Four-Dimensional Vector in Special Relativity

[zhangyang]

About momentum-energy vector ,we have :

\vec{P}=(\vec{p},i\frac{E}{c})

and four dimentianal wave vector :

\vec{K}=(\vec{k},i\frac{\omega}{c})

They also satisfy the ralation :

\vec{P}=\frac{h}{2\pi}\vec{K},

because E=\frac{h}{2\pi}\omega.

It is interesting.

 

[PAllen]

FYI: very few people use the imaginary basis for time anymore, when speaking of 4-vectors. Instead of a (+,+,+,+) metric with one imaginary basis, a mixed signature metric is used.

 

[zhangyang]

ds^{2}=x^{2}+y^{2}+z^{2}-c^{2}t^{2}

In the four dimensional space-time vector,the concept of time has been bent,because time has the meaning of evolution and irreversibility.So it can't convert into space freely.