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Proper lengthby PerpStudent
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#1
Jan513, 01:17 PM

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Proper length is given by $$ L = \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2  c^2\Delta t^2 }$$
So, when $$ \Delta x = \Delta y = \Delta z = 0 $$ there is no motion and $$ L = ic\Delta t $$ What does that mean, if anything? 


#2
Jan513, 02:07 PM

P: 260

It means that the curve in spacetime connecting event A to event B is timelike, so it makes more sense to talk about proper time than proper length. Proper time is the time a clock carried along said curve would read, and is given by:
[tex]\tau =\sqrt{c^2\Delta t^2 \Delta x^2  \Delta y^2  \Delta z^2}[/tex] 


#3
Jan513, 02:09 PM

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It means that that you're computing the "length" of a time interval. Which is of course, [itex]\Delta t[/itex]
The usual name for this (minus the multiplicative factors) is "proper time" rather than proper length. Are you worried about the factor of i? The factor of c? 


#4
Jan513, 02:57 PM

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Proper length
proper length is the distance between two events, as measured by an observer who regards them as being at the same time
if you regard the two events as being at the same place, then only an observer going infinitely fast (as measured by you) could regard them as being at the same time since such an observer can't exist, it would be very surprising if the proper length was real! (alternatively, if you insist on allowing observers who move faster than light, then you have to allow that their times and their distances can be imaginary) 


#5
Jan513, 10:24 PM

P: 848

One context would be to just ask what your final equation is saying at face value. That's easy, you just put the equation into words: An incremental distance, dL, is traversed by moving at the speed of light over a time increment of dt. Beyond that you may be expecting a comment about the meaning of the incremental distance, dL, in this example. If you are searching for some physical meaning about dL, you might need to look for it in the context of a particular universe model. For example you might assume a 4dimensional spacetime model of physical reality. Then, at face value, the equation could be interpreted as giving the incremental distance, dL, that an observer at rest in his own "rest frame" moves during the time increment, dt. In this case the dL is interpreted as distance along the rest frame 4th dimension, i.e., the observer moves along his own 4th dimension at the speed of light. This picture of course raises more questionsfor example, what is the meaning of "observer", pictured here as moving along the 4th dimension? And what exactly is the 4th dimension? However, this forum is not intended for discussions of these types of questions, so you should not expect to pursue these kinds of ideas here. Others could provide other models providing a context for interpreting the "meaning" of dL. Logical positivists would caution you to avoid assigning physical meaning beyond the observation of measurement results and performing the indicated mathematical calculations. 


#6
Jan613, 09:29 AM

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#7
Jan713, 10:21 AM

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there's no such thing as the proper time between two events … the proper time depends on the path taken (wikipedia (http://en.wikipedia.org/wiki/Proper_length) defines the proper length of any path, and then is forced to define the proper length between two events as the proper length of the straight path between them) so by analogy the proper length or distance between two events should also depend on the path taken however, i dont see any point in defining the proper length of a path …why would anyone want to know it? 


#8
Jan813, 11:12 AM

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#9
Jan813, 11:13 AM

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