A maximum force c4/4G and a maximum power c5/4G hold in nature – in addition to maximum speed c.

Maximum speed c = 3⋅10⁸ m/s defines and implies special relativity.
Maximum force c4/4G = 3⋅10⁴³ N and c define and imply general relativity.

Talk Max F pdfSlides of a talk on the maximum force and the maximum power in nature – covering experiments, arguments, paradoxes, tests and consequences.

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The first published statement on the maximum force c4/G was by Elizabeth Rauscher in 1973, probably even in 1968. The first statement on maximum force in a research paper that included the correct factor 1/4 in c4/4G was by Gary Gibbons in 2002. For an overview that includes the most recent results, see this 9-page publication pdf that appeared as Physical Review D 104 (2021) 124079.

About a dozen people independently rediscovered maximum force after Elizabeth Rauscher. Public statements on maximum force c4/4G also appeared around 2000 in the Motion Mountain Physics Textbook, and in 2003, in the preprint arxiv.org/abs/physics/0309118. That preprint includes the principle of maximum force, i.e., the statement that general relativity follows from maximum force. In the meantime, maximum force, maximum power and maximum mass flow rate became a topic of research around the world.

Maximum force contains Einstein's field equations of general relativity, and vice versa. Maximum force contains the first law of horizon mechanics, and vice versa. Maximum force also appears to contain the hoop conjecture. Also in this case it appears that the reverse is correct.

The principle of maximum force predicts – since 2003 – the lack of any deviation from general relativity for strong gravitational fields. Two recent experimental papers, "Strong-field Gravity Tests with the Double Pulsar" https://arxiv.org/abs/2112.06795 (with 30 authors) and "Tests of General Relativity with GWTC-3" https://arxiv.org/abs/2112.06861 (with over 1600 authors), confirm the prediction.

Astonishingly, Einstein, Wheeler, Hawking, Dyson and many others overlooked the concept. In 2011, I exchanged emails with Freeman Dyson on maximum force, power and luminosity, explained the limits, and asked whether he had explored them as well. In his answer he wrote: "It is not true that I proposed the formula c^5/G as a luminosity limit for anything. I make no such claim." On the other hand, he did not contradict the limit either. In 2021, when I discovered that Elizabeth Rauscher was the first to have written about maximum force, she had already passed away.

The principle of maximum force completes the proof that physics can be summarized in 9 lines. The principle of maxmimum force also transforms the Bronshtein cube into a Bronshtein limit cube.

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Main references on maximum force

E.A. Rauscher, Einstein’s Field Equations and the Quantal Force, Lawrence Livermore National Laboratory, UCRL-71435, October 1968. (This paper cannot be found on the internet.)

E. A. Rauscher, The Minkowski metric for a multidimensional geometry, Lett. Nuovo Cim. 7S2, 361-367 (1973). doi.org/10.1007/BF02735134

V. de Sabbata & C. Sivaram, On limiting field strengths in gravitation, Found. Phys. Lett. 6, 561-570 (1993). doi.org/10.1007/BF00662806.

L. Kostro & B. Lange, Is c4/G the greatest possible force in nature?, Phys. Essays 12, 182-189 (1999).

G.W. Gibbons, The maximum tension principle in general relativity, Found. Phys. 32, 1891-1901 (2002). doi.org/10.1023/A:1022370717626.

C. Schiller, General relativity and cosmology derived from principle of maximum power or force, Int. J. Theor. Phys. 44, 1629-1647 (2005). doi.org/10.1007/s10773-005-4835-2.

M.P. Dabrowski & H. Gohar, Abolishing the maximum tension principle, Phys. Lett. B 748, 428-431 (2015). doi.org/10.1016/j.physletb.2015.07.047. The paper shows that in other models of gravity, the maximum force does not hold.

Numerous additional papers have treated the topic of maximum force, mostly confirming it. The latest attempts to construct counter-examples were published by V. Faraoni, Phys. Rev. D 103, 124010 (2021) and by A. Jowsey & M. Visser, arXiv:2102.01831. However, because these publications added forces acting at different locations in space, the counter-examples turn out to be only apparent. A detailed exploration shows that, in the claimed configurations of those papers, local maximum force is never exceeded, as explained in C. Schiller, Comment on "Maximum force and cosmic censorship", Physical Review D 104 (2021) 068501.

An general update on the topic is C. Schiller, Tests for maximum force and maximum power, Physical Review D 104 (2021) 124079, 10.1103/PhysRevD.104.124079. Also at arxiv.org/abs/2112.15418.

The first paper treating maximum mass flow rate c3/4G is Li-Ming Cao, Long-Yue Li and Liang-Bi Wu, A Bound on the Rate of Bondi Mass Loss, Physical Review D 104 (2021) 124017. Also at arxiv.org/abs/2109.05973.

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Personal publications on maximum force

C. Schiller, From maximum force to inverse square gravity, preprint (2021).
pdf   Download the preprint here (2 pages).

The equivalence of maximum force c⁴/4G and the field equations of general relativity provides a simple derivation of inverse square gravity – and suggests a lack of gravitational physics beyond general relativity.

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C. Schiller, Tests for maximum force and maximum power, Physical Review D 104 (2021) 124079, 10.1103/PhysRevD.104.124079.
pdf   Download the preprint here (9 Pages).

Two ways to deduce the equivalence of the field equations of general relativity and the principle of maximum force c⁴/4G – or the equivalent maximum power c⁵/4G – are presented. A simple deduction of inverse square gravity directly from maximum force arises. Recent apparent counter-arguments are refuted. New tests of the principle in astronomy, cosmology, electrodynamics, numerical gravitation and quantum gravity are proposed.

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C. Schiller, Comment on "Maximum force and cosmic censorship", Physical Review D 104 (2021) 068501, 10.1103/PhysRevD.104.068501.
pdf   Download the preprint here (2 pages).

Despite suggestions to the contrary, no counterargument to the principle of maximum force or to the equivalent principle of maximum power has yet been provided.

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C. Schiller, Simple derivation of minimum length, minimum dipole moment and lack of space–time continuity, International Journal of Theoretical Physics 45 (2006) 213–227. Download it at doi.org/10.1007/s10773-005-9018-7. Read the published paper online for free at rdcu.be/cdG3E.
pdf   Download the preprint here.

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C. Schiller, General relativity and cosmology derived from principle of maximum power or force, International Journal of Theoretical Physics 44 (2005) 1629–1647. Download it at doi.org/10.1007/s10773-005-4835-2. Read the published paper online for free at rdcu.be/cdG3C.
pdf   Download the preprint here.

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C. Schiller, Maximum force and minimum distance: physics in limit statements (2003), preprint at arxiv.org/abs/physics/0309118.

The paper explains how the force limit F≤c⁴/4G implies general relativity. As a result, it became possible to state that the speed limit v≤c yields special relativity, the action limit W≥ yields quantum theory, and the force limit F≤c⁴/4G yields general relativity.

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Additional consequences

Maximum force is predicted to hold also in any unified theory.

Maximum force implies that there is no trans-Planckian physics.

Maximum force was the trigger that led to the description of fundamental motion with the help of the strand conjecture. The strand conjecture predicts that there is no physics beyond general relativity and the standard model, but that the fundamental constants can be calculated.

Maximum force might well be the "last" law of physics to be discovered. The argument is strengthened by the past decades of precision experiments. Maximum force completes the summary of physics in 9 lines, and together, these 9 lines describe all nature. If there is really nothing beyond the standard model and general relativity, then maximum force completes the laws of physics. If, instead, any one effect beyond general relativity or beyond the standard model is found, then, of course, maximum force is not the last law of nature. (I propose a bet on the topic.)

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No statement in physics is ever definitively correct. In the case that you have a pretty paradox or an interesting argument against maximum force or maximum power, feel free to write.

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