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41-494: The term is also used as "the Fifth force" when referring to a specific theory advanced by Ephraim Fischbach in 1971 to explain experimental deviations in the theory of gravity. Later analysis failed to reproduce those deviations. The term fifth force originates in a 1986 paper by Ephraim Fischbach et al. who reanalyzed the data from the Eötvös experiment of Loránd Eötvös from earlier in

82-576: A bit more precise as follows. Suppose we wish to measure the position of a particle to within an accuracy Δ x . Then the uncertainty relation for position and momentum says that Δ x Δ p ≥ ℏ 2 , {\displaystyle \Delta x\,\Delta p\geq {\frac {\hbar }{2}},} so the uncertainty in the particle's momentum satisfies Δ p ≥ ℏ 2 Δ x . {\displaystyle \Delta p\geq {\frac {\hbar }{2\Delta x}}.} Using

123-475: A fifth force   —   possibly one with infinite range. This is because gravitational interactions, in theories other than general relativity, have degrees of freedom other than the "metric" , which dictates the curvature of space, and different kinds of degrees of freedom produce different effects. For example, a scalar field cannot produce the bending of light rays . The fifth force would manifest itself in an effect on solar system orbits, called

164-656: A fifth force. Fischbach has been a fellow of the American Physical Society since 2001, and a professor at Purdue since 1979. He also was an associate professor at the Institute for Theoretical Physics in Stony Brook, New York from 1978 to 1979. He received a B.A. in physics in 1963 from Columbia University and a Ph.D. in 1967 from the University of Pennsylvania . Compton wavelength The Compton wavelength

205-537: A form of energy called dark energy . Some physicists speculate that a form of dark energy called quintessence could be a fifth force. There are at least three kinds of searches that can be undertaken, which depend on the kind of force being considered, and its range. One way to search for a fifth force is with tests of the strong equivalence principle , one of the most powerful tests of general relativity , also known as Einstein's theory of gravity. Alternative theories of gravity, such as Brans–Dicke theory , postulate

246-640: A nucleus (see the semi-empirical mass formula ). Searches have been done from very short ranges, to municipal scales, to the scale of the Earth , the Sun, and dark matter at the center of the galaxy. In 2015, Attila Krasznahorkay at ATOMKI , the Hungarian Academy of Sciences's Institute for Nuclear Research in Debrecen , Hungary, and his colleagues posited the existence of a new, light boson only 34 times heavier than

287-432: A particle, taking into account quantum mechanics and special relativity . This limitation depends on the mass m of the particle. To see how, note that we can measure the position of a particle by bouncing light off it – but measuring the position accurately requires light of short wavelength. Light with a short wavelength consists of photons of high energy. If the energy of these photons exceeds mc , when one hits

328-452: A photon of the same energy. For photons of frequency f , energy is given by E = h f = h c λ = m c 2 , {\displaystyle E=hf={\frac {hc}{\lambda }}=mc^{2},} which yields the Compton wavelength formula if solved for λ . The Compton wavelength expresses a fundamental limitation on measuring the position of

369-492: A submarine, USS Dolphin (AGSS-555) , while deeply submerged. A further experiment measuring the gravitational constant in a deep borehole in the Greenland ice sheet found discrepancies of a few percent, but it was not possible to eliminate a geological source for the observed signal. Another experiment uses the Earth's mantle as a giant particle detector, focusing on geoelectrons. Jain et al. (2012) examined existing data on

410-416: Is 320 m eters high. A comprehensive review by Ephraim Fischbach and Carrick Talmadge suggested there is no compelling evidence for the fifth force, though scientists still search for it. The Fischbach–Talmadge article was written in 1992, and since then, other evidence has come to light that may indicate a fifth force. The above experiments search for a fifth force that is, like gravity, independent of

451-443: Is a quantum mechanical property of a particle , defined as the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence ). It was introduced by Arthur Compton in 1923 in his explanation of the scattering of photons by electrons (a process known as Compton scattering ). The standard Compton wavelength λ of a particle of mass m {\displaystyle m}

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492-689: Is a natural representation for mass on the quantum scale, and as such, it appears in many of the fundamental equations of quantum mechanics. The reduced Compton wavelength appears in the relativistic Klein–Gordon equation for a free particle: ∇ 2 ψ − 1 c 2 ∂ 2 ∂ t 2 ψ = ( m c ℏ ) 2 ψ . {\displaystyle \mathbf {\nabla } ^{2}\psi -{\frac {1}{c^{2}}}{\frac {\partial ^{2}}{\partial t^{2}}}\psi =\left({\frac {mc}{\hbar }}\right)^{2}\psi .} It appears in

533-463: Is a natural representation of mass on the quantum scale and is used in equations that pertain to inertial mass, such as the Klein–Gordon and Schrödinger's equations. Equations that pertain to the wavelengths of photons interacting with mass use the non-reduced Compton wavelength. A particle of mass m has a rest energy of E = mc . The Compton wavelength for this particle is the wavelength of

574-652: Is about 3 times larger than the proton radius , and is written: r e = α ( λ e 2 π ) = α λ ¯ e ≃ λ ¯ e 137 ≃ 2.82   fm {\displaystyle r_{\text{e}}=\alpha \left({\frac {\lambda _{\text{e}}}{2\pi }}\right)=\alpha {\bar {\lambda }}_{\text{e}}\simeq {\frac {{\bar {\lambda }}_{\text{e}}}{137}}\simeq 2.82~{\textrm {fm}}} The Rydberg constant , having dimensions of linear wavenumber ,

615-905: Is also present in Schrödinger's equation , although this is not readily apparent in traditional representations of the equation. The following is the traditional representation of Schrödinger's equation for an electron in a hydrogen-like atom : i ℏ ∂ ∂ t ψ = − ℏ 2 2 m ∇ 2 ψ − 1 4 π ϵ 0 Z e 2 r ψ . {\displaystyle i\hbar {\frac {\partial }{\partial t}}\psi =-{\frac {\hbar ^{2}}{2m}}\nabla ^{2}\psi -{\frac {1}{4\pi \epsilon _{0}}}{\frac {Ze^{2}}{r}}\psi .} Dividing through by ℏ c {\displaystyle \hbar c} and rewriting in terms of

656-618: Is given by λ = h m c , {\displaystyle \lambda ={\frac {h}{mc}},} where h is the Planck constant and c is the speed of light . The corresponding frequency f is given by f = m c 2 h , {\displaystyle f={\frac {mc^{2}}{h}},} and the angular frequency ω is given by ω = m c 2 ℏ . {\displaystyle \omega ={\frac {mc^{2}}{\hbar }}.} The CODATA 2022 value for

697-580: Is roughly the same as the cross-sectional area of an iron-56 nucleus. For gauge bosons , the Compton wavelength sets the effective range of the Yukawa interaction : since the photon has no mass, electromagnetism has infinite range. The Planck mass is the order of mass for which the Compton wavelength and the Schwarzschild radius r S = 2 G M / c 2 {\displaystyle r_{\rm {S}}=2GM/c^{2}} are

738-852: Is written: 1 R ∞ = 2 λ e α 2 ≃ 91.1   nm {\displaystyle {\frac {1}{R_{\infty }}}={\frac {2\lambda _{\text{e}}}{\alpha ^{2}}}\simeq 91.1~{\textrm {nm}}} 1 2 π R ∞ = 2 α 2 ( λ e 2 π ) = 2 λ ¯ e α 2 ≃ 14.5   nm {\displaystyle {\frac {1}{2\pi R_{\infty }}}={\frac {2}{\alpha ^{2}}}\left({\frac {\lambda _{\text{e}}}{2\pi }}\right)=2{\frac {{\bar {\lambda }}_{\text{e}}}{\alpha ^{2}}}\simeq 14.5~{\textrm {nm}}} This yields

779-542: The Dirac equation (the following is an explicitly covariant form employing the Einstein summation convention ): − i γ μ ∂ μ ψ + ( m c ℏ ) ψ = 0. {\displaystyle -i\gamma ^{\mu }\partial _{\mu }\psi +\left({\frac {mc}{\hbar }}\right)\psi =0.} The reduced Compton wavelength

820-515: The Nordtvedt effect . This is tested with Lunar Laser Ranging experiment and very-long-baseline interferometry . Another kind of fifth force, which arises in Kaluza–Klein theory , where the universe has extra dimensions , or in supergravity or string theory is the Yukawa force , which is transmitted by a light scalar field (i.e. a scalar field with a long Compton wavelength , which determines

861-483: The fine-structure constant , one obtains: i c ∂ ∂ t ψ = − λ ¯ 2 ∇ 2 ψ − α Z r ψ . {\displaystyle {\frac {i}{c}}{\frac {\partial }{\partial t}}\psi =-{\frac {\bar {\lambda }}{2}}\nabla ^{2}\psi -{\frac {\alpha Z}{r}}\psi .} The reduced Compton wavelength

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902-456: The relativistic relation between momentum and energy E = ( pc ) + ( mc ) , when Δ p exceeds mc then the uncertainty in energy is greater than mc , which is enough energy to create another particle of the same type. But we must exclude this greater energy uncertainty. Physically, this is excluded by the creation of one or more additional particles to keep the momentum uncertainty of each particle at or below mc . In particular

943-454: The Compton wavelength of the electron is 2.426 310 235 38 (76) × 10  m . Other particles have different Compton wavelengths. The reduced Compton wavelength ƛ ( barred lambda , denoted below by λ ¯ {\displaystyle {\bar {\lambda }}} ) is defined as the Compton wavelength divided by 2 π : where ħ is the reduced Planck constant . The inverse reduced Compton wavelength

984-497: The Yukawa interaction is engaging at a certain length. Australian researchers, attempting to measure the gravitational constant deep in a mine shaft, found a discrepancy between the predicted and measured value, with the measured value being two percent too small. They concluded that the results may be explained by a repulsive fifth force with a range from a few centimetres to a kilometre. Similar experiments have been carried out on board

1025-426: The century; the reanalysis found a distance dependence to gravity that deviates from the inverse square law . The reanalysis was sparked by theoretical work in 1971 by Fujii proposing a model that changes distance dependence with a Yukawa potential -like term: The parameter α {\displaystyle \alpha } characterizes the strength and λ {\displaystyle \lambda }

1066-428: The composition of an object, so all objects experience the force in proportion to their masses. Forces that depend on the composition of an object can be very sensitively tested by torsion balance experiments of a type invented by Loránd Eötvös . Such forces may depend, for example, on the ratio of protons to neutrons in an atomic nucleus, nuclear spin, or the relative amount of different kinds of binding energy in

1107-418: The data. The force may explain the muon g − 2 anomaly and provide a dark matter candidate. Several research experiments are underway to attempt to validate or refute these results. Ephraim Fischbach Ephraim Fischbach (born 1942) is an American physicist and a professor at Purdue University . He is best known for his attempts to find a fifth force of nature and his research relating to

1148-487: The detection of neutrinos . He has also done work relating to the prediction of solar flares and the detection of radiation by cell phones. Fischbach studies variation in radioactive decay rates, suggesting that neutrino emission from the Sun reduces the rate of nuclear decay. He reanalysed the Eötvös experiment , which he saw as evidence for a fifth physical force. However, in 1992, he and Carrick Talmadge conducted an experiment which found no compelling evidence for

1189-865: The electromagnetic fine-structure constant ( α ≃ 1 137 {\textstyle \alpha \simeq {\tfrac {1}{137}}} ). The Bohr radius is related to the Compton wavelength by: a 0 = 1 α ( λ e 2 π ) = λ ¯ e α ≃ 137 × λ ¯ e ≃ 5.29 × 10 4   fm {\displaystyle a_{0}={\frac {1}{\alpha }}\left({\frac {\lambda _{\text{e}}}{2\pi }}\right)={\frac {{\bar {\lambda }}_{\text{e}}}{\alpha }}\simeq 137\times {\bar {\lambda }}_{\text{e}}\simeq 5.29\times 10^{4}~{\textrm {fm}}} The classical electron radius

1230-489: The electron (17 MeV). In an effort to find a dark photon , the Hungarian team fired protons at thin targets of lithium-7 , which created unstable beryllium-8 nuclei that then decayed and ejected pairs of electrons and positrons. Excess decays were observed at an opening angle of 140° between the e and e , and a combined energy of 17 MeV, which indicated that a small fraction of beryllium-8 will shed excess energy in

1271-399: The existing models of general relativity and quantum field theory , and also between the hierarchy problem and the cosmological constant problem . Both issues suggest the possibility of corrections to the gravitational potential around 100 μ m {\displaystyle 100\mu {\text{m}}} . The accelerating expansion of the universe has been attributed to

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1312-551: The form of a new particle. In November 2019, Krasznahorkay announced that he and his team at ATOMKI had successfully observed the same anomalies in the decay of stable helium atoms as had been observed in beryllium-8, strengthening the case for the X17 particle's existence. Feng et al . (2016) proposed that a protophobic (i.e. "proton-ignoring") X-boson with a mass of 16.7 MeV with suppressed couplings to protons relative to neutrons and electrons and femtometer range could explain

1353-435: The minimum uncertainty is when the scattered photon has limit energy equal to the incident observing energy. It follows that there is a fundamental minimum for Δ x : Δ x ≥ 1 2 ( ℏ m c ) . {\displaystyle \Delta x\geq {\frac {1}{2}}\left({\frac {\hbar }{mc}}\right).} Thus the uncertainty in position must be greater than half of

1394-415: The particle whose position is being measured the collision may yield enough energy to create a new particle of the same type. This renders moot the question of the original particle's location. This argument also shows that the reduced Compton wavelength is the cutoff below which quantum field theory – which can describe particle creation and annihilation – becomes important. The above argument can be made

1435-434: The range of the interaction. Fischbach's paper found a strength around 1% of gravity and a range of a few hundred meters. The effect of this potential can be described equivalently as exchange of vector and/or scalar bosons, that is a predicting as yet undetected new particles. However, many subsequent attempts to reproduce the deviations have failed. Theoretical proposals for a fifth-force are driven by inconsistencies between

1476-461: The range). This has prompted a much recent interest, as a theory of supersymmetric large extra dimensions   —   dimensions with size slightly less than a millimeter —   has prompted an experimental effort to test gravity on very small scales. This requires extremely sensitive experiments which search for a deviation from the inverse-square law of gravity over a range of distances. Essentially, they are looking for signs that

1517-409: The rate of pulsation of over a thousand cepheid variable stars in 25 galaxies. Theory suggests that the rate of cepheid pulsation in galaxies screened from a hypothetical fifth force by neighbouring clusters, would follow a different pattern from cepheids that are not screened. They were unable to find any variation from Einstein's theory of gravity. Some experiments used a lake plus a tower that

1558-479: The reduced Compton wavelength ħ / mc . Typical atomic lengths, wave numbers, and areas in physics can be related to the reduced Compton wavelength for the electron ( λ ¯ e ≡ λ e 2 π ≃ 386   fm {\textstyle {\bar {\lambda }}_{\text{e}}\equiv {\tfrac {\lambda _{\text{e}}}{2\pi }}\simeq 386~{\textrm {fm}}} ) and

1599-547: The reduced Compton wavelength sets the cross-section of interactions. For example, the cross-section for Thomson scattering of a photon from an electron is equal to σ T = 8 π 3 α 2 λ ¯ e 2 ≃ 66.5   fm 2 , {\displaystyle \sigma _{\mathrm {T} }={\frac {8\pi }{3}}\alpha ^{2}{\bar {\lambda }}_{\text{e}}^{2}\simeq 66.5~{\textrm {fm}}^{2},} which

1640-632: The same, when their value is close to the Planck length ( l P {\displaystyle l_{\rm {P}}} ). The Schwarzschild radius is proportional to the mass, whereas the Compton wavelength is proportional to the inverse of the mass. The Planck mass and length are defined by: m P = ℏ c / G {\displaystyle m_{\rm {P}}={\sqrt {\hbar c/G}}} l P = ℏ G / c 3 . {\displaystyle l_{\rm {P}}={\sqrt {\hbar G/c^{3}}}.} A geometrical origin of

1681-410: The sequence: r e = α λ ¯ e = α 2 a 0 = α 3 1 4 π R ∞ . {\displaystyle r_{\text{e}}=\alpha {\bar {\lambda }}_{\text{e}}=\alpha ^{2}a_{0}=\alpha ^{3}{\frac {1}{4\pi R_{\infty }}}.} For fermions ,

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