- #1
nightcleaner
Hi all
I have just had what may be an interesting thought.
Take a square piece of graph paper, label the horizontal axis "Time" and the vertical axis "Length". We will be using natural units so one grid line in the horizontal axis is one natural unit of time, and one grid line in the horizontal is one natural unit of space. Now draw a line on the graph, such that it represents the speed of light...one unit of length for one unit of time. The line will be at 45 degrees from either axis. Color everything below the line blue, for any line drawn from the origin to any point in that region will represent a velocity faster than the speed of light. Color anything above the 45 degree line red, for any line from the origin to any point in that region will be slower than light speed.
Now roll the paper into a cone with the origin at the pointy end. You see we have made a structure in which the axis representing time is joined to the axis representing space. We can do this and be meaningful because Albert introduced us to the idea that space and time are the same thing.
We have made a spacetime cone. You can readily see that it is expanding from the point of origin. You can also see that half of it is blue, and half is red. Now look at the line that we called the speed of light. It was on the diagonal of the graph when the paper was flat, so it is longer than the two axies, and it sticks out farther at the open end of the cone.
The open end of the cone describes a shape which I am going to say is a hyperbola, although I am forced to admit that I am reaching into my memory a ways for this information and it may be suspect to correction. Still, some little kid in me is jumping up and down, insisting that it must be so, or that, even if it isn't a hyperbola (that is a grown up word that I use, but the kid isn't really sure what it means), even if it isn't a hyperbola, it must be something really important, and deserving of a big fine grown up word with lots of letters and syllables.
Well, then, if we consider the idea of an object at rest, and draw the line that object must take on the graph, it is of course nothing more than the length axis, which we now see is really the same as the time axis. It is at the lowest, smoothest part of the open end of the cone. The line representing the speed of light is on the opposite, pointy side of the cone.
Now here is a curious thing. Any object at rest at the origin travels straight up the short side of the cone. Any object at rest from a point after the origin has to follow a spirol path. If you look at the grid lines, one of which the object at rest from a position after the orgin has to follow, you can clearly see that they spirol around the cone. But, curved as they are, they never make it all the way around!
Oh well, if this is the cone of the universe, with the big bang at the origin, then we are at a place far, far from the pointy end, and out in the middle somewhere where things seem pretty flat again. We might as well not have rolled the paper up at all, looking at things on our scale in space and time.
But here is something. Everything that has an origin has a spacetime cone like this. If we look very close to the origin, we can see the unity of spacetime. Usually we can't look that close, but maybe there are some cases where we get a little glimpse. Say, in a cloud chamber where a gamma photon decays into a pair of 'trons, one an electron and one a positron. I have just seen a pretty picture of that today, I'll try to find the link,
http://sol.sci.uop.edu/~jfalward/elementaryparticles/elementaryparticles.html
but I am sure you have seen it too. It has a very pointy end where the gamma photon decays, which goes into two spirols, one above the other, curling in opposite directions.
Something about that picture. It is taken in a strong magnetic field, of course, which is what causes the particles to curl around like that. But what I want to know is, what happens to the particles, once they get to the center of the spirol? Where do they go then? Are they in a rest frame after that? Or do they, as it seems from their tracks, simply dissappear?
Oh well, just thought I'd plunk down my uncertainty, and see if anyone wants to make a play on it.
be well,
Richard
I have just had what may be an interesting thought.
Take a square piece of graph paper, label the horizontal axis "Time" and the vertical axis "Length". We will be using natural units so one grid line in the horizontal axis is one natural unit of time, and one grid line in the horizontal is one natural unit of space. Now draw a line on the graph, such that it represents the speed of light...one unit of length for one unit of time. The line will be at 45 degrees from either axis. Color everything below the line blue, for any line drawn from the origin to any point in that region will represent a velocity faster than the speed of light. Color anything above the 45 degree line red, for any line from the origin to any point in that region will be slower than light speed.
Now roll the paper into a cone with the origin at the pointy end. You see we have made a structure in which the axis representing time is joined to the axis representing space. We can do this and be meaningful because Albert introduced us to the idea that space and time are the same thing.
We have made a spacetime cone. You can readily see that it is expanding from the point of origin. You can also see that half of it is blue, and half is red. Now look at the line that we called the speed of light. It was on the diagonal of the graph when the paper was flat, so it is longer than the two axies, and it sticks out farther at the open end of the cone.
The open end of the cone describes a shape which I am going to say is a hyperbola, although I am forced to admit that I am reaching into my memory a ways for this information and it may be suspect to correction. Still, some little kid in me is jumping up and down, insisting that it must be so, or that, even if it isn't a hyperbola (that is a grown up word that I use, but the kid isn't really sure what it means), even if it isn't a hyperbola, it must be something really important, and deserving of a big fine grown up word with lots of letters and syllables.
Well, then, if we consider the idea of an object at rest, and draw the line that object must take on the graph, it is of course nothing more than the length axis, which we now see is really the same as the time axis. It is at the lowest, smoothest part of the open end of the cone. The line representing the speed of light is on the opposite, pointy side of the cone.
Now here is a curious thing. Any object at rest at the origin travels straight up the short side of the cone. Any object at rest from a point after the origin has to follow a spirol path. If you look at the grid lines, one of which the object at rest from a position after the orgin has to follow, you can clearly see that they spirol around the cone. But, curved as they are, they never make it all the way around!
Oh well, if this is the cone of the universe, with the big bang at the origin, then we are at a place far, far from the pointy end, and out in the middle somewhere where things seem pretty flat again. We might as well not have rolled the paper up at all, looking at things on our scale in space and time.
But here is something. Everything that has an origin has a spacetime cone like this. If we look very close to the origin, we can see the unity of spacetime. Usually we can't look that close, but maybe there are some cases where we get a little glimpse. Say, in a cloud chamber where a gamma photon decays into a pair of 'trons, one an electron and one a positron. I have just seen a pretty picture of that today, I'll try to find the link,
http://sol.sci.uop.edu/~jfalward/elementaryparticles/elementaryparticles.html
but I am sure you have seen it too. It has a very pointy end where the gamma photon decays, which goes into two spirols, one above the other, curling in opposite directions.
Something about that picture. It is taken in a strong magnetic field, of course, which is what causes the particles to curl around like that. But what I want to know is, what happens to the particles, once they get to the center of the spirol? Where do they go then? Are they in a rest frame after that? Or do they, as it seems from their tracks, simply dissappear?
Oh well, just thought I'd plunk down my uncertainty, and see if anyone wants to make a play on it.
be well,
Richard
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