# [time-nuts] Are there limits to the accuracy of clocks?

Magnus Danielson cfmd at bredband.net
Thu Mar 30 22:16:15 EST 2006

```From: "Bill Hawkins" <bill at iaxs.net>
Subject: Re: [time-nuts] Are there limits to the accuracy of clocks?
Date: Thu, 30 Mar 2006 16:40:05 -0600
Message-ID: <016501c6544a\$e40e66e0\$0500a8c0 at darius.domain.actdsltmp>

>
> "While we have been discussing stuff that is about 10E-20 below
> what we can measure, is it possible that the limit of resolution
> of the measurement of time is determined by noise? Specifically,
> thermal or Johnson noise in those 50 ohm impedances that we
> use for our cabling."
>
> This didn't provoke any response, so maybe you think I'm crazy.
> You could still be right, but let me explain.
>
> We are talking about the accuracy of clocks, which are basically
> digital counters that are mostly immune to noise. You also need
> an oscillator that generates something that a clock can count.
>
> Noise gets into it at the interface between the oscillator and
> the clock. Assuming electronics (because mechanical oscillators
> have too many sources of error) then something electronic has to
> detect the periodic oscillations and turn them into pulses for
> the clock's first counter/divider. Noise in the detector will
> cause jitter in the clock.
>
> The problem can be reduced by increasing the signal to noise
> ratio. Can amplifiers be made noise-free? Certainly not in
> 10E-15. Johnson noise in 50 ohms is around 10E-8 volt at 100C
> with a one MHz bandwidth. You would need a signal of around
> 10E+7 volts to swamp the noise.
>
> Precision oscillators are cryogenic these days, which could
> eliminate thermal noise.
>
> Truly random noise can be reduced by filtering or averaging
> over time. The amount of time available depends on the use of
> the clock. A time-of-day clock should have no error from noise.

I'm not an expert in physics, but I have not perceived this uncertainty as
noise such as Johnson noise, even if noise may be a good way to explain it.
It is an uncertainty in measurement of time and space, such as if distances
itself had a background noise (mind you, not temperature dependent).

It's in the fabric so to say. If you figure out a way around it you'd probably
come here to Stockholm after a few years, December time.

Cheers,
Magnus

```