# Cosmological Redshift and metric expansion

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"In physics, a redshift is an increase in the wavelengthhttps://en.wikipedia.org/wiki/Redshift

"One interpretation of this effect (cosmological redshift) is the idea that space itself is expanding." https://en.wikipedia.org/wiki/Redshift

"In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifoldhttps://en.wikipedia.org/wiki/Spacetime

Why do we use classical physics and not GR to interpret cosmological redshift as an increase in wavelength and not a decrease in frequency?

Why do we allow the metric of space to expand, but not the metric of time, when interpreting cosmological redshift as space expansion?

What are the other interpretations of cosmological redshift where something else is happening other than space expanding?

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11 minutes ago, AbstractDreamer said:

Why do we use classical physics and not GR to interpret cosmological redshift

We use GR.

12 minutes ago, AbstractDreamer said:

as an increase in wavelength and not a decrease in frequency?

It is both.

12 minutes ago, AbstractDreamer said:

Why do we allow the metric of space to expand, but not the metric of time, when interpreting cosmological redshift as space expansion?

This how the metric of homogeneous and isotropic universe works. See FLRW metric.

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As mentioned GR is used, the FLRW metric is simply an accurate simplified derivative of GR.

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7 minutes ago, Genady said:

We use GR.

Show me where.

10 minutes ago, Genady said:

It is both.

It is, but show me where cosmological redshift is interpreted as a decrease in frequency then.

12 minutes ago, Genady said:

This how the metric of homogeneous and isotropic universe works. See FLRW metric.

This is how the FLRW fits observations of cosmological redshift and interpretation of it as space expansion.  You can't use a parametisation to prove it's assumptions.

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I can post the equations after work but the FLRW metric derives from the Newton approximation dust solution in commoving coordinates.

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2 minutes ago, Mordred said:

As mentioned GR is used, the FLRW metric is simply an accurate simplified derivative of GR.

It is used in the FLRW metric, AFTER the interpretation of space expansion.  Space expansion is a premise of the FLRW metric  You cant use a metric to justify its premises.  Once we assume cosmological redshift is the observation resulting from space expansion, the FLRW metric ensues.  Before that, it is meaningless to talk about the FLRW.

I'm not asking about the GR used within FLRW, I'm asking about its premise that space is expanding.
Show me where GR is used in the interpretation of cosmological redshift as something other than space expansion.

9 minutes ago, Mordred said:

I can post the equations after work but the FLRW metric derives from the Newton approximation dust solution in commoving coordinates.

If the equations assume space expansion exists in order to describe it, then they wont help question space expansion only reinforce and it.

Where is the evidence for space expansion other than cosmological redshift?

What are alternative interpretations of cosmological redshift other than space expansion?

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16 minutes ago, AbstractDreamer said:

show me where cosmological redshift is interpreted as a decrease in frequency then

In the second part of the first sentence that you've quoted in the OP. It applies to any redshift, the cosmological one included.

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1 minute ago, Genady said:

In the second part of the first sentence that you've quoted in the OP. It applies to any redshift, the cosmological one included.

Right.  So.... why is the metric of space expanding and the metric of time NOT changing, in the specific case of the widely accepted interpretation of cosmological redshift.

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1 minute ago, AbstractDreamer said:

Right.  So.... why is the metric of space expanding and the metric of time NOT changing, in the specific case of the widely accepted interpretation of cosmological redshift.

If you want to suggest a different metric for the homogeneous and isotropic universe, go ahead.

If you want to suggest a better model of the universe, go ahead.

Anyway, there is only one metric, the spacetime metric. In the FLRW metric, the space rather than the metric of space is expanding.

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2 minutes ago, Genady said:

If you want to suggest a different metric for the homogeneous and isotropic universe, go ahead.

If you want to suggest a better model of the universe, go ahead.

Anyway, there is only one metric, the spacetime metric. In the FLRW metric, the space rather than the metric of space is expanding.

I'm not suggesting anything.  I'm asking questions.  All of the answers so far have missed the real crux of my questions.

"There is only one metric, the spacetime metric" and yet it is called space expansion and not spacetime expansion.  Why?

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Just now, AbstractDreamer said:

it is called space expansion and not spacetime expansion.  Why?

In the metric,

the second term on the right is spatial interval. As you see, it depends on the scale factor, a(t), which can change with time. OTOH, the first term which is temporal interval, does not change.

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That's the FLRW metric.  One of it's premises is that space is expanding.  After that assumption it then describes the expansion.  But ill say it again, we can tear apart the FLRW equations all day, you can never use it to justify its own premise.  So please, stop using the FLRW to justify that space is expanding.  The FLRW describes how it expands.  It does NOT justify it.

We have to go back to observational evidence - cosmological redshift.

It is very logical why cosmological redshift is interpreted as space expansion - it makes a lot of sense.

But spacetime is not commonly sensible. And having a sensible interpretation does not mean that there are no alternatives.

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1 minute ago, AbstractDreamer said:

That's the FLRW metric.  One of it's premises is that space is expanding.  After that assumption it then describes the expansion.  But ill say it again, we can tear apart the FLRW equations all day, you can never use it to justify its own premise.  So please, stop using the FLRW to justify that space is expanding.  The FLRW describes how it expands.  It does NOT justify it.

We have to go back to observational evidence - cosmological redshift.

It is very logical why cosmological redshift is interpreted as space expansion - it makes a lot of sense.

But spacetime is not commonly sensible. And having a sensible interpretation does not mean that there are no alternatives.

I am not justifying it. I am answering your question, "it is called space expansion and not spacetime expansion.  Why?"

As I've said above, if you wish to suggest a different interpretation, go ahead.

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1 minute ago, Genady said:

I am not justifying it. I am answering your question, "it is called space expansion and not spacetime expansion.  Why?"

As I've said above, if you wish to suggest a different interpretation, go ahead.

I'm not even really asking to justify the FLRW metric.  It is perfectly justified - given its assumptions and premised.

I'm asking to justify why space expansion is the only interpretation of cosmological redshift.

You've said for me to suggest a different interpretation and then explicitly repeated it.  Stop derailing my thread please.

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6 minutes ago, AbstractDreamer said:

I'm asking to justify why space expansion is the only interpretation of cosmological redshift.

I don't know why you say and what you mean saying that "space expansion is the only interpretation of cosmological redshift." Thus, I don't know what you are asking to justify.

8 minutes ago, AbstractDreamer said:

This is up to moderators.

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2 hours ago, AbstractDreamer said:

Show me where.

It is, but show me where cosmological redshift is interpreted as a decrease in frequency then.

Just on this small point, the relationship between speed, c, frequency, ν, and wavelength, λ, is c = νλ. This is true of any wave (light, sound, water etc). So, given that for light c is constant, as observed by us (that being the basic premise from which relativity starts), once you have said its wavelength increases there is no need to say frequency decreases: the relationship is automatic. Everyone knows this, so that's why you don't see it mentioned.

45 minutes ago, AbstractDreamer said:

I'm not even really asking to justify the FLRW metric.  It is perfectly justified - given its assumptions and premised.

I'm asking to justify why space expansion is the only interpretation of cosmological redshift.

You've said for me to suggest a different interpretation and then explicitly repeated it.  Stop derailing my thread please.

I'm not sure anyone would claim that it is the only interpretation. In science one never formally closes the door to other hypotheses. Surely the claim of science is that it is the leading interpretation, to the extent that there are currently no serious alternatives?

I have read about the "tired light" hypothesis for example. This was tried by some people for a while but soon blew up, as it implied predictions that were not borne out by observation.https://en.wikipedia.org/wiki/Tired_light

So the reason @Genady is asking you to put forward an alternative is that there are no viable alternatives that anyone knows about, at least not at the moment.

Edited by exchemist
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Might help to understand that spacetime is a geometric model describing a volume with variations in time. It is those time variations that require time as a dimension.

Now with a homogeneous and isotropic (roughly) uniform mass distribution you don't really require this for a flat universe. However you do if the universe is positive or negative curved  hence its included.

It isn't accurate precisely to think of spacetime itself expanding. It is more accurate to think of the mean average density of mass distribution is decreasing and that distribution is over a greater volume.

Does that help ?

Edit added aid expansion is literally described via the thermodynamic laws. All calculations involving the expansion history applies those laws via the fluid equations of the FLRW metric.

Edited by Mordred
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Here is the related math The first part will show the FLRW metric and the Newton approximation under GR

FLRW Metric equations

$d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]$

$S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}$

$\rho_{crit} = \frac{3c^2H^2}{8\pi G}$

$H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}$

setting $T^{\mu\nu}_\nu=0$ gives the energy stress momentum tensor as

$T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)$

$T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0$

which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0.

the related GR solution the the above will be the Newton approximation.

$G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}$

As the last post I did glitched, rather than redoing all the latex you can see the most common derivative of redshift here. I don't feel like spending another half hour latexing the formulas here to have it glitch on an edit.

this is the most commonly used derivatives anyways.

You will note no time dilation is involved.

Edited by Mordred
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19 hours ago, exchemist said:

Just on this small point, the relationship between speed, c, frequency, ν, and wavelength, λ, is c = νλ. This is true of any wave (light, sound, water etc). So, given that for light c is constant, as observed by us (that being the basic premise from which relativity starts), once you have said its wavelength increases there is no need to say frequency decreases: the relationship is automatic. Everyone knows this, so that's why you don't see it mentioned.

Yes the relationship between frequency and wavelength automatic.  But wavelength is a measure of space, which we allow to expand as described by the FLRW metric, and frequency is a measure of time... which apparently cant expand (specifically in the case of cosmological redshift and not in the case of dilation).  Why?  Spacetime is a continuum.  Why, in the case of interpreting cosmological redshift, is it not a continuum?

19 hours ago, exchemist said:

I'm not sure anyone would claim that it is the only interpretation. In science one never formally closes the door to other hypotheses. Surely the claim of science is that it is the leading interpretation, to the extent that there are currently no serious alternatives?

So the reason @Genady is asking you to put forward an alternative is that there are no viable alternatives that anyone knows about, at least not at the moment.

If there are no viable alternatives, then it is the only viable interpretation.  Which is rather surprising considering there is no evidence for space expansion other than cosmological redshift observations.   We observe cosmological wavelengths redshifted in 1912, we theorise space can expand, we develop a model (FLRW) to match redshift observations based on that in 1922.  We can use the model to match subsequent observations based on the same assumptions.  But we cannot then go and claim the model and the mathematics proves space expands.

In analogy:  Newton observed an apple fall, he theorised gravity as a force, he developed models and maths to match his "falling" observations.  We can use the model to match subsequent observations and make predictions rather accurately in most circumstances.  But you cannot use Netwon's law to claim gravity is a force.

10 hours ago, Mordred said:

You will note no time dilation is involved.

Why is that?  Why must there be no time dilation?  What is it about cosmological redshift observations that says space expands but time does not dilute?  If relative motion can dilate time, why should non-relative motion not?  Why are we applying "classical reasoning" to cosmological redshift observations?

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You don't have time dilation due to the homogeneous and isotropic mass distribution. At time of the emitter the universe mass distribution is uniform. At time of observer the same applies. During any point in time between the two the same applies. In essence you don't have time dilation when spacetime is flat at any point in travel time of the null geodesic worldline.

Edit a simple analogy that might help. Take an elastic band stretch it just enough to be straight.

There is your null geodesic of the photon path. Stretch it further the density decreases but it will still remain straight.

Edited by Mordred
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10 minutes ago, Mordred said:

You don't have time dilation due to the homogeneous and isotropic mass distribution. At time of the emitter the universe mass distribution is uniform. At time of observer the same applies. During any point in time between the two the same applies. In essence you don't have time dilation when spacetime is flat at any point in travel time of the null geodesic worldline.

But if there was a cosmological, non-relative motion sourced, time dilation effect, could the universal still be homogenous and isotropic wrt mass distribution?

Ignoring a number of observations that could be argued as violations to homogeneity and also ignoring the violations of isotropy for now (https://en.wikipedia.org/wiki/Cosmological_principle), why or how does homogeneity and isotropy directly refute time dilation in flat space?

What makes the premise of homogenous and isotropic mass distribution irrefutable and sacrosanct?  Where is the evidence, other than ΛCDM model which is based (not solely) upon the FLRW metric and inherits the same premises?  We cannot use models and equations to prove their premises, despite the models and equations matching many observations and predictions.

The implications of the premise that space can expand but time does not dilate when spacetime is flat (not the premise of homogeneity) are enormous.  And the only evidence we have is redshifted measurements of wavelengths that have been travelling cosmological distances and times.  Why has so little scientific attention been paid towards a critical point in our progression of knowledge since 1922, such that there are NO viable alternative interpretations of what is a conflated and ambiguous observation.

We have the Many Worlds and Copenhagen interpretations of observations in quantum phenomena.  But we only have the space expanding interpretation of cosmological redshift and absolutely forbid any time dilation in flat space, when GR is screaming spacetime is continuum?  Just seems like an enormous elephant in the room to me.

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Observational evidence tested further by the CMB itself. If you had curvature the CMB would appear fuzzy not clear. It was the COBE dataset itself that gave clear confirmation. Later confirmed to higher degrees of accuracy through WMAP and Planck.

We can readily detect curvature by how we receive light. Curvature will involve lensing effects.

Edited by Mordred
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But why do we allow space to expand and not allow time to dilute in flat spacetime?

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On 5/23/2023 at 3:18 PM, AbstractDreamer said:

Right.  So.... why is the metric of space expanding and the metric of time NOT changing, in the specific case of the widely accepted interpretation of cosmological redshift.

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.

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3 hours ago, AbstractDreamer said:

Yes the relationship between frequency and wavelength automatic.  But wavelength is a measure of space, which we allow to expand as described by the FLRW metric, and frequency is a measure of time... which apparently cant expand (specifically in the case of cosmological redshift and not in the case of dilation).  Why?  Spacetime is a continuum.  Why, in the case of interpreting cosmological redshift, is it not a continuum?

If there are no viable alternatives, then it is the only viable interpretation.  Which is rather surprising considering there is no evidence for space expansion other than cosmological redshift observations.   We observe cosmological wavelengths redshifted in 1912, we theorise space can expand, we develop a model (FLRW) to match redshift observations based on that in 1922.  We can use the model to match subsequent observations based on the same assumptions.  But we cannot then go and claim the model and the mathematics proves space expands.

In analogy:  Newton observed an apple fall, he theorised gravity as a force, he developed models and maths to match his "falling" observations.  We can use the model to match subsequent observations and make predictions rather accurately in most circumstances.  But you cannot use Netwon's law to claim gravity is a force.

Why is that?  Why must there be no time dilation?  What is it about cosmological redshift observations that says space expands but time does not dilute?  If relative motion can dilate time, why should non-relative motion not?  Why are we applying "classical reasoning" to cosmological redshift observations?

Please note I was careful NOT to say there are no viable alternative models. I said it seems there are currently no serious alternatives.

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.

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