The question of why space is three-dimensional (3D) and not some other number of dimensions has puzzled philosophers and scientists since ancient Greece. Space-time overall is four-dimensional, or (3 + 1)-dimensional, where time is the fourth dimension. It's well-known that the time dimension is related to the second law of thermodynamics: time has one direction (forward) because entropy (a measure of disorder) never decreases in a closed system such as the universe. In a new paper published in EPL, researchers have proposed that the second law of thermodynamics may also explain why space is 3D. They propose that space is 3D because of a thermodynamic quantity called the Helmholtz free energy density. In a universe filled with radiation, this density can be thought of as a kind of pressure on all of space, which depends on the universe's temperature and its number of spatial dimensions. Here the researchers showed that, as the universe began cooling from the moment after the big bang, the Helmholtz density reached its first maximum value at a very high temperature corresponding to when the universe was just a fraction of a second old, and when the number of spatial dimensions was approximately three. The key idea is that 3D space was "frozen in" at this point when the Helmholtz density reached its first maximum value, prohibiting 3D space from transitioning to other dimensions. This is because the second law allows transitions to higher dimensions only when the temperature is above this critical value, not below it. Since the universe is continuously cooling down, the current temperature is far below the critical temperature needed to transition from 3D space to a higher-dimensional space. In this way, the researchers explain, spatial dimensions are loosely analogous to phases of matter, where transitioning to a different dimension resembles a phase transition such as melting ice—something that is possible only at high enough temperatures. http://phys.org/news/2016-05-space-three-dimensional.html Paper: http://iopscience.iop.org/article/10.1209/0295-5075/113/40006
Assuming that an open-ended number of dimensions can literally be realized in some manner other than a principle / formulaic approach -- or like instructions in a computer regulating the encountered, compromised appearances of higher dimensions on a screen. Even the so-called "four dimensionalism" of time (block-universe) has to be experienced as sequential "slices" rather than an "a-Ha!" empirically evident or shown circumstance which doesn't require recruiting abstract reasoning and thought experiments just to deal with the idea of more than three dimensions.
One wonders if this can be extrapolated in the other direction. In the far future, will our 3D universe degenerate to 2D? Then 1D?
