Post by Roquefort Raider on Oct 5, 2017 16:05:54 GMT -5
In honour of Jesse who inquired about one, let us break open the Champagne bottle and start talking science!
I have a problem with flat space. No amount of reading or Youtube watching has been able to help me. Perhaps someone here will be able to!
On the flatness of space...
For a few decades I was quite happy with the concept of a curved universe, in which our 3D environment is curved into a fourth dimension just like the 2D surface of a balloon is curved in the third. I even incorporated the concept in my comics.
This curved space makes the concept of an expanding universe very intuitive: as our 4D "balloon" inflates, every point on its 3D surface gets farther and farther away from every other point. This translates, in our own eyes, as a universe in which galaxies are moving away from each other (and in which the farther you are, the faster you recede). There is however no edge to space, just as there is no edge to the surface of a balloon.
Sometimes almost tewnty years ago, physicists determined that the universe was actually flat. Flat-flat, not flat and curved like the surface of a sphere. I do not have the mathematical nor the physics skills to understand how we came to this conclusion, but the lay public explanations given by such luminaries as Lawrence Krause do not seem satisfying to me.
Here is how it goes. Essentially, for the purpose of the explanation, we are comparing a curved universe to the surface of the Earth. If we stand somewhere at the equator and walk straight ahead along its line for a few hundred kilometers, and then turn at a 90 degrees angle towards the north pole before walking the same distance, and then turn right again at a 90 degrees angle before walking the same distance for the third time, we will end up at our starting point. The funny thing is that having walked along what appears to be a triangular path, we will have made three turns totalling 90 + 90 + 90 (or 270) degrees. This is odd, as a triangle is supposed to have 180 degrees. The explanation is that we were walking not on a flat surface, but on the curved surface of the Earth. So far so good.
Now if this is true on the surface of the Earth it should be true if we measure distant stuff in a curved universe. Very distant objects should be so positioned as to form triangles totalling more than 180 degrees. This was tested with very distant structures in the cosmic microwave background at the edge of the visible universe (basically the furthest and oldest points we could find). In a nutshell, the angle between these structures and us add up to 180 degrees, meaning that the observable universe is flat.
But isn't that what we would expect? If we perform the same experiment on Earth, any three points within our range of observation will add up to 180 degrees. To go beyond that number we need to go beyond our horizon; doesn't the same thing hold true when looking at the cosmic microwave background? We're looking at the most distant structures we can find, but by definition they are within our horizon! Hence my dilemma. This result seems to me to be exactly what we'd expect, even if the universe was, after all, curved.
I confess that the main problem I have with a flat universe is philosophical. I like things that can be explained easily. With a curved universe, no need to ask "what is beyond the universe" because there is no beyond. The universe is endless but finite (though growing), and if you could go far enough in one direction (at several times the speed of light!) you should end up where you started. With a flat universe, you really have an infinite space; galaxies might get away from each other, but they do so in a space that is already there, not one that grows along with them. (Either that or the universe does have an edge, like the flat Earth of old, but then we must ask "what is that edge like and what lies on the other side of the edge"?
I'm pretty sure the fault lies in my limited comprehension, but I sure do miss my old curved space!
Does anyone understand how flat space is supposed to work? Any explanation would be greatly appreciated.
I have a problem with flat space. No amount of reading or Youtube watching has been able to help me. Perhaps someone here will be able to!
On the flatness of space...
For a few decades I was quite happy with the concept of a curved universe, in which our 3D environment is curved into a fourth dimension just like the 2D surface of a balloon is curved in the third. I even incorporated the concept in my comics.
This curved space makes the concept of an expanding universe very intuitive: as our 4D "balloon" inflates, every point on its 3D surface gets farther and farther away from every other point. This translates, in our own eyes, as a universe in which galaxies are moving away from each other (and in which the farther you are, the faster you recede). There is however no edge to space, just as there is no edge to the surface of a balloon.
Sometimes almost tewnty years ago, physicists determined that the universe was actually flat. Flat-flat, not flat and curved like the surface of a sphere. I do not have the mathematical nor the physics skills to understand how we came to this conclusion, but the lay public explanations given by such luminaries as Lawrence Krause do not seem satisfying to me.
Here is how it goes. Essentially, for the purpose of the explanation, we are comparing a curved universe to the surface of the Earth. If we stand somewhere at the equator and walk straight ahead along its line for a few hundred kilometers, and then turn at a 90 degrees angle towards the north pole before walking the same distance, and then turn right again at a 90 degrees angle before walking the same distance for the third time, we will end up at our starting point. The funny thing is that having walked along what appears to be a triangular path, we will have made three turns totalling 90 + 90 + 90 (or 270) degrees. This is odd, as a triangle is supposed to have 180 degrees. The explanation is that we were walking not on a flat surface, but on the curved surface of the Earth. So far so good.
Now if this is true on the surface of the Earth it should be true if we measure distant stuff in a curved universe. Very distant objects should be so positioned as to form triangles totalling more than 180 degrees. This was tested with very distant structures in the cosmic microwave background at the edge of the visible universe (basically the furthest and oldest points we could find). In a nutshell, the angle between these structures and us add up to 180 degrees, meaning that the observable universe is flat.
But isn't that what we would expect? If we perform the same experiment on Earth, any three points within our range of observation will add up to 180 degrees. To go beyond that number we need to go beyond our horizon; doesn't the same thing hold true when looking at the cosmic microwave background? We're looking at the most distant structures we can find, but by definition they are within our horizon! Hence my dilemma. This result seems to me to be exactly what we'd expect, even if the universe was, after all, curved.
I confess that the main problem I have with a flat universe is philosophical. I like things that can be explained easily. With a curved universe, no need to ask "what is beyond the universe" because there is no beyond. The universe is endless but finite (though growing), and if you could go far enough in one direction (at several times the speed of light!) you should end up where you started. With a flat universe, you really have an infinite space; galaxies might get away from each other, but they do so in a space that is already there, not one that grows along with them. (Either that or the universe does have an edge, like the flat Earth of old, but then we must ask "what is that edge like and what lies on the other side of the edge"?
I'm pretty sure the fault lies in my limited comprehension, but I sure do miss my old curved space!
Does anyone understand how flat space is supposed to work? Any explanation would be greatly appreciated.
