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Newton’s law of gravity and Coulomb’s law for the electric force between two charges have the same mathematical form, so how come we have both positive and negative electric charges but not both negative and positive gravitational masses?

The quick answer to the question is, well, we’ve never seen anything fall up. But if there was anti-gravitating matter, it would be repelled by our planet. So maybe it’s not so surprising we don’t see any of it here. Might there be anti-gravitating matter elsewhere?

It’s a difficult question, more difficult than even most physicists appreciate. The difference between gravity and the electromagnetic interaction – which gives rise to Coulomb’s law – is the type of messenger field. Interactions between particles are mediated by fields. For electromagnetism the mediator is a vector-field. For gravity it’s a more complicated field, a 2nd rank tensor-field, which describes space-time itself.

In case an interaction is quantized, the interaction’s field is accompanied by a particle: For electromagnetism that’s the photon, for gravity it’s the (hypothetical) graviton. The particles share the properties of the field, but for the question of whether or not there’s anti-gravity the quantization of the field doesn’t play a role.

The major difference between the two cases comes down to a sign. For a vector-field, as in the case of electromagnetism, like charges repel and unlike charges attract. For a 2nd rank tensor field, in contrast, like charges attract and unlike charges repel. This already tells us that an anti-gravitating particle would not be repelled by everything. It would be repelled by normally gravitating mass – which we may agree to call “positive” – but be attracted by gravitational masses of its own kind – which we may call “negative.”

The question then becomes: Where are the particles of negative gravitational mass?

To better understand the theoretical backdrop, we must distinguish between inertial mass and gravitational mass. The inertial mass is what gives rise to an object’s inertia, ie its resistance to acceleration, and is always positive valued. The gravitational mass, on the other hand, is what creates the gravitational field of the object. In usual general relativity, the two masses are identical by assumption: This is Einstein’s equivalence principle in a nutshell. In more detail, we’d not only talk about the equivalence for masses, but for all types of energies, collected in what is known as the stress-energy-tensor. Again, the details get mathematical very fast, but aren’t so relevant to understand the general structure.

All the particles we presently know of are collected in the standard model of particle physics, which is in agreement with data to very high precision. The standard model also includes all anti-particles, which are identical to their partner-particles except for having opposite electric charge. Is it possible that the anti-particles also anti-gravitate?

Theory clearly answer this question with “No.” From the standard model, we can derive how anti-matter gravitates – it gravitates exactly the same way as normal matter. And observational evidence supports this conclusion as follows.

We don’t normally see anti-particles around us because they annihilate when they come in contact with normal matter, leaving behind merely a flash of light. Why there isn’t the same amount of matter and anti-matter in the universe nobody really knows – it’s a big mystery that goes under the name “baryon asymmetry” – but evidence shows the universe is dominated by matter. If we see anti-particles – in cosmic rays or in particle colliders – it’s usually as single particles, which are both too light and too short-lived to reliably measure their gravitational mass.

That, however, doesn’t mean we don’t know how anti-matter behaves under the influence of gravity. Both matter and anti-matter particles hold together the quarks that make up neutrons and protons. Indeed, the anti-particles’ energy makes a pretty large contribution to the total mass of neutrons and protons, and hence to the total mass of pretty much everything around us. This means if anti-matter had a negative gravitational mass, the equivalence principle would be badly violated. It isn’t, and so we already know anti-matter doesn’t anti-gravitate.

Those with little faith in theoretical arguments might want to argue that maybe it’s possible to find a way to make anti-matter anti-gravitate only sometimes. I am not aware of any theorem which strictly proves this to be impossible, but neither is there – to my best knowledge – any example of a consistent theory in which this has been shown to work.

And if that still wasn’t enough to convince you, the ALPHA experiment at CERN has not only created neutral anti-hydrogen, made of an anti-proton and a positron (an anti-electron), but has taken great strides towards measuring exactly how anti-hydrogen behaves in Earth’s gravitation field. Guess what? So far there is no evidence that anti-hydrogen falls upwards – though the present measurement precision only rules out that the anti-hydrogen’s gravitational mass is not larger than (minus!) 65 times its inertial mass.

[Correction added April 19: There is not one but three approved experiments at CERN to measure the free fall of anti hydrogen: AEGIS, ALPHA-g and GBAR.]

So, at least theoretical physicists are pretty sure that none of the particles we know anti-gravitates. But could there be other particles, which we haven’t yet discovered, that anti-gravitate?

In principle, yes, but there is no observational evidence for this. In contrast to what is often said, dark energy does not anti-gravitate. The distinctive property of dark energy is that the ratio of energy-density over pressure is negative. For anti-gravitating matter, however, both energy-density and pressure change sign, so the ratio stays positive. This means anti-gravitating matter, if it exists, behaves just the same way as normal matter does, except that the two types of matter repel each other. It also doesn’t give rise to anything like dark matter, because negative gravitational mass would have the exact opposite effect as needed to explain dark matter.

To be fair, I also don’t know of any experiment that explicitly looks for signatures of anti-gravitational matter, like for example concave gravitational lensing. So, strictly speaking, it hasn’t been ruled out, but it’s a hypothesis that also hasn’t attracted much professional interest. Many theoretical physicists who I have talked to believe that negative gravitational masses would induce vacuum-decay because particle pairs could be produced out of nothing. This argument, however, doesn’t take into account that the inertial masses remain positive which prohibits pair production. (On a more technical note, it is a little appreciated fact that the canonical stress-energy tensor isn’t the same as the gravitational stress-energy tensor.)

Even so, let us suppose that the theoretically possible anti-gravitating matter is somewhere out there. What would it be good for? Not for much, it turns out. The stuff would interact with our normal matter even more weakly than neutrinos. This means even if we’d manage to find some of it in our vicinity – which is implausible already – we wouldn’t be able to catch it and use it for anything. It would simply pass right through us.

The anti-gravitating weight that I’d want to tie to the couch, therefore, will unfortunately remain fiction.

*[This post previously appeared on Starts With A Bang.]*

## 40 comments:

Very nice post!

Sabine said,

“Both matter and anti-matter particles hold together the quarks that make up neutrons and protons.”Learning that alone is fascinating; why don’t they annihilate? I'm guessing somehow they don’t come into contact within the quark, if that is so then theoretically would that possibly change at the densities within a black hole?

Another great explanation for the general structure of a topic with very complex underpinnings, thank you.

It's reasonable to expect anti-matter gravitates like normal matter. Within a hadron it behaves normally, else protons and neutrons would violate equivalence principle. But anti-matter within a hadron could behave differently. CERN experiments rule out anti-gravitational mass for anti-hydrogen at 65 times inertial mass. But of course this is very far from the regime of interest, where the ratio is 1, so they have a long way to go. Bottom line, there still isn't direct experimental evidence.

It seems to me (off the top of my head) "dark matter" could, in fact, be anti-gravitating matter. Of course it wouldn't be distributed like regular "dark matter". Instead, the spaces between galaxies, and galactic clusters, could be filled with very weakly interacting "anti-dark matter". By repelling regular matter, it would confine it, allowing stars in galaxies, and galaxies in galactic clusters, to reach escape velocities without escaping. They'd be "fenced in" by the surrounding anti-DM. Is something obviously wrong with that idea?

The striking thing about this topic is that it's treated like real science! Although theory indicates absence of anti-grav, real scientists still want to see experimental evidence. That's good. But in other areas like string theory and dark matter and (I'd say) the simulation hypothesis, experimental evidence seems to be ignored or considered superfluous. AFAIK, no one is calling you an idiot for considering the possibility of anti-grav. Why the difference? Why are theoretical physicists sensible about this topic, but "faith-based" fanatics in other areas?

Hi Sabine, thanks, very nice post like always.

One question, you state: "...for example concave gravitational lensing", which almost anticipate my question. What would negative mass do to photons? - which have no mass. How would that react to usual curvature? Would clocks made of negative mass accelerate near a black hole? Would rods shrink?

J.

Louis,

They do annihilate, sometimes. As they say, in quantum mechanics anything that can happen does happen. The point here is that both matter and antimatter can be exchanged between the constituents and contributes to (what's classically called) potential energy. Indeed, it may sound strange, but neutrons and protons have for that reason also a photon content!

George,

I've tried the 'fencing in' and it doesn't work: The necessary solutions are unstable.

akidbelle,

It's not a simple question to answer because you first have to solve the field equations, after this you can just calculate the photon trajectories. It's reasonable to expect, however, that in the Newtonian limit you can just swap M with -M.

Dear Dr B.

I do not think that anti-gravitational matter would be useful for moving a couch ;-) . As you write, all such existing matter would have been pushed out into the voids between the galaxy super clusters by now. And the energy needed to create anti-gravity matter particle by particle could be used more efficiently.

What would be interesting would be a way to negate the local gravity field.

I was wondering whether a "white hole" does not have the features of anti-gravity?

Rob van Son,

No, a while hole has nothing to do with anti-gravity.

Sabine, as I also mentioned on fb, we know from SN 1987A that GR is CP invariant"> to within a factor of 10^-6.

Hi, I'm not a physicist but I'm a regular reader of your great blog.

Would the fact that the hypothetical graviton would, presumably, be its own anti-particle, have any impact on this question?

Re Shantanu

http://sci-hub.ac/10.1103/PhysRevD.38.3313

..."it can be concluded that neutrinos and antineutrinos have the same infall velocity

in the gravitational field of our Galaxy to an accuracy of 4.6×10(-6) to 7.7×10^(-7).

Hadrons are not constrained. 1.74 solar-mass 465.1 Hz PSR J1903+0327 (millisecond pulsar, neutron star) (neutron star) and a 1.05 solar-mass star form a 95.17-day binary system. It verifies the Equivalence Principle for orbit, periastron precession, and gravitational radiation orbital decay despite huge divergences in all measurable properties.

Equivalence Principle violation must contrast a property outside general relativity. Only one such observable is stable, large divergence, high concentration, and obtainable.

My understanding was that while opposite sign masses generate a repelling force, a negative mass particle is actually attracted by a repelling force. So you have a situation where the positive mass particle wants to get away, the negative mass particle wants to get closer, and you have a runaway instability that drives both particles to the speed of light.

Another pathology is you can have pair production of particles out of nothing, so the vacuum would be unstable.

I always thought negative masses were excluded on these grounds. But you seem to be saying that inertial masses must always positive, but gravitational masses negative. Can one implement this idea explicitly in the context of relativistic field theory? For example, can you compute some analogue of a Bhabha scattering process and show that the "opposite mass" particles repel?

Re Original Post:

Which just goes to demonstrate the most profound wisdom that anyone can acquire:

"MOVERS ARE WORTH IT!"

still remains true. (A lesson I learned the hard way try to move my piano to its new home at a cost in pain, health care and lost wages far in excess of what movers charge).

;)

@Shantanu Great catch re the CP invariance of GR per SN 1987A. Not sure that this resolve the issue, however.

@UncleAl Great catch on the neutrino study. The precision involved clear rules out different gravitational properties for antimatter with observational evidence, unless neutrinos are somehow an exception to the rule (which wouldn't be entirely implausible).

@SabineH (Not expecting meaningful answers to all or any of these questions, but putting them out there for argument's sake in case someone finds any of them interesting or worth considering.)

*Are fundamental Majorana particles of any kind inconsistent a gravitational force distinction between matter and antimatter?

If true we have a theorem that creates three way split between linking two seemingly disparate issues - one being the nature of neutrino mass in the SM and the other being the gravitational properties of antimatter in GR or QG, even though it doesn't answer either of them by itself.

(1) If Majorana neutrino mass exists, then antimatter can't gravitate differently than matter.

(2) If antimatter gravitates differently than matter, then Majorana neutrino mass in impossible.

(3) Of course, you could also have antimatter that can't gravitate differently than matter and Dirac neutrino mass with no fundamental Majorana particles.

(I suppose a fourth option would be that Majorana mass is a third kind of mass distinct from both matter mass and antimatter mass that follows its own rules.)

* Could this reasoning be extended to composite Majorana fermions?

My intuition says "no" but I haven't really processed it analytically. Because, if that were the case, you could conclude from the existence of Bogoliubov quasiparticles in superconductors that matter and antimatter are identical gravitationally in a manner independent of other kinds of tests.

* Along the same lines, suppose that matter and antimatter gravitate differently. What about contributions to the stress-energy tensor from particles that are neither matter nor antimatter such as photons and Z bosons or Higgs bosons or hypothetical gravitons? Like fundamental Majorana fermions, there is no distinction between the particle and the antiparticle, so you either can't have such a distinction or they are all in some special third kind of mass in addition to matter mass and antimatter mass.

* What about contributions to the stress-energy tensor from gluons which have both color and anti-color contributions but are overall neutral? If matter and antimatter gravitate differently, would this systemically align gluons every so slightly with local gravitational fields? The effect might not be big enough to observe in ordinary QCD experiments, but surely such a universal bias would have some aggregate effect that would be observable since it would be acting on every single one of gillions upon gillions of gluons in every hadron everywhere.

A few other questions (to which I don't expect answers) inspired by this post.

* Is there any meaningful sense in which virtual particles gravitate?

My intuition says yes in this case, because theoretically, virtual particles give rise to a distinction between tree-level bare masses and observed masses (at least in some very SM-like theories if not in the SM itself as well) and would play a part in the gluon component of hadron masses, and virtual particle loops ought to affect the properties of reasonable model of the graviton if a QG theory is real. But, I'm not sure I could imagine an experiment that would test this more directly with observational evidence.

* Is there any theoretical leverage one can obtain for other purposes by formulating GR/QG in a manner that makes it more self-evident than it is in some formulations that anti-matter mass and matter mass are identical? Do formulations of gravity that have that ambiguity on the surface have a subtle flaw that could lead to other plausible but wrong understandings of gravity, or is this the sole consequence of such an ambiguity?

* Does an identical matter mass and antimatter mass have any impact on the formulation or operation of CPT conservation in the SM or otherwise?

* Does formulating QG as a non-abelian chiral theory, or a theory with non-commutative geometry have any bearing on the matter mass v. antimatter mass properties debate?

* Is there any sensible formulation of GR/QG in which gravity and inertia actually only act upon the square of mass, in which case the sign doesn't matter?

* Are there formulations of the QM/GR/QG in which mass is a complex valued quantity rather than a real number? Likewise, is there ever a case in which mass is something other than a scalar? I'm not sure what a vector or tensor generalization of mass would look like, but tinkering with fundamental concepts along these kinds of lines is what theoretical physics do, right?

It seems as if complex numbers in physics often have to do with the directionality of time, and IIRC, there is a Noether's theorem that relates time symmetry to conservation of mass-energy, so naively it would make sense for imaginary numbers related to time to bleed into numbers related to mass-energy. My intuition says this is probably gibberish, but it is a concept that seems plausible at least for a moment.

* I'm surprised that it is so hard to measure the sign of gravitational mass experimentally. Some experimental concepts that could come immediately to mind would be:

1. Wouldn't it be possible to distinguish between the scenarios because various B mesons and various anti-B mesons would behave differently?

2. Shouldn't it be easier to study this with leptons than with hadrons? A lepton is a much simpler beast than any kind of hadron and the precision of the theoretical expectation of how leptons behave is so much greater than anything you can do with a hadron.

To answer the title of your blog post it is best we apply Einstein's original thought experiment that first led him to the equivalence principle namely the lift experiment and substitute the man in the lift for an anti matter particle. One can easily deduce that the equivalence principle still holds for matter or anti matter and that both fall in a gravitational field.

Are gluons not their own anti-particle?

"From the standard model, we can derive how anti-matter gravitates – it gravitates exactly the same way as normal matter."

The standard model has nothing to do with gravity.

qsa,

That the standard model doesn't include a quantum theory of gravity doesn't mean it's not possible to couple matter to gravity using the expectation value of the stress-energy tensor. The standard model has something to do with gravity in that all matter couples to space-time (through the metric tensor that appears in the standard model Lagrangian and the respective generally covariant derivatives).

Unknown,

Well, yes, but the question is whether they gravitate the same way.

The Big Bang was too hot for anything but photons, if that, absent electrical charge, baryon number, etc., to conserve. Somewhat later...photons plus 0.61 ppb net matter. Strop Occam’s razor. Baryogenesis only produced neutrons. The universe was born of photons and beta-decay ignoring parity conservation. Primordial neutrino abundance should mirror primordial hydrogen, trimmed by helium production during initial decay plus fusion.

Gravitation is fundamentally simple in composition though complex to describe. Giving it an eldritch basis will fail, for there is none. "8^>)

"For a 2nd rank tensor field, in contrast, like charges attract and unlike charges repel."

It does have to be a Symmetric 2nd rank tensor field, doesn't it?

You must still get rid of the anti-symmetric part to make it spin 2

Hi Sabine,

As a further investigation of your response I made a post in physicsforum, can you please comment on the comments:)

https://www.physicsforums.com/threads/is-gravity-a-quantum-phenomena-or-not.911324/#post-5740525

Thanks

qsa,

Can't see the relation to this blogpost, sorry.

Ok, let me put it in another way. We are talking about if the theory of gravity indicate that whether anti-particles repel, so is the effective theories(as shown in PF) are accepted as established theory and if so can they prove(or disprove) any conjecture as in you thread.

qsa,

Of course it's not accepted as an established theory because there's no experimental evidence.

So, by the same token black hole science is just physicists past time until they can find out more about fundamental issues like why the proton/electron mass ratio is what it is.

qsa,

That a theory isn't yet established doesn't mean there should be no research on it.

Dear Dr B.

"That a theory isn't yet established doesn't mean there should be no research on it."

Many people seem to think it ought to be forbidden.

I cannot understand why theoretical physics evokes such hostility. There are still websites that organize hate campaigns against Einstein and claim quantum mechanics is a hoax that should be fought tooth and nail. Verlinde might be wrong, but that should not be a reason for aggression.

Is there anyone who can explain that?

Let me put the question this way: What would you propose replaces the geodesic equation for a particle with negative gravitational mass but positive inertial mass?

The point is that I know how to think of particles with negative mass relativistically provided their gravitational and inertial masses are both negative. But this possibility is instantly ruled out by experiment, since the we live in a universe with a stable vacuum.

In Newtonian gravity I can imagine the possibility of that gravitational and inertial masses have opposite sign. But to take this idea seriously purely on the basis of Newtownian gravity seems to ignore 400 years of progress in physics.

Do I understand your intention? Maybe you have some concrete idea theoretical idea in mind. Or perhaps you just think it is neat to think about how you might try to measure the relative sign of the gravitational and inertial mass, as a matter of principle.

Tchovi,

Yes, that's exactly the right question to ask: What does the geodesic equation look like for an anti-gravitating particle?

The obvious answer is that it'll have to use a covariant derivative, but that derivative can't be the same as the usual Christoffel connection. That of course only leads to the question, well, then which derivative is it? Since torsion terms don't contribute to the geodesic equation, the derivative will have to be not metric compatible.

In principle then, you could go and pick any such derivative and see if it fits the bill but clearly that's very unsatisfactory. The other thing you hence would like to do is assume that you have a symmetry under the exchange of 'normal' with 'antigravitating' matter. This leads you to the conclusion that there should be a second metric so that the second derivative is compatible with that metric.

Where do you get the second metric from? Well, you need a second set of field equations. I explained here how this works. Note that I'm not claiming this is the only possible theory that realizes an effect like antigravitation. But I think it's the one that employs the symmetry assumption in the most obvious way.

(Note that there are no direct coupling terms between the metrics. Ie, it's a bimetric theory but the coupling is merely mediated through the matter sources. Sometimes I think there should be way to solve the second equation and reinsert the solution into the usual field equation so that the second metric no longer appears. Then again I'm not sure this works. In other words, I don't know, more work is needed etc.)

Rob,

Well, you just did :o)

PS: There are websites explaining quantum mechanics is a hoax? Seriously? Like, all these computers and digital cameras actually don't work, it's just your imagination and all?

Rob,

Wow, thanks. Got the links but won't post them, I think you'll understand.

@Rob

Perhaps some wisdom from Carl Jung can soothe our frustrations over such hostilities ,)

" Thinking is difficult, that's why most people judge "

Best, Koenraad

Hi Bee,

I am reading with lot of interest your blog and comments. To my understanding ultimately experiment is the final judge.Theories have to accommodate whatever experiments confirm.It seems that GR or gauge theory can be simply modified by some extra terms of different signs without any difficulty. Thus theory is of no guide to answer the basic question raised in this blog. Do you agree?

https://arxiv.org/pdf/1410.3881.pdf

..."At extremely high densities existing in black holes and in the very early Universe, the minimal spinor-torsion coupling manifests itself as gravitational repulsion, which avoids the formation of singularities from fermionic matter"

Anti-gravitation may be beyond reach. Default expectations remain vulnerable. Test spacetime geometry with geometry. Extreme enantiomorphic test masses will pursue non-identical minimum action vacuum free fall trajectories, violating the Equivalence Principle. Look.

kashyap,

No, I disagree. You cannot just 'modify GR by some extra terms of different signs without any difficulty'. First, the result is generically unstable. But more importantly, second, this doesn't change anything about the equivalence principle and hence doesn't have an effect similar to antigravitation.

@Koenraad

"Thinking is difficult, that's why most people judge "

That does sound convincing.

I think it was Barbara Tuchman who defined fools as those who thought they knew so they do not need to think. The same for those who think they are so all knowing, they can judge without understanding.

Thanks Bee for the reply. So my feeling was wrong! No problem!But are you saying that if the experiments find antimatter have opposite behavior to matter in gravity, that will be a big crisis even for classical GR?

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