## Summary

This is a curious essay that shows that crowding resulting from all mass 'exploding' would indeed be perceived as an attractive force by us observers within the system (see the animation below). As an auxiliary postulate, this essay points out that closure in the universe due to it being wrapped around on itself as a sort of hairy manifold Klein bottle would provide the necessary expansion for mass particles if the universe were expanding. The universe itself would then resemble a picture Einstein's head ;-)

## Paper

### Expanding Mass Observed as an Attractive Force of Gravity Postulate

#### by Tom Lynch, 1997 04 10, minor revisions 2011 02 15

This is one of those head scratchers I've been hoping to find more time to work on. This essay explains how observers in a system of expanding particles will view the particles as mysteriously attracting each other rather than seeing them as expanding.

### Given the following two postulates:

1. That each and every particle in the universe is expanding.
2. Without an external force, all particles remain on their current path, as described by Newton and Einstein (the mass/energy - space time interaction isn't modelled here).

It follows that we can not build a ruler that is also expanding. When using a ruler that is expanding at the same rate inertial particles are expanding, the net effect is that we observe using our expanding ruler that particles of constant size approach each other until they collide.

Consider the following analogy. Suppose that two balloons are placed above gas helium bottles and are being filled. So initially we have the following picture: Figure 1: Expansion level at time t0

I have added a ruler above the bottles. Each balloon measures one unit across on the ruler. The distance between the balloons is two units.

Now consider the picture at time t1 where the balloons and the ruler have doubled in size: Figure 2: Expansion level at time t1

The balloons used to measure one unit across on the ruler, and they still do because the ruler has expanded at the same rate. Note however, as the balloons have doubled in size, the distance between them is only ¼ of what it used to be. The distance between the balloons using our expanded ruler is now one half unit. The centers of the balloons have not moved.

Had we scaled the picture so that one unit on the ruler was a constant size on the paper, we would have witnessed that two balloons started two units apart, and they maintained their size but came closer together under some magical force of attraction.

The animation below shows the same system from two different points of view. In the top blue section the observer is outside the system. In the bottom red section the observer is in the system. The observer outside the system sees the balloons expand. The observer in the system sees them attract. In both cases the center points of the balloons remain fixed to the grid as there are no forces applied that would give them momentum.