Redshift Issues: Understanding the Light-Metric Coupling in Cosmology

[Emreth]

I have some issues with the current understanding of the cosmological red shifts and their interpretation using the spatial variation in the metric with time.To make the argument clear, I'm also posting pictures. The universe is depicted as the surface of a sphere but that doesn't affect the reasoning.
Let's say a star just started sending light from its hydrogen atoms to Earth at time t1. The light traveled through space for a certain amount of time during which the universe expanded a certain amount. At time t2 the light reached the earth.Current cosmological understanding tells us that the emitted light in the original spectra got stretched as it traveled from the local space of the source to intergalactic space due to expansion of the universe and we receive the redshifted light in our local space.The assumption here is that light is coupled to the spatial metric (which can be called the fabric of space) at a certain time in such a way that as the metric changes, the light wavelength changes. Now we know that our local space exists and does not vary with time and it exists for the source as well.
So what I can't comprehend is: if the light is so inherently coupled to the metric that it stretches as the metric changes timewise and spatially between the source local space and intergalactic space, wouldn't the same coupling cause it to blueshift as it enters our local space?I would expect that case rather than light not being affected as in the regular explanations of cosmic redshift. That would mean that we shouldn't see any redshifting as long as metric does not change locally(local space).In the case that we accept that the local metric changes, then we would see a redshift associated with it. However that would mean our destruction probably due to effects on massive objects.
I have a feeling that its possible that light is the vibration of space itself but space is not perfectly elastic and that there are some losses by hysteresis over long distances.These losses are apparently not frequency dependent (as the astronomical data shows same redshift for all frequencies as far as I know)
So does anybody have any ideas?Maybe I'm missing a point somewhere?

 

[jonmtkisco]

Hi Emreth,

I followed you up to the point where you said that the light should blueshift when it enters our local space. You don't explain why it would do so. To the extent that our local space is stable (neither expanding nor contracting), then the light should pass through with no net added redshift or blueshift.

Blueshift would occur if the light passed through a region that was contracting. There are some places like that in the universe (where matter is infalling into gravitational wells of galaxy clusters, etc.) but it's probably much more the exception than the rule. To the extent that our nearby Local Sheet is contracting, the total contraction is insignificant compared to all of the expanding space which light from a typical distant star has passed through.

Is this answer clear to you?

Jon

 

[Wallace]

Hi Emreth,

I followed you up to the point where you said that the light should blueshift when it enters our local space. You don't explain why it would do so. To the extent that our local space is stable (neither expanding nor contracting), then the light should pass through with no net added redshift or blueshift.

I'm also confused here, why indeed do you think a photon should blueshift as it approaches us? Emreth you may want to clarify exactly what you mean by local space.

In addition to Jon's response, light will blueshift as it enters a gravitational potential well even if that region is not collapsing. This effect however is fairly small and requires a very large potential gradient, such as a black hole, to produce a large effect. Falling into the potential well of say the Milky Way will blueshift light but not by a large amount.

As Jon said, the biggest problem with your reasoning is the assumption that the photon that has redshifted passing between the distant galaxy and us will for some reason blueshift again as it approaches us. If you can more clearly explain why you thought this would occur than may help.

 

[Emreth]

To clarify things

Hi,
I tried to make it clear but let me try again.
First for wallace-local space is the area in our vicinity where there's little or no Hubble flow due to local gravitation and includes milky way etc. Likewise, the source has a similar area within its galaxy which means the metric stays the same there as well.
What I'm trying to understand is this:
When light leaves the source and reaches intergalactic space, it expands an amount dictated by the increase in the metric by some mechanism(light-space coupling, whatever). If you agree to this, then you should also agree that light will contract to its original form when it leaves int. space and arrives an area where the metric is less, such as our local space(same mechanism working in the opposite direction). Not from dense gravitational fields but because the metric gets smaller.
But cosmologists are saying it doesn't.Thats what i can't understand.
To make an analogy tho its not the same(and don't explain why because I know why!,likewise the universe is not a dough), consider a beam of laser going through a sheet of glass(from air into glass back into air again). The c decreases from air to glass. But then increases as it goes from glass to air. Similarly, you have small metric-large metric-small metric line of sight(source local space-int space-earth local space). So even if it gets redshifted from source to int space, it should revert back to its original spectra(so you blueshift the redshifted beam) as it goes from int space to Earth local space.
Or does the redshifting occur from a change of metric rather than the current value of the metric?(which does not make sense to me)
Edit..by change of metric, i meant rate of change of metric with time(not spatial).

 

[Nickelodeon]

Hello - to make things a bit easier I would take the wavelength of your source just outside the source's own galaxy on its way to us and, for arguments sake, call it yellow. Due to the Hubble flow, by the time it gets to the edge of our galaxy it has gone orange. On its way to our solar system through our galaxy, the Hubble flow is superseded by several other factors, some more dominant than others. Passing by a large mass may not intrinsically alter the orange because, I would imagine, it will go yellow on approaching the mass then back to orange on leaving. Our Earth's gravity is obviously too small to have any noticeable effect so we are left with the red shift.

Nick

 

[marcus]

...
When light leaves the source and reaches intergalactic space, it expands an amount dictated by the increase in the metric by some mechanism(light-space coupling, whatever). If you agree to this, then you should also agree that light will contract to its original form when it leaves int. space and arrives an area where the metric is less, such as our local space(same mechanism working in the opposite direction). Not from dense gravitational fields but because the metric gets smaller.

NO! The stretching occurs due to expansion during the passage of time.

It does not depend on any absolute size of the metric. It depends on the experience of waves propagating in a medium undergoing expansion and it is the cumulative effect of traveling for (like) a billion year in a slowly expanding geometry.

If along the way the light happens to enter a region where distances are contracting at a comparable rate, but only spends a million years there, then it will only be slightly affected. Because a million years is a short time, comparatively.

It is the cumulative effect of spending time where the geometry governing wave propagation is expanding, versus contracting, that leaves its mark on the light.

Or does the redshifting occur from a change of metric rather than the current value of the metric?(which does not make sense to me)
Edit..by change of metric, i meant rate of change of metric with time(not spatial).

WHOAH! Yes! You got it! I didn't have to type the above, you figured it out on your own.
The rate of change of the metric is a'(t) the timederivative of the scalefactor. It is the experience of spending a long time traveling in a geometry where a'(t) is positive.

To reverse it you would have to spend a long time traveling where a'(t) is negative.

It doesn't depend on any absolute value of the metric, even if that could be covariantly defined.. Indeed it is the rate of change.

this may not help you, I will tell you my mental image, it may or may not be right. I think of Maxwell equations, how they are drawn in a basic physics text, the undulating B field and the E field undulating at right angles say, each one making the other undulate. And I think about the geometric FRAME in which that happens. And I say, what if, with every cycle, with every undulation, the geometry gets stretched a tiny tiny bit. Not in space. Stretched as a function of time. as the B is influencing the E, and viceversa, each one leading the other by 90 degrees phase, the geometry is changing in TIME. So I picture this having a longterm cumulative effect, through many cycles, on the light.

I don't think of the light bolted to one version of the metric. the light is a free agent and its wavelength is independent of what the metric is at any given moment. It doesn't know what wavelength it started with, but we know it has absorbed its experience of a changing metric over many years of travel.

 

[Emreth]

Thanks for the clarification. I guess my confusion comes from the fact that scale factor is a function of local curvature in friedmann equations. So I assumed that at the boundaries between int. space and local spaces, the sudden spatial change in the curvature and the resulting metric would have an equivalent effect as a different scale factor,one which would be equal to a deeply contracting space locally. In any case, quoting this "I don't think of the light bolted to one version of the metric. the light is a free agent and its wavelength is independent of what the metric is at any given moment.", why would we expect any change in the wavelength at the first place, since the metric and scale factor are so closely related. Of course friedmann equations cannot be directly applied to this case as the assumptions of homogeniety and other things are not met, yet I would at least expect qualitative similarities.

 

[Wallace]

Thanks for the clarification. I guess my confusion comes from the fact that scale factor is a function of local curvature in friedmann equations.

No this is not correct and may lie at the heart of your problems here. Take for instance a flat FRW Universe (one that contains the critical density of matter). The spatial curvature is always zero throughout the entire history of that universe, yet the scale factor a(t) always increases, a'(t) remains positive and photons fired between galaxies will be observed to be redshifted. The evolution of the scale factor does not relate directly to the curvature in the way you are suggesting.

 

[jonmtkisco]

I agree with Wallace.

Jon

 

[Emreth]

Yeah that is not correct. Since I made the images for a curved space, i thought it would be more intuitive to talk in terms of curvature. Yet..:)..I still have the issue with light traveling across a metric jump.Basically you're implying that regardless of the extent of the spatial change in metric(even if it's huge), light should not experience any redshifting due to traveling across that boundary in a relatively short time. Can that be true?I mean shouldn't it be similar to gravitational redshift where light get stretched instantly in the vicinity of the field where metric shows spatial variation?That is due to change in metric rather than gravitational pull on photons..right?
I don't know if we can go further without actually solving the problem numerically for which I don't have time for right now(but I'm experienced in solving complex nonlinear systems)

 

[Wallace]

I still have the issue with light traveling across a metric jump.Basically you're implying that regardless of the extent of the spatial change in metric(even if it's huge), light should not experience any redshifting due to traveling across that boundary in a relatively short time.

I'm really not sure what you're referring to? The perturbations to the background FRW metric that are present due to a galaxy or cluster are neither huge or sudden. Rather the potential well of a galaxy causes a small gradual perturbation to the background that smoothly connects with the background. There is no harsh boundary.

Can that be true?I mean shouldn't it be similar to gravitational redshift where light get stretched instantly in the vicinity of the field where metric shows spatial variation?

Redshift is caused by the metric being different for the emitter and observer. Redshift happens when you observe the photon, not during flight. In this way redshift always happens 'instantly', i.e. when you observer it.

That is due to change in metric rather than gravitational pull on photons..right?

Hang on, the metric is the gravitational pull, that is, the metric (or rather the derivatives of the metric) describes the effect of gravity. The metric, as applied by the geodesic equations is gravity.

 

[Emreth]

Hi Wallace,
Relatively speaking the boundary is quite sharp (compare the transition length versus the whole distance traveled, prob million vs billion light years).
"Redshift is caused by the metric being different for the emitter and observer." I agree with that.That was what i was trying to emphasize, that the travel should not matter, and the redshift may be due to the difference in local spaces of emitter and observer(their metrics.)(or something else if they are equal, i don't know)
(The metric results in the gravitational force but I just wanted to make sure nobody answers me like- the situation is different between the metric around a large mass compared to the metric with no mass but with Hubble flow.The overall effect should be similar albeit causes being different)

 

[Wallace]

Hi Wallace,
Relatively speaking the boundary is quite sharp (compare the transition length versus the whole distance traveled, prob million vs billion light years).

The effect is tiny, regardless of how big any 'boundary' might be.

"Redshift is caused by the metric being different for the emitter and observer." I agree with that.That was what i was trying to emphasize, that the travel should not matter,

Yes

and the redshift may be due to the difference in local spaces of emitter and observer(their metrics.)(or something else if they are equal, i don't know)

No. An expanding Universe is well described by the FRW metric in which a(t) directly determines the redshift via

$$1 + z = \frac{a(t_{observed})}{a(t_{emitted})}$$

The very tiny gravitational blueshift due to the local perturbation from the FRW model due to say a galaxy is negligable compared to this. The difference in the background metric (a(t)) between emission and observation is what causes a photon to be observed to be redshifted.

 

[Emreth]

FRW describes a uniform universe. So that equation would be right if there was no local space and all the metric was uniform,around us,the source and everything in between(so it just changed with time).I don't have a problem with that.But it's a different situation that I'm trying to describe. When we assume local space, the spatial variation in the metric between the void (sick of saying int. space) ,which is expanding,and loc space increases with time. So the metric as a function of time in a uniform universe is equivalent to metric as a function of coordinates in a non uniform universe.