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Dear Efthimios
I read the response to Lieu's paper you cited above. Again the assumption is that quantum foam is a reality. This idea is speculative and is based on Born's probability interpretation. In my Beautiful Universe paper on which my present fqxi paper is based I have suggested that on the contrary nature may be precisely local, causal and deterministic at the minutest scale - and still produce quantum effects including probability. I also suggested that the Planck scale itself may be a fiction or much too tiny: G is determined by macroscopic experiments. It may well be that at the granular, ether (or whatever you call it) scale, its value is quite different.
Concerning your question "If spacetime is granular, then what is there between the grains?"I would say it may be impossible to determine the physical nature of the granularity or any other hidden large dimensions the granules may reside in. We are talking about the stuff that makes stuff so we cannot project (what is the inverse of 'project'?) or macroscopic notions onto the granules of the universe. It will be sufficient to presume they have certain qualities (i.e. in my theory the lattice nodes have angular momentum, density, polarity, etc}.
You said " disproving the granularity of space is equivalent to preserving the autonomy of the world. In my opinion, it is now too late for that." Can you please explain that interesting statement? thanks.
Dear Ray et al,
Concerning Zeno's paradox of divisibility and motion - in an ordered universal lattice where motion occurs by momentum transfer from node to node (as in my theory) , such questions will have obvious answers and will no longer pose any logical difficulties. There may be a message spelled out with the ether granules: "reductionism stops here!".
Dear Anonymous
The story of Feynman telling the story of the philosopher (who contemplated the reality of food and the light from it) is typical of his cavalier attitude to foundational questions. Feynman seems - perhaps wisely as far as his great work was concerned - to have adopted a pragmatic stance to unanswered quantum puzzles, using ad-hoc solutions and mathematical formulations even if they were not derived from more basic concepts. By the way a simple phrase like "just reflections of light?" was the foundational question of the 10th century answered for all time by the father of the scientific method, Al-Hassan Ibn Al-Haytham (Hazen) by his meticulous experiments with the camera obscura and their logical analysis in his book Kitab Al-Manazir. Before him it was believed (after Aristotle, I think) that we see because the eye projects visual rays onto an object. Hazen's book, translated from Arabic into Latin influenced the Renaissance and modern science. Moral of the story: foundational questions have to be answered eventually and not swept under the carpet, Feynman-style!!
Good luck to us all! Vladimir