Causal Sets

Fay Dowker has a nice descriptive introduction to the Causal Sets approach to Quantum Gravity:
gr-qc/0508109
No equations, but very lucid explanations of the ideas and accomplishments.
Every approach to quantum gravity in this broad conception must embody answers to two fundamental questions: “What is quantum mechanics?” and “What is the deep structure of spacetime?” This article will touch on the former question and focus on the latter and the answer to it provided by the approach known as causal set theory which marries the two concepts of discreteness (or atomicity) and causality.

The view that causality is a more fundamental organising principle, even than space and time, is an ancient tradition of thought...
She brings in a supporting quote from big Al:
“But you have correctly grasped the drawback that the continuum brings. If the molecular view of matter is the correct (appropriate) one, i.e., if a part of the universe is to be represented by a finite number of moving points, then the continuum of the present theory contains too great a manifold of possibilities. I also believe that this too great is responsible for the fact that our present means of description miscarry with the quantum theory. The problem seems to me how one can formulate statements about a discontinuum without calling upon a continuum (space-time) as an aid; the latter should be banned from the theory as a supplementary construction not justified by the essence of the problem, which corresponds to nothing “real”. But we still lack the mathematical structure unfortunately. How much have I already plagued myself in this way!”

A. Einstein in a letter to Walter D'allenbach,
The real punchline is that causal sets, unlike any of those more fashionable approaches to quantum gravity, seems to have an actual confirmed, or at least tentatively confirmed prediction:
In this regard, causal set theory already has the advantage of a long-standing prediction of the current order of magnitude of the cosmological constant, or “dark energy density”... that has apparently now been verified.
Yep. Kinematics, dynamics, and an actual prediction, made before the discovery, and, apparently, now confirmed by supernova and cosmic microwave background measurements.

A very nice article for anybody interested in the foundations of quantum mechanics, sum-over-histories, and quantum gravity.

Comments

  1. Anonymous8:11 PM

    CIP,

    the link you provide is broken.
    Nice paper though ...

    ReplyDelete
  2. Anonymous10:40 PM

    Pig,
    the alleged prediction of Lambda (order of magnitude) is in
    [9] R. D. Sorkin, Forks in the road, on the way to quantum gravity, Int. J. Theor. Phys. 36, 2759–2781, (1997).
    http://www.arxiv.org/abs/gr-qc/9706002

    the prediction comes way at the end and it is not at all clear to me how it is supposed to derive from a causal sets picture---it looks to me like he derived it from other strange assumptions which he urges on us as plausible.
    In what I have seen of Dowker, she tends to toss off this prediction citing Sorkin but never to summarize or reproduce the argument.

    so I am left in doubt about why Sorkin, in 1997, published the number 10^-120, on what basis. is it really a hard prediction from some CausalSet setup? If, in 1998 when the supernova data came out, a different value for Lambda emerged, would that have rendered CausalSet invalid? I don't have a clue. So I can only suggest you have a look at the Sorkin 1997 paper where there is the alleged prediction.

    have to say that 10^-120 looks right though

    ReplyDelete
  3. CapitalistImperialistPig7:05 PM

    iso42 - I tested the link before and I've tested it since, and it always works for me.

    ReplyDelete
  4. CapitalistImperialistPig7:11 PM

    identity - I have (now) read parts of Sorkin's article, and I agree that the prediction is a bit "soft," but I think it would have been a blow to causal sets if it hadn't tested out. He did get it from a real equation, even if the equation was not quite as well motivated as one might hope.

    Supersymmetry is, at present, also a rather soft prediction of string theory, since there is no solid reason for supersymmetry to require strings. The difference is that it hasn't been found yet.

    ReplyDelete

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