One of the most important things we will ever learn about the universe is just how big it is, practically, for our purposes. In the last century we’ve learned that it it is far larger than we knew, in a great many ways. At the moment we are pretty sure that it is about 13 billion years old, and that it seems much larger in spatial directions. We have decent estimates for both the total space-time volume we can ever see, and all that we can ever influence.

For each of these volumes, we also have decent estimates of the amount of ordinary matter they contain, how much entropy that now contains, and how much entropy it could create via nuclear reactions. We also have decent estimates of the amount of non-ordinary matter, and of the much larger amount of entropy that matter of all types could produce if collected into black holes.

In addition, we have plausible estimates of how (VERY) long it will take to actually use all that potential entropy. If you recall, matter and volume is what we need to make stuff, and potential entropy, beyond current actual entropy, (also known as “negentropy”) is they key resource needed to drive thus stuff in desired directions. This includes both biological life and artificial machinery.

Probably the thing we most care about doing with all that stuff in the universe this is creating and sustaining minds like ours. We know that this can be done via bodies and brains like ours, but it seems that far more minds could be supported via artificial computer hardware. However, we are pretty uncertain about how much computing power it takes (when done right) to support a mind like ours, and also about how much matter, volume, and entropy it takes (when done right) to produce any given amount of computing power.

For example, in computing theory we don’t even know if P=NP. We think this claim is false, but if true it seems that we can produce vastly more useful computation with any given amount of computing power, which probably means sustaining a lot more minds. Though I know of no concrete estimate of how many more.

It might seem that at least our physics estimates of available potential entropy are less uncertain that this, but I was recently reminded that we actually aren’t even sure that this amount is finite. That is, it might be that our universe has no upper limit to entropy. In which case, one could keep run physical processes (like computers) that increase entropy forever, create proverbial “perpetual motion machines”. Some say that such machines are in conflict with thermodynamics, but that is only true if there’s a maximum entropy.

Yes, there’s a sense in which a spatially infinite universe has infinite entropy, but that’s not useful for running any one machine. Yes, if it were possible to perpetually create “baby universes”, then one might perpetually run a machine that can fit each time into the entrance from one universe into its descendant universe. But that may be a pretty severe machine size limit, and we don’t actually know that baby universes are possible. No, what I have in mind here is the possibility of negative mass, which might allow unbounded entropy even in a finite region of ordinary space-time.

Within the basic equations of Newtonian physics lie the potential for an exotic kind of matter: negative mass. Just let the mass of some particles be negative, and you’ll see that gravitationally the negative masses push away from each other, but are drawn toward the positive masses, which are drawn toward each other. Other forces can exist too, and in terms of dynamics, it’s all perfectly consistent.

Now today we formally attribute the Casimir effect to spatial regions filled with negative mass/energy, and we sometimes formally treat the absence of a material as another material (think of bubbles in water), and these often formally have negative mass. But other than these, we’ve so far not seen any material up close that acts locally like it has negative mass, and this has been a fine reason to ignore the possibility.

However, we’ve known for a while now that over 95% of the universe seems to be made of unknown stuff that we’ve never seen interact with any of the stuff around us, except via long distance gravity interactions. And most of that stuff seems to be a “dark energy” which can be thought of as having a negative mass/energy density. So negative mass particles seem a reasonable candidate to consider for this strange stuff. And the reason I thought about this possibility recently is that I came across this article by Jamie Farnes, and associated commentary. Farnes suggests negative mass particles may fill voids between galaxies, and crowd around galaxies compacting them, simultaneously explaining galaxy rotation curves and accelerating cosmic expansion.

Apparently, Einstein considered invoking negative mass particles to explain (what he thought was) the observed lack of cosmic expansion, before he switched to a more abstract explanation, which he dropped after cosmic expansion was observed. Some say that Farnes’s attempt to integrate negative mass into general relative and quantum particle physics fails, and I have no opinion on that. Here I’ll just focus on simpler physics considerations, and presume that there must be some reasonable way to extend the concept of negative mass particles in those directions.

One of the first things one usually learns about negative mass is what happens in the simple scenario wherein two particles with exactly equal and opposite masses start off exactly at rest relative to one another, and have any force between them. In this scenario, these two particles accelerate together in the same direction, staying at the same relative distance, forevermore. This produces arbitrarily large velocities in simple Newtonian physics, and arbitrarily larger absolute masses in relativistic physics. This seems a crazy result, and it probably put me off from of the negative mass idea when I first heard about it.

But this turns out to be an extremely unusual scenario for negative mass particles. Farnes did many computer simulations with thousands of gravitationally interacting negative and positive mass particles of exactly equal mass magnitudes. These simulations consistently “reach dynamic equilibrium” and “no runaway particles were detected”. So as a matter of practice, runaway seems quite rare, at least via gravity.

A related worry is that if there were a substantial coupling associated with making pairs of positive and negative mass particles that together satisfy relative conservation laws, such pairs would be created often, leading to a rapid and apparently unending expansion in total particle number. But the whole idea of dark stuff is that it only couples very weakly to ordinary matter. So if we are to explain dark stuff via negative mass particles, we can and should postulate no strong couplings that allow easy creation of pairs of positive and negative mass particles.

However, even if the postulate of negative mass particles were consistent with all of our observations of a stable pretty-empty universe (and of course that’s still a big if), the runaway mass pair scenario does at least weakly suggest that entropy may have no upper bound when negative masses are included. The stability we observe only suggests that current equilibrium is “metastable” in the sense of not quickly changing.

Metastability is already known to hold for black holes; merging available matter into a few huge black holes could vastly increase entropy, but that only happens naturally at a very slow rate. By making it happen faster, our descendants might greatly increase their currently available potential entropy. Similarly, our descendants might gain even more potential entropy by inducing interactions between mass and negative mass that would naturally be very rare.

That is, we don’t even know if potential entropy is finite, even within a finite volume. Learning that will be very big news, for good or bad.

I accept your claim that this tension exists. Yes, any theory must deal with many difficulties.

The point of my comment was not to present an impossibility theorem, but to suggest that there are several highly nontrivial challenges that any theory of negative mass particles must confront and I know of no plausible solution to any of these, but maybe someone will find a way around them.

You're right that there are many known examples of forces getting stronger or weaker as the universe evolves (both the strong and the weak forces did this in opposite ways in the early universe). However, with regard to negative mass particles, there is generic tension between having a sufficiently large coupling to populate them after inflation while keeping this coupling sufficiently small to avoid all the problems associated with radiating extremely large numbers of conventional particles (and other tachyons) in a runaway process that endlessly fills the universe with more stuff.