# Sync time between two points

Suppose we have two points, A and B, each point has its own clock.

We are able to send messages between A and B, the message takes some random delay to be delivered: $$min < delay < max,$$for each message the actual delay is unknown.

In this setup:

• Can we sync clock at this points perfectly?
• Can we prove that it is impossible to sync perfectly?
• Can we prove that it is impossible to sync this clock with a precision, which is better than some $f(min, max)$? (In other words, that after any sync process, this clock will still have difference at least $f(...)$)

Precision is the difference between this clock after actually syncing.

• I asked the same question in physics, physics.stackexchange.com/questions/94488/… but I bet that was the wrong place. – Rustem Mustafin Jan 21 '14 at 10:27
• Is the delay fixed? i.e. if A sends B a couple of messages, will the delay be the same? – R B Jan 21 '14 at 14:36
• @RB for each message the delay is random. Although, nothing forbids you to pack several data items in one message. – Rustem Mustafin Jan 21 '14 at 20:08
• What distribution do the random delays take? If it's from a fixed distribution and min,max are bounded (or, rather, the variance is bounded), A and B can keep sending timestamps back and forth (replying as soon as they get the message) to identify the average ping within a small error (via CLT), and then adjust the clocks as necessary based on the timestamps. – Yonatan N Jan 21 '14 at 21:19
• Time is relative. en.wikipedia.org/wiki/Twin_paradox In general you are screwed unless you can ensure that they keep their pings (speed of light distance) within a tight tolerance. – Chad Brewbaker Jan 21 '14 at 23:00