Classical Travel of Light Back from B to A

  The Flaw

 

 

 

 

 

 

 

 


Here we derive classically (without STR) the time interval t'A - tB of the reverse travel of the photon from B back to A for a source of light at rest with the stationary system. In Classical Physics we can always arrange matters so that the source of light at rest with the stationary system flashes when it coincides with the end B of the rod.

The classical laws of motion (no STR) of the photon F and of A are as follows:

F(t) = F(tB) - c(t - tB)
A(t) = A(tA) + v(t - tA)

Thus, for time t = t'A we have purely classically (no STR)

F(t'A) = F(tB) - c(t'A - tB)
A(t'A) = A(tA) + v(t'A - tA)

At time t'A the positions of the photon and A coincide, therefore the distance between F and A is zero and we may write:

0 = F(t'A) - A(t'A) = F(tB) - c(t'A - tB) - A(tA) - v(t'A - tA) =
= F(tB) - A(tA) - c(t'A - tB) - v(t'A - tB + tB - tA) = F(tB) - A(tA) - v(tB - tA) - (c + v)(t'A - tB),

However, from the law of motion of A we have, purely classically (with no STR), that

A(tB) = A(tA) + v(tB - tA),

which we substitute in the above expression to obtain

0 = F(tB) - A(tB) - (c + v)(t'A - tB).

or

t'A - tB = (F(tB) - A(tB))/(c + v)

When the photon reaches B the position of the photon and B coincide and, therefore, F(tB) = B(tB), which leads purely classically (with no STR) to

t'A - tB = (B(tB) - A(tB))/(v + c) = rAB/(v + c) (see why B(tB) - A(tB) = rAB ...).