There are often discussions as to the "shape" of the space in the universe. An illustration of what the space of the universe might be shaped like revolves around what happens to a spacecraft, or a beam of light, that travels outward into space.
If the light or the spacecraft, moving at a constant velocity, continually gets further and further away, at a constant rate, then the shape of space in the universe is considered to be "flat".
If the light or the spacecraft, moving in a straight line, eventually returns to it's starting point then the shape of space in the universe is referred to as "closed". The question of whether the universe is "flat" or "closed" is related to the question of whether it is finite or infinite. With a flat universe it could be infinite but a closed universe implies that it is finite.
There is also a debate as to whether the universe is "open" or "closed", although this is not the same thing as the shape of space in the universe, it refers to the expansion of the universe. If the matter of the universe will ultimately fall back together by it's mutual gravity, the universe is referred to as "closed", if not then it is "open".
The analogy that is naturally used for the closed universe is the surface of the earth. From any given perspective on the earth's surface it appears to be flat. But if we continue in a straight line for long enough we eventually end up back at our starting point. This means that the earth's surface is closed and finite, even though it has no boundaries.
Although the shape of space appears to us, at first glance, to obviously be flat the argument in favor of a closed universe is that the default gravitational form in the universe, for stars and planets, is a sphere. Since these spheres are within the space of the universe, then shouldn't that space have the same form?
Einstein's General Theory of Relativity, as opposed to the Special Theory which deals with the speed of light, explains how space is curved by gravity. An object in orbit is defined as actually moving in a straight line but through curved space. The space being curved by the mass of the star or planet around which the orbit is taking place.
The space of the universe does not necessarily have to be either "flat" or "closed", these are just the examples at either end of the scale. The space of the universe might have a negative curvature, as opposed to the positive curvature of a sphere, this would give it a "saddle" shape. There are other ideas that the space of the universe might have some kind of torus shape. This means, like the closed sphere, that the space of the universe is finite yet has no boundaries.
The mathematical rules of geometry are different for different shapes of space. Ordinary textbook geometry is known as "Euclidean" geometry, for the ancient Greek named Euclid. A presumption of Euclidean Geometry is that the surface is flat. Euclidean Geometry does not apply for surfaces that are not flat, and non-Euclidean geometries have been developed for non-flat surfaces.
As a simple example in Euclidean Geometry the three interior angles of a triangle always add up to 180 degrees. But if we take a curved surface, like the surface of the earth, the rules change. If we consider a triangle of two lines of longitude, from the equator to the north pole, and the stretch of the equator between them, the angles add up to more than 180 degrees. The intersection of each line of longitude with the equator forms two 90 degree right angles, so we already have 180 degrees, plus the angle between the two lines of longitude at the north pole, giving us more than 180 degrees.
The general consensus today is that the shape of space in the universe is "flat". This means, again, that a rocket or beam of light that is sent out into space in a straight line will forever continue getting further and further away from us. But what I wanted to do today is to add my input to it.
What we have to consider, in deciding on the shape of space in the universe, is the actual nature of straight lines. A straight line being defined as the shortest possible distance between two points. A straight line is not as absolute as it may seem.
Straight lines are a matter of dimensions. If we, confined as we are to three-dimensional space, see a straight line it may in fact be curved in higher-dimensional space and we would in no way be aware of it.
If there could be a two-dimensional sheet of plastic, and a two-dimensional being lived inside the sheet of plastic, it would always perceive itself as moving in a straight line in going from one side of the plastic to the other. No matter how we might bend and twist the sheet of plastic the being could not be aware of it, since that would require the two-dimensional being to be aware of the third dimension.
A straight line can also mean the least energy expenditure between two points, although in space that would usually mean the same thing as the shortest distance between the two. If an electron could think it would always perceive itself as moving in a straight line as it moved through a wire as part of an electric current, no matter how the wire might zig-zag across the floor.
The trouble with our general conclusion that the space of the universe is "flat" is that we rely on light and other electromagnetic radiation, specifically the leftover radiation from the Big Bang, to bring us our information about the universe. But we get our very definition of what a straight line is by the path of light.
Since we rely on light, and other electromagnetic radiation for information, we will always perceive that radiation as moving in a straight line. While it is true that the light would follow the path of least expenditure of energy, because we know that the universe always seeks the lowest energy state, there may be other possible definitions of what a straight line is.
Just as an example humans are of the scale that we are and this gives us a certain perspective. We define the electromagnetic spectrum as ranging from very short-wavelength gamma rays to longwave radio waves. But couldn't there be, due to our scale perspective, still longer waves that we cannot detect? Isn't it possible that the shorter waves that we depend on for information, particularly visible light, are affected by the longer wavelengths as they move through space? What if the shorter wavelengths "ride" the longer wavelengths, somewhat like a duck paddling across the waves in water so that it also moves up and down as it proceeds along?
That would mean that light actually "zigzags" through space. But since we are dependent on light for information we will always perceive it as moving in a straight line.
Einstein's General Theory of Relativity showed that gravity bends light. So why shouldn't there be other things that bend light that we haven't yet found? What about magnetism? It has been found that the sun lacks a south magnetic pole. We know that the sun is a second-generation star and this means that it has come back together gravitationally but not magnetically.
The former south magnetic pole of the star that preceded the sun, until it exploded in a supernova, must exist somewhere else. Since electromagnetic radiation is so-called because it is electric and magnetic in nature, couldn't this affect it from moving in what would otherwise be defined as a straight line?
Now, let's get back to the debate about the shape of space in the universe. Since we are dependent on electromagnetic radiation for information about the universe, and since this means that we will always perceive electromagnetic radiation to be moving in a straight line, this will always make it seem as if the space in the universe is "flat", since that is the only model of space where light moves in straight lines.
Just for something to ponder suppose that the space in the universe is "closed". This means that a beam of light sent out into space will eventually return to us from the opposite direction. Just as if you traveled in a straight line on the earth's surface you would eventually return to your starting point from the opposite direction.
This means, at least theoretically, that, if we had a powerful enough telescope, we should be able to see our own earth by looking out into space. But that gets complicated too. If the number of different objects made of matter is finite, but yet the universe is infinite, this means that objects made of matter must repeat themselves. This then would mean that there would have to actually be an infinite number of identical earths in identical solar systems, in orbit around identical suns.
The point of all this is that we cannot be so quick to say that the shape of space in the universe is flat.
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