Dear Sir,
Though your essays is not exactly on the required topic, you have brought it in at the end. We thoroughly enjoyed your well written essay and like to suggest some extensions.
Mathematics describes only the quantitative aspect of Nature - how much one quantity, whether scalar or vector; accumulate or reduce linearly or non-linearly in interactions involving similar or partly similar quantities and not what, why, when, where, or with whom about the objects. These are subject matters of physics.
Time dilation, like length contraction, flow from SR. Relativity is an operational concept, but not an existential concept. The equations apply to data and not to particles. When we approach a mountain from a distance, its volume appears to increase. What this means is that the visual perception of volume (scaling up of the angle of incoming radiation) changes at a particular rate. But locally, there is no such impact on the mountain. It exists as it was. The same principle applies to the perception of objects with high velocities. The changing volume is perceived at different times depending upon our relative velocity. If we move fast, it appears earlier. If we move slowly, it appears later. Our differential perception is related to changing angles of radiation and not the changing states of the object. It does not apply to locality. Thus, length contraction is only apparent. Time dilation (including that noticed in GPS) is caused due to refraction caused by changing density of local medium (what you call tired light). Time dilation, like light, is density variant and not uniform everywhere. This affects red-shift data also.
Still there is much confusion over the precise value of the Hubble Constant. The expanding universe concept was introduced to explain galactic red-shift. But now blue-shift and galactic mergers have also been confirmed. What if the measurements of the last sixties are also true? Further, it is linked to inflation. It is assumed that it is an open universe that is expanding since big bang 13.7 billion years ago. Ancient Indian astronomers give a much bigger date for it. What if the universe is closed? If you throw a pebble into a circular pond, the waves reach out to the boundary and then reverse. Ancient Indian astronomers described the evolution of the universe like that repeatedly, which can explain the current rate of 'expansion' without inflation. They believed that the universe is rotating on its axis with galaxies like planets around Sun. The orbits are all circular, but appear elliptical because of the moving center. Just like the planets appear to be receding at times to come close at other times, we may be seeing red-shift at some stage and blue-shift at other times. Thus, the galaxy rotation curve needs to be re-looked.
All the objects in the universe radiate far more energy compared to the cosmic microwave background. The ancient Indians classified bodies into five categories based on albedo. According to that classification, the CMB is without reflectivity (ajyoti called Parameshthi). It is the universal background structure. It is well known that light is a transverse wave, which is background invariant, but which requires one point to be fixed (tied) to be generated. Sound is a longitudinal wave, which cannot travel without a dense medium. Electromagnetic radiation exhibits both characteristics and the intersection point of the electric and magnetic planes with the medium in the direction of motion (they called it agni-somaatmaka) shows up as photon. Since the background structure does not move, it does not radiate light. But the reflected waves from the big bang interact with each other, which leads to not only evolution of forces (15 types), but also all material formation. It should be noted that though proton and neutron both are said to consist of up quarks and down quarks, in reality, each is a pullulating mass of countless quarks, anti-quarks, and gluons. It is so messy that physicists cannot say exactly how it's most basic properties, such as its mass and spin, emerge from the tangle. We have written about these, dark matter and dark energy variously.
Regards,
basudeba
