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I think they should start teaching special relativity in Kindergarten and general relativity in junior school as they seem to be the two subjects that cause the most confusion if this forum is anything to go by.
We have two inertial frames of reference, K and K* (for example K could be a railway station and K* a train) in relative motion at velocity v > 0 along the positive x.The coordinate transformation (x , t) -> (x*, t*) (t is time) have to be linear, since a uniform, rectilinear motion in K, is such in K* too. The most general linear transformation is:x* = A x + B t ( 1 )t* = C x + D t ( 2 )where A, B, C, D donít depend on the coordinates but, at maximum, on v only.According to ( 1 ) and ( 2 ) a signal (or an object) velocity in K* is:u* = dx* / dt* = ( A u + B ) / ( C u + D ) ( 3 )where u = dx / dt is the signal velocity in K.Clearly,u* = 0u = 0implies, respectively:u = v since a stationary body in K* moves, in K, at v u * = - v since a stationary body in K moves, in K*, at -v so, for (3), B = - Av; B = - Dv, and so:D = AB = -AvFrom which:u* = ( u - v ) / [ 1 + ( C u / A ) ] ( 4 )which can be wrote as :u* = ( u - v ) / [ 1 - ( u v / F2 ) ] ( 5 )where: F2 = - A v / C ( 6 ).First case: F2 = infinite.We get the galileian transformation law of velocities: u* = u Ė v.Second case: F2 < 0.We have to exclude it because, if it were true, a signal which has in K negative velocity u (that is from the head to the tailorís train) and such that u < F2 / v, would have in K* positive velocity u* (that is from the tailor to the headís train) and this is absurd since the impact of signal with the trainís head is an objective fact on which K and K* must agree (if the signal destroyes the trainís head, K and K* must agree on this destruction).We are left with F2 > 0.Since F has the dimensions of a velocity, we can imagine a signal which has velocity u = F in K. According to (5) the velocity of the same signal in K* is u* = F, that is is the same value F.So, according to the couple K-K*, there is an absolute velocity F.Conclusion: the existence of (at least one) an absolute velocity (finite or infinite, this can only be determined by experiment) that is, the fact light speed doesnít depend on the sourceís velocity, comes from pure cynematics, without using the second postulate of SR. In the text: W. Rindler, Relativity (special, general and cosmological) 1977 edition, there is the proof that the absolute velocity F doesnít depend on v.
When I took first year college Physics...Hmmm...They combined the lab activities for the Physics with Calculus and the Physics without Calculus courses.Some of the COLLEGE students had a lot of troubles with the basic concepts of Newtonian physics...If the average college student has troubles understanding Newtonian Physics... how can you imagine that a kindergarten student could understand concepts of light, waves, and relativity?