Antimatter and Neutral-Particle Gravity

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Antihydrogen, neutrons, positronium, and other neutral quantum systems are not force-free merely because their net charge vanishes. Magnetic moments, polarizability, patch fields, mirror potentials, preparation tails, diffraction, collisions, detector acceptance, and field gradients can all reshape a measured trajectory. The gravitational parameter is obtained only by forwarding a prepared phase-space distribution through those effects to the actual detector counts.

Required background. Equivalence Principles and Gravitational Measurement supplies the operational meaning of free fall and the limited scope of WEP. Probability and Statistical Inference supplies likelihood and nuisance parameters; the count model below gives the self-contained statistical bridge.

Helpful background. Weak-Field Gravity connects the Earth potential to trajectories, while Tests of Gravity places antimatter beside other composition tests.

From a prepared ensemble to counts

For a neutral particle of inertial mass $m_I$ , passive gravitational mass $m_G$ , magnetic moment $\boldsymbol\mu$ , and polarizability $\alpha_E$ , a nonrelativistic apparatus model has

m_I\ddot{\mathbf x} =m_G\mathbf g +\boldsymbol\nabla(\boldsymbol\mu\!\cdot\mathbf B) +\frac12\alpha_E\boldsymbol\nabla E^2 +\mathbf F_{\rm surf}+\mathbf F_{\rm coll}.

The target ratio is $m_G/m_I$ or an equivalent gravitational acceleration $a_g$ . The equation is a forward model, not a claim that every term is known analytically. For trapped antihydrogen, time-dependent three-dimensional magnetic fields and nonadiabatic release require trajectory simulation. For ultracold neutrons above a material mirror, the surface boundary condition and Earth’s linear potential form discrete gravitational states. These experiments test different particles, energies, and nuisance forces and cannot be pooled by particle neutrality alone.

Let $z_i$ and $t_i$ be detected annihilation or arrival coordinates. If simulation and detector response predict bin probabilities $p_j(a_g,\boldsymbol\nu)$ , then

\mathcal L(a_g,\boldsymbol\nu) =\prod_j \operatorname{Poisson}\!\left(N_j\mid \lambda_s p_j+b_j\right),

with expected prepared signal count $\lambda_s$ , expected background count $b_j$ , field and preparation nuisance parameters $\boldsymbol\nu$ , and a declared prior or confidence construction. Here $p_j$ includes the probability of reaching and being detected in bin $j$ , so $\sum_j p_j=\epsilon\leq1$ is the total efficiency. If the background-free analysis instead conditions on the total detected count, its shape likelihood is multinomial with probabilities $p_j/\epsilon$ . The Poisson model retains the missed fraction through its expected detected rate $\lambda_s\epsilon$ ; the conditional model divides by that efficiency. This distinction matters when efficiency depends on $a_g$ . Selection includes trapping and state-preparation requirements, valid field cycles, detector quality, geometric acceptance, and the time window.

The scale of the magnetic problem is instructive. A moment of order the Bohr magneton $\mu_B=9.27\times10^{-24}\ {\rm J\,T^{-1}}$ feels a force comparable to $m_Hg$ when $\lvert\partial_zB\rvert\simeq m_Hg/\mu_B$ . Using $m_H=1.67\times10^{-27}\ {\rm kg}$ and $g=9.81\ {\rm m\,s^{-2}}$ gives only $1.8\times10^{-3}\ {\rm T\,m^{-1}}$ . Neutrality therefore leaves a substantial magnetic force even for a modest gradient; the sign is set by the prepared magnetic state.

ALPHA’s escape-curve measurement

The ALPHA experiment slowly reduced magnetic confinement and counted whether trapped antihydrogen escaped upward or downward under imposed magnetic bias. The central observable is the downward escape probability versus derived bias, not a set of ballistic parabolas. Its Fig. 5 compares data with three-dimensional simulations for attractive, zero, and repulsive gravity; Tables 1–3 separate counts, bias uncertainty, and uncertainty in $a_g$ ALPHA Collaboration 2023, pp. 716–722, Fig. 5, Tables 1–3.

The field model is constrained by electron-cyclotron-resonance and magnetron measurements, actual coil currents, persistent-field corrections, and detector calibrations. Magnetic-field modeling shifts the horizontal bias axis; detection efficiencies and count statistics shift the vertical escape probability. These are correlated through the simulation and cannot be collapsed into one generic “systematic.” The experiment supports attractive terrestrial gravity for antihydrogen and a simulation-dependent approximate magnitude. It is not yet a precision comparison of antihydrogen and hydrogen free fall.

An independent check should propagate separately sampled initial conditions through measured field maps, blind the input $a_g$ , and recover it after the full selection. Field-bias reversal and top/bottom efficiency calibration must reproduce their expected transformations. A neutral-species control with comparable magnetic moment and phase-space support would be especially discriminating, but “neutral” alone does not guarantee the same force model.

Evidence and open interpretations at 2026-08-19

System or position	Evidence/status at 2026-08-19	Limitation or counterevidence
Trapped antihydrogen	ALPHA escape counts favor attraction and disfavor a repulsive acceleration of ordinary-gravity magnitude in its model	Approximate magnitude depends on field maps, prepared distribution, detector efficiency, and trajectory simulation
Ultracold neutrons	Gravitationally bound states and neutron-interference phases demonstrate gravitational response of neutral matter waves	Material mirror and neutron interactions differ from antihydrogen; this is not a matter–antimatter comparison
Other neutral systems containing antimatter	Positronium (electron–positron), muonium (electron–antimuon), and complementary antihydrogen concepts offer different magnetic and preparation controls	No single proposal supplies a current general universality verdict; short lifetimes and electromagnetic forces remain severe

The conservative interpretation is direct evidence for the sign of antihydrogen’s terrestrial acceleration under the measured trap model. The competing claim that this already constitutes a high-precision WEP test is not supported: ordinary hydrogen was not measured in the same apparatus with matched response, and the magnitude uncertainty is simulation-dominated. The precision universality question therefore remains open and model-dependent. Conversely, the absence of “antigravity” at roughly ordinary strength in this domain does not falsify every CPT-respecting or CPT-violating theory; the theory must specify how inertial, gravitational, electromagnetic, and internal energies map to the observable.

Adversarial discriminator. Analyze blinded attractive, zero, and repulsive injections with independently perturbed field maps and preparation tails; then reverse magnetic bias and repeat with a matched neutral control. A gravity conclusion survives only if electromagnetic alternatives cannot reproduce the escape asymmetry without failing those controls.

What could change the conclusion. The conclusion could change after a public event-level and field-map product, a substantially more precise antihydrogen measurement with independently validated simulation, a matched hydrogen comparison, or a neutral-particle result that changes the force-degeneracy structure rather than merely increasing counts.

Exercise

Why can an observed downward excess in antihydrogen annihilations not be converted directly into $a_g$ by fitting $z=z_0+v_0t-a_gt^2/2$ ?

Solution

The detected atoms are selected from a trapped ensemble whose release time, position, velocity, magnetic moment, and internal state are distributed. Time-dependent magnetic gradients act throughout release, and the detector has position-dependent acceptance. Therefore the downward count is an integral of trajectories and response over latent initial conditions, not one trajectory. One must compare counts with a normalized forward simulation, propagate field and efficiency covariance, and verify field-reversal and injection controls before interpreting the fitted parameter as gravitational acceleration.

References

ALPHA Collaboration. “Observation of the Effect of Gravity on the Motion of Antimatter.” Nature 621 (2023): 716–722. DOI.