A particle moving with speed greater than light will violate this.

One such possibility is Tachyons (theoretical particle) travels always with v > c. For more details...see

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

and 

https://en.wikipedia.org/wiki/Tachyon

In [1] Dabrowski and Gohar discuss the maximal tension principle in the context of gravitational models other than general relativity.  This is all I am aware of. The claim is the GR implies the maximal force and that GR can be derived from a maximal force. 

You might just have to think outside GR to get rid of the maximal force.

Reference

[1 ] M. P. Dabrowski and  H. Gohar, Abolishing the maximum tension principle, Physics Letters B 748, Volume 748, pp 428-431 (2014).

David,

My answer is going to be the opposite of the proof that you requested because it gives further evidence that Planck force Fp = c4/G is indeed an important fundamental property of nature.  In the attached paper below I propose that there is a single constant of nature that converts all electrical or magnetic equations which incorporate the unit of coulomb into a strain of spacetime.  Equation (26) of this paper identifies this charge conversion constant as: η ≡ (G/4πεoc4)1/2 ≈ 8.61x10-18 meters/coulomb.  The reason for mentioning this is that one of the tests of this proposed constant (equation 28) is to convert the Coulomb force constant 1/4πεo into a property of spacetime. This conversion is:  

(1/4πεo)(1/η2) = c4/G = Fp

Therefore the point is that it appears that c4/G not only holds a special place in general relativity and Planck units, but it also is equivalent to 1/4πεo, the Coulomb force constant.  There are also several other tests of this conversion constant that give reasonable answers.

Chapter Spacetime Based Foundation of Quantum Mechanics and General Relativity

To give a comprehensive answer to this question i include a number of publications/ links.

In summary tensor calculus breaks down at the event horizon yielding infinities.The space time curvature seen in gravity can be translated into a algebraic format - which explains black hole more comprehensively gives a maximum force at the event horizon and allows even the inner workings of the black hole to be calculated.

Moreover this approach can also be used to explain dark matter, in so far as the dark matter is exactly 6.25 multiplied by baryonic matter.

Article The formulation of dynamic Newtonian advanced gravity, DNAg

Article Corroboration of Dynamic Black Hole Gravitational Physics fr...

Article Advances in Black Hole Physics and Dark Matter Modelling of ...

Article An advanced dynamic adaptation of Newtonian equations of gravity

Herein a video link which explains gravity better

https://www.youtube.com/watch?v=FDJJODXFqxo

Andrew, thanks for the input. Do you have an algebraic derivation for your central equations for modifying the Newtonian formula? I didn't spot any in your papers. Also, how does your model relate directly to the Maximum Force/Power Principle associated with General Relativity? Does your model predict a maximum force? (I see that you suggest that the force on a test mass near/at the Schwartzschild Radius is a multiple of the Newtonian prediction, but this is probably not the maximum force that your model allows....)

John, thanks for the links - I will be reading your papers and book. From your post, however, I assume that you are suggesting that the Maximum Force is 4 times that proposed by Gibbons and Schiller? If this is correct, do you have any explanation for the difference?

David,

If you read my papers and book you will discover that I do not make any attempt to keep track of numerical constants near 1.  Therefore a factor of 4 is unimportant to me as long as I get the basic physics correct and the other terms in the equations correct. For example, I start from first principles and use Planck length and Planck time to derive many things including wave amplitudes.  The truth is that physicists do not know the value of the numerical constant associated with Planck length and Planck time. There are even two different ways of defining Planck length which differ by 2π.  My rational is that I am covering such a large part of physics that a single mistake in a numerical constant would be perpetuated everywhere.    

You will see that Planck force appears in many different ways throughout the book.  Slight differences in the treatment of spin or maximum frequency produce a factor of 2 difference which then gets squared producing a factor of 4 difference in the maximum force.  It is surprising, but when I test ideas with plausibility calculations, I usually get the correct answer by assuming k = 1. Please keep in touch. - John Macken

David,

I note you give maximum force and maximum power can you give me the maximun acceleration, and I can give you a definitive answer.

It is far easier and accurate to work with accelaration,because graviational force depends on M and m, I have a maximum M, but m can be entirely arbitary anywhere between maximum M and the minimal Planck mass.

Thus a formula for maximum accelaration would yield a far more accurate answer as it  just deals with M.

Andrew, the gravitational acceleration at the Schwartzschild Radius of a non-rotating black-hole of mass M is F/M, where F is the Maximum Force. Thus, the acceleration depends on the size of the black-hole. In order to find an expression for an absolute limit one must invoke Quantum Mechanics to obtain (c^7/2G{h/2π})^1/2

John, Christoph Schiller has an excellent analysis of the numerical factors associated with the limits allowed by modern physics at

http://arxiv.org/abs/physics/0309118v5

Given your apparent approach with it's major use of Planck Units, Christoph's analysis may be of interest to you - if you haven't already seen it. Certainly, I will keep Christoph's analysis in my mind as I read your analyses. I have corresponded with both Christoph and Gary Gibbons (and John Barrow) and the factor of 4 in Fmax is important - and none of them is aware of any evidence that violates the Principle. Indeed, Gary believes that the Principle is implied by GR, Christoph thinks that it is completely equivalent to GR (and has derived the full GR Field Equations from it), and I agree with both and think further that it can be used to predict that the total average density of the Universe is the Critical Value that makes space flat (as the latest observations indicate to a high degree of accuracy).

Hi Sachin and Vikash, to my knowledge, there is no observational evidence for any particles exceeding the speed of light. I'm aware that 'tachyons' are potential mathematical faster-than-light-speed particle solutions to Special Relativity, but particles with their predicted properties have never been observed. Moreover, even admitting tachyons into the theoretical analysis, it's not obvious that they would violate the Principle of Maximum Force/Power. Do you have an analysis that would indicate such a violation? Indeed, Christoph Schiller has published a very clever analysis deriving the full General Relativity Field Equations just assuming the Principle of Maximum Force/Power as the foundation, and, of course, General Relativity incorporates Special Relativity......

David

Thank you for answering my question

It turns out the maximum acceleration is the Planck acceleration a2 and this gives an answer equal to  the gravitational formula     a= GM/R2(1+3GM/Rc2)2 in the cosmological black  hole as given in the papers below

Slightly intriguing result.

Article The formulation of dynamic Newtonian advanced gravity, DNAg

John, I've begun to read your papers/book, and am enjoying it. I thought that I'd offer two early comments:

I think that the Maximum Force enters your model via your use of the impedance from a paper analyzing the propagation of gravity waves - that is, by using Z = c^3/G. In view of my earlier comments, I feel that it should be c^3/4G, though I fully understand your response in this connection, that you are unconcerned about such relatively small factors of 4.

I think that your approach might be somewhat comparable to the so-called Nexus Model, developed by Stuart Marongwe. Stuart also takes a conceptual approach that Spacetime is the fundamental foundation of Nature, but explores the concept in 'Fourier-transformed Spacetime', rather than Spacetime itself.

I'll touch base again if/when I have any additional comments/questions.

John, have you seen the year 2000 publication 'Light is Heavy' by t'Hooft?

http://arxiv.org/pdf/1508.06478.pdf

As of 2018, I would sum up the the answer by saying no, there is no evidence yet invalidating the limits.

Hi Christoph, yes, I agree with you. The original report of gravitational waves from coalescing black holes seem to have generated a maximum power of only about 10^-4 of c^4/4G. I hope that everything is going well for you and yours.

Indeed, I heard similar numbers - up to 0.3% of the maximum power given by c^5/4G in black hole mergers. Test for the maximum force c^4/4G are much rarer - but there is also no counter-argument or observation getting near that value yet. Tests for the maximum mass flow rate c^3/4G are also rare - and no numbers even near this value have been observed.

Yes, indeed. Sorry for my typo - of course, I meant c^5/4G!

Christoph Schiller There is a calculation (apparently “well-known”, according to Freeman Dyson) in General Relativity that predicts that the maximum gravitational-wave luminosity of a binary system of two identical masses is equal to (2c)^5/5G – which is (significantly) greater than c^5/4G.

This is mentioned in a footnote in the 2017 paper by John D. Barrow and G. W. Gibbons:

‘A maximum magnetic moment to angular momentum conjecture’ (arXiv:1701.06343v2)

The footnote states:

“In reply to an enquiry by Christoph Schiller, Dyson replied on 14th Feb 2011: ’It is not true that I proposed the formula c^5/G as a luminosity limit for anything. I make no such claim. Perhaps this notion arose from a paper that I wrote in 1962 with the title, “Gravitational Machines”, published as Chapter 12 in the book, “Interstellar Communication” edited by Alastair Cameron, [New York, Benjamin, 1963]. Equation (11) in that paper is the well-known formula 128V^10/5Gc^5 for the power in gravitational waves emitted by a binary star with two equal masses moving in a circular orbit with velocity V. As V approaches its upper limit c, this gravitational power approaches the upper limit 128c^5/5G. The remarkable thing about this upper limit is that it is independent of the masses of the stars. It may be of some relevance to the theory of gamma-ray bursts.’”

Since it mentions your name, you must be familiar with this result. Did you ever manage to reconcile it with your and Gary’s Maximum Force/Power conjecture?

Yes, Dyson wrote that email to me back in 2011. There is little doubt that c^5/4G, with the factor 1/4, is the correct limit on power, and Gary and John agree for sure. I suspect that the factor 128/5 is due to some post-Newtonian expansion that does not take into account the full nonlinearity of the field equations.

Christoph Schiller For whatever it is worth, I also think that the conjecture is correct, at least in General Relativity - and an extremely important insight and result. Nevertheless, I always keep my eyes open for any mathematical or empirical information that relates to it, either positively or negatively......

After 20 years the answer to the original question "Is there any theoretical or observational evidence to invalidate the Principle of Maximum Force/Power in General Relativity?" is still "No!". A summary of the situation, including a few new results and tests, is in the attached preprint, soon to be published.

Christoph, as you note, the maximum force can only be reached on a horizon - which must exist in a Universe or space of finite age with a finite speed of information transmission. However, it is not reached, for example, at the cosmic (i.e. outer) horizon of the Kottler metric. Thus, such an inequality is, in a certain sense, an ‘approximate’ statement. However, one can make an ‘exact’ statement that the average energy density inside any horizon is always equal to the Critical Density that makes space ‘flat’.

David, thank you for your point. While I am sure that maximum force is valid for every black hole horizon (as shown in the preprint), I am not sure at all about the force value on a test mass located at or near the cosmological horizon. This situation is hard to capture in all its aspects. I have not seen it discussed anywhere. The issues start with the very simple question whether there is a force at all at the cosmological horizon, and if so, which sign it has. All this is not easy to answer and to check.

However, Christoph, some inequalities can indeed be derived for force values at a Kottler Cosmic (outer) Horizon, as was done after our discussions with Gary Gibbons and John Barrow regarding Maximum Force values for a finite Cosmological Constant. In their resulting paper on the topic, equation (33) states fc_Λ