3

If I was looking towards the horizon while standing on an infinite, perfectly flat plane, what would I see?

3 Answers3

3

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.

PM 2Ring
  • 11,873
  • --I've upvoted your answer, but, on 2nd thought, wouldn't it require a two-dimensional being? (I think the answer might still hold, as I've read somewhere that sentience might be a characteristic of beings comprised entirely of heat--i.e., photons, whose particulate form has no spatial extent in any relativistic theory I've heard of--but, in a present that Barrow has described as the point of transition between wave and particle characterizations of light, I'm curious as to whether that instaneity is a condition of your answer.) – Edouard Jan 11 '21 at 19:50
  • 1
    Sorry, @Edouard, I don't understand why you think it'd require a two-dimensional being. Note that eyes (and cameras) have an image sensor surface; our brains use the image data from our eyes to construct a 3D visual model of the world. – PM 2Ring Jan 12 '21 at 05:54
  • @Edouard Also, I'm highly sceptical of the notion of a sentient being composed entirely of photons. As Luboš Motl says here, "Collections of photons propagating in some direction, because they move by $v=c$ exactly, can't have brains that would send signals back and forth". – PM 2Ring Jan 12 '21 at 05:54
  • Re the two-dimensionality, maybe I'm considering the OP's notion of "flat" as being a bit more exact than he'd intended: If a surface was two-dimensional, wouldn't it be imperceptible either to eyes containing various surfaces or to devices producing analogous effects? (However, such devices might exceed the capabilities of their designers.) As far as Motl's remark is concerned, I think such collections might coincidentally (or randomly) happen to resemble brains on occasions sufficient to have some huge effects far more durable than such occasions would be common. – Edouard Jan 12 '21 at 06:13
  • Sorry; I'll let my previous comment stand so you can see my reasoning, but I think the OP was using "flat" in the sense, specialized for physics, of "lacking any curvature perceptible even in principle". – Edouard Jan 12 '21 at 06:31
1

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.

DrC
  • 697
0

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.

Edouard
  • 848
  • 1
    I declined your tag edit, because the OP doesn't give any indication as to if he wants a general relativity answer. Note that this doesn't make your answer irrelevant. –  Mar 10 '20 at 04:52
  • @Programical Is the situation you've depicted based on one of the theories more recent than General Relativity? (If it's based on its simpler predecessor, Newton's theory of gravity, its setting--assuming your "horizon" to be a material surface in surroundings which might be circumscribed by any abstract sphere of sufficient size-- runs into a problem described in a very simple algebraic proof by Guth on p.296 in the 1997 ed. of his pop. sci. book titled "The Inflationary Universe": The relativistic curvature involved would, of course, be entirely temporal, per your specifications.) – Edouard Jan 12 '21 at 00:04