Each
year the Foundational Questions Institute (FQXi) holds an essay contest inviting
writers to submit missives addressing the question chosen by the FQXi board
as being particularly thought-provoking. In their words, "FQXi catalyzes,
supports, and disseminates research on questions at the foundations of physics
and cosmology, particularly new frontiers and innovative ideas integral to
a deep understanding of reality, but unlikely to be supported by conventional
funding sources." The 2011 question was "
Is
Reality Digital or Analog?"
Scientific American magazine, being one of three partners, published
the runner-up entry in the December 2012 issue: University of Cambridge professor
of theoretical physics professor David Tong's paper argues that the world
is in fact fundamentally analog.
Professor Tong actually tied for second
place, but for some reason SciAm does not tell us whether the other second
place paper supported an analog or digital viewpoint. For that matter, it
did not say which side the winning paper came down on. Strange. I looked it
up on the FQXi website. First place went to
Jarmo Makela, who believes reality is digital in nature based on a personal
discussion with Isaac Newton in his London home in the year 1700. When confronted
with the question, Newton replied, "Why, digital of course"... "Because I
have calculated it." No wonder it won top honors - who can argue with Newton
himself? The tying second place entry was by Tobias Fritz, who agrees with his
peer that the world is indeed analog. Says Mr. Fritz, "...continuous three-dimensional
relativistic spacetime emerges from the discrete hexagonal crystal lattice
of graphene." Personally, I am soundly on the analog side of the fence.
The digital proponents typically rely on the strength of quantum mechanics
theory in defending their position. While this might seems obvious since the
word 'quantum' implies discreteness, the reality is that in theoretical physics
nearly every major 'known' truth ends up being reversed or significantly modified
as more and more is learned through empirical experimentation. Frictional
heat was originally attributed to the presence of '
caloric',
stars and planets were believed to reside in the upper atmosphere; the ability
of a particle to breech an impenetrable barrier (
tunneling)
was impossible; light first had a wave nature and then also a particle nature;
space had only three dimensions and then eleven or more according to string
theory; electrons, protons and neutrons comprised all of the elementary particles,
then came the
Standard
Model with quarks and leptons, then added fermions (massive particles)
and
bosons (force-carrying particles); Bohr logically concluded based on observation that the
atom could be described using a discrete planetary model for electron orbitals and then the probability distribution
model came along and literally clouded
Bohr's theory. Long-held beliefs in medicine, mathematics,
economics, psychology, and astronomy are constantly being revised or even
completely abandoned.
Watch Gibbs Phenomenon animation using various numbers of harmonics. Animated
GIF from the
Wikipedia website.
The deeper we delve into quantum physics, the more infinitesimally small nature's
building blocks become.
If we apply at a high level the definition of an integral to the concept of
quantum mechanics, we have expressed the very method by which we are able
to calculate, say, the area under the curve of a continuous (analog) function.
It is the same way we define a continuous function waveform by taking samples
at discrete intervals to obtain a digital representation, and are then able
to reverse the process to recover the original function. By summing an infinite
number of discrete entities over some interval, we arrive at the entirety
of a function. This always seems to work for real-world subjects. Summing
one discrete packet less than all available, no matter how large the sample,
will never result in completeness. Anything less is an approximation.
One of the most familiar examples of this for electrical engineers is one
of the concepts that most impressed me in school - the
Gibbs
Phenomenon. The Fourier series for a square wave is comprised of a weighted
summation of the fundamental frequency and
ALL of its odd harmonics.
If even the least significant addend is omitted, even the one at ∞-1,
then the resultant waveform exhibits an overshoot at the edges (see
animation above).
Of course there will never be a way to be absolutely certain about
the analog versus digital debate. We will never be able to know
whether any particle or energy quantum we detect today is as fundamental as it can be.
The next smaller increment might just take us into a
yet-to-be-discovered dimension of spacetime.
BTW, FXQi's
2012 question is:
"
Questioning
the Foundations Which of Our Basic Physical Assumptions Are Wrong?"
Posted on 11/21/2012
These items are an archive of past Topical Smorgasbord items that have appeared on the RF Cafe
homepage. In keeping with the "cafe" genre, these tidbits of information are truly a smorgasbord of topics. They
all pertain to topics that are related to the general engineering and science theme of RF Cafe.
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