Special Relativity - Length Contraction

Questions 69-71

A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.

Which of the following statements is the best response to the question: “Was the car ever inside a closed garage?”

1. No, because the car is longer than the garage in all reference frames.
2. No, because the Lorentz contraction is not a “Real” effect.
3. Yes, because the car is shorter than the garage in all reference frames.
4. Yes, because the answer to the question in the garage’s rest frame must apply in all reference frames.
5. There is no unique answer to the question, as the order of door openings and closings depend on the reference frame.

(GR8677 #71)

Solution:

In the garage’s frame:
The length of the garage = 4 m
The length of the car = 3 m
L_car  L_garage → A. FALSE

In the car’s frame:
The length of the garage = 2.4 m (from problem GR8677 #70)
The length of the car = 5 m
L_car L_garage → C. FALSE

→ No unique answer, it depends on the reference frame

Answer: E