🕒Absolute Clock Design that Accounts for Time Dilation
99% of people believe in absolute time: that time passage / flow is the same everywhere and always. One of such believers was Newton himself: despite having invented math for gravity, he acknowledged not understanding the nature of gravity. Since Einstein, 1% of people are aware that time flow varies from place to place and from time to time. Einstein coined the term “time dilation” for time slowing down around massive objects or in fast moving objects, and explained that gravity is caused by time dilation. Actually, time flow varies everywhere outside in the Universe and everywhere inside atoms and particles: it is more than ubiquitous, it is in time nature. Without time variability there would be no matter — our Universe would be empty. Absolute Time is just an approximation for real time.
Modern technologies account for time variability already. We discussed that time in Geolocation Satellites runs at about half nanosecond per second faster compared to the time on the Earth. Our smartphone triangulates its position by calculating distances to GPS satellites. How the distance to a satellite is calculated: time it takes for a signal from a satellite to reach the smartphone is multiplied by the speed of the signal, which is the speed of light c ≈ 300,000 km/sec. For a half nanosecond time discrepancy, the error in distance calculation is miniscule: 0.5 ns × 300,000 km/sec = 0.15 m = half a foot or so. But this is the error per second, and in a day (which is 24 × 3600 = 86400 sec) it accumulates to 7 miles. In a week, the error would be 49 miles. Thus, 24 GPS satellites, worth billions of dollars, become useless, if time dilation is ignored. There are known ways for solving this problem.
Here I suggest a simple modification to the electric circuit of an atomic clock, which makes clocks “absolute” — synchronized among each other, everywhere and always. Usual clocks do two things: they “tick” — generate a second, and they “tock” — count seconds. Instead of counting seconds, we will measure a capacitor’s capacitance every second (or every hour) and accumulate square root of that measurement, like that:
— Atomic clock generates a second;
— Multimeter measures capacitance X of the capacitor then (or less often);
— Calculator adds √X (square root of X) to the previous total;
— Such total is the synchronized time between all such clocks, always.
Why is that? That is because capacitors “feel time dilation”: if time slows down by a factor D, their capacitance in such a slow time environment increases by D²-factor. Let’s compare work of such clocks in “normal” time and in 10-times-slower time, to watch synchronization:
- On every tick of the clock in “normal” time, multimeter shows capacitance of the capacitor as X = 1. So, we add √X = √1 = 1 to the total. After 10 ticks, the total is increased by 10 × √1 = 10.
- In the same time period, in 10-times-slower time, clock ticks only once, indicating 1 local second passed, and multimeter shows the capacitor’s capacitance X = D² = 10² = 100: thus, calculator adds √100 = 10 to the total.
- Both clocks remain synced. Otherwise, the first clock would show 10 seconds passed while the second clock showing 1 second passed.
