Relation between coordinate time and proper time

[ash64449]

However, doing it in a real situation, as you requested and as Einstein described, is not easy. You basically would require a number of synchronized clocks all along the tracks that could record when each end of the rod reached them and then you would have to go back and examine the records to find two times on two different clocks that were the same and each indicated the passing of one end or the other of the rod.

No,You don't need a number of synchronized clocks all along the tracks that could record when each end of the rod reached them

Your method lacks any means to determine the same time at both events, but Mentz pointed this out already so I won't belabor the point.

Yes.Now i understood the meaning of what Mentz was actually saying-You cannot measure at the same time,both events. Well,there is a way to measure both events at the same time:

Take a Snapshot.

Think that i have a detector in my hand,which immediately photographs the whole events taking place when the rod meets at point "A". Now whatever we see in that snapshot are the simultaneous events with the event of which one end of the rod meets at point A.

So,here we see that observing only 'one' event helps us to know all other events that are 'simultaneous' with other events.

What is wrong with this?

 

[Popper]

I don't know why you would express Proper Time in this way. It makes it sound like there is a single Proper Time between two events but as you correctly point out, it is measured by a clock which moves through both events, but what you didn't point out is that it is dependent on the path of that clock between those two events so two different clocks taking two different paths can end up with different accumulated times on them.

Because the OP asked what the difference was between proper time and coordinate time. He didn't ask what the properties of proper time are. I was only attempting to explain what the definition is and that definitions I stated is precisely correct. In my opinion just because I didn't say that there are many ways for a clock to move between two clocks doesn't mean that my answer was wrong or lacking.

But if you insist on being complete; the proper time between two events is the time measured by a clock (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events.

Also, when you are talking about coordinate time, you should not be connecting it with actual clocks.

I disagree. Coordinate time refers to actual clocks so it was very important to mention them.

 

[ghwellsjr]

But if you insist on being complete; the proper time between two events is the time measured by a clock (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events.

It's not a matter of being complete--it's a matter of adding so much extraneous stuff. Let me take your definition and purge it of what isn't needed:

the proper time [STRIKE]between two events[/STRIKE] is the time measured by a clock[STRIKE] (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events[/STRIKE].

Since a clock can only travel on a timelike worldline, why do you include that? And why do you want to limit it to two events? Every clock continuously measures out Proper Time.

Also, when you are talking about coordinate time, you should not be connecting it with actual clocks.

I disagree. Coordinate time refers to actual clocks so it was very important to mention them.

If Coordinate Time refers to actual clocks and Proper Time refers to actual clocks, then what's the difference? Remember, you said:

Because the OP asked what the difference was between proper time and coordinate time.

 

[ghwellsjr]

George,i cannot see the images that you posted in this post.

You need to be logged on in order to see images that are uploaded to the Physics Forums.

Anyway i understood the significance of this post-it says that you cannot conduct experiment by only observing.There always include assumptions and the fact that we cannot observe 'two' events at the same time. But please clarify a little bit by answering to the post that is present below to this one.

Please log on an study my post. It can teach you a lot. That's what you are badly in need of.

 

[ash64449]

You need to be logged on in order to see images that are uploaded to the Physics Forums.

Please log on an study my post. It can teach you a lot. That's what you are badly in need of.

George,i don't understand.Still i cannot find the images.

What do you mean i need to be logged on?

Shouldn't i need to log on to reply post? Do you mean that? Well,then i am logged on and still i cannot see them. The images that you posted on #47.I am not talking about the images in the quote.i am not seeing images that you posted..

 

[ash64449]

George,when i open the image in new tab,this message appears:

vBulletin Message

Invalid Attachment specified. If you followed a valid link, please notify the administrator

 

[ghwellsjr]

I re-uploaded them, even though I could see them. Can you see them now?

 

[ash64449]

I re-uploaded them, even though I could see them. Can you see them now?

YES! I can see them now.. I will read them very carefully and then reply

 

[ghwellsjr]

However, doing it in a real situation, as you requested and as Einstein described, is not easy. You basically would require a number of synchronized clocks all along the tracks that could record when each end of the rod reached them and then you would have to go back and examine the records to find two times on two different clocks that were the same and each indicated the passing of one end or the other of the rod.

No,You don't need a number of synchronized clocks all along the tracks that could record when each end of the rod reached them

Your method lacks any means to determine the same time at both events, but Mentz pointed this out already so I won't belabor the point.

Yes.Now i understood the meaning of what Mentz was actually saying-You cannot measure at the same time,both events. Well,there is a way to measure both events at the same time:

Take a Snapshot.

Think that i have a detector in my hand,which immediately photographs the whole events taking place when the rod meets at point "A". Now whatever we see in that snapshot are the simultaneous events with the event of which one end of the rod meets at point A.

So,here we see that observing only 'one' event helps us to know all other events that are 'simultaneous' with other events.

What is wrong with this?

Mentz already pointed out what is wrong with taking a snapshot when you said the same thing way back in post #29:

well,there is a way to do that. Take a camera,when the observer sees the rod reach at the points B,take the picture. In it i am sure that he can determine that.

I don't know why you think a camera would be any better than an observer's eyeballs. Both are subject to the light travel time from each event to the camera/eye and since it is different for the two events in question, they will not see both events at the same time, even though we specify that they must be in order to determine the correct length of the rod.

Are you aware that if you set up a row of clocks and synchronized them and then looked at them, they would all have different times on them? Each further clock would be for an earlier time. That's why taking a picture won't help.

 

[ash64449]

George,in shorter terms,you were trying to show that Black observer cannot know which IRF he is using so as a result he cannot know what the length contraction is?(#47)

Makes sense to me!

 

[ash64449]

Mentz already pointed out what is wrong with taking a snapshot when you said the same thing way back in post #29:



I don't know why you think a camera would be any better than an observer's eyeballs. Both are subject to the light travel time from each event to the camera/eye and since it is different for the two events in question, they will not see both events at the same time, even though we specify that they must be in order to determine the correct length of the rod.

Are you aware that if you set up a row of clocks and synchronized them and then looked at them, they would all have different times on them? Each further clock would be for an earlier time. That's why taking a picture won't help.

oh,So RoS does not help us to make measurements in a right manner as a result we cannot determine what is the actual length of the rod. Because of RoS, We cannot perform and cannot understand by observing actually which events are simultaneous with which.Correct?

 

[ghwellsjr]

oh,So RoS does not help us to make measurements in a right manner as a result we cannot determine what is the actual length of the rod. Because of RoS, We cannot perform and cannot understand by observing actually which events are simultaneous with which.Correct?

The only time that two simultaneous events will be observed simultaneously is when the observer is equidistant from both events. (That's the definition of simultaneity.) But in terms of measuring the length of a moving rod, it's best to record as much information as possible and then go back and figure out which events taken at the two ends of the rod meet the criterion of being at the same time.

 

[Popper]

It's not a matter of being complete--it's a matter of adding so much extraneous stuff.

Different people are going to have different views and different ways of describing things. If something is unclear then its my experience that the person seeking the answer will ask about it.

Let me take your definition and purge it of what isn't needed:

That will be purely your opinion, of course.

the proper time [STRIKE]between two events[/STRIKE] is the time measured by a clock[STRIKE] (or person attached to the clock/wristwatch) which travels on a timelike worldline between the two events[/STRIKE].

I strongly disagree.

Since a clock can only travel on a timelike worldline, why do you include that?

The reason I referred to a timeline worldline was to intentionally be redundant for clarity. Who knows? Someone might think of a way to speak of the decay of a tachyon (a theoretical particle which travels faster than the speed of light) and perhaps it can decay. The one might want to speak of the proper time along a spacelike worldline so I made sure that I said timelike so that it's not used for tachyons. I'm not sure about proper time concerng tacyons and whether they can decay and what iwould mean to speak of the proper lifetime of a tachyon. So I leave it into make sure the tachyon people know that the definition I gave does not apply to tachyons.
In any case it doesn’t hurt it. If you disapprove then leave it out of the definition the nest time you post one.

And why do you want to limit it to two events? Every clock continuously measures out Proper Time.

Since proper time refers to the time interval between two events. That’s its very meaning. Please post an example of what you’re referring to.

Since proper times is path dependant this gives the integral the limits its required. A starting event and a terminal event so that the proper time has meaning. To speak merely of “proper time” as in “Hey frank! What’s the proper time along my worldline?” would have no meaning since the proper time refers to the integral of the proper time differential dT over the worldline and that integral must have two limits.

If you disagree then please post an example of the proper time pertaining to an arbitrary worldline.

If Coordinate Time refers to actual clocks and Proper Time refers to actual clocks, then what's the difference?

I guess I didn’t make that clear. Perhaps I wrongly assumed that the OP knew about how coordinate time was defined, i.e. in terms of an array of clocks. There is no requirement for anything to move between coordinate clocks.

Let me describe how to define coordinate time: Visualize a Cartesian coordinate system which is marked off with xy-axes and has tick marks which describe distances, like, for example, your everyday average meter stick has a series of lines marked on it with numbers above the marks telling you how far from the “origin” end of the meter stick to the mark on the meter stick. Now think of where these axes intersect and think of a clock placed at all intersections. Each clock has an identical construction to a clock used as a standard. Each clock will be set to start ticking when it receives a light signal from the systems origin. If the clock is at the location (x, y) then the distance from the origin to the clock is d = sqrt(x^2 + y^2). It will take a time t for the light to reach the clock. Since the speed of light is the same in all frames it’s the same in this frame and has the value c = d/t. Therefore when the clock at (x, y) receives a light signal it sets the time to t = d/c. The clock at the origin is the one that sends out the light signal (which is referred to as a timing signal). When the timing signal is sent the origin clock is set to read t = 0.

That is conceptually how you synchronize clocks. It’s all done in the imagination for purposes of solving problems. People don’t really build systems like that of course.

Now suppose we want to ask what the coordinate time interval was between two events. Here’s what we do. First we define the events.

Event #1 = (t1, x1, y1)
Event #2 = (t2, x2, y2)

Then we say that the coordinate time interval Dt between these two events is Dt = t2 – t1. If Dt > 0 then event #1 occurred before event #2. If Dt < 0 we say that event #1 occurred after event #2

 

[ghwellsjr]

The reason I referred to a timeline worldline was to intentionally be redundant for clarity. Who knows? Someone might think of a way to speak of the decay of a tachyon (a theoretical particle which travels faster than the speed of light) and perhaps it can decay.

But you said the Proper Time is measured by a clock and since no clock can travel faster than the speed of light, there is no need to be concerned about this extra stipulation. Saying a timelike worldline is the same as saying a clock's worldline. The redundancy implies the need for additional requirement which is never necessary.

The one might want to speak of the proper time along a spacelike worldline so I made sure that I said timelike so that it's not used for tachyons.

Anyone who talks about the proper time along a spacelike worldline doesn't know what they are talking about. Couldn't you dream up a whole lot of other impossible situations that you should guard against and include them in your definition of Proper Time?

I'm not sure about proper time concerng tacyons and whether they can decay and what iwould mean to speak of the proper lifetime of a tachyon. So I leave it into make sure the tachyon people know that the definition I gave does not apply to tachyons.
In any case it doesn’t hurt it. If you disapprove then leave it out of the definition the nest time you post one.

It doesn't help, which is why I asked you why you saw fit to include it and I'm still not getting a good reason.

Since proper time refers to the time interval between two events. That’s its very meaning. Please post an example of what you’re referring to.

Ok, look up coordinate time in wikipedia. There you will see:

In the special case of an inertial observer in special relativity, by convention the coordinate time at an event is the same as the proper time measured by a clock that is at the same location as the event, that is stationary relative to the observer and that has been synchronised to the observer's clock using the Einstein synchronisation convention.

Just like Coordinate Time is not an interval, so Proper Time is not an interval. If you want to refer to the Proper Time interval between two times on a clock, you just subtract them and call it a Proper Time interval.

Now of course we understand that the time on a clock is actually measuring a time interval between the time that the clock was set (or synchronized or reset) and some later time that we care about but we don't normally bother to call that a time interval, we just refer to the time that is on the clock. In this thread, I have drawn numerous spacetime diagrams in which I mark off Proper Time ticks with dots and label some of them with a Proper Time value. Are you suggesting that this is incorrect, that I should always make it clear that I'm talking about an interval between two events?

Since proper times is path dependant this gives the integral the limits its required. A starting event and a terminal event so that the proper time has meaning. To speak merely of “proper time” as in “Hey frank! What’s the proper time along my worldline?” would have no meaning since the proper time refers to the integral of the proper time differential dT over the worldline and that integral must have two limits.

If you disagree then please post an example of the proper time pertaining to an arbitrary worldline.

This is the same issue that I just discussed with regard to setting a clock and then referring to times on the clock later on. You can use the integral to determine what Proper Time is on the clock at the second event. Nothing wrong with that.

If Coordinate Time refers to actual clocks and Proper Time refers to actual clocks, then what's the difference?

I guess I didn’t make that clear. Perhaps I wrongly assumed that the OP knew about how coordinate time was defined, i.e. in terms of an array of clocks. There is no requirement for anything to move between coordinate clocks.

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

Let me describe how to define coordinate time: Visualize a Cartesian coordinate system which is marked off with xy-axes and has tick marks which describe distances, like, for example, your everyday average meter stick has a series of lines marked on it with numbers above the marks telling you how far from the “origin” end of the meter stick to the mark on the meter stick. Now think of where these axes intersect and think of a clock placed at all intersections. Each clock has an identical construction to a clock used as a standard. Each clock will be set to start ticking when it receives a light signal from the systems origin. If the clock is at the location (x, y) then the distance from the origin to the clock is d = sqrt(x^2 + y^2). It will take a time t for the light to reach the clock. Since the speed of light is the same in all frames it’s the same in this frame and has the value c = d/t. Therefore when the clock at (x, y) receives a light signal it sets the time to t = d/c. The clock at the origin is the one that sends out the light signal (which is referred to as a timing signal). When the timing signal is sent the origin clock is set to read t = 0.

That is conceptually how you synchronize clocks. It’s all done in the imagination for purposes of solving problems. People don’t really build systems like that of course.

Now suppose we want to ask what the coordinate time interval was between two events. Here’s what we do. First we define the events.

Event #1 = (t1, x1, y1)
Event #2 = (t2, x2, y2)

Then we say that the coordinate time interval Dt between these two events is Dt = t2 – t1. If Dt > 0 then event #1 occurred before event #2. If Dt < 0 we say that event #1 occurred after event #2

But can you tell me the Proper Time between those two events?

 

[Popper]

Tthe redundancy…

The ignore it. Don’t waste your time trying to convince me of something I already understand quite well and merely disagree with you. It’s not as if my goal is to force my viewpoints on you.


Just like Coordinate Time is not an interval, so Proper Time is not an interval.
[/quote]
That is quite incorrect. If I set the clock to read zero when it passes through event A and when it gets to event B it records 12 s have past then the proper time interval is 12 seconds. If I set the clock to read 350 s when it got to event A then it would read 362 and the proper time interval would be 12 s. Same idea as coordinate time. I’m stating this as a fact and not as a matter of opinion that this is how its defined, like it or not. But it’s quite meaningless to speak of time as an absolute. All times are referenced to something. Our calendar has a zero to it and it was supposed to reflect the event of the birth of Jesus and all times are time intervals between that event and now. When you read a clock all you’re doing is reading part of a time measurement since the calendar part is assumed.

Now of course we understand that the time on a clock is actually measuring a time interval between the time that the clock was set (or synchronized or reset) and some later time that we care about but we don't normally bother to call that a time interval, we just refer to the time that is on the clock. In this thread, I have drawn numerous spacetime diagrams in which I mark off Proper Time ticks with dots and label some of them with a Proper Time value. Are you suggesting that this is incorrect, that I should always make it clear that I'm talking about an interval between two events?

I haven’t looked at those diagrams but it sounds to me as if you’re doing exactly what I said above. You labeled events with a proper time and gave them a value. That value has a zero to it. If it reads 10 hrs then the proper time interval is the time between the event where the clock was set to zero and the time where there is a tick mark.

I’m going to leave it at that since anything more and we’re merely going to try to impose our views on each other and I understand what you’ve said.

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

There absolutely is. The reference is as I described it above where I explained how to synchronize clocks.

But can you tell me the Proper Time between those two events?

As I said, that is a meaningless question unless one makes an assumption about it such as the worldline is a geodesic (i.e. in this case a straight line). It’s very possible that one cannot define a proper time between two events. If the events have a spacelike spacetime separation than it can’t be done. Remember that if a single clock cannot be present at each event then a proper time cannot be defined. For example; suppose a firecracker goes off in Dallas Texas and t = 0 and at t = 1 s another firecracker goes off on Pluto. Then since no single clock could possible be present at both events then a proper time between those events cannot be defined. But know this – All times are time intervals. That must be kept in mind when you’re using the spacetime interval to determine either the proper distance or proper distance between two events.

If you want to disagree with me then that’s fine. But if you want me to view it all the same way that you do then you’re wasting your time. This is not my first clambake you know. :)

 

[Mentz114]

oh,So RoS does not help us to make measurements in a right manner as a result we cannot determine what is the actual length of the rod. Because of RoS, We cannot perform and cannot understand by observing actually which events are simultaneous with which.Correct?

Your earlier suggestion that one can use cameras with clocks synchronised in our stationary frame to 'observe' length contraction is correct. This is the same setup we would use to measure the length of the rod as it moves past. From our calculations (observations), the rod will appear to have shrunk. One reason is that the measurements we made were not simultaneous in the rest frame of the rod. So this experiment confirms what is predicted - that the the length of the rod in our coordinates is less than the length of the rod in it's rest frame coordinates. It does not mean that the rod shrank.

 

[Popper]

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.

 

[Fredrik]

Personally I find the term "coordinate clock" pretty weird, but it's probably because I spend so much time talking and thinking about the fundamentals, where everything is idealized. My first thought is that if the numbers displayed by a "clock" are time coordinates, then it's not really a clock.

But I guess that's why they call them "coordinate clocks" instead of "clocks". "Coordinate clock" is obviously a natural term for such a device, if they are useful at all. So the question is, are they useful? I think Pervect made a good case for that when he defended his usage of the term a couple of weeks ago, by mentioning international atomic time. (French acronym TAI).

In general the rate of the real, physical clock needs to be adjusted (because it keeps proper time) when one wishes to define a coordinate time. This is routinely done with TAI time, the atomic clocks that define TAI time are rate adjusted by height above sea level before being averaged into the TAI time standard.

I thought this was well known, and totally noncontroversial, in case there's some remaining doubt, I'll post a reference from wiki:

http://en.wikipedia.org/w/index.php?title=International_Atomic_Time&oldid=550649840

In the 1970s, it became clear that the clocks participating in TAI were ticking at different rates due to gravitational time dilation, and the combined TAI scale therefore corresponded to an average of the altitudes of the various clocks. Starting from Julian Date 2443144.5 (1 January 1977 00:00:00), corrections were applied to the output of all participating clocks, so that TAI would correspond to proper time at mean sea level (the geoid). Because the clocks had been on average well above sea level, this meant that TAI slowed down, by about 10^−12. The former uncorrected time scale continues to be published, under the name EAL (Echelle Atomique Libre, meaning Free Atomic Scale).[10]

 

[Nugatory]

Personally I find the term "coordinate clock" pretty weird, but it's probably because I spend so much time talking and thinking about the fundamentals, where everything is idealized. My first thought is that if the numbers displayed by a "clock" are time coordinates, then it's not really a clock.

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.

 

[Dale]

Personally I find the term "coordinate clock" pretty weird, but it's probably because I spend so much time talking and thinking about the fundamentals, where everything is idealized. My first thought is that if the numbers displayed by a "clock" are time coordinates, then it's not really a clock.

But I guess that's why they call them "coordinate clocks" instead of "clocks". "Coordinate clock" is obviously a natural term for such a device, if they are useful at all. So the question is, are they useful? I think Pervect made a good case for that when he defended his usage of the term a couple of weeks ago, by mentioning international atomic time. (French acronym TAI).

Another example are the satellite clocks for GPS. Those measure cooridinate time, not proper time. And I wouldn't fight you on the claim that they aren't really clocks.

 

[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.