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
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
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
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 November 21, 2012