One big issue that we often encounter while doing theory is about the physical reality of a quantity. For example, a negative number. A quantity which has negative values is often discarded on the ground of physicality. Scalar quantities like temperature, mass, time, and energy were initially believed to be always positive. However, after Dirac introduced relativistic quantum mechanics, we find an interpretation of negative energy (energy of a ‘hole’, later identified as a positron by C. D. Anderson in 1932, as the negative energy counter-part of an electron) . Similarly the concept of time reversal led us to go backward in time and hence can be negative. What about negative mass? But before we look for an answer, we must understand how a particle with negative should behave. If we recall Newton’s equation F=ma, then we realize that if we push a conventional positive mass particle, it moves away from me and hence the acceleration is the direction of the force. For a negative mass particle the opposite thing will happen, i.e. it will move towards me. Now Einstein’s general theory of relativity (GR) tells about the possibility of arising of negative mass through the wormhole. The idea came up from Einstein and Rozen in their 1935 Physical Review paper. I must confess that I am not very comfortable with GR. May be later time I’ll make a post on wormhole on this blog. If you are little disappointed by my confession, then you may take a look at http://pashalaw.blogspot.com/2008/02/travel-to-parallel-universes.html (and of course, Wiki is always there).
Now the last quantity of our interest is the temperature. Can temperature be negative in absolute scale? You may tempt to say that laws of thermodynamics prevent us to go beyond zero Kelvin. But I’ll suggest you to take deep breath and think about what would happen if we could have gone below the absolute zero. Can we imagine a different physics to come out?