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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.Scientists have created a fluid that exhibits the bizarre property of "negative mass" in an experiment that appears to defy the everyday laws of motion.

Push an object and Newton's laws (and common experience) dictate that it will accelerate in the direction in which it was shoved.

"That's what most things that we're used to do," said Michael Forbes, a physicist at Washington State University and co-author of the paper, which shows that normal intuitions do not always apply to physics experiments. "With negative mass, if you push something, it accelerates toward you."

Negative mass has previously cropped up in speculative theories, including those suggesting the existence of wormholes, a form of cosmological shortcut between two points in the universe. Just as electric charge can be either positive or negative, matter could, hypothetically, have either positive or negative mass.

For an object with negative mass, Newton's second law of motion, in which a force is equal to the mass of an object multiplied by its acceleration (F=ma) would be experienced in reverse.

Theoretically, this sounds straightforward, but picturing how this behaviour would work in the real world is bewildering, even for experts.

"It's very counterintuitive and weird," said Jon Butterworth, a physicist at University College London, who was not involved in the latest work.

For instance, you might expect a ball with negative mass to be repelled from the Earth's surface, but theory predicts that it would behave just like ordinary matter and fall downwards.

No fundamental particles with negative mass have ever been discovered, meaning that there have never been any experimental insights into how they might behave – if, indeed, they exist. The latest study provides a new platform to study this hypothetical form of matter, by showing that under certain precise conditions, normal particles can be made to behave as though they had negative mass.

"It provides another environment to study a fundamental phenomenon that is very peculiar."

The experiment, described in the journal Physical Review Letters, created the conditions for negative mass by cooling rubidium atoms to just above absolute zero, creating something called a Bose-Einstein condensate.

In this cooled state, particles move extremely slowly and, following the principles of quantum mechanics, behave like waves. This state of matter is already known to exhibit strange properties such as superfluidity, in which a liquid can creep up the sides of jars and over the top.

The cooling was achieved by using lasers to slow the particles until they were confined in a laser trap, less than 100 microns across. Breaking the trap causes the rubidium atoms to rush out, expanding in a spherical formation.

However, when researchers applied a second set of lasers that kicked the atoms back and forth within the trap, they started to behave as though they had negative mass on exiting the trap.

"Once you push, it accelerates backwards and it looks like the rubidium hits an invisible wall."

Martin McCall, a professor of theoretical optics at Imperial College London, described the paper as a neat demonstration of a system exhibiting "effective negative mass" – something that has only rarely been created before in laboratory conditions.