Finite Nature

Finite Nature[1] is the hypothesis that ultimately every quantity of physics, including space and time, will turn out to be discrete and finite; that the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities. We call models of physics that assume Finite Nature "Digital Mechanics". In Digital Mechanics[2], the basic element of physics is the cell and the rules. Things like particles are the consequence of stable patterns over a volume of space-time. The Finite Nature hypothesis makes no assumption about the scale of the quantization of space and time. Digital Mechanics is too immature a concept to say more about the scale of length other than it is probably around Planck's length, 1.6x10^-33cm. Some considerations make it hard to understand why the unit of length should be less than about 10^-17cm. The question can be settled by experimentally determining the value of the scale of length.

We simply do not yet know whether Finite Nature is true or false. Today, nearly every scientist in the world believes that there is insufficient experimental evidence in hand to decide the issue in favor of Finite Nature. The author, on the other hand, has managed to convince himself that the odds are greatly in favor of the Finite Nature Hypothesis. What has been decided up to now is that many things of our world that were once thought of as possibly continuous are now known to be discrete. The most famous is the atomic hypothesis. Dalton[3] wrote his papers in the early 19th century but as recently as 1900, a famous physicist (Ernst Mach) said that while there was evidence for the atomic theory, since no one had seen an atom and since no would ever see an atom, he was not convinced that the atomic theory was true. Times have changed and now we can see atoms with the scanning tunneling microscope. Now, we all ardently believe in the atomic theory.

The next to fall into the realm of the discrete was electricity. Originally thought of as a fluid, Thompson discovered the electron in 1897 and with it came the discovery that charge was a discrete or quantized phenomena. Einstein proposed that Planck's quanta of action could determine the relation between the energy and frequency of particles of light, which he called photons. Planck thought that Einstein was a very smart person in spite of Einstein's belief that light was made up of discrete particles! Today we all believe that photons are real and that light, electro-magnetic and other kinds of forces are made up of discrete particles.

As the consequences of the Quantum Theory became better understood, it became clear that the angular momentum of particles can only exist in multiples of 1/2 units of spin. This has the amazing consequence that a flywheel cannot have a continuous range of angular momenta, rather it must only have multiples of -1/2h. Angular momentum is now known to be discrete. The story goes on with phonons and vibrons as quantized units of sound and other forms of energy.

So far, there is no convincing argument based on experimental evidence that points to any quantity of physics as definitely continuous. What we can often say is "If it is discrete, then the quantization must take place below some level." It is difficult to even propose a test that could verify that some quantity of physics was indeed continuous.

Since we know of no verified continuous quantity in physics, and since there has been a steady historical progression of finding that more and more of the fundamental quantities of physics are discrete, it is perfectly reasonable to assume the possibility that all quantities of physics will prove to be discrete. What we shall reveal is the amazing consequences of such an assumption; consequences that are independent of the scale of the quantization!

 

[1] E. Fredkin, "Finite Nature" Proceedings of the XXVIIth Rencontre de Moriond (1992)

[2] E. Fredkin, "Digital Mechanics", Physica D, (1990) 254-270 North Holland

[3] J. Dalton, "New System of Chemical Philosophy" (part I, 1808; part II, 1810)