Due to W. Pauli, the original approach to the problem of missing energy in beta decay was to postulate the existence of a particle, but this was not a definitive solution, and even today, more and more particles have been postulated, attempting to explain this phenomenon. Here is W. Pauli's famous letter where this idea was proposed (English translation below).
Contrary to W. Pauli, N. Bohr explained this phenomenon as a violation of energy conservation, but his solution was not popular at the time. In virtue of Noether's theorem, the conservation of energy in a system is equivalent to the time-invariance of its Lagrangian.
Let's consider computational time to be one step in the evolution of the Wolfram Model. Here is a material explaining what I called computational time, in contrast to ordinary time (the time measured by a clock), the computational time is different from the time component of spacetime.
We, the macroscopic observers, are vast objects concerning the scale of the computational time. Hence, our time t is a function f of computational time tau, i.e., t = f(tau). The nontrivial results are obtained if and only if f is non-linear, i.e., ordinary time is not just a linear change of scale of computational time, but a genuine emergent phenomenon involving non-linearity.
Substituting t (ordinary time) by tau (computational time) in equations of quantum field theory, the Lagrangian will be no longer time-invariant (with respect to our ordinary time). Indeed, the operation
d/dt t = 1
giving rise to the time-invariance of the Lagrangian will be substituted by something like
d/dt tau = d/dt g(t) = 1/(df/dt (g(t)) )
where g is the inverse of f. Notice that the time in the derivatives was not substituted by tau, because the derivatives are used to find the Lagrangian with respect to our ordinary time, whereas the computational time is used to describe quantum field theory at a fundamental level. It should be possible to derive these equations of quantum field theory, replacing t by tau, from first principles, using a model like the cellular automata fluids.
Concerning the connections between particles and time, here is the model that I am following in the research program of the Wolfram Physics Project:
Anyone interested in this problem is welcome to post a simulation of the missing energy during beta decay, using the hypothesis that our time (with respect to a reference frame) is a non-linear function of the computational time. Also, it would be interesting to know where this nonlinearity of time comes from.
