If we were somehow able to see or experience the fourth spatial dimension, how would gravity act on us in there? Does the direction of the pull change? Will it have any effect on light or anything else?


closed as off-topic by Danu, yuggib, ACuriousMind, John Rennie, Waffle's Crazy Peanut May 31 '15 at 18:02

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    $\begingroup$ "If we were somehow able to see or experience the fourth spatial dimension"...that doesn't really make sense to me. $\endgroup$ – ACuriousMind May 31 '15 at 12:36

I'm not sure I can give a good answer, but the 4th dimension gets pretty weird and a few things would happen.

First, the direction of pull wouldn't change, it would be towards the massive object. There would be more directions to travel (up/down, back/forward, left/right and 4th-one way/4th-the other), but the pull would still be directly towards the object and any orbit would still be elliptical around the object.

The strength of gravitational pull would weaken by the cube of the distance, not the square of the distance, so gravitation would weaken over distance quite a bit faster.

There's a cool video that touches on what solar systems and galaxies would look like in 4D (the 4D part starts about 2 minutes in). https://www.youtube.com/watch?v=tmNXKqeUtJM

Also, in 4d, density could grow much faster cause there's more space, matter could pack more tightly (and I don't want to guess how the electron shells would be affected). But a cubic KM of water is 1 billion cubic meters, a bit over 1 billion tons. a quadric (not sure that's the right word), or a KM to the 4th, in 4 dimensions would be a trillion meters to the 4th, a thousand times as many. In theory, gravity would be much stronger close to a large object, but it would grow weaker faster. - this is, of-course, a pretty rough answer, as the 4th dimension doesn't exist in that sense, so it's only theoretical.

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    $\begingroup$ I gave you an upvote, but your statement about elliptical orbits in higher dimensions is not correct. According to Bertram's theorem en.wikipedia.org/wiki/Bertrand%27s_theorem only the harmonic oscillator and the 1/r potential (i.e. the Kepler problem in three dimensions) have closed orbits, so at the very least 4d planets would show strong perihelion shift and possible orbital instability. One can possibly extend this result to the non-existence of regular quantum mechanical solutions, i.e. the non-existence of 4d matter as we know it. $\endgroup$ – CuriousOne May 31 '15 at 14:55

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