Does Anti-Gravity Explain Dark Energy?

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]


One of the lesser known facts about me is that I’m one of the few world experts on anti-gravity. That’s because 20 years ago I was convinced that repulsive gravity could explain some of the puzzling observations astrophysicists have made which they normally attribute to dark matter and dark energy. In today’s video I’ll tell you why that didn’t work, what I learned from that, and also why anti-matter doesn’t fall up.

Newton’s law of gravity says that the gravitational force between two masses is the product of the masses, divided by the square of the distance between them. And then there’s a constant that tells you how strong the force is. For the electric force between two charges, we have Coulomb’s law, that says the force is the product of the charges, divided by the square of the distance between them. And again there’s a constant that tells you how strong the force is.

These two force laws look pretty much the same. But the electric force can be both repulsive and attractive, depending on whether you have two negative or two positive charges, or a positive and a negative one. The gravitational force, on the other hand, is always attractive because we don’t have any negative masses. But why not?

Well, we’ve never seen anything fall up, right? Then again, if there was any anti-gravitating matter, it would be repelled by our planet. So maybe it’s not so surprising that we don’t see any anti-gravitating matter here. But it could be out there somewhere. Why aren’t physicists looking for it?

One argument that you may have heard physicists bring up is that negative masses can’t exist because that would make the vacuum decay. That’s because, if negative masses exist, then so do negative energies. Because, E equals m c squared and so on. Yes, that guy again.

And if we had negative energies, then you could create pairs of particles with negative and positive energy from nothing and particle pairs would spontaneously pop up all around us. A theory with negative masses would therefore predict that the universe doesn’t exist, which is in conflict with evidence. I’ve heard that argument many times. Unfortunately it doesn’t work.

This argument doesn’t work because it confuses to different types of mass. If you remember, Einstein’s theory of general relativity is based on the Equivalence Principle, that’s the idea that gravitational mass equals inertial mass. The gravitational mass is the mass that appears in the law of gravity. The inertial mass is the mass that resists acceleration. But if we had anti-gravitating matter, only its gravitational mass would be negative. The inertial mass always remains positive. And since the energy-equivalent of inertial mass is as usual conserved, you can’t make gravitating and anti-gravitating particles out of nothing.

Some physicists may argue that you can’t make anti-gravity compatible with general relativity because particles in Einstein’s theory will always obey the equivalence principle. But this is wrong. Of course you can’t do it in general relativity as it is. But I wrote a paper many years ago in which I show how general relativity can be extended to include anti-gravitating matter, so that the equivalence principle only holds up to a sign. That means, gravitational mass is either plus or minus inertial mass. So, in theory that’s possible. The real problem is, well, we don’t see any anti-gravitating matter.

Is it maybe that anti-matter anti-gravitates. Anti-matter is made of anti-particles. Anti-particles are particles which have the opposite electric charge to normal particles. The anti-particle of an electron, for example, is the same as the electron just with a positive electric charge. It’s called the positron. We don’t normally see anti-particles around us because they annihilate when they come in contact with normal matter. Then they disappear and leave behind a flash of light or, in other words, a bunch of photons. And it’s difficult to avoid contact with normal matter on a planet made of normal matter. This is why we observe anti-matter only in cosmic radiation or if it’s created in particle colliders.

But if there is so little anti-matter around us and it lasts only for such short amounts of time, how do we know it falls down and not up? We know this because both matter and anti-matter particles hold together the quarks that make up neutrons and protons.

Inside a neutron and proton there aren’t just three quarks. There’s really a soup of particles that holds the quarks together, and some of the particles in the soup are anti-particles. Why don’t those anti-particles annihilate? They do. They are created and annihilate all the time. We therefore call them “virtual particles.” But they still make a substantial contribution to the gravitational mass of neutrons and protons. That means, crazy as it sounds, the masses of anti-particles make a contribution to the total mass of everything around us. So, if anti-matter had a negative gravitational mass, the equivalence principle would be violated. It isn’t. This is why we know anti-matter doesn’t anti-gravitate.

But that’s just theory, you may say. Maybe it’s possible to find another theory in which anti-particles only anti-gravitate sometimes, so that the masses of neutrons and protons aren’t affected. I don’t know any way to do this consistently, but even so, three experiments at CERN are measuring the gravitational behavior of anti-matter.

Those experiments have been running for several years but so far the results are not very restrictive. The ALPHA experiment has ruled out that anti-particles have anti-gravitating masses, but only if the absolute value of the mass is much larger than the mass of the corresponding normal particle. This means so far they ruled out something one wouldn’t expect in the first place. However, give it a few more years and they’ll get there. I don’t expect surprises from this experiment. That’s not to say that I think it shouldn’t be done. Just that I think the theoretical arguments for why anti-matter can’t anti-gravitate are solid.

Okay, so anti-matter almost certainly doesn’t anti-gravitate. But maybe there’s another type of matter out there, something new entirely, and that anti-gravitates. If that was the case, how would it behave? For example, if anti-gravitating matter repels normal matter, then does it also repel among itself, like electrons repel among themselves? Or does it attract its own type?

This question, interestingly enough, is pretty easy to answer with a little maths. Forces are mediated by fields and those fields have a spin which is a positive integer, so, 0, 1, 2, etc.

For gravity, the gravitational mass plays the role of a charge. And the force between two charges is always proportional to the product of those charges times minus one to the power of the spin.

For a spin zero field, the force is attractive between like charges. But electromagnetism is mediated by a spin-1 field, that’s electromagnetic radiation or photons if you quantize it. And this is why, for electromagnetism, the force between like charges is repulsive but unlike charges attract. Gravity is mediated by a spin-2 field, that’s gravitational radiation or gravitons if you quantize it. And so for gravity it’s just the other way round again. Like charges attract and unlike charges repel. Keep in mind that for gravity the charge is the gravitational mass.

This means, if there is anti-gravitating matter it would be repelled by the stuff we are made of, but clump among itself. Indeed, it could form planets and galaxies just like ours. The only way we would know about it, is its gravitational effect. That sound kind of like, dark matter and dark energy, right?

Indeed, that’s why I thought it would be interesting. Because I had this idea that anti-gravitating matter could surround normal galaxies and push in on them. Which would create an additional force that looks much like dark matter. Normally the excess force we observe is believed to be caused by more positive mass inside and around the galaxies. But aren’t those situations very similar? More positive mass inside, or negative mass outside pushing in? And if you remember, the important thing about dark energy is that it has negative pressure. Certainly if you have negative energy you can also get negative pressure somehow.

So using anti-gravitating matter to explain dark matter and dark energy sounds good at first sight. But at second sight neither of those ideas work. The idea that galaxies would be surrounded by anti-gravitating matter doesn’t work because such an arrangement would be dramatically unstable. Remember the anti-gravitating stuff wants to clump just like normal matter. It wouldn’t enclose galaxies of normal matter, it would just form its own galaxies. So getting anti-gravity to explain dark matter doesn’t work even for galaxies, and that’s leaving aside all the other evidence for dark matter.

And dark energy? Well, the reason that dark energy makes the expansion of the universe speed up is actually NOT that it has negative pressure. It’s that the ratio of the energy density over the pressure is negative. And for anti-gravitating matter, they both turn negative so that the ratio is the same. Contrary to what you expect, that does not speed up the expansion of the universe.

Another way to see this is by noting that anti-gravitating matter is still matter and behaves like matter. Dark energy on the contrary does not behave like matter, regardless of what type of matter. This is why I get a little annoyed when people claim that dark energy is kind of like anti-gravity. It isn’t.

So in the end I developed this beautiful theory with a new symmetry between gravity and anti-gravity. And it turned out to be entirely useless. What did I learn from this? Well, that I wasted a considerable amount of my time on this was one of the reasons I began thinking about more promising ways to develop new theories. Clearly just guessing something because it’s pretty is not a good strategy. In the end, I wrote an entire book about this. Today I try to listen to my own advice, at least some of time. I don’t always listen to myself, but sometimes it’s worth the effort.