Classical Spheres, Division Algebras, and the Illusion of Quantum Non-locality:

Tom,

"I've never said differently."

And that what is present is dynamic?

Regards,

John M

Hi Joy,

Well, it looks like the message you posted earlier has disappeared so posting a reply here. Yeah, the conversations on the original topic have gone way off topic. In fact, let's see what I originally posted that started all of this... Oh yeah, it was this on Oct 4th.

"The path to truth is thinner than a razor's edge."

"The fact that a great many people believe something is no guarantee of its truth."

- W. Somerset Maugham, The Razor's Edge

LOL! That sure did start up a long discussion! I guess people here just like hangin' out on your forum topics. You are one of the very few FQXi members that actually respond on these forums. Sure would be nice if posts and replies didn't disappear.

Best,

Fred

Actually I attributed the quote,

"The path to truth is thinner than a razor's edge."

wrongly to Maugham when it is my saying that I derived from "The Razor's Edge". I am surprised no one asked more about what it means because it can have two meanings. Of course you might think it means that the truth is very hard to get at as a standard straight forward meaning but here is what it really means (hidden meaning. There is nothing thinner (figuratively) than a razor's edge so you are already at the truth. You just have to open your mind to see it. Those that have read the book might have "gotten" the hidden meaning.

Best,

Fred

Fred,

I certainly apologize to Joy for cluttering his forum and should take my arguments to other threads, but as you point out, Joy is the only FQXI member willing to join in and since he is primarily focused on his own argument, most of any serious debated about it is happening elsewhere. I do certainly applaud his efforts to bring physics back to a more physical basis and I doubt few in here would seriously question that. What seems doubtful is any significant conversations about some of the broader issues some of us here see as problematic, such as Robert's argument that physics has become too focused on its mathematical tools and the particular obsessions involved are a large part of what is distorting the picture. Or my contention that distilling time to only a measure of duration, it only treats a measure of an effect, that of the state of the present moving from past to future events, rather than the physically broader context of change, which turns probability into actuality and then residuals, ie. future becoming past. While it may seem a basic point, it does affect how we think of these processes, which I've pointed out endlessly. Obviously it seems no one in any position of authority is going to discuss anything other than the most abstract elements, such as firewalls or multiverses and only with those equally committed, so we are here, knocking on one of the few portals into the ivory tower.

Regards,

John M

John,

I kept having hopes that you would learn the fundamentals and stop harping on things that are absolutely in left field. It has become too tiresome to reply and I feel foolish to continue. This is the last of it:

"Presumably the model is created prior to experiments testing it."

*Not* the model of conventional quantum theory, which is based *strictly* on experimental outcomes, not physical first principles (like Einstein's relativity and Joy's measurement framework).

"'That has nothing to do with spacetime as a physically real phenomenon.'"

"It has to do with the fact that no experiment has shown time to be symmetric."

*Countless* experiments show time symmetry. Conservation of continuous quantities in classical physics, such as time, is extremely basic.

Tom,

You are right that we are not convincing each other of anything. I just don't see time as a quantity. Is temperature a quantity?

Regards,

John M

Eckard,

Now I think we are getting back to the mathematical fundamentals of what Joy Christian has demonstrated.

"While you and others consider C, H, and O indispensable, I see basic adequacy in the opposite direction, i.e. with just R."

Personally, I reserve my opinion on whether the hyper numbers (H,O) are indispensable to describe physical phenomena, though I know they are indispensable for solutions to Joy's framework, and to Rick Lockyer's octonionic construction.

The real positive integers, though, are reversible only to describe locally discrete, not globally continuous, events -- while the loss of commutativity (H) and associativity (O) guarantee global reversibility (which is the crux of the dot product result -a.b). Topology is all about global continuous functions. Joy's remarkable result is that the global function *does not differ* from the local continuous function -- a result that is now extremely difficult to argue with, since it has been simulated five different ways in a local computer model.

My personal hope is that the simulation will lead to a simpler model on C*, where the algebra is closed and compactification leaves only one simple pole at infinity. That is, the 2-dimensional complex plane in which the Hilbert space lives, may be entirely adequate for physical events up to and including the 8 dimensions of the division algebras. Then there will be absolutely no escape for Bell loyalists claiming that continuous function physics is not foundational. Hilbert space continuity will have been demonstrated independent of the axiom of choice. The choice function, just as Joy has demonstrated, will have been invested in nature's choice of space for the physical events we observe.

Forgive me for not getting into the rest of your post dealing with mathematical philosophy -- perhaps some other time and place.

All best,

Tom

Eckard, if the forum will indulge me, I would like to re-post in one spot a puzzle (from an episode of the American TV detective show "Columbo") and the solution, each of which I posted separately elsewhere:

1. "Imagine you are in a sealed room with sacks of coins -- three sacks filled with as many coins as you wish. All of these sacks except one are real gold coins of uniform weight. One sack is full of fake coins of uniform weight differing from the real coins by some slight measure -- any difference you choose, so long as it is slight enough to be undetectable by holding the bags in your hand.

"The problem is, you have a penny scale -- and you have only one penny; you can therefore make only one weight measurement. How do you tell the real from the fake?

2. "I made the solution easier, because I specified 3 bags -- I could have said choose any number of bags you please, with any number of coins in them that you please. The small finite number, though, makes the solution easier to explain:

"Label the three bags, A, B, C. From bag A, remove one coin. From bag B, remove two coins. From bag C, remove three coins. Place all six coins on the scale.

"Suppose the weight you assign to the real gold coins is 1 oz, and to the fake coins, .90 oz.

"If the scale reads 5.1 oz, the fake coins are in bag A. If 4.2 oz, the fakes are in bag B, if 3.3 oz, in bag C.

"Rob is absolutely correct that the quantum theorists don't know what information to look for. They assume that of an infinity of 'bags' there are in each a uniform number of uniformly entangled 'coins' so that no matter which bag is 'weighed,' it will always be a uniform multiple of the finite number of coins prepared for the weighing. In our puzzle example, the scale will always read 6 oz.

"Assume on the other hand, that one has a number of bags of space and one bag of time. The bag of time, like the bag of fake coins, has to differ in weight from the bag of space (explained in relativity by a change of sign in the metric signature), such that for a continuous weighing of cumulative units chosen from an infinite number of bags of space, there will be somewhere a bag of time that tells us the single true measure of time we're looking for in any *finite* observation. This bag of time will be present in every finite measure, because if it weren't we chould not choose units of space discretely; we couldn't assign any weight to units of space, because it's the move of time that facilitates the choice function.

"The Bell-Aspect choice function assumes entangled units of space and no time parameter (T = 1, a constant). The finite measure of a continuous function, however, acknowledges the move of time that in fact forces the measure to be finite. Only continuous spacetime guarantees a *scalar* result - a.b from n number of measures in the N finite set of measurements -- because the weight of the time vector differs from the weight of the space vector. Without a time parameter in fact, no scalar result is possible. And because there is only one true time measure in any sequence, the correlated 'quanta' of continuous measurement functions in spacetime have minima and maxima that are self similar at every scale."

Tom

To try and make the last post a little more numerically formal, this is how the bags A, B, C appear:

A. 6 - (1).9 = 5.1

B. 6 - (2).9 = 4.2

C. 6 - (3).9 = 3.3 ...

for n iterations:

6 - (n).9 ~ 0 epsilon

This epsilon term is present in every finite measure. It falsifies the assumption of Bell's theorem that time is unitary ( = 1) for quantum measurement, rather than continuous with the measure space at every scale, with no boundary between quantum and classical domains.

Therefore: no wave function collapse.

Tom

Tom,

It is not logically permissible to use the completeness of the real numbers in their own construction. Furthermore, modern topology is even unable to perform a logically acceptable cut between R- and R. For such reasons I don't trust in pebble-set topology. My last essays did further elaborate my criticism and suggested a way out while it is not my business to purify topology from set-theoretic burden.

You are certainly prudent when reserving your "opinion on whether the hyper numbers (H,O) are indispensable to describe physical phenomena though ...".

Functions of radius or of elapsed time don't have support for negative abscissa. Such semigroups fit completely to R. Of course, for those like you who used to see the world from the perspective of C, there are several seeming deficits.

I appreciate your effort to explain.

Regards,

Eckard

Someone didn't like my last reply, showing that if reality is independent of mind, your conclusions ("Quantum mechanics is unique, cannot be generalized, has nothing to do with classical mechanics, and Nature is quantum at core.") do not and cannot hold.

1. The "core" of your description of quantum mechanics is only in the discrete parsing of events by probabilistic interpretations in the mind of the observer. That's called "thinking." It has nothing to do with classical mechanics, because it has no connection to the classically continuous and objectively described functions ubiquitous in nature.

2. Conventional quantum theory is based on no physical first principles.

3. Your argument for composability classes is a red herring, since all of the classes of spacetime curvature (parabolic, elliptic, hyperbolic) are incorporated into continuous function physics and easily accounted for.

Tom

I'm suprised that no more dialogue has been generated over Lucien Hardy's five reasonable axioms of quantum theory.

The fifth -- "There exists a continuous reversible transformation on a system between any two pure states of that system" -- Hardy allows is the only one inconsistent with classical probability theory (classical randomness). And that hinges on only one word -- "continuous."

My opinion is that probability measure is not and cannot be independent of mind and therefore cannot be a physical first principle.

In other words, the reversibility of a continuous measurement function is independent of the discrete processing of measurement information propagated by wave mechanics.

Joy Christian's measurement framework is the only one I know of, that allows correlation of quanta independent of discrete mental processing using the classically random functions that Hardy identifies.

Tom

Joy, I'm glad to hear that. I will take my copy of O'Shea's book home with me over the holidays, and perhaps comparing notes in the forum will shed more light for some, on the torsion issue. It wasn't easy for me to understand, and I like your distillation, "quantum correlations are a measure of torsion within our physical space." Right on.

All best,

Tom

Tom,

Probably because human nature and its subcategory of academic disciplines, does not go in reverse.

When a particular concept becomes accepted, subsequent work is built on and around it, so if someone is to later go back and with the hindsight of broader knowledge, point out where it is wrong, this doesn't simply put the model in reverse and effortlessly turn it back to what was the starting point. There is the combined inertia of all that other work radiating out from it.

What's the old saying; Open a can of worms and you need a bigger can to put them back in.

Models are closed, but reality is not.

Regards,

John M

Post returned approved, thank you:

" ... final nail in the coffin of theories seeking to recover quantum from classical mechanics ..."

etc.

"... if there is no reality independent of mind, quanta are not distinct natural phenomena; they are creations of discrete perception rather than elements of a continuous spacetime physics. Classical mechanics accommodates every one of your composability classes of positive, negative and zero spacetime curvature in each of its relativistically distinct and locally correlated quanta."

Is wave/particle duality being dismissed above?

James Putnam