### Missing Momentum & Missing Mass

**Where Do These Expressions Come From?**

Both expressions are common in papers describing decay processes. Yet there is no doubt that all phenomena in NATURE adhere to the principle of energy and momentum conservation. It is universally accepted because energy is neither created or lost: it is merely transformed. Momentum is conserved because action and reaction are equal.

Then why do scientists talk about “missing mass” and “missing momentum”?. These expressions need to have a context to make sense: “missing mass” is in the context of expected energy, and “missing momentum” is in the context of some expected momentum value. These two expressions are directly related to particle decay.

When it comes to particle motion, classical (Newton’s) mechanics applies to particles at slow speeds, while Special Relativity equations are applied to particles described in terms of light speed. “Missing mass” or “missing momentum” appear when SR’s equations are used to calculate energy and momentum.

In an accelerator, a particle normally receives energy from an externally applied electromagnetic field. A particle’s energy increases in the form of kinetic energy, and to calculate its momentum, the particle’s mass is also increased.

Even though a “philosophy” has been invented to explain the “double increase of energy” (KE + mass increment), to calculate the particle’s momentum the increasing mass is real and momentum is bigger than the momentum calculated without the mass increment.

The same SR equations applied to particles accelerated inside accelerators are used when the particle is going through decay process.

In this case, there is no external energy. The new particle’s energy comes from the rest mass energy of the original particle, committed to the mass-energy equivalence principle. That is, to create the new particle’s kinetic energy, we need to expend mass taken from the particle’s rest mass in the quantity required by energy-mass equivalence. The mass of the new particle will be smaller than the mass of the original particle.

As the energy and momentum experimental values – calculated via classical mechanics concepts(*) – are less than the values calculated with SR’s equations, we need to talk about “missing mass” (as lost energy) and “missing momentum”. But this “missing mass” and “missing momentum” are not real, are not lost in NATURAL phenomena. They are “missing mass” and “missing momentum” because using SR’s equations we get values bigger than the real values in NATURE. That is, SR’s equations are not appropriate to calculate those values in a decay phenomenon.

If we replace SR’s equations by appropriate equations and use the experimental values, we can no longer speak about “missing mass” or “missing momentum”. This is the case when we use the AD’s Kinetic Energy and Momentum equations.

(*) This doesn’t mean to use the classical energy and momentum formulae, because these only apply to small velocities. But we will use the time between two points to calculate velocity, the caloric energy measured inside a calorimeter, etc..

The following example shows this for momentum:

Pion Program Example