Further Questions About the Expansion of the Universe
Further Questions About the Expansion of the Universe
If we apply these considerations to a two-dimensional surface, we see that, in the case of a rectangular surface, the expansion in both directions follows the rules that apply to straight lines.
The purpose of the following simple visualisations is to examine how distances and areas behave when an expansion takes place simultaneously in several spatial directions.
Extension of a Rectangular Grid
As the rectangular surface expands, both dimensions increase according to the rules that apply to straight line segments.
Rectangular Surface
During the expansion, the area increases because both dimensions of the rectangular surface increase. Each individual grid cell is affected by the same expansion factor.
Circular Area with a Uniform Distribution of Points
In the case of a circular area, the change in diameter is defined by the rules governing a line segment, whilst distances along the circumference are governed by the specific properties of the circle.
Uniform Distribution of Points
Here the points are distributed regularly around several concentric circles. When the circles expand, the points remain at their corresponding angular positions.
Circular Expansion with a Random Distribution of Points
With a more complex distribution of points, the expansion effect is no longer immediately apparent.
Random Distribution of Points
The dots are randomly distributed here and are repositioned every time the page is refreshed.
Expansion in Three-Dimensional Space
In the case of a three-dimensional solid, both sets of rules must be taken into account in all spatial directions.
A simple two-dimensional example cannot reproduce the complete geometry of a three-dimensional expanding space. It can nevertheless illustrate an important principle: when expansion takes place simultaneously in several directions, distances, surfaces and volumes can change together.
The central question of this thought experiment:
If an expansion occurs everywhere and simultaneously, how should the resulting changes in measured distances and areas be interpreted by an observer located within the expanding space?
The simple examples above are intended as geometric thought experiments. They do not by themselves constitute a cosmological model. Their purpose is to examine whether apparently different expansion effects can arise naturally from the geometry of an expanding space.
Further Considerations
The simplified examples show that expansion can affect line segments, areas and volumes in systematically different ways.
In a rectangular surface, the expansion of the individual dimensions directly determines the increase of the area.
In a circular surface, the radial distances and the distances along the circumference must be considered together.
In a three-dimensional solid, the corresponding relationships extend into all three spatial directions.
These considerations raise further questions about whether some apparently accelerated effects of cosmic expansion could be related to the geometry of the expanding space itself.
The thought experiment is therefore continued on the following page.