Asked by: Jim Larkin

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

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

Answered by: Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley

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'Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.'**Bertrand Russell**

(*1872-1970*)

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