# 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.

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