Dear Conrad,

I just finished reading your essay. To the extent that you were able to be precise about relatively profound issues in such a short format, I think I agree with most of what you say. Let me itemize a few remarks.

1. Regarding the information/communication-theoretic point of view, I think it's ironic that the very theories (relativity and quantum theory) whose development and application brought to light the importance and universality of such concepts continue to suffer from failing to completely incorporate their implications. For instance, if modern computer science could have pre-dated relativity and quantum theory, I have no doubt these theories would be viewed in different ways.

2. At the end of your introduction, you state that you're not proposing any modification of GR and QM. However, as you know from looking at my essay, I believe that it's becoming increasingly clear that modifications will be necessary, and that the clues for which modifications to make come precisely from information and order-theoretic principles.

3. Regarding the contextual nature of measurement, you know of course about Rovelli's work. The "decoherence" view of measurement is closely related by attributing "collapse" to interaction with the environment, and there are attempts to refine this view further. (See, for instance Pullin and Gambini's essay in this contest. I asked them some questions about this, but haven't heard back.) I don't feel that I understand this subject sufficiently, but I don't disagree with anything you said.

4. In your section 3, you mention Einstein's original "vague" physical views and how his mathematical friends "reconceived them." I think that Minkowski and company may have let Einstein down to some extent, and that Riemann or possibly even Liebniz would have served him better had they been alive, since they possessed broader views and took fewer things for granted. "Lorentzian manifolds" represent a very specific (and hence limited) way of expressing Einstein's physical ideas that shackles them to a convenient mathematical formalism admitting a lot of nonphysical baggage. Just because this formalism happened to be available at the time, while information theory, category theory, etc. were not, does not mean that we should continue to be limited by it today.

5. You mention "two geometries" in relativity, given by spacelike foliations and light cones. More generally, if we drop the manifold assumption, there are two partial orders, one a refinement of the other, and as you point out it is the causal order (defined by the light cones) that is physically meaningful.

6. Regarding your section 4 on quantum theory, this is where things become more complicated in my view. This is because the version of quantum theory one chooses seems to matter if one discards the static background manifold. The questions of what an "observer" is and where it resides become critical. For instance, consider Feynman's sum-over-histories version (the 1948 paper). Feynman discussed summing over particle trajectories in Euclidean spacetime and thereby recovered "standard" quantum theory, with its Hilbert spaces, operator algebras, Schrodinger equation, etc. Feynman was able to take all the trajectories to be in the same spacetime because he was working with a background-dependent model; the ambient Euclidean space is unaffected by the particle moving in it. Now, if GR has taught us anything, it is that "spacetime" and "matter-energy" interact, so different particle trajectories mean different spacetimes. Hence, in a background-independent treatment, Feynman's sum over histories becomes a sum over "universes," with a different classical spacetime corresponding to each particle trajectory. His original version is a limiting case in which the effect of the particle on the spacetime is negligible. You can still make predictions in this context, but everything is tangled up with everything else; the transition amplitudes I discuss in my essay a priori depend on the entire universes involved, and it is hard to think about what an individual observer even is, except as some sort of approximation. There are also self-referential and free will issues involved. You can begin to understand why I said little about the theory of observation in my own essay, especially considering the length limitation!

In any case, your essay rates high in my opinion. I would be grateful for any further thoughts you might have on these issues. Take care,

Ben

    Ben,

    Thank you very much for your thoughtful response. As to your historical comments 1 and 4, I certainly agree.

    Regarding your point 2 above -- I have no doubt you're right that our current theories need to be modified. But that's beyond my level of competence; the best I can do is to recognize when some brave explorer like yourself has sound instincts about fundamental principles. But, since I do in fact propose looking at SR and QM from a fairly unusual viewpoint, I wanted to emphasize that I'm arguing only from elementary and well-established aspects of current theory, not presuming to offer a new theory of my own.

    Regarding 3 -- I don't think any of us are close to understanding "contextuality" sufficiently. Decoherence is surely relevant. As to the Gambini/Pullin essay, I agree with them that we shouldn't be assuming perfectly exact spacetime measurement, and I'm interested in their work on this. However I don't think there's anything to be gained by claiming decoherence solves the measurement problem, as their essay suggests. Most physicists already happily ignore the measurement issue without requiring any such solution in principle. I much prefer Rovelli's approach, which didn't pretend to "solve" the measurement problem but instead tried to make it the basis for a new way of thinking.

    The main point I wanted to make about measurement-contexts is (I think) new, although obvious -- namely that measuring any parameter necessarily involves measuring other parameters. To me this means we shouldn't be looking to understand measurement as a single process (e.g. decoherence, or through a theory of objective "collapse"). I think that a universe that can support any kind of observing or communicating of information must have significant structural diversity in its foundations... though we might be able to come up with an evolutionary scenario to show how this sort of functional diversity could emerge from random interaction (see below).

    5 -- I apologize for my ignorance on the subject of order theory, but could you please explain to me which partial order is a "refinement" of the other? Is it correct that refinement means adding another set of connections to an existing partial order?

    6 -- Your comment makes sense to me, and I too think of Feynman's approach as the one that takes us deepest. As to understanding what an "observer" is, at a fundamental level -- this is indeed difficult. We tend to think of observing and communicating as if they were simple data-transmission processes, ignoring the complicated contexts needed to make data meaningful and empirically definable. If it's true that many different kinds of interaction-contexts are needed to make measurement possible, then we need to ask if there could be simpler "precursors" to what we know as measurement / observation.

    For example, suppose we start with completely random interaction, imagined as an infinite randomly connected graph. As a first step toward an observable universe, we could prune off all the vertices that only connect to a single edge, since an isolated interaction can't convey definable information or contribute to a context for defining other information. Whether or not such interactions "exist" in some absolute sense, they remain "virtual" in relation to the remaining graph -- i.e. the vertices that connect other vertices, in a superposition of paths. So far there's nothing like an "individual observer" in the picture.

    The next stage might be to distinguish cylic ("self-observing"?) paths from acylic paths. (We might identify the former with all the Feynman-histories that cancel each other out, and so again remain "virtual" relative to the graph of acyclic paths.) Then the question is how to assign directions to the acyclic paths, according to internally-definable rules, that would presumably give us the causal-set structure.

    I don't have any clear notion about this, but I have vaguely in mind the way the law of charge-conservation gives us continuous connected paths, and the way charged particles "observe" each other in electromagnetic interaction. There's an intriguing inter-referential structure here relating the spatial direction of the charges' accelerations to the orthogonal E and M components of the field and to the direction of time.

    At any rate, the point is that "observing" -- what Rovelli calls "systems having information about other systems" -- may be a combination of many distinct functionalities, some very primitive, defining interaction-structures that provide a basis for the emergence of other more complicated ones. If this conjecture makes any sense, I would imagine the spacetime metric as emerging at quite a high level -- since as I pointed out in my essay, the possibility of measuring intervals in space and time appears to depend on atomic structure, hence on a lot of very finely-tuned physics.

    So maybe your "binary relation that generates the causal order" belongs to a quite primitive level of interaction, while your "overall scale factor" that provides "the measure-theoretic information" for the metric may only become definable much later on?

    In any case, I very much appreciate your reading the essay and responding so kindly.

    Conrad

    Peter -- thanks very much! I'll take a look at your essay soon. As to your initial comment, though I agree that physics badly needs a non-mathematical grounding, I'm afraid the failure lies much more with the philosophers than the physicists, over the past century.

    Best wishes -- Conrad

    Saibal -- thanks for reading and responding to the essay. I agree that identifying observers with classical states is inadequate... but the question of defining observers is complex, and I'm not sure whether an algorithmic approach is appropriate (as you suggested in your essay) -- see my note below in the thread Ben Dribus started.

    Thanks again -- Conrad

    Conrad,

    I appreciate the further explanation. Let me itemize a few more remarks.

    1. I am not satisfied with decoherence or the "Montevideo interpretation" either, but I think decoherence is better than the Copenhagen interpretation. Your initial quote from Rovelli is relevant here, though; at least part of the "problem" is surely our effort to fit the facts into a "sensible explanation" rather than taking them at face value.

    2. You're correct about the refinement of a causal relation; a good general picture of this is adding new edges to a directed graph.

    3. I agree that the metric may emerge at a staggeringly high level; I mentioned near the end of my essay that an single "elementary particle interaction" might easily involve Avogadro's number of fundamental relations. This does not bother me too much, since I believe we are very very far from the "bottom" in physics, if there is one.

    Take care,

    Ben

    6 days later

    Dear Conrad Dale Johnson,

    I have not spent as much time as I would like with your essay but I have found a lot to like about it. It very clearly written and set out. There is a lot in it that I agree with. Reality and the role of the observer are things that I have also given a lot of thought. I am not sure you have said which physical assumption is wrong but you have set out some really important ideas to consider. I would like to return to it to read it more thoroughly,

    In my explanatory framework, of reality in the context of physics, there is the source of potential sensory data, the potential sensory data in environment itself and the output of processing of that data.The potential data is that pool from which an observer can select giving his unique singular output reality. The de-coherence or wave function collapse can then be viewed as the transition from considering that which exists (or might exist in the case of a single particle) as many possibilities and is still unobserved to considering the output of processing of selected data received from the environment.

    I have not written in detail about that framework in my essay as I was following the guidelines given by the organisers. However there is a diagram of it that was used to answer the essay question, and also a high resolution version in my essay thread. I think it may be something you will find interesting as I can see there is some convergence of our ideas. I would be very grateful indeed for any feedback on it or my essay.

    Good luck in the contest, Georgina : )

      Hi Georgina -- I'll take another look at your essay. I do think there's some overlap between our approaches.

      To clarify: the assumption I think is wrong is that whatever's not objectively real (describable from no point of view in particular) is therefore "subjective", mental rather than physical. But this assumption is rarely stated as such. Rather, it's built into the Cartesian/Kantian framework that still guides most of our thinking.

      In physics, this translates into the assumption that physical theory can describe the world at a fundamental level without taking the viewpoint of "the observer" into account. Of course the observer does appear both in Relativity and QM, in different ways. But because of this tacit assumption, the observer's role remains problematic, a foreign element to be eliminated from our theory, if possible. We haven't yet worked out a framework that explains how the objective view and the observer's view relate to each other, and why a fundamental theory needs to describe the world in both ways.

      My basic point is that the world is structured not only as a body of objective fact, but also as an interactive nexus that communicates those facts. That nexus is physical, not mental, and of course it's what connects objective reality with the subjective perception of an observer.

      Thanks -- Conrad

      This is just to send my good wishes Conrad, you were one of the four people, along with Edwin, Ben and Daryl, who made the discussions really worthwhile and enjoyable for me. And I think your essay is very good. I hope we'll be in touch in the future,

      Best wishes, Jonathan

      Dear Conrad Dale Johnson,

      As discrete times that emerges from eigen-rotational quanta in Coherently-cyclic cluster-matter paradigm of universe differs, expression of unreality of time also differs in this paradigm, in that temporal ordering of events with A-series and B-series is not appropriate as block time is the discrete time in holarchy. Thus the hypersurface of the present, expressional with Minkowski space-time is not applicable in this paradigm.

      With best wishes

      Jayakar