Gravity

[PatrickPowers]

Ed Witten says the (approximate) 1/d^2 rule of gravity in general relativity comes directly out of there being three spatial dimensions. So we could expect in N D that the rule is 1/d^(N-1).

[New Kid on the 4D analog of a Block]

They were discussing this before, or sometimes just assuming it. In fact, you were involved in the first discussion, although it was five years ago.
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You made the interesting point that even in 3D, not all forces obey an inverse-power law.

[PatrickPowers]

That's true. But Ed Witten is the smartest man in the world so I pay attention to him.

[Vector_Graphics]

I personally use 1/d^2 even in 4D, just to make it so you can have orbits.

[Vector_Graphics]

??? Did my post go through? I personally use inverse square even in 4d to allow stable orbits to exist.

[PatrickPowers]

??? Did my post go through? I personally use inverse square even in 4d to allow stable orbits to exist.

So do I. The pedagogical value of a planet orbiting a sun in 4D is too high to pass up. But it appears the smart money says no dice.

[Vector_Graphics]

??? Did my post go through? I personally use inverse square even in 4d to allow stable orbits to exist.

So do I. The pedagogical value of a planet orbiting a sun in 4D is too high to pass up. But it appears the smart money says no dice.

I was honestly in disbelief at first when I saw that inverse cubic orbits were unstable. I just thought they would be a weird shape (while remaining periodic) but apparently they spiral. I thought maybe the app I was using was broken or something.

I do wonder if solar system formation would be affected in any way by the existence of double rotations.

[PatrickPowers]

I do wonder if solar system formation would be affected in any way by the existence of double rotations.

It might. I can imagine a solar system with two ecliptics at right angles to one another. Suppose you have two planets in perpendicular circular orbits. Then the force each planet exerts on the other is of constant magnitude. If you consider vectors instead, then the net force exerted over time could also be zero.

Even the stability of our own solar system is unproved over long periods of time. But a simulation of 4D orbits would be good enough for me. I think there is a good chance it would work.

Even more intriguing was a recent analysis of a star-black hole binary system that revealed that their rotational planes were at right angles to one another. That was the first such system ever studied so such might be common.