In physics, exotic matter is a term which refers to matter which would somehow deviate from the norm and have "exotic" properties. There are several uses of the term.
Negative mass would possess some strange properties, such as being repelled rather than attracted by gravity and accelerating in the direction opposite of applied force. For example, an object with negative inertial mass and positive electric charge would accelerate away from objects with negative charge, and towards objects with positive charge, the opposite of the normal rule that like charges repel and opposite charges attract. This behaviour can produce bizarre results: for instance, a gas containing a mixture of positive and negative matter particles will have the positive matter portion increase in temperature without bound. However, the negative matter portion gains negative temperature at the same rate, again balancing out.
Despite being completely inconsistent with a common-sense approach and the expected behavior of "normal" matter, negative mass is completely mathematically consistent and introduces no violation of conservation of momentum or energy. It is used in certain speculative theories, such as on the construction of wormholes. The closest known real representative of such exotic matter is the region of pseudo-negative pressure density produced by the Casimir effect.
A hypothetical particle with imaginary rest mass would always travel faster than the speed of light. Such particles are called tachyons. There is no confirmed existence of tachyons.
If the rest mass is imaginary, then the denominator must be imaginary since the total energy must be real; therefore the quantity under the square root must be negative, which can only happen if v is greater than c. As noted by Gregory Benford et al., among others, special relativity implies that tachyons, if they existed, could be used to communicate backwards in time (see Tachyonic antitelephone article). Since time travel is considered to be non-physical, tachyons are believed by physicists either to not exist, or else to be incapable of interacting with normal matter.
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