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How can something have a negative mass, and what does that mean?
Asked by: Jim Larkin
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
E2 = m2*c4 + p2*c2.
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 (see http://www.physlink.com/ae247.cfm). 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