Difference between revisions of "4-vectors"
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− | <center><math>\ | + | <center><math>\underline{\textbf{Navigation}}</math> |
[[Relativistic_Units|<math>\vartriangleleft </math>]] | [[Relativistic_Units|<math>\vartriangleleft </math>]] |
Latest revision as of 18:47, 15 May 2018
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).
We can express the space time interval using the index notation
Since
is nothing more than a dot product of a vector with itself, we should expect the components of the indices to follow a similar relationship. Following the rules of matrix multiplication, the dot product of two 4-vectors should follow the form:
This gives the desired results as expected.
The change in signs in the covariant term,
from the contravarient term
Comes from the Minkowski metric
Similarly, for two different 4-vectors,
This is useful in that it shows that the scalar product of two 4-vectors is an invariant since the time-space interval is an invariant.