I got a bit crimped for space towards the end. The philosophy part got clipped. Discrete things tend to be things which count as data points, a spot on a photoplate in a 2-slit experiment, the click of a photomultiplier tube that registers a count, a Raman spectrogram and so forth. These things are ontological, the reduced state of a particle, or the energy level of an atom and so forth. The continuous stuff are all the fields and waves and the like, which we sort of infer by a collection of the discrete stuff --- the data. The continuous stuff is frankly what makes the discrete stuff happen, but largely these are not directly measurable, or ontological. These tend to be more epistemological.

Physics then has this duality between the two. So this relationship is in a way existential, for it involves the question of what is existence and it seems to somehow involve the nature of an observer. In that way there may be some future work for philosophers, though this will have rather indirect impact on actual physics.

Cheers LC

I will have to get back to you on this. I gave your paper a first look. Yes I do remember this sort of idea last summer. I will have to make an assessment of this and write back in the next day or two.

Cheers LC

Lawrence

Good, You are starting to grasp an initially very tricky set of variables. The fact it seems a bit odd shows you've glimpsed the important adjustment.

I agree SR simply tells us 'c' is constant IN all frames. I suggest another way of conceiving that; If you're not ON that bus going past you're not IN the same frame. (after all - all light you receive FROM that or any frame you receive at 'c' in your frame, so nothing breaks the rule!!)!

200 other people walking, running, driving past or flying over the bus on every possible vector will ALSO receive the light at 'c' IN their frame. What is more, that light (scattered from particles inside the bus) will only ever have DONE 'c' anywhere LOCALLY.

i.e. It does 'c' (or c/n) with respect to (wrt) the bus Inside the bus and within the glass (n=1.5) of the windows, then c/n through the air (n=1.0003), then c/n through the FINE STRUCTURE free electron plasma of your eye or glass instrument lense, then c/n through your eye lense (n=1.38).

Yes, you're spot on about plasma, and the density and frequency correlate to speed. (Yes - through the 'condensate,' 'combined' or 'C' field!- See Edwin Klingman's essay for some sums, which I think Ray now agrees with).

If you didn't feel uncomfortable it wouldn't be the NEW door onto reality the discrete field concept represents. NO absolute background frame, but a background no less. It's a new level of dynamic understanding of SR you only really see the value of when you start to apply it. I pointed it at some Galaxies, and 2 weeks later has a paper accepted for Peer Review. It also takes us a giant step towards GR, effectively simply condensing the mass with motion for equivalence.

As with Edwin, we think very differently Lawrence. That is a fantastic advantage the human race has! - if we USE it. I've just done the initial dynamic conception bit, your skills will be needed, (once you fully understand the conceptual basis), to take it on and make the necessary adjustments to both it and the jigsaw puzzle bits of current physics so it ALL fits together seamlessly at last.

You may now be ready for a pint of beer, and a description of how this can be explained to a barmaid... etc..! I hesitate, but I'm now starting to trust you; http://vixra.org/abs/1102.0016 (You may also find links to many earlier papers there).

Have fun as Ray would say.

Peter

In reading your paper I find one curious question. This is I think the same as the question I raised last summer. The equation δt/ħ = 1/kT defines a scale of fluctuation, here with a Euclideanized time. This is a scale of time where the observable uncertainty or disorder of a quantum system is equivalent to thermal fluctuations at some temperature. However, in much of what you do it appears to be used as a variable. It is used as a time in various integrations and as units in a time line. This step actually requires some subtle justification.

Cheers LC

Dear Lawrence,

In "A World Without Quanta" there are no "scales of fluctuation" or "disorders of a quantum system". All the simple logic and mathematical derivations in my essay become clear and convincing if viewed without using the prism of current theory. I am not a physicist! I have no idea what you are talking about. But we can have a good conversation on the results in my essay if you keep to the language and terms I use in it.

The time variable t is a continuous variable, but the equation you point to δt/ħ = 1/kT does not appear anywhere in my essay in that form. The closest to it, I think, is Δt = h/kT. If that is what you are referring to than I can explain that this duration of time is for an 'accumulation of energy' h to occur. This is a result shown in the essay.

You write,

"... in much of what you do it appears to be used as a variable..."

If the 'it' is time t, then yes. It is a continuous variable. The view in all of this is of a 'continuous Universe'. The amazing think is that it is possible to have such a naïve view, and still explain and derive basic results in physics. That's all I can do! Perhaps you and others can do much more. Take it as 'food for thought' and see if it can nourish your physics.

The key result in the essay is "Planck's Law is an exact mathematical tautology that describes the interaction of measurement". The mathematical derivation is simple and elegant. It does not use 'energy quanta' or statistics. Furthermore I argue that it can fully explain why the experimental blackbody spectrum is indistinguishable from theory. Please comment on that!

As a further enticement, I am about to post a paper that proves the following proposition using and extending the same ideas in my essay:

"If the speed of light is constant, then light is a wave"

Please help me get this essay to the 'church'!

Best regards,

Constantinos

What is funny is that you write:

"The time variable t is a continuous variable, but the equation you point to δt/ħ = 1/kT does not appear anywhere in my essay in that form. The closest to it, I think, is Δt = h/kT. If that is what you are referring to than I can explain that this duration of time is for an 'accumulation of energy' h to occur. This is a result shown in the essay.

You write,

"... in much of what you do it appears to be used as a variable..."

If the 'it' is time t, then yes. It is a continuous variable. The view in all of this is of a 'continuous Universe'. The amazing think is that it is possible to have such a naïve view, and still explain and derive basic results in physics. That's all I can do! Perhaps you and others can do much more. Take it as 'food for thought' and see if it can nourish your physics."

This is basically what I said in the first place. The use of a time scale computed from δt/ħ = 1/kT, or equivalently as you say Δt = h/kT, as a continuous variable is a funny procedure. It would be a bit like computing a standard deviation for some variable, and then using that as units of a continuous variable. This is potentially the main weakness in your program, for this is mathematically very questionable.

I have not given out scores yet, except for some cases. Your paper clearly shows a serious amount of work. This above I do see as a problem, so in giving out scores, maybe on Sunday I will give not a top score but maybe enough (if I guestimate right) to put you over the top into the 35. Right now you are at 38.

Cheers LC

Lawrence,

Your support of this effort is greatly appreciated. Please understand that this is not about me.

I will like to continue my conversation about the main objection that you have raised (regarding the scaling of time) perhaps after this contest is over. But as a preliminary thought I am beginning to understand what you are saying regarding the time scale. The problem that I have is that I am not using scales along the t-axis or any other axis. My approach is very simply mathematical, using variables as continuous. More on this perhaps at some other time.

But I do want to elicit some comments concerning two notes I have just posted today on the web.

"What is the Matter with de Broglie Waves?"

and,

"If the speed of light is constant, then light is a wave"

These are very short! I could have combined them into one. But I wanted both titles!

Best wishes,

Constantinos

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  • Post #75

Dear Lawrence,

interesting essay, interesting connections you find between entanglement for black holes and AdS spacetime.

Best regards,

Cristi

    Cristi,

    thanks. The three-fold discrete structure I argued for above turns out to have very rich and deep properties. This turns out to be related to the Calabi-Yau form and the three terms in the Hodge diamond h_{1,1}, h_{2,0) ~ h_{0,2} and h_{3,0} ~ h_{0,3}. The three fold structure is then an aspect of the three-form of G_2 and N = 2 supersymmetry. The G_2 is the centralizer of F_4 in the exceptional E_8. This 3-folding is then an F_4 restriction to the E_6 on the manifold as a form of twistor space. Also the three fold structure defines modular forms, or the Picard modular function with some number theoretic connections with zeta functions.

    So it is turning out there is a much deeper structure to this than what I thought at the time I wrote the essay. I am hoping that this FQXi contest might be a way of promoting this further in the future.

    Cheers LC

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    • Post #78

    Hi ,

    The zeta function, it's interesting that, let's assume a Sum where n=o and infinity with fourier....f(x)=pi²/3+4Sum(-1)exp n/n² cos nx .....where are these connections please with pi exp 4 if we substitute and set correctly.Now let's assume also a good approximation where the thermodynamics are as always proportional and relevant.Debye will agree at my humble knowledge.Now let's see the link with pi ...if the real serie of the zeta function is inserted ...1+1/x+1/y.....= pi exp4/z...

    The properties are thermodynamical ....and thus we understand why it's essential to have REAL AND RATIONAL variables for intergrations, substitutions and settings..........pi exp4 /90.....if we consider -pi smaller or equatl to x and x smaller or equal to pi....where are these connections without complexs and imaginaries, x can have so many settings ....the thermo is rational.Could you please resume the link.

    Regards

    Steve

    The Riemann zeta function is

    ζ(s) = sum_{n=1}^∞ n^{-s},

    which is a rather simple looking formula, but this has some mysterious properties. The function is zero at s = -2, -4, -6, ... , and zeros at s = 1/2 it, where the value of t gives the prime distribution.

    LC

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    • Post #80

    Hello dear Maverick Lawrence

    Thanks I know the zeta function,in fact It's a proof of the distribution of primes inside a sphere .....the line of 0 and pi dear Lawrence . Indeed indeed the properties of the sphere are fascinatings.R+ and Q are better than C .....when we want explain the pure physicality.it's the same with the utilization of the -, the infinity and the 0...that can be harmonized in a pure 3D distribution.

    Dear Lawrence, could you develop please with the euler formulation....e exp z=1+z/1!+z²/2!+z³/3!.....the convergences ......

    Regards

    Steve

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    • Post #81

    Lawrence,

    You know that I read and rated your paper (highest) over a month ago. Having just gotten around to Phil Gibbs's excellent essay, though, and knowing that our results in general almost converge (albeit by different methods), I felt compelled to leave a comment.

    It occured to me, in the context of quantum error connection coupled to quantum least action, that any measurement by any observer at any instant of "the present" (which is the only kind of instant that quantum mechanics accommodates, since all quantum action is instantaneous)is the lowest energy state possible. That makes the estimated 10^500 vacuua of string theory seem pretty small. I had made the same conclusion, without rigorous mathematical support, in my ICCS 2007 paper

    Best,

    Tom

    in my

      The 10^{500} vacua are an estimate from the number of Dp-brane wrapping conditions and T-duality. The question of course we might ask is whether most of these are "real," where by real I mean they define a spacetime cosmology that has some classical content. I suspect most of these are really quantum amplitudes which are small corrections to the grand path integral of the universe.

      The one point of my essay is that with an equivalency between the horizon of a black hole in an AdS spacetime and the field theoretic information on the boundary there is a 3-cycle which is associated with the compactification of fields in the Calabi-Yau manifolds. I have been doing more calculations and work on this and it is getting into some very deep territory. In particular the coset construction leads to Eisenstein series which give an integer counting of quantum bits. This turns out to have strong relationships with the integer partition recently proven by Ono and his group Brunier, Folsom, and Kent. This then accounts for the number of qubits on the horizon of a black hole and the boundary of an AdS spacetime.

      This of course touches on the whole multi-verse construction. This is an interesting thing to play with. It also suggests something is funny with our scientific paradigm. We normally have in science the idea that we can prepare experiments with various initial or boundary conditions. The theory then predicts some constant process which is transformed by those initial or boundary conditions, but not removed by them. With the universe we have in effect one grand scattering experiment. We also did not set it up. As such we have no ability to "prepare" systems to test theories, and further we have an ambiguity over what represents initial or boundary conditions and what represents fundamental principles. The current issue over why the universe started out with such low entropy is potentially of this nature.

      The number of branchings which occur with measurements or state reductions involves the many world interpretation (MWI), which may be related to the multi-verse concept. With eigenbranching of the universe the numbers do become absolutely bewildering. Tegmark has written considerably on this, and in the context of a sort of platonia concept of universes or cosmologies which obey all possible mathematical structures. I don't know exactly what to think about that idea. In general my approach to things is a bit more conservative.

      Cheers LC

      The Taylor expansion of the exponential function is not directly related to the Riemann zeta function. The Riemann zeta function function determines a prime distribution on the complex plane C. If you map C to the Riemann sphere, say by stereographic projection, then you can talk about spheres.

      Chhers LC

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      • Post #84

      Lawrence,

      the new developments of your ideas sound like great news!

      Good luck with them,

      Cristi

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      • Post #85

      Cristi,

      The general trend here is not looking too good. I seem to be sinking. At this rate I will be below the 35 by end of the day tomorrow. I am not sure what you think, but there are about 5 essays ahead of mine which are pure bilge water, and about 5 that are highly questionable. There are a number below mine which are better than some above. So I am somewhat unhappy at the turn of events lately. My essay in the last month has been up as high as 16 and last week as low as 33, then back up to 20 by midweek. I can only hope this current downward trend is arrested.

      I scored yours a while back, where I gave it an 8. The two points off are due to what I see as some incomplete concepts with respect to the "warping." Ch. Corda has some interesting ideas about intrinsic curvature, where I have worked some plausible argument that this is due to the Heisenberg uncertainly principle. It sounds as if buried beneath what you are doing is something of that nature.

      The sort of moduli space constructions of SLOCC state constructions Gibbs writes about, where our papers in some way complement each other, can be extended to E_{7(7}}/SO(8) type of moduli space. The E_8 decomposes into E_7 to E_6 and then E_6. The F_4 group has G_2 as its centralizer. The Calabi Yau construction which can exist is one then based on the invariance of F_4 with an h_{1,1} Hodge diamond with respect to the 3-form of G_2. The G_2 is then a dual of the Calabi-Yau 3-form. My essay touches on this with the G_2 - -> SU(3)xS^6, which gives a triality.

      Cheers LC

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        • Post #87

        Dear Lawrence,

        Hope my rating of your essay helps a lot.

        Constantinos