Is there a fundamental difference between coordination systems in classical, relativistic, and cosmological physics, what establishes a difference?

A body at rest has rest Energy, so it should also have rest Momentum.

Lao Tzu said, “Gravity is the root of lightness; stillness, the ruler of movement”(重为轻根，静为躁君)*. The meaning of this statement can be extended in physics to mean that "big-G determines how light or heavy an object is, and rest-m determines how easy or difficult it is to move".

According to the mass-energy equation** [1], E=mc^2, any object with mass m has "rest energy" [1], regardless of its inertial frame†. Note that E here is meant to be the energy lost when radiating the photon γ, which is absolute and unchangeable in any inertial frame. The mass-energy equation has been experimentally verified [2] as the correct relation.

According to special relativity [3], the mass of the same object is different in different inertial frames, m' = βm. Therefore, the energy of conversion of m of an object into photon γ is different in different inertial frames. This issue has been discussed in [4], but there is no consensus. Our view is that the "rest energy" is theoretically not Lorentz invariant, and the existence of a minimum value is a reasonable result. The most rational explanation for this is that the minimum corresponds to an absolutely static spacetime, i.e., absolute spacetime(Later we will show that absolute space-time and relative space-time are not in conflict). Analytically, this is one of the reasons why absolute spacetime should exist. The constant speed of light is another reason.

In all cases in physics, energy and momentum coexist and have a fixed relationship, not independent metrics. The energy-momentum ‡ of a photon, E=hν[5], P=h/λ[6]; the energy-momentum relation of Newtonian mechanics, E=P^2/2m; and the relativistic energy-momentum relation, E^2=c^2p^2+m^2c^4. Therefore, it is assumed that if there is a body of mass m that has "rest energy", then it should also have "rest momentum". There is a "rest momentum", and the rest momentum cannot be zero. The rest energy is not intuitive, and the rest momentum should not be intuitive too. The calculation of the rest momentum is the same as the calculation of the rest energy. The nature of mass looks more like momentum; after all, energy is a sign of time, while momentum is a sign of movement. Therefore, instead of calling it the principle of equivalence of inertial mass and rest-energy[1], it should be called the principle of equivalence of inertial mass and rest-momentum.

When positive and negative electrons meet and annihilate [7], -e+e→γ+γ, radiating two photons in opposite directions. Their energy is conserved and so is their momentum. Energy is a scalar sum, while momentum is a vector sum. It seems that the "rest momentum" inside the object should be zero. However, one could argue that it is actually the momentum of the two photons that is being carried away, but in opposite directions. The momentum of the two photons should not come out of nothing, but rather there should be momentum of the two photons, also in some balanced way, and probably playing a very important role, such as the binding force.

Our questions are:

1) Since energy and momentum cannot be separated, should an object with "rest energy" necessarily have "rest momentum".

2) Elementary particles can be equated to a " energy packet ", and energy is time dependent. If an elementary particle is also equivalent to a "momentum packet", the momentum in the packet must be related to space. Does this determine the spatio-temporal nature of the elementary particles? And since momentum is related to force, is it the force that keeps the "energy packet" from dissipating?

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Notes：

* Lao Tzu，Tao-Te-Ching，~500 BCE. This quote is a translation of someone else's. There are some excesses that I don't entirely agree with. Translating classical Chinese into modern Chinese is just as difficult as translating classical Chinese into English.

** There is a historical debate about the process of discovery of the mass-energy equation, and digging into the history shows that there were discoverers and revisers both before and after Einstein, see literature [8][9]. Important contributions came from Poincaré, F. Hasenöhrl, Planck et al. Their derivations do not have the approximation of Einstein's mass-energy equation. And there is also a debate about the interpretation of the mass-energy equation. Notable debates can be found in the literature[10].

† There is a question here, i.e., is the rest mass Lorentz invariant? That is, is the rest mass the same in different inertial systems? Why?

‡ Einstein questioningly emphasized that energy and momentum seem to be inseparable, but did not explain it.

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References：

[1] Einstein, A. (1905). "Does the inertia of a body depend upon its energy-content." Annalen der physik 18(13): 639-641.

Einstein, A. (1935). "Elementary derivation of the equivalence of mass and energy." Bulletin of the American mathematical society 41(4): 223-230.

[2] Rainville, S., J. K. Thompson, E. G. Myers, J. M. Brown, M. S. Dewey, E. G. Kessler, R. D. Deslattes, H. G. Börner, M. Jentschel, P. Mutti and D. E. Pritchard (2005). "A direct test of E=mc2." Nature 438(7071): 1096-1097.

[3] Einstein, A. (1905). "On the electrodynamics of moving bodies." Annalen der physik 17(10): 891-921.