures, it looks to me as though all three of that paragraph's references to proper distances should have referred to comoving distances. It seems to me that is a matter of some importance, because (in an expanding universe, in the context of that paragraph) proper distances differ from comoving distances by a factor of 1+z. Can you comment on this?

I'd also be interested to hear your comments with regard to Figure 3 and its caption, whose concluding sentence says "The predictions of the expanding and nonexpanding universes are presented as the solid and dashed lines, respectively." From the figure, it is rather obvious that the solid line (which is said to be the prediction for an expanding universe) fits the data better than the dashed line (which is said to be the prediction for a nonexpanding universe).

hecd2 · Jun 27, 2023

W.D.Clinger said:
hecd2 said:

That’s the Schwarzschild metric which describes the effect of gravity outside a spherically symmmetric central mass, so it’s obviously not homogeneous and is completely inappropriate for cosmology.

Click to expand...

No, that is not the Schwarzschild metric. It is a metric form for de Sitter space, expressed using a certain set of static coordinates that (misleadingly) makes the space appear to be inhomogeneous: the g_tt component depends upon the spatial coordinate r.

Yeah, my only excuse was my unseemly haste to reply to Mike, and being beguiled by the similarity, I didn't pay enough attention to the details.

Excellent post, by the way.

Mike Helland · Jun 27, 2023

W.D.Clinger said:
I can help with that.

...

That gives you a metric form that is the same as metric form 2 except it is expressed in terms of u and du instead of r and dr. Simply rename u to r, and you get metric form 2.

Very interesting. Thanks for the detailed, informative response.

So in eq1 we have a 1 (well, -1) as the coefficient for dr², and in eq2, that Schwarzschildy looking coefficient for it. The steps you give to get from one to the other make sense. Though I'm still working toward an intuition what's going on in both.

The stack exchange answer gives a reason for why eq2 has static coordinates, as opposed to "length contracted" coordinates, but I'm still working out why that is. The reason given has to do with that integral, which wolfram alpha says equals an arcsin() expression.

To prove the rest of the theorem, I'm going to let Wikipedia do the work.

Metric form 2 is the metric form of Wikipedia's static coordinates for de Sitter space. Wikipedia gives equations that define another set of coordinates x_i in terms of those static coordinates. (Wikipedia's presentation actually starts with the x_i coordinates and defines the static coordinates in terms of those x_i, but we can go in the other direction.)

Metric form 3 is obtained from metric form 2 via transformation to Wikipedia's closed slicing coordinates, which are defined (implicitly) by equations that have the x_i on the left hand side.

Metric form 4 is obtained from metric form 2 via transformation to Wikipedia's flat slicing coordinates, which are also defined (implicitly) by equations that have the x_i on the left hand side.

Metric form 4 is the metric form that makes it easiest to see that de Sitter space describes a universe that is expanding at an exponentially increasing rate. It is also the metric form that makes it easiest to see that the relationship between redshift and distance in a de Sitter universe coincides with the relationship postulated by Helland physics, for an allegedly non-expanding universe (with absolutely no attempt to explain how a non-expanding universe could possibly give rise to the same cosmological redshift as the exponentially expanding de Sitter universe).

From the flat slicing, I think I understand that x₀ and x₁ sort of disappear from the result, or combine in a sense, while x₂, x₃, x₄ become the spatial coordinates.

The one that I mentioned when I first cited the de Sitter Sightseeing Tour is:

http://www.bourbaphy.fr/moschella.pdf

Figure 8:

Here time is defined by relation:

http://latex.codecogs.com/gif.latex?x_0 + x_4 = Re^{\frac{t}{R}}

From this you get that static time coefficient and the dynamic space coefficients that satisfy the equation for the hyperboloid.

As the caption says, http://latex.codecogs.com/gif.latex?x_0 + x_4 > 0 covers half the manifold. So I'm thinking, how about this:

http://latex.codecogs.com/gif.latex?x_0 + x_4 = Re^{\frac{t}{R}}-R

When t=0, http://latex.codecogs.com/gif.latex?x_0 + x_4 = 0, and as t goes to -infinity, http://latex.codecogs.com/gif.latex?x_0 + x_4 goes to -R.

If the standard FLRW metric were derived from this, there would be a short period of contraction, and then an indefinite period of expansion.

Not very useful for expanding space. But if we could turn it around so space is static and time is dynamic, then this describes a time dilated past and time contracted future.

What about choosing the time coordinate as the dynamic one, and the space coordinates as static ones? Could you still satisfy the equation for the hyperboloid?

Does it help if you flip the hyperboloid on its side? I think that means you're in anti-de Sitter territory: http://latex.codecogs.com/gif.latex?-x_0^2 - x_1^2 + x_2^2 + x_3^2 + x_4^2 = \alpha^2?

Still learning about all that and working that out.

One thing (out of many things) I find fundamentally confusing is whether it makes more sense to state http://latex.codecogs.com/gif.latex?g_{tt} = -(e^{H_0t})^2 c^2 as we have been, or instead http://latex.codecogs.com/gif.latex?g_{tt} = -(\ln(H_0t + 1))^2 c^2 makes more sense.

The scale factor in FLRW takes t as the cosmic time.

But the time scale factor in TDP (http://latex.codecogs.com/gif.latex?g_{tt} = -(e^{H_0t})^2 c^2) takes t as the measured time.

The slicings are "hypersurfaces of equal cosmic time". So if the slicings should be of equal amounts, is it naive to think that means something like t=0, t=-1, t=-2, t=-3? Because if that's what's up, it seems that should be using the latter, the ln() expression in the metric form.

That probably might not make a ton of sense.

Basically the time we measure (t) should be:

http://latex.codecogs.com/gif.latex?t = \frac{1}{H_0} \ln (H_0 \tau + 1)

Here I suppose http://latex.codecogs.com/gif.latex?\tau takes the place of "constant cosmic time" in the slicings, but that doesn't end up being t in the resulting 4-D spacetime.

http://latex.codecogs.com/gif.latex?x_0 + x_1 = R \ln(\frac{\tau}{R} + 1)

Cont: Why James Webb Telescope rewrites/doesn't the laws of Physics/Redshifts (2)

Philosopher

Master Poster

Philosopher

Philosopher

Philosopher

Master Poster

Master Poster

Philosopher

Philosopher

Master Poster

Philosopher

Master Poster

Philosopher

Philosopher

Penultimate Amazing

Philosopher

Penultimate Amazing

Philosopher

Master Poster

Master Poster

Master Poster

Penultimate Amazing

Philosopher

Philosopher

Philosopher

Penultimate Amazing

Philosopher

Master Poster

Penultimate Amazing

Philosopher

Penultimate Amazing

Philosopher

Penultimate Amazing

Philosopher

Penultimate Amazing

Philosopher

Philosopher

Philosopher

Master Poster

Philosopher