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BruceW

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EDIT: Split from https://www.physicsforums.com/showthread.php?t=704345

after a bit of searching, I found "An introduction to general relativity and cosmology" jerzy plebanski, andrzej Krasinski, where they don't use different terms for proper time and proper length. They just use the word 'arc length' to mean either. And they use the equation:

[tex]l = \int \left( | g_{\alpha \beta}( \gamma ) \frac{d x^{\alpha}}{d \gamma} \frac{d x^{\beta}}{d \gamma} | \right)^{1/2} \ d \gamma[/tex]

Where the line | means 'take absolute value'. So maybe I should use the phrase 'arc length' instead. But then it still implies a length, when I might be measuring proper time. I guess at least they are using a different phrase, instead of what I was doing, which was using the old phrase 'proper time' to mean a new thing.

The main reason to use a definition that does not discern between proper time and proper length is that in general relativity, we often don't define a coordinate time, and we can do lots of useful calculations, without ever caring about whether we have a proper length or a proper time. In this sense, the difference between proper time and proper length in general relativity is artificial. (i.e. sure we can add in a coordinate time, but it is not necessary for using relativistic equations). Further, I thought it would be OK to say that the 'arc length' along a null geodesic is just zero. But as wannabenewton said, null worldlines can't be parameterised by proper time. So I think I was wrong to say that the 'arc length' is zero along a null worldline, since it is not possible to define it along a null worldline?

Also, several of our lecturers at undergraduate would use non-standard definitions, to force us to get used to the fact that people don't always play by the same definitions. This is why I have a spirit of using whatever definitions, and making sure I don't assume that someone I am talking to is using a certain definition that I am used to. But I suppose that since I am not an expert in any field of physics, maybe I should not be so carefree with using non-standard definitions myself. And about being homework helper here, if the other helpers think that I should stick to the standard definitions, then I will do that.

after a bit of searching, I found "An introduction to general relativity and cosmology" jerzy plebanski, andrzej Krasinski, where they don't use different terms for proper time and proper length. They just use the word 'arc length' to mean either. And they use the equation:

[tex]l = \int \left( | g_{\alpha \beta}( \gamma ) \frac{d x^{\alpha}}{d \gamma} \frac{d x^{\beta}}{d \gamma} | \right)^{1/2} \ d \gamma[/tex]

Where the line | means 'take absolute value'. So maybe I should use the phrase 'arc length' instead. But then it still implies a length, when I might be measuring proper time. I guess at least they are using a different phrase, instead of what I was doing, which was using the old phrase 'proper time' to mean a new thing.

The main reason to use a definition that does not discern between proper time and proper length is that in general relativity, we often don't define a coordinate time, and we can do lots of useful calculations, without ever caring about whether we have a proper length or a proper time. In this sense, the difference between proper time and proper length in general relativity is artificial. (i.e. sure we can add in a coordinate time, but it is not necessary for using relativistic equations). Further, I thought it would be OK to say that the 'arc length' along a null geodesic is just zero. But as wannabenewton said, null worldlines can't be parameterised by proper time. So I think I was wrong to say that the 'arc length' is zero along a null worldline, since it is not possible to define it along a null worldline?

Also, several of our lecturers at undergraduate would use non-standard definitions, to force us to get used to the fact that people don't always play by the same definitions. This is why I have a spirit of using whatever definitions, and making sure I don't assume that someone I am talking to is using a certain definition that I am used to. But I suppose that since I am not an expert in any field of physics, maybe I should not be so carefree with using non-standard definitions myself. And about being homework helper here, if the other helpers think that I should stick to the standard definitions, then I will do that.

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