Dear Thomas,
I just read Jim Cowan's short story "The Spade of Reason" at your suggestion. Indeed, it is great: philosophical science-fiction just the way I like it! I especially like it when the main character says that "one kind of madness is not knowing that the model is all we will ever know."
Marc
Dear Thomas,
Thank you for your comments about my essay. I have left a reply on my page.
Yours is an intriguing and very ambitious essay!!! You tackle deep fundamental issues such as probability and free will, and I have to confess that I'm having some difficulty in following all the details, since I am not familiar enough with many theoretical results that you build upon.
I have questions about the "quadratic" relationship that you postulate between math M and physics P: M = P q^2, which becomes M = 4P because q = 2.
1. Why does the constant have to be the square of something? I see the parallel with E = m c^2, but I don't see why it has to hold.
2. Is your equation M = 4P dimensionless? In E = m c^2, E is in joules, m is in kilograms and c^2 is in joules per kilogram (or in meters squared by seconds squared). What are the "units" (if any) of physics P and math M?
So far, your essay is looking good in the ratings... Good luck!
Marc
Tom,
An excellent essay. Although I am not certain I fully understand your solution, but the issue of whether or not reality is objective or observer dependent is critical to understanding how math integrates with science. Might it be the case that the reality is objective but measurement is observer dependent and is that consistent with your thinking?
thanks
Rob
Marc, that's my favorite line, too. :-) Thanks.
Tom
Rob, that's exactly right. The question -- "What determines the objective result of a measurement, hidden variables or hidden assumptions"? -- refers to metaphysical realism (measurement outcome) vs anti-realist assumptions.
The assumption of non-locality is obviated by the time parameter (Hess-Philipp) in that every point of a 4 dimension Minkowski space is an operator.
Because the time parameter is not real, independent of spacetime (special relativity), pairwise measurement outcomes are simultaneous with past-future local spacetime states that obviously include the observer as an element. The assumption of nonlocality is therefore superfluous, with the implication that the assumption of a nonlocal measurement value is superfluous. The observer -- whether human or point particle -- is one more degree of freedom than allowed by 3 dimension measure.
In a continuous function classical measure, the macroscopic description of position in time as well as space is bounded only by the cosmological state. A microscopic state is therefore dependent on the cosmological state, and not discontinuous with the operator that exists at every point of local 4 dimension spacetime.
All best,
Tom
Thanks, Marc. Indeed, I fretted all the time I was writing it, over whether this work might be *too* ambitious. Details can run away from one, if the scope gets too big. In the end, I could not escape the conclusion that if free will exists, it cannot be a property of random observer choice. This being so:
Only a binary decision that is square integrable can share a reciprocal relation *continuously* with a continuous range of variables in a finite interval of time (Buridan's principle is limiting). The linear relation M = 4P is not physically meaningful in the first degree, because it is not dynamic; M - 4P = 0. The second degree equivalent, M = Pq^2, q = 2, accounts for the full range of possible binary decisions in any finite interval where M = P. Tracing the relation back to the cosmological initial condition, the rest state of the universe is a "fourity" of possibilities in any locally bounded interval.
The units of M and P are dimensionless to the extent that M = P is unitary. In the reciprocal relationship M = Pq^2, the fundamental dimensionality M = 4P (P = M/4) gives us the division algebras we know to exist (R, C, O, H) as a complete algebraically closed range of computational fields relating binary choice to a continuous range of variables limited by a finite time interval.
Physical units are derived from empirical observations in a bounded measure space. Since four pure physical states imply the Hawking-Penrose singularity theorem, and insofar as four are the minimum necessary and sufficient for dynamic interaction between physics and mathematics (i.e., between measure and model), maybe we can move a little closer to Hawking's question of what "puts the fire in the equations" with number-theoretic arguments alone. Just thinking out loud here.
All best to you and your essay, too!
Tom
Thanks, Michel! I look forward to productive dialogue and wish all the best to you and your essay in the competition.
Tom
Tom,
I was just looking in and your responses to both Robert and Marc are helpful to understanding your maths and your thinking. You do speak to mathematicians, and that assumes an 'ideal reader'. I've been hoping good questions would draw you into something of tutorial discussion.
Robert puts it succinctly that reality is objective and measurement is observer dependent. Math, like the color purple, is a figment of human imagination. The reality is that randominity is limited by necessity. 'There is no such thing as cold, cold is the absence of heat' - (Louie Ritchey). When we reach absolute Zero Kelvin, they can have pure randominity. I won't care. ;-> jrc
Tom,
Let me elaborate on my last comment before returning to some personal matters.
I think your identification of escape velocity with any point in space is a profound insight. It is both physical and at the same time mathematically versatile. It is where the path of least resistance is provided to the random walk. The escape velocity at any given point in space will naturally vary with the dynamics of change in position of masses that come within relativistic proximity to that point. Conversely, the escape velocity initially observed will migrate to another (and potentially others) as the dynamic evolves.
If I am meandering in a crowd of people, my easiest path will be toward an adjacent space that momentarily opens up, which will effectively reduce that openness. Continually. I will eventually find my way to the periphery.
This generality was touched on in dialogue I've been having with Constatinos Ragazas and in communication with Ed Klingman in regard to Planck's solution to the violet catastrophe. The exponential increase in the possible numbers of waves per second as frequency increases across the continuous spectrum, would result in an equal chance of thermal energy in Wien's furnace, to choose an ever higher frequency over a lower one. That doesn't happen, obviously. The curve of intensity of spectroscopic frequency analysis was only matched
when Planck introduced a finite constant energy value into his equation of probability distribution. Effectively showing that a specific quantity of energy in any given wave event results in the energy in the furnace seeking equilibrium with the ambient environment, must avail itself of lower frequencies as well as randomly chosen higher ones. The Quantum is causal of that distribution by the physical necessity that the furnace must shed thermal energy in every path available to maintain a stable temperature. Wien's furnace was a furnace, it was continuously heated. It would melt if the energy didn't take the path of least resistance in its random walk.
Well, I've indulged in putting things off this morning long enough. Do continue to expound the elements in your math arguments. The pedagogical role is part of scientific writing, and it should not offend anyone if you present things as if rudimentary operations need explained. The explosion of mathematics in the last couple centuries actually require it. Maybe we should call it Accumulated Math Disorder. Best, jrc
Thanks, John. So as not to confuse the reader, though -- your comments refer to something I sent you privately, and not the contents of the essay per se. I'm not quite ready for wide distribution of that Email piece.
All best,
Tom
Dear Tom,
Your essay is multivalued in the sense that
* you clarify the relationship between physics P and mathematics M, postulating a linear (Tegmarkian) equation E = k*P,
* you put this in perspective with Bell's (or CHSH) inequality and a establish a link to number theory (the unsoved Goldbach conjecture as revisited by Popper),
* you question the role of probabilty in the MP correspondance (as commented by John Cox in his post),
* you relate to Euler's identity (James Hoover has an essay on this topic as you know)...
All this aspects are justified in technical terms sometimes in an unexpected way. You received many valuable comments, a proof of respect. I add my congratulations and my good community mark.
Best wishes.
Michel
Tom,
Mia culpa. jrc
No problem, John. I've given it some limited exposure, just not prepared to take questions yet. :-)
Best,
Tom
Michel, I am deeply honored. Thank you so much for your careful reading, feedback, and vote of confidence.
All best wishes for success in the essay contest,
Tom
I find myself in the position of defending the views of both Alan Kadin and Michel Planat, who crossed swords in Alan's blog.
No surprise -- there is probably no sharper demarcation of philosophies in physics, than between Einstein-Bohm represented by Kadin, and Bohr-Peres represented by Planat.
I'm not neutral -- I agree with Karl Hess (*Einstein was Right* 2015) and the late Walter Philipp that introduction of a time parameter generates the Bell "impossible" result E (a,b) = - a . b
That's only half the story, though. The other half is that the assumption of fundamental particle reality obviates that dot-product result a priori, while the assumption of a fundamental field theory requires no a priori assumption of fundamental particle existence (Kadin's claim).
Though I don't mean to be self-promoting -- my own view, that the Hilbert space (and the linear superposition of particles to which Alan refers) is deficient, is based on my prior research that metric continuity in the Hilbert space depends on deriving a real valued well ordered sequence without invoking the axiom of choice.
This would be true, regardless of whether one assumes particle discreteness or wave continuity. It comes down to the perennial question of what is being measured. Alan is very clear that his program obviates a domain boundary between classical and quantum. Bell-Aspect and CHSH programs, on the other hand, actually create a domain boundary, by observer dependence, and therefore cannot survive without an assumption of particle nonlocality.
So how would one show what is being measured, unless 'what' is discrete? And Is it a sharp point particle, or a wave packet? A quantum of something only implies measurability; it does not imply a definition of something. A field of something presents the same problem.
I think we are left with the same question that Einstein identified so many years ago -- that if we don't improve the mathematical methods, we can't expect resolution of the gap between quantum and classical mechanics.
I think that Planat and Kadin are equally sincere, honest and competent in their mutual quest to improve the mathematical methods. That's how science progresses.
Tom
Tom,
'So how should one show what is being measured..." You do say a lot in short posts.
Many times we all have imperfect knowledge of the fullness of measures that have become used in particular ways that tend to relegate one parameter or another to obscurity. So what the quantum is as a measure, is generally treated as if it is only a specific quantity of energy because it doesn't tell us whether it is a particle or a wave. Added to that, the time normalization in QM denudes the quantum of its 'per second' realism.
But the original Quantum finds more measure than given credit for. Boltzman's Constant obtains from the Gas Constant/Avagadros Number, and so Boltzman is a physical proportion that gives the energy/temperature associated with a single source particle. By relation with Planck's Constant as a physical proportion of energy/time, there is a complex measure of a single physical wave at any specified frequency which carries the celebrated energy quantity per every 1/f from a single source. That's a lot of information to start with.
To an experimentalist, CHSH isn't half the story. What is the wave doing and how, such that some ranges of frequencies penetrate deep into the dirt and others bounce off airplanes? Each single wavelength carries the same energy. How's it do that?! - Duhhoohhhh - :) jrc
Hi John,
Perceptive and interesting, as always. :-)
I expect you will relish reading this Andrei Khrennikov paper on sampling contextually with different statistical properties.
My own answer to the question of time-dependent quantum measurement in a number theoretic context is in the attached.
All best,
Tom,
Thanks for the links, anybody looking in can access them also, and that is one of the real values of this forum. When participants assume the role of sounding board in the bouncing of ideas off one and another 'The Beat Goes On'. If it starts sounding like a Ping-Pong match, its time to quit the game.
The Khrennikov link is a free sign in to what looks to be an extensive archive, I'll content myself with the download of your att'mt but others might find it fruitful. You are obviously enjoying your retirement giving you the time to pursue what you have long wanted, and that's refreshing, and perhaps more satisfying than those whom have had careers requiring intense research and find themselves now in real proximity to 'publish or perish'. Enjoy! jrc
Thanks for pointing that out, John. I learned that the site accepts my publications, so I signed on as a member myself.
I've been a professional writer since teenage, so it's always been "publish or perish" for me in terms of making a living. The career I'm retired from (government service) is my third career, that I undertook after going bankrupt in 1999, and finding myself in need of some security for my family and me.
It's still publish or perish -- the level of security we need isn't there -- and that's fine with me also, and I do enjoy it, because it's all I've ever known. The academic form of publish or perish isn't something I would have been happy with, I think, seeing all of the publications from academics who have so very little of significance to say. It's a bit of a crime for a talented researcher to have to survive on a publication list of questionable content -- when given the freedom of serious research, she or he might have produced just one work of importance.
All best,
Tom
My attachment of 2 April -- which demonstrates reversibility of the counting function by the natural properties of recursion and parity -- got me thinking about the Monty Hall problem and why reversibility of the time metric is equivalent to experimenter free will in a Bell-Aspect type experiment. Switching choices implies physical time reversibility, and here's why:
Mathematicians will always agree -- that given n contestants choosing 1 of 3 doors, two of which hide a goat, and the third a new car -- one can predict that over many iterations, or even if many contestants simultaneously choose from sets of doors, that by the law of large numbers 1/3 of the contestants will win cars. This how Richard Gill describes the independent "counts" of four 2 X 2 tables of results in a Bell-Aspect type experiment, with 4 instead of 3 "doors.".
The singular case in which the host (Monty) opens one door of the two that a contestant has not chosen -- and reveals a goat, then asks the contestant if she would like to switch choices -- raises the question of whether the contestant has a winning advantage by switching the choice, or staying with the first.
Naively, one thinks that -- because Monty has shown one of two doors that the car is *not* behind, that the odds of choosing the winning door have been increased some 16% (from 1/3 to 1/2) by choosing to switch. In fact, though, the odds are still 1 in 3 whether the contestant switches the choice or not. The question is whether one has a better choice of winning the car by switching choice, or not.
Even though the contestant knows in advance that Monty will never open the door with a car behind it, this information adds nothing to her knowledge of what door the car is behind. In other words, a potential choice (the door identified but not yet opened), does not change the energy state of the system. It does, however, add to the information of the energy state -- one now has a 66.6% chance of winning the car if one switches choices of door -- and this is equivalent to the Hess-Philipp result ( 3) for their Bell-Aspect type inequality that I cited in the attachment; i.e., there is a 3 to 1 advantage (my paper explains) for the result not observed, over the P(1/2) probability for the result that is observed. That difference of initial condition vs. measurement outcome is a hidden variable.
To see why, compare this scenario to the Schrodinger Cat experiment. The decay rate of the substance that emits a particle and triggers the hammer that breaks the vial that releases the poison that kills the cat -- is precisely known. The energy potential of the hammer is identical to the pre-choice of door in the MH problem -- If Monty lifts the lid on the box and declares "the cat is alive," or "the cat is dead," it has no effect on the decay rate of the material or the energy potential of the hammer.
Monty, however, *cannot choose* to say "the cat is dead," because we *know* that the conditions under which the cat dies are fully determined, even though hidden in a black box. There is absolutely no point in Monty communicating to us that the cat is dead, because:
If the cat were dead, the experiment is ended -- just as if Monty opened the door with the car behind it while the contestant still has a choice pending. It doesn't happen, because Monty knows which door the car is behind. He isn't an observer making a binary choice; he's the guiding principle *behind* the measurement choice. This is the same principle by which Joy Christian successfully argues for the choice that Nature makes independently of conscious observers, and which guarantees real binary measurement in a locally real and objective way.
Ultimately, the free will hypothesis prevails, because -- and I made this point repeatedly in the great "debate" over Christian's result -- *unless* Nature has a choice, human observers have no free will. The energy cost to remove the middle value is equal to the observer's choice to change the state of the system.
So in support of Tegmark's hypothesis and Christian's measurement framework (which was published by the International Journal of Theoretical Physics recently as "Macroscopic Observability of Sign Changes under 2(pi) Rotations"-- nature is not fundamentally random, even though conscious observers switch their choices.
As my attachment shows, observer choices that change the measurement outcome deterministically, also change the initial condition randomly -- consonant with my claim that free will exists IFF nature is not fundamentally random. The question of whether the initial condition is positive or negative obviates the independence of tables that Richard Gill describes. The measurement is observer entangled -- and that entanglement is equivalent to classical orientation entanglement (spinor property).
More to come.
