You ask, "How do we describe mass to the aliens, who don't know about our (g)?" This is an example of a class of questions referred to by Martin Gardner as "Ozma problems." The classic Ozma problem is how we describe to aliens the distinction between right and left; the answer is that we do it by describing the weak nuclear force.
Your statement of your Ozma problem seems a little ambiguous to me. Essentially you're asking how we describe to the aliens a unit of gravitational mass. (You don't say so explicitly, but it seems clear from context that you don't mean inertial mass.) Futhermore, there is a distinction bewteen active gravitational mass (the ability to create spacetime curvature) and passive gravitational mass (what we measure with a balance). Not only that, but your question could be interpreted as asking whether we can compare with the aliens and see whether the value of the gravitational constant $G$ is the same in their region of spacetime as it is in ours.
We can easily establish 1 g as a unit of inertial mass. For example, we can say that it's the inertia of a certain number of carbon-12 atoms.
The equivalence principle holds for us, so presumably it holds in experiments done by the aliens as well. This establishes that our 1 g unit of inertial mass can also be used as a unit for the passive gravitational mass of test particles.
You didn't ask about active gravitational mass, but the equivalence of active and passive gravitational mass is required by conservation of momentum, and has also been verified empirically in Kreuzer 1968. Cf. Will 1976 and Bartlett 1986.
The other issue is whether $G$ is the same for the aliens as for us. Duff 2002 has an explanation of the fact that it is impossible to test whether unitful constants vary between one region of spacetime and another. However, there are various unitless constants that involve $G$, such as the ratio of the mass of the electron to the Planck mass.
A more fundamental difficulty in the fundamental definition of mass is that general relativity doesn't seem to offer any way of defining a conserved, global, scalar measure of mass-energy. See, e.g., MTW, p. 457
Bartlett, Phys. Rev. Lett. 57 (1986) 21.
Duff, 2002, "Comment on time-variation of fundamental constants," http://arxiv.org/abs/hep-th/0208093
Kreuzer, Phys. Rev. 169 (1968) 1007
MTW: Misner, Thorne, and Wheeler, Gravitation, 1973.
Will, “Active mass in relativistic gravity: Theoretical interpretation of
the Kreuzer experiment,” Ap. J. 204 (1976) 234, available online at adsabs.
harvard.edu.
I think you have a few misconceptions here. You start by talking about the particles in the beam "not interfering with each other" so the "wave function of each particle is lambda/p".
There are at least two problems with this statement. I'll take the last part first. It looks like you are confusing "wave function" with "wave length". The wave function doesn't have a value. It is a function. In a case like this we would write it as a function of position and particle momentum. We would find this function by solving the Schrodinger equation, but let's not get into how that is done.
Next is not useful to think of the particles "interfering" with each other. A wave function of a single particle "interferes with itself" but wave functions of different particles don't interfere with each other. The wavefunction of each particle needs to be solved for from the Schrodinger equation. Without going into gory detail about how that is done, it depends on what the interactions are with the rest of the system (in this case, interactions with the slits and with the other particles).
Essentially your question is "why do the slits affect the wavefunctions of the particles but the other particles don't". There are two answers:
Typically the distances between particles in the beam are so large that the interactions between the particles are very weak and can be neglected.
Even if the interactions are not very weak (a very high intensity beam) then each particle in the beam has many particles around it (in all directions). Typically, these particles are all charged. For sake of argument let's say that they are electrons. So they all repel each other. But that means that the repulsion due to all of the nearby electrons will tend to cancel out and once again, at least for most of the electrons, we can ignore the interactions.
An accelerator physicist could answer this better, but I'm guessing that reason 1. is more important most of the time.
Best Answer
OK, I watched the video.
It consists of two parts. The first part talks about General relativity and the introduction of a cosmological constant, which from the argument should not exist in completely empty space.
He then goes to the Quantum Field Theory vacuum which has the continuous creation and annihilation of all possible fields of virtual particles all the time, and illustrates it with the proton. His discourse assumes that the proton is made up of three quarks and the rest is empty space. The theory I know does not say so, it says the rest is a gluon to quark antiquark and back sea, that holds everything together to form the proton. It is not empty space because energy exists within the proton, it is not zero.
So the presentation is incomplete and seems to me misleading, if we are to project the inside energy momentum conditions of a proton to cosmological scales and the cosmological constant. They are not the same.
Anyway the argument he seems to be leading to is incomplete.
In the double slit experiments, mass does not wave. The elementary particles are point particles as far as our experiments have explored, when they appear as particles, the appear at a specific (x,y,z,t). What "waves" is the probability of finding that particle at a specific (x,y,z,t) which probability is calculated by squaring the quantum mechanical amplitude describing the "particle/wave" entity which probability shows interference patterns in collective observations at double slit experiments.
In my opinion, until we have a solid theory which quantizes gravity and includes the standard model of particle physics speculation about how fields appear in cosmological terms is not productive. We have to wait for a theory, and a string theory seems to be the only candidate that can do this , to examine the cosmological constant of classical general relativity.