Einstein’s Theories of Relativity led to a revolution in our understanding of the movement of bodies, particularly at speeds approaching that of light in an empty medium. The mathematics of which are unassailable, having been proven in so many practical applications such as the ubiquitous GPS systems, by the Perihelion precession of Mercury and by the deflection of light by the sun.
Yet it seems difficult to visualise these effects without being confronted with paradoxes or counter-intuitive phenomena.
For the most part these seemingly irrational consequences seem to derive from the inability to abandon classical Newtonian Mechanics and embrace Einstein’s second postulate, when drawing diagrams of relativistic phenomena; viz. “that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body”
A prime example of this is seen in the following diagram of two Light Clocks with the relative speed of 0.6c. The diagram on the left is drawn of the perspective from Clock A, using Newtonian mechanics. We see the light flash travel both 1 light second within clock B and 0.6 light seconds with clock B.
So after one second using Newtonian Mechanics, the light flash has travelled
√(0.62 + 1.02) = 1.166 light seconds which contradicts the second Postulate.
The diagram on the right is drawn from the perspective of clock B, using Relativistic mechanics. The light in clock A has travelled 0.6 light seconds from clock B when that same light has travelled 1 light second from the light source in clock B.
After 1 second the light has reached (0.6,0.8), clock A’s Frame of Reference, while it has travelled 1 light second along clock B’s time axis which is rotated through angle β.
The time in the moving clock A t’ = 𝜸t where the Lorentz factor 𝜸 for 0.6c = 1.25, in accord with Time Dilation.
We see this same discrepancy in so many diagrams that are drawn to show features of relativity, where the Maths is right, yet the diagrams still hold fast to Newtonian Mechanics because that is the way we have been taught to think.