Relativity and Clocks on Airplanes Calibrated from the Ground

[Les Sleeth]

I asked this question in another thread, but wonder about the answer I got:

Question: I bought an atomic-timed clock and wondered if while I am taking off from an airport my clock would record time slower than a clock inside the airport. Since time on the clock is actually maintained by a radio signal it receives from the US atomic clock in Fort Collins, would my clock be affected the same way as if it were keeping time all by itself on board the plane?

Answer: No. Your clock will run slow while on the plane, but that will not affect the synchronism of the time updates. Every time your clock receives an update from the Fort Collins WWVB 60kHz atomic-clock radio station, it will revert to Fort-Collins-synced time

Follow-up Question: Why wouldn't the Fort Collins signal, once entering the plane's frame of reference, especially accelerating for take off, be affected and so give a relativity-adjusted impulse to the clock? I can see how light speed of the signal would be the same, but wouldn't the signal's oscillation rate be speeded up/shortened?

 

[Les Sleeth]

Give it to me straight, is my question too obvious to answer? It can't be too hard can it?

 

[Garth]

It depends on how the clock works.

If it is being told the time by the Fort Collins clock, acting only as a repeater, then the distance between the plane and the transmitter will be most important. At 186 miles distance it will be 10^-3 second slow.

If the clock we are taking about is simply a radio receiver, receiving time signals from Fort Collins, and counting the pulses, then the rate of the clock will be retarded/advanced as those signals are red/blue shifted according to the plane's velocity relative to the Fort Collins transmitter. The typical speed of an airliner is about 10^-6 c, which will be the order of magnitude of the red or blue shift.

On top of that effect there will be the SR time dilation effect of the order of one part in 10^-12, which can be ignored.

There will also be a gravitational time dilation. If the plane is flying 4 miles high that will of the order 10^-13 and so that can be ignored as well.

Garth

 

[pervect]

My impression is that Les has a clock of very limited accuracy (compared to an atomic clock) that is synchronized every so often via a radio signal from an atomic clock.

I would expect that this synchronization is done without regard to the position of the clock (unless the clock has a GPS system this would have to be the case).

So my guess is that Les's clock is not really a suitable clock for preforming test of gravitational time dilation.

This is based on the statements that Les himself made about his clock (that's the only source of information I have).

I'm not sure why he wants verification of these statements from us when all we know about his clock is what Les wrote. It sounds like Les contacted the clock's manufacturer to me (that's also a guess).

 

[russ_watters]

It also depends on how the signal is encoded - 60kHz is just the carrier wave and shifting it a little probably won't affect the encoded data.

 

[Les Sleeth]

My impression is that Les has a clock of very limited accuracy (compared to an atomic clock) that is synchronized every so often via a radio signal from an atomic clock.

I would expect that this synchronization is done without regard to the position of the clock (unless the clock has a GPS system this would have to be the case).

So my guess is that Les's clock is not really a suitable clock for preforming test of gravitational time dilation.

This is based on the statements that Les himself made about his clock (that's the only source of information I have).

I'm not sure why he wants verification of these statements from us when all we know about his clock is what Les wrote. It sounds like Les contacted the clock's manufacturer to me (that's also a guess).

I only wanted to know because the answer someone gave me (see my original post) wasn't how I understood relativity worked. I thought the signal, once in the accelerating plane's frame of reference, should be subject to time dilation just like everything else, and therefore would not stay perfectly synchronized time with the US atomic clock even if the signal from Fort Collins were maintained full time.

You are right, it is just an inexpensive clock (though more accurate than any other clock I own) that has a weekly alarm (a rare thing for a clock, in fact, the only one I could find), which is what I wanted; then I started wondering about the effects of relativity out of curiosity. Here's the clock:

http://www.weatherconnection.com/product.asp?itmky=213391

 

[Les Sleeth]

It depends on how the clock works.

If it is being told the time by the Fort Collins clock, acting only as a repeater, then the distance between the plane and the transmitter will be most important. At 186 miles distance it will be 10^-3 second slow.

If the clock we are taking about is simply a radio receiver, receiving time signals from Fort Collins, and counting the pulses, then the rate of the clock will be retarded/advanced as those signals are red/blue shifted according to the plane's velocity relative to the Fort Collins transmitter. The typical speed of an airliner is about 10^-6 c, which will be the order of magnitude of the red or blue shift.

On top of that effect there will be the SR time dilation effect of the order of one part in 10^-12, which can be ignored.

There will also be a gravitational time dilation. If the plane is flying 4 miles high that will of the order 10^-13 and so that can be ignored as well.

Garth

Thanks for the great answer Garth.

 

[Les Sleeth]

It also depends on how the signal is encoded - 60kHz is just the carrier wave and shifting it a little probably won't affect the encoded data.

Hmmmmm, this is probably why the original answer I got from Hitsquad confused me. You mean it will shift the radio wavelength, but the information from Fort Collins will arrive intact, right? I guess for some strange reason I thought the frequency of the radio signal itself calibrated my clock, but that doesn't make sense does it? According to Hitsquad the timing of the US atomic clock is based on 9,192,631,770 vibrations of a Cesium 133 atom in a vacuum, which a little faster than a radio wave.

However, let's say there is a 2nd clock like mine on the ground exactly the same distance from Fort Collins as my clock on the plane is. Shouldn't the carrier wave's shift on plane cause that signal to arrive later than the signal on the ground and therefore my clock will run slower afterall?

 

[TheAntiRelative]

Hmmmmm, this is probably why the original answer I got from Hitsquad confused me. You mean it will shift the radio wavelength, but the information from Fort Collins will arrive intact, right? I guess for some strange reason I thought the frequency of the radio signal itself calibrated my clock, but that doesn't make sense does it? According to Hitsquad the timing of the US atomic clock is based on 9,192,631,770 vibrations of a Cesium 133 atom in a vacuum, which a little faster than a radio wave.

However, let's say there is a 2nd clock like mine on the ground exactly the same distance from Fort Collins as my clock on the plane is. Shouldn't the carrier wave's shift on plane cause that signal to arrive later than the signal on the ground and therefore my clock will run slower afterall?

There'd prolly be some simultaneity issue between the exact moments the two clocks were updated, but updated is updated. The data still remains the same.

After a Very Very long time of flying in a straight line, the minute difference in the time between the arrivals of the updates compared to the time interval that they were sent in would eventually have the clock off by a growing amount, and in addition the time it would take for the signal to arrive would grow with the distance. However, you're flying around on our planet and you'd never get far enough away or go fast enough to see any appreciable difference.

Theoretically, the question would be, if you had a superfine measuring clock and the time for the updating signal to arrive was taken into account in the time update being sent, then you were not updated again after you landed but compared to the reference clock side by side, there should be a difference...

Another question would be, how do you calculate what time to send to the moving clock to have it in sync with your own when you consider that it is in a different frame and therefore not truly simultaneously syncronized.

Then again I could just be chock fulla BS