Implications of the orbits thread.

[PWrong]

In skimming through my physics text book, I realised how many things in 3D follow an inverse square law. Magnetic fields, electric fields, sound waves, light (when described as a wave, not a particle), gravity, and possibly friction all seem to follow it.

Clearly most of these will follow an inverse cube law in 4D. I'd like to discuss whether this will have disastrous effects on stability, just like gravity does.

The biggest problem is the electric field. In classical mechanics, electrons orbit the nucleus of an atom in a similar way to planets orbiting the sun. If the electric field obeyed an inverse cube law, the electrons would surely spiral inwards just like the planets.

I've heard that this happens before, but I didn't believe it until now. Isn't there any way around this? Can we still have a vaguely sensible 4D universe?

[jinydu]

Actually, from what I've learned in Physics class, its impossible for an electron to spiral inwards, or outwards for that matter. Electrons can only exist in discrete energy levels.

Any accelerating charged body is supposed to emit electromagnetic radiation, causing it to lose energy. In other words, the classical picture is unstable, even in 3D. My teacher said that the best way to think about why this doesn't happen to electrons is to think of them not as particles, but as stationary waves. Since the stationary wave isn't accelerating, they are stable.

None of that seems to make any reference to 3 dimensions. But then again, it was only a high school course.

[pat]

In classical mechanics, electrons orbit the nucleus of an atom in a similar way to planets orbiting the sun.

Yes, except for the fact that classical mechanics does a particularly poor job of describing electron orbits in three-dimensions, too. So, any problems with the classical mechanics model for four-dimensional atoms wouldn't cause me much fret.

I'll have to look into how Schroedinger's Wave Equation works out in more dimensions.

[PWrong]

Hmm. I guess we'll have to wait for that before we can understand 4D magnetism or anything. I've seen Schrodinger's equation, but I have no idea how it works. But, apart from particle physics, how could you have a universe with stable planet motion, despite the inverse cube law of gravity?

[jinydu]

Well, there may be several ways you could try to rescue 4D planetary orbits. Most of these ideas were already mentioned in the "Fourth Dimension Calculation" thread:

1) Try a system with more than 2 masses

2) Try setting up a system where it takes tens of billions of years, or more, for the unstable orbit to spiral inwards or escape.

3) See if General Relativity (GR) differs more significantly from Newtonian gravity than it does in 3D. If so, see if GR orbits are stable in 4D.

4) IF ALL ELSE FAILS: Adjust Newton's Second Law (but I really don't think you would want to resort to that).

[PWrong]

Yes, I mentioned them. I hoped there might be some others. This is just a guess, but I don't think any of us are qualified to investigate any of those, except 2 or 4, and they wouldn't really be satisfactory. The three body problem is still unsolved in 3D, and from what I've seen, the equations of general relativity are beyond anyone here.