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Need answer fast. give the four components of the position-time vector x^u

Need answer fast. give the four components of the position-time vector x^u

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Expert Solution

The relationship between the time t and the coordinate time is given by

Taking the derivative with respect to the proper time , we find the velocity component for ? = 0:

Using the chain rule, for 1, 2, 3, we have

where we have used the relationship

Thus, we find for the four-velocity :

In terms of the yardsticks (and synchronized clocks) associated with a particular slice of flat spacetime, the three spacelike components of four-velocity define a traveling object's proper velocity i.e. the rate at which distance is covered in the reference map frame per unit proper time elapsed on clocks traveling with the object.

genius_generous answered 3 weeks ago
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