Forces in Spacetime
Spacetime Density and Emergent Forces
In Part 1, several figures illustrate the geodesics of spacetime. These geodesics may be either straight or curved, depending on the proximity of a closed volume. As a result, the density of spacetime is not uniform throughout the universe.
These variations in density give rise to forces within spacetime. A similar phenomenon occurs in our everyday lives: for instance, differences in atmospheric pressure can generate wind, which is a force. On weather maps, these pressure differences are represented by lines that resemble the geodesics of spacetime.
This chapter therefore explores the forces that emerge in spacetime due to its density variations.
For now, we will simply seek to understand how forces manifest within spacetime.
Principle of Least Action
Since 1744, Maupertuis' principle has stated that nature always tends toward the least amount of action. Translated into the language of spacetime, this implies:
Spacetime naturally tends
toward the least action
Principle of Least density
The principle of least action can be reformulated in terms of density. Given that the overall density of spacetime in the universe is neutral, polarized zones of spacetime tend to return to a state of neutral density.
In this website, we adopt the convention that:
- High spacetime density corresponds to positive polarity,
- Low spacetime density corresponds to negative polarity.
Spacetime naturally tends
toward a neutral density
Waves in Spacetime
The figure below shows an electromagnetic wave on the left and its simplified mathematical expression on the right.
Annihilation
Let us consider the two wave regions labeled A and B on this web page. When brought into contact, one might intuitively expect these two parts of spacetime to annihilate each other. Specifically, the high-density zone A would cancel out the low-density zone B (see figure below).
On Earth, we observe similar phenomena in meteorology: high and low pressure systems tend to neutralize when they meet. The same applies to masses of hot and cold air.
This behavior can be shown to align with Maupertuis’ principle, adapted here to the context of spacetime. In fact, zones A and B must annihilate each other in order to produce even the slightest variation in spacetime density.
Attractive force
The figure below shows two zones of spacetime, A and B, with opposite densities. Zone A, characterized by high density, will be attracted to zone B, which has low-density — and vice versa.
The Maupertuis principle, as previously described, leads to the same conclusion when applied to spacetime: the force of attraction precedes annihilation.
Repulsive force
Similarly, two regions with the same polarity will tend to repel each other. This repulsive interaction is consistent with the principle of lower relative density, as previously discussed.
Fusion force
Fusion occurs when the energy of one region exceeds the potential barrier of another region with the same polarity. In this case, the repulsive force vanishes and is replaced by fusion. Physicists are well acquainted with this phenomenon — examples include ITER, NIF, and Tokamak reactors.
In the universe, spacetime is not uniform. Its density varies from one point to another, and these variations give rise to forces. Weather on Earth provides an example of such effects.
In this chapter, we have seen that forces emerge from differences in spacetime density. These forces include annihilation, attraction, repulsion, and fusion.
The following chapter will attempt to connect one of these forces to a familiar phenomenon. This will help us progress in our understanding of elementary particles.