The uncertainty principle of Heisenberg is usually written as dp.dx~hbar and it says that the uncertainty in momentum of a quantum object (dp) times its uncertainty in position (dx) is always a constant (hbar). If a quantum object knows well where it is (dx=small), then it loses the ability to know its speed (dp=big). Conversely, if it knows its speed very well (dp=small), it'll be lost in space (dx=big). This relation from quantum mechanics, and special relativity also, are two clues that physics is due to be reworked around the concept of information. This is what quantised inertia does, joining these two pillars of physics (QM and relativity) on the large scale.

Imagine a red mass (see diagram, top part, red circle). Suddenly you put another mass on the left of it (the black circle). The uncertainty of position of the red mass is shown by the black quadrilateral around it. The red mass can see a large amount of empty space up, down and rightwards (forgetting directions perpendicular to the page for now) so its uncertainty in position (dx) is large in those directions because it cannot position itself well in empty space. However, it can see less far into space to the left because the other mass blocks its view, so its uncertainty of position that way (dx) is lower. The quadrilateral represents dx in each direction. It is skewed outwards to the up, down and right where dx is large, and skewed in to the left where dx is small. Therefore, according to Heisenberg, the quadrilateral showing the uncertainty in momentum has to be the opposite: skewed out to the left and skewed in for the other directions (see the blue envelope). Since momentum involves speed, this predicts that it is statistically or quantum mechanically more likely that the object will move to the left. In a formal derivation I have shown this not only looks like gravity but predicts it (see reference below).

Now, as the red object approaches the black one (see lower panel) its uncertainty in position (dx) to the left gets ever smaller, so dp must increase and the red object must accelerate. "Aha!" Says the other great fundamental pillar of physics: relativity, "I now become relevant!". Since the red object is now accelerating away from the space to the right, information from far to the right cannot get to old Red, and a horizon forms (the black line) beyond which is unknowable space for Red. This Rindler horizon is like the black mass. It blocks Red's view and so Red's uncertainty in position to the right reduces (dx, see the black quadrilateral contract from the right) and so the uncertainty in momentum to the right increases (see the blue quadrilateral now extends further to the right). Red now has a chance of moving both left and right and this has the effect of cancelling some of its initial acceleration towards the black mass. This looks like inertia, and indeed it predicts quantised inertia (see reference below).

In this way, you can derive something that looks like quantised inertia (if you consider also the cosmic horizon) and gravity, just by allowing quantum mechanics and relativity to mix at large scales. The whole package could be called horizon mechanics. The word 'horizon' from relativity, the 'mechanics' from the quantum side. As a happy side effect, quantised inertia or horizon mechanics solves a lot of problems in physics that you may have heard of: it explains cosmic acceleration, predicts galaxy rotation without dark matter, and its redshift dependence, and predicts the emdrive. These successes should not be sneezed at, representing 96% of the cosmos, and with the emdrive practically offering a new kind of propulsion. Oddly enough, for a theory intended to replace general relativity, the behaviour I have just described looks quite tensor-ish..

References

McCulloch, M.E., 2016. Quantised inertia from relativity & the uncertainty principle, EPL, 115, 69001. ResearchGate preprint, arXiv preprint

## 14 comments:

Cool

Why would they be diamonds? Isn't it kind of an orbital of positional probability based on the ideal that the distance to the next object in that direction is influencing its momentum directionally?

Here's a new preprint of relevance...

Universal Properties of Centripetal Accelerations in Spiral Galaxies

James G. O'Brien, Thomas L. Chiarelli, Philip D. Mannheim

(Submitted on 12 Apr 2017)

In a recent paper McGaugh, Lelli, and Schombert (Phys. Rev. Lett. \textbf{117}, 201101 (2016)) showed that in a plot of the observed centripetal accelerations against those predicted by the Newtonian gravity of the luminous matter in spiral galaxies the data points occupied a remarkably narrow band. While one could summarize the mean properties of the band by drawing a single mean curve through it, we show here that the width of the band is just as physically significant. We show this by fitting the band with the illustrative conformal gravity theory, with fits that fill out the width of the band. We show that at very low luminous Newtonian accelerations the plot can become independent of the visible matter contribution altogether, with luminous matter not just inside individual galaxies but outside of them as well (viz. the rest of the visible universe) jointly producing the band.

The connection of uncertainty principle to particle mass looks most interesting for me. I'd recommend the review Nigel Cook's approach in this direction - he also utilizes projective geometry of sort for renormalization.

Congratulations Mike! Isn't this a big step forward for you? My previous understanding was that while you suspected something similar to QI could explain gravity, you hadn't nailed it down yet. Sounds like you have now - terrific!

Andrews: IMO key sentence from article IMO there is

..."let us imagine that the (Planck) masses within m and M are being buffeted

from all sides by particles from the zero point field and moving at random. The

net effect, forgetting horizons for a moment, will be zero.."

Where we could read about it first? Well, already in May 1693, when Nicolas Fatio de Duillier proposed an explanation of gravity in which an omni-directional flux of small particles permeates all of space and tends to push objects together because they mutually shield each other from this flux. According to David Gregory “Mr. Newton and Mr. Halley laugh at Mr. Fatio’s manner of explaining gravity”. His friendship with Newton abruptly ended this moment.

Dan: You are right of course: they are not quite diamonds. It's just the way I drew it in powerpoint. The reality is a smoother, more rounded shape.

/* This is very close to the mass of the electron measured in experiments */

Well - it should be even better, because the Compton wavelength of electron can be calculated just by using of electron mass and by anything else - or not? You wrote, that you neglected only term, which is by 38 orders of magnitude smaller than the first one - from where such a difference emerges? You somehow managed to lose an information during your algebra?

Peter: Thanks. It is not quite a complete system yet, there is still the issue of time.

Zephir: You're missing the overall. The agreement demonstrates a deeper paradigm: mass is caused by changes in how aware a photon is of its environment.

Can you elaborate on why this theory is "tensor-ish"??

3e: This is my first very vague attempt to embed QI in GR but in QI an object's movement is determined as horizons appear or dissappear around it changing its information about the world (releasing energy). As a result the inertial mass is not the same in different directions, and since we have an acceleration vector determining horizons and an inertial vector being determined by them, this needs a tensor representation. This looks a bit like GR in that whereas in GR objects follow the curve of spacetime, in QI their inertia varies with bent space (ie: horizons which are more observable). The difference is, and this is one way to think of it, very distant horizons are close to the cosmic one, reducing inertia in a new way for the low accelerations so QI can be thought of as being like GR at high acceleration, but with this cosmic boundary condition appearing at low acceleration.

Hi Mike,

Isn't this paper basically the same as your MiHsC theory?

https://arxiv.org/abs/1704.00780

tammor: It is not the same as quantised inertia, but it is getting closer. After someone else told me about this paper I emailed Lee Smolin to say that he should have cited me (I've sent him a few of my papers by email over the past few years) and he kindly replied saying he hadn't noticed them, but would cite me from now on. I hope he does and we can develop a working relationship. He'd be a great person to help to embed QI into GR, if that is possible.

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