Isn't mathematics a language; what exactly do you mean?
Glad to see you are still around, Bw/S.
Yes, mathematics is a symbolic language. We have already covered the Gödel incompleteness discussion, which applies to any such system of reasoning. This is the reason why if your intention is to provide a mathematical description of the universe from first principles, using no empiracal observations of particle behavior, it will fail. The mathematics simply can't (yet) capture enough of the truth about the nature of particles all by itself to do so.
Be that as it may, the Standard Model of particle physics owes a great deal (understatement) to Emmy Noether. Using her mathematics, conservation laws and symmetries (some of which are confirmed by SM experimentation, others not), particle physics has gone from the days of "the particle zoo" to a much more coherent and predictive science model of the statistical behavior of subatomic particles.
Einstein was one of the earliest to recognize the importance of Noether's work to that purpose. And yet...
It breaks many of Noether's derived conservation laws if it is by any means possible to construct a neutrino (particle of lowest mass) from photons ("particles" of zero mass).
E = mc^2 is an important conservation law, and it suggests this should be possible, but I have it on the best authority I can find, it won't work It will never work.
The behavior of the Higgs field is why. Photons are not "really" particles, you see? They are directed energy. They are produced by pairs of entangled electrons, and they can carry inertia in a single direction, but nothing with any mass actually travels through space when a photon propagates. Photons may also carry quantum spin of sorts, which we refer to as polarization. This behavior suggests the wave of propagation is most likely carried in a given direction by interaction with particles that have spin zero until such a wave passes by. How about the "time dilation" that you would get if something with mass could travel as fast as a photon in a vacuum? Well, that exists for things like neutrinos alright, but not for a photon. Wavelengths of photon energy may stretch into the red or shrink into the blue, but nothing but energy actually travels from point A to point B.
What about relativistic time dilation as it affects those entangled electrons that produced the photon? Here is where it gets a bit trickier. It's actually going to be difficult to relate time dilation to a first principles calculation within atomic structure, as it applies to radioactive decay or anything else. This is largely because of the way quantum entanglement works. Spin flips between entangled electrons in the outer shells of atoms are likely to occur faster than light propagates between them, but at a different rate than spin flips or color charge exchanges between TRIPLETS of up/down quarks within an atomic nucleus or inside of protons and neutrons. Those quarks and electrons get their inertial masses from interaction with the Higgs field, but these fermions only account for about 2% of the total mass / energy of atomic structure. AND QCD and particle physicists both swear that this amount of mass doesn't come close to accounting for General Relativity's Principle of Equivalence between total inertial mass of atomic structure and its gravitational mass. Why not? Because they don't believe that E=mc^2 means what 20th century physicists were taught that it means. I can see their point (finally) that if you can't build a neutrino out of photons, you probably can't attribute the entire inertial mass of atomic structure to interaction with the Higgs field. But then these same particle physicists turn around and say that neutrinos too get their tiny masses from Higgs. So, what's going on here? A lot of inconsistency and incompleteness. That's what. Higgs bosons most often decay into gluons too. Looks like total conversion of matter to energy to me. Just like we always knew matter and antimatter behaved when you put them together.
It was in 2002 that QCD verified a detailed calculation of the mass of a proton from Standard Model and QCD principles with a supercomputer. They still couldn't achieve a proton spin calculation anywhere close.
The Higgs interaction, like neutrinos, penetrates all the way through a planet to its core. The interaction isn't one way because all forces in the universe occur in pairs. Everyone knows this. When you let go of a bowling ball near the surface of the Earth, it falls to the ground in the direction of the center of the Earth because the Higgs interaction on that side caused a loss of energy from the Higgs field in the space penetrating and surrounding the Earth. Time dilation at the exact center of the Earth (or even a rotating black hole) will be the same rate as though the clock were removed to infinity. SHOW ME the detailed calculation, using the gravitational field equations of your own choice which include a radius R=0, that can render this prediction with the certainty I just did with no effort at all. I just did it with nothing more than reasoning with what we learned on July 4, 2012. Any takers?
The mass of a planet doesn't abruptly end at the surface. The gravitational field in the space surrounding a gravitating body also carries mass. Second prediction with no effort at all. Predicts the origin of Dark Matter. Does your theory of gravity do that? Maybe it does, but you are stuck in the archaeic notion that "curvature of space" is more important than time dilation. The former effect has no physical consequences. The second effect is what bends a passing beam of light around a gravitating body as though it had inertia. Because space can have inertia. It gets inertia from interacting with matter.
You can't use new science to make new predictions while refusing to use those results. That's what I mean when I say that physics and the math that goes with it seems to be stuck in the late 19th century. If you refuse to use new science and I do, then my ignorance of your 19th century calculations is as good as your knowledge.
