The Universe Is Flat And Infinite

It was recently announced that scientists generally believe the universe to be "flat and infinite". But I find this to be redundant and the reason involves the nature of infinity.

Saying that the universe is infinite simply means that it goes on forever. Describing the space of the universe as "flat", as opposed to "curved", is a question of cosmology. The surface of the earth is curved so that, if we keep flying in a straight line in a plane we will eventually return to our starting point.

Likewise, if the space of the universe is "flat", it means that, if we send a spacecraft out into space in a straight line, it will forever keep getting further and further from us. But if the space of the universe is curved, and we wait long enough, the spacecraft will eventually return to us just as the plane flying around the world will eventually return to it's starting point.

If we had an infinitely powerful telescope, and we looked out into space with it, if the space of the universe was curved we could theoretically see ourselves from behind.

There are other theories of the shape of space in the universe, such as saddle-shaped, but it is not something that we can observe directly. A sphere is defined as having "positive curvature", in that it curves toward itself. A saddle-shape, in contrast, is a negative curvature because it curves away from itself.

We get our information about the universe from light, and other electromagnetic waves. But light will follow whatever the shape of space is and we will always see light as traveling in a straight line. This means that we will always perceive the universe as being "flat".

This is not exactly the same thing as whether the universe is "open" or "closed", which is also debated. Most people believe the universe to have begun with the "Big Bang", and having been expanding outward ever since. If the expansion of the universe slows down, so that it will possibly fall back together by it's own gravity, the universe is referred to as "closed". If it will keep expanding forever, never falling back together, it is referred to as "open".

If the universe is infinite that means that it goes on forever. But if the universe is infinite that means we would have to travel an infinite distance before we would experience any curvature, no matter what the shape of space in the universe was. This is nothing to do with cosmology but with the nature of infinity.

To describe the universe as "flat and infinite" is redundant because, if the universe is infinite, we can never perceive it as anything but flat. The space in the universe might be shaped like a pretzel but, even if we had a way to detect the curvature, we would have to travel an infinite distance in space to be able to detect any curvature at all.

The surface of a sphere is curved. The smaller the sphere the greater the surface curvature per distance, and the larger the sphere the less it's curvature per distance. This means that, if there was an infinite sphere, the surface curvature would have to be zero even though it would still be a sphere. We would have to travel an infinite distance on the surface of the sphere before we could detect any curvature at all. So it is with the universe if it is infinite, we cannot perceive it as anything but flat.

This is related to my concept of straight lines. The trouble with straight lines is that we get our information from light and we will thus always perceive light as traveling in a straight line. If an electron moving in a wire could think it would always perceive itself as moving in a straight line, no matter how tangled the wire was. In a similar way, if the universe is infinite we must always perceive it as flat.

I proposed defining a straight line as an arc of an infinite circle, as well as discussing the nature of infinity, in the posting "Infinite Geometry" on the Progress Blog, markmeekprogress.blogspot.com .