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All clocks always record proper time, unless they are defect.

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Chestermiller

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GR does not only use proper time. The time parameter in the Schwartzschild metric is not proper time, except in the limit of large distances from the central mass.

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Proper time is the same thing as clock time in both SR and GR.

This is incorrect. Proper time plays the same role in GR that it does in SR. Your example of the time in the Schwarzschild metric (presumably expressed in Schwarzschild coordinates) is an example of a timelike coordinate in GR. Timelike coordinates exist in GR and are not the same thing as proper time.GR does not only use proper time. The time parameter in the Schwartzschild metric is not proper time, except in the limit of large distances from the central mass.

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Then what is incorrect about Chestermiller's response?Your example of the time in the Schwarzschild metric (presumably expressed in Schwarzschild coordinates) is an example of a timelike coordinate in GR. Timelike coordinates exist in GR and are not the same thing as proper time.

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WannabeNewton

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The clocks still measure proper time regardless (as you and Ben and others noted). Coordinate time is irrelevant. In fact coordinate time is present in SR too and is not the same as proper time there as well in general (unless of course we are in the rest frame of the observer whose worldline actually passes through the two events in between which the proper time is being measured) so there is no value in pointing out there are "other kinds of time" in GR as if this was special to GR. Clocks measure proper time - doesn't matter if it's GR or SR.Then what is incorrect about Chestermiller's response?

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I must be missing something, what do you think is wrong about Chestermiller's response?The clocks still measure proper time regardless (as you and Ben and others noted). Coordinate time is irrelevant. In fact coordinate time is present in SR too and is not the same as proper time there as well in general (unless of course we are in the rest frame of the observer whose worldline actually passes through the two events in between which the proper time is being measured) so there is no value in pointing out there are "other kinds of time" in GR as if this was special to GR. Clocks measure proper time - doesn't matter if it's GR or SR.

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WannabeNewton

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There is nothingI must be missing something, what do you think is wrong about Chestermiller's response?

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Proper time is the same thing as clock time in both SR and GR.

The notion / existence of coordinate time doesn't change the fact that the time measured on an observer's clock between two events in space - time is the proper time.

So in a time dilation experiment we have an atomic clock in an airplane which has a proper time and as it moves it passes through events that use the earth's proper time as a coordinate value in order to measure time dilation. The two times are not the same. So how can you have an event with two time coordinates?All clocks always record proper time, unless they are defect.

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?GR does not only use proper time. The time parameter in the Schwartzschild metric is not proper time, except in the limit of large distances from the central mass.

I realize that proper time is measured between two events, but earth time is a continuum so that shouldn't matter when they are being compared.

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ghwellsjr

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Every coordinate system assigns a different time to each event. Just like you can refer to the rover landing on Mars in Eastern, Mountain, Pacific Time or any of many other coordinate systems. If a clock is stationary in an Inertial Reference Frame (IRF) then its Proper Time will tick at the same rate as the Coordinate Time for that IRF. The significance of Coordinate Time is that it ticks everywhere simultaneously whereas individual clocks, say those on earth, even if they tick at the same rate as the Coordinate Time only tick at the location where they are at.So in a time dilation experiment we have an atomic clock in an airplane which has a proper time and as it moves it passes through events that use the earth's proper time as a coordinate value in order to measure time dilation. The two times are not the same. So how can you have an event with two time coordinates?

YouYou 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?

You can only use the Proper Time on a real clock to measure the Coordinate Time between two events if those two events are at the same location in the selected IRF.I realize that proper time is measured between two events, but earth time is a continuum so that shouldn't matter when they are being compared.

Another subject is the spacetime interval between two events. If that interval is timelike, then you can use a real clock that is inertial to measure the spacetime interval if it is present at those two events. In other words, in the IRF in which those two events are at the same location, a clock that is also stationary in that IRF and present at the same location will tick at the same rate as the Coordinate Time in that IRF between those two events.

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WannabeNewton

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Coordinate time is different from proper time. Lets say we are in the rest frame of an observer ##O## whose worldline passes through two events ##A## and ##B##. Furthermore lets say ##O## has set up his frame with coordinates ##(t,x,y,z)##. In the rest frame of ##O## he measures no spatial displacement when he goes from ##A## to ##B## of course so ##\Delta \tau_{AB} = \Delta t_{AB}## so the time measured on a clock held by ##O## coincides the coordinate time in the coordinates set up by ##O## with the proper time, between the two events.

Let's say now we have another observer ##O'## who is moving with velocity ##v## in the ##x## direction relative to ##O## and say ##O'## has set up in his frame coordinates ##(t',x',y',z')## (assume they have synchronized their clocks etc.). According to ##O'## the proper time for ##O## to go from ##A## to ##B## will be ##\Delta \tau'_{AB} = \sqrt{\Delta t_{AB}'^{2} - \Delta x_{AB}'^2}##.

We know how the coordinates ##(t,x,y,z)## of ##O## will related to the coordinates ##(t',x',y',z')## of ##O'## through the lorentz transformations ##t' = \gamma (t - vx), x' = \gamma (x - vt)##. We see that ##\Delta t_{AB}'^{2} = \gamma^{2} \Delta t_{AB}^{2}, \Delta x_{AB}' = \gamma ^{2}v^2\Delta t_{AB}^{2}## so ##\Delta \tau'_{AB} = \sqrt{\gamma ^{2}\Delta t_{AB}^{2}(1 - v^2)} = \sqrt{\gamma ^{2}\Delta t_{AB}^{2}\gamma ^{-2}} = \Delta t_{AB} = \Delta \tau_{AB}##. Indeed, both ##O## and ##O'##'s measurements yield the same proper time between events ##A## and ##B## even though ##O## has set up different coordinates in his frame from those of ##O'##. Proper time is a frame invariant quantity in this sense whereas the coordinate times ##t## and ##t'## are not.

Let's say now we have another observer ##O'## who is moving with velocity ##v## in the ##x## direction relative to ##O## and say ##O'## has set up in his frame coordinates ##(t',x',y',z')## (assume they have synchronized their clocks etc.). According to ##O'## the proper time for ##O## to go from ##A## to ##B## will be ##\Delta \tau'_{AB} = \sqrt{\Delta t_{AB}'^{2} - \Delta x_{AB}'^2}##.

We know how the coordinates ##(t,x,y,z)## of ##O## will related to the coordinates ##(t',x',y',z')## of ##O'## through the lorentz transformations ##t' = \gamma (t - vx), x' = \gamma (x - vt)##. We see that ##\Delta t_{AB}'^{2} = \gamma^{2} \Delta t_{AB}^{2}, \Delta x_{AB}' = \gamma ^{2}v^2\Delta t_{AB}^{2}## so ##\Delta \tau'_{AB} = \sqrt{\gamma ^{2}\Delta t_{AB}^{2}(1 - v^2)} = \sqrt{\gamma ^{2}\Delta t_{AB}^{2}\gamma ^{-2}} = \Delta t_{AB} = \Delta \tau_{AB}##. Indeed, both ##O## and ##O'##'s measurements yield the same proper time between events ##A## and ##B## even though ##O## has set up different coordinates in his frame from those of ##O'##. Proper time is a frame invariant quantity in this sense whereas the coordinate times ##t## and ##t'## are not.

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WannabeNewton

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In order to avoid confusion that *might* arise, this is the sameYou can only use the Proper Time on a real clock to measure the Coordinate Time between two events if those two events are at the same location in the selected IRF.

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ghwellsjr

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Well then, they are the same event, aren't they?In order to avoid confusion that *might* arise, this is the samespatiallocation. There might be an ambiguity because "location" in SR can be interpreted as an event.

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WannabeNewton

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How do you mean? There is a temporal displacement between the two events even if there is no spatial displacement (I'm talking about two distinct events, both lying on the image of observer ##O##'s wordline and doing measurements in observer ##O##'s rest frame).Well then, they are the same event, aren't they?

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ghwellsjr

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This, to me, isCoordinate time is different from proper time. Lets say we are in the rest frame of an observer ##O## whose worldline passes through two events ##A## and ##B##. Furthermore lets say ##O## has set up his frame with coordinates ##(t,x,y,z)##. In the rest frame of ##O## he measures no spatial displacement when he goes from ##A## to ##B## of course so ##\Delta \tau_{AB} = \Delta t_{AB}## so the time measured on a clock held by ##O##, the proper time, is just the coordinate time in the coordinates set up by ##O##.

Let's say now we have another observer ##O'## who is moving with velocity ##v## in the ##x## direction relative to ##O## and say ##O'## has set up in his frame coordinates ##(t',x',y',z')## (assume they have synchronized their clocks etc.). According to a clock held by ##O'## the proper time for ##O## to go from ##A## to ##B## will be ##\Delta \tau'_{AB} = \sqrt{\Delta t_{AB}'^{2} - \Delta x_{AB}'^2}##.

We know how the coordinates ##(t,x,y,z)## of ##O## will related to the coordinates ##(t',x',y',z')## of ##O'## through the lorentz transformations ##t' = \gamma (t - vx), x' = \gamma (x - vt)##. We see that ##\Delta t_{AB}'^{2} = \gamma^{2} \Delta t_{AB}^{2}, \Delta x_{AB}' = \gamma ^{2}v^2\Delta t_{AB}^{2}## so ##\Delta \tau'_{AB} = \sqrt{\gamma ^{2}\Delta t_{AB}^{2}(1 - v^2)} = \sqrt{\gamma ^{2}\Delta t_{AB}^{2}\gamma ^{-2}} = \Delta t_{AB} = \Delta \tau_{AB}##. Indeed, both ##O## and ##O'##'s clocks measure the same proper time between events ##A## and ##B## even though ##O## has set up different coordinates in his frame from those of ##O'##. Proper time is a frame invariant quantity in this sense whereas the coordinate times ##t## and ##t'## are not.

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WannabeNewton

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Just to make sure I am on the same page, coordinate time refers to the euclidean space tangent to curved space-time, right? and I assume Euclidean space would also be used to describe the stress-energy.The significance of Coordinate Time is that it ticks everywhere simultaneously whereas individual clocks, say those on earth, even if they tick at the same rate as the Coordinate Time only tick at the location where they are at.

Youuse Coordinate Time when specifying the time coordinate of an event in a particular IRF.always

You can only use the Proper Time on a real clock to measure the Coordinate Time between two events if those two events are at the same location in the selected IRF.

Another subject is the spacetime interval between two events. If that interval is timelike, then you can use a real clock that is inertial to measure the spacetime interval if it is present at those two events. In other words, in the IRF in which those two events are at the same location, a clock that is also stationary in that IRF and present at the same location will tick at the same rate as the Coordinate Time in that IRF between those two events.

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No, coordinate time can be anything.Just to make sure I am on the same page, coordinate time refers to the euclidean space tangent to curved space-time, right?

Imagine a 2 year old drawing horizontal and vertical wiggly (but not so much as to cross its direct neighbor) but smooth great circles on a football, then that is a perfectly valid coordinate system.

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WannabeNewton

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This is getting into the more advanced realm of differential geometry and general relativity (GR) and away from the physics of special relativity (SR) but we can take a crack at it.Just to make sure I am on the same page, coordinate time refers to the euclidean space tangent to curved space-time, right? and I assume Euclidean space would also be used to describe the stress-energy.

There is no a prioi relationship between the coordinates set up by an observer in a neighborhood of space - time and the tangent space to space - time at some point in this neighborhood (by the way this tangent space is not Euclidean space itself but is isomorphic to it in the category of vector spaces).

Let ##M## be a space - time and let ##O## be an observer. On an open subset ##U\subseteq M##, observer ##O## can set up coordinates ##(t,x^1,x^2,x^3)## on ##U## so that he can represent events ##p\in U##

Your final sentence, "and I assume Euclidean space would also be used to describe the stress energy" doesn't make sense to me unfortunately.

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ghwellsjr

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In order to avoid confusion that *might* arise, this is the sameYou can only use the Proper Time on a real clock to measure the Coordinate Time between two events if those two events are at the same location in the selected IRF.spatiallocation. There might be an ambiguity because "location" in SR can be interpreted as an event.

If you say that the word "location" can mean "event" and isn't specific enough because it might denote something more than "spatial location" then it seems that something more must be time. So if I say two events are at the same location, then it seems to me you are saying that my statement can be interpreted that the two events (both their spatial and temporal locations) are all the same.How do you mean? There is a temporal displacement between the two events even if there is no spatial displacement (I'm talking about two distinct events, both lying on the image of observer ##O##'s wordline and doing measurements in observer ##O##'s rest frame).Well then, they are the same event, aren't they?

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WannabeNewton

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Yes, but I'm not saying everyone will of course - it just might be a possibility. What you said in your original post is true either way, trivial in the case of two identical events, but if someone does get mixed up then they might miss the point of your post, which is a crucial point in understanding the relationship between proper time and clocks. Cheers friend :)!So if I say two events are at the same location, then it seems to me you are saying that my statement can be interpreted that the two events (both their spatial and temporal locations) are all the same.

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ghwellsjr

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Can you please provide an authoritative online reference for "location" that defines it as "time"? Thanks.Yes, but I'm not saying everyone will of course - it just might be a possibility.So if I say two events are at the same location, then it seems to me you are saying that my statement can be interpreted that the two events (both their spatial and temporal locations) are all the same.

Clocks are associated with Proper Time. Events are associated with Coordinate Time. That is the point of my post. Can someone get that mixed up?What you said in your original post is true either way, trivial in the case of two identical events, but if someone does get mixed up then they might miss the point of your post, which is a crucial point in understanding the relationship between proper time and clocks. Cheers friend :)!

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WannabeNewton

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A location in space - time is an event, not just a spatial location. It's an elementary definition. If you are talking about observers in some neighborhood of space - time and talk about their "location" in space - time this is by definition an element on the image of their wordline, which is a subset of space - time, thus the element is an event. Do you actually need a reference for that? Take a look at any GR textbook.Can you please provide an authoritative online reference for "location" that defines it as "time"? Thanks.

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You are talking about curved space-time. I am talking about a measurement taken from the curved metric. In order to take a measurement (get a real number) you have to evaluate the metric on a locally Euclidean space. See Wikipedia below. Maybe I didn't use all the right words but that's what I wanted to say. How is that wrong?Imagine a 2 year old drawing horizontal and vertical wiggly (but not so much as to cross its direct neighbor) but smooth great circles on a football, then that is a perfectly valid coordinate system.

Explicitly, the metric is a symmetric bilinear form on each tangent space of M which varies in a smooth (or differentiable) manner from point to point. Given two tangent vectors u and v at a point x in M, the metric can be evaluated on u and v to give a real number:

This can be thought of as a generalization of the dot product in ordinary Euclidean space. This analogy is not exact, however. Unlike Euclidean space — where the dot product is positive definite — the metric gives each tangent space the structure of Minkowski space.

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ghwellsjr

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OK, I looked in several relativity textbooks as well as online references and I did not find any that defined "location" as "time" which is what I asked for. I did find some that referred to a "spacetime location" as an "event" which is something that I was not previously aware of so I thank you for bringing this to my attention.A location in space - time is an event, not just a spatial location. It's an elementary definition. If you are talking about observers in some neighborhood of space - time and talk about their "location" in space - time this is by definition an element on the image of their wordline, which is a subset of space - time, thus the element is an event. Do you actually need a reference for that? Take a look at any GR textbook.Can you please provide an authoritative online reference for "location" that defines it as "time"? Thanks.

It's interesting that in the two editions of Taylor and Wheeler, they changed their terminology. The first edition, from the 60's when I had my formal education uses the term "location" in the sense that I used it, to mean "spatial position", a term they also use in both editions. They talk about the location of an event and never refer to "spacetime location". In the second edition, from 1992, they changed the phrase "coordinates of an event" to "spacetime location of an event".

I thought when you started this issue that you were saying that just like we have three spatial coordinates and one temporal coordinate for an event, a spacetime location (or event) is made up of three spatial locations and one temporal location. But now I think your point is that the confusion is not over spatial versus temporal, but over spatial location versus spacetime location (or event, as you said). However, I really don't see how anyone could be confused by my statement:

They would have to think I meant:You can only use the Proper Time on a real clock to measure the Coordinate Time between two events if those two events are at the same location in the selected IRF.

I think the context makes it abundantly clear that when I talk about the location of two events, I'm not saying they are the same event, otherwise, I would have said that.You can only use the Proper Time on a real clock to measure the Coordinate Time between two events if those two events are at the sameeventin the selected IRF.