Negative mass is the hypothetical idea that matter can exist with mass of the opposite sign to the ordinary stuff. Instead of 2 kg, a lump of negative mass would be -2 kg.

Nobody knows whether negative mass can exist but there have nevertheless been plenty of analyses to determine its properties. In particular, physicists have investigated whether negative mass would violate various laws of the universe, such as the conservation of energy or momentum and therefore cannot exist. These analyses suggest that although the interaction of positive and negative mass produces counterintuitive behaviour, it does not violate these conservation laws.

Cosmologists have also examined the effect that negative mass would have on the structure of space-time and their conclusions have been more serious. They generally conclude that negative matter cannot exist because it breaks one of the essential assumptions behind Einstein’s theory of general relativity.

Today, Saoussen Mbarek and Manu Paranjape at the Université de Montréal in Canada say they’ve found a solution to Einstein’s theory of general relativity that allows negative mass without breaking any essential assumptions. Their approach means that negative mass can exist in our universe provided there is a reasonable mechanism for producing it, perhaps in pairs of positive and negative mass particles in the early universe.

Their conclusion has far-reaching consequences. They point out that if positive and negative matter particles exist in the universe, they would form a plasma that would have important implications for the future of astronomy.

First some background. When Einstein published his general theory of relativity in 1916, it immediately piqued the interest of the German physicist, Karl Schwarzschild. He studied the mathematics and soon discovered the first exact solution of the equations other than the trivial one of flat space.

The Schwarzschild solution describes the nature of space-time around a point-like mass. This is the well-known black hole solution, which is hidden behind a surface called the event horizon. At least, for positive mass.

These objects are probably the best studied in theoretical cosmology. So it’s no surprise that cosmologists have long asked what happens when the mass is negative.

It turns out that for negative mass, there is no event horizon and this leads to a naked singularity. Although this sounds odd, it needn’t be a problem given that physicists have considerable experience similar kinds of mathematical singularities.

Physicists already deal with exactly this kind of singularity when considering a point charge in electrodynamics, which is also a singularity.

Here’s how they cope. When the distance from the singularity is large, physicists simply ignore it. And they also have a mechanism for dealing with it when the distance is small. “At close distance, we expect that the singular nature of the charge will be smoothed out by a concentrated but non-singular charge density,” say Mbarek and Paranjape.

So it’s not hard to imagine that a similar approach ought to solve the problem of a naked singularity generated by a negative mass. Indeed, a couple of years ago, theoretical physicists showed that it was straightforward to smooth out such a singularity in this way.

But there was an important downside: this was only possible by violating one of the essential assumptions behind Einstein’s theory of general relativity. Consequently, physicists concluded that negative mass must be impossible.

What is this this essential assumption? It comes about because the field equations in general relativity place no limits on the states of matter and non-gravitational fields that can exist in the universe. But physicists are well aware that these can only take certain forms.

So the additional assumption they impose on general relativity is that only reasonable states of matter and non-gravitational fields are admissible. This is known as an energy condition.

The problem with negative mass is that it appears to violate this energy condition. Indeed, that’s how theoretical physicists have been able to show how negative mass could be used to create exotic objects like wormholes.

The crucial breakthrough by Mbarek and Paranjape is to show that negative mass can produce a reasonable Schwarzschild solution without violating the energy condition. Their approach is to think of negative mass not as a solid object, but as a perfect fluid, an otherwise common approach in relativity.

And when they solve the equations for a perfect fluid, it turns out that the energy condition is satisfied everywhere, just as in all other solutions of general relativity that support reasonable universes.

That’s an interesting result with significant implications. The first and most obvious of these is that negative mass can exist in the universe just as we see it. All that’s missing is a mechanism for the production of pairs of particles with positive and negative mass in the early universe. That’s surely not beyond the capability of the modern cosmologist.

But here’s an interesting thought. If positive and negative mass particles do, or did, exist, they would create a kind of plasma that would absorb gravitational waves. “Such a plasma would in principle cause an effective screening of gravitational waves, being essentially opaque for frequencies below the plasma frequency,” conclude Mbarek and Paranjape.

Nobody has ever seen a gravitational wave but not through lack of trying. Physicists have built a number of advanced gravitational wave detectors that have been seemingly on the verge of discovering these exotic waves for the last few years.

For various reasons, these machines have always turned out to be slightly less sensitive than required to actually detect gravitational waves. But having significantly increased the sensitivity of their machines over the years, physicists are running out of excuses. These machines must soon detect gravitational waves or leave physicists with the both exciting and embarrassing task of having to explain what went wrong.

The existence of a plasma of positive and negative mass particles is one such explanation. And the evidence that could back it up would be the discovery of the threshold frequency above which the waves do propagate, just as Mbarek and Paranjape predict.

So an interesting question is where does this threshold lie and is it within the sensitivity range of the devices currently in operation.

Interesting stuff!

Ref: arxiv.org/abs/1407.1457 : Negative Mass Bubbles In De Sitter Space-Time

Update 21 July 2014

On behalf of the authors of this paper, Manu Paranjape writes:

“Thanks for highlighting our article on negative mass in de Sitter space on the arxivblog.

I would like to correct a notion in your description that seems to be giving the wrong impression of our work. It is not that we use a perfect fluid as the matter content that allows us to eschew the positive energy theorem, but the fact that we do our analysis in De Sitter space. The positive energy theorem denies the possibility of negative mass in asymptotically flat spacetime. But there is no such theorem in non-asymptotically flat spacetimes. Hence we consider de Sitter space, and there show that there is no problem with the dominant energy condition and having non-singular energy momentum distribution in a perfect fluid having a negative mass.

But since we are in de Sitter spacetime, this mass is not the ADM mass, that makes no sense here, (I think it is the Komar mass that is relevant, but I am actually not sure). Basically we have to think of what will be the mass of our bubble as seen by an observer who is inside the Hubble radius of the de Sitter spacetime. This will be the negative mass parameter of the Schwarzschild-de Sitter spacetime that our bubble assumes outside its outer radius.

I hope you can clarify this in your write up. “

Happy to oblige!