A high Q tuned circuit will have very poor temporal resolution, due to the uncertainty principle. This is not the way to get highly accurate temporal synchronization.
On Dec 18, 2017, at 2:18 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I'll have to beg your forgiveness about the sketchiness of this description. I'm trying to operate at a very high level of generality, so the details must necessarily be somewhat sketchy.
We have 2 processes/devices A,B who want to "communicate" with one another, but must first "synchronize".
Let's assume that the processes/devices are at a fixed constant distance d from one another, so there are no Doppler/relativity issues.
If one process A "sends"/"emits" a sinusoidal signal, the other process B may "see"/"feel" the signal, and if there is some sort of *tuned circuit* (e.g., RLC "tank" circuit with a center frequency f and a Q of q) in the receiving process, then the receiver may see an amplification of the received signal as a result of the incoming energy being absorbed by the receiver *in phase*. Indeed, if the energy of the incoming sinusoidal signal is high enough, and it falls within the width of the frequency window of the RLC circuit, the receiver could actually explode! Think of a bell tuned to the sound of an incoming tone, and if the Q of the bell is high enough relative to the incoming energy and if the frequencies are matched well enough, the receiving bell could vibrate strongly enough to destroy itself.
[I.e., the "R" in the RLC circuit loses less energy per cycle than the incoming energy per cycle, after which point the energy in the receiving RLC circuit "runs away".]
Although the 2 processes/devices may have once been calibrated w.r.t. one another, it may have been a long time, so the two devices may not agree on either the absolute time or even the *rate* of time ("drift"), so for the two processes to communicate, they may first have to synchronize their clocks.
By lowering the Q of the circuit, the receiver's sensitivity is reduced, but its frequency width is increased, so the receiver can "hear" incoming signals with greater difference between the sender's notion of frequency and the receiver's notion of frequency.
So one strategy for the listener is to start with a low Q, and attempt to detect *any* energy increase due to an incoming signal. Let's assume that there is some mechanism to adjust the receiver's phase, so that the receiver can determine if its receiving frequency is too low or too high, and can therefore adjust the frequency in the correct direction for improved reception. The receiver then adjusts its receiving frequency by a small delta, and simultaneously increases the Q by a small amount.
The improved center frequency and the improved Q should enable the receiver to more easily detect the incoming signal.
If this process is *iterated*, then the receiver should be able to hone in on the correct frequency and reduce the *width* of the RLC frequency response. Of course, as noted above, the receiver needs to be careful to keep the Q low enough to avoid catastrophe.
Question #1: What is the optimum search strategy for the receiver to hone in on the correct frequency of the sender as quickly as possible? Does the number of bits in the frequency precision grow linearly? Is there a strategy which allows quadratic increase in # of bits of frequency precision?
So far, we have assumed that the sender unilaterally sends, and the receiver unilaterally receives. But in any real system, the sender and receiver are *symmetrical*: the receiver's RLC circuit also radiates its own signal which is "received" by the sender's RLC circuit. So both A & B are sending and receiving at the same time.
So now, what strategy should be used by both A & B *simultaneously* to *converge* upon an extremely narrow frequency that they can both "agree" upon? Since only A & B want to communicate with one another, they don't really care about the *absolute* frequency, but only upon reducing the *difference* between their frequencies to the smallest amount possible, in terms of the number of bits of precision in the frequency.
Question #2: What is the simultaneous & *symmetrical* optimal frequency "search" strategy?
For the moment, we assume *classical* (non-quantum) physics, so we don't have to worry about discrete energy chunks.
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