Pilot Wave Hydrodynamics

Jonathan,

It looks interesting.

I have to say, though, that I think order is still emergent from dynamics and Mandelbrot sets are a good expression of this, in that it requires the process of following the steps to create complex structure from simple rules. Their regularity creates the impression they must be fundamental, but I don't think it contradictory to consider order as emergent, because it follows rules. Change an instruction and the patterns change.

It is not as though the result isn't implicit in the process, but that is exactly the point, that the pattern emerges from the process and doesn't exist prior to it.

Pattern describes. Dynamics explains. Energy manifests information, while information defines energy.

Stop the dynamic and you have a pattern, but keeping it going and you have a process.

Regards,

John M

Of course the form is emergent...

And there are lots of 'Mandelbrot Sets' with different formulas. But the familiar form with z = z2 c as the formula is maximally complex, when compared to any other polynomial. Likewise; the butterfly figure shows maximum detail when you color in values where the iterand's magnitude decreases over 3 calculation cycles. Why not for 2 or 5 cycles? But those figures are simpler.

I view E8 as the embodiment of maximal symmetry, while the Mandelbrot Set shows the ways symmetry can be broken - in a grand catalog of symmetry breaking forms or modes. So there is an implication that somehow nature knows that these maximally complex examples exist, and it employs them in its handiwork. How cool is that?

All the Best,

Jonathan

In a kind of fun aside...

It's likely I walked right past the lab of Couder and Fort, at some point in time during FFP11 - which was at Paris Diderot Universite, with sessions in rooms throughout the Physics buildings.

All the Best,

Jonathan

Jonathan,

Consider the implications of "nature knows." Knowledge is a feedback loop and energy is naturally following the paths of least resistance, which is either pushing along the order it can and or seeking out its weaknesses, so that boundary between complexity and chaos is really energy reacting to order.

This then gets to the relationship between determinism/probability and past/future. While what has been determined is past, it often seems the future is a continuation of it and thus also ordered/determined, when we can discern the patterns being propagated, but then it becomes a reaction to this order and we lose the pattern, thus it seems chaotic or probabilistic and yet the better we get at detecting these patterns, the better nature gets at surprising us, as though it seems she reads our mind, because we are part of the patterns. Even when we think she is finding ways to be even more complex, she turns around and becomes simple again, while we are off chasing unicorns and supersymmetry.

I'm trying to tie up some of the loose ends on that thought process, but.....

Regards,

John M

Ps,

For example, consider when you have different patterns interacting and how the points they meet, the angles, velocities, other patterns, etc. can all create input and so more complex, or more regular patterns result. Then when you have masses of such patterns, different energies, etc, so add in thermodynamics and it gets to be like what nature is doing.

Pps,

Which also goes to these sets physically emerging as crystalline structures at various phase transition points along the spectrum and scales of this dynamic of energy and order.

Zeeya,

Important topic. t'Hooft etc seem right in that that de Boglie-Bohm could never give a complete account. I've suggested a completed version consistent with Jonathan's fractal approach. It seems hard to explain but do please advise (anybody!) if this gives an insight to a coherent logic;

The spin-orbit relation in optics is the helical path taken by a spinning 'charge'. The charge itself is a smaller 'fractal' so we have two quantum 'gauges' We then consider the pilot wave as the 'greater' of two fractals, the smaller of which is the 'particle'. (the pattern may continue up and down in scale, for which evidence can be identified right up to the CMB helical anisotropy).

The +/- binary orbiting charges may then be considered in 2D as represented by a sine wave, with +1 -1 values each side of a median (mid height) 'ground state', only then NOTIONALLY 'zero' (flat line = undetectable). That state may be equivalent to the 2.7 degree ambient medium of space, or the 'dark energy' essential to concordance cosmology.

However the real value of the model is in it's application in Mach-Zehnder/ quantum eraser etc set ups, where it overcomes the need for any assumption that photons are indivisible (an assumptions rather inconsistent with Stern-Gerlach splitter creating pairs anyway!).

Only the positive charge will reach the required level to 'manifest' as a quantization ('photon'), and there's a 50:50 probability which path it took, but the positive charge is NOT the whole 'wave' energy, which is the 'change' (fluctuation) value. The model fits the standard PMD harmonic resonance model of refraction in optical science, 'half silvered' mirrors or s crystals.

Recombination is then simple and logical, fine tunable by a slight delay in either path to either maximise the 'peak' or flatten the whole pattern ('constructive or destructive interference'). No mysterious 'counterfactual' explanation is required.

Could anybody follow and make any sense of that description? Any falsification?

My essay described how 'non-locality' and the cosine distribution can then be classically derived, precisely in the way anticipated by John Bell (p175 and 194), consistent with both Copenhagen (the detector influences the finding) and SR (causal, but only down to the 'next' smaller fractal gauge). The essay includes an experimental proof and a number of important supporting references.

http://fqxi.org/community/forum/topic/2104

Or short updated summary here.

Best wishes

Peter

Thanks Peter,

This summary/refresher is helpful. Perhaps the most important point buried in the account above is the idea that points of inflection are "NOTIONALLY 'zero' (flat line = undetectable)," because of gauge invariance, but have an absolute value that becomes relevant in experiments like Mach-Zehnder and Stern-Gerlach, because the 'signal' is spread out, but the split point sets the overall tone.

All the Best,

Jonathan

I think I got that reversed..

The absolute value at the crossing point is normalized by the experimental apparatus (because all part of it share the same displacement from true zero), but the overall tone is impressed upon the whole local universe.

Perhaps you can clarify that point Peter.

Regards,

Jonathan

I find it satisfying to look here..

If we contemplate the far side of chaos, we find that a lot of things appearing complicated are actually simple in their roots, either owing to the generating equation or some bounding surface that makes itself known only when there is something expansive to bump into it. Things simply cannot get infinitely chaotic, and there are limits to complexity as well - though such limits may seem far off at the outset. Perelman's proof of the Poincare conjecture illustrates this.

The book "Chaotic Mirror" by Briggs and Peat does not use the term far shore of chaos, but takes that notion as its central theme of investigation. This same sort of thing is seen in experiments with non-linear entropy, where order appears to emerge from the maximum of chaos, or where there is an alternating pattern of orderly and chaotic regimes. Check out the work of J. Miguel Rubi for more on this angle.

All the Best,

Jonathan

Jonathan,

I still think the relationship between order and energy would be a fruitful dichotomy to provide a deeper understanding of these concepts of complexity and chaos. As it is, they emerge from our understanding of order, while energy explains the process by which order is such a fluid concept in the first place.

Regards,

John M

Peter,

Old theory is like that square wave. We ignore nature and keep fixing it back up, because it was the "original signal."

Regards,

John M

John, don't confuse chaos with probabilism. You write:

" ... when we can discern the patterns being propagated, but then it becomes a reaction to this order and we lose the pattern, thus it seems chaotic or probabilistic and yet the better we get at detecting these patterns, the better nature gets at surprising us ..."

Chaos is deterministic. There are no surprises. The experiment under discussion here is a refinement of David Bohm's research into what he called the Implicate Order; his original analogy was of a droplet of ink in a vat of glycerin -- the vat is equipped with a mechanism that allows it to rotate, which causes the droplet to spread linearly, until it disappears. When the rotation is reversed, the ink blob returns to its original shape and position. Bohm and Basil Hiley extended this thinking into what they called The Undivided Universe. It's completely deterministic and classical.

"Why quantum?" Because quanta are integrated elements of nature's continuous and reversible function, its relative becoming, in Joy Christian's precise terms. So much for the sophistication and hubris with which certain physicists surround their theories in one breath, while reserving the other for harsh criticism of Joy's framework, without the least understanding of its mathematically complete structure -- only to witness the rediscovery of his results, all the while reinterpreting and rationalizing their meaning into something that suits their non-classical convictions. The ink droplet that disperses and recombines non-linearly, is not a product of statistical probability, any more than the linear version.

To borrow from Melanie Safka, "Look what they done to my song, Ma."

Are we allowed to ponder things like massively complex quantum entanglements that are generally undetectable, but might for example interconnect all biological life on the Earth, for example? What about deconstructing general relativistic geometry down into a weave of quantum entanglements? Can the physics laws, like Maxwell's equations and the Einstein equations be deconstructed into an enormous set of correlations of some quasi-existent wave-functions?

Tom,

I didn't say they were the same, which is why I listed both as causes of unpredictability, though we might still assign both different meanings. I would describe chaotic as not being able to know all input into a situation, while probabilistic as having far too much input to effectively determine the outcome before hand. This goes to my oft repeated observation about time being the process of future probabilities becoming current actualities and then residual effects, rather than a vector from past to future. Therefore the future remains inherently probabilistic, sometimes bordering on chaotic, because all input into a particular event cannot be fully known from a prior frame, ie. all input only comes together with the occurrence and since information cannot travel instantaneously, there is not a method to fully know what will be affecting it.

While I take your word for the physics of your example, it would seem both directions of spin would create centrifugal, not centripetal forces.

Regards,

John M

Though possibly stopping the spin altogether would allow the ink to coalesce.

Jason,

On the classical level, I suppose pilot waves are what we would refer to as feedback loops.

In eastern philosophy, as karma.

Regards,

John M

Aether has mass. Aether physically occupies three dimensional space. Aether is physically displaced by the particles of matter which exist in it and move through it.

The Milky Way's halo is not a clump of dark matter traveling along with the Milky Way. The Milky Way is moving through and displacing the aether.

The Milky Way's halo is the state of displacement of the aether. The Milky Way's halo is the deformation of spacetime.

A moving particle has an associated aether displacement wave. In a double slit experiment the particle travels through a single slit and the associated wave in the aether passes through both.

In a double slit experiment it is the aether that waves.

Jonathon,

I look forward to your explanation of the Mandelbrot Set (I'm reminded of the Buddha by the originating circles) and appreciate your years of serious effort in mathematical physics. Contributors such as you and Tom Ray are essential guides in learning enough about the necessary maths to follow the discussion of what is intuitively attractive about Pilot Wave Theory, but which displays such an immediate complexity when one tries to conceptualize application of the planar analogy into 4-D. I think Tom is quite correct in topology being the most suitable measurement framework to further development. The videos you posted were quite impressive, a picture may be worth a thousand words but you show us that a mathematical expression is worth thousands of pictures. Thank-you, jrc