- #1
neurobio
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A few "paradoxes" in STR
As you can guess from my username, I come from a biology background. I've recently had the dubious pleasure of discussing evolution with a guy who is also a major physics crank; now, my physics is good enough to dismiss most of his nonsense, but he gave me pause with the following problems (actually, I thought that I had an answer, but after reading about Bell's spaceship paradox, I'm confused). I'm assuming you guys can make short work of them :)
1. Two buildings are connected by a straight, rigid wall. The wall is strong enough to stand for centuries, but is made of crushable material. An alien vessel passes by the Earth at 99% speed of light.
From the reference frame of the buildings, absolutely nothing happens. From the reference point of the alien ship, two buildings and the wall suddenly got shorter. The wall either breaks apart since the distance between two buildings has been increased, or it is crushed from its own contraction (to great surprise of everyone on the ground).
My assumption was that the space in which the buildings and the wall are situated also contracts from the reference frame of the spaceship; therefore, everything stays "in proportion", so to speak. But upon reading the solutions to Bell's spaceship paradox (where the string does break, if I understand correctly), I find myself utterly confused.
2. Related to the previous. A train sits at the train station. It is composed of wagons that are touching each other, but are not physically connected otherwise. An alien vessel flies overhead at 0.99c.
Does the alien vessel "see" a bunch of shortened wagons with spaces between them, or does it "see" the whole train as being shortened (with wagons still touching)?
3. And again related to the previous. I have two rods, AB and CD, which are aligned lengthwise so they touch each other (point B of AB touches point C of CD). The rods are stationary relative to myself, and I measure their coordinates: length AB = x, length CD = x, length AD = 2x.
The rods suddenly accelerate to relativistic speeds, and then they stop accelerating, maintaining a constant velocity relative to my frame of reference.
I now measure length A'B' = x/2, and length C'D'= x/2. What is the length A'D' - i.e. did the rod remain in contact (in which case A'D' = x), or did they become separate?
Furthermore, let us say that during the period of acceleration, between my first and my second measurement, point A traversed a length of 10x. But if the rods remain in contact, point D traversed a length of 9x (10x-2*x+2*x/2). How is this possible?
*
I expect that the answer to these problems is humiliatingly simple. :)
As you can guess from my username, I come from a biology background. I've recently had the dubious pleasure of discussing evolution with a guy who is also a major physics crank; now, my physics is good enough to dismiss most of his nonsense, but he gave me pause with the following problems (actually, I thought that I had an answer, but after reading about Bell's spaceship paradox, I'm confused). I'm assuming you guys can make short work of them :)
1. Two buildings are connected by a straight, rigid wall. The wall is strong enough to stand for centuries, but is made of crushable material. An alien vessel passes by the Earth at 99% speed of light.
From the reference frame of the buildings, absolutely nothing happens. From the reference point of the alien ship, two buildings and the wall suddenly got shorter. The wall either breaks apart since the distance between two buildings has been increased, or it is crushed from its own contraction (to great surprise of everyone on the ground).
My assumption was that the space in which the buildings and the wall are situated also contracts from the reference frame of the spaceship; therefore, everything stays "in proportion", so to speak. But upon reading the solutions to Bell's spaceship paradox (where the string does break, if I understand correctly), I find myself utterly confused.
2. Related to the previous. A train sits at the train station. It is composed of wagons that are touching each other, but are not physically connected otherwise. An alien vessel flies overhead at 0.99c.
Does the alien vessel "see" a bunch of shortened wagons with spaces between them, or does it "see" the whole train as being shortened (with wagons still touching)?
3. And again related to the previous. I have two rods, AB and CD, which are aligned lengthwise so they touch each other (point B of AB touches point C of CD). The rods are stationary relative to myself, and I measure their coordinates: length AB = x, length CD = x, length AD = 2x.
The rods suddenly accelerate to relativistic speeds, and then they stop accelerating, maintaining a constant velocity relative to my frame of reference.
I now measure length A'B' = x/2, and length C'D'= x/2. What is the length A'D' - i.e. did the rod remain in contact (in which case A'D' = x), or did they become separate?
Furthermore, let us say that during the period of acceleration, between my first and my second measurement, point A traversed a length of 10x. But if the rods remain in contact, point D traversed a length of 9x (10x-2*x+2*x/2). How is this possible?
*
I expect that the answer to these problems is humiliatingly simple. :)