Section 30

# Cosmological Difficulties Of Newton’s Theory

March 4, 2022

## Einstein (Universe has no center) vs Newton (Universe has a center)

The astronomer Seeliger explained a problem in classical celestial mechanics aside from the problem explained in Section 21.

How should we see the universe as a whole?

Regarding space and time, the universe is infinite. There are stars everywhere. So the density of matter, although very variable in detail, is nevertheless the same on the average everywhere.

Everywhere there is an attenuated swarm of stars of approximately the same kind and density.

This view does not match Newton’s theory which requires that=

• the universe have a centre where the density of the stars is at a maximum, and
• as we go outwards from this centre, the group-density of the stars should diminish, until there is only infinite emptiness

His idea is that the stellar universe is a finite island in the infinite ocean of space.

His idea is not very satisfactory. It is still less satisfactory because it leads to the result that starlight are perpetually going out into infinite space, never to return. Such a finite material universe would eventually be systematically impoverished.

## Proof Against Newton

According to Newton, the number of “lines of force” which come from infinity and terminate in a mass `m` is proportional to the mass `m`. If, on the average, the mass-density `ρ0` is constant throughout the universe, then a sphere of volume `V` will enclose the average mass `ρ0V`.

Thus, the number of lines of force passing through the surface `F` of the sphere into its interior is proportional to `ρ0V`. For unit area of the surface of the sphere, the number of lines of force which enters the sphere is thus proportional to `ρ0V` * or `ρ0R`.

Hence, the intensity of the field at the surface would ultimately become infinite with increasing radius `R` of the sphere, which is impossible.

To escape this dilemma, Seeliger suggested a modification of Newton’s law – for great distances, the gravity between two masses diminishes more rapidly than would result from the inverse square law.

In this way, the mean density of matter can be constant everywhere, even to infinity, without infinitely large gravitational fields being produced.

Thus, our universe having a center is impossible. However, this requires us to modify and complicate Newton’s law. Our modification has neither empirical nor theoretical foundation.