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The mathematics of redshift

  1. May 20, 2004 #1

    turbo

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    All other issues aside, a mathemetician who is asked to explain cosmological redshift (more distant objects regularly appear redshifted) could easily come up with a couple of reasons:

    1) the universe is expanding rapidly in all directions, and the light from distant galaxies is redshifted due to that expansion. The expansion is driven by dark matter, which we can't detect, but must be real because it fits the models for expansion.

    2) our frame of reference is contracting with respect to the universe at large, and instead of all the galaxies shooting away from us, we are receding from one another into our gravity wells. The dark matter isn't needed to supply the expansion, because there isn't any expansion.

    If our local neighborhood were receding into a steep gravity well, like the black holes postulated to lie at the hearts of galaxies, would we not see light from more and more distant objects more and more redshifted?

    If so, it seems to me that situations 1 and 2 are mathematically equivalent. It also appears that situation 2 is by far the more likely, since we don't have to include a fudge factor like dark matter that says in essence "this is how it is, and it's mathematically consistent, except that we have to posit the existence of massive amounts of unseen energy that we can't explain and may never begin to measure". I may be missing something critical here, but it seems invoking dark matter to justify cosmological expansion is one step short of laying the blame to angels. Occam's Razor says that given two equally plausible explanations for a circumstance, the simpler one is the right one.

    I know that cosmologists are pretty well locked into the expanding universe world view, and tenure and research support do not favor contrarians, but is there anybody who from a purely mathematical stance is presently exploring the possibility that each galaxy might be receding into its own gravity well producing the redshifts that we see. Objects in a steady-state universe could appear more and more redshifted the more distant they are from us and the longer the time the light had to travel. We shouldn't have to think about light being "tired", or other constructs. We should be able to think of it as invariable, with the variances being due to the changes between the states of the emittor and the receptor. Changes in relative physical position (Doppler effect) should be much smaller than (but empirically identical to) changes in acceleration, as in the effects due to the differences in gravitational gradient.

    I know my terminology may not be up to date, but I watched Kip Thorne's presentation on space/time recently, and I was struck with the way that steep mass/gravity gradients can distort space-time. It occured to me then that looking for the "missing" 95% of the mass of the universe might be avoided if we adopted a steady-state model and attempted to explain the differences between the states of our neighborhood and more distant objects in more practical terms.
     
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  3. May 21, 2004 #2
    1)It's not dark matter, but dark energy what is causing the acceleration of the expansion
    2)If you are able to find a solution of the Einstein field equations in which whole galaxies are falling inside a gravitational well, then possibly you will win the Nobel Prize. Nowadays, the Robertson-Walker metric with the adding of a cosmological constant explain reasonably well the observations
     
  4. Jun 22, 2004 #3

    Nereid

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    meteor said it "... explain reasonably well the observations."

    If the redshift-distance relationship were between mere unresolved points of light with completely uniform spectra (gammas to radio), trubo-1's mathematician friend would really be onto something.

    However, a great many of the objects whose redshifts we can observe with considerable accuracy are not just point-spread functions in the camera, or not just quite uninformative spectra. So, for example, we see that there are galaxies that look just like those in the Local Group (whose distances aren't determined by their redshifts), complete (in many cases) with SMBHs in their nuclei. Makes interpretation 2) rather difficult to square with the observations, doesn't it?
     
  5. Jun 23, 2004 #4

    Garth

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    Indeed there is a theory that describes your second option; it is Self Creation Cosmology. You will find the latest paper, "Self Creation Cosmology - An Alternative Gravitational Theory" at http://arxiv.org/abs/gr-qc/0405094 , it is to be published in 'Progress in General Relativity and Quantum Cosmology Research', Nova Science
    Publishers, Inc. New York.
     
  6. Jun 23, 2004 #5

    Nereid

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    Welcome to Physics Forums Garth!

    An interesting paper. Maybe we could provide it as a model, in the Theory Development sub-forum, of the kind of thing which folk who aspire to develop an alternative to today's text-book physics (and cosmology) might consider. (Note: I'm NOT saying that I think Garth* Barber's idea really has legs - we can discuss that later - rather that he has obviously done much of the necessary 'homework' before presenting the idea).

    Why does the paper look as if it could be such a model? It:
    1) explains the new theory (OK, nearly everyone with a new idea does this)
    2) shows how the new idea relates to existing observations and data; in this case, that it is consistent with all (nearly all?) of the tests of GR done to date (GPB excepted, but there are no results from that yet), WMAP, distant Type Ia supernovae, primordial nuclide abundance, Hubble redshift, etc
    3) suggests some experiments which could be used to test the new idea, and makes predictions of what the results would be (inc cf today's standard theories)
    4) accommodates some apparently solid, anomalous results, in this case the Pioneer anomaly, Morrison and Stephenson's residual length-of-day changes (ancient solar eclipse analyses; I'd not heard of this previously), solar system celestial mechanics data hinting at a secular change in G (I hadn't heard of this before either)
    5) briefly summarises how the idea fits with current observational cosmology.

    *Any relation to the new PF member Garth, I wonder? :wink:
     
  7. Jun 23, 2004 #6

    Nereid

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    Leaving aside Morrison and Stephenson's residual length-of-day changes (ancient solar eclipse analyses) and the solar system celestial mechanics data hinting at a secular change in G (I need to go check these out first), some comments on fitting with present data and experiments, and proposed ones:
    - how well will planned space missions, such as LISA test this SCC idea?
    - what other observations and experiments have been done on time changes in G? Garth's paper mentions just two, one possibly consistent with SCC, the other not inconsistent (null result expected in both SCC and 'G is truly constant')
    - nuclide abundances: more work on expected 2H and 3He vs 4He; also "one prediction of the theory is that a significant proportion of intergalactic medium metallicity, observed from the Lyman a forest of distant quasar spectra, should be primordial"; there's surely tonnes of data on abundances which can be used to test the SCC predictions
    - dark matter. It's not only WMAP data and cosmology models which point to DM, there's a wide range of observations which are interpreted in terms of DM (I'll include a link here to some of my earlier posts on this topic*). If in SCC "this component [DM] of the cosmic density parameter is in the form of intergalactic cold baryonic matter", then all those other "DM" observations need to be explained (not just the 'cosmological' ones). Also, if there is so much cold baryonic matter, why haven't we seen it yet?
    - LSS (large scale structure) and galaxies. Similar story to DM, though as Barber correctly notes, the observational data doesn't constrain models much yet (e.g. "[the concordance cosmology models predict] galaxy mass profiles that have a too pronounced cusp at small scales and a too steep galaxy luminosity function")

    *Here's one with a discussion of the IGM; there are several on DM, this one may be a good one to start with (also relevant to turbo-1's threads)
     
    Last edited: Jun 23, 2004
  8. Jun 23, 2004 #7

    Nereid

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    Just remembered; outandbeyond2004 gave us a post a while ago, with a link to some very cool work done with ring lasers. It's not quite the same as the Garth's proposed space-based test, but maybe the sensitivities etc that the group have attained, and their understanding of the set-up, may lead to a 'test' involving analysis of data already on hard-drives! After all, if they think they may be able to detect the motion of the solar system wrt Sag A* ... :bugeye: :cool:
     
  9. Jun 23, 2004 #8

    Chronos

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    Substituting dark energy for dark matter, if you dont mind: Gravitational red shift and doppler red shift have different implications. If you substitute gravitational force for acceleration as an explanation for red shift, you end up with a universe that collapses before we have enough time to observe it. The cosmological constant is necessary to explain why the universe has endured long enough for us to witness it. Dark energy is necessary to explain the repulsive force required to resist gravitational collapse.
     
  10. Jun 24, 2004 #9

    Garth

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    Yes indeed the new PF member Garth is the author of the SCC papers. It is good to have a decent critical discussion about the theory. Key points about the theory are 1. test particles follow the geodescis of GR so all standard tests that verify GR also do so for SCC. 2. G is inversely proportional to M so GM is constant. Most tests on the variability of G actually test GM and therefore give a null result. The intergalactic DM has been observed; it is the Lyman alpha forest observed in distant quasar spectra. Only about 20% of which can be explained from galactic outflow, the rest may well be primordial. I was waiting for somebody else to pick that point up! The theory will be tested soon - GPB should enter its science phase at the end of this month.
     
  11. Jun 30, 2004 #10

    turbo

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    Garth, is your paper near release? I will be very interested to see the implications of local conservation of energy....
     
  12. Jul 1, 2004 #11

    Chronos

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    Garth, getting rid of dark matter and dark energy is very attractive. I resent unobservable features of the universe. And having testable predictions is also attractive. I look forward to the experimental results. My main concern is how your model behaves thermodynamically. It appears there is more wiggle-room for Lorentzian invariance than expected. Not a bad thing [Lorentz was not a nice person, Einstein was a very nice man]. Your predictions should make or break the case either way. Excellent work, regardless of the results.

    ps: i despise string theory. Those annoying extra dimensions make the math too hard for me to follow.
     
  13. Jul 1, 2004 #12

    Garth

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    The SCC theory was published in 2002, a paper is appearing as a chapter in 'Progress in General Relativity and Quantum Cosmology Research', Nova Science Publishers, Inc. New York to be published later this year. A brief description and references to the six papers on SCC can be found in the Theory Development sub-forum https://www.physicsforums.com/showthread.php?t=32713.
     
  14. Jul 2, 2004 #13
    So what is the mathematical relationship between the velocity of galaxies and the redshift of the light we see from them? Does this formula take into account both Dopler effects and gravitation?

    Thanks.
     
  15. Jul 2, 2004 #14
    Maybe Garth can speak to the ideas of Glast and speak accordingly about Redshift and Blue shift from this perspective?
     
  16. Jul 4, 2004 #15

    Garth

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    There are two frames of measurement in my theory, the Jordan frame and the Einstein frame. In the Eistein frame energy-momentum is conserved and a particle's mass is constant. The universe expands linearly from a big bang. As in normal GR gravitational red shift can be seen either as a doppler effect as the galaxies receed from each other, or a gravitational effect due to the fact that light coming from early in the universe's history was emitted deep down within the cosmological gravitational well. Both expalnations are equivalent, they are different ways of interpreting the same effect. However in my theory in the Jordan frame energy is locally conserved and a particle's mass varies with gravitational potential energy. Here a particle increases expontentially with cosmological time [m(t) = m' exp(Ht)] and atoms and rulers consequentially shrink with time. The expanding universe with fixed rulers is reinterpreted as a static universe with shrinking rulers.Cosmological red shift is due not to a doppler effect, or to a 'tired light' effect, but instead the photon maintains a constant energy and it is the atoms it interacts with that increase in mass. When the energy of photon is compared with the mass of the atom it interacts with the photon appears to have lost energy and a red shift is observed.
     
  17. Jul 4, 2004 #16
    I would think that if a photon loses energy and is redshifted because it gains potential energy (since it distances to gravitating objects increases as the universe expands), then so must any particle's rest mass decrease when it gains potential energy. For there should be no difference between photons losing energy as the universe expands, and those same photons being converted to mass first, the universe expand, and then those particles be converted back to photons. So if the photon loses energy then so do any particles that could be made from it.

    So... if rest mass is decreasing with expansion, then were things heavier in the past? Is this the source of the extra mass (dark matter) we see in ancinet galaxies? Is the gravitational lensing more powerful in the far past then in the near past?
     
  18. Jul 4, 2004 #17

    Garth

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    First please pardon my typos, I type in a hurry and seem to be unable to proof read on the monitor screen!
    You have it the wrong way round! A particle's mass increases with cosmological time. (It is the size of an atom and frequency of atomic vibrations, which are inversely proportional to mass, that decrease - I think this is where your confusion lies) Secondly a key feature of the theory is the principle of mutual interaction, which is described in my papers. The increase of mass-energy affects massive particles like atoms but not massless relativistic photons and the like. This increase is a result of the acquisition of inertial mass by particles determined by Mach's Principle. A free photon is of constant energy, after all no work is being done on or by it, and it is the atom it interacts with that gains mass - energy over time. Secondly G is inversely proportional to mass so GM is constant. It is always GM that is measured and that is why measurements of gravitational lensing and variation of G give a null result. Finally this increase of mass does affect the earth and shoul mean that the earth is spinning up at the rate of Hubble's constant. This is indeed observed from ancient eclipse records - see my papers - but it has not been recognised as such - yet.
     
  19. Jul 4, 2004 #18
  20. Jul 4, 2004 #19
    If space itself is expanding, then the increase in potential energy due to distance is not accompanied by a equal decrease in kinetic energy. For such formula apply only with respect to a coordinate system that does not change from initial to final states. So in order for energy to be conserved, I supose the rest energy of particles must decrease as space itself expands. What do ya think?
     
  21. Jul 5, 2004 #20

    Chronos

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    There is no net energy loss. Thermodynamics forbid it. Garth, one thing i object to in your theory relates to information theory. There cannot be any Shannon information in the universe. I dont have the math at hand to support that supposition, so my position is not defendable. So, it is no more than a postulate. I do, however, believe it strongly agrees with observations.
     
    Last edited: Jul 5, 2004
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