Gibbons and various other people (including myself) claim that there is no higher force value than
c^4/4G = 3.0 * 10^43 N
and no higher power than
c^5/4G = 9.1 * 10^51 W
in any physical system in nature. Research so far has shown that boosts cannot help to exceed the limit, neither do black holes, nor quasars. In all cases explored so far, horizons, in combination with the proper dimension of the bodies involved, prevent exceeding the limits. Recent attempt to construct counter-examples, found on arxiv, have been shown to contain mistakes. The maximum power radiated from the brightest black hole mergers observed so far is about 200 times smaller than the limit. Even the highest electric or magnetic forces are much smaller. The limits also appear to be related to general relativity, so that higher values might be possible in alternative theories of gravity.
What counter-example or paradox comes to mind?
How could one try to achieve a larger force or power value?
Any suggestion is of interest. The question is interesting also for another reason: it resembles the question whether there is no higher speed that c = 3.0 * 10^8 m/s for physical systems.
I think the hypothesis has to be reconstructed because force = mass x acceleration and by choosing a big enough mass you could exceed the limit. I haven’t worked it out but if you were to accelerate the Earth to half the speed of light and then crash it into another Earth coming in the opposite direction then the force of impact would exceed your force limit. If it doesn’t then you could try the same thought experiment with a mass a million times greater. So I don’t believe there is a theoretical physical limit just a practical limit on what is physically achievable:
On the other hand, if you take mass out of the calculations and ask if there is a maximum possible acceleration I would suggest that the highest accelaration would be whatever created cosmic rays which are travelling close to the speed of light. Again my view would be that there is no theoretical limit on the magnitude of acceleration.
I see these cases as quite different from the speed of light case where the laws of physics clearly show that there is a theoretical limit.
Richard
Richard Lewis
If you smash two earths together, the force (be it gravitational or mechanical) is not that large. "A million times more mass" is about the mass of the Sun (more precisely, 3 solar masses). The forces involved are not much bigger.
Using F=m a, you can make use of a famous result from special relativity. Special relativity limits the acceleration a of a body of length l by the value c^2/l. A higher acceleration is not possible.
You thus get that a body of mass m and length l cannot experience a larger force than F= c^2 * (m/l).
The largest ratio m/l for a body is that of a Schwarzschild black hole, which is c^2/4G.
As a result, F is limited by c^4/4G.
If a higher value than c^4/4G would be possible, the limit would indeed be falsified.
But F does not transform under boosts to F'=gamma^3 ma, please check this. Any better book on relativity can help. In fact, proper force is larger than the force in any other coordinate system. And proper force is limited by c^4/4G.
The question is "Are force values above c^4/4G or power values above c^5/4G possible in nature?". Not more not less.
That question cost me a sleepless night.
If the attracting objects carry different charges, does the electric force come into play !?
I tried to set up an electron model that satisfies the laws of Maxwell's equations and the GTR. For this, the electron must have in the center a string-shaped event horizon.
The energy in the cylindrical event horizon is 1/137 of the total energy of the electron. If two of these cylindrical event horizons rotate around each other at the smallest possible distance (1.5 x r_EH) with the speed of light, the centrifugal force is c ^ 4 / 4G.
F=m*c^2/r
r=1,5 * 1,241*10^-39 m
m=9,11*10^-31 kg
https://www.researchgate.net/publication/344230650_Are_Elementary_Particles_Black_Holes_What_shape_would_an_event_horizon_have_in_an_elementary_particle_so_that_a_stable_particle_with_an_elementary_charge_can_arise
Well, you seem to confirm the limit in your electron model.
In general, yes, c^4/4G is supposed to be the limit even if other forces than gravity come into play.
The issue of maximum force and maximum power is treated in detail in the attached preprint. It is a complete discussion of the topic at present (end of 2021), including a full literature search, a few new test proposals, and a derivation of inverse square gravity from maximum force.
That text is now published in Phys Rev D as Article Tests For Maximum Force and Maximum Power
As usual in science, every potential counter-example to the maximum force c^4/4G or the maximum power c^5/4G must be studied. The cited Phys Rev D does so - but more potential counter-examples could arise.
The paper by Liu and Peng Article A conjectured universal relation for black holes and horizon...
also confirms that energy divided by diameter is never larger than maximumm force c^4/4G.
Hi Christoph, you may wish to take a look at:
Preprint Hubble tension and absolute constraints on the local Hubble parameter
Dave
PS If the maximum values of Force and Power are indeed twice as large as suggested in this thread, the calculation we discussed elsewhere for the total energy density generated by maximum power at the Hubble Sphere over the ‘life’ of the Universe would generate the Critical Energy Density - as observed - and not half this value, as you note in Motion Mountain and your RG thread on Strand Cosmology.....
One well-known researcher in general relativity claims that no upper limit exists on force and on power. As much as I respect this decision, I do not agree. It is good to believe in the lack of limits. But measurements clearly tell us otherwise.
This is an example: Preprint Two Novel Observational Tests of General Relativity
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