Why is space three-dimensional?

This question of whether space is three-dimensional or if it has more dimensions have always challenged physicists from ancient times.

Time is considered many times as the fourth dimension along with the three that we live in.

The scientists 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.

In principle, it’s possible for the Universe to have many more space dimensions; some attempts to explain the fundamental forces ofnature assume no fewer than six extra ones. Yet for reasons still unclear, any additional dimensions that may have existed at the BigBang somehow failed to take part in the cosmic expansion and remained far smaller than the three dimensions we inhabit. What is certain isthat, had they grown in size, the Universe would be a very different place. Theoreticians have shown that any extra dimensions would make atoms unstable, while any fewer would eliminate the force of gravity. Max Tegmark, acosmologist at the Massachusetts Institute of Technology, has gone further, arguing that the very fact we exist to ask about extra dimensions of space proves they don’t exist.

Here is a paper by Ingemar Bengtsson. Take a look.

Paper by Ingemar Bengtsson

Check out this video on the 3 dimensions for easy understanding.

Thank You!

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