In a recent paper (https://www.nature.com/articles/s41586-023-06527-1), the authors state that

we find that the local gravitational acceleration of antihydrogen is directed towards the Earth and has magnitude a g = (0.75 ± 0.13 (statistical + systematic) ± 0.16 (simulation))g, where g = 9.81 m s−2. Within the stated errors, this value is consistent with a downward gravitational acceleration of 1g for antihydrogen.

The plot they refer to is Figure 5:

enter image description here

It looks to me like most of the error bars are fairly small, and don't enclose 1g at all. What am I missing? Are they adding the statistical, systematic and simulation errors (0.75 + 0.13 + 0.16)g? If so, why is this valid?

  • 2
    $\begingroup$ The measurements are significantly closer to the curve for normal gravity than they are to no or negative gravity. $\endgroup$
    – hdhondt
    Nov 14, 2023 at 4:27
  • $\begingroup$ You have to look at the totality of points. A number of points are spot on, others are off by up to two error bars. Without digging into what their statistical model is exactly, it seems like that the average deviation would end up being one error bar's worth and thus consistent with standard gravity. Given that neighboring points seem to behave similarly, a proper analysis would have to take that into account, but the point that you cannot dismiss the good points and just look at the bad ones is still valid. $\endgroup$
    – tobi_s
    Nov 14, 2023 at 13:18

1 Answer 1


Usually these error estimates are "one sigma" error bars, which is roughly the same thing as a 68% confidence limit. If you have an ensemble of data with $1\sigma$ error bars, you expect about a third of your error bars to miss the curve. That's basically what's happening here, with three-ish of eleven data points missing the curve. How to interpret that the three biggest outliers are consecutive, and all low? That's a tough question, and runs the risk of overanalyzing the data.

If we assume that the errors add in quadrature, we have

$$ \sigma_\text{total}^2 = (0.13)^2 + (0.16)^2 = (0.20)^2 $$

The hypothesis that $0.75 \pm 0.20 = 1$ (that is, normal gravity) is a $1.2\sigma$ discrepancy, which is unremarkable: that is, normal gravity is consistent with this measurement. The hypothesis that $0.75 \pm 0.20 = 0$ (that is, no gravity) is a $3.6\sigma$ discrepancy, which happens by chance in somewhere under one experiment per thousand. The antigravity hypothesis, $0.75\pm0.20=-1$, would be an $8\sigma$ discrepancy, which is basically impossible to observe as a statistical fluctuation.

The folk wisdom in physics, where we have lots of data and can construct lots of hypotheses, is that a $4\sigma$ result is an "observation" and a $5\sigma$ result is a "discovery." So we really can say from this data that "antimatter falls up" has been experimentally ruled out. We have strong evidence against zero gravity, but it doesn't pass the "discovery" threshold; we cannot exclude the boring hypothesis that the antimatter falls with normal gravity.


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