Hello Fady Tarek :

Your question is interesting !, please let me know more about the particular scenario of your question.. Can you elaborate further ?

e.g. What are the kind of interactions you are talking about? I also didn't understand the part of: "$\Sigma^{0} \rightarrow \Lambda + \pi^{0}$" .

No matter what interactions you think of, in particle physics... Energy has to be conserved, globally, there is no other alternative. Conservation of Energy in Particle Physics (e.i. when we see physics using the Particle-behavior approach, not QFT, not Wave Quantum Mechanics) is a constraint of nature in our experiments.

On the other hand, maybe I know what you are to ask from your second paragraph. The question you are trying to ask is:

Specifically, in collisions between two beams (or paquets) of particles (lets encompass the terms of scattering and interact into 'collide') ...cont. In the collision of two beams of particles; you cannot end up with a particle with a greater rest mass of any of the initial particles ?

Is it so ? if so, I think you are considering just the mass conservation..

But, can you elaborate more of the question,

Regards !

Because time translation invariance isn't present. Conservation of energy is equivalent to time translation invariance. Global Poincaré invariance (global Lorentz invariance along with translations in space and time) includes time translations, therefore implies that energy is conserved.

Rest mass is a quantity that's invariant under global Lorentz transformations.

Stam Nicolis

Is there an easy test for time translation invariance of these interactions?

Sure-all the measurements at any accelerator the last hundred years test deviations from global Lorentz invariance and set bounds on it; and general relativity shows precisely how global time translation invariance becomes local time translation invariance when spacetime curvature is relevant.

I have sometimes wondered, when a simple free neutron decays to a proton and low-velocity electron, and a anti-neutrino is deemed needed and emitted by that action to conserve energy --- the following: Is there a measurable momentum recoil of the resulting proton and low-velocity electron (net proton and electron 'mv') opposite the direction of the presumed anti-neutrino's 'flight' direction? And, if so, how we would conceptualize the 'mv' momentum recoil or the proton and electron masses vs. a neutrino flying away from the scene with no? neutrino mass and velocity 'c'. Wonder what Compton would think -- on the subject? (Pardon any imperfection in the question -- trying to go by my memory which could be imperfect.)

The proper or rest-mass energy plus the kinetic energy of the ingoing particles must equal always the proper or rest-mass energy plus the kinetic energy of the outgoing particles (for any reaction in absence of external influences). Moreover the three components of the total linear momentum, of the total angular momentum + spin and other different charges (electric, baryonic etc.) must also be conserved. These conservation laws restrict the set of possible reactions among given particles. If the energy balance is apparently non-conservative in an observed reaction is often due to the presence of outgoing unobserved particles which carry the lacking energy. A famous example of this was the discovery of the neutrino, first postulated in 1931 for explaining the energy lost in beta-decay reactions and finally identified in 1956 in laboratory experiments.

Dear Fady,

To your question, the answer is rather simple from the electromagnetic perspective. It is related to the adiabatic changes in the amount of energy induced in elementary particles or larger masses as they switch between the various stable axial stationary action equilibrium states:

Ref: Michaud, A. (2020) Electromagnetism according to Maxwell's Initial Interpretation. Journal of Modern Physics, 11, 16-80. https://doi.org/10.4236/jmp.2020.111003.

https://www.scirp.org/pdf/jmp_2020010915471797.pdf

Best Regards, André

Dear Carl,

From the electromagnetic perspective, neutrinos can escape only by pairs moving in opposing directions transversely to the direction of motion of the electron, to evacuate the momentary excess mass energy, this is why no longitudinal recoil can be observed.

Ref: Michaud A. The Mechanics of Neutrinos Creation in the 3-Spaces Model. International Journal of Engineering Research and Development. e-ISSN: 2278-067X, p-ISSN: 2278-800X, Volume 7, Issue 7 (June 2013), PP. 01-08

http://www.ijerd.com/paper/vol7-issue7/A07070108.pdf

Best Regards, André