Idealism: The Bridge Between Science and Religion Episode 3: The Field


During lecture entitled discourses on
molecules given in Bradford at St. George’s Hall in 1873 James Clerk
Maxwell launched into a politely veiled critique of Darwin’s theory of evolution.
“In the heavens we discover by their light and by their light alone stars so
distant from each other that no material thing can have passed from one to the
other and yet this light which is to us the sole evidence of the existence of
these distant worlds tell us also that each of them is built up of molecules of
the same kinds as those which we find on earth. A molecule of hydrogen for example
whether in Sirius or an Arcturus executes its vibrations in precisely the
same time. Each molecule therefore through the universe bears impressed on it the stamp of a metric system as distinctly as does the metre in the
archives at Paris or the double royal cubit in the temple of Karnak. No theory
of evolution can be formed to account for the similarity of molecules, for
evolution necessarily implies continuous change and the molecule is incapable of
growth or decay, of generation or destruction. None of the processes of
Nature since the time when nature began have produced the slightest difference
in the properties of any molecule. Science is incompetent to reason upon
the creation of matter itself out of nothing. We have reached the utmost limit
of our thinking faculties when we have admitted that because matter cannot be
eternal and self existent it must have been created. It is only when we
contemplate not matter in itself but the form in which it actually exists
that our minds find something on which it can lay hold.” As a devout Christian
Maxwell was troubled and rejected the far-reaching implications of Darwin’s
theory of evolution, namely that the laws of nature could somehow organize itself
into the observed structure and complexity of the universe without the
apparent need for a deity. He saw the irreducible and consistent form of
molecules and atoms as indicative of a creator, since to him at the time there
was no understood mechanism for these forms to arise. Ironically a few years
later scientists would actually perform what Maxwell claimed was impossible, to
show how matter can arise from a theory of fields based upon the developments
which he himself pioneered. Yet I think on a more abstract level there is some
merit to his analysis. While physicists can effectively describe how fields give
rise to quarks, electrons and all the fundamental units that matter, the fact
that the laws of nature give rise to such uniformity of form on the smallest
level or even the fact that these laws are comprehensible is an interesting and
profound point which many have wondered at. In 1960 physicist Eugene Wigner
penned an article entitled “The Unreasonable Effectiveness of
Mathematics in Natural Sciences”. In this article he was expressing the
core of the sentiment that had been bubbling up even before the birth of
quantum mechanics. That is how mathematics developed to describe one
type of physical phenomenon can be so easily used to explain other phenomenon
which had little to do with the original? Of course from an idealistic point of
view this would seem natural since the rise of mathematics provided a manner to
represent platonic forms in better and better ways. So for example while a
perfect circle or other geometric shapes can be represented using a simple
formula, more complex platonic forms or ideas began to become possible to be
represented using more and more complex forms of mathematics. Over the time
mathematicians have learned to express ideas as abstract as different sorts of
infinities, sets or classes of motion. In fact one might view mathematics in
general as developing a means to unambiguously represent the platonic
forms of the universe. I think it is due to this fact that some theoretical
physicists, in an apparent return to Pythagorean philosophy, entertain a much
more radical view of math, that it somehow represents the true nature of
reality. Thus the physical universe is not just
described by mathematics but is mathematics. This view was given particular force
with the introduction of the quantum wave equation by Schrodinger and the
matrix representation by Heisenberg in the mid-20s. The wave equation was
introduced to describe the trajectories and behavior of subatomic particles like
electrons. Without it the behavior of electrons in the atom or diffracting
through a double slit made no sense. But the new wave function presented a
problem it was explicitly non-physical, because it was in mathematical terms an
imaginary or complex valued object. Additionally when evaluated to generate
measurable quantities, it operated in a probabilistic manner. With Paul Dirac’s
incorporation of special relativity into the framework of quantum mechanics, the
new field theory approach was developed to account for more than a single
species of particle. However with quantum field theory, a
radical new view of the concept of a field emerged. In many physical theories
there exists a concept of a field. The idea of the field originally was
imagined to have a physical basis, for example the magnetic and electric fields
were conceived to arise from a physical medium called ether. The gravitational
field, when it was first described by Newton required action at a distance. It
was for this reason that Newton believed it was profoundly flawed. It was only
with Einstein that the modern view of a gravitational field, described as a
product of a medium of curved space-time emerged.
As we will discuss in much more detail later, with the advent of quantum
mechanics the concept of a field transcended the need for physical medium,
mind you a medium still exists, but it was explicitly non-physical an abstract
mathematical function that permeates all space. This new abstract understanding of
the field is a large reason why Plato’s idealism appears to fit well in modern
physics. But this was not always so and even today this fact seems lost in
the popular understandings of the subject. I think it’s safe to say that
the birth of the concept of the modern field began with James clerk Maxwell’s
derivation of the equations for electromagnetism between the years 1862
to 1864. Maxwell came up with a theoretical
framework which united the electric and magnetic fields showing that light was
basically a type of wave propagating in the electromagnetic field. He
demonstrated this by calculating the speed of a traveling wave in his theory,
showing that it was the same speed as what had been measured for light. The
field or medium which light propagated in was termed ether, because since Thomas Young’s double-slit experiment around the Year 1800, it had been understood
that light behaved as a wave and the different colors of light represented
different wavelengths. This double slit experiment which demonstrated lights
diffraction, later would be applied to electrons representing a very important
experiment validating quantum mechanics. There was however one odd thing about
his theory. While it united the electric and
magnetic field into one field there was a strange thing about how relative
motion was handled. Since Galileo, it was understood that fixed relative motion
shouldn’t affect the behavior of the laws of physics. So for example if I was
on a train traveling at a constant high velocity relative to the earth and threw
a ball, the trajectories and behavior of it relative to me and everything on the
train would be the same as if I was standing on the earth not moving. Further
if I observe this event outside the train, stationary relative to the earth,
I would see the same physics only with the trains velocity added to all the
objects on the train. This idea is encapsulated by saying that the laws of
physics are invariant or the same for different inertial or non accelerating
frames. In Maxwell’s theory the force on a charged particle generated by moving
magnetic field was treated as arising from a different source depending on the
relative motion of the magnetic field. This is despite the fact that in both
cases the strength of the force from the resultant field is the same. So for
example if one waves a loop of wire across a magnetic bar a force is created
in the wire that can push on the electrons in the wire via the Lorentz
force law part of Maxwell’s equations, however if instead I keep the loop
stationary and wave the magnetic bar to generate the exact same relative motion
the change in magnetic flux creates the force due to Faraday’s law part of
Maxwell’s equations. That these forces are equal is in part due to the constant
speed of a wave propagating in the electromagnetic field regardless of the
relative velocity of the frame of reference.
That is the speed of light must be independent of the inertial frame. While
there is some indication that Maxwell may have recognized this fact, that the
speed of light was constant, it wasn’t until Einstein that the
constancy of the speed of light was stated and used to build up the special
theory of relativity. The constancy of the speed of light explained the failure
of the famous Michelson–Morley experiment to measure the effect of
relative motion on the speed of light. It also suggested a startling fact that
there was no physical ether, that these electromagnetic waves were waving in a
non-physical medium. With Einstein’s special theory of relativity, several
other important physical consequences were shown to follow. The constancy of
the speed of light meant that no matter how fast or slow one was moving the
measured speed of light would be the same. Normally when calculating the speed of an object in a moving frame of reference one can simply add the
velocity of the frame to the velocity of the object relative to the frame. For
example a ball thrown on a train with a velocity V would if looked at from a
person stationary on earth travel with a velocity of V plus the speed of the
train. This addition of velocities didn’t work for light. The profound consequences of this required that both time length and mass
would be modified based on the velocity of the frame of reference which one
inhabits. The idea that space-time and mass could change depending on which
inertial frame of reference it is observed in also demonstrated that mass
was actually another form of energy and years later with general relativity led
to a new understanding of gravity as due to the distortion of space and time
caused by mass and energy. Einstein went on to cause more problems for the
standard understanding of light as waves of ether. He later explained a phenomenon
known as the photoelectric effect, where when light above a certain frequency was
shined on a material it would suddenly start emitting charged particles. He
explained this effect by arguing that at the smallest level light behaves not as
a wave but as a particle with the energy and momentum of the light parceled up
into quanta of light called a photon. Later this quantum like absorption and
emission was used successfully by Niels Bohr to model how an electron in a
hydrogen atom absorbed and emitted light only now it was the electrons orbit
about the nucleus which jumped quanta like from higher to lower orbits. These
orbits were related to its energy, but the strange thing was that these
orbiting distances were discrete and well defined. In fact the whole idea of an electron orbiting moon like about the nucleus had
a well-known and serious physical problem, since Maxwell’s equations tell
us that charged particles when accelerating, which happens when
something orbits another thing, will give off electromagnetic radiation or light.
That any electron actually orbiting a nucleus in this manner would radiate all
its energy away and collapse into the nucleus, this fact was well understood
ever since the planetary model of the atom was proposed yet it’s solution had
remained a mystery. It was the French physicist Louie de Broglie who proposed
a radical new idea, that electrons actually behaved like a wave. This
proposal as strange as it seemed resolved all the problems with the Bohr
atom. The electron was behaving like a spherical standing wave with the
discrete energy levels due to the different oscillating modes permitted by
this system. Just like a guitar string can only vibrate at certain modes.
Another bizarre thing was that when Schrodinger worked out the mathematical
form which these waves must take it turned out that they were not physical,
since as mentioned before, it was in mathematical terms an imaginary or
complex valued object. The fact that electrons can behave like
waves was also shown using a similar double slit experiment as Young had used
to prove light was a wave, only now instead of light a beam of electrons hit
a screen containing two slits and a second screen which registered the
distribution of electrons which pass through these slits. In the case that the
electrons would behave like normal particles, then two clear bands should
appear on the second screen which correspond to the two slits in the first
screen. If the electrons would behave like waves then one will see a series of
high and low intensity bands appear across the whole width of the second
screen. These series of bands are due to the waves interfering with each other
and themselves or diffracting. Interestingly this is true even if just
a single solitary electron were to be shot at the double slit. So in reality
the electron behaving as a wave traverses both slits at the same time. It
exists in two locations at once. This ability to exist in two locations at
once is also known as the quantum mechanical property of superposition. As
we will learn later superposition can exist for many other physical properties
outside of just position. The debate over what this quantum mechanical wave
function represented physically was somewhat resolved by 1927 with the
so-called Copenhagen interpretation. At the heart of this view is Max Born’s
thesis that the wave function is simply a mathematical object which can yield a
probability density function. Thus it has no physical meaning outside of the
statistics and its ability to predict a particles behavior. Needless to say
physicists hated this interpretation though it has become increasingly
accepted in the ensuing 80 years. Initially many clung to the belief that
the wave function was masking some other local physics that we just couldn’t
measure. These were known as the hidden variable theories. To support this thesis
physicists Albert Einstein, Boris Podolsky and Nathan Rosen and others
came up with a thought experiment now known as the famous EPR paradox to
expose what was considered an absurd consequence of quantum mechanics, the
fact that two particles after interacting and becoming ‘entangled’
quantum mechanically could affect the state of each other after being
separated by great distance. However this phenomenon which Einstein
derisively called ‘spooky action at a distance’ was subsequently demonstrated
through many experiments and the notion of quantum entanglement is now not only
accepted but used to develop new technologies. In 1964 John Bell put
forward his famous theorem which states no physical theory of local hidden
variables can ever reproduce all of the predictions of quantum mechanics. He
further proposed an approach to test the validity of this theorem by measuring
the occurrences of correlations between measured states of particles which were
quantum mechanically entangled. Experiments testing bells inequality in
1972, 1981 and more recently 2015 have so far laid to rest any
theory of local hidden variables. It was actually Heisenberg himself who grasped
the connection between quantum mechanics and the Platonic viewpoint regarding the
essence of reality. ” I think that modern physics has definitely decided in favor
of Plato. In fact the smallest units of matter are not physical objects in the
ordinary sense. They are forms, ideas which can be expressed unambiguously
only in mathematical language.” There are several important aspects of quantum mechanics that lend themselves to the Platonic interpretation. The first is a
clear separation between the object measured and the mathematical form which
gives rise to the object, to use the cave allegory the shadow and the object
casting it. Then there is as Heisenberg acknowledged, the fact that the units of
matter are not physical objects in the ordinary sense. There is also additional
subtle evidence for the correctness of Plato’s views which flows from the fact
that the fundamental physical interactions are governed by probability
and not pure determinism. If we accept the assumption that the universe is
either spatially infinite or eternal, assuming a finite different scale, the
logical consequence is that all forms are eternal, because probabilistic physics operating over any kind of infinity will ‘most surely’ yield all outcomes that have a nonzero probability of occurring even if
that probability is infinitesimally small. This means in a universe with infinite
space all these forms must exist with an infinite number of occurrences and even
if the universe is eternal all these forms would occur an infinite
number of times. In fact the only escape from an infinite multiplicity of
identities is offered by the idea of a unique human soul. Either way death and
decay would seem to be an illusion a simple product of our limited sampling.
It’s safe to say that we are currently in the midst of a mini renaissance in
our understanding of questions related to the fundamental nature of quantum
mechanics. I believe this has in part been fueled by the recent drive to
develop quantum computing, which at some level has forced applied and theoretical
physicists to try and resolve these outstanding issues. Additionally in
recent years there have been some profoundly interesting and exciting
theoretical developments in string theory and the decades-long quest to
understand how gravity might arise within the framework of quantum field
theory. These ideas suggest that the very construction of space-time is a product
of quantum entanglement or quantum correlations, here the quantum
entanglement structure which builds up space-time retains quantum information
about the whole system on the boundaries. Thus the very construction of space-time
in this model represents a type of error correcting code. The upshot of all these
new understandings is that fundamentally relational information may not only
underlie matter but also the very structure of space and time which we
inhabit.

1 thought on “Idealism: The Bridge Between Science and Religion Episode 3: The Field

  1. Excellent job!
    I highly recommend listening to this lecture series called Science Wars-What Scientists Know and How They Know It:
    https://www.dropbox.com/sh/u5j4xc4pudf1r7o/AABy7NMLtawwyiVsyaIJqZGma?dl=0

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