I have been studying electromagnetism lately, as in the practical application of Maxwell's equations to realistic physical systems. I find it an amazing fact, that even if we assume that point charges send out their electric fields instantaneously as in deliberately ignoring the postulates of special relativity, we none the less can find the wave equation inside of Maxwell's equations, which of course equates the speed of propagation of electromagnetic waves to c, the speed of light. I must mention now that before you read further, that I would appreciate any feed back on the soundness of my logic in what you are about to read. I must preempt you now with a message, that these are the products of my musings and are prone to contain mistakes. Please find it to your pleasure to correct any haneous errors and false logic you detect in my writings.
Electromagnetism can derive the speed at which electromagnetic radiation will propagate, but it cannot predict without separate assumptions, the postulates of special relativity, that specify at what speed the electric field is "updated." What if we would have said that the electric field is sent out at a speed less than or greater than c. Supposedly we should still end up with a electromagnetic wave relation that gives the speed of the wave as the speed of light, regardless of how fast we actually "declare" the speed of light to be. If we ignore for a seond that nothing can travel faster than the speed of light, does the assumption that electric fields change instananeously violate other physical principles?
Physicists are constantly trying to ignore infinities that wind their way up in problems. Often the infinities are describing forces, which leads to a concept of infinite energy, which would seem to violate our most sacred guiding post to understanding the nature of things - always follow the path of Conservation of Energy. Is violation of energy conservation what happens when we believe the electric field from a point charge is updated instantaneously?
Suppose we have two electrons a certain intial distance apart called d, that are not moving relative to each other. Each one is getting its electric field instantaneously updated. An obersver moving at constant velocity relative to the two stationary electrons observes a Lorentz contraction of the distance between the two electrons. Although we have contraction, we never said that it was due to the fact that information must travel less than c. I am saying we have experimental evidence of this effect, and in that sense we are adding it ad hoc to our theory which ignores the postulates of relativity. According to the observer the electrons are closer to each other, than the observer in the rest frames of the electrons, so they feel a greater force in one frame than the other. Now lets add another element to the setup. I am going to introduce a neutron that was really there all along, that lies on the same line as the two electrons and is the same distance away d from one of the electrons and is relatively at rest to the two electrons. The observer moving relative to the two electrons and neutron sees the whole lot of them contracted in the relative distance apart they are from each other. This observer sees the electrons closer together and so calculates a larger Coulombic acceleration, and therefore sees one of the electrons hit the neutron before the observer at rest. This theory can't preserve causality, without first stating that information about the fields must be sent at speed c relative to every reference frame. From that we can deduce the only way to remove the discontinuity in casuality in relation to the time between two oberservers moving relative to each other, is to make each observer's time separate of each other, while keeping constant instead the speed at which each reference frame sees itself send out information and at which it sees other frames send out information, i.e., c.
It is not necessarily the passge of time that all things of matter in the universe must share with each other. The one thing we have in common with everything physical in existence, with all form of matter and energy alike is the speed at which we send out information can never be greater than c. If I accept the postulates of relativity, I can have no doubt of anykind upon this matter. If any doubt shoud occur at whether or not I am existing, then I can redefine existence as the ability to confirm the postulates of relativity, that information cannot be sent out faster than the speed of light by anything. Perhaps it's the only way a universe can exist. It's the only way to keep the universe aware of itself to make the interaction of its matter meaningful by imposing causailty restrictions, by incorporating the postulates of relativity.