The Summer Hill Journal Of New Physics

Field Theories and Point Particles

Field Theory

We can make some predictions for zero in field theories when viewed as null.

Let us review our earlier Principle #2 when using zero as { }:

Dimensionless points are purely imaginary and can play no part as quantities in the mathematics of physics.

We could also say "a circle with a radius of zero is not a circle - it isn't anything".

Taking this a step further, if dimensionless points are actually prohibited from physics then any attempt to use them would produce unreliable results and, when zero is viewed as { 0 }, Type 2 infinities result whenever division is attempted.

For example, we calculate the mass of a charged particle to include the mass-energy in its electrostatic field. If we assume that the particle is a charged spherical shell and use the conventional { 0 } view of zero, the energy in the field is infinite if the radius is zero. The null view instead predicts that the density is nothing if the radius is zero, i.e.it is simply outside the scope of the calculation as there is no volume.

Black Holes and Infinite Density

Density = Mass / Volume

When viewing zero as null, then spaces of (Type 2) infinite density are impossible. Either matter cannot be squeezed to zero size or else it ceases to exist when you do. Zero volume would mean zero density.

This is another Type 2 Infinity, division by zero. That is not to say you cannot have Type 1 infinities - ever increasing or decreasing quantities, just that division by zero is meaningless.

This also applies to other singularities such as the "Big Bang". If zero is treated as null, then zero space-time does not equal infinite density - it equals no density at all.

Stated another way, the reason we find infinities using { 0 } is because we put them there ourselves with the assumption that 1/0 = Infinity.

"We do not divide by zero" - Gottfried Leibnitz (1646 - 1716)

Other Cases

It is not the purpose of this article to catalogue the various types of infinities and zeros in all theories. There are many types of infinities and many uses of zero. However, when treating zero as null, we can apply the Principles #1 and #2 and come to these general interpretations:

(a) Type 2 infinities (1 / 0) are actually nulls.

(b) Imaginary points can play no part in the mathematics. If non-null results are required, then a non-zero point size must be used.

Quantum field theory is an example where these may be applied. It routinely assumes the existence of zero-dimensional objects and is plagued by infinities and the need for "renormalisation" to remove them.

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