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# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. You are welcome to comment upon or question anything said on my website (http://www.relativity-4-engineers.com), in the eBook or in the snippets I post here.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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### Scotty and Spock's Vulcan Clocks

Posted December 29, 2011 1:00 AM by Jorrie

We know that two ideal clocks permanently at rest relative to each other can be synchronized by means of the Einstein method.(1) Simply stated it means: measure the distance (d) between the clocks (Alpha and Beta); send a light pulse from Alpha to Beta at time t; when that pulse reaches clock Beta, set its time to t+d/c.

An equivalent method is to start with the two clocks in close proximity, set both to the same time and then slow-transport either Alpha or Beta (or both) to end up a distance d apart. Their synchronization can then be verified in both directions, using the above method, ensuring that they are indeed "Einstein-synchronized".

These two clocks were of Vulcan origin and Starship Enterprise performs a flyby at a (mild) speed of 0.6c. When adjacent to clock Alpha, Scotty records the time on its display and also the ship's clock's time. He does the same when adjacent to clock Beta, so that he could compare the elapsed time between the two flybys, as given by clocks Alpha and Bravo and by the ship's clock. To his surprise, Scotty finds that the elapsed time between the flybys according to the two clocks is larger than what the bridge clock has shown.(2)

At the debriefing Captain Kirk requests: "Right Mr. Scott, did we learn anything about the Vulcan clocks in this experiment?

Scotty: "Ay, Captain, we found that Vulcan clocks tick faster than our bridge clock".

Spock: "How can you say so, Mr. Scott? All Vulcan clocks conform to the United Federation of Planets standards of time. What is more, Starfleet physics predicts exactly the opposite. The Vulcan clocks were moving relative to our ship, so to us they will appear to tick slower than the bridge clock".

Scotty: "Sorry Mr. Spock, but I measured it and as Kepler once said: to measure is to know."

Spock: "Captain, Mr. Scott never measured the rate of the Vulcan clocks".

Kirk cuts them short: "Scotty, I spot a difference of opinion here. Mr Spock, will the two of you please settle the issue off the bridge and then report back".

If you were Spock, how would you have resolved the disagreement?

-J

Notes

1. "Permanently at rest relative to each other" implies free-fall in zero (or at least extremely weak) gravity and not too far apart.
2. Take c as one foot per ns, the distance (d) between the clocks as 1000 ft in the Vulcan frame. Clocks Alpha and Bravo will then show an elapsed time of 1667 ns between the flybys, while the bridge clock will record the elapsed time as 1333 ns.

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#1

### Re: Scotty and Spock's Vulcan Clocks

12/30/2011 10:00 PM

Apply the Vulcan nerve pinch on Scotty...

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#2

### Re: Scotty and Spock's Vulcan Clocks

01/01/2012 11:42 AM

(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.

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#3

### Re: Scotty and Spock's Vulcan Clocks

01/02/2012 12:18 AM

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

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#4

### Re: Scotty and Spock's Vulcan Clocks

01/03/2012 12:05 AM

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: ??

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#5

### Re: Scotty and Spock's Vulcan Clocks

01/11/2012 10:26 PM

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."

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#6

### Re: Scotty and Spock's Vulcan Clocks

01/12/2012 1:51 AM

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

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#7

### Re: Scotty and Spock's Vulcan Clocks

01/14/2012 2:45 PM

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).

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#8

### Re: Scotty and Spock's Vulcan Clocks

01/14/2012 11:40 PM

Spock: "Precisely, Mr. StandardsGuy."

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

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