Questions About the Expansion of the Universe?
The observed accelerated expansion – a question of physics or of geometry?
When measuring the expansion rate of the universe, it was found that more distant galaxies are moving away from the Milky Way faster. From this, an accelerating expansion was inferred – usually explained by the so-called dark energy, which has, however, never been directly detected. The following summary of the three thought-experiment pages shows step by step that the apparent acceleration already follows from the geometry of any expansion.
1. The Line: Expansion Happens Everywhere Simultaneously
Hand analogy: If you spread the fingers of a hand, fingers located further outward move away from the little finger faster. The middle finger itself does not move – only the others move away from it. From the little finger's perspective, this cannot be noticed.
Rubber band: If a band with evenly spaced markings is stretched, all segments expand from the middle at the same rate. Each segment begins where the previous one ends – this creates the impression of an accelerating expansion, even though the stretching occurs uniformly everywhere.
Sample calculation (distances of 11 points from the left edge point, uniform stretching per step):
| Time | Point 1 | Point 2 | Point 3 | Point 6 (middle) | Point 9 | Point 11 |
|---|---|---|---|---|---|---|
| t₀ | 0 | 30 | 60 | 150 | 240 | 300 |
| t₁ | 0 | 36 | 72 | 180 | 288 | 360 |
| t₂ | 0 | 42 | 84 | 210 | 336 | 420 |
| t₃ | 0 | 48 | 96 | 240 | 384 | 480 |
| t₄ | 0 | 54 | 108 | 270 | 432 | 540 |
More distant points cover greater distances, even though all points move away from their neighbours at the same speed. The effect occurs with any positive expansion – even if the rate of expansion slows down.
The Circle: A Different Rule at the Circumference
For a circle, the radial distances follow the rule of the line, while the segments along the circumference grow according to (diameter × π) / number of segments. The point-to-point distances can be calculated using the law of sines:
The distances between the points therefore depend on the change in the circumference – a further indication that the apparent acceleration is produced by the geometry of the expansion.
2. The Area: Rules of the Line and the Circle Combined
Transferred to a two-dimensional surface, the following applies:
- For a circular area, the change in diameter is defined by the line rule, while the distances along the circumference follow the specific rules of the circle.
Interactive illustrations (circles with uniform and random point distributions) confirm: the findings regarding the line and the circle are correct – with a random point distribution, however, the effect is no longer immediately apparent.
3. The Sphere: Three-Dimensional Expansion
For a three-dimensional body, both rules must be taken into account in all spatial directions. Every point on the surface of a sphere moves away from the centre at the same speed – yet the distances on the surface do not grow linearly:
Summary: If the radius doubles, the surface area quadruples and the volume increases eightfold. The uniform expansion from the centre leads to a non-linear increase in the distances between the galaxies – without any additional energy being required.
4. Application to the Universe
The observed accelerated expansion of the universe would therefore not be evidence of dark energy, but rather a geometric necessity of any three-dimensional expansion.
Critical questions raised by the theory:
- Where is the centre of the universe?
- Why do we not observe a preferred direction?
- How does this align with the cosmological principle (homogeneity and isotropy)?
Analogy: On the surface of an inflating soap bubble, it appears – from the perspective of any given point – as if all other points were moving away from it, and the further away they are, the faster. There is no "centre" on the surface.
Conclusion: Geometry as the Explanation
The accelerated expansion of the universe may be less of a mystery of physics and rather a question of geometry:
The apparent acceleration is a fundamental property of any expansion – on the line, on the circular area, with the volume of the sphere, and thus in space as a whole.
Whether this theory can fully explain the observations must be verified through further calculations and comparisons with astronomical data. It does, however, offer an interesting approach that does without dark energy.