I happened upon Phys-L as I was searching Scirus for extant research on the
relationship between the Bernoulli effect and relativistic time dilation,
in an attempt to confirm/disconfirm a recent "brainwave" of mine. I
haven't yet found what I was looking for, so I turn to Phys-L list members
for a little assistance.
I particularly liked the idea of describing the net (anisotropic) pressure
exerted by a fluid with a net directional velocity as the sum of two
pressure components - an isotropic Brownian "static" pressure and a
directional "ram" pressure, as Mark defines these terms in his webpages.
Doubtless this is common knowledge, but I admit to not having encountered
it before.
Armed with this "revelation", even a naive viewing of the "jostling demo"
leads directly to a visceral realisation that Bernoulli's principle is a
simple and direct consequence of the conservation of energy and momentum.
If energy/momentum is to be conserved, the undirected (Brownian) component
of the energy/momentum of the particles must decrease as the directed
(flow) component of their energy/momentum increases. Even if I learn
nothing else, this is a valuable insight.
So far, so unremarkable. But then, my thoughts wandered from fluid
mechanics to statistical mechanics and on to quantum mechanics, and the
idea that Bernoulli's principle might also find application in the
description of interactions between elementary particles.
Perhaps a little too simplistically, I can imagine how matter particles
might be semi-permanent higher-order vortex-like structures in some or
other elastic, fundamentally particulate quantum 'foam'; the individual
Planck-sized corpuscles of which jiggle about more or less energetically in
some quasi-random "Brownian" motion as might be described statistically by
Maxwell's kinetic theory and speed distribution equations. I can further
imagine that these complex, feedback-reinforced solitonic structures might
form local minima in the energy distribution within the quantum foam, and
therefore be in more or less stable, local equilibrium states. And,
granted these imaginings, I can further imagine how these higher-order
structures might themselves move more or less randomly through this quantum
substrate, both propelled and impeded only by the quasi-random Brownian
motion of other such structures, and the various motions of the quantum
foam itself. Although on the wrong scale and quite the wrong shape, this
is not too unlike how I imagine a tornado to move through the dynamic
substrate of atmospheric air molecules.
On this visualisation, I can interpret the notion of mass as a particle's
resistance to a macroscopic directed acceleration against the background
"static pressure" exerted by its quantum substrate; and thereby even
explain to myself how the mass of a proton inside a helium-4 nucleus might
be less than the mass of a "free" proton. Evidently, mass is not an
intrinsic property of a particle, but an extrinsic property that describes
how it moves within/through its quantum environment. (In fact, I remember
reading somewhere that mass is not even isotropic!) Anyway, unlike Robert
Laughlin (who has publicly declared that "light is made of waves of
nothing"), I can also interpret light waves as ripples of ordered and
directed motion superimposed onto the underlying jiggling motion of the
quantum foam, and propagating through this foam at a speed c determined by
the elasticity (inverse of permittivity) and density (permeability) of the
medium. Even the spontaneous formation/disappearance of virtual particles
is not too hard to imagine, as the manifest product of the statistical
distribution of energy in the quantum foam itself.
Further, I can extend my imagination to interpret radioactivity and
particle decay in a similar way, as the destructive perturbation of the
particle's local equilibrium state by a suitably energetic interaction with
other similar 'particles' and/or the virtual particles manifest by the
quantum foam. For such disruption to be destructive, I imagine that the
particle interaction must be "harmonic" (in the sense that the de Broglie
wavelengths of the interacting particles must be in some suitable ratio and
phase), and powerful enough to overcome the energy well of the local
equilibrium states of each particle. In this way, I can visualise
matter-antimatter annihilation, and also statistical, quasi-spontaneous
particle decay.
All this is relatively unremarkable too, I suppose; and there are even a
few physicists working on such a stochastic statistical mechanical
interpretation of quantum mechanics. But it is currently less in vogue
than it used to be, which concerns me to the extent that it might indicate
that I am missing something important. Nevertheless, I recall that James
Clerk Maxwell based his work on a physical model comprising vortices in a
now discredited "lumininferous aether"; and draw some comfort from the
observation that a gravitationally-entrained quantum foam is perhaps not
all that far from Maxwell's original conceptualisation.
Anyway, my thoughts then wandered even further, to General Relativity. I
have recently read a little about how the apparent lengthening of the
lifetime of high-speed muons created in the upper atmosphere is evidence of
relativistic time dilation. And, indeed, Einstein's relativistic
description of the effect in terms of a Lorentzian transformation seems to
fit the observed data.
But I note that this is just to describe the effect of time dilation, and
not to provide a causal mechanism for it. And so I thought, what if the
apparent lengthening of the muon lifetime is not due to some or other
metaphysical stretching of time, but the rather more practical product of
some kind of Bernoulli effect?
My imaginings meandered along the following lines:
[a], if the little particles in Mark Mitchell's "Jostling Demo" were muons
(or, for that matter, any other fundamental particles); and
[b], if, at the prevailing ambient temperature, those particles were
jostled into some quasi-random Brownian motion; and
[c], if the movements of, and collisions between, the particles were
describable statistically in Maxwellian kinetic (speed distribution) terms;
and
[d], if the particles were somehow "fragile" (i.e., sensitive to those
collisions such that the more energetic collisions could disturb them to
the point of destruction); and
[e], if, perhaps in accordance with the Bernoulli principle, the
number/rate and energy of such Brownian collisions fell as the directed
velocity of the particles increased relative to the frame of reference
defined by the gravitationally entrained quantum foam;
then [f], as the average number and energy/momentum of these collisions
fell, so might the rate of particle decay, and this might be a possible
causal mechanism for the apparent lengthening of the particles' lifetime,
and the attendant 'time dilation' effect.
Now, that's a lot of "ifs", and there are probably a number of immediately
obvious objections to such an idea. But, they're not entirely obvious to
me, and I'm rather hoping that at least some of them might be addressed by,
inter alia, Richard Feynman's "path integral" formulation of the particles'
self-interaction with the quantum foam.
So, that's my "brainwave", and this is my plea for assistance: to help me
confirm/disconfirm - in language and mathematics that a layman like me
might understand - whether the rate at which a particle's energy/momentum
of Brownian motion (static pressure) might fall as a function of its
directed relative velocity would result in a statistical drop in the number
of sufficiently energetic interactions and produce an apparent lengthening
in the lifetime of the particle that is numerically equivalent to gamma,
the Einstein/Lorentz time dilation factor.
As is probably painfully evident from the above, my own training is more in
philosophy than in physics; and hence my understanding of physics is
mediocre (and in any case dated), and my mathematical competence is
humbling. Nevertheless, my curiosity and interest are genuine, and my
request for assistance is well-intentioned. If it is not too absurd an
idea, I appeal to fellow Phys-L members to enlighten me. I'll even supply
the raspberry cordial...
Tibor Molnar
Centre for Continuing Education
University of Sydney
NSW Australia
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tibor G Molnar (: 61 2 9130 3963
Brainwaves Information Services (: 61 2 (0)41 041 2963
P.O. Box 2 -: info@brainwaves.com.au
Bondi NSW 2026 -: george963_au@yahoo.com.au
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