by RJN » Tue Jun 29, 2010 3:55 pm
I believe the best answer is "Yes, I have no problem with that." Much of the analysis given below is correct. In fact, this discussion thread is the best general analysis of this problem of which I am aware, and possibly even a good example of "Citizen Science."
In sum, the vertex of a scissors is not a physical object and can exceed the speed of light. If you could close a one light-year long scissors in one second, for example, then the vertex would need to move much faster than light.
The guillotine-scissors example, given below, makes this particularly clear. Here consider two lines with a very small angle between them. Now consider the tilted line slowly dropping past the straight line. The intersection of them is the vertex and can move down either line arbitrarily fast, even faster than light.
Conversely, however, the "no" answer is actually correct in the most classic example of a scissors closing -- that when the two blades start as rigid, straight, at rest, and the time when the scissors will start to close is only known at the handle. For this case, the information that the scissors is closing can only move up the blades at the speed of light, so that the end of the scissors, say one light year away, could not know to close before that information arrives from the handle. In that sense this example has similarities to the Twirling Pole GRED posted earlier here:
http://asterisk.apod.com/vie ... 30&t=19641
A neat twist, posted below, which I had not previously considered, is that of a scissors that does NOT start with straight blades. This scissors, when closing, can have a vertex or even multiple vertexes that can actually break the speed of light even when the starting time is known only at the handle.
- RJN
I believe the best answer is "Yes, I have no problem with that." Much of the analysis given below is correct. In fact, this discussion thread is the best general analysis of this problem of which I am aware, and possibly even a good example of "Citizen Science."
In sum, the vertex of a scissors is not a physical object and can exceed the speed of light. If you could close a one light-year long scissors in one second, for example, then the vertex would need to move much faster than light.
The guillotine-scissors example, given below, makes this particularly clear. Here consider two lines with a very small angle between them. Now consider the tilted line slowly dropping past the straight line. The intersection of them is the vertex and can move down either line arbitrarily fast, even faster than light.
Conversely, however, the "no" answer is actually correct in the most classic example of a scissors closing -- that when the two blades start as rigid, straight, at rest, and the time when the scissors will start to close is only known at the handle. For this case, the information that the scissors is closing can only move up the blades at the speed of light, so that the end of the scissors, say one light year away, could not know to close before that information arrives from the handle. In that sense this example has similarities to the Twirling Pole GRED posted earlier here: http://asterisk.apod.com/viewtopic.php?f=30&t=19641
A neat twist, posted below, which I had not previously considered, is that of a scissors that does NOT start with straight blades. This scissors, when closing, can have a vertex or even multiple vertexes that can actually break the speed of light even when the starting time is known only at the handle.
- RJN