Behavior of Light

 

Most of the ensuing discussion will involve the consideration of how events look in different coordinate systems, either to an outside observer or to an observer in a system under consideration. This is made somewhat easier by assuming that such systems have a uniform time throughout. This is similar to considering the systems to be inertial ones, which have uniform linear velocity with respect to each other. Actual inertial systems probably do not exist, but it is useful to assume that they do in order to develop some basic ideas about the behavior of light and matter with respect to different systems. Thus an object can be ‘moved’ from one system to another without considering what happens at the border(s) of the two systems since the amount of time the object interacts with the border can be assumed to be insignificant.

 

In reality, if a system is considered as an area with a uniform clock rate, then it would appear that every point in space must be considered as a separate system. Thus an object is continuously interacting with one or more borders between different systems, and this interaction can no longer be considered insignificant. Basically, this is simply saying that a gravitational field is everywhere, and cannot be ignored even though that has been done before and will be done here to simplify things. By ignoring this reality, the behavior of light and matter can be evaluated as they move from one system to another without worrying about interactions with the borders between systems. This only considers one aspect of the behavior. The aspect of the behavior that is involved with interactions with system borders is generally not considered here or is only briefly and indirectly mentioned in some of the sections[1].

 

The Maxwell equations

 

The Maxwell equations show that changing electrostatic and electromagnetic fields evolve, or change, as a function of time. Experimental evidence is compelling in indicating that the flow of time varies with position (in a gravitational field) and probably with velocity (of an object). Thus the behavior of changing electro-magnetic fields should also change as a function of the local time (clock rate or time base) in which they exist.

 

For example, consider a time dependent device that flashes every second in our system. If a similar one is in another system where the time base is twice as long as ours, the device should also flash every second in the other system. But if we observed the other system, we would see that the device in that system flashes every 2 seconds according to our time. If an observer in the other system observes ours, our device would appear to be flashing 2 times per second according to the other system’s time. The time in the other system can be measured by counting the number of flashes sent out from the other system over a given period of local time (this would only be valid if the systems were at rest with respect to each other, otherwise velocity corrections would be required). Essentially the same thing should be true for the speed of light if that speed is determined by the clock rate. For inter-system measurements (measurements made totally within a single system), the speed of light would have the same value in either of the above systems. But the intra-system measurement values (values measured with respect to some behavior in a system from another system) would be different just as the intra-system flash rates of equivalent devices would be different in the above systems.

 

There is one aspect of the Maxwell equations for electricity and magnetism that requires evaluation. The Maxwell equations contain two constants, e₀ and e₀c², that appear in the following equations[2]:

 

  and   .

 

Both e₀ and e₀c² do not have values specified by the equations, but are determined experimentally, and should therefore be dependent on the conditions under which they are measured. The constant e₀ is related to the flux of both electric and magnetic fields. Since the equations in which they occur for changing electric and magnetic fields are functions of time, the experimentally determined values should be different when measured using different time bases. Although the ratio of the constants is always c², and the value of c would be the same whenever the constants were evaluated with inter-system measurements, c would not necessarily have that same value if the constants were evaluated using intra-system measurements.