I feel like I am now entering the end game, which probably just means my troubles are just beginning. For a while now I've had a theoretical goal that can be boiled down to two things:

1) Reproduce the bending of light by the Sun, just like general relativity.

2) Retain the ability of quantised inertia to predict MoND-like behaviour in galaxies.

It was Alex Unzicker's books (especially "Einstein's Lost Key") that convinced me that the best way to do this would be to focus on a curious path followed by Einstein in 1911-1912 just before he was persuaded away into untestable geometry by Marcel Grossman. While in Prague Einstein devised a version of GR that treated space as if it had a refractive index. The idea was that the speed of light c=fL reduces close to masses because relativity reduces both f (frequency) and L (wavelength) there, and so light beams bend around the Sun twice as much as Newton would have predicted. Unfortunately, at the time he forgot the reduction in L and predicted only half the correct bending of light. This error was corrected by Dicke in 1957 but by then it was too late and the later geometrical-tensor GR had taken over because it was not stymied by the factor of two error.

To agree with the data on light bending by the Sun (data: the only important consideration), the correct theory must predict this equation for the speed of light c a distance r away from a mass M:

For a lot of last year, on and off, and for several weeks this year I have been trying to get this relation from QI. I did it last year and rejected it for various intuitive reasons. Last week I did it again and realised that it was the right way! The solution is obvious and beautiful in a way that cannot be explained until you actually see it, but it's not published yet so I can't tell you the whole story.

What quantised inertia says is that the zero point field (and its energised version: Unruh radiation) close to matter is damped (reduced) so light bends towards the matter, sliding down the zpf gradient. This gives Newtonian gravity (see my 2013 paper), but in QI we also have to consider the cosmic horizon of the light which reduces the inertial mass of the photons even more than expected so they bend towards the Sun twice as much as expected. It all works out nicely and gives the equation above. The great advantages of the new QI dynamics are that it gets rid of dark matter, it predicts cosmic acceleration and practical thrust and, unlike bent space which cannot be directly tested, it could be directly tested by measuring the zpf in different places with, say, a Casimir probe.

Given the lab results that are starting to come in (see my blog last month) and this latest theoretical result I expect breathless requests for zoom presentations will come flooding in from physics departments all over the globe! (I always like to end on a humorous note).

**References**

McCulloch, M.E., 2013. Gravity from the uncertainty principle. Astrophys & Space Science, 349, 957-959. Link to Pdf

Unzicker, A., 2015. Einstein's Lost Key.

## 9 comments:

One immediate question I would ask is does your theory predict the same time delays seen in gravitational lensing of quasars by foreground galaxies as GR? If it doesn't, then that would imply different values of H0 and/or the lensing mass distribution to give the observed results. Kochanek (2002) derived the results for GR: https://iopscience.iop.org/article/10.1086/342476

Here are some questions which a reviewer may well ask (unless they are already addressed in the preprint):

1. How do you explain the results of LIGO? Surely the speed of light along both interferometer arms is identical as they are both resting on Earth. If space is not compressed and rarified what causes the fringes?

2. Can you reproduce the perihelion precession of Mercury?

I just became aware of the

othertype of gravity from GR, the gravitomagnetic field... which is only caused by mass in motion, and results in frame dragging, etc.I'm no physicist, but how does that fit into all of this? Recently this new (to me) gravity was used to possibly explain away dark matter.

Mike,

A quick comment on, "Dark Matter":

When a concept does not derive from logic it is hard to refute, as you have been trying to do, using logic. What is more likely to succeed is to use rhetoric, the basis of "Dark Matter", to slay the beast. In that vein I would simply recommend that the term "Dark Matter" be referenced by its equivalent definition, "Fictitious Matter" or more in keeping with a similar politic problem of this day, "Fake Matter".

Trying to use logic against rhetorically derived self serving concepts has little probability of succeeding. The gestalt shock of hearing the "Fictitious Matter" might just jar loose any brain cells in the pious proselytizers for "Dark Matter". This, call it what it is technique, has certainly been successful in the political arena in awakening the people about the real nature of the "News Media".

Keep up the good work,

Jimmy Johnson

Jimmy. Thank you for the advice. As you will see, if you look at my twitter, I am now using 'fakematter' as you suggested. Let's see if rhetoric beats logic.

Mike Warot. Thank you for your comment. I've seen the paper attempting to explain galaxy rotation with gravitomagnetism. A quote from the paper that shows this is just another fudge: "the velocity profile is a function of the 3 free parameters a, b & rs. These parameters can be varied so that β(r) fits the observed galactic rotation curve". In contrast, QI works without fudging.

Mike - I've previously put forward the idea that it's the progressive slowing of time in the vicinity of a mass that results in the effect of gravity. If you consider a plane wave passing by a mass, then there is is a time gradient with the wave closer to the mass being slower and with a shorter wavelength. The wave is thus deflected simply by the time gradient. Your equation cr/cinf = 1-(2GM/rc²) can thus be used to define the rate of time slowing, or alternatively maybe the matter-wave density if we assume that time is slowed proportional to the matter-wave density. That matter-wave density suddenly hits zero at the Hubble radius, though, so in fact c(infinity) should really be replaced with c(Hubble radius) instead. Outside that radius we can't define c and we have no way of knowing it either.

Being able to derive the same relationship via different methods is useful. It may not tell us which is the more-fundamental explanation of the effects, but at least gives the feeling that things hang together and that the relationships are likely to be true.

Your gravity derivation predicts an abrupt drop-off of particles above the Planck mass, and that particles below that mass are not gravitationally attracted. This seems to clash with the experiment using individual neutrons in a gravitational field (Nevizhevsky et al, 2002). Also it seems photons do see an attraction on their mass as well as the wave-deflection above. Also note that Einstein's equivalence principle is shown to be false by the extra deflection of a photon in a gravitational field as opposed to a frame acceleration. Can't get away from some paradoxes yet.... Another paradox with Unruh waves is that an infinite-velocity wave cannot exist as a wave, since it would be the same phase at each point and thus has no wavelength either.

I figure with the paradoxes they'll get solved, and in the meantime if the equations work out and the experiments work then we're on the right path. It seems likely that infinities do not actually exist, so equations with infinities in are a bit wrong. Thus there may be a few Planck-time delays in those waves in reality, but we can't measure them.

Normally, the horizons are equidistant. Your experiments break that symmetry, and bring one a lot closer. Break the symmetry, and you break the conservation law that results from that.

Sorry to bring half-formed ideas to the party, but maybe it helps in that someone can push them the rest of the way.

Another tact you could use as opposed to "fakematter" is to join in with the fakery. QI is the latest dark matter candidate. It requires no new particles and is the only dark matter candidate that has any positive lab results. Dark matter has finally been found and it's been right in front of us all this time! Becoming a dark matter candidate will make getting published much easier and you can get millions in funding.

Mike - maybe an interesting point about the deflection of a photon in a gravitational field. Assuming that the effective mass of a photon also produces a gravitational force, then the force times time this exerts on the mass is half the momentum change of the photon, and so momentum is not conserved in gravitational bending of the path of a photon. If we assume instead that the photon's effective mass has no gravitational effect, the violation of CoM is twice as much, since the momentum of the photon is changed without affecting the momentum of the matter creating the gravitational field.

I wonder if anyone else has noticed this blatant violation of CoM?

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