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With all due respect, is there going to be mud wrestling?

  1. Aug 3, 2005 #1


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    I believe the job of the Loops05 conference at Potsdam in October is to forge an alliance of research programs into a field called "Nonperturbative Quantum Gravity" so that there can be faculty positions in NQG in physics departments at various major universities.

    well that sounds serious and dignified, and even historical, but everybody knows the stakes are high and in its own way it means there is going to be a circus maximus

    like Fay Dowker for whom it is an axiom that spacetime is discrete (a causal set is about as discrete as you can get) is going to collide head-on with Renate Loll, who has found no evidence of spacetime discreteness, or of a minimal length scale, in her computer experiments with CDT.

    Personally, I think that CDT and Causets are similar: a causal triangulated manifold is actually an excellent example of a certain kind of causal set----the set of simplexes causally ordered by the way they are glued. And the only difference I can see is that Renate goes to the limit as the simplexes get small. You might think that was just a LITTLE difference

    The difference is Fay does not go to the limit. She has all these, like, beads or beans of spacetime with each one being exactly equal to the planck volume, arranged in a partial ordering (causality) with a certain finiteness condition (which is automatically satisfied in Renate's triangulated manifolds). So it is like she was going to do Renate's thing but at a certain size or scale of simplex, at a certain point, she STOPPED MAKING IT SMALLER.

    So even tho the two approaches Causet and CDT are extremely similar and almost indistinguishable in some sense, all hell is liable to break loose when you put them together. Because for one it is an axiom that spacetime is made of discrete beans and in the other approach not.

    I think we should try to understand this issue. Why is it so important to so many Quantum Gravitists that spacetime be in some fashion or other discrete? What is at the root of this urge or drive or intuition or feeling that it ought to be that way?

    If you go surf the website of Loop05, you will see that Renate Loll is WAY OUTNUMBERED by QG people who have espoused this discretness idea in one way or another. Loop, for instance, is CONSTRUCTED on a continuum but it gets discrete volume and area spectra as a result. (they are not however simple wholenumber multiples of planck units, as you might expect from Fay's picture!) so Rovelli and Ashtekar and Smolin all include the idea of discretness in their statements about Loop even though it is not so cut-and-dried full frontal discretness as with Fay. Fay is radically discrete and they are sort of politely and modestly discrete.

    Like a spin network in LQG is a GRAPH so that is not so discrete as a heap of beans. But still it is rather more discrete than a chunk of continuum out of differential geometry.

    how shall we understand this conference? Is it a series of headon collisions?
    the stakes are very high (I feel) but I can't quite say what they are. Now is the time (I feel) for this fragmentary bunch of programs to coalesce into a kind of Nonperturbative Alliance.

    But my feeling about academics is they dont come together easily, when they are intellectually at odds. This discreteness issue is a FAULT LINE. (or so I'm thinking)

    I wonder if there are other irreconcilable differences.

    Well, in case anyone else is interested, I will get some links:

    here is the Loops05 website ("programme" has a list of speakers like Fay and Renate)

    here is a Fay Dowker manifesto
    here is a Raphael Sorkin manifesto
    here is a nontechnical statement from Loll about CDT

    Here is the opening shot from Loll, page 2 paragraph 2 of
    [PLAIN]http://arxiv.org/hep-th/0505113 [Broken]

    Slow progress in the quest for quantum gravity has not hindered speculation on what kind of mechanism may be responsible for resolving the short-distance singularities. A recurrent idea is the existence of a minimal length scale, often in terms of a characteristic Planck-scale unit of length in scenarios where the spacetime at short distances is fundamentally discrete. An example is that of so-called loop quantum gravity, where the discrete spectra of geometric operators measuring areas and volumes on a kinematical Hilbert space are often taken as evidence for fundamental discreteness in nature [CITES ASHTEKAR AND SMOLIN]. 1 Other quantization programs for gravity, such as the ambitious causal set approach [CITES SORKIN], postulate fundamental discreteness at the outset.


    ... We have recently begun an analysis of the microscopic properties of these quantum spacetimes. As in previous work, their geometry can be probed in a rather direct manner through Monte Carlo simulations and measurements. At small scales, it exhibits neither fundamental discreteness nor indication of a minimal length scale. Instead, we have found evidence of a fractal structure (see [7], which also contains a detailed technical account of the numerical set-up). What we report on in this letter...

    Actually didn't Newton and Leibniz have it out over some issue or other? this is in the good old academic tradition. It's how things happen, how WORK gets done.

    Now here is Renate citing Fay on page 2, paragraph 2 of ANOTHER paper
    http://arxiv.org/hep-th/0507012 [Broken]

    A time-honoured part of this discussion is the question of whether a sum over different spacetime topologies should be included in the gravitational path integral. The absence to date of a viable theory of quantum gravity in four dimensions has not hindered speculation on the potential physical significance of processes involving topology change [CITES HOROWITZ, CITES DOWKER]. Because such processes necessarily violate causality, they are usually considered in a Euclidean setting where the issue does not arise. Even if one believes that Euclidean quantum gravity without a sum over topologies exists nonperturbatively as a fundamental theory of nature – something for which there is currently little evidence –, ...
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  3. Aug 3, 2005 #2


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    Leibniz really got the short end of the stick too. He had to share credit for calculus with Newton (who played some really dirty tricks with journal editors), but Newton gets top billing, despite the fact that Leibniz invented the notation that we use today, while you wouldn't even recognize Newtonian notation as calculus.

    Also, while the conference may very well be dramatic, I would disavow you of the notion that the stakes are high. No one's career is on the line (all the important players have tenure and none are in a strong position of authority over each other). I have yet to become aware of a single important scientific discovery made at a conference. And, ultimately, science is not democratic. Winners win because they are right, and losers lose because they are wrong.
  4. Aug 4, 2005 #3


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    My vote is let the chips fall when they bootstrap themselves into existence. My opinion - no model is background independent when you force units of measure into initial assumptions. Don't get me wrong, I like coordinate systems as much as anyone, but, I am convinced they must be emergent, not first principles. That is the allure of CDT. It is the most BI approach I have seen to date.
  5. Aug 4, 2005 #4
    Marcus, I'm no expert on quantum gravity but I have done a bit of work on this particular issue in the history of human thought. You will know that the ancient Greeks wrangled over whether the elements were continuous or discrete. And continuous vs discrete has been a burning issue ever since.

    There are three positions you can take. You can believe that reality is monadic - whenever faced with some sort of basic metaphysical dichotomy like this, you can say that reality must be one or the other. So either it must be continuous or it must be discrete in this instance.

    The second stance is dualism. You say both alternatives are fundamental and irreduciable. So reality is BOTH continuous and discrete. This would be an unusual position to take with this particular dichotomy (I can't think of any examples off hand), but its the stand often taken with other dichotomies such as mind~matter.

    The third stance would be the unfamiliar one. This is a triadic view. The idea is that all things begin in vagueness, a state of raw potential. So there is a oneness of a sort. There is then a symmetry-breaking of that vague potential in which two contrasting poles of being get expressed. Reality gets separated towards two limit states. The threeness or triadicity is in the fact that you end up with a hierarchical system that has two boundary states (the contrasting extremes) and then the third thing of a middle ground - all the possible grades of being that now lie between these two limits.

    So in this case, the discrete and the continuous would be the two most extreme possible contrasting limits. A reality could separate towards both these goals, and perhaps come asymptotically close to attaining them, but reality itself always lies just inside these limits. So reality itself would be neither discrete nor continuous in a fundamental way.

    As to which is the right view, they are all of course modelling approaches - free epistemological choices. Monadism would usually be the most efficient or pragmatic stance. The triadic approach is certainly the most complex but probably closer to the actual truth of the world.

    So what would this say about quantum gravity? The scientific community would generally be trying to find the most effective, pragmatic model. Whether this ends up being based on the idea of discreteness or continuity would not seem to matter. Neither would be "true" in a deep sense. I would only note that discreteness is more mathematically tractable and so most progress usually gets made by scientists who stick to the intuition "it must be discrete".

    But if like me you are also interested in getting closer to the complex truth, then the larger view may be that the system - quantum gravity - arises out of vagueness and then we find both poles of being (the apparently discrete, the apparently continuous) emerging together as a symmetry breaking. What this actually means in practice is what you would have to discover.

    In loop quantum gravity, it might mean something like the vagueness is the quantum space of possibility - all the potential paths represented by the "space" between the lattice of connections. The lattice then emerges out of this vagueness as a crisp geometry that maximises both the discrete and the continuous. You have both definite intersections/nodes and definite connections. So the geometry sort of swims into view out of a generalised murk to become a self-organising coherent mesh.

    There are some people who have recently begun working on "ontic vagueness" as a way of thinking about the quantum realm (Chibeni, French, Krause). Though of course the idea itself is as old as history (Anaximander, 600 BC).

    A final comment would be that discrete~continuous is unlikely to be the most fundamental kind of dichotomy anyway. Rather like change~stasis and random~determined, it does not really speak to scale. So a deeper kind of dichotomy is usually local~global, where scale becomes critical. And also substance~form, where again scale tends to become a necessary feature of the story.

    Cheers - John McCrone.
    Last edited: Aug 4, 2005
  6. Aug 4, 2005 #5
    I had a dream about 10 years ago...

    I saw this thing spinning in space but it was just a blur as it was moving to fast. I asked for it to slow down and it did just enough for me to make out what it looked like. I woke up drew it and went back to sleep. When i woke in the morning I had completely forgot about it until I checked the picture

    I keep ascribing meaning to it as it appears to have helical, cyclical, dimensional, symmetrical, balance, duality, inflammable, linguistic properties...

    ...it is 2 contrasting birds of prey with 3 head feathers feeding of each other forming a single entity and in constant circular motion it also connects to form chains

    why i posted it here is cos McCrone's post reminded me of it and thought it might mean something to others...

    does it ???

    http://img201.imageshack.us/img201/1291/kontraribbons7yn.jpg [Broken]
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  7. Aug 4, 2005 #6
    Hey I don't want to get off track with this thread. But the "third way" I describe is of course something like yin-yang and other forms of mutual causality to be found in eastern philosophy. And you might want to read Hofstadter's Godel, Escher, Bach for its direct connections with your bird image.

    But beyond this pop culture there is some serious stuff. One of the things that is "wrong" about your bird image as an illustration of this logic of dichotomies is that it is symmetric - you have bird and anti-bird. The kind of symmetry breaking I am talking about is asymmetric - so you would have something that is actually very hard to illustrate. It would have to be some kind of figure~ground or local~global phase transition. So you would have a picture of "birdness as figure" constrasting with "birdness as ground" - whatever that might mean. Some of Escher's work would get close I guess.

    I should note that symmetry~asymmetry is itself a metaphysical dichotomy and so itself would be subject to the same monadic/dyadic/triadic question. Just as Marcus was asking why do so many focus on "discrete" instead of "continuous", I would want to ask why do so many focus on "symmetry" when "asymmetry" would seem the more fundamental? And then think of the way in which both extremes were a constrasting pair of limit states.

    But anyway, if we stick to the particular case of LQG as a current scientific project that illustrates standard metaphysical quandries, then this could be quite enlightening. The advantage LQG has over strings is that it attempts to be background free. And this is taking the thinking of physicists closer to an exploration of the concept of ontic vagueness perhaps.

    Here is an excerpt from a popular article for which Marcus supplied the link.http://arxiv.org/abs/physics/0401128
    Author: Ruediger Vaas

    This is where the "swimming into view" metaphor crops up.

    (snipped) - "Ashtekar and his colleagues call them spin networks. This concept was coined by Penrose, who already in the 1970s had formulated his Twistor theory with similar motivations, and introduced spin networks as a kind of spacetime dust. Ashtekar compares the spin networks - mathematically known as graphs - to a fabric of polymer-like one-dimensional threads. If one could observe nature with maximum possible enlargement, space and time would dissolve and the granular mesh of the spin network would come to light - or more precisely: the quantum physical superposition of all possible configurations of these entities. There is .nothing. between these graphs. Those entities rest only on themselves, so to speak. "The spin networks do not exist in the space. Their structures produce the space," Smolin stresses. "And they are nothing but abstractly defined relations - which determine how the edges come together and interlock at the joints ."

    Cheers - John McCrone.
  8. Aug 5, 2005 #7


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    I would like to get this thread back on topic and mention, as a reminder, that this is not the Forum on "Philosophy of Science and Mathematics" and overly philosophical posts are OFF TOPIC.

    We were talking about the Loops05 conference, which you can learn about at the website http://loops05.aei.mpg.de/
    ("programme" gives a list of invited speakers)

    At this conference, the triangulation people will be in the minority and will have to maintain certain points against the mental tendencies of the majority. Assuming some form spacetime discreteness has become a widespread habit among QG people BECAUSE for a long time IT HAS BEEN SEEN AS A CURE FOR SINGULARITIES.

    The widespread idea is that if there is a minimum length scale it can serve as a cut-off preventing bad things from happening, infinite densities, infinitely short wavelengths and high energies.

    So for a long time people developing quantum gravity have been expecting discreteness and/or a minimal length scale, and hoping for it, and either POSTULATING it as an axiom (as do Fay Dowker and Raphael Sorkin) or else being very happy when they can derive one or both as a result. Because with a minimum length cutoff you never have to worry

    But I suspect that it will turn out that DISCRETENESS IS NOT NECESSARY because the threatened singularities will be resolved another way. So it will be possible to discard it as an UNNECESSARY EXTRA ASSUMPTION for which there is no justification.

    Here is what Loll has to say about this, page 2 paragraph 2 of
    http://arxiv.org/hep-th/0505113 [Broken]

    Slow progress in the quest for quantum gravity has not hindered speculation on what kind of mechanism may be responsible for resolving the short-distance singularities. A recurrent idea is the existence of a minimal length scale, often in terms of a characteristic Planck-scale unit of length in scenarios where the spacetime at short distances is fundamentally discrete. ... Other quantization programs for gravity, such as the ambitious causal set approach ... postulate fundamental discreteness at the outset.
    One variant of Occam's razor is the commonsense adage
    IF IT AIN'T BROKE, DON'T assume extra axioms in an attempt to FIX IT.

    the spacetime we use at everyday macroscopic scale is a continuum, it works fine, it is not discrete and a discrete grid would be a poor substitute, good for approximations at best. LOLL'S PROGRAM IS USE THE CONTINUUM WE GOT, AND TRIANGULATE IT AND THEN LET THE SIZE OF THE TRIANGLES SHRINK TO ZERO. Notice at no point in this process does anything need to be discrete. A continuum, or manifold, that is triangulated is still a continuum. It is like a piece of paper with triangles drawn on it. Triangulated does not need to mean CUT UP, the continuum can be imagined having simplexes drawn on it. when you do Loll "moves" you separate simplices and glue them back together a different way, but they still form a triangulation of the continuum.

    So in Loll program you never at any point deal with anything grainy. It is a triangulated continuum at every stage, and you are going to the limit where triangle size shrinks to zero

    GRAINY THEORIES ARE BACKGROUND DEPENDENT. they have this extra structure, graininess, that we do not observe in the world which is added into the picture. A grainy theory, like causal sets, DEPENDS ON BACKGROUND STRUCTURE of a heap of beans or points or grains, which has to be imposed. that graininess is EXTRA BAGGAGE.

    Now it is a different matter if a QG theory derives some discreteness as a result. that happens with Loop. They don't put it in as an assumption, they just start with a familiar continuum, and as a mathematical consequence of how they quantize Gen Rel they get discrete spectra of some geometrical operators. Areas can only be chosen from this discrete list of possible areas, like the energylevels of an atom.

    But still Loop does not have grains of space or of spacetime. so it is quite puzzling. Could Looptheorists be wrong? Might they redo it and find continuous spectra?

    I think this is a physics issue and that it is undecided so far. There should eventually be experimental tests. At present Loll and friends are exploring the consequences of their model by running computer simulations and here is what they find:

    We have recently begun an analysis of the microscopic properties of these quantum spacetimes. As in previous work, their geometry can be probed in a rather direct manner through Monte Carlo simulations and measurements. At small scales, it exhibits neither fundamental discreteness nor indication of a minimal length scale. Instead, we have found evidence of a fractal structure (see [7], which also contains a detailed technical account of the numerical set-up). What we report on in this letter...

    EDIT replying to Chronos next post here to save space. hi Chronos, causal sets people conjecture that's how spacetime fundamentally is. it is not proposed as an approx. but that spacetime is really discrete, made of "atoms of process" each one with volume equal to planck volume. beans. Look at Dowker's lecture. It's a caution.
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  9. Aug 5, 2005 #8


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    I lean toward fuzziness rather than granularity when talking about the 'structure' of spacetime [hasn't the 'granular spacetime' notion been discredited by gamma ray surveys??]. IMO, discreteness is just a mathematically convenient way to approximate perturbative effects.
  10. Aug 5, 2005 #9
    uh yeah, sorry bout that marcus...:blushing:

    ...cheers for the look out on that book McCrone, I'll hunt it out and read it

    I'd like to hear more about asymmetry as it relates to my bird image...

    ...It's weird but the first bit of meaning I ascribed to it was the spirit/energy exchange of heaven and earth one rising one descending

    maybe start a thread in the "philosophy of science and math forum" as i would like to hear how you might think the spinning blurry factor changes the symmetry aspect and what it might mean ???
  11. Aug 7, 2005 #10


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    this quote from the 1997 Sorkin paper confirms that the tendency to posit or hope for discreteness is ROOTED IN CONCERN ABOUT SINGULARITIES.

    If one could get rid of singularities some other way, one could chuck out discreteness as excess baggage, a conceptual trinket which, however it may appeal to the verbal thinking of philosophers or be in harmony with language, is not necessary to physical models of spacetime.

    first let's look at Sorkin 1997 about why he likes discrete. He brings in a couple of quotes from Einstein and then invokes the "Three Infinities", a list of troublesome singularities which discreteness might be hoped to cure:

    ---key Sorkin quote on discreteness---

    ...the answer I want to discuss follows from still another question: is spacetime ultimately continuous or discrete? Here, I cannot resist quoting Einstein, who wrote in 1954,

    “The alternative continuum-discontinuum seems to me to be a real alternative; i.e., there is no compromise . . . In a [discontinuum] theory space and time cannot occur . . . It will be especially difficult to derive something like a spatio-temporal quasi-order (!) from such a schema . . . But I hold it entirely possible that the development will lead there . . . ” [56]

    (In this quotation the exclamation point is mine, put there because the words ‘spatio-temporal quasi-order’ seem so obviously to be calling for a theory based on causal sets!) Referring to the argument against the continuum, Einstein goes on to say

    “. . . This objection is not decisive only because one doesn’t know, in the contemporary state of mathematics, in what way the demand for freedom from singularity (in the continuum theory) limits the manifold of solutions.”

    Here, the objection was that quantum mechanics teaches that a bounded system can be described by a finite set of “quantum numbers”, and such a description conflicts with the infinite number of degrees of freedom posited by a continuum theory. (The loophole referred to was the possibility that excluding singular solutions of the field equations might suppress these unwanted degrees of freedom (and reproduce all the characteristic quantum effects as well, all without leaving the domain of classical field theory)).

    In addition to this argument for a fundamental discreteness there are several contradictions in existing theories which speak powerfully for the same conclusion. These contradictions, which I call “the three infinities” (or perhaps four depending on how you count them), include the

    divergences of Quantum Field Theory,

    the singularities of classical General Relativity,

    the apparent non-renormalizability of naively quantized gravity [57],

    and the apparently infinite value of the black hole entropy

    if no cutoff is present. The final item in this list rests on an interpretation of horizon entropy to which I will return below; to my mind it is the least adequately appreciated of the common arguments for discreteness.

    ---end quote from Sorkin---
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  12. Aug 7, 2005 #11
    Hi Marcus and all...

    Reading this with great interest. So if I understand, Loll et al are invoking a fractal structure at small scales. Fractal structures rely on the idea that the unit length can be reduced infinitely, somewhat as is done in calculus to find a limit, except that in fractal maths, the limit is replaced by self-similar forms on smaller and smaller scales. So instead of coming up to a nice smooth line, as in calculus, fractals find that the foamy, spiroling, lacey shapes continue at finer and finer scales, forever.

    I have played with fractal programs based on Mandlebrot and Julia sets, and while in theory the sets go on downward forever, it turns out that no computer program can follow them down forever. You see, as the scale gets smaller and smaller, the numbers needed to calculate the positions of the structures get larger and larger. Eventually, the numbers get so large that the computer is no longer able to calculate them. This has, of course, to do with the limits of the crunching power of the computer, not with any limits on the fractal sets, which presumably do go on forever, self-similar at all scales.

    The image works something like this: you start with the Mandelbrot set, which is a nice little ink blot having several notable symmetries. You select one small spot on the edge of the inkblot, and bring it up to the full size of the screen. Now you find that there are many variations of the same inkblot shape, all interconnected by very pretty spirol lines. You pick another small spot on one of the lines or on the edge of one of the inkblots, and you blow that spot up to full screen, with the same result. Again, there are variations, and the variations can be rather extreme, mostly forming increasingly elaborate paisley patterns. I will suppose that we have all done this.

    However, when you continue this process long enough, perhaps going down this way for twenty or thirty or sixty steps, eventually the interesting patterns smooth out, and finally you are left with a screen showing nothing more than a line down the middle with a very small gradient difference between the two sides. As I said, this result has to do with the limits of your computer, not with the limits of the fractal set. If your computer were large enough to crunch bigger numbers, presumably you could repeat the select and blow up procedure hundreds or thousands of times. Or, if you have a computer that can handle infinite numbers, you could go on infinitely. You would never reach the condition of having two more or less equal states seperated by a smooth line, but would always find the same, complicated tracery of self-similar variation on the original set.

    Now I come to what I believe could be the point of truce between Loll and the others, that is between discrete and continuous models. Here it is. No universe can contain an infinite computer.

    David Bohm, in his book "Quantum Theory", at the end of chapter 16, "The Harmonic Oscillator," says "no wave packet ever spreads out indefinitely, because after a period it must return to its original shape." So it must be, even with the wave packet of the entire universe. In human terms, we as observers have a particular shape and size. We do not go on forever, just as our computer cannot go on forever. We have fixed limits. If the entire universe is some size, then we are some fraction of that size. Inverting that ratio, we find that if we divide our size by the size of the universe, we come up with a quanta so small that no computer we can ever access can calculate differences smaller than that scale.

    So I conclude that in theory, Loll et al are correct, and there is no bean at the center of everything. However, from a practical standpoint, there is a nugget, and that nugget is present in every measurement and in every observation because of the physical limit on our computational power. This limit on computational power, in theory and in practice, is something that cannot be overcome. We must accept it, just as we must accept that it is a limit on our own being, not a limit on the Universal Being, if you like, or Multiverse.

    The universe is not a pile of beans, Marcus, you are quite right. But we cannot take the universe in a single bite, we have to cut it down to our size, and then smaller. Any such cut results, inevitably, in a sense of graininess. Is this truce acceptable to you, Marcus, or must we go to the mud wrestling?

    My thanks to the honorable librarian, and my apologies for this graffiti:

    Bean Eaters, Unite!

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  13. Aug 7, 2005 #12


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    for some reason I was laughing out loud by time I finished reading.
    the truce seemed acceptable to me, for sure, but I have no say in the matter

    Loll et al only found fractal-LIKE geometry at very small scale or in very thin spatial slices (as I remember) and I do not know quite how to interpret that, or picture it----also don't know as much about PROPER true fractals as must you and several others. So I am in my usual position of waiting to hear more from the researchers, in their own good time.

    it wasnt something they especially wanted or arranged to have happen, they just found it when they constructed 4D quantum spacetimes by simulation. and this could be wrong the finding still could be reversed I should imagine.

    So there is a good chance there IS beans down there Richard, it could well BE discrete at the planckity planck scale. (as Sorkin and Dowker, among others, would have it) But being just a mite contrarian, the fact that so many Gravitists seem to LIKE discreteness be expecting discreteness makes me more alert to the Lollish possibility of continuum all the way down.
    so glad you also willing to look at it this way as well
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  14. Aug 7, 2005 #13


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    no bean at the center of everything

    continuum all the way down

    I like it
    Last edited: Aug 8, 2005
  15. Aug 8, 2005 #14
    Hi Marcus and all

    I am pleased to give you something to smile about, and even laugh. But I hope you have not missed the point....

    Consider what a "grain" is...a very small object, the interior of which appears to be uniform, even blank, and yet within which there is some hidden, invisible structure, the germ of a new universe. It is true that the perfection of mathematics demands a continuum all the way down, but it is equally true that physical reality, that world of phenomena which we percieve and measure, demands the grain.

    Math may be continuous, but physics is discrete. To answer the question here, we have to pose it in terms of one, or the other.

    I have said this before in different words. "Being is not conserved in the fourth dimension." Being is necessarily limited, defined, not infinite, but contained within some natural boundaries. These boundaries are extended in every possible direction, in every possible dimension, but only extended to some limit.

    We have evolved in a world of three dimensional space, and we have developed the quality of memory, which gives us an imaginary fourth dimension. In this imaginary dimension, we are allowed 'temporarily' to step outside of ourselves, conceive of our own natural limits. But when we do so, every time we do so, in all cases, we discover that there is a little hidden spot in our otherwise flawless vision, a tiny germ in the plasm of the egg, a connection to another world, through which we are not limited, not conserved, not defined, and which therefore challenges the very idea of our "being" in the sense of a seperate, integrated creation at all.

    If we are to progress, we must learn to live in the imaginary dimension, not just visit it. We do not have to surrender our notion of seperate being, individual self awareness, but we have to give it a new relitivity. In this more relaxed vision, it is not a conflict for a line, a plane, a space, to be both discrete and continuous, any more than it is a conflict for one object to pass behind and be temporarily obscured by another object in space.

    CDT seems to insist on the continuum, and that is fine, but it does not negate the usefulness of and need for discretion. The Monte Carlo method itself is a way of approximating a larger reality. You can't count every path, so you take a random walk along some of the possible paths, counting as you go, and then you assume that the little sphere you have explored is more or less like every other little sphere, all the way out to infinity. Multiply and there it is, a granular view of the universe.

    Now for the argument that this is anthropocentric. That is true, in so far as we are anthropos. However, we can now see that it is not an anthropocentric argument at all, since it has to apply not only to anthropos, but to every intelligent observor, every observation, every registration of change. It is not merely central to apes, but central to phenomena. And this brings me to my next point.

    Phenomena are time dependent. If there is no time, there is no phenomena.

    We need to revisit our idea of spacetime geometry. Does light pass through spacetime geometry? No. Light is part of the structure of spacetime geometry. It is meaningless to wonder if the speed of light still holds at the Planck scale. The Planck scale is fundamentally an expression of spacetime geometry. It exists before and below the stage at which light comes into existance.

    Perhaps you will recall from "A Brief History of the Universe" or from "The First Three Minutes" or from elsewhere that in the earliest part of the big bang scenario, there is no light. The universe at that scale is too dense to allow light to exist.

    But it is not only the speed of light that has to be re-thought. Motion and change, energy and mass, the most fundamental concepts in physics, are not what we think they are. Gravity is not what we think it is. The only way to get a grip on the reality is to re-evolve ourselves, not in a world-view where there are three dimensions of space and one of time, but in a universe where space and time are the same thing, and time has as many degrees of freedom as space has.

    Be it a grain of dust or a beam of light, we need to remove it from our eye. It is something else. It is the illusion of seperation.

    Be well,

  16. Aug 8, 2005 #15
    the ultimate fundamental level is the existential bit- either on or off- either exist:yes or exist:no- before metrics and dimensionality and causality is the fundamental ‘ontologics’ of bits- how can a bit be half existing and half non-existing? it can't- so at the bottom you MUST have formless bits interacting to emerge a continuum-

    perhaps our spacetime is not itself discrete- but even if it is a continuous fractal it would still be an EMERGENT continuity- you still must face that fundamental discreteness
  17. Aug 9, 2005 #16


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    I'm not very convinced at all that there is another way to resolve this problem, at least not a better way. The singularities we see flow very directly from a space-time structure that is continuous and smooth. If you have equations that involve division by a distance or time unit, and those equations don't have sensible limits as the distance-time quantity approaches zero, you are going to get singularities. If that same equation is on a discrete background, in contrast, you won't.

    A lot of people have been worried that renormalization is a form of cheating mathematically. But, that isn't true if you have a discrete space-time structure. In that case, renormalization is a reflection of the fundamental physics of space and time and isn't cheating at all.
  18. Aug 9, 2005 #17


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    Ohwilleke, the argument from singularities, or from Sorkin's "Three Infinities", that discreteness must be there for things to work---and must be assumed or somehow be a feature of the spacetime model---is a strong one. I agree that the case for it is very persuasive.

    But I am not ready to burn my boats and commit to a discrete spacetime. At least not yet. Even though I don't know of any other way these infinities could be resolved, I still think there COULD be a way. And that would, in a sense, vindicate the continuum. It would no longer be necessary to throw out the continuum and replace it with some more discrete contraption with a built-in minimal length.

    I am tantalized by the possibility that the 4D spacetime of CDT behaves microscopically as if it is of lower dimension---closer to 2D---and that there are theories which in lower dimensions are renormalizable though they fail to be so in 4D. This encourages me to hope that something will be found to happen at microscopic scales that will take care of singularities without spacetime being discretized into little grains or droplets, and without the need for a minimal length.

    I suppose it is possible that the feathery fractal-like stuff found in Loll's computer experiments down at microscopic scale could in some fashion be akin to the spin networks of the Loop picture, but so far Loll and friends have not unearthed any minimal length.

    Anyway, i have no logical argument to make about this. You have all the force of argument, but it the case is not air-tight. So I choose to wait and see if the Triangulations people can offer other ways to settle those infinities.
  19. Aug 9, 2005 #18
    It would seem unlikely that fractals would decrease dimensionality. Normally it raises it.

    I would suggest a different interpretation. The Universe is fractally structured in that it has lightcones (events with event horizons and holographic effects) over all spatotemporal scales. Each event~event horizon fractal marks an act of QM environmental decorence by the Universe as a system.

    In this picture of how things work, a flat and coherent (ie: continuous looking) spacetime would emerge once there was enough global scale in the universe to create an average decoherence value. A prevailing ambience.

    If you zoom in towards the Planck scale, you are effectively isolating a scrap of spacetime from its normal decohering environment and the QM values of that scrap will start to roil. At the Planck scale, the curvature of spacetime would become maximally disorientated - it could curve locally in any direction as it is not being constrained (Ising model-like) to curve in a way that smoothly fits in with the wider ambient story. So in a way, the gravity curvature would appear to have broken up into something discrete. This Planck scrap would still have the potential to "be continuous" but that desire is being frustrated as the experimental set-up would have isolated it from a wider context that would tell it which way it ought to flex.

    So at the Planck scale of observation, spacetime would appear to be hyberbolic, an open geometry, that flexes in any and all directions. This would appear to be an increase in dimensionality (as more triangles, connections, or whatever metric you choose) could be packed into such a space.

    At the other end of the scale hierarchy, the Universe would appear to flex in the other direction. It would bend towards a closed, or hyperspheric geometry. And is a hypersphere continuous or discrete? Well it is continuous as a manifold and discrete because it is finite - countable as one thing.

    Then across our normal scales of measurement, the Universe would look flat. A continuum punctuated by discrete events with discrete (though ever expanding) event horizons.

    A metaphor for the situation can be found in the dissipative branchings of a river as it hits the sandy plains of a delta. If you look upstream towards the head of the river, it is a single fat channel. Its geometry seems to become closed like a hypersphere. The effect would be even more pronounced if you imagine viewing this river over a million years - the head of the river would now seem quite fixed in place compared to the river about halfway down where you stand which now wriggles about the landscape like a snake, perhaps breaking and combining in a few dozen large channels.

    Now look downstream and the river breaks up into a fractal set of branchlets. At some point - from where you stand - it all just becomes a vague blur. The dimensionality turns from discrete features in a continuous landscape into a roil of dissipative activity.

    The difference between this model and the real universe would be that with the river, we can imagine walking down to the delta and now being able to tell again the difference between the discrete and the continuous - the branchlets and the landscape. We are assuming the fractal nature of spacetime extends all the way to the Planck scale (and even beyond in Loll's model?). But with the environmental decoherence story of spacetime, walking down to the delta's edge would in effect isolate each branchlet from the sustaining flow of the river. Our own feet would stamp all over the trickles of water, cutting them off and allowing the flows to become disorientated - flowing in no particular direction anymore.

    For the sake of simplicity, it is quite likely that LQG will see the Planck scale as essentially discrete or essentially continuous. A model of how things are at the mesoscale of observation will be projected to infinity without any consideration of scale effects or the triadic causality of hierarchies. The models will "work". But there is no point getting too uptight about discrete vs continuous as both are likely to be emergent properties (or rather, views) in the real world situation.

    Cheers - John McCrone.
  20. Aug 12, 2005 #19


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    returning to the main themes of the upcoming Quantum Gravity conference and the principle issues that divide nonperturbative quantum gravitists. As a way of getting my bearings I will quote post #1 of this thread and take a closer look at one of the links:

    to me as an onlooker, this Sorkin manifesto is especially interesting because I agree with sorkin's prejudices (or reasoned opinions) on almost every one of the main issues that he lists. I differ only about the discreteness---this makes me think that perhaps I dont fully understand his position on that.

    also i am impressed by the foresightfulness of sorkin, in the sense that he is posting in 1997 what he asserts to be a talk he gave in 1993, in which he takes positions which seem very "up to date" to me---they are well adapted to the CDT path integral developments of the past year or so.

    Also he includes an estimate that Lambda the cosmological constant is on order E-120 natural. But people like me just heard about Lambda being E-120 earliest 1998 with the type IA supernova data. Don't know what to say about this. Did he know something in 1993 or 1997 that others didn't, or was it just a wild guess? Don't like how he gets the estimate but the fact that it was right makes me look twice at the rest of what he says.

    Sorkin is one of the invited speakers at Loops05 (along with Loll, Smolin, Dowker, Rovelli, and other interesting folks) here is the 1997 abstract:

    Forks in the Road, on the Way to Quantum Gravity
    Rafael D. Sorkin (ICN-UNAM and Syracuse University)
    29 pages
    Int.J.Theor.Phys. 36 (1997) 2759-2781

    In seeking to arrive at a theory of "quantum gravity'', one faces several choices among alternative approaches. I list some of these "forks in the road'' and offer reasons for taking one alternative over the other. In particular, I advocate the following:

    the sum-over-histories framework for quantum dynamics over the "observable and state-vector'' framework;

    relative probabilities over absolute ones;

    spacetime over space as the gravitational "substance'' (4 over 3+1);

    a Lorentzian metric over a Riemannian ("Euclidean'') one;

    a dynamical topology over an absolute one;

    degenerate metrics over closed timelike curves to mediate topology-change;

    "unimodular gravity'' over the unrestricted functional integral;

    and taking a discrete underlying structure (the causal set) rather than the differentiable manifold as the basis of the theory.

    In connection with these choices, I also mention some results from unimodular quantum cosmology, sketch an account of the origin of black hole entropy, summarize an argument that the quantum mechanical measurement scheme breaks down for quantum field theory, and offer a reason why the cosmological constant of the present epoch might have a magnitude of around 10-120 in natural units.
    Last edited: Aug 12, 2005
  21. Aug 12, 2005 #20


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    ---quote Sorkin's 1997 abstract---
    the sum-over-histories framework for quantum dynamics over the "observable and state-vector'' framework;

    relative probabilities over absolute ones;

    spacetime over space as the gravitational "substance'' (4 over 3+1);

    a Lorentzian metric over a Riemannian ("Euclidean'') one;

    a dynamical topology over an absolute one;

    degenerate metrics over closed timelike curves to mediate topology-change;
    ---end quote---

    Most of this program are things Loll is trying to achieve in CDT! Well obviously what Sorkin calls "sum-over-histories" is the path integral which is the key feature in Loll's CDT. But there is a lot more overlap. For instance a dynamical topology with crotchpoints allowing for brief micro wormholes was the subject of recent Loll/Westra papers.
    Loll uses spacetime, as Sorkin likes, instead of space by itself and she
    uses Lorentzian metric rather than "euclidean", again as Sorkin likes.
    CDT, being sum-over-histories---that is, path integral---is distinct from the canonical style of LQG which Sorkin calls "observable+state vector". So I could see Sorkin approving of CDT on most of the points that he mentioned.

    For my part, I find myself mostly agreeing with Sorkin's list of preferences, or quite sympathetic anyway. I don't see much in Causal Sets, though. The idea of postulating discreteness as an axiom---and also what I perceive as a NAIVE discreteness of Causal Sets---puts me off.
    But I want to take a careful look. maybe Sorkin's idea of discreteness could be reformulated mathematically, defined in some way that agrees with the quantum continuum that comes out of CDT.

    One thing: Sorkin doesnt like a differentiable manifold for spacetime, and neither does Loll.
    Back in 1997 maybe there were only two alternatives.

    he says to take a discrete underlying structure instead of the differentiable manifold

    I can agree to take something that is not a differentiable manifold! I think this new kind of continuum comes out of what Loll is doing. It does not have a uniform dimensionality same at all scales (as a manifold would). It clearly does not have a differentiable structure like a smooth manifold.
    But it is not just a bunch of points either!

    I can agree with Sorkin (as a bystander on the sidelines) to say no to the differentiable manifold. But I can't agree with what he apparently thought was the only alternative back in 1997.

    it is a complicated tangle. Could it be that Loll continuum simply hasnt been studied enough and that Sorkin will like it when more is known about it?
    Last edited: Aug 12, 2005
  22. Aug 12, 2005 #21
    It would seem to me that any discretized version is necessarily background dependent. For you are specifying points or regions as being a particular distance (as marked off in the background) in relation to other points or regions. That's presupposing the very space that you're trying to explain.

    Whether there is a technical manifold at the heart of it, one thing seems sure. It must be a topology of some sort. I can't imagine parts and protions of reality not also being members of reality too.

    At this point for me, is still seems inconsistent to say space can be either 4D or 2D depending on how close you look at it.
  23. Aug 21, 2005 #22


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    three important issues raised in your last post

    I tend to agree---interpreting "background dependent" in a vague general sense. We should discuss this more, although we may not be able to settle it to our satisfaction.

    Again I tend to agree, and with me it is just an intuitive feeling again.
    I can accept the idea that the continuum could be modeled by something that is not a differentiable manifold but (for now at least) I can't imagine a model continuum which is not a topological space. Perhaps some people can...

    I disagree with you here. It does not seem inconsistent to me.

    Here is an analogy (and admittedly an imperfect analogy, not to pushed too far):

    Imagine you have a long strand of hair-thin copper wire (like for winding magnets) and you wad it up so it looks like a 3D ball. At very short range it looks one dimensional, but as you expand out from a point it starts acting 3D.

    A useful idea of dimensionality here (where something is not a vectorspace or a smooth manifold) is Hausdorff's notion---the relation of radius to volume. Here's a mathworld link

    Let's imagine that the wire is infinitely thin, so it is really one dimensional. (I told you it was an imperfect analogy :smile:) now we define a metric on this wad of wire by considering it a subset of ordinary 3D Euclidean space----it becomes a so-called "metric space" with the "metric topology"

    To an ant crawling along the wire at some point inside the wad, it seems 1D because he isnt big enough to reach across to a nearby section. If he measures the weight of wire inside a neighborhood of a certain radius, then, since the radius is small the weight of wire depends LINEARLY on the radius. the weight of wire inside some region is the metaphorical volume in this analogy

    vol = const x radius

    the neighborhood of some radius R is just a linear segment of length on the order of 2R

    But if you take a larger radius, then the space starts to behave 3D, if you double the radius of a large neighborhood then the weight of wire contained in it will go up approx by a factor of 8.

    vol = const x radius3
    WARNING SEMANTIC HAZARD: a topological metric space is not the same as a differentiable manifold with a (Riemannian or other) metric. This is a dreadful semantic screw-up by mathematicians. Everyone should realize that the word "metric" is used in two totally different senses by mathematicians: in topology and in differential geometry!

    In topology a "metric space" is simply a topological space with a distance function d(x,y) satisfying the triangle inequality. There is no differentiable structure assumed here, no tangent spaces, no (riemannian or other) "metric" in the sense of bilinear form, no (riemannian or other) "signature". When people say BACKGROUND INDEPENDENT meaning "no background metric" they mean no prior metric in the Diff. Geom. sense.
    Last edited: Aug 21, 2005
  24. Aug 21, 2005 #23


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    Well I vote for the continuum. But it really doesn't matter.

    On the other hand, I've always been fascinated by lattices that are able to approximate a continua to arbitrary accuracy. For example, consider a 2-d array of conductive points with the lattice spacing given by "d", with each point connected to its four nearest neighbors by a resistor of resistance R.

    It is clear that this material does not possess rotational symmetry. Instead, it has two axes corresponding to the lattice directions. But if the only probe we have is the ability to measure the overall total resistance between macroscopic regions, then for a lattice spacing small compared to our regions, we will not be able to distinguish this resistor lattice from a plate with square resistance of R.

    This is true for arbitrary large regions, but to see it in a simple way, compute the total resistance from one end to the other for a square region parallel to a lattice direction. You obtain N resistor lines each with N resistors. The total resistance is therefore R. The same calculation is easy to make for a square region angled with respect to the lattice.

    From this sort of example, I believe that it is impossible to distinguish between a continuum and a sufficiently fine lattice. But until we derive an experiment that actually measures the size of the lattice, I would prefer to assume the continuum.

    Historically, this reminds me of the argument for and against the existence of atoms. Uh, the atomicists won that one.

  25. Aug 21, 2005 #24
    What you are suggesting is that the illusion of 4D is obtained by a process of approximation from the actual 2D? It is like calculus where we approximate the area under a curve with rectangular area for a given section.

    So that the actual reality is only 2D, but the effective approximation is 4D. Is this right? If so, I don't think this allows us to say that reality actually IS 4D at larger scales, only that it appears 4D, right? No wait, they start out with a 4D lattice and obtain 2D at small scales. Doesn't make sense to me, sorry.
  26. Aug 21, 2005 #25


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    In the wire-wad example I am not suggesting that.
    I am not talking about the 4D spacetime continuum, or somebody's mathematical model of it.

    what I am responding to is a statement of yours that you found
    something with variable dimensionality INCONSISTENT
    In mathematics, one way to show that some features are NOT inconsistent is to give an example.

    So I provided an example. this is a topological metric space that could have dimensionality 2 at very short scale
    and dimensionality 2.3 or 2.4 at some other scales
    and dimensionality 2.9 or 3 at some larger scale.

    All that example does is show you that it is NOT inconsistent for dimensionality to vary in a topological space with distance function.

    The example does not say anything specific about realworld spacetime because it is not about realworld spacetime. It does not say anything specific about Loll CDT model of spacetime because it is not about that either.

    All the example is intended to illustrate is that

    there simply is no reason for dimensionality not to vary
    Last edited: Aug 21, 2005
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