Grice's Nostalgia of the Stars -- the infinity between physics and metaphysics

^Speranza

"Physics is too complex for physicists" -- Griceian graffito.


In physics, approximations of real numbers are used for continuous measurements and natural numbers are used for discrete measurements (i.e. counting).

It is therefore assumed by physicists that no measurable quantity could have an infinite value, for instance by taking an infinite value in an extended real number system, or by requiring the counting of an infinite number of events.

It is for example presumed impossible for any body to have infinite mass or infinite energy.

Concepts of infinite things such as an infinite plane wave exist, but there are no experimental means to generate them.

 

The practice of refusing infinite values for measurable quantities does not come from a priori or ideological motivations, but rather from more methodological and pragmatic motivations.

One of the needs of any physical and scientific theory is to give usable formulas that correspond to or at least approximate reality.

As an example if any object of infinite gravitational mass were to exist, any usage of the formula to calculate the gravitational force would lead to an infinite result, which would be of no benefit since the result would be always the same regardless of the position and the mass of the other object.

 The formula would be useful neither to compute the force between two objects of finite mass nor to compute their motions.

If an infinite mass object were to exist, any object of finite mass would be attracted with infinite force (and hence acceleration) by the infinite mass object, which is not what we can observe in reality.

Sometimes infinite result of a physical quantity may mean that the theory being used to compute the result may be approaching the point where it fails.

This may help to indicate the limitations of a theory.

This point of view does not mean that infinity cannot be used in physics.

For convenience's sake, calculations, equations, theories and approximations often use infinite series, unbounded functions, etc., and may involve infinite quantities.

Physicists however require that the end result be physically meaningful.

In quantum field theory infinities arise which need to be interpreted in such a way as to lead to a physically meaningful result, a process called renormalization.

However, there are some theoretical circumstances where the end result is infinity.

One example is the singularity in the description of black holes.

Some solutions of the equations of the general theory of relativity allow for finite mass distributions of zero size, and thus infinite density.

This is an example of what is called a mathematical singularity, or a point where a physical theory breaks down.

This does not necessarily mean that physical infinities exist.

It may mean simply that the theory is incapable of describing the situation properly.

Two other examples occur in inverse-square force laws of the gravitational force equation of Newtonian gravity and Coulomb's law of electrostatics.

At r=0 these equations evaluate to infinities.