The Unruh Effect: Insight from the Laws of Thermodynamics

When an observer experiences uniform acceleration it has been postulated that empty space will appear as an infinite extent emitting a blackbody spectrum at a temperature proportional to the acceleration: the Unruh Effect. The Effect has been tied to the Hawking temperature of a black hole and is purportedly one account of the origin of black hole thermal emission, where the acceleration in the black hole case is due to gravity. The Unruh and Hawking temperatures have the same mathematical form: T = ha/4π²ck_B, were T is temperature, h is Planck’s constant, a is acceleration, c is the speed of light in vacuo, and k_B is Boltzmann’s constant. Acceleration for Hawking temperature is a = GM/(r_S)² where r_S = 2GM/c² (Schwarzschild radius) where G is the universal constant of gravitation, M the black hole mass. Temperature is always an intensive property. Acceleration is not an intensive property. The Unruh temperature, as with the Hawking temperature, although dimensionally balanced, is not thermodynamically balanced. Temperature cannot be equated to a term, or combination of terms, that is not intensive. The Unruh temperature therefore, violates the 0^th and 2^nd laws of thermodynamics, as does Hawking temperature. Consequently, it is invalid. The Unruh Effect does not exist.