Are clocks used in general relativity?

[ghwellsjr]

Yes in the case of the Twin Paradox the proper time won't be the same because there is an acceleration involved. In SR, the proper time between two events is only preserved between inertial observers i.e those related by a lorentz transformation. So if you have an observer moving uniformly relative to the first then you can apply a lorentz transformation and the proper time will remain invariant. However if one is accelerating then yeah it won't work. There will be discrepancy in the measured proper time. As far as your first question goes, "what is proper time", you already gave a definition in your own post as the time read on a clock passing through the two events in between which the proper time is being measured.

I'm trying to disconnect the Proper Time of a clock from the Coordinate Time of events. We should not be thinking that there is such a thing as an invariant Proper Time between two events. We should make it clear that the invariant spacetime interval between two events is only the Proper Time on an inertial clock that is present at those two events but other clocks that accelerate between those two events will have a different Proper Time.

 

[WannabeNewton]

We should not be thinking that there is such a thing as an invariant Proper Time between two events.

Indeed it is only for the case of inertial observers that this is true. The proper time is not invariant amongst all frames, just the inertial ones.

We should make it clear that the invariant spacetime interval between two events is only the Proper Time on an inertial clock that is present at those two events but other clocks that accelerate between those two events will have a different Proper Time.

Agreed.

 

[ghwellsjr]

We should not be thinking that there is such a thing as an invariant Proper Time between two events.

Indeed it is only for the case of inertial observers that this is true. The proper time is not invariant amongst all frames, just the inertial ones.

You keep wanting to associate Proper Time with a pair of events and frames instead of with the time on a clock. The Proper Time on any clock is invariant as it has nothing to do with any frame. If we assign a single event to a single Proper Time on a clock, all frames will agree on the Proper Time on the clock but they will all assign different Coordinate times to that single event.

 

[WannabeNewton]

You keep wanting to associate Proper Time with a pair of events and frames instead of with the time on a clock.

How would you even make non-trivial sense of proper time for a single event? Proper time in SR is defined as $\tau =\int_{\gamma }(-\eta _{ab}u^{a}u^{b})^{1/2}$ where $\gamma$ is the worldline of an observer carrying a clock that passes through the two events in between which we are measuring the proper time; different worldlines result in different proper times even if it is between the same two events. The line integral has to have some pair of endpoints otherwise we are just dealing with sets of measure zero and get nothing useful. The infinitesimal version links nearby events on an observer's worldline.

If we assign a single event to a single Proper Time on a clock...

Again how would you even make non-trivial sense of proper time for a single event? Proper time is an elapsed time whether you are looking at the infinitesimal form or the integrated form.

 

[Passionflower]

Again how would you even make non-trivial sense of proper time for a single event? Proper time is an elapsed time whether you are looking at the infinitesimal form or the integrated form.

Exactly!

 

[ghwellsjr]

I'm just re-emphasizing what both of you stated early on in this thread:

All clocks always record proper time...

The clocks still measure proper time regardless...

... to answer the OP's question:

You are saying that you can use either proper time or coordinate time depending on where you use it? Is there a convention to know when?

... and in contrast to his statement:

I realize that proper time is measured between two events...

His statement has no meaning apart from an additional specification of the arbitrary history of a clock that spans between those two events, if there is one, which there doesn't have to be.

How would you even make non-trivial sense of proper time for a single event?

Every tick of every clock can be considered a single event.

Proper time in SR is defined as $\tau =\int_{\gamma }(-\eta _{ab}u^{a}u^{b})^{1/2}$ where $\gamma$ is the worldline of an observer carrying a clock that passes through the two events in between which we are measuring the proper time; different worldlines result in different proper times even if it is between the same two events.

You are talking about how to calculate the difference between two Proper Times on a particular clock--a delta Proper Time or a Proper Time interval.

The line integral has to have some pair of endpoints otherwise we are just dealing with sets of measure zero and get nothing useful. The infinitesimal version links nearby events on an observer's worldline.

We don't have to start with a frame and describe the worldline of a clock and then calculate the advance of its Proper Time, we can start with a description of the Proper Time and then calculate what the Coordinate Time is for any arbitrary frame.

Again how would you even make non-trivial sense of proper time for a single event?

We often talk about two clocks with a relative speed between them and at the moment of their colocation, we synchronize them. That's a single event concerning the Proper Time on two clocks.

Proper time is an elapsed time whether you are looking at the infinitesimal form or the integrated form.

To me, this is no different than the terminology we apply to Coordinate Time. If we talk about Coordinate Time, we mean the time that is advancing throughout the reference frame with respect to its origin. If we want to talk about how long it takes for something to get from event A to event B, we don't say that is a Coordinate Time, we say it is a Coordinate Time interval or delta or an elapsed time or something similar.

I think the same thing should apply to avoid confusion with regard to Proper Time. Unlike Coordinate Time which is the same everywhere throughout an IRF, each individual clock can have a different Proper Time on it. We can consistently talk about the Proper Time on each clock at each event and if we care about an elapsed time between two events involving a single clock, then we subtract the two Proper Times at those two events, just like we do for Coordinate Time and we call it something like an elapsed time or a delta time or a time difference or an accumulated time or an amount of aging or something similar but we should not call it simply the Proper Time any more than we would call it the Coordinate Time. But unlike for Coordinate Time, we cannot talk about the delta time between any two events unless there happens to be a clock that is present at those two events and we know its history. And if there are two or more such clocks, then there are two or more delta Proper Times.

 

[Passionflower]

Every tick of every clock can be considered a single event.

But a single event is not proper time.
However there is proper time between two ticks of a clock, again proper time it is a path between two events.

You are talking about how to calculate the difference between two Proper Times on a particular clock--a delta Proper Time or a Proper Time interval.

Nonsense, proper time is always a path between two events.

 

[ghwellsjr]

The OP has stated some erroneous concepts in his first post:

In special relativity clocks are used to record events and proper time gives the time in an inertial frame so two times are used.

Suppose he had said:

In special relativity rulers are used to record events and proper length gives the distance in an inertial frame so two distances are used.

Wouldn't you feel the need to point out where he is confused and to make clear the difference between Coordinate Length and Proper Length? Would you state uncategorically that Proper Length is always associated between two events?

My point is that you can pick any two events and in every reference frame there will always be a Coordinate Time associated with them (and a Coordinate Length) but you cannot say that there will always be a Proper Time (or a Proper Length) associated with them. And you can always say that wherever there is a Proper Time (or a Proper Length), it is never associated with any reference frame.

 

[nortonian]

The OP has stated some erroneous concepts in his first post:

Wouldn't you feel the need to point out where he is confused and to make clear the difference between Coordinate Length and Proper Length? Would you state uncategorically that Proper Length is always associated between two events?

My point is that you can pick any two events and in every reference frame there will always be a Coordinate Time associated with them (and a Coordinate Length) but you cannot say that there will always be a Proper Time (or a Proper Length) associated with them. And you can always say that wherever there is a Proper Time (or a Proper Length), it is never associated with any reference frame.

The thread took a roundabout path but your description cleared it up for me. The proper time or length represents the physical content and the reference frame is used to give a description if one is possible.