Consider a distant observer traveling towards Big Ben in London at the customary .867c. When the distant observer and BB are separated by one light year, between them lies a helical path of light originating from the tip of Big Ben's little hand. At the aforesaid distance of one light year, the reader can easily calculate that the aforesaid helix has precisely 730.5 turns.

At the velocity of .867c it will take the distant observer 1.1534 years to travel one light and reach Big Ben, during which time Big Ben's little hand will have produced another 848.33 turns of the helix, for a total of 1579 turns. So the distant observer is able to count at most 1579 turns of the helix on his 1.1534 light year trip to Big Ben from one light year away at a velocity of .867c

Now we apply the relativistic Doppler formula to the revolution of Big Ben's little hand from the stand point of the distant observer. With the direction of travel towards BB, and beta equal to .867, we arrived at a doppler multiplier of 3.747. Therefore the distant observer must count 2737 revolutions per year due to relativistic doppler, for a source frequency of 730.5 revolutions per year. So during his 1.1534 year trip, according to the relativistic doppler formula, the distant observer must count 3157 revolutions of Big Ben's little hand.

Gentle reader, I ask you to consider which answer to this conundrum are we to choose? Does the distant observer count 1579 revolutions or 3157 revolutions? Must it be one or the other? Or can it be both? Careful.

Part Two coming soon...