Question

Suppose you are told that the linear size of everything in the universe has been doubled overnight can you tell the statement by measuring sizes with a metre stick ? can you test it by using the fact that the speed of light is universal constant and has not changed ? what will happen if all the clocks in the universe also start running at half the speed ?

Answer 1

Yeah it can be tested remembring that the speed of light is constant.
Suppose you measured the time taken by speed of light from one place to another in normal world, in the altered world although the length will be doubled but the time is still running at the same pace, so light will take more time to travel the same distance in this way we can observe that the length has been altered.
We can not test this statement by measuring sizes with a metre stick because its length will also increase.

Now if the clock also starts running at half speed then there will be no time difference in both the cases and hence we wont be able to observe the change.
because the light will travel a distance that travelled in 1 second in normal world by half second in the new system because clock running at half speed
so 1 second in normal world = half second in new system

hope you understand this