# Fifth force
A fifth force is any hypothetical force of nature beyond the four established interactions, the electromagnetic, weak, strong, and gravitational forces, whose mediator would be an as-yet-unknown particle or field[1](https://arxiv.org/abs/1604.07411). The term entered mainstream physics in 1986, when a reanalysis of a 1922 torsion-balance experiment suggested a weak, composition-dependent modification of Newtonian gravity; the hypothesis was later refuted, but it launched a continuing experimental program that now constrains new forces across scales from micrometers to the solar system[2](https://doi.org/10.1103/PhysRevLett.56.1427) • [3](https://plato.stanford.edu/archives/sum2013/entries/physics-experiment/app4.html).
| Key fact | Detail |
|---|---|
| Origin of the term | 1986 reanalysis of the Eötvös, Pekár, and Fekete experiment by Ephraim Fischbach, Daniel Sudarsky, Aaron Szafer, Carrick Talmadge, and S. H. Aronson, published in *Physical Review Letters* 56, 1427 on 31 March 1986[2](https://doi.org/10.1103/PhysRevLett.56.1427) |
| Original parameters | Strength about one percent of gravity (α ≈ 0.01) with a Yukawa range of roughly 100 m, coupling to baryon number so that the force depended on composition[4](https://doi.org/10.12942/lrr-2006-3) • [3](https://plato.stanford.edu/archives/sum2013/entries/physics-experiment/app4.html) |
| Standard parameterization | A Yukawa correction to the Newtonian potential, \( V(r) = -\frac{GMm}{r}\left(1 + \alpha\, e^{-r/\lambda}\right) \), with strength α relative to gravity and range λ[5](https://doi.org/10.1007/s41114-023-00047-0) |
| Fate of the original claim | Torsion-balance repetitions in different locations and with different substances gave consistently negative results, and the community concluded the proposed force does not exist[3](https://plato.stanford.edu/archives/sum2013/entries/physics-experiment/app4.html) |
| Equivalence-principle limit | The MICROSCOPE satellite found no violation of the weak equivalence principle, constraining the Eötvös parameter of a titanium–platinum pair to \( \eta(\mathrm{Ti},\mathrm{Pt}) = [-1.5 \pm 2.3\,(\mathrm{stat}) \pm 1.5\,(\mathrm{syst})] \times 10^{-15} \)[6](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.121102) |
| Short-range limit | The Eöt-Wash group at the University of Washington has tested the inverse-square law down to 52 μm separations (*Physical Review Letters* 124, 101101, 2020)[7](https://www.npl.washington.edu/eotwash/) |
| Long-range limit | Fitting the LAGEOS II satellite orbit constrains the Yukawa coupling to \( |\alpha| < 10^{-5} \) to \( 10^{-8} \) at distances of order \( 10^{9} \) cm[8](https://www.sciencedirect.com/science/article/abs/pii/S0375960102005807) |
## The 1986 hypothesis
The fifth-force hypothesis grew out of a reanalysis of the experiment of [Loránd Eötvös](https://www.edgepedia.org/lorand-eotvos), Pekár, and Fekete, which had compared the accelerations of different materials in Earth's gravity field. Fischbach and collaborators reported that the old data showed a correlation between the measured fractional acceleration differences of sample pairs and the differences of their baryon number-to-mass ratios, which they interpreted as evidence for an intermediate-range field sourced by baryon number[9](https://www.sciencedirect.com/science/article/pii/0003491688902941).
They proposed modifying the gravitational potential between two masses from \( V = -Gm_{1}m_{2}/r \) to \( V = -Gm_{1}m_{2}/r\,[1 + \alpha\, e^{-r/\lambda}] \), with α approximately 0.01 and λ approximately 100 m[3](https://plato.stanford.edu/archives/sum2013/entries/physics-experiment/app4.html). Clifford M. Will, a physicist at [Washington University in St. Louis](https://www.edgepedia.org/washington-university-in-st-louis) who studies experimental tests of gravitation, summarizes the episode in his review of general relativity: the suggested force had a strength of about a percent of gravity and a range of a few hundred meters[4](https://doi.org/10.12942/lrr-2006-3).
## The refutation
The first two experiments gave contradictory answers. Peter Thieberger, using a float apparatus near the Palisades cliff in New Jersey to enhance the effect of an intermediate-range force, measured a steady horizontal drift of a copper sphere relative to water and concluded the results were compatible with a medium-range, substance-dependent force. The Eöt-Wash group, using a torsion pendulum on a hillside at the University of Washington in Seattle, found no evidence for such a force at the parameter values then considered best[3](https://plato.stanford.edu/archives/sum2013/entries/physics-experiment/app4.html).
The discord was resolved by repetition. Torsion-balance experiments modeled on Eöt-Wash were repeated by other groups in different locations and with different substances, giving consistently negative results, and Bizzeti and collaborators, using a float apparatus similar to Thieberger's, also found no evidence. The preponderance of negative results was accepted as conclusive[3](https://plato.stanford.edu/archives/sum2013/entries/physics-experiment/app4.html). A Nature commentary marking six years of the hypothesis noted that no compelling evidence for any new weak force had emerged, while the searches had produced a large body of experimental and theoretical results[10](https://www.nature.com/articles/356207a0).
## How fifth forces are parameterized and searched for
Modern searches describe any deviation from Newtonian gravity with the Yukawa form \( V(r) = -\frac{GM}{r}(1 + \alpha\, e^{-r/\lambda}) \), where α is the dimensionless strength relative to gravity and λ the range[5](https://doi.org/10.1007/s41114-023-00047-0). Whether the force is composition-dependent or composition-independent depends on whether the additional field couples universally to matter; composition-dependent tests are in practice tests of the weak equivalence principle, the statement that inertial and gravitational mass are equal[5](https://doi.org/10.1007/s41114-023-00047-0).
**Laboratory tests** probe sub-centimeter ranges, where torsion pendulums, micromachined oscillators, and Casimir-force measurements set limits. The Eöt-Wash group's stated goals include searching for violations of the equivalence principle and the inverse-square law and probing interactions weaker than gravity[7](https://www.npl.washington.edu/eotwash/). Reviews of short-range tests cover the range from a few microns to a few centimeters[11](https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705%2803%2900042-2/).
**Space and planetary tests** constrain long-range, composition-independent forces. Lunar and planetary ephemerides, satellite laser ranging to LAGEOS, and Mars orbiter tracking data all bound α as a function of λ; by 2011, constraints from planetary ephemerides had reached the level of those from lunar ephemerides[5](https://doi.org/10.1007/s41114-023-00047-0) • [8](https://www.sciencedirect.com/science/article/abs/pii/S0375960102005807).
**Equivalence-principle tests** bound composition-dependent forces. The MICROSCOPE mission compared the free-fall accelerations of two collocated test masses of different composition, titanium and platinum alloys, aboard a drag-free satellite over two and a half years, and found no violation at the \( 10^{-15} \) level in the Eötvös parameter[6](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.121102).
**Screened dark-energy candidates** motivate a distinct class of searches. One proposal holds that dark energy is a fifth force much weaker than gravity, mediated by a particle dubbed a chameleon because its reach shrinks in dense surroundings, so it would act over cosmic distances in space but be nearly undetectable in a laboratory. In 2024, UC Berkeley physicists using an optical-lattice atom interferometer that holds cesium atoms in free fall for up to 70 seconds found no deviation from Newtonian gravity, improving on the previous most precise measurement by a factor of five[12](https://news.berkeley.edu/2024/06/26/with-a-new-incredibly-precise-instrument-berkeley-researchers-narrow-search-for-dark-energy/).
## The X17 anomaly
A separate, particle-physics line of fifth-force searches began in 2016, when the ATOMKI institute in Debrecen, Hungary reported a 6.8σ anomaly in the opening angle and invariant-mass distributions of \( e^{+}e^{-} \) pairs produced in excited \( ^{8}\mathrm{Be} \) nuclear transitions. Jonathan L. Feng, a particle physicist at the [University of California, Irvine](https://www.edgepedia.org/university-of-california-irvine), and colleagues showed the data could be explained by a 17 MeV vector gauge boson X, produced in \( ^{8}\mathrm{Be}^{*} \to {}^{8}\mathrm{Be}\,X \) and decaying through \( X \to e^{+}e^{-} \), which would mediate a fifth force with a characteristic range of 12 fm and milli-charged couplings to up and down quarks and electrons, with the proton coupling suppressed relative to the neutron, a property called protophobic[1](https://arxiv.org/abs/1604.07411).
A 2020 analysis by Feng, Tim M. P. Tait, and Christopher B. Verhaaren found that the same protophobic vector boson proposed for the \( ^{8}\mathrm{Be} \) anomaly also explains the analogous \( ^{4}\mathrm{He} \) anomaly within experimental uncertainties, while scalar and pseudoscalar mediators are excluded or disfavored under parity conservation[13](https://doi.org/10.1103/PhysRevD.102.036016).
## Current status
No fifth force has been confirmed. At the energy scales and precision of current experiments, any such force must be weak enough, or short-ranged enough, to have escaped detection across laboratory, satellite, and planetary tests[1](https://arxiv.org/abs/1604.07411) • [5](https://doi.org/10.1007/s41114-023-00047-0). The searches continue to narrow the allowed (α, λ) parameter space, and a large region remains open at submillimeter scales[5](https://doi.org/10.1007/s41114-023-00047-0). Recent theoretical work argues that some UV-complete scalar-tensor models predict Yukawa forces in regions of parameter space that improved fifth-force searches could directly test and potentially falsify[14](https://journals.aps.org/prl/abstract/10.1103/q1gq-sgy3).
## References
1. [Ephraim Fischbach et al. (1986). Reanalysis of the Eötvös Experiment. *Physical Review Letters* 56, 1427.](https://doi.org/10.1103/PhysRevLett.56.1427)
2. [Clifford M. Will (2006). The Confrontation between General Relativity and Experiment. *Living Reviews in Relativity*.](https://doi.org/10.12942/lrr-2006-3)
3. [Allan Franklin. Appendix 4: The Fall of the Fifth Force, supplement to Experiment in Physics. Stanford Encyclopedia of Philosophy.](https://plato.stanford.edu/archives/sum2013/entries/physics-experiment/app4.html)
4. [Testing theories of gravity with planetary ephemerides. *Living Reviews in Relativity* (2023).](https://doi.org/10.1007/s41114-023-00047-0)
5. [MICROSCOPE Collaboration (2022). MICROSCOPE Mission: Final Results of the Test of the Equivalence Principle. *Physical Review Letters* 129, 121102.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.121102)
6. [The Eöt-Wash Group: Laboratory Tests of Gravitational and sub-Gravitational Physics, University of Washington.](https://www.npl.washington.edu/eotwash/)
7. [Constraints on a Yukawa gravitational potential from laser data of LAGEOS satellites. *Physics Letters A* (2002).](https://www.sciencedirect.com/science/article/abs/pii/S0375960102005807)
8. [Fischbach, Sudarsky, Szafer, Talmadge, Aronson (1988). Long-range forces and the Eötvös experiment. *Annals of Physics* 182, 1–89.](https://www.sciencedirect.com/science/article/pii/0003491688902941)
9. [Six years of the fifth force. *Nature* 356, 207 (1992).](https://www.nature.com/articles/356207a0)
10. [Current short-range tests of the gravitational inverse square law. *Comptes Rendus Physique* (2003).](https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705%2803%2900042-2/)
11. [Robert Sanders (2024). With a new, incredibly precise instrument, Berkeley researchers narrow search for dark energy. UC Berkeley News.](https://news.berkeley.edu/2024/06/26/with-a-new-incredibly-precise-instrument-berkeley-researchers-narrow-search-for-dark-energy/)
12. [Jonathan L. Feng et al. (2016). Protophobic Fifth Force Interpretation of the Observed Anomaly in 8Be Nuclear Transitions. arXiv:1604.07411.](https://arxiv.org/abs/1604.07411)
13. [Feng, Tait, Verhaaren (2020). Dynamical evidence for a fifth force explanation of the ATOMKI nuclear anomalies. *Physical Review D* 102, 036016.](https://doi.org/10.1103/PhysRevD.102.036016)
14. [Bonanno, Glaviano. Fifth-Force Constraints from UV-Complete Scalar-Tensor Gravity. *Physical Review Letters* 136, 201501.](https://journals.aps.org/prl/abstract/10.1103/q1gq-sgy3)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Relativity and gravitation › General relativity and curved spacetime › Foundations and field equations › Equivalence principle › Violations and speculative departures*
*Initially written Sep 17, 2026 · Reviewed: Sep 30, 2026; Oct 15, 2026 · Edited: Sep 30, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*
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