# MOND and magnetism

1. May 25, 2004

### kurious

It’s interesting that MOND splits Newtonian gravity into two cases
and the Modified version of Newtonain dynamics seems to happen in galaxies and clusters of galaxies with magnetic fields.What is the physical reason that MOND could be right?
If we assume that there is another force interacting with the stars in a galaxy –
which modifies the Newtonian force law, what generates this force?

One answer to this question could be this:
suppose some charged particles flow over the plane of a spiral galaxy and parallel to the plane, from intergalactic space. They encounter the magnetic field lines of the galaxy and a force acts on them obeying the equation force = qvB.
Assuming q v and B stay roughly constant as the charged particles cross the galaxy,
since in normal Newtonian dynamics acceleration = Force / mass of charged particle,
the charged particles experience a constant acceleration as they move (we will assume the particles are separated widely enough to make their coulomb attractions and repulsions insignificant).
Negative charges will experience a push in the opposite direction to positive charges-
the negative and positive charges will move closer together.
How much do they move?
Using s= ut + (a t ^ 2) / 2 , s = sideways distance moved,
and setting u, the initial and sideways speed of the charges as they just reach edge of the spiral galaxy disc ( we are assuming that this location is an approximation that will yield useful results) to zero:

s = (a t ^ 2) / 2

since the normal Newtonian acceleration on the charges is constant,
s is proportional to t ^ 2.

A charge moving towards the centre of the galaxy takes half the time to move
to a position 0.75 the distance from the centre to the edge of the disc, as it does to move to 0.5 that distance from the centre to the edge.

So if it moves to 0.75 the distance the value of s is (1/2) ^2 i.e
1 / 4 of what it would be for a movement of a particle to halfway across the galactic plane.So the force exerted on a star would be a force exerted by 1/4
the number of particles because the negative and positive charged particles
will not have moved so much sideways and so will not be so densely packed at 0.75 units distance as they would be at 0.5 units distance from the galactic centre.
The gravitational force depends on 1/ r^2 so at 0.75 units it would be
( 0.75 / 0.5 ) ^ 2 2.25 times weaker than at 0.5 units distance from the galactic centre.

So if at 0.5 units distance a star experiences a force due to gravity of X newtons
and a force due to the charged particles of Y Newtons, the force on the star
is X + Y Newtons towards the galactic centre.

at 0.75 units distance, the star would experience a force of:

1 / 2.25 X + 0.25 Y
This will apply only for charged particles moving through a homogeneous region
of the galactic magnetic field and it is assumed that the electric forces between charges are negligible.The idea outlined above may need modifying but
hopefully it gives some insight into a physical mechanism for MOND.
It attempts to show that Newton’s laws are still valid and that MOND
is right just because it considers only the gravitational force and not other forces that could act upon stars.