# Tag Info

1 vote

### Connection between contra-/covariant vectors in SR and complex numbers?

I think the thing you're looking for here is the Wick rotation. You start with a real vector space with coordinates $(t,x) \in \mathbb{R}^2$ and replace the real $t$-coordinate with a purely complex ...
• 51

### Why the normal vector addition does not seem to work in centripetal acceleration?

If the curve is given in parametric polar coordinates (r(t),θ(t)) , the velocity and acceleration vectors can be calculated in the moving base . (We denote by a point the derivation with respect to ...
• 1,452

### Why the normal vector addition does not seem to work in centripetal acceleration?

You cannot add acceleration and velocity by vector addition because they are quantities of different dimension. You cannot add m/s and m/s$^2$. What you can add is velocity and the product of ...
• 10.1k
1 vote

• 2,170
1 vote
Accepted

In general, $\delta \mathbf{L} = \delta \mathbf{r} \times \mathbf{p} + \mathbf{r} \times \delta \mathbf{p}$, which in this case becomes $\delta \mathbf{L} = \mathbf{r} \times \delta \mathbf{p} = \... 5 votes ### Pauli matrix relation of dot and cross products with complex numbers This is a confusing form of the Clifford-algebraic identity$ab = a\cdot b + a\wedge b$, where$a$and$b\$ are vectors. It's confusing because it mixes Clifford-algebraic and 3D-vector-algebraic ...
• 28.2k

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