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Anton, thanks for reading and commenting.

Actually though, I do see physics without atomism as a physical world without atoms (which are quite distinguishable from field quanta, which we can certainly allow). Not only that, I also see physics without atomism as a physical world without a physical space which exists without matter in it - that is, without space as either a "theater of operations" or as an actor in its own right (although we may certainly allow spaces in the mathematical rather than physical sense). It really is only an argument for a background independent field theory, which is not really very outrageous - GR is already such a thing.

I think (at least I hope) that my essay explains clearly how physics, especially quantum theory and the process of unification, would benefit if we were to eliminate both localized particles and background physical space.

To relate a little to the theme of your essay, I would say that I do not think is sensible to say that empty space has a geometry. Empty space is the absence of anything, and therefore of any characteristics. We cannot travel 1 light-year through empty space, spend a fortnight in empty space, nor scoop up 2 cubic meters of empty space, nor for that matter even identify a point in empty space. I can certainly agree with the theme of your essay that new physics might require both new physical laws and new geometries, however I would simply argue that those laws and geometries should describe a continuum - a field - rather than a localized particles and space which somehow exists and has properties, even a geometry, without anything in it.

Best of luck and thanks again for commenting.

Mark

Dear Mark

I quite agree with you that it is necessary to have an alternative to atomism. You think about a monistic field. Another idea is the Theory of Infinite Hierarchical Nesting of Matter as the matter of my Essay.

Sergey Fedosin Essay

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That was an extremely great essay.

16 days later

Hello Mark Feeley,

Thank you for your essay. You have raised a question others instinctively avoid. I agree with you! I too think the 'particle view' that currently dominates physical theory and intuition is at the heart of many of the paradoxes of physics. This is the 'mind set' that has interjected 'photons' and 'discrete quanta' into modern physics; going back to Planck and Einstein more than 100 years ago.

In the Endnotes of my essay, "The Metaphysics of Physics", I present a simple derivation of Planck's Law of blackbody radiation using only continuous processes and not statistics. This derivation shows that Planck's Law is actually a mathematical tautology describing the interaction of energy. And not some physical law based on the existence of 'energy quanta'. Furthermore, at the same endnotes I give a mathematical proof of the proposition: "if the speed of light is constant, then light propagates as a wave". Thus showing the Photon Hypothesis of 'particles of light' is wrong!

I think you will enjoy reading my essay. I look forward to any comments you may have on it.

Best wishes,

Constantinos

7 days later
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Hi Mark,

"... given the essay topic, all of the essays are highly speculative and focus on possibilities of an idea rather than its problems, ..."

I speculate that there are possibly foundational mistakes to be found. This would of course include the option that you are right. When I decided to favor 1296, this was just a guess of mine.

Regards,

Eckard

7 days later

After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

Dear Mark,

I enjoyed your essay! You have sound ideas, an excellent historical perspective, and a pleasing command of the English language. A few thoughts come to mind.

1. The statement by Parmenides that you quote on page 2 might possibly be the earliest formulation of the principle of "background independence," which you cite on page 3. Thanks for pointing this out; I had no idea this concept went so far back! Background independence is crucial to understanding unification and quantum gravity (at least, in my opinion!)

2. Coming from the math side, I can't resist pointing out that atomism and the continuum are only two of an uncountable number of different types of possible structures for modeling the physical world. Personally, I am bothered by some aspects of the continuum. What is a "continuum," after all? Well, it is a "linearly-ordered interpolative-complete set satisfying the least upper bound property." Sounds horrible, right? Personally, I think that two of these properties (interpolative completeness and the least upper bound property) have nothing to do with physics. Whenever I hear a physicist say "continuum or discrete?" I want to respond, "how about neither?"

3. If you want to know what I would put in place of atomism or the continuum, I say, "cause and effect!" If you are interested, my essay attempts to describe how the universe might be built out of cause-and-effect relations. In light of your introduction, I am a bit trepidatious that you might consider some my ideas "absurd," but I draw comfort from the fact that neither of us included a single equation in the body of our texts, as you note for your essay on page 9. So much the better! The ideas come first, and the mathematics comes afterwards. My view is that the physical principles should be simple and clear, and that the mathematics should be whatever it has to be to get the job done.

4. You point out that Making do without proper particles is not at all easy (page 8). Very true... I am still trying to figure out how to describe "particles" with causal structures.

5. You say that "A non-atomist causal perspective would instead be that there are two boundary conditions imposed on the field by emission and absorption events, which create a quantization of the field between them." This, and the ensuing discussion, is interesting and requires more thought. The music analogy is a good one.

Thanks for the great read! Take care,

Ben Dribus

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    Ben,

    Thanks a lot for the comments and good luck as you go forward.

    With regards to your 2nd and 5th comments especially:

    I think that the cause-effect picture and a continuum field picture are extremely closely connected. Before I wrote the essay I actually considered focusing the essay on the relationship between "events" and a continuum, but decided that some rationale for the continuum picture needed to be presented first.

    I actually think that instead of neither continuum nor discrete, the answer is really more like both. This is essentially the idea that you refer to on in your 5th comment. If we consider both cause and effect to be "events", then causes and effects are necessarily countable or discrete entities. Conceptually however, an event picture requires two types of entities: events and connections between events. The follow-up question then is what is the nature of connections, and I have suggested that the connection between is a physical field, which we can indeed define in a background independent way. The relationship is even deeper though, and as I describe, suitably defined events can act as boundary conditions on the field and thus induce quantization effects in the field (in a quite classical way). Thus the cause-effect picture (what I would call the event picture) and a field picture are intimately and almost recursively connected. Both seem valid and necessary. I think it is a little easier to think of the field as more physical or "real" and the events as more abstract, but I admit this might really be nothing more than a naming convention or some sort of vague "realist" bias on my part.

    Cheers and good luck, Mark