It took me a bit to realize that you're using "M" for momentum - I keep thinking of a mass when I see capital "M"s

But what you've done is pretty cool and noteworthy, actually. For instance, consider this:
We currently have two basic "pillars of physics". We have the Standard Model (related to Quantum field theory), which describes particle interactions and, basically, everything apart from gravity (since gravity is too weak to be of concern there). Then, we have General Relativity, which describes how gravity shapes and curves spacetime.
But here's the thing - they can't both be right. It is well-known that GR is a classical theory that cannot be quantified in the same way that, say, electrodynamics can.
In fact, what happens is that infinities appear that we can't get rid of (Note: Infinities appear also in the Standard model, but they can be taken care of and "absorbed", in a process that's known as renormalization). Usually, that means that GR is only an approximation, and valid only to a certain energy scale.
And where does that happen? It happens if we consider masses larger than the Planck-mass, or times shorter than the Planck-Time, etc.

So there's a real physical meaning to those.



What Alberto says is also true - it's incredibly interesting to think about this. There is this one super-fundamental quantity - the speed of light - so it does make sense to set it to "1". Planck's constant is similary "fundamental", so often it is also set to 1.
If we do that, which is very often done in physics, then an inverse mass is nothing but a length (the Planck-length), or even a time (remember that c=1 implies that metres and seconds are "the same kind of unit") (the planck time).

[[Edit: While I know this kind of defeats the point, what I am saying with the above is that while the numerical value of the units is interesting because it gives us real "barriers" where we expect physics to behave differently, from a fundamental, qualitative standpoint, length and time (for instance) can be looked upon as something fundamentally similar - the difference between Planck time and Planck length is just a constant - a fundamental constant, yes, but still - it's just a number.]]

Does that answer your question? I hope I wasn't too technical.



Also, I'm really glad Hilbert's Hotel is more active again