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Conformal gravity challenges string (Mannheim)

  1. Jul 16, 2007 #1


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    The Wikipedia article on Conformal Gravity encourages skepticism about its usefulness
    On the other hand Mannheim may have countered some of the objections to it.

    Conformal Gravity Challenges String Theory
    Philip D. Mannheim
    8 pages. Proceedings write-up of talk presented at PASCOS-07, Imperial College London, July 2007
    (Submitted on 16 Jul 2007)

    "The cosmological constant problem and the compatibility of gravity with quantum mechanics are the two most pressing problems in all of gravitational theory. While string theory nicely addresses the latter, it has so far failed to provide any compelling solution to the former. On the other hand, while conformal gravity nicely addresses the cosmological constant problem (by naturally quenching the amount by which the cosmological constant gravitates rather than by quenching the cosmological constant itself), the fourth order derivative conformal theory has long been thought to possess a ghost when quantized. However, it has recently been shown by Bender and Mannheim that not only do theories based on fourth order derivative equations of motion not have ghosts, they actually never had any to begin with, with the apparent presence of ghosts being due entirely to treating operators which were not Hermitian on the real axis as though they were. When this is taken care of via an underlying PT symmetry that such theories are found to possess, there are then no ghosts at all and the S-matrix is fully unitary. Conformal gravity is thus advanced as a fully consistent four-dimensional alternative to ten-dimensional string theory."
    Last edited: Jul 17, 2007
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  3. Jul 16, 2007 #2


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    I can't evaluate this with confidence. It could be an important paper. For one thing Mannheim has a respectable publication trackrecord and is a recognized authority. He was invited to write a 90-page article for Progress in Particle and Nuclear Physics on the dark matter and energy problems surveying alternative proposed solutions.

    The paper that just came out has two main references which I'll put link for here as a convenience for anybody who wants to get into it.

    Reference [1] is:
    Alternatives to Dark Matter and Dark Energy
    Philip D. Mannheim (University of Connecticut)
    87 pages, 3 figures. To appear in Progress in Particle and Nuclear Physics, 2005
    (Submitted on 12 May 2005 (v1), last revised 1 Aug 2005 (this version, v2))

    "We review the underpinnings of the standard Newton-Einstein theory of gravity, and identify where it could possibly go wrong. In particular, we discuss the logical independence from each other of the general covariance principle, the equivalence principle and the Einstein equations, and discuss how to constrain the matter energy-momentum tensor which serves as the source of gravity. We identify the a priori assumption of the validity of standard gravity on all distance scales as the root cause of the dark matter and dark energy problems, and discuss how the freedom currently present in gravitational theory can enable us to construct candidate alternatives to the standard theory in which the dark matter and dark energy problems could then be resolved. We identify three generic aspects of these alternate approaches: that it is a universal acceleration scale which determines when a luminous Newtonian expectation is to fail to fit data, that there is a global cosmological effect on local galactic motions which can replace galactic dark matter, and that to solve the cosmological constant problem it is not necessary to quench the cosmological constant itself, but only the amount by which it gravitates."

    Reference [2] is:
    No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
    Carl M. Bender, Philip D. Mannheim
    4 pages
    (Submitted on 1 Jun 2007)

    "Contrary to common belief, it is shown that theories whose field equations are higher than second order in derivatives need not be stricken with ghosts. In particular, the prototypical fourth-order derivative Pais-Uhlenbeck oscillator model is shown to be free of states of negative energy or negative norm. When correctly formulated (as a PT symmetric theory), the theory determines its own Hilbert space and associated positive-definite inner product. In this Hilbert space the model is found to be a fully acceptable quantum-mechanical theory that exhibits unitary time evolution."

    Here are 100-some articles by Mannheim

    Last edited: Jul 17, 2007
  4. Jul 18, 2007 #3
    I have readed the first paper and it looks interesting, but to have a proper judgement would require, at least, read the two others and that requires time (mianly the first one).

    Searching for some hints I have found the two following links:



    Untill now the maybe greater problem with these theory could be dark matter. I mean, these tehory seems to not require dark matter and recently there have been indirect proofs of it´s exitence. Althought beeing a cosmologist surelly Manhein is aware of these and maybe there is some room for dark matter in that theory.
  5. Jul 18, 2007 #4
    This sounds very interesting marcus. Thanks. I'll print the papers and read them properly. I'm off for a fortnight from next week so I've got plenty of time coming up. Talking of skepticism, I'm particularly skeptical about string theory myself. Thanks too Sauron.
  6. Jul 18, 2007 #5


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    Everybody please note the warning on the label :blushing:
    Voltage, it might be good to take some other vacation reading along besides this. I'm not sure about this "conformal gravity" stuff.
    I'd like to see a critique----not just writing by a proponent such as Mannheim. I apologize if it should turn out that I have put you on a false lead!

    Sauron, thanks for the link to Valdosta site. I was not aware of Tony Smith's notes on conformal gravity, or of the long history going back to 1980 and Irving Segal. Segal is associated with brilliantly conceived lost causes, in my mind. so this business could simply be just some Ancient History. It may have some fatal flaw, so that only die-hard believers stick to it.

    Garrett Lisi could tell us. Alejandro Rivero might know. I was initially quite interested, but right now I am in confusion about it, and can only urge caution.
    Last edited: Jul 18, 2007
  7. Jul 19, 2007 #6


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    I have a soft spot in my heart for Tony Smith - a brilliant and genuinely original thinker. He just needs to work on his 'plays well with others'.
  8. Jul 19, 2007 #7


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    Like many modifications of Gravity, on the classical side, it tends to have enough freedom to fit things to within at least a handwavey ballpark.

    One might object on the grounds that it will lead to the wrong structure formation models people use, and the darkmatter paradigm is hard to fit even in vanilla GR, much less something with extra residual broken symmetries, tho apparently there is some references in that paper to work thats done on it.

    Then theres how it may or may not affect structure formation, BB nucleosynthesis, baryogenesis and so forth. Read a lot of work.

    As a quantum theory, I don't know much about it. Like all four derivative theories, it has subtle problems with causality, though the author claims to have fixed the unitarity ghost problems. Then theres the exact phenomenology for conformal breaking. What are the matter couplings? Shouldn't various particles be frozen out in the high energy sector leading to very observable signatures in the early universe? etc etc

    As is the trademark for GR+ theories, the phenomenology tends to get much more messy and so people tend to work with them less.
  9. Jul 19, 2007 #8
    Noted marcus. I've got a stack of papers a foot high to read through, so I'll just chuck this into the mix. Chronos and Haelfix, thanks for the input. Haelfix, I pay special attention to the issues you raise such as causality and matter couplings or particles frozen out. I've been doing a little "handwavey independent research" on this sort of thing, and one day I hope to have something of sufficient rigour to post on PF. I might need a collaborator to do this, we'll see.
  10. Jul 22, 2007 #9
    I looked at these Conformal Gravity papers, marcus. It was a reminder to me what an amateur I am. The mathematics was over my head, and there's just so much I don't know. There's what looks like some good stuff in there, like getting back to the Weyl tensor, which really lights my fire, and getting rid of Dark Matter and Dark Energy instead of playing whack-a-mole with things like wimps. But at the same time IMHO it takes other things too much for granted instead of getting all the way back to basics. So far I've gotten as far as page 14 of the large paper "Alternative to Dark matter and Dark Energy", but have read the conclusion. This struck a chord on page 72:

    "..However attempting to critique the standard theory is not an easy enterprise, in part because what constitutes the standard theory is something of a moving target.."

    I was however a little alarmed to read that this conformal gravity would render the Standard Model "wrong". In my ignorance I tend to think of models and theories as being wrong in part, and being improved and refined instead of being cast down shattered into a thousand pieces. It seems that only String Theory is allowed to change as much as you like, and anything must be destroyed by any flaw. The sort of question I ask is this: If Einstein had come up with something like this in 1955, would it have still been Relativity?

    I'll have to learn more about all this stuff. Thanks for the info.
  11. Jul 22, 2007 #10
    I'm unsure what you meant by these remarks.
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