Relation between coordinate time and proper time

[ghwellsjr]

The same device can be used both ways, and in daily life we switch between the uses almost without noticing it. I get on a plane when my wristwatch reads 4:00 PM, get off when it reads 6:00 PM, and my flight was two hours long and I used my watch to measure proper time. If I text someone right before takeoff to say "I land at 6:00; please meet my plane" I'm talking coordinate time for the landing event.

I expect that this is part of the difficulty with explaining coordinate and proper time to students. They have spent their entire lifetime drawing conclusions about proper time and about coordinate time from the same clock readings taken from the same device; it's hard to accept that the same number on the same display is two different statements about two different things.

If your plane went fast enough, and in principle any speed is fast enough, then your wristwatch will not display coordinate time when you get off the plane. Any clock that is going to display coordinate time must remain inertial. And according to Pervect, no clock on Earth can display coordinate time without being rate adjusted anyway.

 

[ghwellsjr]

In physics, there's no such thing as coordinate clocks. Can you find a reference?

See http://openlibrary.org/books/OL15206606M/An_earth-based_coordinate_clock_network

It's not as if everyone uses the exact same words as everyone else. For example; Taylor and Wheeler use the term "far-away time" to refer to coordinate time and they refer to the clocks which keep such time as far-away clocks.

I use the term "coordinate clock" to refer to those clocks which keep coordinate time. This is pretty much standard terminology.

I recommend searching the internet for the terms "coordinate clock" and "coordinate time." using google.

Good idea. Here's a hit I found:

What is a coordinate clock? That is also a non standard term. Is it defined somewhere or are you just making things up?

I would ask you the same thing.

 

[pervect]

Not too suprpisingly, google finds lots of uses of the term.

https://www.amazon.com/dp/B004H8GN66/?tag=pfamazon01-20

An Introduction to Tensor Calculus, Relativity and Cosmology
By D. F. Lawden

"...as measured by his coordinate clock, will be additionally retarded

More uses in:

arxiv.org/pdf/astro-ph/0208234‎
arxiv.org/pdf/gr-qc/0405001‎

 

[Fredrik]

So basically, a "coordinate clock" is a device that displays its own time coordinate in some coordinate system, and the easiest way to build one is to take a clock and have it automatically turn itself back or forward a little once in a while, so that the numbers agree better with the time coordinate of the event, than with the proper time of the world line.

 

[DrGreg]

For what it's worth, Rindler⁽¹⁾ doesn't use the term "coordinate clock", but does use the terms "rate-synchronized clock" and "lattice clock" to refer to the same concept (in the context of "clocks" at rest in a stationary⁽²⁾ coordinate system, not necessarily inertial). He calls proper-time clocks "standard clocks" rather than just "clocks", which is unconventional.

Personally, I see no problem in using the term "coordinate clock" provided you explain what it means the first time you use it.
(1) Rindler, Wolfgang (2006), Relativity: Special, General, and Cosmological, 2nd Ed, Oxford University Press, Oxford, ISBN 978-0-19-856732-5, pp. 184-6

(2) "Stationary" in the technical sense, as in "stationary spacetime".

 

[Nugatory]

If your plane went fast enough, and in principle any speed is fast enough, then your wristwatch will not display coordinate time when you get off the plane. Any clock that is going to display coordinate time must remain inertial. And according to Pervect, no clock on Earth can display coordinate time without being rate adjusted anyway.

Given a simultaneity convention, I can use the value on my wristwatch to assign a time coordinate to any event anywhere, and the motion and inertialness of the watch doesn't matter. I'm just associating events on my world line with events on other timelike worldlines. And that's pretty much what I'm doing anytime I look at my watch and then say into a telephone "It's 4:00".

The resulting coordinate system is pretty awful for purposes of calculation, but it's quite good enough for arranging to have someone meet my plane, which is why we use such coordinates in daily life.

 

[atyy]

For what it's worth, Rindler⁽¹⁾ doesn't use the term "coordinate clock", but does use the terms "rate-synchronized clock" and "lattice clock" to refer to the same concept (in the context of "clocks" at rest in a stationary⁽²⁾ coordinate system, not necessarily inertial). He calls proper-time clocks "standard clocks" rather than just "clocks", which is unconventional.

Personally, I see no problem in using the term "coordinate clock" provided you explain what it means the first time you use it.



(1) Rindler, Wolfgang (2006), Relativity: Special, General, and Cosmological, 2nd Ed, Oxford University Press, Oxford, ISBN 978-0-19-856732-5, pp. 184-6

(2) "Stationary" in the technical sense, as in "stationary spacetime".

Are the lattice clocks in Rindler also proper time clocks, ie. they are the proper time of some clock?

 

[DrGreg]

Are the lattice clocks in Rindler also proper time clocks, ie. they are the proper time of some clock?

No. Rindler describes them as having a lever on them that can be moved, as a one-off adjustment, to make the clock tick faster or slower than proper time, by a constant factor. You adjust them to rate-synchronise them with one clock deemed to be the master lattice clock. And here "rate-synchronisation" means that each clock synchronises its rate to match the rate of the master clock as visually observed at the clock being adjusted. (There is also a question of offset-synchronisation, i.e. choosing a time zero, which depends on the choice of coordinates used.)

Of course in the special case where the lattice clocks are at rest in an inertial frame in SR, no rate adjustment in necessary (although offset adjustment still is). Rindler is considering the more general problem of stationary coordinates in GR.

 

[pervect]

No. Rindler describes them as having a lever on them that can be moved, as a one-off adjustment, to make the clock tick faster or slower than proper time, by a constant factor. You adjust them to rate-synchronise them with one clock deemed to be the master lattice clock. And here "rate-synchronisation" means that each clock synchronises its rate to match the rate of the master clock as visually observed at the clock being adjusted. (There is also a question of offset-synchronisation, i.e. choosing a time zero, which depends on the choice of coordinates used.)

Of course in the special case where the lattice clocks are at rest in an inertial frame in SR, no rate adjustment in necessary (although offset adjustment still is). Rindler is considering the more general problem of stationary coordinates in GR.

This problem (keeping time in a non-inertial frame) has some very important practical applications. Specifically, our atomic time standard, TAI time, is a coordinate time standard in a non-inertial frame (on and near the Earth's surface).

Thus the rate-adjustment procedure described by Rindler (as summarized by DrGreg) is necessary. Rate adjustment has been done since about the 1970's, when the improving precision of timekeeping made it necessary.