I like to consider the pole and the barn paradox (as you said, it's the same thing) In my opinion it is impossible for the pole to cross the barn. (if the proper length of the pole is less than the proper length of the barn) If two equal distances are in relative motion to each other at speed v, the distances overlap. In my opinion, if we denote with t the elapsed time in the frame of the barn and if we denote with t_1 the elapsed time in the frame of the pole, it is t = t_1. (and two equal distances overlap, in this case no problem) The length of the pole contracts in the barn frame and the length of the barn contracts in the frame of the pole, the two lengths are equal! (suppose they are equal to d) d = gamma * v * t and d = gamma * v * t_1. When the two equal distances overlap it is t = t_1 = d / (gamma * v), for each value of d. If the length of the barn is shorter, in my opinion it is impossible to close the doors of the barn! The length of the pole is "shorter" (it takes less time for the entire length of the pole to cross the origin of the frame of the barn, this is for me the meaning of the lengths contraction), but subsequently the pole length returns to the initial one. (in the frame of the barn) I understand that what I say is strange, I have different ideas than what SR says! If an athlete runs at speed v without the pole, then the situation is different. (there are no two distances in relative motion between them) In this case x = v * t and t_1 < t. (the athlete's clock slows down compared to the barn clock) I consider the two Lorentz transformations: a) x_1 = gamma * (x - v * t) b) x = gamma * (x_1 + v * t_1) With gamma I obviously indicated the Lorentz factor, and I do not consider the other two Lorentz transformations because they depend on a) and b). If x_1 = - x, then t = t_1 If x = v * t, then t_1 < t.
I like to consider the pole and the barn paradox (as you said, it's the same thing)
In my opinion it is impossible for the pole to cross the barn. (if the proper length of the pole is less than the proper length of the barn)
If two equal distances are in relative motion to each other at speed v, the distances overlap. In my opinion, if we denote with t the elapsed time in the frame of the barn and if we denote with t_1 the elapsed time in the frame of the pole, it is t = t_1. (and two equal distances overlap, in this case no problem)
The length of the pole contracts in the barn frame and the length of the barn contracts in the frame of the pole, the two lengths are equal! (suppose they are equal to d)
d = gamma * v * t and d = gamma * v * t_1.
When the two equal distances overlap it is t = t_1 = d / (gamma * v), for each value of d.
If the length of the barn is shorter, in my opinion it is impossible to close the doors of the barn!
The length of the pole is "shorter" (it takes less time for the entire length of the pole to cross the origin of the frame of the barn, this is for me the meaning of the lengths contraction), but subsequently the pole length returns to the initial one. (in the frame of the barn)
I understand that what I say is strange, I have different ideas than what SR says!
If an athlete runs at speed v without the pole, then the situation is different. (there are no two distances in relative motion between them) In this case x = v * t and t_1 < t. (the athlete's clock slows down compared to the barn clock)
I consider the two Lorentz transformations:
a) x_1 = gamma * (x - v * t)
b) x = gamma * (x_1 + v * t_1)
With gamma I obviously indicated the Lorentz factor, and I do not consider the other two Lorentz transformations because they depend on a) and b).
If x_1 = - x, then t = t_1
If x = v * t, then t_1 < t.