Difference between revisions of "4-vectors"
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Where
Where
is the Lorentz transformation matrix for motion in the z direction.
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− | <center>Where <math>\Lambda</math> is the Lorentz transformation matrix for motion in the z direction. | + | <center>Where <math>\Lambda</math> is the Lorentz transformation matrix for motion in the z direction.</center> |
Revision as of 01:56, 6 June 2017
4-vectors
Using index notation, the time and space coordinates can be combined into a single "4-vector"
, that has units of length, i.e. ct is a distance.
Using the Lorentz transformations and the index notation,
This can be expressed in matrix form as
Letting the indices run from 0 to 3, we can write
We can express the space time interval using the index notation