The Role of Mathematics in Science
David W. Talmage
It is impossible to question the fact that mathematics has been very useful to science. One needs only to consider the accuracy with which eclipses of the sun or moon can be predicted. Or the exactness with which space vehicles can be launched and landed. Even in biology where there is a great deal of variability between subjects, mathematics can calculate the probability of causal association. So what is the problem?
The problem is that mathematics is often used as a substitute for reality, the search for which is the goal of all science. Mathematics is excellent as a tool to describe reality, but mathematics alone cannot find reality. Ptolemy thought that by the use of geometry alone he could explain the movements of the sun, the moon and the planets. He was very clever with his epicycles but he was wrong. Copernicus destroyed Ptolemy’s view of reality, not with mathematics, but with a few simple observations. One was Columbus’ dramatic demonstration of the old idea that the earth was a sphere. You could reach the Indies by sailing West. Copernicus was 19 years old at the time (1492). The other observation Copernicus made himself. He noted that if a star was rising in the East at the same time another star was setting in the West, then 12 hours later the opposite would be true. From this he concluded that the stars were very far away, too far to circle the earth in 24 hours. The most important conclusion Copernicus came to was, when writing of the movement of the stars, “The appearance is in the heavens but the reality is in the earth.”
Thus began modern sciences’s search for reality. But how far have we strayed? Einstein spent the last thirty years of his life searching for the equation that would unify all the fundamental forces. And now there is the String Theory. Like Ptolomy’s epicycles the String Theory is a pure invention of the human mind. Beautiful though it may be, it replaces Ptolomy’s epicycles with rolled up dimensions for which there is not a single piece of observational evidence.
General Relativity (GR) and Quantum Mechanics (QM) are a different matter. Supporting both of them there is a great deal of observational evidence but no single view of reality to unify them. Could it be that almost all the attempts to unify them have been mathematical? For example, according to GR the gravitational field is a curvature of space-time, but with QM it is a gradient of virtual particles called gravitons.
My attempt to unify Relativity and Quantum Mechanics has started with several observations, which though very strange, have been confirmed by numerous observers and are widely accepted. One of these is the observation that there are only two stable matter particles in the universe, although there are hundreds of unstable particles. Even stranger is the fact that one of the stable particles, the proton, is approximately 1836 times more massive (more energy content) than the other particle, the electron. Both particles are electrically charged but in opposite directions. And every electron behaves exactly like every other electron under the same conditions. The same is true with all protons.
Particles of free energy, photons, are different. Although they all travel at the same speed under similar conditions, they can have widely different amounts of energy. And they respond to forces such as gravity in a different way than matter particles. The elusive neutrino is difficult to place. Is it a photon or a matter particle? Unlike matter particles neutrinos exist with many different energies. They all travel at the same speed which is equal or nearly equal to the speed of light. It is not known whether they respond to the gravitational force that attracts all matter particles.
From the above information about matter and free energy I have built the attached theory, called the Particle Energy Requirement Force Theory or PERFecT.