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July 26, 2020
Updated: Jan 16, 2022
Causality: What It Means to Me
How and what we know about an object in a system is through the object's
relationship with the other things in the system. In the physical world,
especially the world of quantum mechanics, the objects we're trying to
understand are inter-dependent on each other. The world is a dance with
each member object dependent on the other. However, each member of this
material reality dependents on some universal law without exception.
As a student studying classical optics, I learned that you can compute
the propagation of light by using the idea that light moves through space
in the most efficient manner possible. The method of computation uses
optimization techniques, namely, the action principle of Fermat. From
Fermat's principle, with the help of Huygen's principle, you can get
But Fermat's principle, to me, had a little bit of quantum mechanics'
mystery (or problem) in the way light propagated. I remember clearly
wondering if Fermat's principle was dependent on local causality.
When I had thought about this for awhile, I realized that there was
a paradox because light waves had to "know" the path it would take,
before it took it, to satisfy Fermat's principle. This paradox could
only be solved if I used Huygen's principle of wave interference
which happened instantaneously and globally in this particular case
which is Fermat's principle (like a principle enfolded in a principle.)
I came to the conclusion that Fermat's principle could not be derived
using "local" causality. I think Fermat's principle works for all
waves: classical and quantum mechanical. Throughout the years, I never
depreciated this idea.
Later as a graduate student, I studied the math of Fermat's principle
further by investigating the total internal reflection of light,
and light propagation as evanescent waves which is characterized by
a coherent flow of a lateral wave along the reflection boundary layer.
The only explanation for this important phenomena I found to be
satisfactory consistent was in Max Born's book on optics . The
explanation for this was that the lateral waves along the boundary
layer was caused by destructive wave interference along the reflection
boundary layer. This destructive wave interfence kept the wave energy
traveling as transverse wave in a duct along the boundary layer. This
explanation is based purely on Huygen's principle, and in some sense is
a "global" versus local kind of action at a distance.
For me, Fermat's principle which uses temporal optimization in the
limit for which time ceases to exist. It is a kind of action at a
distance principle. It's a kind of "global" causality constraint.
It seems to me that optimization methods necessarily grind out globally
constrained results. (But I also have to admit that I wonder if I don't
understand this.) The point is that back then, I felt I could stop
thinking about this problem if I considered light propagation as a purely
wave phenomena based on the superposition principle. I "feel" that the
superposition principle is a limiting kind of prinicple which is
incredibly simple to understand on one level which we take for granted,
but its foundational reason for existing is a real mystery. Superposition
in holography enfolds waves in a multi-dimensional kind of world.
The unlying multi-dimensional kind world which we might imagine
could enable us to find a solution to this abstract problem with
respect to causality.
If you think of the interaction of objects in the physical world in
terms of classical causality in the way ancient philosophers did,
then I think global "instantaneous" causality is possible if objects
are always dependent on each other when any interaction occurs.
Objects may seems to interact "instantaneously" because the objects
which seems separated are not truely separate objects; they are
connected in some sense. For example, a pair of Pauli electrons, are
coupled together somehow by the atomic "system" in which they exist.
Statistical mechanics considers the interaction of objects in the
physical world as an ensemble. This is the way I like to think about
There were a few times when I tried to think about the possibility
of describing the world without using probability, but I was not really
successful. But I'll keep trying. I have the sense that we use
probability because the enfolding of an event is innately dependent
on chance. This is very important. It's "innate". Something about
our universe is fundamentally random. In particularily, it tells you
how likely an event will happen in the future and so has a temporal
feeling with its use to me. Obviously, we usually never speak of the
probability of an event happening in the past.
Hence, for me the causal occurrance of an event, the causality, is
associated with probability. I suppose I've come to this conclusion
mainly from conditioning. My awareness is limited living the
macro "big" world, the "classical" (versus quantum) world, which
"seems" naively to unfold with complete certainty. It was quite
uncomfortable at times to learn about the strange the sub-atomic world.
(Similarily, I've frequently thought that I never really felt comfortable
with some mathematical concepts. I only got use to math, like the math
of Hilbert, by repeated use of it.)
Finally, this model of causality to me works with how neurons interact
or communicate with each other. Single neurons send signals to
each other based on the idea that the signal is to be evaluated by
network of other neurons. The brain is a network in which a single
neuron is like a wave in the field. The neuron behaves as an entity
in an ensemble. I've model the interaction of neurons using classical
physics in which causality is a kind of time-ordered Markov operation.
 Principles of Optics, 4th Edition, 1970. An explanation for
this evanescent wave by a lateral phase shift of interfering waves
is given by Goos-Hanchen. The original paper describing this effect
was written by Goos and Hanchen in Germany in 1947.