How far is this definition of time correct?

[Fredrik]

I prefer to think of time dilation as the ratio of coordinate time and proper time.

Since one of the coordinate times is a proper time in the standard time dilation scenario, that's equally correct.

 

[DrGreg]

what if a network of clocks are moving relative to another network of clocks?
If what you say is correct,then won't co-ordinate time of event measured by the one moving relative to observer change as proper time change?

Lets suppose we have two networks A and B. All the clocks in network A are inertial and at rest relative to each other. All the clocks in network B are inertial and at rest relative to each other. But each network is moving at a constant velocity relative to the other network.

If we pick one clock from network A and compare its proper time against the coordinate time of network B, we find A's proper time runs slow compared with B's coordinate time: one second of the A clock's proper time is longer than one second of B network coordinate time. (Remember, the beginning and end of the time period gets measured by a single A clock but two different synchronised B clocks.)

If we pick one clock from network B and compare its proper time against the coordinate time of network A, we find B's proper time runs slow compared with A's coordinate time: one second of the B clock's proper time is longer than one second of A network coordinate time. (Remember, the beginning and end of the time period gets measured by a single B clock but two different synchronised A clocks.)

(And in case you haven't noticed, the last two paragraphs are identical except that I've swapped "A" and "B".)

If we try to oversimply all of the above you get the apparently contradictory "A is slower than B and B is slower than A", but that's because we've failed to distinguish between coordinate time and proper time. The correct statements are

One B clock's proper time is slower than A network's coordinate time.
One A clock's proper time is slower than B network's coordinate time.​

I'm not sure if that answers your question.

 

[aleemudasir]

Why has my IP address been blocked? I had to use a proxy to access this forum. I am the one who posted the OP.

 

[Fredrik]

Why has my IP address been blocked? I had to use a proxy to access this forum. I am the one who posted the OP.

The IP address that you used to post the OP has not been blocked as far as I can tell, but it's close to a range of IP addresses that was blocked in February for spam. It's possible that your ISP assigned you an IP address from the blocked range today. I will discuss this with the other mentors. Please be patient while I do.

Do you know what IP address you tried to post from today? (If you've left the computer on, you should still have it). It would be interesting to know if it's one of the addresses that were blocked in February. You can tell me in a PM if you don't want to say it here.