Brain Teaser: Einstein Challenged


The next brain teaser is optional and it ismeant to challenge your understanding of the previous lessons. It reaches anerroneous conclusion because one of the assumptions is wrong.


It is a Brain Teaser because the answerwill not follow immediately from the video lectures and the primer. However ifyour intuition is strong, you should be able to guess the answer.


Einstein ChallEnged


We have seen that a light clock behavesweirdly: a moving light clock slows down compared to a fixed light clock. Butis this only because of a weird property of light or does it apply to allclocks?


In other words, does Einstein's specialrelativity apply only to the behavior of some particular objects or moregenerally to our understanding of time?


A contender of Einstein could claim thatour result about the dilation of time only holds for light clocks, but it saysnothing deep about time itself. Everyday clocks are not made out of light raysor particles, but hard matter. The anti-Einstein physicist might pick anotherclock – let's say a basketball clock. His claim would be that both the restbasketball clock and the moving basketball clock would agree with each other. Nocorrection needed here!


The Anti-Einstein Reply


The Anti-Einstein physicist could reasonlike this:


We bounce a ball with a constant, uniformvelocity u, and every beat corresponds to a unit of time



When we move the clock with constantvelocity v, we keep the whole mechanism intact (such that the basketball isstill projected with velocity u perpendicular to the mirrors). Then a unit oftime for the moving clock will be (see fig. 2). But this implies that 


Even if we follow the same derivation as inthe case of the light-clock, we would get the same answer. The basketball moveson a diagonal of length ,with a total velocity, or in absolute terms.


A unit of time corresponds to the ratio ofthe length covered by the basketball divided to its total velocity, i.e. 


We know that and , and replacing above weget:


With either derivation, the anti-Einsteinphysicist would reach the same conclusion: his basketball clock shows the sametime in both frames. How can this be?


Einstein's reply


What would Einstein reply to such achallenge? 


He would reject the claim that for themoving clock the perpendicular velocity is u


He would reject the claim that for themoving clock the total velocity is , and itsabsolute value