- #1

- 31

- 6

## Homework Statement

Special relativity: A rod travelling with the relativistic velocity of 0.866c moving towards a garage. The length of the rod is L, that of the garage is L/2. From the reference frame of the garage, we find the value of Lorentz factor = 2 we say that rod would fit inside garage momentarily. Now we take this scenario from rod's frame and find the length of garage L/4. Since mechanical pressure can't travel faster than light, so we find by the time light(mechanical pressure) reaches the free end the rod has shrunk without any resistance to a size of L times (1-0.866) = 0.134L<0.25L, and therefore can easily fit inside garage.

My question is - In garage's frame of reference rod barely fits inside while in rod's reference frame it can fit inside with margin to spare, is this difference in observation valid?

Also if this is correct then what happens if I increase the size of rod and keep the size of garage fixed so that it can fit inside garage from rod's frame but not from garage's frame?

**2. The attempt at a solution**

I do understand that concept of simultaniety holds little value in SR because simultaneous event in one frame may not be so in other, but I think that observation like the one in this case should be same although explanation may differ, but I don't see how that would happen in the given question.

Here by observation I mean the end result of whatever events occur.