Cosmological redshift: how much energy has gone missing?

  1. marcus

    marcus 23,947
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    In the cosmol. redshift thread (Q) asked
    [[I would like to hear some interpretations of this phenomenon, especially in regards to what happens to the energy of photons in cosmological redshift – where do YOU think it goes? Is it lost or is it conserved?]]

    It is clear that a whole lot of energy has been lost by the stretching out of light over the course of billions of years and
    in that thread some people were speculating that it had gone somewhere (instead of being simply lost) like into fueling the dark energy or something. I can't say just what the idea is, but I can try a rough estimate of how much energy has been lost.

    (I don't think it is very much compared with the present amount of dark energy.)


    Up to a factor of order one, the volumetric density of radiation at temp T is (correct me if I am mistaken) T4 times k4/hbar3c3

    The temp of the CMB in absolute units is 2.0E-32
    So raise that to the fourth and you get 16E-128

    That is the current energy density in the space around us of the CMB (or about 2/3 that because of the order-one factor I omitted)

    And the CMB is at redshift 1100. So, if the CMB had not been being redshifted all these billions of years since socalled "recombination" (estimated 300,000 years after bigbang) then its photons would each be 1100 times as energetic.

    So the amount of lost energy (per unit volume of space) is about
    1000 x E-127 which is E-124

    But the dark energy density I have calculated a couple of times here (being 70 percent of critical) as 1.3E-123

    So this redshift loss is only an order of magnitude smaller than the cosmological constant or dark energy density!

    I did not realize that when I first calculated---and also made
    a multiplication error I just corrected---so got a different conclusion.

    Light from all the galaxies is a smaller density---it does not noticeably effect the temperature of space so I neglect it. So the energy lost from the CMB by space-expansion is (admittedly a huge huge amount of energy) is smaller but roughly comparable with Lambda, or Dark or "quintessence" whatever you call it.

    (Q)'s question is provocative in that it tempts us to speculate that the energy lost by cosm. redshift as gone into something like expanding space and creating more dark energy.

    I have no clue as to how that could happen and assume that the energy is simply lost.

    Note that I calculated the CMB energy density in space simply by raising the temp to the fourth. (c=G=hbar=k=1) Would someone show how to calculate the joules per cubic meter of the CMB in metric terms? Probably not, but it would provide a check.

    The actual CMB temp is 1.93E-32 absolute (corresponding to
    2.725 kelvin) but for back-of-envelope I took it to be 2E-32.
    E-32 of the planck temperature is what corresponds roughly
    in size to a kelvin, more accurately 1.4 kelvin.
     
    Last edited: May 23, 2003
  2. jcsd
  3. russ_watters

    Staff: Mentor

    No energy has been lost. Thermodynamics states that the amount of energy in the universe is constant. Its just spread out over a larger volume which decreases its DENSITY.
     
  4. marcus

    marcus 23,947
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    Re: Re: Cosmological redshift: how much energy has gone missing?

    Hello Russ, thanks for responding. what you say is a fascinating and novel idea. I never heard of thermodynamics being applicable to the universe as a whole.

    Into what form do you suppose the energy of the CMB has gone?

    By current estimates, the CMB that is observed today has lost 2999/3000 of its energy. Where could this have gone?
     
  5. marcus

    marcus 23,947
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    In the cosmol. redshift thread (Q) asked
    [[I would like to hear some interpretations of this phenomenon, especially in regards to what happens to the energy of photons in cosmological redshift – where do YOU think it goes? Is it lost or is it conserved?]]

    It stikes me as an odd coincidence that the dark energy density calculated from MAP and supernova data is roughly equal to the amount lost from the CMB---within a factor of ten. I do not suppose that one feeds the other, it is just a curious coincidence.

    Let's calculate the number of CMB photons per unit volume in space. The observed temp is 1.93E-32 (in natural units c=G=hbar=k=1)

    Stefan-Boltzmann says the volumetric density of radiation at temp T is (pi2/15 ) T4 times k4/hbar3c3. This last factor is just equal to one in natural terms, so the energy density is just

    (pi2/15 ) T4 = 9E-128

    The Planck blackbody curve says the average energy of a photon is 2.701 x 1.93E-32-----it is always 2.701 times kT. This is the energy of all the photons in a volume of space divided by the number of photons.

    So the average photon carries 5.2E-32 of the natural unit of energy. The number of photons per unit volume of space has to be 9E-128 divided by the average. It works out to

    1.75E-96

    To look at that in human scale, use the fact that a mile is E38 and a cubic mile is therefore E114. so the density of CMB photons is
    1.75E18 per cubic mile. Or about a quarter of that per cubic kilometer. On the order of a quintillion---don't know if that helps.

    Anyway, each of those quintillion or so photons has lost
    1100/1101 of its energy since the moment the light got loose
    ("recombination", a moment of clearing when the plasma cooled
    to where it could condense to neutral hydrogen and the light which had been trapped in the plasma went flying in a suddenly transparent universe).

    Pick a photon and look at it, the photon has lost 1100/1101 of its energy because it has been stretched out. Its wavelength is 1100 times longer than when it first got loose.

    So we are surrounded by the concrete results of a huge loss of energy. In a cubic mile or cubic km of space there are roughly a quintillion things that have each lost 1100/1101 of their original energy. And no one, as far as I know, has suggested that the lost energy went into any new form. It did not "go" anywhere. It simply ceased to exist.

    Energy is an idea, not a real substance. It is not conserved except in very specific types of models, of which apparently General Relativity, our prevailing model of space and gravity, is not one.

    But it is eerie that the amount of energy which the CMB photons in a cubic mile have lost (since "recombination" some 13 billion years ago) should be roughly, within a factor of ten, the same as the amount of dark energy believed to be in the same cubic mile
    volume.
     
    Last edited: May 23, 2003
  6. russ_watters

    Staff: Mentor

    Re: Re: Re: Cosmological redshift: how much energy has gone missing?

    Is CMB the background radiation? I think the energy is either still in the background radiation or condensed into matter. Isn't this where the dark matter/energy question comes from? There is missing matter/energy, but I think cosmologists believe it exists.

    The wording of the laws of thermodynamics is different for different situations, but they apply to all closed systems. The universe is (believed to be) a closed system.
     
    Last edited: May 13, 2003
  7. marcus

    marcus 23,947
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    Re: Re: Re: Re: Cosmological redshift: how much energy has gone missing?

    Hello Russ, so you are still around this morning!
    Yes by CMB I mean CMBR cosmic microwave background radiation.
    Get tired of long acronyms sometimes and write CMB for short.
    You and I need a guru. the universe is believed to be infinite. I cannot think of it as a closed system, tho perhaps you can.
    the energy in it would be infinite and so the conservation law would not seem to say very much. but perhaps it says something meaningful to you.

    I don't think the conservation of energy applies, actually. The CMB has lost a huge amount and no one that I know has proposed any mechanism for the energy to have flowed into
    any other form
     
  8. russ_watters

    Staff: Mentor

    Re: Re: Re: Re: Re: Cosmological redshift: how much energy has gone missing?

    Our current understanding of the unvierse does indeed suggest that the universe is FINITE but without boundaries. This is what the Big Bang theory describes. It is analogous (but in 3d, not 2d) to an expanding balloon with dots on it - it has a finite surface area (that is increasing) but no boundary. So hypotetically, if you could travel fast enough in one direction, you'd eventually get back to where you started - just like on the surface of that balloon.

    As such, there was also a finite amount of energy in the Big Bang.
     
  9. marcus

    marcus 23,947
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    Re: Re: Re: Re: Re: Re: Cosmological redshift: how much energy has gone missing?

    Russ, please download this review article by M. Turner.

    http://xxx.lanl.gov/PS_cache/astro-ph/pdf/0202/0202008.pdf
    It is the accepted view. Professional journal article Feb.2002.
    The universe is not like a balloon for gods sake!
    It is flat----infinite in other words.
    You do not come back to the same place by going in a straight line in the real universe.

    That was the pretend universes of 10 years ago. Wake up. Cosmology has changed.
    Please do not use the balloon analogy any more!

    The field has changed radically because there are finally sufficiently accurate observations to check models
    and exclude the finite (positive curvature) balloon-type case
    and stuff. Observations are what count, finally.
     
  10. russ_watters

    Staff: Mentor

    That link isn't working for me. I'll try again later. This is related to that poll you just posted I'm sure, but in any case, I don't think you are correct. The expansion of a finite universe is central to the Big Bang theory. The Big Bang theory is still valid. Certainly there are a few people who disagree, but the vast majority of Cosmologists still consider the Big Bang to be valid.
     
  11. marcus

    marcus 23,947
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    the prevailing idea of the big bang is not something that begins at a single point with a finite amount of energy

    you are mistaken about what the majority of cosmologists think.

    the big bang is generally accepted by the great majority
    but has no assumption of finiteness
    (the finiteness and the balloon analogy is a popular misconception stemming from deceptive analogies used to
    explain things mathlessly

    it is like the "rubber sheet" analogy for general relativity that has
    damaged so many people by making them think that spacetime is somehow like a rubber sheet

    journalists and science writers have a lot of sins to atone for)

    the point is that as close as anyone can measure, the universe is flat (has curvature zero). It might still be curved some, pos or neg, a tiny tiny bit. But there is no evidence of it. The simplest thing is just to take it as flat. And this fits the inflation scenario.
    A flat universe is infinite. Lines do not curve around to the starting point. It never recollapses. It has infinite energy. And its big bang is not localized in a bounded region.

    There was an article in sci am recently based on the infiniteness of the universe and people made a long thread about it here at PF. It had several versions of "multiverse" of which the first and simplest was elaborated merely from the idea of infinite extent.
    Because of observed flatness it would be hard to find a professional cosmologist who would quarrel with the infiite extent business. Intellectual fashions change in every field of research and sometimes it is to the better---I think in this case it certainly is.
     
  12. russ_watters

    Staff: Mentor

    If the Big Bang is correct, doesn't that mean that at one time the universe was extermely small? Thats what the Big Bang Singularity was. And after the Big Bang it expanded. And it continues to expand. So when did the expansion of a finite universe cause it to go from finite to infinite? Further, since the Big Bang started with a singularity, there is a maximum size to the universe - with an age of about 15 billion years, the universe could not possibly be more than 30 billion light years across as that would require the expansion to be faster than the speed of light.
     
    Last edited: May 14, 2003
  13. marcus

    marcus 23,947
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    Bravo! these are just the right questions to ask!
    I was asking them myself not long ago!
    I cannot reply as an authority---only as a fellow student.
    It is really interesting.
    the current view of the universe is that it is flat which means
    infinite

    (or if not precisely flat and positively curved then thousands of billions of LY, for all practical purposes infinite, huge----might as well take it as infinite which is the simplest way to interpret the data)

    do you trust Ned Wright of UCLA astro and physics dept?
    Teaches cosmology and has a website that other physicists
    like to link to. A member of the team that owns MAP (the microwave
    anisotropy probe observatory orbiting the sun out at the Lagrange point L2) Do you trust him? I do he has excellent credentials and in my judgement is careful and rigorous. Plus
    other experts confirm what he says.

    So yeah-----if you start reading his site it will contradict a lot of what you think now.

    In GR (as opposed to SR) things CAN move faster than light and most of the universe IS moving away from us at speeds faster
    than light.

    thats surprise number one.

    SR is all true but only in the neighborhood of a point
    you cant have two things moving relative to each other
    faster than light IN THE SAME LOCALE
    or, as some people say, you cant have somebody pass by
    somebody else at greater than c.

    Also in cosmology there is a rest frame. a special preferred frame
    that is used out of all the billions of possible frames, to define the
    preferred distance scale.
    this is the frame which is at rest with respect to the CMB
    and distance defined in that frame is called the "comoving distance" and is considered to be measured AT THE PRESENT MOMENT
    The Hubble parameter is only defined in terms of the comoving
    distance. (this is a key fact, should be emphasized, when it says 71 km/sec per megaparsec of distance that megaparsec is of
    comoving distance at the present instant of time)

    Even tho the age of the universe is only 14 billion Y the radius of the observable universe is almost 42 billion LY (comoving distance)----which is much more than just the age of the universe multiplied by the speed of light. Surprising as it seems, this is stuff everybody in beginning cosmology learns. dont blame me Russ I am just reporting.

    cosmology is the most amazing mindboggling field!

    And yes, somehow the big bang was not confined to a bounded finite region-----this is devlish hard to understand, I know.

    And yes, there are galaxies out there that are receding from us
    at twice the speed of light and it is real easy to say what the
    comoving distance to them is. It is 28 billion LY-----that is, twice the Hubble length.

    Ned Wright has a calculator at his website that I can use to'
    turn that 28 billion LY into redshift or "z" terms. Maybe I will
    just to see what comes out.

    check this out:
    http://www.astro.ucla.edu/~wright/cosmolog.htm

    and from there go to the "cosmology FAQ" and the
    "cosmology tutorial"

    Good luck, it is a hard subject to stretch yer brain around
     
    Last edited: May 15, 2003
  14. marcus

    marcus 23,947
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    redshift z= 6.4
    corresponds to distance 28 billion LY
    and to something receding at the present moment
    from us at twice the speed of light

    I went to
    http://www.astro.ucla.edu/~wright/CosmoCalc.html
    the cosmology calculator page
    and did the calculation

    to check it, enter z = 6.4 and press the "flat" button.
    there is no finite universe button, that would say "closed"
    but there is a button that says "open" which is
    another option----also infinite

    the calculator also gives "light travel time" of 12.8 billion years
    from an object with redshift 6.4
    astronomers do not like to use light travel time as a measure
    of distance because it is not a good measure and hard to use
    and does not fit into the hubble parameter definition etc
    but it is still legit to ask "how long was that light traveling on its way to us?" and the answer is 12.8

    BTW a quasar with redshift 6.4 has been observed and Bob Becker of UC Davis
    bob@igpp.ucllnl.org
    is one of the people who has studied its spectrum.
    If you dont believe me write email to Bob Becker and ask
    "did you really see a z=6.4 quasar and is that mother
    really 28 billion LY away and receding from us at twice c?"

    It is your universe, so you have the right to ask.
     
    Last edited: May 15, 2003
  15. Heh, I don't know if this is true .. I just read it one time in a place far-far away. Can't remember where.

    What happens to the energy of a photon on redshift, or by transformation of coordinates, is that we see it as the energy redirected from the electric component to the magnetic component of the photon.
     
  16. This seems like a repeat of another post, but the case is that when z=infinity, v=c. So no quasar that we can see is receeding faster than c, or by definition we wouldn't be able to see it. The energy from light emmitted at near the beginning of the universe is redshifted because there is more SPACE now than there was then. It does not violate conservation of energy.
     
  17. This might be a minor point, but strictly speaking, energy is not a conserved quantity. From "Space Time and Quanta" by Robert Mills (of Mills/Yang fame), page 170:

    "... Note that energy conservation alone is not consistent, because the energy in a new frame depends, by the Lorentz transformation law (eq. 14), on the momentum in the old frame; thus momentum nonconservation in one frame leads to energy nonconservation in the other. The point is that the energy and momentum in the new frame depend only on the energy and momentum in the old frame, and nothing else. If they're both conserved in one frame, then they're both conserved in the other, even though momentum and energy get mixed together by the transformation."
     
  18. Re: Re: Cosmological redshift: how much energy has gone missing?

    Marcus, why are you often talk what you have no idea about (say, energy, or conservation laws)? Piling a mistake over another.

    Energy can't be lost. In expansion of photons their kinetic energy (color) went into their potential (spread in vast gravitational field), same way as a kinetic energy of atoms of supernova goes into their gravitational potential energy when a star expands.
     
    Last edited by a moderator: May 18, 2003
  19. marcus

    marcus 23,947
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    I'm with you on this Nacho
    It is simplistic to imagine that energy conservation holds
    in contexts where it is not proven.

    I dont have a copy of Mills book so I cannot tell exactly what
    he is talking about----it may be in a context of Special Relativity---I'm not sure what the quantities are and can't comment specifically.

    I had in mind a General Relativity context where space is expanding and there I believe it is simply a fact that energy is not conserved. I never heard of someone proving an energy conservation law for GR.

    People seem to have tried and have apparently invented a formulary of "pseudo-tensors" in their attempts---but this is marginal, I understand, not generally accepted. In mainstream cosmology, according to my understanding, there is no energy conservation.
     
  20. Of course, there is. Flatness of universe is the consequence of energy of universe conservation.
     
  21. marcus

    marcus 23,947
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    Re: Re: Re: Cosmological redshift: how much energy has gone missing?

    this is a beautiful idea but it sounds like your own fantasy, Alex.

    If it is not just your own imaginings, please cite an online reference where some expert is asserting this.

    The CMB is distributed roughly uniformly throughout space and the loss from it (by expansion) is occurring as we speak uniformly throughout space

    where is the energy going, where is the gravitational potential, in your picture, in what direction does the field point?

    I understand the conversion of energy in a supernova explosion from kinetic (outward motion) to potential (distance from center). but in the expansion of space there is no center. It is not a useful analogy as far as I can see. Or would you like to explain?
     
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