Light and energy

 

Light can be characterized by frequency  and wavelength , where . The energy of a photon is considered to be , which essentially makes the energy a function of the frequency of the photon. Let the reference frame (RF) associated with a body in space be S’, and the RF associated with the surrounding space be S. The clock rate in S’ will be slower than that in S. Let an observer in S’ be O’, and an observer in S be O. Let E be a specific electron transition in a specific type of atom that produces a photon that has some frequency  relative to the observer in the RF in which E occurs. We will assume that E occurs in S’ and that the photon travels from S’ to S. The frequency of the photon at the time it is produced will be called  as determined by O’. Let’s look at the energy of that photon as it appears to both O and O’.

 

When the photon is produced, O’ will calculate the energy to be  with inter-system measurements. After the photon enters S, O’ will calculate the same energy using intra-system measurements. This would be the case since it is assumed that the frequency does not change (relative to O’) when the photon changes speed as it travels from S’ to S. Thus the photon does not change energy as far as O’ is concerned.

 

Now consider that O makes intra-system measurements of the photon when it is produced and then follows its progress from S’ to S. The photon’s frequency will not be the same for O as it was for O’ since O is using a different clock rate than O’. The frequency determined by O will be called , which represents a lower frequency than . Thus the energy of the photon calculated by O will be . This is less energy than calculated by O’. As the photon travels from S’ to S, and O switches to inter-system measurements of the photon, the energy will remain the same as far as O is concerned.

 

Thus the energy of the photon remains the same for each observer as it travels from S’ to S, although the calculated energy of the photon is different for each observer[1]. For O, the energy of the photon is less than it is for O’. This assumes that the value of Plank’s constant h is the same for all measurements for all observers. Does the photon lose energy when it travels from S’ to S? Most physicists (at least relativists) would presumably say it does. The reasoning for this might be that the transition E in S is known to produce a photon with a certain energy level. Thus the transition E in S’ should produce a photon with the same energy level. Since the photon produced in S’ has a longer measured wavelength when measured by O in S, the calculated energy of the photon must be less than it should be, and thus it must have lost energy going from S’ to S. However, the energy as calculated by O when tracking the photon from S’ to S does not change. So is there justification for saying that the photon lost energy?

 

This suggests that energy content might be relative to the observer and the clock rate used for its calculation. Consider the energy content of matter, which has been shown to be . Since the value of c might vary between inter- and intra-system measurements, the energy content of matter might also vary depending upon the observer and clock rate used for measurements. Thus the energy of an object would be the same when calculated using inter-system measurements, but might be different when calculated using intra-system measurements. When measured by O, an object in S’ would have less calculated energy using intra-system measurements than the same object in S using inter-system measurements. This is similar to the equivalent calculation of energy for a photon.

 

This section has just scratched the surface of an interesting implication of the theoretical considerations presented in this discussion. It is relevant with respect to the concept of the conservation of energy, and suggests that the concept may be somewhat more complicated than seems to be generally assumed.