why is ?=0? what does that have to do with anything? I have been staring at this
ID: 1323561 • Letter: W
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why is ?=0? what does that have to do with anything? I have been staring at this for like 20 minutes I still don't understand what he is talking about... it's giving me problems because i need to understand this part later because it is relevant to how tensors transform also he says ? is a measure of a length along the curve... i don't really follow that point either... i though ? could be any parameter like proper time etc.
any help on this??
I am trying to understand Herbert Goldstein's introduction to 4-vectors. He describes a 1-D curve in spacetime P(?) then he says a 4 vector is defined as the tangent vector to this curve v = ( frac {dP} {d lambda} )_{lambda =0} why is ?=0? what does that have to do with anything? I have been staring at this for like 20 minutes I still don't understand what he is talking about... it's giving me problems because i need to understand this part later because it is relevant to how tensors transform also he says ? is a measure of a length along the curve... i don't really follow that point either... i though ? could be any parameter like proper time etc. any help on this??Explanation / Answer
he says a 4 vector is defined as the tangent vector to this curve
That is not true in general. A four-vector is not always defined as the tangent vector to a curve. In the book they are computing a tangent vector to a curve in 3+1D spacetime; the tangent vector is just one example of a four-vector.
In particular, the formula given tells you how to compute the tangent vector at a specific point A. Since the curve runs from A to B and is parametrized by ??[0,1], ?=0 is the value which corresponds to the point A. So if you're going to define the tangent vector at A, you need to set ?=0.
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