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.