1.01.2011

Light Train Paradox

Imagine a moving train was equipped with a sensor which received a photon of light, and caused the train to stop, this must mean that the information contained in the photon is equal to the energy used in stopping the train, minus losses due to heat and work. Thus e=mc^2=i, where i is the information content of a message which causes matter energy to be transformed from one to the other.

Update 04.01.2011:
Continuing with this gedankenspiel, would this not mean that if the speed of light and the perceived mass of the photon as it strikes the receptor is truly constant, the information content is not. This can be shown as  the same photon sensor from the train experiment can be used with say, a small car. However, the amount of energy transformed is much smaller. This can be if either continuity does not hold, which I do not believe. Another possibility is that the rate of change of momentum is changed via a change in the rate of change of space time.

Update 11.01.2011:
The answer is that all of the energy in stopping the train is converted into the brakes, via friction, noise and the like, and the energy used by the receptor cannot be more than the photon's energy (in an ideal case), thus no energy leaves or enters the system throughout the process of transformation. Thus the amount of information (1 bit) the photon contained is exactly equal to that of all the energy used in bringing the train to a complete stop. Thus energy = information.