A Close Shave for a Mediaeval Monk

William of OccamThe tiny village of Ockham is located about 7 miles north east of the Guildford in southern England. Its history is largely agricultural and it currently boasts a population of just under 400, probably not much different to the Ockham of the middle ages when Ockham was home to its most famous son, William of Occam (mediaeval spelling was a bit of a hit and miss affair).

We know little of his early life, but William was born in Ockham around 1287 or 1288.  He was educated by the Greyfriars, the Franciscans, probably in London.  When he was 23 around 1310 he began his theological training and by 1318 we can place him in Oxford where he began a two year course of study there.  He never completed the course and because of this he acquired the name Veneralbilis Inceptor, or Worthy Beginner, but was also later known by the name Doctor Invincibilis, the Invincible Teacher.  Despite his never having completed his formal training, William was nevertheless heavily involved in the intellectual debates of the times.

His views proved controversial and he was summoned in 1323 first to Bristol to defend them.  News of William’s beliefs spread and eventually reached the pope, John XXII, who at the time was in exile from Rome and living in Avignon.  William was subsequently summoned to Avignon in May 1324 to appear before the pope to answer these charges.  While in Avignon William was effectively under house arrest, required to be on hand should the need arise to answer questions. Nevertheless after a protracted period of investigation he was effectively cleared of all charges.

This was a time of religious turmoil and at the time there was a conflict between the pope, John XXII and the Franciscan order which centred on the idea of “Apostolic Poverty”.  William was asked to adjudicate on the matter on behalf of his order.  He eventually came down on the side of the Franciscans, declaring the pope guilty of  seventy errors and seven heresies, in effect declaring that John XXII’s position as pope was illegitimate and that he was not entitled to call himself pope.  Not surprisingly the John XXII was not best pleased with this verdict.

Fearing for his life, William and a group of fellow Franciscans, stole some horses and fled Avignon, initially for Italy and eventually to Munich in Germany where they sought sanctuary under the protection of Louis of Bavaria.  William was to spend the rest of his life in Munich and died there in 1347 aged sixty.

William’s ideas on human freedom and on the nature of reality greatly influenced the political thinker Thomas Hobbes and helped fuel the Reformation.  You cannot fail to admire someone who during his turbulent career managed to offend the Chancellor of Oxford University, disagree with his own ecclesiastical order and get himself excommunicated by the Pope.

Among his many writings, William was the first person to advocate the separation of church and state, pre-dating the authors of both French and US constitutions by over four centuries. He also recognised the position of the governed and declared that the authority of rulers derives from the people they govern.  He is however best remembered for the Principle of Parsimony. Although he did not originate the idea, he was a firm proponent and so it has come to bear his name – “Occam’s Razor”.  The term “Occam’s razor” first appeared in 1852 in the works of Sir William Hamilton (1788–1856), centuries after William’s death.  William did not invent this “razor”; its association with him is due to the frequency and effectiveness with which he used it. William stated the principle in various different ways, but in essence it holds that the explanation for a phenomenon which makes the fewest assumptions is most likely to be the correct explanation.  The Razor is not a law, it is a principle, and this means that is not always going to be the case that the simplest explanation is correct.  It deals with the probability or likelihood that an explanation is correct.

The razor underpins much of the scientific developments which took place during the Reformation and the Age of Enlightenment.  Both Newton and Einstein recognised the importance of the razor as a scientific principle, to quote Isaac Newton, “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Therefore, to the same natural effects we must, so far as possible, assign the same causes.”   And Einstein:  “It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience”. Which is frequently paraphrased as: “Everything should be kept as simple as possible, but no simpler.”

The importance of Occam’s razor in formulating scientific thought is difficult to under estimate and it is especially relevant here.

Modern quantum theory and the so called standard model can trace as their theoretical basis the idea that angular momentum is quantized.  This idea underpins the theories of Bohr, de Broglie, Schrödinger and wittingly or unwittingly all of the contributors to the standard model.  In Quantization of Angular Momentum I explore some of the difficulties that this idea entails.

The problem arises because in order for angular momentum to be quantized all three of its constituent variables, the orbital radius, the mass and the orbital velocity must somehow be interconnected with one another in just such a way that angular momentum can only take on certain values.  The constituent variables must somehow each be discrete in nature and this must be in such a way that they interrelate with one another to produce the correct value for angular momentum.  The mass term itself violates this rule, since it is subject to the effects of special relativity and so there must be some other compensating value which offsets this effect.  The radius must somehow ‘know’ the value of the velocity in order that it can follow a sequence of values related to the square of the energy level and finally the velocity must vary as the reciprocal of the energy level.

Compare this to the situation that I advocate in A Mechanistic Model for the Hydrogen Atom.  Here the energy level follows a series of discrete values as a consequence of the value of Gamma (the Lorentz factor) being quantized.  Unlike angular momentum there is a clear and simple mechanism that brings this about.  Equally important Gamma is a function of just one variable, the orbital speed of the electron, and so there is no need for the complex interplay of values that quantization of angular momentum invokes.

A Mechanistic Model for the Hydrogen Atom is based on just one simple assumption, that certain velocity terms can themselves be considered as being affected by special relativity when dealing with matters relating to orbital velocity.  In Relativity and Angular Momentum I explore this idea in more detail, deriving the formula for centripetal and centrifugal forces from first principles.

Having made this simple assumption then it follows that the laws of physics remain the same independent of scale and that the electron is an objectively real particle, having both deterministic position and deterministic velocity.  Heisenberg’s uncertainty is relegated to be a practical issue concerned with measurement when the measurement tool is of the same order of magnitude as the object being measured.  The wave nature of the particle is simply related to the orbital path of such an objectively real particle and Schrödinger’s cat is as dead as a doornail.

Quantum theory on the other hand is forced to introduce a whole raft of absurd (I use the word in its literal sense) assumptions.  Particles are no longer objectively real, somehow the observer plays a role in determining the nature of the particle.  Particles somehow hover between the state of a particle and that of a wave, a wave that somehow manages to exist in an environment which has no structure and is therefore not capable of supporting a wave.

Credibility is stretched even further when it becomes apparent that particles can only ever be described in terms of mathematical functions and not in terms of physical entities.  Particles are seen as probability density functions rather than physical entities.  They somehow possess energy but this is expressed in ways that are not defined. They do not have deterministic position or velocity, unless one of these parameters is sought by an observer, at which point they somehow collapse to obtain one or the other.  Heisenberg’s uncertainty thus somehow becomes an intrinsic property of the particle in ways that are never fully explained.  And the laws of physics have to operate in different ways when considering the dynamics of the atom, although this cannot be a function of scale alone, since it is only for energy levels 2 and above that these strange behaviours apply and at these energy levels the atom is bigger than it is in the base energy state where they do not need to apply.  In the end all of these weird properties and phenomena have to be accepted as articles of faith, in effect they themselves become assumptions about the nature of reality.

So on the one hand we have just one simple assumption concerning the way in which orbital velocity is measured and takes effect when close to the speed of light, while on the other hand we have a whole set of complex, difficult to grasp concepts which must exist for the model to work.  There is little doubt as to which side Occam would take.

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