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The singularity moment at the beginning of the universe

  1. Aug 13, 2009 #1
    Being no more than a pop-sci reader in this subject, I'd like to ask the experts a naive question:

    At that instant where the entire universe was concentrated at a single point, it seems to me all matter had a definite position and momentum. Isn't this a spectacular fall of the uncertainty principle?

    The same question applies also to black hole singularities, how do we understand these points? And how do we save the quantum theory?

    Thank you very much for the responses...
     
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  3. Aug 13, 2009 #2

    Ich

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    It's rather definite position and infinite momentum, from a classical point of view.
    We do simply not understand these points. Singularities are not a physical fact overriding quantum physics. They are a hint that we need a more general theory that deals with this kind of extreme conditions. Maybe marcus can brief you a bit on today's approaches.
     
  4. Aug 13, 2009 #3

    marcus

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    It is an active field of research, several different approaches are being investigated. You can do a keyword search in the professional (not popular) literature with keyword "quantum cosmology". You might get some kind of rough impression from doing that.

    Here are the "quantum cosmology" papers from 2007 onwards ("date > 2006") in the Stanford database. The list is ordered by the number of citations each paper has received---how often other research papers have referred to it, a rough gauge of the paper's usefulness/importance.

    http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]

    The search shows over 230 papers since 2006. Click where it says "abstract" for a brief summary. A lot of the top-cited papers about the big bang use computer modeling. A quantized version of the old classic (Einstein-based) cosmology model is used. So there is no singularity breakdown (no place where the numbers blow up, no dividing by zero.)

    So using the quantized equations they build a simplified computer model of the universe and run it back to before the big bang.

    Some of the papers you see in the listing suggest ideas for testing these various quantum cosmology models. That's in its infancy. The Planck spacecraft which was launched this year, and is now taking data, may help. Making a more detailed map of the microwave background sky, including polarization. Improved mapping of the early light.
    Research interest in quantum cosmo, and how to rule out various alternative models by tests, is growing, but presumably it will take a long time.

    There is no very good popularized account of this that I know of. One of the top research institutions---Albert Einstein Institute, near Berlin---has a public outreach website called Einstein-Online. It is in English language and reasonably up-to-date (post 2006). I have a link to the cosmology section in my signature. You could try the essay called "A Tale of Two Big Bangs". It explains why scientists still talk about the "singularity" as a convenient time marker, even though they may not think of a singularity as actually having existed in nature. What actually was happening instead of a singularity is, in fact, the subject of a lot of investigation.

    To directly answer your question "how do we save quantum mechanics?" It is a good question and I think the answer is that quantum mechanics saves itself, in this instance. The illusory "singularity" breakdown occurred in a classical, vintage 1915 theory (Einstein Gen Rel) which did not use quantum theory math tools. If one introduces quantum methods into the cosmo model then the breakdown does not occur and time-evolution continues smoothly back into the past. You don't get an infinite density point. You don't get some catastrophic violation of the Uncertainty Principle. Things may look pretty weird briefly, right around the bounce. Gravity at extreme density acting repulsive instead of attractive, but quantum theory itself seems to survive OK.

    The key innovation seems to be that to get everything to work right quantum mechanics (or quantum field theory) has to be reformulated without a fixed spacetime geometry as a basis. The underlying spacetime geometry that serves as a background has to be freely variable---subject to quantum uncertainty itself. So quantum fields have to be defined somehow on an unfixed background. We keep quantum mechanics, the essential principles, but we make the theory of fields background independent. This is the basic direction things seem to be going overall, in the research related to your question.

    For a taste of background independent quantum geometry, you might read this illustrated Scientific American article by Jan Ambjorn and Renate Loll that I have link to in my signature. It is the "signallake" link. That also uses computer models of small quantum universes, but it is still very rudimentary and cannot duplicate full cosmology.
    Sorry things are so undeveloped as yet but that's just how new research is.
     
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  5. Aug 13, 2009 #4
    Hi Marcus,

    Thank you so much for the fantastic response. I have read the whole thing in a flash. And I was quite taken aback with the fact that time evolution smoothly goes backwards in time right up to the singularity point and gravity being repulsive at extreme densities?! These are amazing...

    The stanford papers are surely very good and instructive but unfortunately there's probably going to be too much dB loss for me, so I'll try the SciAm article and the Einstein-online website for now...

    Thank you so much,,
     
  6. Aug 13, 2009 #5

    marcus

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    Thank you for the good questions! I'd advise anyone to be cautious and skeptical about these things. The new quantum cosmology models are interesting and some do describe a bounce---a collapse of an earlier phase of the universe down to very high density and then a rebound, resulting in the expanding geometry we see.

    Some of these models even match the observational data as well as the classical model does. They duplicate it's success, and have the additional nice feature of not blowing up.

    But that isn't enough, to be adopted a new model has to run the risk of predicting new things to observe, some fine detail that future instruments can see, perhaps. It has to be tested where it goes out on a limb and predicts something that the old model didn't, so that it puts its life on the line.

    the QC models still have to be tested in this rigorous way. So don't believe them until they are and unless they pass.

    The Stanford data base of papers is not to read, just to scan if you are curious about what the actual research papers are about these days and who is writing them.

    I like Renate Loll and her model is clearly described in that Sci Am. That would be a good choice to start with. Even though her model has not shown a bounce yet. It is interesting and more than average comprehensible, but it doesn't answer the question where the universe comes from and what conditions preceded the bang. It gives a good taste of what quantum geometry is like, but it doesn't answer the questions that everybody is so anxious to know about.

    We just have to be patient. Maybe in another couple of years.
     
  7. Aug 13, 2009 #6
    Watch out your math if you want to study quantum gravity, Heisenberg inequalities do not prevent infinitely precise position measurements (at least before quantum field theory). Even better, with infinite momentum, the indeterminacy can actually be relatively small.
     
  8. Aug 14, 2009 #7

    Chalnoth

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    I'd just answer this shortly: there is no singularity. The singularity that pops up in our equations in the finite past of the universe is a failure of our theories to understand what happens as matter gets really, really dense. Some people have made use of possible quantum gravity theories to try to say something about what happens when matter gets incredibly dense, but nobody really knows. So before a certain time in our early universe, we just can't say what happened. Yet.
     
  9. Aug 14, 2009 #8
    Einstein's GR has singularity existence theorems. I think it is worth pointing out that studying QG before knowing those kind a basic theorem is not a very good strategy.
     
  10. Aug 14, 2009 #9

    marcus

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    Humanino, these theorems do not tell us about nature, they tell us about a man-made theory.
    I imagine that you are well-aware of this and would immediately acknowledge it. So your comment does not appear to respond to what Chalnoth is saying.

    I believe what Chalnoth means is that we have no reason to believe there is a singularity in nature.
    So when vintage-1915 GR develops a singularity (breaks down, blows up) this is a failure of the theory.

    It is not a failure of nature, it merely shows that a certain mathematical model has limited applicability. It only gives meaningful answers in a certain range, within its "domain of applicability".

    I think Chalnoth is making a valid and important point. Do you disagree? Please let me know if I am missing something.
     
  11. Aug 14, 2009 #10
    The preliminary results indicating a possibility for the disappearance of the initial singularity are some of the most important and exciting results in the development of QG during the last few years, I certainly agree with that.

    However, one should not loose sight of the fact that they answer hopes which have been around ever since those singularity existence theorems, and possibly even before. Although I do not believe in such a scenario, we must not forget that it may only because of those hopes that people finally manage to get encouraging results in this direction. As a consequence, although your points are more interesting than the one I raised, I think it is appropriate to notify whoever only begins to investigate QG of the general historical context in GR.

    I will not accept that reviewing such important work is not necessary. Sure it has nothing to do with Nature. But
    • It is far fetched to claim that newly published QG developments have more to do with Nature than classical GR. As interesting as they are, we are not talking about established results, even within the very community of QG, much less to mention tested results
    • I suppose it is also not necessary to study classical mechanics, classical electromagnetism, and quantum mechanics before studying QED.
     
  12. Aug 14, 2009 #11

    marcus

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    I basically agree. Although you may be putting it a bit too forcefully. One of my favorite quotes from Einstein-Online is from this essay:
    http://www.einstein-online.info/en/spotlights/big_bangs/index.html [Broken]

    This is dated October 2006. Einstein-Online is the public outreach website of a top research institution, part of Max Planck Institute. Saying "Most cosmologists would be very surprised..." is putting it mildly---I would call it a quaint understatement.
     
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  13. Aug 14, 2009 #12

    George Jones

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    Our most predictive theory of gravity, GR, predicts singularities. There is no empirical for the existence of singularities, but there is some empirical evidence for black holes. There is no empirical evidence for the non-existence of singularities, but there is some theoretical evidence which, in my opinion, is at best somewhat suggestive, that quantum gravity is singularity-free.

    In my opinion, any definitive, unqualified statement on the existence or non-existence of singularitiers, such as
    is quite unjustified.

    Clearly, the opinions of Chalnoth and marcus differ from mine.
     
  14. Aug 14, 2009 #13

    Chalnoth

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    Yes, I am aware of this. As Marcus states, this is a problem with GR.
     
  15. Aug 14, 2009 #14

    Chalnoth

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    I don't understand. You accept a prediction of an energy density vastly greater than the energy scale of General Relativity (the Planck scale)?
     
  16. Aug 14, 2009 #15

    marcus

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    That's a good point. The new results in quantum cosmology need to be tested. Until there is empirical evidence I think it is fair to say that we have no reason to believe one way or the other!
     
  17. Aug 14, 2009 #16

    George Jones

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    I didn't say that.

    We have no empirical evidence for the existence or non-existence of singularities. GR gives come theoretical evidence for the existence singularites, but this evidence is suspect, because, as you say, it is widely believed (and I believe) that some quantum theory of gravity take over from GR doesn't at high densities. Theoretical quantum gravity gives some evidence theoretical for the non-existence of singularities, but this evidence is either qualitative and vague (e.g., quantum "fuzziness"), or very preliminary.

    This is a very exciting, open research question, about which I think it is impossible to make an unqualified statement.
     
  18. Aug 14, 2009 #17

    marcus

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    That sounds like something I could say myself, or could agree with.

    Right now there is no empirical evidence either way.

    I'm not sure what you mean by theoretical evidence that QG is singularity free. I don't know of any general result. Certain singularities (such as at the big bang) do not appear in certain quantum cosmology models. Loop QG may have singularities which are simply not of the type usually considered (black hole, cosmological). I saw one paper to that effect.

    Anyway, my only problem with what Chalnoth said is that he put it flatly, without qualification. I like the way the idea is expressed in the passage I quoted from Einstein-Online. We have no scientific basis for believing that a cosmological singularity occurred in nature and it would be quite surprising if it turned out that one actually did!
    (But of course it can't be ruled out :biggrin:)
     
  19. Aug 14, 2009 #18

    Chalnoth

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    No, but the problem is that actual singularities are mathematical nonsense. I don't think we need an understanding of quantum gravity to say that these singularities are almost certainly not real.

    Basically, the problem is that GR predicts a singularity, but you can't apply Einstein's Equations in a singularity, which makes no sense.
     
  20. Aug 14, 2009 #19
    I am trying to follow the discussion, so I think it's in order to ask what a "singularity" is in reality?

    Is it only a mathematical problem or can it objectively exist in Nature? So my question is what does it mean to say "a singularity occurred in Nature" really?

    Thanks for the responses,
     
  21. Aug 14, 2009 #20

    Chalnoth

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    A singularity, were it to exist, would be a point of infinite density. General Relativity has singularities at the centers of black holes, as well as a cosmological singularity in the finite past of our universe (it's actually a proof that you must have such singularities if GR is accurate). Many people call this cosmological singularity the "big bang", even though it almost certainly never existed.
     
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