June 9th, 2010
The Big Bang theory is the idea that about fourteen billion years ago all matter and energy was contained within a single point, which then expanded to the current size of the universe and is still expanding. Matter and energy are different forms of the same stuff so let’s just call it Stuff. For long enough to draw some diagrams, let’s pretend that there are only eight bits of Stuff in the universe:
The diagram shows that, as time goes by, every bit of Stuff moves farther away from the origin point and farther away from the other bits of Stuff. You see, it was drawn from God’s perspective. From where we’re sitting in the universe, the bits of Stuff do not appear to be moving away from an origin; they appear only to be moving away from Us:
This one shows expansion in action (G moves to G', etc.) :
The above diagram demonstrates quite prettily that distant objects are moving away from us faster than nearby objects. In the same time it took G to move to G’, E moved all the way to E’. The idealized Hubble’s Law words it thus: Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.
What seems at first very unpretty about the above is that the circles of points representing all the Stuff in the past and present universes are not concentric. "Where's the origin?" you ask, "the single point where everything was fourteen billion years ago." To find it, think of the diagram as a not-quite-top-down view of a cone that’s getting longer. Here’s another view:
The tip of the cone is the origin. The rim of the cone is the entire universe that exists at any given moment. Our position on the ring isn’t changing really but everything is getting farther away from us, E much faster than G.
There’s another trippy difference between E and G. The appropriate soundtrack for discussing it is Regina Spektor’s Samson. “The stars came falling on our heads,” she sings, “But they’re just old light.” Light is the fastest thing going, but the other bits of Stuff are so far away that even it takes ages to travel from them to us. Suppose that G is Andromeda, the nearest spiral galaxy. It is 2.5 million lightyears away, which means that when we look at Andromeda, we’re actually seeing it as it looked 2.5 million years ago, just before the genus Homo evolved. That seems like a long time ago until you consider that E is the galaxy IOK-1. Its light shines to us from 12.88 billion years ago. Very distant objects, then, are very early objects, close in time to the beginning of time, the Big Bang.
We cannot possibly see objects beyond 13.7 billion lightyears away because in order for light to have travelled that far it would have to be more than 13.7 billion years old, older than the universe. This somewhat silly diagram shows the theoretical limit of our observation as a bubble around us with a radius of 13.7 billion lightyears. Notice that the D is a bit of Stuff outside of the observable universe:
The final thing I want to discuss today is the actual shape of the universe. Our original drawing was just eight points. When we boost the number of points to infinity, we get a circle, the rim of the cone:
This is an intriguing visual metaphor but that's all it is. We know the universe is not a circle because we can move about it in three physical dimensions. Let us suppose, then, that the universe is the three dimensional equivalent of a circle, an infinite amount of space. What then, is the equivalent of the cone, the object with one more dimension than the circle necessary to explain the circle’s growth over time? The spacetime continuum! But more on that later, when I’ve read more about general relativity.
The diagram shows that, as time goes by, every bit of Stuff moves farther away from the origin point and farther away from the other bits of Stuff. You see, it was drawn from God’s perspective. From where we’re sitting in the universe, the bits of Stuff do not appear to be moving away from an origin; they appear only to be moving away from Us:
This one shows expansion in action (G moves to G', etc.) :
The above diagram demonstrates quite prettily that distant objects are moving away from us faster than nearby objects. In the same time it took G to move to G’, E moved all the way to E’. The idealized Hubble’s Law words it thus: Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.
What seems at first very unpretty about the above is that the circles of points representing all the Stuff in the past and present universes are not concentric. "Where's the origin?" you ask, "the single point where everything was fourteen billion years ago." To find it, think of the diagram as a not-quite-top-down view of a cone that’s getting longer. Here’s another view:
The tip of the cone is the origin. The rim of the cone is the entire universe that exists at any given moment. Our position on the ring isn’t changing really but everything is getting farther away from us, E much faster than G.
There’s another trippy difference between E and G. The appropriate soundtrack for discussing it is Regina Spektor’s Samson. “The stars came falling on our heads,” she sings, “But they’re just old light.” Light is the fastest thing going, but the other bits of Stuff are so far away that even it takes ages to travel from them to us. Suppose that G is Andromeda, the nearest spiral galaxy. It is 2.5 million lightyears away, which means that when we look at Andromeda, we’re actually seeing it as it looked 2.5 million years ago, just before the genus Homo evolved. That seems like a long time ago until you consider that E is the galaxy IOK-1. Its light shines to us from 12.88 billion years ago. Very distant objects, then, are very early objects, close in time to the beginning of time, the Big Bang.
We cannot possibly see objects beyond 13.7 billion lightyears away because in order for light to have travelled that far it would have to be more than 13.7 billion years old, older than the universe. This somewhat silly diagram shows the theoretical limit of our observation as a bubble around us with a radius of 13.7 billion lightyears. Notice that the D is a bit of Stuff outside of the observable universe:
The final thing I want to discuss today is the actual shape of the universe. Our original drawing was just eight points. When we boost the number of points to infinity, we get a circle, the rim of the cone:
This is an intriguing visual metaphor but that's all it is. We know the universe is not a circle because we can move about it in three physical dimensions. Let us suppose, then, that the universe is the three dimensional equivalent of a circle, an infinite amount of space. What then, is the equivalent of the cone, the object with one more dimension than the circle necessary to explain the circle’s growth over time? The spacetime continuum! But more on that later, when I’ve read more about general relativity.