[time-nuts] Q/noise of Earth as an oscillator

Tom Van Baak tvb at LeapSecond.com
Sun Jul 31 22:16:46 EDT 2016

> Is there a term other than Q that is used to describe the rate of energy loss 
> for things that aren't oscillators?

> cooling (as in hot things)
> discharge (as in capacitors and batteries)
> leakage (as in pressure vessels)
> loss

> An irreversible process would be a better description versus energy loss.
> Like joule heating (resistance, friction).

Notice that these are all energy losses over time; gradual processes with perhaps an exponential time constant, but without cycles or periods. We know not to apply Q in these scenarios.

But when you have an oscillator, or a resonator, or (as I suggest) a "rotator", it seems to make sense to use Q to describe the normalized rate of decay. So three keys to Q: you need energy; you need energy loss; you need cycles over which that loss repeatedly occurs.

We use units of time (for example, SI seconds) when we describe a rate. But here's why Q is unitless -- you normalize the energy (using E / dE) *and* you also normalize the time (by cycle). No Joules. No seconds. So having period is fundamental to Q. It's this unitless character of Q (in both energy and time) that makes it portable from one branch of science to another. And if you measure in radians you can even get rid of the 2*pi factor ;-)

Without controversy, lots of articles define Q as 2*pi times {total energy} / {energy lost per cycle}. To me, a slowly decaying spinning Earth meets the three criteria. It appears to follow both the letter and the spirit of Q.

> ummm…. Q is the general term of rate of energy loss and we just happen to apply 
> it to oscillators in a very elegant fashion….

Oh, no. Now we have both quality factor and elegance factor!


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