On the Premise of a Variable Speed of Light
There exists the possibility that the speed of light, both in terms of the propagation of an electro-magnetic wave and in terms of the theoretical maximum speed in which matter can travel, varies according to reference of scale.
If such is the case, it would imply that, in the world of distances, if we were to measure any distance according to the speed of light x=ct there would need to be a 2+2 = 5 way of thinking, in which, the distance does not equal the sum of its parts.
For instance, if we were to define a certain finite distance by the time of propagation of light to arrive at a distance (D) and then divide the distance evenly into a certain number of parts (n), and then were to individually measure each of those parts by the propagation of light across any one of them, we would find that the sum distance of these intervals to be less than the distance they combined constitute. If the constancy of light is preserved it would appear to be a contradiction to the concept of summation - And perhaps the speed of light is constant, but to arrive at such a conclusion would be to also arrive at the conclusion that the concept of summation is logically incorrect when describing distance.
If the speed of light was not conserved and the concept of distance was, if we were, for instance, to measure the time interval between light traveling along a distance of .0001 microns we should find that at that distance, the speed of light would be greater than if we were, for instance, to measure the speed of light across an interval of several thousands of meters.
According to this idea (of distance summation constancy), for most practical purposes, the speed of light c = 299792458 m/s is a close approximation to distances ranging from .01 microns all the way to several parsecs. Beyond this domain, the approximation for c becomes noticeably varied from what is the actual value for c for that distance.
Be careful not to make the misconception that according to this theory, "the speed of light observed by distant stars would be less than the speed of light c". That would not be true, if one were to measure the speed of light from a distant star the same way they measure the speed of light of a nearby object, the observer would reach the same value of speed for both lights. So as long as the measure of distance used to calculate the speed of light (in a vacuum) is the same, the actual speed of light will be the same.
To clarify this;
If we were to measure the speed of light, we would have to know both the distance the light traveled and the time it took to travel this distance.
If the distance interval used to calculate the speed of the light is the same, then the person should arrive at the same speed for light, no matter how far away the source of the light is. Because the speed of light should vary according to the distance used to calculate it. If one were to change the interval of distance, they would arrive at different speeds for light.
This would lead to either one of two conclusions, the speed of light varies according to the distance used to measure it, or that summation is an insufficient way of describing distance. When I state that 2 + 2 = 5 I am not making a mathematical argument but simply describing what would be arrived upon if both modes of measuring distance are conserved.
Therefore there would be two separate solutions or any combination of the two, either the speed of light is a variable - according to the distance used to measure it, or the speed of light is constant and the distance does not equal the sum of it’s parts, it may indeed be possible to unify both premises through a sort of distance transformation that would both describe the contradiction of summation while conserving the constancy of the speed of light.
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