Laboratory and Short-Range Gravity

Laboratory tests ask whether gravity retains its inverse-square form across controlled separations and whether additional fields respond to composition or environment. Their distinctive strength is experimental intervention: geometry, material, distance, chamber density, source position, and modulation frequency can be changed deliberately. Their central difficulty is that electromagnetic and surface forces are usually larger than the gravitational signal.

Helpful background. Weak-Field Gravity reviews potentials and observable forces; Probability and Statistical Inference reviews likelihoods, covariance, priors, and selection; Classical Field Theory reviews massive Green functions and nonlinear boundary-value problems.

Enter this chapter

The recurring task is to turn a proposed interaction into an apparatus response:

$$\begin{aligned} &\text{field law and sources} \longrightarrow\text{finite-geometry force or torque}\\ &\longrightarrow\text{calibrated sensor data} \longrightarrow\text{likelihood and bounded conclusion}. \end{aligned}$$

For a linear finite-range force, the first two arrows use the Yukawa kernel

$$\frac{e^{-r/\lambda}}{r}$$

integrated over real density and composition distributions. For chameleon, symmetron, or another screened field, the apparatus response instead comes from a nonlinear field equation with chamber and material boundary data. These two calculations cannot be interchanged.

The evidence discussion is current through 2026-08-19. Numerical bounds and exclusion contours are meaningful only with a named dataset, calibration, selection, statistical construction, geometry model, theory domain, and date. This chapter develops the durable reasoning behind such results; it does not treat one contour as a theory-independent verdict.

Two routes through the material

The experimental-design route begins with modulation and null geometry, then studies backgrounds and microscopic probes. It is best for readers planning an instrument or data analysis.

The theory-to-apparatus route begins with the Yukawa Green function, continues to screened boundary-value problems, and ends with joint inference. It is best for readers translating a model into a testable response.

Both routes meet at the same discipline: predict the measured quantity before inspecting a residual, constrain backgrounds with independent controls, and preserve shared nuisance covariance.

Chapter contents

1. Inverse-Square-Law Experiments develops patterned sources, harmonic torques, calibration, selection, and null configurations.
2. Yukawa and Fifth-Force Searches derives point and extended-body responses and separates universal from composition-dependent charges.
3. Casimir, Electrostatic, and Material Backgrounds builds a reproducible force budget with analytic limits, numerical refinement, and correlated metrology.
4. Atom, Neutron, and Molecule Gravity Tests connects phases, levels, and counts to gravity while tracking preparation, surfaces, and detector response.
5. Screened Scalars in the Laboratory treats walls, vacuum, geometry, field branches, and source screening as part of the prediction.
6. Combining Short-Range Gravity Experiments shows when likelihoods share a parameter and when an overlay would exceed their physical or statistical domains.

Recurring checks

Three checks recur across every platform.

Dimensional and limiting checks. Recover Newtonian gravity at zero new coupling, exponential suppression beyond a mediator range, ideal plate or point limits when their assumptions hold, and the correct dependence on mass, thickness, or area.

Control transformations. Reverse fields, move the source, alter material, change chamber density, rotate a null pattern, or hold out an analysis channel. A proposed signal and its leading background should not transform identically under every control.

Inference checks. Recover a blinded injection, repeat the fit with alternate background and prior models, preserve shared covariance, and withhold data for prediction. Failure of any check narrows the conclusion before it changes the force law.

Review the chapter

1. Linear versus screened response. Two experiments have identical source and detector separations but different chamber radii and wall densities. When may their Yukawa constraints be combined directly, and why is the same step unsafe for a chameleon?

Solution

For a linear mediator with fixed microscopic charges, each apparatus response is a convolution of the same Green function with its measured bodies. The two likelihoods can therefore share the mediator parameters after their distinct geometry and nuisance variables are included. A chameleon field is different because chamber radius and wall density change the background field, effective mass, and screened source charge. Combining a universal effective Yukawa amplitude would erase that environmental map. One must solve each boundary-value problem and combine only at the shared action parameters.

2. Transfer task. A residual follows the expected Yukawa separation dependence but vanishes after replacing a gold coating with another conductor. What conclusion is justified?

Solution

Recompute the gravitational template before deciding. A universal finite-range force weights material within a few $\lambda$ of the surface, so changing a coating’s density or thickness can change even a universally mass-coupled signal. The coating also changes patch potentials, optical response, roughness, charging, and distance calibration. If the calculated gravitational response remains nearly unchanged while the residual vanishes, the result is counterevidence to that universal-force interpretation. Fit both configurations with their actual layered geometry, shared metrology, and separate surface-background models, then repeat voltage and source-modulation controls. Material sensitivity alone identifies neither a background nor composition-dependent gravity.

Further reading

• Adelberger, E. G., Heckel, B. R., and Nelson, A. E., “Tests of the Gravitational Inverse-Square Law,” Annual Review of Nuclear and Particle Science 53 (2003) 77–121, DOI.
• Burrage, C., and Sakstein, J., “Tests of Chameleon Gravity,” Living Reviews in Relativity 21 (2018) article 1, DOI.
• Murata, J., and Tanaka, S., “A Review of Short-Range Gravity Experiments in the LHC Era,” Classical and Quantum Gravity 32 (2015) 033001, DOI.