Relativistic hidden variable quantum mechanics?

[Demystifier]

But (for a curve) this tangent vector is unique only up to a (positive or negative) factor.

One way to fix this factor is indeed to fix the parametrization. But the point is that it is not the only way.

 

[A. Neumaier]

One way to fix this factor is indeed to fix the parametrization. But the point is that it is not the only way.

So how do you fix it without getting a spurious sign in your ds?

 

[Demystifier]

So how do you fix it without getting a spurious sign in your ds?

If the curve is oriented (which is a much weaker requirement than that it is parameterized), then the sign is chosen such that $s$ increases in the direction of orientation. In my case, the orientation at each point is defined by the direction of the vector $V^{\mu}$, to which the curve is tangent. Note also that in my paper $\Omega$ in Eq. (111) is positive.