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Space is flat?

  1. Aug 29, 2012 #1
    I was watching a Horizon program the other night on the BBC and was interested that they were able to repeat the "triangle on the surface of a sphere" experiment on the universe as a whole.

    When this experiment is performed on the surface of the Earth on a large enough scale the angles of the triangle don't add up to 180 degrees and shows that the earth is not flat to someone even though they may not be able to leave the surface.

    So , to recap, they were somehow able to draw these lines in the universe (I have no idea how!) and came back with the discovery that the angles of the triangle actually added up to180 degrees.

    They said that this showed that space was flat and not curved!

    My question is this.
    If space is flat why is space-time curved?
  2. jcsd
  3. Aug 29, 2012 #2
    From what I understand there are 3 main theories on the form of space.

    1. "Big Crunch Theory" A closed universe (such as a sphere) with sufficient matter of all kinds to allow gravity to eventually halt the expansion of the cosmos. Expansion become contraction and the universe would disappear from where it came.

    2. "Flat Universe" where space has a curvature of zero and where total matter equals critical density, meaning that the universe would have no boundary and expands forever eventually slowing in infinite time but by definition "Infinity" has no limit.

    3. "Open Saddle Shape" where total matter is less then critical density and would expands forever and its acceleration is driven by dark energy (an anti gravitational force) is currently quite a popular theory.

    Q: If space is flat why is space-time curved?
    A: Basically it is due to the contribution of matter that distorts the fabric of space-time.
    Similar to the effect on light by Gravitational lensing.
    Last edited: Aug 29, 2012
  4. Aug 29, 2012 #3


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    Because the space is expanding in time.
  5. Aug 29, 2012 #4
  6. Aug 29, 2012 #5
  7. Aug 30, 2012 #6
    @ d3mm
    As I previously said they are all but theories..
    The WMAP can show what ever it wants, but how one interprets the mathematics, it is still just another theory ready to dispute.
    But the fact is space-time geometry is manipulated by matter.
  8. Aug 30, 2012 #7
    What is the evidence for the curvature of space?

    How does it deal with the results from WMAP survey?

    So are gravity and quantum mechanics, you will have to do better than "it's just a theory".
  9. Aug 30, 2012 #8


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    And what "data" do you think confirms this fact? You seem to misunderstand how science works, which is unfortunate. The WMAP data cannot show "whatever it wants" -- it shows the actual universe. Then we have a theory that predicts what the CMB should look like. Then we compare these predictions with the WMAP data. Science occurs. Wash, rinse, repeat.
  10. Aug 30, 2012 #9


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    d3mm -- are you seeking answers to these questions or were you posing them to Cyghost -- can't tell.
  11. Aug 30, 2012 #10
    bapowell, I was asking Cyghost to defend his position.
  12. Aug 31, 2012 #11
    Yes I think we are probably going a little off topic of the original question "If space is flat why is space-time curved?"
    but I will say I certainly do not claim to agree or disagree to the 3 models I fore-mentioned as I was only presenting a few of the popular examples of late I have not once in this post stated that I disagree that space is flat so I'm not certain what I am supposedly defending but here is a link to your request for a response to your question.

    Q : What is the evidence for the curvature of space?


    Also what is your definition of flat?

    From what I understand WMAP measured the "curvature" of space to within accuracy to 0.6% of "flat"

    Is that truly flat?


    And to answer your 2nd question.

    Q2: How does it deal with the results from WMAP survey?

    How does your question even relate to the posters question of "If space is flat why is space-time curved?"
    which I answered 3 times now (Where there is significant gravitation due to matter space-time will become curved)
    Last edited: Aug 31, 2012
  13. Aug 31, 2012 #12
    I think you may have misunderstood what I was trying to say regarding (how one interprets the mathematics from the data received) I think it would be naive to simply "Wash, rinse, repeat." and not consider any other possibilities. To me that is not what science is about either (which apparently I seem to misunderstand) and I appreciate the personal attack BTW.
    It's like saying ok we have received this data from WMAP and as you stated "we have a theory that predicts what the CMB should look like then we compare these predictions with the WMAP data"
    What if there is another theory that also produces the same data outcomes?
    Is that not possible?
    To simplify it for you :
    1+1 = 2.
    4-2 = 2.
    Different equation but same result.
    Again you have taken this way off topic from the original question.

    I'm not sure I agree with your answer to the question he asked "If space is flat why is space-time curved?
    Last edited: Aug 31, 2012
  14. Aug 31, 2012 #13
    Is it possible to know why matter should have this effect on SpaceTime or is it simply a mathematical consequence that when we model the situation that the outcome resembles the dimpled cushion effect?

    Does antimatter have the same effect?

    If space time is severely distorted (as in the spinning binary black holes scenario ,say) would that create the opportunity for a massless object to travel practically instantly from one side of the (SpaceTime) region to the other a bit like in an anciently active area of the earth you might dig down and cross millions of geological years in a very short space because the strata have been stretched and thinned at that place (in other places the same amount of geological years might take longer to dig through)?
  15. Aug 31, 2012 #14
    I think the point he was trying to make is that you can only measure the angular diameter distance of the acoustic peaks from CMB, and then you infer the curvature by comparing your observation to the model. Interestingly enough, there are also direct ways of measuring curvature, but so far our observations are not good enough for constraining it enough to be useful. You can check out http://arxiv.org/abs/1102.4485 for more details.
  16. Aug 31, 2012 #15
    What kind of explanation would satisfy you? At some point you're going to have to take something for granted. The laws of physics can't explain themselves. For general relativity, what is taken for granted is that matter curves spacetime according to the famous Einstein equation, and everything else follows from this assumption (well, and a few others)

    It does seem likely but very difficult to verify. Antimatter is so rare and gravitation is so weak, it seems unlikely that we'll be able to confirm this any time soon
  17. Aug 31, 2012 #16
    Any kind at all (I mean any theory). I can understand that it is acceptable to make a hypothesis and to then to test it to death but why should any phenomenon not have a physical( maybe not the right word? preceeding?) cause.
    Maybe mathematics are the fundamental reality (as was believed by Pythagoras(?) I think).
    Last edited: Aug 31, 2012
  18. Aug 31, 2012 #17
    And if you knew the cause, what makes you think you wouldn't be asking for the cause of the cause? Let's say I explain gravity by saying that there are these tiny invisible butterflies that fly around, pour glue into your watch to make it run slow and stretch space by flapping their wings. Would you feel that is a satisfactory explanation, or would you then ask: "but why butterflies?"

    There is one perhaps more physical explanation for gravity, but unfortunately it has turned out to be very difficult to make it work. It turns out that the usual GR description of gravity is completely equivalent with the force being carried by virtual spin-2 particles (like electromagnetism is carried by photons). Unfortunately to describe the theory like this, you'd need to dress it into the language of quantum field theory, and that is a project that's still not quite finished.
  19. Aug 31, 2012 #18
    I am predisposed to believe that I would almost certainly be asking for the "cause of the cause" (otherwise I would be a believer in a God -which I am not)

    And I don't mind outlandish causes if they fill the gap.

    But I didn't ask for a theory of gravity -just ,in particular why an object with mass should distort spacetime (aside from a mathematical explanation).

    Or is that the be all and end all of gravity-objects with mass distort SpaceTime and no further questions on the subject are relevant? (I don't mean to come across as indignant!)

    Are you saying that my question "what in particular causes an object with mass to distort SpaceTime?" is a nonsensical question with the only possible answer "because it does" or "because that is what gravity is"
  20. Aug 31, 2012 #19

    My question is about the overall shape of observable universe, not what happens locally in the vicinity of a large mass. I am asking which of the three theories you mention, do you believe is the most appropriate after new evidence such as WMAP and the accelerating expansion of the universe.
  21. Aug 31, 2012 #20


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    Yes, I'm aware that multiple theories can offer competing explanations for a given data set. The reason that I misunderstood what you wrote is because you were not being clear. You state that "The WMAP can show what ever it wants, but how one interprets the mathematics, it is still just another theory ready to dispute." How one interprets the mathematics? I guess you mean -- how one uses mathematics to explain the data. OK, got it. But it's still not "just another theory to dispute." There is an entire program for comparing the merits of competing theories given data, and yes, this program needs to be exercised in the face of any scientific data. The argument you seem to be advancing is not specific to the CMB -- it can apparently be applied to any body of data. It is simply impossible to use induction to obtain a uniquely correct theory. So, I am interested in knowing how your argument differs from that made by Hume et al. hundreds of years ago regarding the problem of induction.

    If you want to debate the merits of competing explanations for the CMB, then fine. If you are just pointing out the obvious limitations of all experimental science, then I think you are taking this thread way off topic.

    His question has to do with the fact that if space is flat (in the sense that R, the curvature scalar, is zero), how is it that space-time is curved? It has to do with the fact that the spatial metric components, [itex]a(t)x^i[/itex], while indeed giving flat hypersurfaces, are function of time. In this case, the curvature scalar is non-zero,
    [tex]R \propto \frac{\ddot{a}}{a} + \left(\frac{\dot{a}}{a}\right)^2[/tex].

    Do you still not agree?
  22. Aug 31, 2012 #21
    I'd probably trust the astrophysicists on this and would say model of the universe that is “flat and infinite" (although I use the term infinite loosely as the visible region of space) it seems to match the results pretty closely.

    There is always the possibility of some form of galactic foreground contamination also the long delays in releasing the results was confusing, or if data was incorrectly inserted such as if the wrong spectral index is used to convert the difference between power spectra at different frequencies into a point-source contribution, then there will be a systematic error in the cosmological parameters.
    Last edited: Aug 31, 2012
  23. Aug 31, 2012 #22
    Okay, let me rephrase my answer more clearly: This question is not answerable using general relativity. That theory has nothing to say about the mechanism. If you want to invent something, like the butterflies I mentioned in the previous post, then if that satisfies you, fine. It would be even better if you could come up with a mechanism which has some observable effect on physics, like small deviations in the gravitation field around massive bodies or in the path of photons, or whatever. If the mechanism has observable consequences, then you can make experiments and decide whether it's true or not. If it's something you've invented to keep you sleeping at night (like the many worlds interpretation of quantum mechanics), that's possible too.

    Let me give you another example. In quantum electrodynamics, you describe the interaction between electrons and photons. The theory is extremely successful and accurate - it can predict basically everything you can see, and more. However, an inquisitive soul like yourself might ask: what's the mechanism through which the photons and electrons interact? And to that question the theory has no way to answer; they simply do.
  24. Aug 31, 2012 #23
    Ok I may have been a little ambiguous with my statement regarding the WMAP.

    No :)
  25. Aug 31, 2012 #24


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    OK. What exactly do you disagree with?

    EDIT: Or, "No", you agree?
  26. Aug 31, 2012 #25
    The recent WMAP data has narrowed the range of possible curvatures of the universe, but unfortunately, it still leaves open the possibilities of a universe with positive or negative curvature. I suppose you could say it makes the possibility of a flat universe more likely, but if the universe truly is flat, will any measurements ever make us 100% sure of its flatness? It seems like we're just doomed to continue narrowing the range of possible curvatures further and further without really putting the nail on a curvature of 0.
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