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

Mon Aug 1 00:51:10 EDT 2016

At the risk of boring everyone, here is an "Alice and Bob" thought
experiment concerning linear and circular movement:

Condition A: Let's say that Alice is in her spacecraft in inertial
straight line travel through nearly free space containing a thin gas
which creates a slight friction to movement. She is traveling at 628
meters per 24 hours adjacent to a distance scale with markers every 628
meters on the space highway. Passing a marker results in a tick. So she
can check her atomic clock every 24 hours at the tick. The thin gas
causes a slight reduction of her velocity (about a 2 millisecond
increase in tick interval every century).

Question: Does the movement of Alice exhibit Q? If so, how can we compute the value? If there a resonant frequency?

Condition B: Bob is in his spacecraft, which is identical to Alice's
model. A rod 200 meters long connects Alice's craft and Bob's craft. Bob
is moving at 628 meters per 24 hours in the opposite direction of Alice,
so that the midpoint of the rod is fixed and unmoving with regards to
the distant stars. Alice will return to the same point in space every 24
hours and pass a marker, generating a tick so she can check her atomic
clock once a day at the tick. Her linear motion has been constrained to
circular motion due to the stiff rod. The same thin gas is present,
resulting in a 2 millisecond increase in tick interval every century.

Question: Now does the movement of Alice exhibit Q? If so, how can we compute the value? If there a resonant frequency?

Consider that in either Condition A or Condition B Alice (and Bob) can
increase or decrease their velocity to receive timing ticks at a
faster or slower rate. But there is no tendency for the velocity to
return to the one tick per day rate (628 meters per 24 hours), as
there would be with a harmonic oscillator. Due to Newton's First Law,
the velocity remains constant unless slowed by friction or affected by
external forces.

We could have started with a rod which was in the limit very long, so
the motion of Alice was only slightly diverted from a straight line
during a 24 hour interval. We could still measure the motion in 628
meter distance intervals on a circular or angular scale. Note that
nothing is fundamentally different if the rod is the exact length which
causes one rotation every 24 hours. The distance traveled and the
inertia resisting change in velocity is the same if the motion is linear
or circular, isn't it?
--
Bill Byrom N5BB

On Sun, Jul 31, 2016, at 10:27 PM, Bill Byrom wrote:
> I still claim that there is no natural frequency associated with the
> rotation of a body. The periodic nature of the rotating body motion is
> confusing you. The choice of a coordinate system is what is confusing.
>
> As I pointed out, what's the difference between an inertial
> body moving
> in a straight line and a rotating body? Let's say you take a
> body moving
> in free space with a small energy loss due to interactions with thin
> interstellar gas. You measure it on a ruler with marks every
> 628 meters
> (to use my example of a point on the Earth 100 meters from the
> pole as a
> comparison). That's the same as making an astronomical measurement on
> the Earth at a distant star which is overhead every 24 hours. In both
> cases the point moves 628 meters every 24 hours (measured with
> an atomic
> clock). We generate a tick when the Earth has rotated to the same
> relative position and when the body moving in a straight line reaches
> the next 628 meter mark. Both objects generate a tick every 24 hours,
> but the velocity is each case (angular or linear) is unconstrained by
> any periodic physical processes.
>
> What makes the rotating body (Earth) suitable for study as a harmonic
> oscillator with Q in this case? There is no energy transfer
> during each
> rotation. Should we establish a Q value for the body in free space
> straight line motion?  Both bodies have mass, inertia, a nearly
> constant
> velocity (linear and angular), and a slight loss. Each
> generates a tick
> every 24 hours (using the atomic clock as a reference). If we
> unwrap the
> polar coordinates and view the Earth rotation angle as increasing
> monotonically (or make marks every 628 meters on the scale
> measuring the
> free space body with straight line travel) they are identical.
>
> The geometry of the rotating body (Earth) is fooling you into thinking
> it's a periodic oscillator. Just because the position is similar after
> 24 hours doesn't mean anything, since there is no energy storage and
> transfer during each rotation. The Earth is reasonably symmetric (for
> this discussion), and it has no field which matters for this
> discussion
> which is rotating. It's just matter moving in a constrained circular
> fashion due to the geometry and constraints of a rigid body.
> Change the
> coordinate scale to linear (628 meters for each rotation at 100 meters
> from the axis) and compare it to the free space object moving in a
> straight line. What's the difference?
>
> --
> Bill Byrom N5BB
>
>
>
> On Sun, Jul 31, 2016, at 09:16 PM, Tom Van Baak wrote:
>> Hal:
>>> Is there a term other than Q that is used to describe the rate of
>>> energy loss
>>> for things that aren't oscillators?
>>
>> Jim:
>>> cooling (as in hot things)
>>> discharge (as in capacitors and batteries)
>>> leakage (as in pressure vessels)
>>> loss
>>
>> Scott:
>>> 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.
>>
>> Bob:
>>> ummmâ€¦. Q is the general term of rate of energy loss and we just
>>> happen to apply
>>> it to oscillators in a very elegant fashionâ€¦.
>>
>> Oh, no. Now we have both quality factor and elegance factor!
>>
>> /tvb
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