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What would the horizon on an infinite flat surface look like?

Physics Asked by programical on May 1, 2021

When I look at the sea, which is somewhat flat, the horizon appears to be “higher” than in other cases. I know that I can’t see all the way to the other shore because of the earth’s shape. But what if it was flat, infinite and there was nothing to obstruct the view?

3 Answers

In theory you would see whatever is on the other side. It would be very small and anything at the same height as you would be level with you.

In practice it would appear very hazy because of all the dust and other pollutants in the atmosphere, and the slightly different refractive index of air masses at different temperatures.

Correct answer by DrC on May 1, 2021

If you were looking straight ahead, so that your line of sight were parallel to the ground, then the horizon line would appear to be at eye height, in all directions.

Answered by PM 2Ring on May 1, 2021

Upon your appearance (by whatever means) in that place, you would instantaneously be flattened (to a thickness so infinitesimal that it would be inherently imperceptible), by the gravity of whatever substance or energy comprised the infinitely wide and infinitely long (but totally flat) surface, unless your mass would (somehow) be of an equal or greater magnitude: In that last-mentioned case, you would be integrated into that surface, or vice-versa. (The lack of any relation between the rate of these changes and our own speed of light--in vacuum or otherwise--would be required by the fact, made very plain by Einstein in his 1916 pop.-sci. version of General Relativity, that the speed of light is local: The locality you've described could not exist anywhere, as, if it did, it would literally exist everywhere, per your definition of it as infinite.)

Any flat-earth survivalists among interstellar tourists will note that the horizon of planets much larger than earth is a much longer stroll from them than earth's horizon had been when they boarded the rocket. But it will still be infinitely closer than an infinitely flat universe's horizon could (even in principle) be.

Answered by Edouard on May 1, 2021

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