Mathematics: Science of the Possible, or the Probable? by Thomas Howard Ray

John Cox has an elegant way of bringing the issues in line with everyday experience.

Having devoted part of my misspent youth to the pool table, John's reference to the relation between shooting pool and moment-to-moment instinct got me thinking about Hess-Philipp's timelike correlated parameters (TLCPs) .

Because initial condition changes with time, moment-to-moment action (event by event in QM simulation terms) avoids action at a distance " ... by letting the probability measure be a superposition of setting-dependent subspace product measures with two important properties: (i) the factors of the product measure depend only on parameters of the station that they describe, and (ii) the joint density of the pairs of setting-dependent parameters in the two stations is uniform."

The multiple time scales of a pool game range from the interval of contact of hand with cue, cue with cue ball, cue ball with object ball, ball with rail, etc. These are well understood causal events whose outcomes are all dependent on initial condition and energy content in the specified interval.

Gill, et al, criticism of Hess-Philipp completely avoids the causal framework -- they claim, " ... "(Hess-Philipp) forgot one of three subscripts somewhere deep in the computations and failed to normalise a measure to be a probability measure" -- which is completely irrelevant to the point made by H-P above (and well supported by the mathematics of the paper). Normalization of probability density in a time dependent causal relation is independent of energy density and initial condition. Hess-Philipp show that initial energy condition determines joint probability -- while Gill et al avow that (" ... because of Bell's theorem" as Gill claims) probability is prior to measurement. The measurement protocol of Bell-Aspect merely demonstrates its own prior conclusion.

While Gill et al are completely off the mark in convincing themselves that they have refuted Hess-Philipp -- the science of complex systems, in line with Bar-Yam's theory of multi-scale variety, supports timelike correlated parameters at multiple scales: http://home.comcast.net/~thomasray1209/ICCS2007PP.ppt

Tom

More should be said about why the Karl Hess and Walter Philipp PNAS paper of 2001 is a breakthrough in our understanding of time dependent systems, because it accents the physical identities among time, information and energy that characterizes complex systems -- and as the authors make explicit, the problem of decidability between Einstein and Bohr.

Criticisms of Hess-Philipp have failed to even address the key issues of Einstein separability and special relativity that drive the paper's conclusions. The critics know that these issues cannot be confronted head-on, because they are well-understood physical principles that cannot be refuted.

Let's return to a point I made in my essay (p.6), that Einstein's original quest for E = mc^2 substituted the Lagrangian (a system's energy content) for the E term, where E was then generalized to rest energy, so we get that famous equation. The continuous values of the Lagrangian, however -- vary with mass -- local measured. In reply to critics, Philipp-Hess simplified their explanation of the model (attached), such that " ... Imagine the time axis wrapped around a circle of circumference that corresponds to a time interval related to a simple measurement and normalized to 1. We suppose that for a fixed N each interval [(m в€' 1)/N, m/N ], m = 1, 2, . . . , N of arc length 1/N on the circle gets about its proper share of time measurement points over the measurement period." The authors go on to show time correlations that the critics ignore, and reproduce quantum correlations in a complete framework of distributed time-dependent energy/information. These results satisfy Einstein separability and special relativity in a way that the critics do not and cannot:

Because a continuous range of time-dependent energy values attends every classical measure, normalization of the time interval locally does not imply a global normalization (as Gill claims) -- because of the special relativity limit. Each measure carries its own time stamp, and it is always local.

TomAttachment #1: Walter2002.pdf

Peter,

Thank you, that's very kind. There's no mystery to why my score languishes below the cut -- never in my memory, from the first time I entered these competitions (which dates from the very beginning), has a fully relativistic viewpoint in foundational physics gotten due respect, while some of the fringiest views in quantum theory have won big prizes. So I have long abandoned any illusions I might have had. It is enough that the FQXi forum gives voice to a minority viewpoint that it de facto opposes, and I am grateful to the Institute for that, even when I think it could do more.

There is an even lower score than mine, given for a far better essay by Vesselin Petkov, and -- I expect -- is low for the same reasons. I am going to do a lazy thing, and quote Vesselin's reply to a recent forum participant, because it matches my opinion: " ... if Minkowski had lived to see the advent of general relativity, he would have realized, as a mathematician, that the mathematical formalism of general relativity implies that gravitational phenomena are merely manifestation of the non-Euclidean geometry of spacetime (not an interaction). Einstein made a gigantic step by linking gravity with spacetime geometry, but even he was unable to overcome the seemingly self-evident 'fact' that gravitational phenomena are caused by gravitational interaction (which, unfortunately, is still the accepted view in physics)."

Things are changing. I got an Email from The Minkowski Institute Press just a few days ago that they are publishing Cristi Stoica's PhD thesis (congratulations, Cristi!) , which is relativity-based, with a perturbative path to quantum gravity (my own solution is non-perturbative, but we are pretty close).

In regard to your own defense of conventional quantum theory in the Bertlmann's Socks analogy, I applaud your expansion of the pedagogy, and give high marks for that. It is deservedly among the best of Bell's output.

If you don't mind, I am going to do another lazy thing, and reproduce this reply in your forum.

All best,

Tom

Cristi,

I'm honored. Thanks.

Tom

Thanks, Akinbo. Looking forward to it. :-) You got my upvote, too.

Best wishes,

Tom

Dear Alma,

A writer's greatest reward is to be understood. Thank you! I sometimes feel I should apologize for being subtle, and yet I find that one can't apply natural language with the desired precision, without putting a fine point on it. Someday, I expect, we will communicate in a universal language -- if not mathematics as we know it, then something like mathematics -- that smooths the edges of ambiguity and allows a polished thought to reflect its intended glow. (Computer science maverick Lev Goldfarb is making strides in this direction.)

It's remarkable that you caught the irony of Lamport's "Buridan's Principle." There's a story behind that -- several years ago, I was perusing Leslie's publication page and ran across what I considered an important unpublished paper (though it was written over 30 years ago) and I suggested he try Foundations of Physics, where it was reviewed and published in 2012. To Lamport, the paper is not ambitious -- it is simply an acknowledgment of a hard problem (decidability) in computer programming, along with strategies to deal with it. To me, the principle implies deeper fundamental issues. I made the mistake, in referencing Lamport, of calling him a mathematician (he is most certainly educated and highly competent in the art) -- in which he corrected me, "I am not a mathematician; I am a computer scientist." I subsequently corrected the mistake, though it stuck with me, the difference between mitigating a problem in computer science and trying to solve it mathematically. Perhaps all programming is mitigation -- there are hardly any computer scientists who think P = NP. Do you?

That "the donkey still dies" led me to ponder the perfect first question. For if we could actually do the Schrodinger cat experiment with a dead cat as the initial condition, there would be no decidability problem. Dead cat in, dead cat out, with probability 1 in a bounded interval of time. The same principle that keeps a computer-simulated "cat" alive, assures us that dead cats don't spontaneously come to life.

Yet, conventional quantum theory would have us believe the contrary -- all life is a superposition of alive and dead. So you are right on point that I take the view that " ... the path analyticity that you require as a condition ..." is the sum of all Feynman path integrals in every bounded interval, i.e., -- to use the words of Karl Hess and Walter Philipp, every "timelike correlated parameter" (TLCP). This view supports Einstein's finding from special relativity that all physics is local.

Tegmark actually provided his own criterion for falsifiability. If all measured events are random choices between "alive and dead" the MUH is refuted. Probability without randomness, however, falls to cosmology -- the initial condition of the universe. That's why the multiverse hypothesis (an extension of Everett's many worlds interpretation of quantum theory) is inevitable in Max's program. Every free will choice, of what to measure, being a product of local events, implies global continuity; i.e., analytical continuation that I equate to the sum of Feynman path integrals. The multiverse is totally ordered, to satisfy our partially ordered measures of the universe.

Thanks again and all best,

Tom

P.S. -- thanks for the skinny on Ionesco. I didn't know that! LOL!

Some of my further work in the origin of probability

Tom