2-07.htm

2.7 The Sagnac Effect

Blind unbelief is sure to err,

And scan his work in vain;

God is his own interpreter,

And he will make it plain.

William Cowper, 1780

If two pulses of light are sent in opposite directions around a stationary circular loop of radius R, they will traveled the same inertial distance at the same speed, so they will arrive at the end point simultaneously. This is illustrated in the left-hand figure below.

The figure on the right indicates what happens if the loop itself is rotating during this procedure. The symbol a denotes the angular displacement of the loop during the time required for the pulses to travel once around the loop. For any positive value of a, the pulse traveling in the same direction as the rotation of the loop must travel a slightly greater distance (12 - 1 ccw) than the pulse traveling in the opposite direction (12-11 cw). As a result, the counter-rotating pulse arrives at the "end" point slightly earlier than the co-rotating pulse at exactly the same time.

HAHAHA!

As you can clearly see, the red pulse arrives at the "end" point earlier than the blue pulse after 12 time units by taking 12 time units. Moreover, the speed of the counter-clockwise red ray between 12 and 6 is at least a whole c, whereas the speed of the clockwise blue ray between 12 and 6 is only c.

Q. Why do the idiots replace

t = (2p+a)R / (c+v)

and

t = (2p-a)R / (c-v)

with

t₁ = 2pR / (c+v)

t₂ = 2pR / (c-v)

when we clearly have

t = 2pR / c

in the rotating frame?

A. Because they are stupid.