Why uncharged particles do not feel the Lorentz force? Why uncharged particles do not feel the Lorentz force? Please do not answer with the formula $ \vec F = q\left( \vec E + \vec v \times \vec B \right) $.
Edit after an answer which is an circular reasoning.
Let me explain this question with an example. Imagine, you nothing know about car traffic and you are standing at a traffic light junction. What is the law you could formulate? The green light moves the cars. In my question the moving charged particles are the cars, the light junction is the magnetic field. A running horse does not stop on red and the deeper answer is that the driver accelerate the car when he see green. So what "saw" charged particles what don't "saw" uncharged particles? Why an charged and not moving relatively to a magnetic field particle does not feel this force?
 A: The Lorentz force is by definition the force acting on a charged particle due to electric and magnetic fields. Therefore, if the particle has no charge, then any forces on it, by definition, cannot be Lorentz forces. Thus, it is easy to say that uncharged particles do not feel the Lorentz force because it is only defined as the Lorentz force when acting on charged particles.
That does not mean that uncharged particles do feel forces from electric and magnetic fields (that would be an invalid interpretation). It means that were they to feel such forces, we would call these forces by a different name.
A: An uncharged particle has $q=0$. And by definition of the Lorentz force
$$
F = q\left(E + v\wedge B \right) = 0 \left(E + v\wedge B \right) = 0 
$$
So it experiment no Lorentz force. I wonder why you ask us not to use the definition of Lorentz force, do you know another definition? why such a request?
EDIT: After the aclaration you made, i'll extend this answer. The thing that charged particles "see" and uncharged don't is the electromagnetic field. For an uncharged particle the electromagnetic field doesn't exist at all, the charge is the measure of how much the electromagnetic field (a physical entity in its own right) interact with the particle. The fact that a charged particle moving parallel to the magnetic field doesn't feel force is a experimental fact, could be less confusing if you think in terms of the electromagnetic field $F_{uv}$. If in one coordinate system you see only magnetic field, in another you will see an electric field and a magnetic field (but never a zero magnetic field), this is because
$$
2\left(|E|^2-|B|^2 \right)
$$
is an invariant quantity, so is the same for all inertial observers, because of that it'll never change sign in another coordinate system.
A: The charge of a particle indicates how strongly that particle feels the electromagnetic force.  No charge, it can't feel the force.
A: If uncharged particles have dipole moment, it will be influenced by the electric field by a torque, or a force under electric field gradient.
