Dear Ian,

your essay has the merit, I think, to discuss with more clarity than other participants the distinction between the ontological and epistemological spheres.

There is a (minor) point on which I tend to disagree, or at least I need clarification. You write:

"This idea simply formalizes the somewhat intuitive notion that causality is somehow related to continuity. To get a better conceptual understanding of this, suppose two events, A and B, are causally connected. Then there must be some way to get information from one to the other without exceeding the speed of light (or, more formally, they must be either timelike or lightlike separated). If spacetime is discontinuous, how do we know that this information couldn't 'jump around' from point to point? Continuity guarantees that the information follows a nice, orderly 'path' between A and B. This should make it easy to see the conceptual attraction of a continuous reality."

I really do not see the coupling between causality and continuity as something that matches common intuition. In particular I am not sure I understand what you mean by writing that one might be worried by the possible uncontrolled jumps of information (possibly messing up causality, you probably imply) under a discontinuous spacetime assumption.

I am indeed tempted to say that a discrete spacetime assumption, as embodied in a partial order/directed-graph model (a causal set) would create less problems to intuition, as far as causality flow is concerned, due to the explicitly represented paths that information may follow in the discrete structure: you explicitly indicate which event influences which other event. (And Lorentz distance, in the continuum, in nicely approximated by graph-theoretic longest-path distance, in the discrete setting.)

Tommaso

    Dear Ian,

    Effectively, there is three different (dx/dt): the mathematical (dx/dt)_math where x and t are just mathematical objects; the theoretical (dx/dt)_th where x is the physical quantity "position" and t the physical quantity "time" (each with its respective unit); and (dx/dt)_exp related to an experimental realization given according to a concrete operational recipe and system.

    However, for the case (dx/dt = c) discussed here, there is not difference between the theoretical and the experimental because the experimental value of c is exact in the SI and as said in a previous post: "Relations as (Dx/Dt = c = dx/dt) given by me in this forum are independent of the «given existing technology»".

    • [deleted]

    • Post #84

    Hi Ian,

    Another nicely constructed and argued essay -- and of course I'm glad you arrived at the conclusion that the next question to ask is whether it's possible to have a "quantum" theory that's not discrete. I'm looking forward to hearing more of your thoughts on that topic.

    Only a couple of nitpicks:

    - I didn't follow your leap from "imprecision" to "discontinuity". Yes, measurements are imprecise. Does that mean the knowledge we gain from them is "discrete"? Well, maybe, but that's not how I tend to think of the word. But then in your conclusion you used the word "discontinuous", which I think is a much stronger claim (and more akin to how I view "discrete" in the first place). Was that word a slip, or is that what you really mean?

    - In my view of the world, "Classical, Newtonian physics" did indeed have competition after 1788 via Lagrange. A point I like to make, because I still don't think that people have properly wrapped their heads around how different variational principles are from what Lee Smolin calls the "Newtonian Schema".

    Best,

    Ken

      Tom,

      Yeah, I agree with you. In fact that's a bone of contention I have with field theories. That's also why I'm not a huge fan of Kuhn's "paradigm shift" interpretation of the history of science.

      Ian

      Peter,

      I will promise to look over your essay. I have a stack I have to read so it may be awhile before I get to it, but I promise to do so before too long.

      Ian

      Georgina,

      Thank you so much for the kind words! I am glad I made it accessible. It gives me faith that I'm in the right line of business (teaching at a small college, I mean).

      There is definitely some overlap with last year's question. In fact it has made me consider putting together a longer treatise on the subject that includes both last year's and this year's essays, perhaps as the core of a class I might offer.

      Ian

      Thanks Tommaso!

      I understand where you are coming from in regard to the directed graph approach (in fact, I would go one step further and use category theory). But what I was saying was that, at least to some people (this is obviously not all), a causal spacetime would necessarily seem like it had to be continuous. In fact, Hawking and Sachs wrote an interesting article on this back in the '70s and suggested that, at least in macrophysics, causal continuity should be a fundamental postulate.

      My argument, which was brief due to length restrictions, essentially is as follows. Imagine a simple 2-D spacetime with coordinates x and t. If spacetime is continuous, then we can think of it as an infinite "world-sheet," so-to-speak, and we can overlay our x and t axes anywhere on it. Now, in a discontinuous spacetime, we can think of it rather as a collection of disconnected points. It makes no sense to globally overlay x and t axes here because x and t are not defined in between the points. So the x and t can only be defined locally *on* the points. But then, it might be perfectly possible for information to hop from point to point even if it is "sideways." It would seem to violate a macro-causality, though wouldn't really on a micro scale since spacetime would only be locally defined. At some point I should work up some diagrams to help better explain what I am trying to say here.

      Hey Ken,

      Thanks! I've read yours, by the way. I just haven't had a chance to post my comments yet (or did I?). Regarding "discontinuous" v. "discrete" I do, admittedly, use them interchangeably in that essay, though they are not necessarily the same. In the sense that I'm using it, I'm saying truly continuous measurements are not technologically (perhaps physically) possible due to the imprecision of measurements. I'm not sure how to better explain it, but basically continuous measurements require instantaneous measurements (or at least the ability to make them) and the latter are physically impossible.

      I'm not sure I see how Lagrange's variational principles differ from Newtonian mechanics. In fact, Newton was the first to develop variational principles (famously, though perhaps apocryphally, in a debate with the Bernoulli brothers).

      Ian

      • [deleted]

      • Post #90

      Ian,

      Just so! Despite Kuhn's wider popularity, I was always more drawn to Popper's rejection of all forms of historicism (Kuhn, Hegel/Marx, etc.) in favor of the progressive model of critical rationalism (although I admit my personal philosophy is more rational idealist).

      Anyway, when you spoke of "hopping sideways" among points, it struck a chord, because a week or so ago I happened to be thumbing through an old copy on my bookshelf of Roscza Petr's book on infinity. One of the illustrations had to do with mapping a discrete point to every locus of another independent set of points -- possible only if the point is of sufficient distance from the other set. Because we assume that there are no such isolated points in our universe, your "hopping" model would be the only physical way to connect all the dots (so to speak). For this reason, I think if quantum field theory is to succeed, it will have to be topological (Witten) where distance has a different meaning. More insight in my essay, if you get a chance.

      Tom

      • [deleted]

      • Post #91

      complementarity

      Dear Ian,

      thanks for spelling my name correctly, and not with swapped doubles, as many people in your continent do.

      I am afraid I still don't see your point. Perhaps the source of confusion is in the idea of trying to bring around the x-axis and t-axis on a discrete structure exactly as one would do on a continuous manifold. (I do understand that you are not the one who wants to do this!) This is inappropriate. On a causal set (our discrete structure) one cannot rely on cartesian axes for obtaining the space and time values of an event. So, it is true, as you wrote, that x and t are not defined in between the points, BUT they are not even defined *on* the points: if one insists for having definite (x, t) coordinates for an event, he should embed the whole causal set in a manifold, and read out the coordinates from the latter. These would be coordinates relative to a specific reference frame. But one of the nice features of causal sets is that they describe the pure causal structure of events while abstracting from any specific embedding/frame, in the same way as Lorentz distance is invariant for all inertial observers.

      So I still do not see why it should be easier to be trapped in the erroneous belief that information might hop from point to point, and event 'sideways', w.r.t. a discrete structure, than to be trapped in the analogous error w.r.t. a continuous structure, picturing information jumping outside the light cone.

      But, as I said, this was really a minor point. Thanks for the pointer to Hawking and Sachs. I have one for you, if you are interested: a one-page discussion of causal sets by R. Sorkin. My essay is in line with those basic ideas, but departs from them in the causet growth dynamics, which in my approach is algorithmic and fully deterministic.

      Tommaso

      Dear T H Ray,

      The own page that you link says at the very start "This article needs attention from an expert on the subject".

      The literature about Bohr's complementarity principle that I know is rather ambiguous and often completely incorrect.

      It must be emphasized that the standard formulation of QM is based in a set of postulates, none of which is a "complementarity principle".

      • [deleted]

      • Post #96

      It's hardly worth a debate. Complementarity is now part of the history of quantum theory and was never (unlike uncertainty and nonlocality) an essential feature.

      Tom

      Dear Readers,

      There are three kinds of the essays in our contest: 1) the essays with original physics research where all physics' information was created by their authors. Often such essays seem to have errors because they often contradict orthodox theory. 2) There are essays-stories about physics which contain generally known physics' information copied from the textbooks or papers and author's commentaries (for example Jarmo Makela, Singh, Durham, Funakoshi and so on). Such essays have ARTISTIC VALUE only but not scientific value; usually these essays-stories do not have any errors by definition because all physics' information was copied from the textbooks and other published papers. 3) There are essays of mixed type containing mixed information. It is clear that the authors of the essays-stories have advantages because their essays never contain errors since all Physics' information was copied from the textbooks.

      What kind of the essay must FQXi community support? If we support the essays-stories, we'll transform FQXi into the entertainment community. For example, instead of my ''interpretation of quantum mechanics'' I could send the jokes about Bohr, Einstein or stories like Gamov's ''Mr. Tompkins in paperback''. It would be very interesting and fun. Another option is to create artistic essays-discussions with Einstein, Bohr, or Aristotle following the example of Jarmo Makela. In this context, the next logical step is to organize a banquet for the authors of essays where we tell jokes and funny stories about physics. What is our purpose?

      Since the goals of the FQXi (the "Contest") are to: Encourage and support rigorous, innovative, and influential thinking about foundational questions in physics and cosmology; Identify and reward top thinkers in foundational questions, therefore I ask readers to vote for essays with original research rather than for essays-stories. In this way we'll encourage the fundamental physics research but not entertainment essays.

      Sincerely,

      Constantin

        Dear T H Ray,

        Effectively, there is not such *principle* in quantum mechanics, but found only in early debates (e.g. Bohr vs Einstein) during the development of quantum mechanics, when many stuff was novel and not still understood.

        However, Lawrence B Crowell wrote on Feb. 27, 2011 @ 00:26 GMT,

        "The relationship between the continuous and discrete aspects of the world seems to be an example of a complementary principle."

        He does not seem to be considering the historical roots of quantum mechanics, but some essential feature of the world, which I see nowhere. Therein my (still unanswered) question to him: what principle?

        Dear Constantin Zaharia Leshan,

        I sympathize with your views.

        I only want to remark two things. The first, that it is not true that the "essays-stories" do not have any errors because were copied from textbooks and papers. I have given some examples of the contrary both in the forums and in my own Essay.

        The second, that I do not consider Singh' Essay to be only of artistic value (see my 'review' of it as well!).

          Dude, did you even read my essay?? I didn't copy anything from a textbook. As far as I am aware, my argument about the radar gun is unique. Whether or not it is correct is another matter that can be debated in a professional manner. But I fail to see how it does not count as original research.

          As for your contention about FQXi essays, you have clearly missed the point of many of them. In addition you seem to think that FQXi's sole purpose is to challenge the "ruling paradigm." That is not true. FQXi's intent is to ask meaningful questions about the universe and stimulate discussion about those questions. I think it does an admirable job in that regard.