Why do we live in three dimensions

Basics of physics: why does space have exactly three dimensions?

Space-time, as physicists have understood since Albert Einstein at the latest, consists of the three dimensions of space and the fourth dimension, time. It has long been known for the time dimension that its properties, such as the unambiguous, irreversible direction in which time runs, can be justified with the second law of thermodynamics. According to this, the entropy never decreases in a closed system. Entropy can be understood as a measure of the number of possible states of a system and therefore also, in simplified form, as a measure of the order of a system. So order does not come about by itself. Time flows in the direction in which disorder increases. Researchers led by Julian Gonzalez-Ayala from the Universidad de Salamanca in Spain have now tried to find the reason for the three spatial dimensions in the second law of thermodynamics. The central concept of their work is the so-called »free energy« F, also known as Helmholtz energy.

If you look at a universe completely filled with radiation - as it probably actually existed shortly after the Big Bang - the density of this free energy can be understood as a pressure that acts on the entire space. This free energy density depends on the temperature and the number of spatial dimensions of the universe. According to the researchers' calculations, it reached a maximum just a few fractions of a second after the Big Bang - a point in time when the temperature of the universe was still very high. In this state it was about three dimensions in space. Since, according to the second law of thermodynamics, the number of spatial dimensions can only change beyond this temperature-dependent maximum, but the universe cools down steadily as it expands, the number of spatial dimensions has been "frozen" since the maximum was reached. "This is the first time that the number 3 for the spatial dimensions has resulted from the optimization of a physical quantity," claims Gonzalez-Ayala in relation to the website phys.org. He and his colleagues now want to further refine their model by including quantum effects.

This article is contained in Spectrum Compact, Thermodynamics - Of Order and Disorder