Thanks for sharing your views Steve. In response I point out a few things arising from your post...
"...let space come from or emerge from proper time and c as cП„. This is the essence of Lorentz invariance".
First, I beg to disagree that emergence of space has anything to do with Lorentz invariance. You always say space 'emerge' without telling us how. And what is the unit of measurement of this thing called 'Proper time'? Are you not aware that 'Proper time' is absolute? That is, it remains invariant under dynamical transformations. If this is so, will this not be robbing Newton of his Absolute time and paying Einstein with it?
On the equation: E2 = m2c4 + p2c2
This is the energy-momentum relation.
Yes, it can be reduced to E = mc2, which is the mass-energy equivalence (MEE as you call it). But this equation is not flawless. In the linked Wikipedia entry, 3 "special" cases or what I would call "excuses" are made for it. You can check them yourself. Of course, you may find the excuses reasonable given your preferred hypothesis.
Light and its behavior are central to physics. But a lot of inconsistencies abound. Saying, YES when it suits some situations and NO, when it does not. For instance because a massless particle will not work with the 'mass increase with velocity' scenario, the photon is excused as it leads to absurdity. We therefore get a NO, E = mc2 and m' = m/в€љ(1 - v2/c2) will not apply to photon, only E = pc will apply.
Yet, in another breath, it is claimed that gamma rays (photons) can decay into a positron and an electron (Оі = e++ e-)and that this demonstrates, YES, E = mc2 is applicable to a light photon and massive particles can arise from the massless photon's energy and not just momentum being manifest.
You might as well scrap the entire edifice of science as we know it...nuclear energy, ring laser gyroscopes, atomic clock variations with gravity...just throw it all out...and then try to make sense out of anything.
It is a commonly used tactic to lump what is correct and true with what is a false dogma, with the hope that some of the truth can rub on what is false. It is also a commonly used tactic to 'blackmail' and say, if you throw this away, you must also do likewise to others. Nuclear energy, ring laser gyroscopes, atomic variations with gravity have nothing whatsoever to do with Lorentz invariance. Go and check them out. And if you insust they do be kind enough to show how. Indeed, some of these things have been earlier rejected or covered up because they negated Lorentz invariance. However, when it became inevitable and can no longer be covered up, it is appropriated in a shameless way as an evidence of either Special or General relativity. An example is the GPS which is a Sagnac effect. An effect covered up and denied for more than 50 years.
But let me ask again, from you and others because it appears this question is being dodged. What is 'v' in the Lorentz factor в€љ(1 - v2/c2), noting the importance of this factor in Lorentz transformation and in experimentally explaining the null result of Michelson and Morley, and even in your mass-energy equivalence.
Regards,
Akinbo