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Strings and Einstein's Spacetime

  1. Nov 6, 2004 #1
    If string theory is based mainly on Minkowsi "flat" spacetime, then how do they account for the proven curvature of our spacetime?

    Thanks to all,

    - Alisa :bugeye:
  2. jcsd
  3. Nov 7, 2004 #2


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    someone more expert can correct me if i am wrong
    I will try an answer to this one

    I think, DN, that the problem is that in the real world the geometry of space is always changing shape, as planets move around etc.

    If one could pick a rigid fixed geometry ahead of time then one could
    build strings on it, even if it were curved.
    the underlying space does not have to be flat.
    You can define strings and all the other gadgets on a fixed curved space.
    (True, mostly they assume flat Minkowski)

    But nature doesnt give us a rigid stage on which the actors play. the geometry is part of the action, and not predetermined.
    So string theory needs to be made background independent that is, free of commitment to any prior choice of geometry.

    General Relativity is background independent.

    Well, around 1992 and 1993, Edward Witten wrote a couple of articles saying that String theory should be made background independent
    (background independence is a keyword in the title of one of them)

    One reason he gave IIRC was to the effect that "until we have a B.I. theory we won't really know what strings represent---we wont know what strings are"

    that was rather deep------since nature is not a fixed Minkowski or othertype geometry with strings wiggling in it, this picture must be unrealistic and strings can't be that----so only by making the theory B.I. do we get contact with reality----I read one of those papers and remember being impressed by the philosophical depth at that point.

    All right, so now some 10 years have gone by.
    I heard a rumor a few months back that Cumrun Vafa (AFAIK Harvard, and outstanding) had made some progress and was maybe finding a way to get background independence

    And aside from that, some people seem to have redefined the words "background independence" in some technical way so that they can say that M-theory is B.I., or they say "background free" and mean something different by it, and then they say string is "background free"----or they say "we can do it on a great variety of different backgrounds, so who cares?"

    But that is not background independence (not e.g. what Witten meant) and I dont hear anyone saying plain flat out yes we have it now, and giving an arxiv link to the preprint.

    Now there is a funny twist to the story. On halloween day a postdoc named Hanno Sahlmann gave a paper on doing strings within the (background independent) context of Loop Quantum Gravity. We havent seen the paper. It was at the 29-31 October conference at perimeter. Loop gravitists have an unpredetermined quantum geometry.
    One way to make string B.I. would be to formulate it within the context of Loop's quantum geometry. (where all the angles and areas and volumes and shapes and distances are uncertain and variable)
    You might think this would make String people like Lubos Motl happy but you would be surprised. Experience indicates it will displease them and they will find it irksome and vexatious.
    the Albert Einstein Institute at Gölm outside Berlin has a page for Hanno, with a snapshot. i will get the link so the name means something.


    I am looking forward to seeing the text of hanno's talk
    It was called "String theory with LQG methods"
    Last edited: Nov 7, 2004
  4. Nov 7, 2004 #3


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    The direct answer to Divine N's question, how do the string theorists deal with the proven curvature of spacetime is that they don't; they deny it. Weinberg famously called it just a metaphor.

    The string idea is that the graviton, a particle which their theory predicts, acts on matter in a way that mimics the Einstein curvature, without requiring that curvature to exist. So they say (but it has been contradicted ) that you can't tell whether spacetime curves or that matter is exchanging gravitons.
    Last edited: Nov 7, 2004
  5. Nov 8, 2004 #4
    Isn't that a bit like giving Newton's "undefined force" a determined "shape", so to speak? he said himself in his book that he would leave it to his readers to figure out exactly what his force of G actually was and how and why it worked... He could only supply the "what happens when it works" bit, which I guess now is the graviton?

    So is that like completely circumventing Einstein?

    - Alisa
  6. Nov 8, 2004 #5
    If the curvature of GR is a metaphor, then wouldn't special relativity also be a metaphor, for the same reasons? If the GR curvature of spacetime is a metaphor of the density of graviton interactions, then wouldn't the SR effects also be a metaphor of some other kind of particle interactions that accelerate the particles? This would erase lorentz invariance of things like world sheets, right? So.. if lorentz invariance is valid, then SR is valid, and GR is valid for the same reasons, right?
  7. Nov 9, 2004 #6


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    The Lorentz transformations are not metaphor, relativistic causality and locatity are not metaphors, and the calculations in RQFT are not metaphors. Weinberg was speaking as a leading relativistic quantum field theorist. From that standpoint virtual particles are metaphors too, and all that is real are the equations and the measurable physical events that provide data for them.
  8. Nov 9, 2004 #7


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    I would urge anyone interested in quantum gravity to check out that thread. It is one that sA started about a recent paper by Thanu Padmanabhan. Maybe a "sleeper". He has a topnotch track record and it is potentially significant.

    A relativist would say that Minkowski space is just one possible solution to the einstein equation----solving for a perfect vacuum: an empty universe neither expanding or contracting---so you get a perfectly flat geometry. It can be a useful approximation, especially of local geometry (like the tangent plane to a surface, or a "coordinate patch": a flat map of part of a curved planet). The universe is nearly perfect vacuum, so it works, but it is not a realistic picture of nature.

    A particle theorist might adopt an alternative attitude (I dont know how actually workable it is) according which Minkowski space is the Absolute Space and the universe is just this Absolute space with gravitons whizzing around in it. And these gravitons reproduce all the bending and expanding and contracting effects we observe----the curved paths that light and planets travel, the differences in time of clocks in orbit, the different rates of expansion seen in redshift, and so on. The attitude would be that you cant tell the difference between that and dynamic spacetime geometry---that maybe in reality there is just the rigid flat Absolute Space with gravitons going around in it and creating these effects by their interaction with matter. Steven Weinberg's memorable dismissal of curvature (as mere metaphor) sounds like a statement of this view.

    One could broaden that particle theorist perspective out beyond just Minkowski space: one could choose some other simple idealized uniformly curved spacetime like de Sitter----something which, say, is expanding and is another solution to Einstein equation (but without realistic clumped matter or black holes etc.) One could take that as Absolute Space and have gravitons whiz around in it doing their interactions.

    If a string theorist really held such a view of things, then he or she wouldnt see a need AFAIK for a background independent version of String.
    You'd just do everything on the flat Minkowski background, with the flat Minkowski metric, in accordance with that view of how nature actually is.
    Or some fixed uniformly curved Absolute Space, if that was how you thought nature was.

    I dont know how widespread that view actually is, though. It seems to me that I've seen indications that string theorists would really like to have a background independent (dynamical curved space) version of the theory-----where it wasnt pinned down to a permanent flat metric. I have the impression that they would like that, but it is hard to get if you want to model stuff with vibrating strings---and they simply have not succeeded in devising a background independent version as yet.

    There are those papers by Witten calling for a background independent version. It suggests that, at least in 1993 or whenever he wrote them, he was not of Weinberg's opinion.
    Last edited: Nov 9, 2004
  9. Nov 9, 2004 #8


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    this troubles me. But I will concede, because I dont know enough
    to be able to generalize about what string theorists think or how they deal with it.
    you know a lot more about it.
    So I retract my previous post, which expressed doubt that they could really deny dynamic geometry (and pretend it's just metaphor)---but I wont erase it just yet
  10. Nov 9, 2004 #9
    Hmm... But what about things such as Einstein's Cross? And the apparent change of the position of stars? Are you suggesting that gravitons are bending the path of light? But whatever happened to geodesics and such? Aren't they a lot simpler? Who was it that said that the correct theory is usually the simplest?

    - Alisa
  11. Nov 9, 2004 #10

    Some portions of Space have an absolute 'minimum' curvature, Vacuum Fields. Vacuum Fields that have 'less' Matter are less curved, and are therefore 'more' flat!

    Maximum Curvature corresponds to a Spacetime With 'less' Vacuum. High curvature that have Less Vacuum 'flat-space' are found throughout the Universe in locations called Galaxies.

    It is an open question if all Galaxies have regions within their core's, that provide a Maximum 'Curvature', Blackholes come to mind?

    Two Galaxies that are a certain 'far' distance apart will have an equilibrium point exactly half-way in the intervening 'vacuum-space' between them. This location is the 'Maximum-Vacuum-Point' or 'Maximum-Flat-Space' area.

    String theory has been grappling with Vacuum solutions, and Blackhole Space-time configurations for some time. Witten I believe tried to hedge his bets with his paper on the constriants for "Proton-Decay?"..whereby he introduced an 'extended' timescale (theorized) for the lifetime decay period for the Proton.

    Many people have asked if this was a pre-cognitive expression for the obvious flaw in ST whereby the 'Time factors' did not fit with 'Space-factors'.

    The question you pose here:If string theory is based mainly on Minkowsi "flat" spacetime, then how do they account for the proven curvature of our spacetime? is exactly one of the reasons that Witten tried to 're-write' one of the most important paramiters for String Theory, this is based on the observational evidence for the liftime of Proton Decay.

    I made a posting to this fact stating that Witten had infact "MOVED-GOALPOSTS!"..but since March this year there have been many behind the scenes action for some sort of clarification of Space, and Space-time generalizations, the 'Vacuum Solution' is the Key to the whole of String Theory, and its many Extensions.
  12. Nov 9, 2004 #11
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