Relativistic Paradoxes Physics 11 Adv

Ladder and Barn Paradox A ladder and barn are both measured in the rest frame of the barn; if the barn is shorter than the ladder, then the ladder can never be completely contained by the barn A ladder and barn are both measured in the rest frame of the barn; if the barn is shorter than the ladder, then the ladder can never be completely contained by the barn However, if the ladder moves quickly enough through the barn, then its length will be contracted relative to the barn and therefore it will be able to fit inside the barn However, if the ladder moves quickly enough through the barn, then its length will be contracted relative to the barn and therefore it will be able to fit inside the barn If barn is 8.0m and ladder is 10.0m, how fast must you run with the ladder in order to completely contain the ladder in the barn? If barn is 8.0m and ladder is 10.0m, how fast must you run with the ladder in order to completely contain the ladder in the barn?

Ladder and Barn Paradox If we solve for the speed, we will see that the ladder must move at 0.6c If we solve for the speed, we will see that the ladder must move at 0.6c However, it is possible to view this from the point of view of the ladder as it moves through the barn which means that the ladder can never be completely contained! However, it is possible to view this from the point of view of the ladder as it moves through the barn which means that the ladder can never be completely contained!

Ladder and Barn Paradox While this result is apparently contradictory, we can address this paradox if you make use of our idea of the relativity of simultaneity While this result is apparently contradictory, we can address this paradox if you make use of our idea of the relativity of simultaneity While a person moving with the ladder will see two events (one end of the ladder arriving at the second door and the other end of the ladder entering the first door) as separated in time, an observer in the frame of the barn will see these happen at the same time While a person moving with the ladder will see two events (one end of the ladder arriving at the second door and the other end of the ladder entering the first door) as separated in time, an observer in the frame of the barn will see these happen at the same time

Ladder and Barn Paradox If we consider two clocks as synchronized to someone moving in the ladder’s frame then we can consider the offset between these two clocks If we consider two clocks as synchronized to someone moving in the ladder’s frame then we can consider the offset between these two clocks Let us consider the simplest example of light travelling from the far end of the ladder to the end closest to the barn, we can determine the transit time for light (33ns). Let us consider the simplest example of light travelling from the far end of the ladder to the end closest to the barn, we can determine the transit time for light (33ns).

Ladder and Barn Paradox According to an observer in the barn’s frame, the ladder is contracted but the clock at the far end of the ladder must be ahead of the clock at the front. According to an observer in the barn’s frame, the ladder is contracted but the clock at the far end of the ladder must be ahead of the clock at the front. We can first determine the time it would take light to travel from the back clock to the front of the ladder (67ns). We can first determine the time it would take light to travel from the back clock to the front of the ladder (67ns). Then, we must account for the fact that this clock runs slow due to SR (53ns). Then, we must account for the fact that this clock runs slow due to SR (53ns).

Ladder and Barn Paradox Now, we can see that according to an observer in the barn’s frame, the difference between the two observations is ~20ns Now, we can see that according to an observer in the barn’s frame, the difference between the two observations is ~20ns If we then consider the time difference for an observer moving with the ladder for the front of the ladder to exit the barn (36ns) and the rear of the ladder to enter to barn (56ns), we see the same ~20ns time difference If we then consider the time difference for an observer moving with the ladder for the front of the ladder to exit the barn (36ns) and the rear of the ladder to enter to barn (56ns), we see the same ~20ns time difference There is no paradox! There is no paradox!

Twin Paradox Alice and Bob are twins who are 20 years old. Alice is going to board a spaceship that will take her to Proxima Centauri (4.24ly away) at a speed of.85c. Once there, she turns around and returns to earth. Alice and Bob are twins who are 20 years old. Alice is going to board a spaceship that will take her to Proxima Centauri (4.24ly away) at a speed of.85c. Once there, she turns around and returns to earth. Determine the length of time that Bob measures for her to complete her journey Determine the length of time that Bob measures for her to complete her journey Determine the length of time that Alice measures to complete her journey Determine the length of time that Alice measures to complete her journey Determine how far she measures Proxima Centauri to be from earth Determine how far she measures Proxima Centauri to be from earth

Twin Paradox The paradox occurs when one considers that if Bob’s clocks run slow when viewed by Alice that Alice’s clocks must run slow when viewed by Bob. However, the result of this would be when the twins are reunited that Alice would say Bob is older and Bob would say that Alice is older The paradox occurs when one considers that if Bob’s clocks run slow when viewed by Alice that Alice’s clocks must run slow when viewed by Bob. However, the result of this would be when the twins are reunited that Alice would say Bob is older and Bob would say that Alice is older This is often dismissed without further discussion due to Alice’s non-inertial reference frame (speeding up, turning around, slowing down) This is often dismissed without further discussion due to Alice’s non-inertial reference frame (speeding up, turning around, slowing down)