Cosmological Redshift and metric expansion

[AbstractDreamer]

3 minutes ago, exchemist said:

But if wavelength alters and frequency does not, then surely the speed must change. Do you want to develop a model in which c has changed over time, or something?

I'm just a chemist, not a GR specialist. I've never worked with tensors.  @Mordred seems to be one, however. If you are bothered that space and time are treated differently from the viewpoint of expansion you will have to listen to him.  

 

I have no model to develop.  I'm only asking questions that we've had for over 100 years since establishing the accepted model.   

There's a giant elephant in the room saying "Spacetime is a single manifold".

There's another giant elephant in the room saying "Space is different from time because we have conditions in flat spacetime where only space expands and time does not dilute".

There is a clear contradiction here.

 

[Genady]

Depending on conditions, different dimensions behave differently. For example, in the spherically symmetric case with central mass, the temporal and the radial dimensions vary while the two spherical dimensions do not. Similarly, in the homogeneous and isotropic case, the spatial dimensions vary while the temporal does not. 

[AbstractDreamer]

41 minutes ago, joigus said:

GR is invariant under re-scalings of time in particular. So a simple re-scaling of time would give you your desired metric. There is no physical information in this distinction. A universe for which the time re-scales as it passes is totally physically equivalent to one in which it's space that expands by means of a time-dependent expansion factor.

First post that addresses my questions.   +1
So time rescaling as it passes is equivalent to space expansion due to a scale factor at that time.  But what determines how much of that change is attributed to which case?

In other words, how much of a redshift measurement is due to space expansion and how much is due to time dilation?  According to the FLRW metric, it is ALL due to space expansion and there is a zero, or at least a net-zero, time dilation effect.   Take in the extreme case where there is no space expansion at all, and all the redshift is caused by time dilation, and the recessional velocity is caused by a  dilation in time rather than by an expansion of space  Why is this such an absurdity?

17 minutes ago, Genady said:

Depending on conditions, different dimensions behave differently. For example, in the spherically symmetric case with central mass, the temporal and the radial dimensions vary while the two spherical dimensions do not. Similarly, in the homogeneous and isotropic case, the spatial dimensions vary while the temporal does not. 

Right, but that is just an artifact of orientation of your coordinate system.  A neat trick to simplify a model.  If you orientate the model to where certain dimensions on a manifold do not vary and other dimension do vary, that does not mean that the dimension that does not vary cannot vary in other models.

So we orientate our redshift observations to one where the temporal dimension does not vary.  That does not mean it cannot vary.

The FLRW metric is orientated towards no allowance for time dilution in flat spacetime - of course it is not going to vary, its orientated that way!  That does not mean there is no time dilution in flat spacetime.

So we go back to my original questions.  Where are the other interpretations / orientations - ones where time dilution can occur in flat spacetime?  Why have we all towed the line fro 100 years with the one accepted orientation where there is no time dilation in flat spacetime?

But more importantly... what are the limitations and consequences of such an orientation?  What might we be missing because of this orientation?

[exchemist]

1 hour ago, AbstractDreamer said:

I have no model to develop.  I'm only asking questions that we've had for over 100 years since establishing the accepted model.   

There's a giant elephant in the room saying "Spacetime is a single manifold".

There's another giant elephant in the room saying "Space is different from time because we have conditions in flat spacetime where only space expands and time does not dilute".

There is a clear contradiction here.

 

Well obviously there can't be, or cosmic expansion would have been blown up as be a failed model, long since. So it's a question of what you don't understand, rather than a contradiction in the model. But it looks as if you are in dialogue with the right people, so I'll get back to being an interested spectator. 

[Genady]

36 minutes ago, AbstractDreamer said:

Right, but that is just an artifact of orientation of your coordinate system.  A neat trick to simplify a model.  If you orientate the model to where certain dimensions on a manifold do not vary and other dimension do vary, that does not mean that the dimension that does not vary cannot vary in other models.

So we orientate our redshift observations to one where the temporal dimension does not vary.  That does not mean it cannot vary.

The FLRW metric is orientated towards no allowance for time dilution in flat spacetime - of course it is not going to vary, its orientated that way!  That does not mean there is no time dilution in flat spacetime.

So we go back to my original questions.  Where are the other interpretations / orientations - ones where time dilution can occur in flat spacetime?  Why have we all towed the line fro 100 years with the one accepted orientation where there is no time dilation in flat spacetime?

But more importantly... what are the limitations and consequences of such an orientation?  What might we be missing because of this orientation?

Right, it is a consequence of the coordinate system choice, called synchronous coordinates. Perhaps, in other choice of coordinates, the time would vary, e.g., conformal time. But physics does not depend on coordinate system. A different coordinate system will not be physically distinguishable from the current one, but it might allow to get some results easier than getting them in the current one. Convenience / symmetry / simplicity / usefulness are the only criteria for the choice of coordinates.

[Mordred]

3 hours ago, AbstractDreamer said:

 

In other words, how much of a redshift measurement is due to space expansion and how much is due to time dilation?  According to the FLRW metric, it is ALL due to space expansion and there is a zero, or at least a net-zero, time dilation effect.   Take in the extreme case where there is no space expansion at all, and all the redshift is caused by time dilation, and the recessional velocity is caused by a  dilation in time rather than by an expansion of space  Why is this such an absurdity?

 

That has been looked into, if you run the time dilation calculations using cosmological redshift as gravitational redshift. You will hit infinity at the Hubble horizon as that is also the point where recessive velocity which is an apparent but not actual kinetic velocity will exceed c.

 It may help to consider that the other major evidence of expansion isn't simply redshift. The most important evidence is the temperature decrease due to an increasing volume.

The other detail to consider is extreme efforts have been made from all the steady state supporters that didn't Like the idea of the BB. Nearly every possible effort to find counter arguments have been tried. They all failed. 

Time dilation aspects included.

If your really looking into an aspect of expansion with a time dilation effect. Look into the integrated Sache Wolfe effect. It should give you some indication  of some of the time dilation aspects many aren't fully aware of. It directly involves the stages where the universe switched from radiation dominant to matter to Lambda  dominant and the surface of last scattering (CMB)

Another detail is the typical cosmological redshift equation ie the one I posted earlier in the article isn't the one a professional cosmologist uses 

It doesn't take into consideration the evolution of radiation, matter and Lambda 

 

Edited May 24, 2023 by Mordred

[Mordred]

I do recall Bunn and Hoggs years ago wrote a paper examining cosmological redshift as a possible time dilation. He also wrote one specifically on gravitational redshift equating to time dilation. So it's been examined, I can see if I can track that paper down.

[Mordred]

Found the paper I was looking for. Bunn and Hogg examines cosmological redshift in context of both gravitational redshift (would thus include time dilation) and Doppler shift. (Only involves time dilation in the relativistic scenario).

He concludes that as free fall observers and emitters apply, then the latter case is more accurate than the previous.

https://arxiv.org/abs/0808.1081

One of the problems with the former and latter case is that you end up applying a large number of  infinitesimal calculations between observer and emitter.

Edited May 24, 2023 by Mordred

[joigus]

21 hours ago, AbstractDreamer said:

But what determines how much of that change is attributed to which case?

A mindless, meaningless, change in coordinates. It's a little bit like asking how much of the girth of the Earth is determined by this or that meridian. The coordinates that determine the FRWL metric (and the 'static' character of g₀₀ ) are simply a matter of convenience.

[AbstractDreamer]

On 5/24/2023 at 10:59 PM, Mordred said:

Found the paper I was looking for. Bunn and Hogg examines cosmological redshift in context of both gravitational redshift (would thus include time dilation) and Doppler shift. (Only involves time dilation in the relativistic scenario).

He concludes that as free fall observers and emitters apply, then the latter case is more accurate than the previous.

https://arxiv.org/abs/0808.1081

One of the problems with the former and latter case is that you end up applying a large number of  infinitesimal calculations between observer and emitter.

Wonderful answer thank you!  I feel somewhat vindicated with posting this thread.  This paper seems to answer my questions, at least to my level of comprehension.

I disagree that they conclude Doppler redshift is more accurate than gravitation redshift.  My understanding is that they conclude Doppler redshift interpretation is more natural.  And by natural I assume they mean because its more simplistic to describe.

"Within this frame, you would, by the equivalence principle, interpret their results as a Doppler shift. In so doing, you would be choosing to regard the Doppler family as the natural one, because this family is the one whose behavior is simplest to describe in your chosen frame" page 8 line 4 from the paper above.

At this point, I have an issue with the free fall requirements of the Doppler shift model. That is, no gravitational difference between an observer and its neighbour  along the path of the radiation, where any difference in observed frequency can be attributed as kinematic .   Would a passing gravitational wave not break this local inertial frame between a pair of neighbours?  Over 13 billions years, its hard to imagine how a photon avoids an encounter with a gravitational wave.

On the other hand, a family of observers where each member is at rest relative to its neighbour seems more "natural" to me.  That is, any difference in observed frequency of the photon can be attributed to gravitational redshift - a time dilation cause of redshift.

More important than this choice of frame, is their conclusion that BOTH interpretations are valid.
"There is no “fact of the matter” about the interpretation of the cosmological redshift: what one concludes depends on one’s coordinate system or method of calculation."  page 8 line 17 
"The common belief that the cosmological redshift can only be explained in terms of the stretching of space is based on conflating the properties of a specific coordinate system with properties of space itself. This confusion is precisely the opposite of the correct frame of mind in which to understand relativity." bit further down

This validates my point entirely.  The interpretation of cosmological redshift as Dopplershift or gravitational shift is a matter of choice, and not of facts.  A choice of your arbitrary orientation of your coordinate system, something which I said even before I knew what I was talking about (or rather less that what I know now which is just marginally above zero).

Space expansion is an ARTIFACT of the coordinate system where we CHOOSE zero gravitational causes to cosmological redshift.   

In other words if you choose to zerolise time dilation causes to cosmological redshift, then space expansion neatly explains superluminal recession speeds.

 

So to address other points of evidence of space expansion as fact rather than choice:

On 5/24/2023 at 7:15 PM, Mordred said:

 It may help to consider that the other major evidence of expansion isn't simply redshift. The most important evidence is the temperature decrease due to an increasing volume.

But I thought space expansion doesn't increase volume.  Unless you are observing the volume from outside using a measurement reference that is independent of such expansion.   If a cube 1m³ expands under space expansion, it's still 1m³ because your ruler also expands with the cube. So wouldn't you have to be outside of the universe to claim any part of it increased in volume?  Or if you are inside the universe measuring another part of it, how do you know your ruler is not being stretched in order to conclude the volume being observed is increasing?

Temperature is measurement of average energy in body/volume right?  "Average" meaning over time.  Even if space expansion "creates volume", how can we say the temperature decreases due to an increasing volume.  Why can we not say "temperature decreases due to a slowing of time" (we are receiving less observables that measure temperature due to time slowing down)?   If I measure 10 photons with a fixed energy propagating from a 1m³ volume over 1 second and we agree to calibrate this reading and call it 10 Hotness.   If I then tell you I have two more experiments, one where I space expanded the volume to 2m³ the volume and another where I time diluted the volume to half the rate of time.   In the space expansion experiment there are now less photons per volume.  In the time dilated experiment there are now less photons per time.   Both experiments would measure a decrease in temperature to 5 Hotness.  But why would we assert that the decrease in temperature is due to only the volume changing?
 

On 5/24/2023 at 7:15 PM, Mordred said:

The other detail to consider is extreme efforts have been made from all the steady state supporters that didn't Like the idea of the BB. Nearly every possible effort to find counter arguments have been tried. They all failed. 

Time dilation aspects included.

 

I don't see why time dilation necessarily contradicts BB or steady state.  Both of which are conclusions from many other factors besides time dilation.  I think its more important to build from the ground up and end up wherever we end up, rather than top down where we want either the BB or a steady state to be a reality and then railroad observations, interpretations and models to fit.  Einstein did that when declaring "God does not play dice", and trying to make QM fit his deterministic belief of the universe.

Ultimately, there is no evidence that excludes time dilation as a factor in cosmological redshift, either through gravitational time dilation or some other kind of mechanics that result in time dilation.   And I don't know why we commonly accept cosmological redshift is fully attributed to kinematic Dopplershift.

Edited August 25, 2023 by AbstractDreamer

[Bufofrog]

49 minutes ago, AbstractDreamer said:

But I thought space expansion doesn't increase volume.

That would be a neat trick.

[AbstractDreamer]

38 minutes ago, Bufofrog said:

That would be a neat trick.

Here's a neat trick.  Which green polygon has greater volume?
 

[mistermack]

How many dimensions does a polygon have?

[exchemist]

35 minutes ago, AbstractDreamer said:

Here's a neat trick.  Which green polygon has greater volume?
 

Actually, this is something that has always bothered me too, about the concept of expansion of the “metric”. I’m hoping someone can explain.

[Genady]

18 minutes ago, exchemist said:

Actually, this is something that has always bothered me too, about the concept of expansion of the “metric”. I’m hoping someone can explain.

Consider the underlined sentence:

Edited August 25, 2023 by Genady

[exchemist]

50 minutes ago, Genady said:

Consider the underlined sentence:

Why then do people speak of the metric, in the context of expansion? Or am I wrong in thinking that they do?

[Genady]

10 minutes ago, exchemist said:

Why then do people speak of the metric, in the context of expansion? Or am I wrong in thinking that they do?

Metric does not expand. Metric defines distances between points. Points are labeled by coordinates. The distances between points expand.

[Genady]

3 hours ago, AbstractDreamer said:

Here's a neat trick.  Which green polygon has greater volume?
 

To answer questions about length / area / volume one needs metric. Coordinates do not have the required information.

[mistermack]

I've always favoured the River Model, of GR, where gravity is modelled as a flow of space into a black hole. 

If space flows into massive bodies like black holes and stars, it must be collapsing on arrival. If there was a mechanism whereby the collapse in one place, was mirrored by instant re-emergence somewhere else, would that lead to the apparent expansion, and redshift? 

[Genady]

The expansion is a feature of a homogenous and isotropic space. Black holes and stars don't fit in this picture.

[mistermack]

4 hours ago, Genady said:

The expansion is a feature of a homogenous and isotropic space. Black holes and stars don't fit in this picture.

That doesn't really answer the question. 

Anyway, if everything is expanding, does that mean I'm expanding and time is expanding, and if it is, how come there's a red shift?

[Genady]

5 minutes ago, mistermack said:

Anyway, if everything is expanding, does that mean I'm expanding and time is expanding, and if it is, how come there's a red shift?

No, not everything is expanding. Only the space on scales of 100 Mpc and up is expanding. The redshift is caused by expanding of the light wavelength together with the expanding space on these scales.

[AbstractDreamer]

On 8/25/2023 at 8:00 PM, Genady said:

To answer questions about length / area / volume one needs metric. Coordinates do not have the required information.

I'm asking which has bigger volume, not how big their volumes are according to some metric.  You don't need a metric to compare volumes, if the coordinate systems are the same, which they are.

The point is stretching axes doesn't change magnitude whatever metric you are using, and so space expansion doesn't change volume.   Both objects are 2x2 square units, and internally consistent with that shape and magnitude - no matter how much an observer stretches the axes, inside the polygon you will never notice any difference.

If you are arguing that space expansion increases volume, then you are saying the square has larger volume than the rectangle, because I changed the magnification and zoomed in significantly on the x-axis.   So then your position is that the volume of each green polygon is a property of the observer and not the polygon.

 

On 8/26/2023 at 2:02 AM, Genady said:

No, not everything is expanding. Only the space on scales of 100 Mpc and up is expanding. The redshift is caused by expanding of the light wavelength together with the expanding space on these scales.

Space does not have to expand at all.  That's the whole point of that paper.  Cosmological redshift does not have to interpreted as due kinematic Doppler shift. 

[Genady]

1 hour ago, AbstractDreamer said:

You don't need a metric to compare volumes

Yes, I do. So, the rest of the conclusions are wrong. Coordinates don't say anything about the length, area, and volume. Coordinates are arbitrary.

1 hour ago, AbstractDreamer said:

Space does not have to expand at all.

Expansion of space is a solution of the field equation in these conditions.

[Genady]

3 hours ago, AbstractDreamer said:

The point is stretching axes doesn't change magnitude whatever metric you are using

Wanted to add a couple of examples to my previous comment and to demonstrate why this ^^^ is incorrect.

One example is metric that measures number of colored pixels. In this metric, the second shape is larger than the first.

Another metric is square of difference between the pixels in vertical and in horizontal directions. In this metric, the first shape is larger than the second.