Apply the Vulcan nerve pinch on Scotty...

(1) Spock should have Scotty pull up the Enterprise along side the Vulcan ship (no speed difference) and then measure the clock rates by taking two readings at two different times.

or

(2) Spock should explain to Scotty that Vulcan scientists are smarter than Human engineers, so he should concede.

Good points, but Vulcan custom will not allow illogical logic, as in your (2).

Hi S

(1)

Scotty: "Ay, Mr. Spock, I agree that those clocks are now ticking at the same rate as ours."

Spock: "So where is the problem, Mr. Scott?"

Scotty: "You have not explained the anomalous elapsed times that I properly measured, Mr. Spock".

Spock: "If this is what you require, I shall now proceed with the explanation".

(2)

Scotty: "But, Mr. Spock, please don't give me those superior Vulcan logic BS. We Scots give it straight and expect it straight."

Spock: ??

It seems to me that the only way the Vulcan clocks can be read is if they are sending out radio transmissions. You must get at least two measurements from each to determine "clock ticks". It seems that on approach to a clock, the ticks would be closer together because of the ships speed, and when past them the ticks would be farther apart. Spock's explanation: "Mr Scott measured only on approach, and failed to compensate by measuring when receding and averaging the results."

Hi S, what you described is similar to 'primitive' missile miss-distance systems, where a continuous carrier wave is transmitted by the test target and the tracking missile has a receiver in the telemetry pack. The Doppler shift is extracted and continuously transmitted to the test center. At flyby, the rate of change of the Doppler shift (from positive to negative) gives the miss-distance, with the time of closest approach at the crossover point.

The Doppler shift gives the relative speed, but if the relative speed is also known from other observations, the Doppler shift can be used to extract the relativistic time dilation from the Doppler. From this, the apparent transmitter base frequency can be obtained, which will confirm Spock's position, i.e. the Vulcan clocks apparently tick slower than the Enterprise master clock.

Reading off values just before and just after the closest approach will, after data reduction, yield the same result. The problem with both methods is that it requires special relativity to prove special relativity, so it is essentially circular. Further, if the Vulcan clocks were on a Vulcan spaceship, also doing Scotty's experiment, they would get identical results in the inverse - concluding that the Enterprise clocks are apparently ticking slower.

One-way time dilation is a relative affair, not an absolute…

-J

Ah, yes time dilation. So if Scotty communicated with the other ship (which might be quite difficult) and asked them to tell him the rate of his clocks to theirs, they would say his were slower. If they said his were exactly the same amount slower as he measured theirs, then he would know both clocks are running at the same rate (to the local observers).

Spock: "Precisely, Mr. StandardsGuy."

I'm adding a little twist to the follow-on entry "Scotty and Spock's CR4 Session".