Thermodynamics and (3+1)-spacetime

On the riddle of (3 + 1)-spacetime

Recently, I have been pondering the puzzle of the (3 + 1)-dimensional spacetime that we observe in our Universe. I previously settled on a solution where the mathematics we know is constant, and even if all possible combinations of spacetime (X + Y) exist, only the (3 + 1) option can lead to the emergence of intelligent observers.

However, I admit that there are other possibilities. One elegant solution is linking the observation that (3 + 1)-dimensional spacetime has almost the minimal number of dimensions with various natural processes that minimize energy. There are many examples of these. Here are some of them:

1. Atoms form molecules by adopting configurations that minimize potential energy.

2. A soap bubble takes a shape that minimizes surface tension.

3. Electric charges arrange themselves to minimize the total potential energy of an electrostatic system.

4. Crystals adopt a lattice structure that represents a state of minimal energy.

Thus, physical systems tend to minimize energy. But how do we connect this observation with the number of spacetime dimensions? A possible mechanism was proposed in a paper titled “Is the (3 + 1)-d nature of the universe a thermodynamic necessity?¹”. The authors point out that spacetime is connected to thermodynamics through the arrow of time. Time has a designated direction—from past to future—because the laws of thermodynamics state that entropy in closed systems (almost) never decreases.

The authors of the paper propose the following scenario:

1. Initially, the Universe had only one spatial dimension. The Universe, according to the second law of thermodynamics, tends toward an increase in entropy.

2. This tendency to increase entropy causes the optimization of thermodynamic conditions (Helmholtz potential density), leading to an increase in the number of spatial dimensions—first to two, then to three.

3. When the Universe reaches three spatial dimensions, the Helmholtz potential density attains its optimal value. Three-dimensional space allows for stable, long-term energy dispersion and the development of complex structures.

4. The second law of thermodynamics acts as a barrier against further increases in the number of spatial dimensions, as it would be suboptimal from the perspective of entropy growth since unstable structures disperse energy less efficiently.

In this example, energy is more fundamental than spacetime and capable of modeling it according to its “needs,” which involve dispersing energy as efficiently as possible. In such a case, minimal spacetime would be a natural manifestation of the physical reality's tendency to optimize thermodynamic conditions to achieve a stable state.

Even if we accept this solution to the puzzle of the (3 + 1)-dimensional spacetime, it does not invalidate my previous conclusions. The mathematics and physical laws known to us would still be special for some reason. If it were otherwise, one could imagine infinitely many Universes that, with different physical laws, would optimize spacetime to (4 + 1), (5 + 1), (6 + 1)... (N + 1) spatial dimensions rather than (3 + 1). In such a case, it would be impossible to explain why we observe precisely (3 + 1) and not any other arbitrary number of dimensions.

Sponsored by: Wiadomości giełdowe GPW

1. [gr-qc/1502.01843v2] Is the (3 + 1) − d nature of the universe a thermodynamic necessity?