Juan,
I am grateful you are questioning certain content of my essay. Reading your remarks, you quote from the essay, then conclude:
"It is not an interpretation. It can be demonstrated the wave function in quantum mechanics describes an ensemble. Precisely those "statistical renderings" are the ones behind most myths and misunderstandings of quantum theory."
Juan, it was not my essay intention to make more fantasy and misunderstanding.
First, I am new to FQXi and wrote for a general audience, but hopefully with enough academic remarks to resonate with deep scientific mathematic minds.
I had learned in 70 years that questioning valid accomplishments of dedicated researchers, where I might be cognizant of additional relations and data that contribute or mitigate their accomplishments and results .. is difficult mind waters to tread. I have chosen to ask colleague scientists, in all fields, to consider co-present parameters that might have been honestly overlooked before.
Especially with the discontinuity separation of QM vis a vis Relativity.
Re my "Gaussian bell curve" remark, I did not have it in the essay, but did include in a conversation post afterwards, the example of a pachinko machine, where an accumulation of balls falling through pegs, generate a Gaussian distribution curve. Consider related circumstances: almost any series of science event experiments results (done over time) that produce a similar curve. Consider also any school test, where the answers generate a gaussian curve, representing the small number of students who know the material least, to a large group who know -most-, to a small number who correctly know -all- the answers.
What is generating these similar gaussian curves? Beyond our simply identifying them? I use this plausible explanation (by example):
Take the pachinko machine up into outer space .. to microgravity, or as far from a gravity well as possible. "Drop" the balls (if you can at all) from your hand, with the hope they fall through the apparatus. They don't. There is no impetus driver for the activity to occur. No movement, let alone all the batch of balls going anywhere near, let alone into and through, the pachinko apparatus.
This alerted me to something that no Gaussian mathematics includes or considers - the co-present action driver (causation parameter) that must be co-present TO GENERATE Gaussian curve results. For the pachinko game, it is the gravity acceleration field. For school tests, it is the (more complicated of course) presence of a social necessity "pressure" to gauge students' knowledge. For general science experiments, it is a similar quest, the 'pressure' to see the variability of parameters or noise/variability in processes under examination.
Some 'activity driver' is co-present .. always. But no such parameter is ever presented with its own -math term- in the equations or calculations.
The whole of the math done in conventional practice works exceptionally well WITHOUT such terms being include. But, I present the notion that there is more insight and data and knowledge to be gained BY INCLUDING, what I call, the "gradient parameter". By examining the parameter in detail in all its incarnations .. because it is more than a modifying term of the already well established calculations groups. It has its own internal sub-structures and relations .. that result in a net-simple 'gradient term'.
I hope this makes sense to you and others.
There is a variant condition I like to discuss, vis a vis the pachinko game machine. So please bear with me.
It is all well and good to examine activity/event arrangements that produce pretty gaussian curve results. Which confirm our established mindsets.
But instead of small balls and robust immovable pegs, we change the apparatus.
Stay on the earth's surface in the gravity field.
Now use bowling balls, or super-dense lead or uranium balls; and make the pegs out of fragile balsa wood. Drop the sequence of balls through the apparatus -- one at a time and removing balls after they are accounted for - their location logged in.
What is the resulting 'curve'? There is no gaussian curve. There is only one repeated result. The accumulated 'answer' is a large tall single line, graphed at that value.
Does this inform us anything useful? Yes, yes it does. It informs us that the INTERNAL RELATIONSHIPS of events are also critically important. They have to be non-destructively appropriately relatable to one another. In proper proportion. Give a college test to a kindergarten child, and you get a single result: Zero correct answers (if you prevent a random hitting of an answer button .. make it a written test, requiring the skill to hold a pencil and place a check mark in a special location :-) ). {Or test newborns) :-) ok ...
I am more concerned, Juan, with the external gradient parameter. And, if -it's- presence as a math term is something of importance to look at, then I also suggest that our by-habit use of numbers is worth reviewing also. From my years of examination, I concluded that how we use exponents .. and when we choose TO use them as 'dimensions' markers, and when we choose TO NOT use them as 'dimensions' markers, is worthy of better examination and defining. I like using the notion that 'reliable' is akin to the notion 'consistent'. I would feel more comfortable if we made the exponent~dimensions correlation CONSISTENT.
My essay presented, within the limited space allowed, an hypothesis to expand the understanding of 'dimension'; to head toward making it more consistent than we have it now. It requires a deeper review of primary math definitions currently used. I think there is room for improvement.
>Ahhh, almost forgot, there is a larger conclusion that I need to SUGGEST, Juan.
You made remark of strong dependability on statistical mathematics. A fait accompli, because of fine experimental results and internal consistency of the math (as I interpret your well phrased concise sentences).
As my examples point to, 'statistical math' does not occur to map physical events and phenomena, without co-present criteria parameters .. which co-present parameters are NOT statistical. They are activity instantiators. They are present, not statistically present. Not 'maybe they are, maybe they aren't.
[Because such motivating driving parameters exist in so many different forms that I am aware of, I am not going to try and depict them here, let alone write that there might be one and only one shared underlying property they have in common. (though they do, but I am still writing that up) :-) ]
I do NOT CHALLENGE the excellence of statistical mathematics and correlation with phenomena events, especially essential physics. I identify and recommend that there are ADDITIONAL relations -- WITHIN MATH LANGUAGE AND TERMS -- that are the missing associations which are preventing us from better understanding the natural relationship between QM phenomena and Relativity phenomena.
That is why I took the essay question in that direction. I propose that another 'fundamental' relationship exists in mathematics, which few if any have identified, let alone explored or dissected.
***
Now, Juan, you mention time-reversible QM & Hilbert spaces. I have some thoughts on those I would ask you to consider as well.
Your opening pgh, and closing remark, are respected by me. Indeed, extraordinary math has been done in both co-fields ... QM and relativity. I make NO ARGUMENT or question the detail and accuracy of the respective math and math accomplishments. MANY have been confirmed by experimentation, in fact. But noting also, that there is a lot that is not yet confirmed and remains simply hopeful hypothesis.
To be honest and clear, I have discomfort with time reversal ... even though it is an interpreted property / result of some of the math. I was in communication with Ilya Prigogine before his death, discussing and comparing our respective ideas, because I also am most interested in other mechanisms of negentropic complexity building in the universe, that addend to his excellent discovery.
He was generous enough to send me copies of all his final papers, where he had turned from his Nobel Prize winning work on 'complexity arising far from equilibrium', to considering the arrow of time. All I can publicly comment (in absence of his publishing himself) is that he tried to pull forward-time out of bi-directional QM time factors. But not successfully to his satisfaction.
It is my own deduction, knowing what I do about different relationships in the general literature, that time-forward COULD be modeled (not 'explained') by a statistical model. I have an alternative non-statistical preference, but, I have to respect and understand this interesting statistical approach.
Much like multi-verse theorists say that the math 'permits' co-alternative universes (whether we interact with them or not), I suggest that the math 'permits' consideration of precluded/prevented statistically possible time lines sets.
All events loci co-produce sets of available and also precluded 'next options'.
If I jump in a swimming pool, I have precluded next time-moment options of staying dry, of ironing a shirt, of remaining on the ground and walking away, et al. It would be massive to calculate, but I have done some initial calculations and it seems to turn out that as new option spaces open up (in the pool, I can swim with dolphins; I could not do that staying out of the pool), that there is an expanding set on both sides of any bifurcation node or multi-furcation node.
It seems that the statistical set of "no-longer possibles" expands much much faster than the set of "could be possibles". This comparison does not -explain-
forward time, but it at least maps it. From which map we might discover relationships we didn't consider before. I am hopeful.
Also, another relation makes itself apparent in comparing those differentiating sets. Option nodes identify that some events are NOT time reversible. The equations are about more than accounting for conservation of energy, momentum.
This gets back to my description about the commendable internal structure of phenomena systems. We presume and rely on the internal waves~architectures being on the same scale per sizes, energies, frames of reference, etc.
It might be the case that when there is synchrony of those factors, then under those special circumstances, there is indeed time reversal events and relations.
But those scale~matched correlations are very local, special, limited, and may be overwhelmed if not precluded, when the events environments become more complicated.
Juan, I am grateful that you were disturbed enough by remarks in my essay, to write an admonition, warning uneducated misunderstanding of the accomplishments (and therefore the underlying conceptual accuracy) of the high math and deep physics. You wrote with a respectful and tolerant tone and use of words. I hope I have done the same in return.
I am a general systems theorist, so I have had to become familiar with many sciences, many uses of mathematics. Please excuse my use of humanistic descriptions. It has been a dream of mine to get people .. scientists and non-scientists alike .. to patiently appreciate companion perspectives, and maybe use other people's insights to improve each of our own personal ones. And to maybe improve our scientific specialties by considering what has been learned in other specialties.
Thank you for commenting on my paper, Juan. I hope I have addressed, and maybe improved, your impression of what I wrote about. :-) This is an excellent community of minds.
James
2018 Feb 16 3:36PM
Nevada USA