Suppose such a particle existed. Question is what would happen if it was to enter an electric field? Consider p (m = 0$p$ ($m = 0$,q > 0 $q > 0$) entering an electric field E_i $E_i$,on on a manifold M (i,j)$M (i,j)$ F_i = q E_i but F_i = m a_i$$F_i = q E_i \; \; \;\text{but} \; \; \; F_i = m a_i$$
It follows that F_i = 0$F_i = 0$ since m = 0$m = 0$ meaning either q = 0$q = 0$ or E = 0 $E = 0$,but but such is not the case, F_i$F_i$ (electric field ) is not equal F_i$F_i$ (newton'sNewton's force)
Consider the same situation, we may write the following
F_j = q E_j & F_i = m a_i$$F_j = q E_j \; \; \;\text{and} \; \; \; F_i = m a_i $$
Again we note that F_i = 0$F_i = 0$ and F_j$F_j$ doesn't exist in the dimension of e^i $e^i$,but but it lies on the same manifold as F_i$F_i$. We may use the matrix (A_i)^j$A_i{}^j$ to transform F_j$F_j$ to F_i i$F_i$, i.e F_i = (A_i)^j F_j$F_i = A_i{}^j F_j$, this means (A_i)^j = 0 the$A_i{}^j = 0$. The only way this can be so is if theta(thethe angle between the two forces ) = 0 + k.90,$\theta$ is given by: $$ \theta= 0 + k90 $$ where k = 1,3,5,...$k = 1,3,5,\ldots,n$.,n So (A_i)^j = g^ik g_jk = ((delta)^i)_j = 0$A_i{}^j = g^{ik} g_{jk} = \delta^i{}_j = 0$ since j$j$ is not equal i$i$.
So such a particle would be stationary in our dimension (or it would be whizzing through space at c$c$,its its speed is indeterminant) but one thing certain it is not bound to our spacetime.
