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Relativity Paradoxes
Just pondering some paradoxes in Special Relativity.
The first one deals with length contraction:
We have a 4foot long pole and a wall of glass with five feet marked out in front of it on the ground like so:
____________________
< 4 ft. >





___________________
< 5 ft. >
The pole is moving towards the wall of glass at such a high rate of speed that from the reference frame of the pole the 5 feet in front of the wall of glass is only 2.5 feet long. From the reference frame of the wall of glass, the pole is only 2 feet long. The pole continues moving at a high rate of speed until the end furthest from the wall of glass reaches the end of the 5 foot line, it then stops. From the reference frame of the pole, the pole smashes through the glass, since the pole is 4 feet long and the 5 feet is now 2.5 feet. From the reference frame of the wall of glass, the 4foot long pole easily fits into the 5 feet since the pole is only 2 feet long. Both reference frames are correct, so we have a paradox: The wall of glass is both smashed and not smashed.
Special Relativity can't use the relativity of simultaneity to explain this because in the reference frame of the wall of glass, the pole never touches the glass. So how does SR explain this?
Here's one concerning the speed of light.
IT IS ALWAYS IMPORTANT TO KEEP IN MIND THAT IF THE SPEED OF LIGHT IS ALWAYS THE SAME RELATIVE TO YOU, THE LENGTH OF TIME REQUIRED FOR THE LIGHT TO REACH YOU DEPENDS UPON YOUR DISTANCE AT THE TIME OF EMISSION.
We have the following situation:
D<1 lighthr>C<1 lighthr> <1 lighthr> C
_____________B___________A____________B______
The observers at the Bs are at rest with respect to each other and with respect to A. A is a light bulb. The distance from A to B is 1 lighthour. The observers at the Cs are moving away from the light bulb A at half the speed of light. D is another light bulb which is at rest with respect to the observer at C on the left. It is one lighthour away from the C on the left. Just when the observers at the Cs reach the Bs, light bulb A emits a flash of light. The light will reach the Cs when they are two lighthours away from A, but from their reference frames it will take only one hour for the light to reach them since the time merely depends on the distance at the time of emission. When the light reaches the Cs, two hours will have elapsed for the Bs from their reference frames. Because time passes at the same rate from the reference frame of the Bs, and the time for the reference frame of the Cs is moving at half that rate, it follows that time is moving at the same rate from the reference frame of the Cs. When we have the light reach observer C on the left, we have light bulb D emit a flash of light. It will take one hour for the light to reach observer C on the left. Whatever the distance is from light bulb D to observer C on the right at the time of emission, it should take that long to reach observer C on the right from his reference frame. In this case it should take 5 hours, but it ends up taking 10 instead. His clock is moving at the same rate as the left C and he is moving away from the left C, therefore in this case because he is moving relative to the left C and his clock isn't running slow, light will travel more slowly relative to him. Let's work this out to make this more clear:
flash is emitted from lightbulb A:
clock for left C: 01:00
clock for right C: 01:00
clock for left B: 01:00
clock for right B: 01:00
light reaches the Bs:
clock for left C: 01:30
clock for right C: 01:30
clock for left B: 02:00
clock for right B: 02:00
light reaches the Cs and flash is emitted from D:
clock for left C: 02:00
clock for right C: 02:00 (right C is five lighthours from D and should receive the flash in five hours, but he receives it in 10 hours instead.)
clock for left B: 03:00
clock for right B: 03:00
light reaches the left C:
clock for left C: 03:00
clock for right C: 03:00
light reaches where the right C was at the time of emission from D:
clock for left C: 08:00
clock for right C: 08:00
In order for the light to reach the right C in 5 hours his clock would need to move slower than the left C.
clock reaches the right C:
clock for left C: 13:00
clock for right C: 13:00 (The light relative to the right C is moving at .5C)
Just pondering some paradoxes in Special Relativity.
The first one deals with length contraction:
We have a 4foot long pole and a wall of glass with five feet marked out in front of it on the ground like so:
____________________
< 4 ft. >





___________________
< 5 ft. >
The pole is moving towards the wall of glass at such a high rate of speed that from the reference frame of the pole the 5 feet in front of the wall of glass is only 2.5 feet long. From the reference frame of the wall of glass, the pole is only 2 feet long. The pole continues moving at a high rate of speed until the end furthest from the wall of glass reaches the end of the 5 foot line, it then stops. From the reference frame of the pole, the pole smashes through the glass, since the pole is 4 feet long and the 5 feet is now 2.5 feet. From the reference frame of the wall of glass, the 4foot long pole easily fits into the 5 feet since the pole is only 2 feet long. Both reference frames are correct, so we have a paradox: The wall of glass is both smashed and not smashed.
Special Relativity can't use the relativity of simultaneity to explain this because in the reference frame of the wall of glass, the pole never touches the glass. So how does SR explain this?
Here's one concerning the speed of light.
IT IS ALWAYS IMPORTANT TO KEEP IN MIND THAT IF THE SPEED OF LIGHT IS ALWAYS THE SAME RELATIVE TO YOU, THE LENGTH OF TIME REQUIRED FOR THE LIGHT TO REACH YOU DEPENDS UPON YOUR DISTANCE AT THE TIME OF EMISSION.
We have the following situation:
D<1 lighthr>C<1 lighthr> <1 lighthr> C
_____________B___________A____________B______
The observers at the Bs are at rest with respect to each other and with respect to A. A is a light bulb. The distance from A to B is 1 lighthour. The observers at the Cs are moving away from the light bulb A at half the speed of light. D is another light bulb which is at rest with respect to the observer at C on the left. It is one lighthour away from the C on the left. Just when the observers at the Cs reach the Bs, light bulb A emits a flash of light. The light will reach the Cs when they are two lighthours away from A, but from their reference frames it will take only one hour for the light to reach them since the time merely depends on the distance at the time of emission. When the light reaches the Cs, two hours will have elapsed for the Bs from their reference frames. Because time passes at the same rate from the reference frame of the Bs, and the time for the reference frame of the Cs is moving at half that rate, it follows that time is moving at the same rate from the reference frame of the Cs. When we have the light reach observer C on the left, we have light bulb D emit a flash of light. It will take one hour for the light to reach observer C on the left. Whatever the distance is from light bulb D to observer C on the right at the time of emission, it should take that long to reach observer C on the right from his reference frame. In this case it should take 5 hours, but it ends up taking 10 instead. His clock is moving at the same rate as the left C and he is moving away from the left C, therefore in this case because he is moving relative to the left C and his clock isn't running slow, light will travel more slowly relative to him. Let's work this out to make this more clear:
flash is emitted from lightbulb A:
clock for left C: 01:00
clock for right C: 01:00
clock for left B: 01:00
clock for right B: 01:00
light reaches the Bs:
clock for left C: 01:30
clock for right C: 01:30
clock for left B: 02:00
clock for right B: 02:00
light reaches the Cs and flash is emitted from D:
clock for left C: 02:00
clock for right C: 02:00 (right C is five lighthours from D and should receive the flash in five hours, but he receives it in 10 hours instead.)
clock for left B: 03:00
clock for right B: 03:00
light reaches the left C:
clock for left C: 03:00
clock for right C: 03:00
light reaches where the right C was at the time of emission from D:
clock for left C: 08:00
clock for right C: 08:00
In order for the light to reach the right C in 5 hours his clock would need to move slower than the left C.
clock reaches the right C:
clock for left C: 13:00
clock for right C: 13:00 (The light relative to the right C is moving at .5C)
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