Randomness in a Deterministic System
Sven Gelbhaar
2 November 2008
“Electron cloud is a term used, if not originally coined, by the Nobel
Prize laureate and acclaimed educator Richard Feynman in The Feynman
Lectures on Physics (Feynman2006 Vol 1 lect 6 pg 11) for discussing
“exactly what is an electron?”. This intuitive model provides a simplified
way of visualizing an electron as a solution of the Schrödinger equation,
an advancement using the scientific method to surprising observations that
could only be explained by introducing randomness.” (1)
The above quotation paves the way for the inception of Quantum Mechanics,
in that it introduces the concept of having purely random events at the
microscopic stratum of reality within a macroscopically deterministic
system. I will show how this cannot occur, and how the closest concept
that could be supported by observation is ostensibly probabilistic events
transpiring at the microscopic level.
Random events at the bottom level in a deterministic system, wherein
macro-, or epi-phenomena, are contingent upon the occurrences at the
micro-level as we find in physics, will have a tendency of eventually
culminating in observable phenomena at the macroscopic level. For
instance, if gravity is contingent upon the emission of gravitons, which
are released every so often by matter, and this emission is subject to a
degree of randomness, then probability theory states that at regular
intervals (however far apart they might be), the planet Earth would stop
exerting a gravitational force on matter situated on top of it. Thankfully
this is not the case, and we shouldn’t worry about suddenly being flung out
into space (unless of course a meteor hits the opposite side of Earth with
enough force to throw us out of its gravitational field, but this is hardly
likely).
Let us invoke the use of another analogy. We will interpolate for
electrons the cells found within the human body, for randomness at the
sub-atomic level we shall impose ultra-violet radiation, and for the world
at large we will substitute the human body. In this analogy we have a
random element, as I’ve just stated: ultra-violet radiation. For a while
this radiation causes acceptable amounts of genetic mutation at the
cellular level and we wouldn’t even notice this random occurrence, but
given enough time and/or frequency of exposure, the genetic mutation (the
randomness percolating upwards into the macroscopic/body level) will
eventually manifest itself as a cancerous growth at the macroscopic/body
level. This would be interpreted as a miraculous break in causality (a
singularity in the theories of physics) if we revert back from our analogy,
which goes against the tenet of repeatability in experiments and as such is
diametrically opposed to the whole notion of the scientific process.
At the level of microscopic particles we find ourselves in a bind. Our
default methods of sampling/observing reality are too bulky to be utilized
to account for the position, trajectory (direction), and velocity of
electrons, for when we collide an electron with a beam of light particles
(photons) we end up changing the direction that the electrons are
traveling, and possibly their speed (if the photons are moving opposite
enough of the direction that the electrons were moving to begin with).
Also, we have to factor in just how fast these electrons are orbiting the
atomic nuclei, which is, if I’m interpreting the source I’m about to cite
correctly, at the speed of light itself. (2) And that’s just electrons
– there is evidence of even smaller particles yet which comprise protons,
neutrons, and electrons, called quarks and leptons.
[Figure 1]
Instead of supposing that electrons (and particles smaller than them) move
randomly, we should rather see their position, trajectory, and velocity as
probabilistic characteristics. From the previous argument we know that
they all have a definite position, trajectory, and speed, but given the
tools at our disposal we cannot ascertain them directly. We have to deduce
how probable it is for an electron to have values for these three
attributes, given the macro- level manifestations of the atom at large, but
rest assured they are in no way random.
References
- http://en.wikipedia.org/wiki/Electron_cloud 2 November 2008
- http://en.wikipedia.org/wiki/Electron 2 November 2008