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masumpatel6Lv1
25 Apr 2022
Please answer all the questions.
(A)
I have a spaceship that is 20 meters long, and a garage that is only 10 meters long. Clearly, the spaceship won't fit inside the garage. Or... would it? If the spaceship flies at relativistic speeds, it will experience length contraction. At what speed, as a fraction of the speed of light, must the ship fly in order to fit into the garage?
(B)
I equip the garage with doors at both ends. Both doors can be opened and closed using a single switch. I set the spaceship on autopilot and instruct it to fly at the speed obtained in (A). I then wait near the garage.
At the instant when the spaceship is completely inside the garage, I press the switch, and both doors close simultaneously (from my point of view). I immediately press the switch again, and both doors open simultaneously (from my point of view). The spaceship exits the garage unharmed.
But now, let us consider this scenario from the point of view of the spaceship. It sees itself as stationary, and the garage is approaching it at the speed you found in (A). In the spaceship's frame, what is the length of the spaceship, and what is the length of the garage? Will the spaceship fit into the garage in this frame?
(C)
In (A) we found that from my point of view, the spaceship will fit into the garage. However, in (B) we found that from its own point of view, it will not fit into the garage. Clearly, we can't have it both ways; either it fits or it doesn't fit. Can you resolve this apparent paradox? Describe how the chain of events from the spaceship's point of view differs from the chain of events from my point of view.
Hint: Notice that I said both doors close simultaneously from my point of view. How is simultaneity affected by relativity? Also, notice that each door reopens immediately after it closes. This is true in all frames of reference.
Please answer all the questions.
(A)
I have a spaceship that is 20 meters long, and a garage that is only 10 meters long. Clearly, the spaceship won't fit inside the garage. Or... would it? If the spaceship flies at relativistic speeds, it will experience length contraction. At what speed, as a fraction of the speed of light, must the ship fly in order to fit into the garage?
(B)
I equip the garage with doors at both ends. Both doors can be opened and closed using a single switch. I set the spaceship on autopilot and instruct it to fly at the speed obtained in (A). I then wait near the garage.
At the instant when the spaceship is completely inside the garage, I press the switch, and both doors close simultaneously (from my point of view). I immediately press the switch again, and both doors open simultaneously (from my point of view). The spaceship exits the garage unharmed.
But now, let us consider this scenario from the point of view of the spaceship. It sees itself as stationary, and the garage is approaching it at the speed you found in (A). In the spaceship's frame, what is the length of the spaceship, and what is the length of the garage? Will the spaceship fit into the garage in this frame?
(C)
In (A) we found that from my point of view, the spaceship will fit into the garage. However, in (B) we found that from its own point of view, it will not fit into the garage. Clearly, we can't have it both ways; either it fits or it doesn't fit. Can you resolve this apparent paradox? Describe how the chain of events from the spaceship's point of view differs from the chain of events from my point of view.
Hint: Notice that I said both doors close simultaneously from my point of view. How is simultaneity affected by relativity? Also, notice that each door reopens immediately after it closes. This is true in all frames of reference.
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