Three years ago I wrote a little chit of a paper that was accepted and published by Astrophysics and Space Science without any modifications (the only time that has happened to me). I thought at the time that it was absolutely beautiful in form, but probably nothing to do with MiHsC/quantised inertia. It is fascinating that recently I have managed to derive MiHsC from this method as well, and it is so suggestive, that it is now taking over my work.

Heisenberg's uncertainty principle is part of quantum mechanics, and says that for a quantum particle the uncertainty in momentum dp (or energy, dE) and uncertainty in position, dx, when multiplied, equal a constant: a very small number called Planck's constant: h-bar. See equation below:

Heisenberg's uncertainty principle is part of quantum mechanics, and says that for a quantum particle the uncertainty in momentum dp (or energy, dE) and uncertainty in position, dx, when multiplied, equal a constant: a very small number called Planck's constant: h-bar. See equation below:

This means that the more you know a particle's position, the less you know its momentum or energy, and vice versa. Hence the joke wherein a policeman stops Prof Werner Heisenberg speeding on the Autobahn "Do you know how fast you were going?". "Nein.." says Heisenberg, "but I know where I am!". This principle has only been applied to tiny quantum particles and not on the Autobahn scale let alone for planets, but a law should be a law at all scales. So why not apply it at planetary scale?

Imagine you have a big planet, with a smaller Moon orbiting it which is quantum-jiggling slightly at random and we apply the Heisenberg uncertainty principle (HUP) to the situation, adding up the uncertainty for every possible interaction between all the Planck masses in both bodies. Let us imagine the uncertainty in position dx is the Moon's orbital radius and suddenly by chance the random perturbations push the two closer together. Now dx decreases and dE must increase. There is now more uncertainty of energy. "But this isn't REAL energy!" I hear you say. True, but what if we, just to see what happens, assume that this energy uncertainty becomes real kinetic energy. What then? Well, I showed in this little paper that you get Newton's gravity law! (You still have to assume the value of G). When you recover from the shock, do read the paper below, which is available for free on research gate (The arXiv refused to accept it, even though it had been accepted and published by ApSS).

This is a derivation of classical gravity, simply (in only eight lines) from quantum mechanics: two theories that are not supposed to be compatible. It suggests that gravity is not fundamental, but emerges from quantum mechanics (QM). This makes sense to me because there's a lot of evidence that QM is a better theory than general relativity (GR). Admittedly QM is completely nuts (but so what: "Nature will come out as she is" - Feynman), but it is fairly simple and very accurate, whereas GR is a lovely idea to us parochial humans, but is complex and is not working right at low accelerations (for example, with galaxy rotation, where it needs the ad hoc dark matter). MiHsC/quantised inertia, which is based on quantum mechanics with relativistic horizons chucked in, is far more successful (no dark matter is needed to predict galaxy rotation, see here) and I can now derive MiHsC from the uncertainty principle approach too (I have submitted a paper). This forms the outline of a new paradigm: what is conserved in nature is not mass-energy, but mass-energy plus uncertainty or information.

I can now quote Francis Bacon, with a nice double meaning:

“If a man will begin with certainties, he shall end in doubts; but if he will be content to begin with doubt (uncertainties), he shall end in certainties.” - Francis Bacon.

References

McCulloch, M.E., 2014. Gravity from the uncertainty principle. ApSS, 349, 957-959. Journal (not free)

PDF is free on research gate: Preprint (free)

Video discussing the paper: https://www.youtube.com/watch?v=4ge_ukRbuOw

## 14 comments:

Your paper is interesting but suffers from two large problems.

First: your assumption that the sum of all the Plank mass uncertainties in position is equal to the radius between the aggregate bodies is completely unjustified. Do you have any reasoning that can lead from DeltaX to R without a pure assumption?

Second: The existence of the Earth's atmosphere, the atmosphere of other planets and and moons and the existence of gas giant planets and stars proves that gravity acts on particles down to the size of gas atoms and molecules and does not stop with dust sized Plank masses.

Ted: Good questions. I don't have complete answers: as I say in the discussion of the paper, it is not a complete model. I was playing around with the maths, with some vague physical intuition, and noticed the derivation worked and ever since then I've been trying to complete the physical model. As regards the dx=r assumption, the way I see it is that the big planet's surface is like a horizon to the small planet and limits the small planet's knowledge of the cosmos to a distance r, in that direction. Another way to see it is to imagine you are galaxy-sized and looking at the system, like we look at an atom. Dx will be something related to r. Your second point is even harder to fully answer. The maths requires the assumption that matter organises into Planck mass 'packets'. I'm not sure what that might mean physically.

Mike: It's fair enough that your model is incomplete. As for the Plank mass, I don't think you can take the use of dimensionless units as too fundamental. Theorists throw in or take out factors of 4pi and 8pi at will depending on what problems they are working on. Reading your paper, it's not even clear to me that your model requires the mass to be organized in plank mass units. It just seems like a convenient set of units to use, as in you paper on the derivation of inertial mass from Unruh radiation. The plank mass is an interesting unit in that it is the largest mass that a fundamental charged particle can have without collapsing to a gravitational singularity, but that is a coincidence and depends on the proper use of the previously mentioned factors of 4pi or 8pi. In reality, the plank mass is no more significant than a kilogram or an ounce. Perhaps a re-assesment of your derivation on the basis of fundamental particles, electrons and quarks, might be a way to go. Something similar to how you did your orbital anomaly paper with each particle pair an independent contribution to the Unruh field.

Mike: I was looking through your paper again and noticed what appears to be a serious error. You use the relation E=pc at one point. The actual relativistic Energy-Momentum relation is E^2 = (pc)^2 + (mc^2)^2. The energy is only equal to pc for massless particles. You are discussing a summation over Planck

masses. This would seem to ruin your entire derivation independent of the more esoteric issues I mentioned previously.I really don't mean to be overly critical. I do not like the continued use of Dark Matter as a crutch for the failures of mainstream astrophysical theories and would like to see a theory such as yours provide a better explanation. This paper doesn't involve MiHsC, so that isn't at issue, but I must conclude that your approach to deriving Newtonian Gravity from the uncertainty principle is wrong. Please let me know if I have missed something.

@ted rippert , @mike McCulloch

If inertia is just an emerging property from ZPE+Casimir what is the mass discussed in E=mc2 ? of E^2=(pc)^2+(mc^2)^2

If I understand well the only cause of inertia is sensibility of the various force field/boson ? the mass would be something like the integration of all the boson interaction cross-section over their average probability in ZPE ?

By the way in MiHsC why is apparent inertial mass increasing when approaching c?

In the paper, you mention Nesvizhevsky's work, saying "they used neutrons, which only feel the gravitational force", but conclude later that the model predicts that "particles of less than [the Planck mass]... are not gravitationally attracted to large bodies". Am I missing something, or are these contradictory? What gravitational force are the falling neutrons (far smaller than the Planck mass) feeling, if not that of a larger body?

I'm also struggling a bit with the sentence "as the radius of an orbit decreases and the uncertainty in position decreases, then the momentum, or force, on the orbiting body must increase": surely it's the

uncertaintyof the momentum that increases, which isn't quite the same thing?(Apologies if I've missed something obvious, my degree's in maths, not physics. But I very much like the idea of MiHsC, dark matter has always seemed to be a bit of a bodge, from my limited understanding. It would be great to see a deeper theory drop out of something relatively simple.)

Ted: Your constructive criticisms are very valuable. I can attempt to answer your E=pc query, so long as it's understood that I'm still trying to work this out! I'd like to suggest that E=pc works here because, in MiHsC, mass is not a 'thing' at all. It is an anisotropy in the Unruh radiation, a net radiation pressure. So when I say p-->E/c I'm saying that the momentum of the Unruh radiation is re-expressed as energy.

Alain: The "m" you note in your first question is the rest mass of a particle. As the name implies, it is the mass of the particle when at rest. Since MiHsC relates to inertial forces on an accelerating object, it does not address the rest mass as far as I can tell. Note that the rest mass energy, as in E=mc^2, is a well established fact due to atomic power plants and atom bombs. Why mass exists as a compact form of energy is still a complete mystery as far as mainstream physics is concerned.

I think this means that your second question is moot as far as MiHsC is concerned, but Mike may have a notion in that regard.

If I understand your third question, you are asking if MiMsC accounts for the increasing relativistic mass of matter moving close to the speed of light. I don't believe that this is necessary for MiHsC, as the inertia can be calculated in the instantaneous rest frame of a particle from MiHsC and then the relativistic effects of velocity in any other frame calculated using a standard Lorentz transform.

Mike: This does bring up an issue I've noted with some of your analyses. Since your theory relies on Unruh radiation, you are explicitly accepting relativistic quantum field theories as correct. Yet you assume that light can accelerate in your EM drive paper and that you can ignore the rest mass term in the energy-momentum relation here. In special relativity, light always travels at c, a constant, in all rest frames. photons can be absorbed or emitted, but can never accelerate. This is the fundamental axiom of special relativity. I already mentioned the correct Energy-momentum relation. If you start trying to utilize assumptions or formula at odds with special relativity, or any part of relativistic quantum field theory, you are contradicting the existence of Unruh radiation. Since the EM drive is a bit fringe, and your paper on gravity from uncertainty is not really a MiHsC paper, none of this really undermines the theory.

As an aside, you might look at the electrons in the copper walls in the the EM drive that are reflecting the microwaves. From the photoelectric effect, we know that a single electron will absorb the momentum of a single reflected photon. Take the time that a photon takes to cross the De-Broglie wavelength of an electron, and the mass of an electron, and you can calculate the acceleration. Looks to me like the little suckers see Unruh radiation in the near infrared.

Jamie: I agree with your queries, but just wanted to note that I had a problem with the neutron paper not describing how the "mirror" below the neutron's path worked. How do we know that the mirror does not contribute to the "quantization" of the neutron paths?

> Since your theory relies on Unruh radiation, you are explicitly accepting relativistic quantum field theories as correct.

That is not necessarily true. If a theory predicts a physical phenomenon which is later detected by experiment, then the phenomenon exists and is fundamentally independent of the theory.

As an example, Maxwell's equations predicted a great number of phenomena which were proven experimentally to be real. But accepting these phenomena does not mean that Maxwell's equations are correct, just that the true physical law reduces to that behavior under particular conditions.

These conditions for a theory are usually not known at first and so the theory is thought to be fundamental. It is only later that we find limitations and develop a more fundamental theory that explain the phenomena of the prior theory as well as a new set of phenomena.

It is possible that horizon mechanics is likewise more fundamental than current theories. If so, then I'd expect the "mindfuck" aspect of it to be just as wild as the previous paradigm shifts have been.

IMO, Mike is definitely on to something, but I think right now the gravity paper is the equivalent of that scene in Close Encounters of the Third Kind where he's sculpting the mountain out of the mashed potatoes.

Analytic D: I agree that experimental observation always trumps theoretical prediction.

Unfortunately, neither Unruh radiation nor the Hubble horizon (or any true information horizon) have been definitively experimentally observed. Mike himself posted a possible observation of Unruh radiation a few posts back, but that was an alternative theory relating to an effect that had already been explained with more mundane physics. Perhaps further experiments will be more in line with the Unruh based analysis and perhaps not, we do not know right now.

The closest thing to an information horizon I know of experimentally is experiments on sound propagation in Bose-Einstein condensates, which is suggestive, but hardly conclusive. Keep in mind that the actual Hubble horizon is approximately twice as far away as the farthest stars or even the microwave background radiation that we have been able to observe to date. It is, in fact, unobservable in the electromagnetic spectrum since the universe was opaque to electromagnetic radiation before about 13.7 billion years ago, and the information horizon Mike quotes in his papers is about 28 billion lightyears away.

That means that Mike's theory relies not only on theoretical predictions from quantum field theory, but also on a theoretical horizon predicted by General Relativity.

Don't get me wrong, I like Mike's theory. I just think it lacks rigor. I like your analogy about the mashed potato sculpture, and I am simply advising Mike to keep his sculpture away from Irishmen during the potato famine and Americans around Thanksgiving.

AnalyticD and Ted: I think your analogy between Richard Dreyfuss moulding mashed potatoes and my gravity paper is apt. It made me laugh anyway. I do often feel exactly like Roy Neery in Close Encounters in that there is something important here and I can't see it all, but I am getting closer slowly, and a paper is going through review now in which I do a better job of the gravity paper, so hopefully it will be accepted soon. You are right that MiHsC lacks some rigour. For example, what needs to be modelled ideally is the subsampling of the Unruh radiation spectrum caused by interaction with relativistic horizons. So far I have only approximated this with a linear function.

Hi Mike: Just read this paper. It seems to a bit circular. You define the Planck mass between equations (1) and (2), "as the mass of two objects whose gravitational potential energy is equal to the energy of a photon whose wavelength is their separation, ie: Gm_p^2/r = hc/r". You then solve for m_p and integrate across all Planck masses.

But the formula for the gravitational potential energy used comes from classical Newtonian mechanics, e.g.: https://en.wikipedia.org/wiki/Gravitational_energy#Newtonian_mechanics

In other words, your derivation appears to implicitly assume Newtonian gravitational potential energy at the Planck scale in defining the Planck mass, and then integrates it to the macroscopic scale by summing both the masses and separation distances and getting back out the form relationship that you put in, that of Newtonian mechanics.

Chad: Only partly circular since I only set the value of the Planck mass (less than ideal) but this does not hardwire the inverse square relation (One value cannot imply the form of the whole relation). The form comes out of the new process. The consistency with G shows it is all self-consistent. If you read my latest paper, I explain better, and clear up some other omissions:

https://arxiv.org/abs/1610.06787

Mike, your suggested derivation of particle masses is not really a valid derivation. Normally, one would use the measured mass of the particle to calculate the Compton wavelength. You have simply reversed the process by using the experimental-mass-calculated Compton wavelength to predict the particle mass - and then compared it to the measured mass! (apart from a completely negligible cosmic-level factor). To actually predict the particle masses from your formalism, you would need to derive values of the Compton wavelengths from your model and then use those to calculate the masses - and then compare with experimental values.

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