4-vector help

[johnoron]

How can define a vector A with components (x,y,z,w)

such that the magnitude |A| = x^2 - y^2 - z^2 - w^2

?

 

[Bung]

Are there any constraints on w,x,y,z? Seems to me you could almost arbitrarily assign values to up to 3 of them, and that will fix the last one.

Bung
Life is non-linear...

 

[johnoron]

The properties of x,y,z, and w are that they're magnitudes of directly measurable quantities. But it doesn't matter if they're mutplied by aritary constants; I've tried mutplying y z and w by 'i' but it doesn't seem to give me the result I want.

 

[johnoron]

I've worked it out, I just can't use the normal way of working out magnitudes of vectors as it's the same process that gives modului of complex numbers so I have to define the components of my vector as:

(x,iy,iz,iw)

and the magnitude as the dot product of I and I.