ken .. i mostly grok where you are going .... and yeah, i read flatland years ago ...
but here is a Q i have about the onespacers on the mobius strip ... tho the 'path' of their 1-d line stays on the strip, the strip exists in 3-space ... so the 1-landers would 'feel' the effects of gravity as their orientation meandered its way back to the starting point ... doesnt that perception of gravity give them more information?
same with a 1-lander living on the 'line' around the circumference of a sphere, right?
t4d
The problem I was turning over before you asked is if we take a 1-D universe and place it so that it intersects a gravitational field at some angle. Funny that we're thinking similarly.
If we orient their 1-space so that the gravitational force is perpendicular to the line of one-space, they will never experience gravity in their own world. Keep in mind that gravity is an "up/down" phenomenon and up and down do not exist in one-space (or two space for that matter). 1-space is infinitesimally thin, so it is impossible to compress (which is basically how we feel gravity on the surface of the Earth, we're compressed...if we're accelerating toward the Earth from above the surface (freefall), we don't feel our own weight...or gravity for that matter. It's just as appropriate to say the Earth is accelerating toward us as it is to say I am falling toward it.
So, for a one-space that exists perpendicular to a gravitational field, I say there is no effect because there is no compression, no perceived change in the 1-D universe.
The interesting thing happening with this in my head is if we tilt our 1-space such that it has some component in the same direction as the gravitational field. I
think what a one-spacer would experience here would be similar to the effects we see in General Relativity (Einstein's theory of gravity) in our own 3-space. The entire "space" of the line would be stretched in the areas feeling the influence of gravity, just as space gets stretched around a black hole (or any ultra massive object).
If we put ourselves immediately inside the field, we cannot feel its effects. But far enough away from it and we can. Perhaps the same thing would happen in one-space if it were subject to a 3-space gravitational field. whatever components of the two line up will tend to "stretch" the one-d space. And I suspect it would have the same redshifting effects that we see now. Time might appear to slow down as the field strength increases.
I guess this might be a "black line" in one-space, similar to how we have black holes in 3-space.
For a one-spacer on a line about a sphere, they would have no perception of the effect so far as I can think. There is no up down, only forward and back, and gravity does not have forward/back components, only up/down. Gravity will only stretch in the direction of the line, it is impossible to compress it. Because the field at the surface is always perpendicular (read: compressing) there should be no apparent effect.
So, your question is whether or not three-dimensional phenomena in one-space allow them access to information about 3-space. I'm not sure. My guy instinct is no, because the three-dimensional effects are going to manifest themselves in a manner that is still explainable in the physics of one-space. A black hole is completely explainable by the physics of our 3-space. That there is the possibility for it to be caused by events in the 4th dimension is not sufficient grounds to say that it IS caused by events in the 4th dimension.
Really, really interesting question, Bill. It's taken me quite a while to come up with what is hopefully a legible response.
What I've said here is what I can call, at best, educated conjecture. I know just enough to get it completely wrong. I'm very cautious about mis-educating people.
I may ask my professor about it in class tomorrow if there's time.
