University of Delaware

PHYS146

Quarks, Gluons, and the Big Bang

Maurice Barnhill
General Syllabus Notes Exam information Announcements

Class Notes: Negative-Mass Particles


We have the expression

E = (+-)m c2 ,

for the energy that an object has due to its mass alone. We could define the mass as having that value necessary to explain the energy left when an object is not moving. In an equation, we would have

mass = E0 / c2 ,

With this definition and the possibility that the energy could be negative because of the ambiguous sign from the square root, there is a possibility that the mass of a particle could also be negative.

How would we know if the mass were negative? The basic equation of all of physics is that the acceleration of an object is given by the equation

acceleration = F / m
where
F is the force (push or pull) acting on the object
m is the object's mass

A negative mass would mean that the particle would accelerate in the opposite direction from the force (push on the particle, the particle comes towards you). Unfortunately we might have some difficulty deciding which direction the force was, since we usually infer that direction by the response of the object! In particular, electrical forces on a charged object are given by

F = Q (Electric Field)

where the electric field is set up by fixed electric charges placed somewhere nearby. With both relations together, the acceleration of the object is

acceleration = (Q/m) (Electric Field)

We would not be able to distinguish between a negative mass and a negative charge; either would produce an acceleration opposite to the electric field.

Let's see where we are. Special Relativity indicates that there might be negative-mass particles as well as positive-mass ones. In fact, if the square root always gave both signs, there might be a negative-mass particle for each positive-mass one. Unfortunately, a negative-mass charged particle would act just like a positive-mass particle with the opposite charge. So we decide that the mass should always be called positive and that we should look for cases where there are two particles with the same mass but with opposite charges. If we find them, we will call them antiparticles. Moreover, since there would be a "negative-mass" particle for each positive-mass one, there should be an antiparticle for every particle.

Last revised 1999/01/21