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In 2011, the ALPHA experiment showed that the gravitational acceleration for antihydrogen was between -65 and 110 times the normal gravitational acceleration. Has there been any improvement on the value of gravitational acceleration for antimatter, whether antihydrogen or otherwise?

I know the AEḡIS (AEgIS) experiment has been working on this, but I'm not familiar with any data, not even that the value falls into the range established by ALPHA.

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    $\begingroup$ The GBAR experiment (home.cern/science/experiments/gbar), also located in the "antimatter factory" at CERN is also trying to directly measure the acceleration of gravity of antihydrogen. If they are successful, their measurement should be the most precise of the three experiments. But GBAR is much newer than ALPHA and AEgIS, and it's much more complicated. So it may be a while before they have their final result. $\endgroup$
    – AXensen
    Commented Oct 4, 2023 at 8:56

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The ALPHA collaboration released their paper answering this today!

The result is that the gravity experienced by antimatter (anti-hydrogen) is

0.75 ± 0.13 (statistical + systematic) ± 0.16 (simulation)

times that of the force experienced by normal matter. This is not only consistent with the expected result of 1, but enough to conclusively demonstrate that antimatter experiences positive gravity, not anti-gravity. (The paper says that the probability of the anti-gravity scenario is $< 10^{-15}$.)

Graph showing a reasonable match to normal gravity and far from other scenarios like no gravity or repulsive gravity.

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    $\begingroup$ Thanks, Charles, for putting the ALPHA result as a reply to your original question. I work for ALPHA and if you have any further questions you can feel free to ask me. I'm working on an answer with a discussion of some other results that put more indirect bounds on the acceleration due to gravity of antimatter. $\endgroup$
    – AXensen
    Commented Oct 4, 2023 at 8:07
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The ALPHA result (which I worked on) Observation of the effect of gravity on the motion of antimatter, which Charles put as an answer to his own question, is the most direct measurement of antimatter's response to gravity. It says that antihydrogen falls down with an acceleration of: $$g(0.75\pm 0.13 (\text{statistical + systematic}) \pm 0.16 (\text{simulation}))$$ However, if you're willing to accept certain well-established ideas about how gravity and mass work, then less direct measurements provide much more precision.

First, the BASE collaboration (in the same building as ALPHA) measures the "double ratio" of the charge to mass ratio of the antiproton divided by the charge to mass ratio of the proton. They do this by measuring the antiproton's cyclotron frequency in a magnetic field. As the Earth orbits the sun, its gravitational potential energy changes, and this changes the rate at which time on earth progresses as seen by a distant observer. This effect is gravity, and if antimatter responded oppositely, or not at all to gravity, it shouldn't recieve the same slowdown as protons. By measuring the cyclotron frequency at different times in the year, they put a 3% bound on the difference between how matter and antimatter respond to gravity. A 16-parts-per-trillion measurement of the antiproton-to-proton charge–mass ratio

Next, the CPLEAR collaboration did a similar analysis with Kaon oscillations. Neutral Kaons are usually created as either $K_0$ or their antiparticle $\bar{K}_0$. However, these aren't mass eigenstates because of CP violation, so the created particle oscillates between being $K_0$ and $\bar{K}_0$. The CPLEAR people argue that like with the antiproton cyclotron frequency, this oscillation frequency would change as we orbit the sun. But in this case the change in frequency would be radical because the mass difference of the mass eigenstates is really tiny but the difference in time dilation (in a hand-wavy sense) applies a factor to the absolute mass. So they get a limit of $6.5\times 10^{-9}$. Tests of the Equivalence Principle with Neutral Kaons

Finally, tests of the equivalence principle on different metals can also be an indirect test of antimatter gravity. As we know from Parton distribution functions, to some extent there are anti-up quarks and anti-down quarks in the proton and neutron. [Ignoring expert-level discussion about how the PDF's run with energy scale, but what we're really interested in is the low-energy-limit contribution to the proton mass from antiparticles, which is investigated by lattice-QCD] And the extent to which "antimatter" contributes to the mass differs from one atom to another. Therefore, if antimatter fell up (or fell differently to ordinary matter), different atoms would also fall differently to eachother. This is tested by many different methods very precisely.

Freely falling test masses in a sattellite: MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle ($3\times 10^{-15}$)

Torsion balances: Test of the Equivalence Principle Using a Rotating Torsion Balance ($3\times 10^{-13}$)

Lunar laser ranging (comparing the lunar orbit to the expected lunar orbit): Lunar Laser Ranging Tests of the Equivalence Principle ($1\times 10^{-13}$)

This argument also reminds us that most of the mass of everyday objects isn't rest mass of particles (and even that is due to the Higgs mechanism), but rather a complex quantum state described mostly by QCD with gluons, kinetic energy, etc. So most, or perhaps all, of the mass of protons vs antiprotons is actually the same thing. So for antimatter to fall up would require us to radically change well established ideas about mass and gravity.

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    $\begingroup$ Wow, what a fantastic, comprehensive answer! Thank you for your time -- and for your research, of course! $\endgroup$
    – Charles
    Commented Oct 4, 2023 at 12:38

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