# Do redshifts really indicate expansion of the universe?

Lino
Good people,

As a 45 year old IT-PM, with no scientific / academic affiliations, can I ask, what I think should be, a relatively simple question please: do measured redshifts really imply universal expansion? I have a strong, but amature, interest in such things,and expected to quickly find the answer to be 'yes' after some time spent on internet searches. But after much reading / investigation, there is still an aspect with which I'm unsatisified.

Everyone is familliar with the ballon / raisis bread analogy, but consider, please, an analogy where were the universe is a (very) large bicycle wheel, add type 1a supernova at various points along the spokes, (for simplicity) assume that I am in the center, and give the system a spin. Won't there be a basic linear relationship between distance and measured redshifts to the standard candles, even though the system is not expanding? The obvious flaw in this analogy is the 'special' location of the viewer, but move me off-center, and I think the outcome is the same, except for the introduction of some blue shifted 'local groups'.

At this point in my little thought expirement, I expected to quickly find a paper / article that covered some aspect that I had not considered, but that was not the case. Infact the more I read, the more consistent the analogy seemed (doesn't require exotic forms of energy / matter, would be a factor impacting on Voyager / Pioneer trajectories, consistent with measured rotations of spiral galaxies / clusters, etc.). Now, while I still hope to find the 'silver bullet' that would explain my oversight, I appreciate that it is more likely to be a 'collection' of other obseverations that make the / an alternative interpretation more likely. .. but I'm having difficulty finding those obseverations / that evidence.

So my 'real' question is, given the above, can you make any comments or suggest / recommend any articles / papers that I might find useful?

Thanking you in anticipation.

Tanelorn
http://en.wikipedia.org/wiki/Zen_and_the_Art_of_Motorcycle_Maintenance

Well they have wheels with spokes on them! :) I apologise I am being terribly facetious.

I personally think it is a good thing to attempt to visualise unlikely explanations for redshift and the expansion of space. But as you say the obvious problem with what you suggest is that we have redshift in all three dimensions and at every point in space rather than the special location that we currently find ourselves in.

Lino
Thanks Tanelorn. Can I ask, do you see the 3D redshift as the main / key problem?

Staff Emeritus
I'm not seeing why your example would cause a redgarbage Lino. Can you elaborate?

Lino
(forgive me if i get some terms wrong here) rotation, as in the example of an object on the rim of a wheel when viewed from the center, has an associated vector (?) which is tangental to the curve of rotation at any point in time. this vector (? again sorry if this is not the correct term) can be expressed as the sum of two vectors (?) - one pointed away from me, the other in the direction of rotation.

assuming that my equipment is appropriate, i can measure the redshift of the object on the rim, but the measure will only reflect the scale of the vector (?) pointing away from me - ignoring the rotational element and the movement in the direction of rotation.

Staff Emeritus
(forgive me if i get some terms wrong here) rotation, as in the example of an object on the rim of a wheel when viewed from the center, has an associated vector (?) which is tangental to the curve of rotation at any point in time. this vector (? again sorry if this is not the correct term) can be expressed as the sum of two vectors (?) - one pointed away from me, the other in the direction of rotation.

assuming that my equipment is appropriate, i can measure the redshift of the object on the rim, but the measure will only reflect the scale of the vector (?) pointing away from me - ignoring the rotational element and the movement in the direction of rotation.

I don't know for sure, but I don't think this would affect the redshift. Maybe someone else can help.

Lino
thanks anyway Drakkith.

Staff Emeritus
thanks anyway Drakkith.

I say that because as far as I know, the only way to get redshift is to have an object move away from you or possibly to have the expansion of space itself spread the light out over billions of light years.

In General Relativity, if you make the whole universe spin, there is zero change in the behavior of stuff within it: an overall rotation is as undetectable as an overall movement.

Gold Member
Firstly, it is possible to construct a cosmological model with isotropic red shifting of all distant light sources, a la deSitter space. In that model the cosmological constant induces curvature so that distant points appear to be deeper in a gravity well than the observer's position and so light is red-shifted from all directions in proportion to the sine of the distance (in appropriate units).

Now if you map the deSitter space in a larger flat space-time it looks like it is, at first contracting, and then expanding. However that is due to a bad mapping of coordinates in the embedding to coordinates people living in the universe would use. What is bad about it is thinking of the universe in terms of a series of parallel snapshots of time.

In a deSitter space the spatial universe at a given moment of time for a given observer corresponds to a different cross-section of the whole space-time universe, but through its "center" at a different (pseudo)angle. In deSitter each observer's spatial universe at any time is the same size.
In an Euclidean-ized analogue every observer's spatial universe would look like a time-zone of the Earth rotating about the poles as time progresses (but upped a couple of dimensions). However with the hypebolic geometry you wouldn't get cyclic time behavior.

It is thus somewhat similar to your rotating bicycle analog, but only somewhat.

The past and future spatial universes of a given observer would intersect at "poles" where he would see time for distant objects stopped. For not-as-distant object time is slowed and thus emitted light is red-shifted relative to equivalent nearer sources.

Lino
thanks jambaugh & chalnoth. i'm travelling (not ftl) at the moment but i'll look at these more carefully later.

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jambaugh said:
it is possible to construct a cosmological model with isotropic red shifting of all distant light sources, a la deSitter space. In that model the cosmological constant induces curvature so that distant points appear to be deeper in a gravity well than the observer's position and so light is red-shifted from all directions in proportion to the sine of the distance (in appropriate units).
In static coordinates, you have $g_{tt}=1-r^2$, so the potential is quadratic to the first relevant order, not linear. Just like the wheel, incidentally.
But I have read your statement about linear redshift in de Sitter space in other places, too, so maybe I'm missing something. Of course, the galaxies should not be moving away in such a picture, but be held in place by some unknow force.
Could you elaborate?

Tanelorn
Jambaugh, is De Sitter and Euclidean-ized space a way of explaining the possibility that the characterstics of the free space into which the light was first emitted and has travelled these past 13B years has changed in such a way as to cause a change in the frequency of this light? I think I could at least consider the possibility of such an effect especially when considering the enormous change in just about every macro physical characteristic that the universe has undergone since the big bang and even the first stars.

Perhaps even the permittivity of free space itself has changed also? Or perhaps the universe was so small and dense that it was no longer approximately free space? We also always state that the velocity of light in free space is and always has been constant to 10 decimal places without question and I suspect just about everything in astrophysics and cosmology relies on this fact.

The interactions and phenomena summarized in the subjects of radiative transfer and physical optics can result in shifts in the wavelength and frequency of electromagnetic radiation. In such cases the shifts correspond to a physical energy transfer to matter or other photons rather than being due to a transformation between reference frames. These shifts can be due to such physical phenomena as coherence effects or the scattering of electromagnetic radiation whether from charged elementary particles, from particulates, or from fluctuations of the index of refraction in a dielectric medium as occurs in the radio phenomenon of radio whistlers.[2] While such phenomena are sometimes referred to as "redshifts" and "blue shifts", in astrophysics light-matter interactions that result in energy shifts in the radiation field are generally referred to as "reddening" rather than "redshifting" which, as a term, is normally reserved for the effects discussed above.[2]

In many circumstances scattering causes radiation to redden because entropy results in the predominance of many low-energy photons over few high-energy ones (while conserving total energy).[2] Except possibly under carefully controlled conditions, scattering does not produce the same relative change in wavelength across the whole spectrum; that is, any calculated z is generally a function of wavelength. Furthermore, scattering from random media generally occurs at many angles, and z is a function of the scattering angle. If multiple scattering occurs, or the scattering particles have relative motion, then there is generally distortion of spectral lines as well.[2]

In interstellar astronomy, visible spectra can appear redder due to scattering processes in a phenomenon referred to as interstellar reddening[2] — similarly Rayleigh scattering causes the atmospheric reddening of the Sun seen in the sunrise or sunset and causes the rest of the sky to have a blue color. This phenomenon is distinct from redshifting because the spectroscopic lines are not shifted to other wavelengths in reddened objects and there is an additional dimming and distortion associated with the phenomenon due to photons being scattered in and out of the line-of-sight.

http://en.wikipedia.org/wiki/Variable_speed_of_light

The varying speed of light cosmology has been proposed independently by Jean-Pierre Petit in 1988,[18][19][20][21] John Moffat in 1992,[22] and the two-man team of Andreas Albrecht and João Magueijo in 1998[23][24][25][26][27][28] to explain the horizon problem of cosmology and propose an alternative to cosmic inflation. An alternative VSL model has also been proposed.[29]

In Petit's VSL model, the variation of c accompanies the joint variations of all physical constants combined to space and time scale factors changes, so that all equations and measurements of these constants remain unchanged through the evolution of the universe. The Einstein field equations remain invariant through convenient joint variations of c and G in Einstein's constant. Late-model restricts the variation of constants to the higher energy density of the early universe, at the very beginning of the Radiation-Dominated Era where spacetime is identified to space-entropy with a metric conformally flat.[30][31] However it should be noted that while this was the first VSL model to be published, and the sole to date where an evolution law is given relating the joint variations of constants through time while leaving the physics unchanged, these papers received few citations in the later VSL literature.

The idea from Moffat and the team Albrecht-Magueijo is that light propagated as much as 60 orders of magnitude faster in the early universe, thus distant regions of the expanding universe have had time to interact at the beginning of the universe. There is no known way to solve the horizon problem with variation of the fine-structure constant, because its variation does not change the causal structure of spacetime. To do so would require modifying gravity by varying Newton's constant or redefining special relativity . Classically, varying speed of light cosmologies propose to circumvent this by varying the dimensionful quantity c by breaking the Lorentz invariance of Einstein's theories of general and special relativity in a particular way.[32][33] More modern formulations preserve local Lorentz invariance.[25]

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Lino
Firstly, all, thank you for your replies.

Tanelorn & Ich, in relation to the 2d/3d issue, a coupke of things cone to mind although I appreciate that they are not conclusive, (1) the lack of redshift is removed once I am off the axis as I am moving relative to the axis, (2) even if there is a point soyrce where there is no relative movement wont this just appear as a remote 'grouping' of which there are many observable examples, (3) I have also started reading a number of articles about the CMBR 'axis of evil' so I'm not sure if an axis is a good or bad thing. Bottomline - I need to think about this further!

Ich, I hear what your saying about the linear versus exponential relationship, and this is something that I have not considered before, but will definitely look into more.

Chalnoth, I think that I understand what you are saying, but I'm not sure that I agree! I accept that the result of the transformation will be '0' when looked at from a macro perspective, but the act of transforming, and measuring that act from a 'local' perspective should yield
Can

Lino
(sorry about my last incomplete post - I was / am trying to work from a smart phone! Me... not so smart! I'll complete the response on Tuesday when I'm back at my desk.)

Chalnoth, I think that I understand what you are saying, but I'm not sure that I agree! I accept that the result of the transformation will be '0' when looked at from a macro perspective, but the act of transforming, and measuring that act from a 'local' perspective should yield
Can
Sorry, seems like you broke off there.

Anyway, if you make the entire universe spin, General Relativity has some rather non-trivial velocity terms in its metric which end up cancelling out all of the observable effects, so you end up with no ability to detect a rotation of the entire universe.

This is because General Relativity follows Mach's principle:
http://en.wikipedia.org/wiki/Mach's_principle

Lino
(All, Again apologies for the incomplete posting last night – I don’t have the fingers of a concert pianist and should have known that something would go wrong trying to type on the phone’s keyboard! When I re read the part of the post that did make it ... uuugh ... again apologies. Anyway, I got my hands on a keyboard, so here I am!)

Chalnoth, I need to investigate / think about your comment (universal rotation has no observable effects) further, and thank you for the reference to Mach’s principle – I’ll definitely follow up on that, but I just not sure it’s logical, given each object / point will move by a different amount (based on distance from the ‘axis’) as a result of the rotation.

Jambaugh, Ich, & Tanelorn, I must confess I have tried to stay away from mathematical models – my own maths is not up to it! I will read up on deSitter space and (Jambaugh) the description that you used is very helpful – I do think that I have grasped the basics of what you are describing. But I’m still not convinced that such an abstract model / construct is critical, although this might be my prejudice against the invention of ‘unknowns’ like dark energy / matter, the possibility of divisors tending toward ‘0’, and the potential for negative numbers / distances / times.

Tanelorn, Can I ask, is there a difference between interstellar reddening and Rayleigh scattering (I'm reasonably familliar with Rayleig scattering and I’m sure that there are many differences between it and interstellar reddening, but maybe one of them is more important than the others)? If so, could you point me at any good articles / papers that discuss, or would help me to understand, the differences.

Thanks to all for your responses / help.

Chalnoth, I need to investigate / think about your comment (universal rotation has no observable effects) further, and thank you for the reference to Mach’s principle – I’ll definitely follow up on that, but I just not sure it’s logical, given each object / point will move by a different amount (based on distance from the ‘axis’) as a result of the rotation.
Well, this can be understood based upon the concept of frame dragging: in General Relativity, when an object rotates, it also drags the space-time around that object with it.

Gold Member
Jambaugh, is De Sitter and Euclidean-ized space a way of explaining the possibility that the characterstics of the free space into which the light was first emitted and has travelled these past 13B years has changed in such a way as to cause a change in the frequency of this light? ...

Qualitatively (deSitter) geometry can give a "tired light" effect it is not as much the frequency of the light changing but the relativity of source and observer. The action of evolving in time at one point in space is an acceleration (away from the one point) as seen at a distant point.

However the last time I did a rough calculation I came out with too small an effect to match observed data. (But I didn't double check my result, it was more of a bar-napkin calculation.)

BTW Euclidean space (what we study in high school geometry) was a means of painting an analogy. We think in Euclidean terms and so sometimes it is helpful by analogy to express qualitatively similar effects.

Gold Member
Perhaps even the permittivity of free space itself has changed also? Or perhaps the universe was so small and dense that it was no longer approximately free space? We also always state that the velocity of light in free space is and always has been constant to 10 decimal places without question and I suspect just about everything in astrophysics and cosmology relies on this fact.

Ultimately we define a time standard and measure distances by relating light and time (via wave-lengths of a light at a given frequency). We could (almost) as easily define a distance standard and measure time by relating light and distance (i.e. the period of light with a given wavelength.)

The variable geometry of space-time in GR is equivalent to a variable speed of light, or more to the point a variable vacuum permittivity tensor. Allowing both to vary is introducing multiple equivalent variables the distinction of which has no observable meaning. This is why the physical constant c is set by convention and not an observed quantity of nature.

You see, once we unify space with time we need common units, seconds and light-seconds and various multiples thereof. The alternative would be like using fathoms for depth and height and using furlongs for lateral distances. The physics of leaning or vertically rotating objects would then need a constant K in units of furlongs per fathom everywhere in the formulas.

The value of c is exact and the second is defined to give a specific value to the frequency of a cesium atom's emitted light. The value of a meter is then fixed by these two quantities. It is ultimately a certain multiple of a light-second. To the theoretician c=1 and the rest is just messy unit conversion.

Tanelorn
OK I recall now that it was decided that the velocity of light in free space is always constant by definition.

Gold Member
Jambaugh is right on right on top of this thread. There is little I can add. My 2c is why vilify redshift? - it is what it is. Expansion is the only explanation left standing after you wade through all the observational evidence. Science, like law, is based on the proponderance of evidence. Neither discipline is capable of revealing absolute truth.

Lino
Chronos, I appreciate what you are saying, and please understand that it is not my intention to vilify anything - including redshift. Prior to my original post, I was considering what I could find on redshift and expansion with a view to understanding it better myself. I came to a point where I had a question that I could not fathom and after much consideration and investigation, I posted on this forum. Even at that point (as with my own investigations) I expected someone to say / point me to something along the lines of "... you haven't factored in the corelation with apple-pie which explains everything ... as per article X ..." (some form of 'silver bullet') - it was not / is not my intention to change what everyone knows (about redshift and universal expansion), just to grow my own understanding. If anything that I have written sounds defensive of the 'idea', I apologies unreservedly.

I am no longer looking for a 'absolute truth', but instead, as you mention, "... wade through all the observational evidence" to see where the "proponderance of evidence" takes me. I fully expect to come full circle with a more complete / better understanding of why it is most likely be (please note: not "must be") redshift / universal expansion as we all know and love it!

Finally, again Chronos, I do thank you for your post - it also forces me to stay focused, objective, and not get personally involved in the defense of 'my idea'!

Lino
I see two main problems:

As already mentioned by Tanelorn, you'd have no redshift at all along the axes of the wheel. We see redshift everywhere.
Then, what you get is the "http://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Transverse_Doppler_effect"", which is not at all linear with distance. You would not have any kind of Hubble's law in such a universe.

Ich, I'm still trying to work through the 3D and transverse effects that yourself and Tanelorn mentioned, but in the meantime I have tried to approach the linear relationship / Hubbles law aspect from a couple of perspectives ... but I just don't see it. Could I outline a basic calculation and it might jump out at you as to where I've gone wrong?

Consider an object at distance X, so distance to travel as part of the rotation is 2piX, and so speed of rotation is 2piX (assuming one full rotation per time unit). Therefore the ‘vector’ reflecting tangential motion, at any point on the circle, is 2piX. Assuming clockwise rotation, split the tangential motion vector into two vectors (one in the direction of clock rotation, and one away from the center), and using my very basic trigonometry (it is always based on a 45degree, right-angled, triangle), the perceived motion away from the centre works out to be 0.707 units. Double the size of X, and the perceived motion away from the centre doubles (1.414 units), triple the size of X and the perceived motion away from the centre triples (2.121 units), quadruple the size of X and …

I have tried using “real” units, calculated values, trigonometric SIN and TAN formula, but (excluding rounding errors) I get the same linear results as the (I think) cleaner ratio calculations above. I am still working through how this relates to the equations / logic of the transverse effect and this will take me (and my limited brain) somemore time ... but heh!

Any help with where I have gone wrong in the above calculation, or how this ties into the relativistic / transverse effect, would be greatly appreciated.

Regards,

Noel.

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Lino
Well, this can be understood based upon the concept of frame dragging: in General Relativity, when an object rotates, it also drags the space-time around that object with it.

Thanks again Chalnoth. I'm still trying to work my way through the article (on the Mach principle), but if I'm right the key difference between what I'm asking about and this principle is that the entire universe would rotate, not just the local reference - the guy in the field looking at the stars (? more apologies here if I am using the wrong terminology). I have spent sometime considering framedragging in the past, and I think that I understand the implications and effects ... a little. I have to say, I do think that framedragging is critical / central but I am missing what it is additionally adding in this instance! I promise I do intend to keep looking at it and thanks for your assistance thus far.

Regards,

Noel.

Lino
... it is possible to construct a cosmological model with isotropic red shifting of all distant light sources, a la deSitter space ...

Jambaugh / Tanelorn / Ich, I'm still looking into the deSitter space, but can I ask a related question that just occured to me? In a simple analogy, either the wheel or a sphere, if I position the viewer 'off axis' does this not remove the 'redshift is all directions' problem since the axis is moving relative (small word 'relative' not the big 'GR') to the viewers position? I know that this is not the full 'answer' to the problem (since the 'redshift' of items not on the same plane as the viewer / wheel will not be consistent with hubble's law - linear at increasing distance), but just want to understand the basics.

Thanks & regards,

Noel.

Tanelorn
Lino, Sorry it doesnt make much sense to me but then I am only an amature so I cant think of anything more to add. Maybe the others can help?

Lino
Thanks Tanelorn. I'll keep looking.

Lino, I think you have not appreciated yet just how big this problem is.
If I understand your model correctly, the redshift effects that we attribute to radial motion / gravity / general cosmological origin are to be explained solely by the kinematical effects of rotation around a single axis.
You can calculate redshifts in such a model by introducing a so-called "effective potential". If the observer is at a higher potential, she observes redshif.
The potential is parabolic, with the lowest point at the axis. It does not change along the axis.
So, if you look along said axis, you will see no redshift at all. It doesn't matter whether you are on or off the axis. And this is some 10000 standard deviations away from observational evidence, which supports isotropic redshift with maximum deviations ~1:10000.
If you're off the axis, you introduce further anisotropies that also not observed, like blueshift in one direction, redshift in the other. But you don't alleviate the other problem.
Additionally, as I said, the relation is generally not linear, you couldn't even derive something like Hubble's law in such a universe.

Lino
Thanks Ich.

I think that I understand what you're saying, so I'll spend some time trying to digest it. But if I can make one comment on first read, I think I may have given the wrong impression - the viewer does not remains in a central location (i.e. on the axis but lifted of the plane of the wheel), but what is on one of the 'spokes' (i.e. between the axle and rim but on the spoke) - not on the axle itself - as an artibary example: say 20% of the distance along the spoke toward the rim (but I don't think that the actual precentage value is critical). Apologies if I was causing confusion rather than clarifying my question.

Regards,

Noel.

Gold Member
Forget about the 'axis of evil', it is busted - selection effect.

Lino
Thanks Chronos. I'll keep reading about it out of interest, but it's good to kow how the story ends.

Regards,

Noel.

I think I may have given the wrong impression [...] but what is on one of the 'spokes'
I understood that part, and answered it:
Ich said:
If you're off the axis, you introduce further anisotropies that also not observed, like blueshift in one direction, redshift in the other. But you don't alleviate the other problem.
That's why I introduced the "effective potential", it allows you to easily calculate redshifts in this scenario. For example, it is a general result that light from bodies that orbit at the same radius as the observer is not redshifted. This is true even if the actual relative velocities are changing all the time. All you need to know is the effective potential, so you can easily prove that your scenario doesn't work.

Lino
Jambaugh, I have been reading what I can on de Sitter space, thanks again for the prompt, and can see what you were get at (... I think). Can I ask a very basic question in relation to it:

Am I correct in saying that every item of mass sits at the bottom of it's own gravity well (understandably of extremely differing depths), and given that the light from any object has to come 'out of its well', across 'flat' space and 'into my well', does this mean that 'I' am always deeper in my gravity well than everything else - since the light from that object must cross 'flat' space?

(I'm not really asking this in relation to my original rotation question - just trying to understand the deSitter model ... to some extent!)

Regards,

Noel.