◇ Why 3 + 1?
Change the number of space or time dimensions and something essential breaks. That tells us why we're here — not why 'here' exists.
Picturing other dimensions
We can't picture a fourth direction, but we can reason one dimension down: a flat creature sees a passing sphere as a circle that grows and shrinks. The same trick shows what a 4D object passing through our world would look like. Analogy (the story) · Established (the geometry).
More space dimensions
Gravity and electric force spread out through space, so in n dimensions they weaken as 1/rn−1. With four or more space dimensions, orbits and atoms have no stable states: planets spiral in or fly off, electrons fall into nuclei or escape (Ehrenfest, 1917, and later quantum versions). Established as mathematics.
Fewer space dimensions
In two space dimensions, gravity doesn't pull separated masses together in the ordinary way (2 + 1 gravity has no local degrees of freedom). Established Whether that makes complex structures and observers impossible is argued, not proved. Contested
More time dimensions
With two times, a complete snapshot of the present no longer fixes the future for general starting data (Craig & Weinstein, 2009), and particles could decay into heavier ones (Dorling, 1970). With no time at all, nothing evolves. Established as mathematics.
So why 3 + 1?
Tegmark (1997) drew these results into one map: only 3 + 1 allows observers like us. That's an anthropic explanation — it says why we find ourselves here, not why the universe had to be this way. Contested Theories with hidden extra dimensions (string theory, two-time physics) are Speculative. This is hole H5.
See it in the labs
Further exploring
- Einstein Online (Max Planck Institute for Gravitational Physics) ↗Short, authoritative articles on relativity, black holes and cosmology.
Sources: Tegmark, Class. Quantum Grav. 14 (1997); Ehrenfest (1917); Dorling, Am. J. Phys. 38 (1970); Craig & Weinstein, Proc. R. Soc. A 465 (2009); Deser, Jackiw & 't Hooft (1984); Abbott, Flatland (1884).