How can something have a negative mass, and what does that mean?

Asked by: Jim Larkin

Answer

If a particle could have a negative mass it certainly would be hard to understand.
That is why physicists define mass to be always positive. So by definition there is
no such thing as 'negative' mass. This is not an arbitrary definition as there are very
deep reasons as to why a negative mass could never be physical.

Sometimes, in employing mathematical models to describe Nature, we come across solutions to
equations that may allow for negative masses. For example, the formula for the energy of a
relativistic particle is

E^{2} = m^{2}*c4 + p^{2}*c^{2}.

So a particle with a certain positive energy but no momentum could presumably have a
positive or negative mass. Dirac interpreted these negative mass states as anti-particles
that he hid away in the 'Dirac Sea.' While this anachronistic interpretation still lives on
in old-textbooks and new-Age books on quantum mechanics, we now know that this picture is
wrong. Anti-particles have positive masses just as any other particle (more info on anti-matter and anti-energy). These 'negative' solutions are simply not physical and
are dropped. Not everything that has mathematical meaning has physical meaning!

Another place where people like to talk about negative masses is in reference to
'tachyons.' The tachyon (whose name comes from the Greek word tachys for swift) was
originally any solution to Special Relativity that had a velocity greater than the speed of
light. Such a state (like Dirac's 'negative energy' states) are non-physical. These
particles would have imaginary masses (that is the mass-squared is negative) and
this is just as unphysical as a negative mass or a negative energy. Thus such solutions are
always discarded or removed from any theory that claims to describe Nature.
Answered by: Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley

'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.'