I chose the title Physics from the Edge because the theory of inertia I have suggested (MiHsC) assumes that local inertia is affected by the far-off Hubble-edge. My webpage is here, I've written a book called Physics from the Edge and I'm on twitter here: @memcculloch

Tuesday, 18 October 2016

Strong evidence for MiHsC/QI

A few days ago Prof Stacy McGaugh kindly sent me the binned galaxy acceleration data they used in their paper (McGaugh, Lelli and Schomberg, 2016, see below) and I've been comparing MiHsC with it. The result is shown in the figure. To explain: the x-axis shows the log of the expected acceleration for stars within galaxies, g_bar. They looked at about 2693 stars, in 153 galaxies and calculated the expected acceleration using Newton's gravity law from the visible distribution of matter. Higher accelerations are shown to the right. The y-axis shows the acceleration of the stars derived from their observed motion, g_obs - a faster more curving path, means more acceleration. Higher accelerations are shown to the top. The data all lie between the two dashed lines, which represent the uncertainties in the values.

If Newtonian physics or general relativity were right without any fudging, then the two estimates of acceleration (g_bar and g_obs) would agree and you would expect all the data (between the two dashed lines) to lie along the dotted diagonal line. It doesn't. For low accelerations, at the edge of galaxies (on the left side of the plot) the observed acceleration is greater than Newton or Einstein predicted, which pushes the two dashed lines up away from the dotted line. This is the galaxy rotation problem. Stars at the edges of galaxies are moving so fast, they should escape from the galaxy, so dark matter is usually added to hold them in by gravity.

However, McGaugh et al.'s study showed that the acceleration is correlated with the distribution of 'visible' matter only, which implies there is no dark matter. Also, dark matter is an unscientific hypothesis because you have to add the stuff to galaxies just to make a theory (general relativity) fit the data and this is a bit like a cheat, especially since so much has to be added with no physical 'reason' for it (beyond saving a theory). Also it means you can't actually predict the motion of stars in a galaxy from its visible mass: you have to add the dark matter arbitrarily, and you can't double check you got it right because dark matter is invisible!

A slightly less fudged alternative is MoND (Modified Newtonian Dynamics) which is a empirical model that does not have an explanation, but fits the data if you set an adjustable parameter to be a0 = 1.2x10^-10 m/s^2. The MoND result is shown by the blue line in the plot. It works, but this is not surprising because the value of a0 is set manually to move the blue curve up and down on the plot so it fits the data.

The red line shows the prediction of quantised inertia (QI), otherwise known as MiHsC, which also fits the data (it is between the dashed lines). Now, this is surprising because MiHsC/QI fits the data without any adjustment. It predicts the observed galaxy rotation from just two numbers: the speed of light and the diameter of the cosmos. I should point out that in this work I am using the co-moving diameter of the cosmos 'now' which is 8.8x10^-10 m/s^2, see Got et al. (2005) and which I now think is correct, rather than the diameter when the light we see was emitted which is 2.6x10^-10 m/s^2. This latter is the value I used in my earlier papers, which means that the MiHsC flyby predictions will worsen, the predictions in my 2012 galaxy paper will improve and the MiHsC emdrive predictions are unaffected (there it depends on the cavity size). Nevertheless, this plot is evidence that MiHsC/QI is a very simple solution to the galaxy rotation problem (see also my 2012 paper). It also elegantly unifies quantum mechanics and relativity, predicts cosmic acceleration, and other MiHsCellaneous anomalies like the emdrive.


McGaugh, S.S, F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett. (to be published). Preprint.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, 342, 342-575. Preprint

 Gott III, J. Richard; M. Jurić; D. Schlegel; F. Hoyle; et al. (2005). "A Map of the Universe". The Astrophysical Journal. 624 (2): 463–484.

Monday, 10 October 2016

Star Trek, Birmingham

This is a more light-hearted blog than normal since I have just been to a Star Trek convention. I know that it is irrational (Star Trek is fiction), but I did enjoy it immensely, like the previous one. Why go? Well, although the people Trekkies come to see are actors, it's interesting to hear the back-story to episodes that you like, to meet people with similar scientific and moral interests, and also when the actors get up on the stage they often talk about the amazing ideas that science fiction writers have forced them to enact. Where else can you hear such ideas presented by passionate and humorous actors?

My friend and I first saw the dignified George Takei (Sulu), who talked about how in World War 2 the US interned even ethnic Japanese orphans, "What's so dangerous about orphans?" and how when his ethnic Japanese family were taken away to the internment camp their neighbours stole their stuff.

The Next Generation panel was a blast with Marina Sirtis who played Troy, Gates McFadden (Dr Crusher) and Will Wheaton (Wesley). Marina Sirtis was hilarious and was the opposite of her psychological 'careful what you say' Betazoid character, and kept dropping loud shock-bombs. When someone said 'When Gene Roddenberry left in 1991..' as if to give the impression that he'd abandoned Star Trek. Sirtis corrected him: 'Actually, he died'. When someone asked her to talk about Shatner's new documentary she said: "Why should I make Shatner richer than he already is!?".

Will Wheaton was in good form, having just rested up in Scotland. He used the collapse of the quantum mechanical wave-function in an analogy, very Big Bang, and when a fellow in a wheelchair apologised for not standing up, Will Wheaton told him not to apologise for something outside his control, which is common sense, but is very Star Trek. My friend and I also met some German Trekkies and we had a frank chat about the terrible corporate-rigged US-western system. Star Trek gives me the sort of feeling that the local church used to give me as a child, that I was with people who at least said decent things, with the huge added bonus that Star Trek is based on logic and science and so is endlessly interesting and makes sense.

William Shatner is always surprising. When I got him to sign something at a convention in 2012 I gave him a short speech about how I've developed a hypothesis that might make faster than light travel possible (see here) and how Star Trek was of course an inspiration, and he showed no interest in astrophysics and just said "You're very welcome". Yesterday, he would not shut up about astrophysics! He's been chatting to bigwigs like Machiu Kaku, DeGrasse Tyson and Stephen Hawking. Hawking apparently, through no fault of his own of course, took half an hour to ask Shatner a question, who was on tenterhooks thinking what profound question it would be, and it turned out to be "What is your favourite episode?". Shatner talked a lot about dark matter, though admirably he teased these three guys for not knowing what it was. I felt like standing up and shouting: "Dark matter does not exist (link) and I have a far better explanation for galaxy rotation!" (see here).

To mix healthy fact in with the science fiction, I was very glad that Al Worden was there too: the Apollo 15 astronaut who orbited the Moon. Worden said he was flying over the Moon one day and when he woke up in the 'morning' the craters looked awful big. He was concerned and phoned Houston who said "Yeah. You're a little close", "How close?" "31 km +/- 10 km" (or something). He then said in his pragmatic American way: "When people give you numbers in a circumstance like that, with a plus or minus after it, you pay attention!". That made me laugh, because I'm always trying to get my students to use error bars. I can use that story in class.

Wednesday, 5 October 2016

Gravity from Quantum Mechanics

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:

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 publish it, even though it had been accepted 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.


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

Saturday, 24 September 2016

MiHsC/QI vs New Galaxy Data

It is crucial to pay close attention to new data, and observational astrophysicist Prof Stacy McGaugh has a habit, like John Anderson, of writing nicely concise analyses of new data that are easy to test against. McGaugh, Lelli and Schombert have just published a paper comparing the data from 153 different galaxies across a large range of scales from dwarfs to large disc galaxies, looking at two things 1) the acceleration within them as predicted using standard dynamics from their baryonic (visible) mass only (g_bar, x axis in the Figure), and the actual acceleration as determined from the observed motion of their stars (g_obs, y axis). The result is shown on a log-log plot here (from McGaugh and Lelli, 2016):
If Newton or Einstein's general relativity were right (without the crutch of dark matter) then you would expect the data to lie along the faint straight diagonal line, so that the predicted acceleration would equal that observed. It does not. As you can see the data lifts from the straight line on the left hand side because for lower accelerations the stars' orbital speed, and therefore acceleration, is greater than expected. This is the famous galaxy rotation problem noticed by Zwicky (1933) and Rubin & Ford (1980). The majority of astrophysicists fix this by adding dark matter to the galaxies where it's needed, but that is an ad hoc solution that no-one should have to resort to in a scientific age. In the paper, McGaugh and Lelli fit a curve to this data using this formula
and show it predicts well if the fitting parameter 'gt' is set to the value 1.2x10^-10 m/s^2 and both McGaugh and Lelli, and Milgrom in a note published soon after, say this looks like some of the possible variants of MoND (Modified Newtonian dynamics). Milgrom in his note even says 'nothing else can give this behaviour' but this is simply not true. MiHsC / quantised inertia also predicts this behaviour far more plausibly and simply than MoND, and without any adjustment at all. The MiHsC formula can be found in McCulloch (2012) (see Eq. 6 in the ref below, and note the comments on a' therein. The Eq. I showed before is based on Eq. 7 and is less general). The MiHsC formula (note, only strictly valid at a galaxy's edge) is
This formula is based on a specific physical model (MiHsC: Unruh waves harmonise with horizons and cause inertia) unlike MoND which is just an empirical relation with no physical model. It is obviously much simpler than McGaugh & Lelli's formula, and crucially there are no fitting parameters in MiHsC/quantised inertia at all! Its predictions of g_obs are exactly right see Figure below and are predicted from just the known quantities of the speed of light (c) and the size of the observable universe (Theta=8.8x10^26 m):

I do feel a bit like a broken record going on about this, but it's necessary because it has not yet been widely appreciated that a theory that predicts real data without any fitting parameters, like MiHsC does, is like a diamond in the mine. Like special relativity, it is a sign of something fundamental.

(Note: MoND is a bit like the early twin patchwork formulas of Wien & Rayleigh-Jeans for blackbody radiation, whereas MiHsC/QI is like the quantum mechanics of Planck et al. which predicted it more concisely with a shocking new assumption).


McGaugh, S.S, F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett. (to be published). Preprint.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, 342, 342-575. Preprint

Monday, 19 September 2016

Unruh Radiation Confirmed?

One of the criticisms of MiHsC (quantised inertia) is that "it relies on Unruh radiation which has not been seen". The fact that MiHsC predicts a whole range of important anomalies is some evidence for its use of Unruh radiation, but it is not direct evidence. In this blog entry I'd like to show you why I'm fairly confident that Unruh radiation has also been directly detected, based on papers by Beversluis et al. (2002) and Smolyaninov (2008).

Unruh radiation is usually difficult to see, to put it mildly, because its wavelength is L=8c^2/a, where a is acceleration and c is the speed of light, so for a typical acceleration of 9.8 m/s^2 the wavelength is eight light years. You'd have to wait eight years for the wave to pass by and be confirmed. It would make for a nice quiet sinecure, but there is a quicker way to see them. The formula shows that to produce Unruh waves near the more familiar EM spectrum you need to increase the acceleration, hugely!

This was done unwittingly by Beverluis et al, 2002. They shone a 780 nm laser at a gold nanotip, a very sharp pin if you like, so that the 'plasmons' (quantised waves of free electrons) formed had to travel over the very sharp tip (radius of curvature, r=10^-6 m) at a very fast speed (v) and were therefore accelerated by

a = v^2/r = c^2/10^-6 = 9x10^22 m/s^2.

They noticed an anomalous photoluminescence from the nanotip with a wavelength of about 900 nm (see the Figure below, from Beversluis et al., 2002, which shows the intensity of the radiation emitted on the y-axis, as a function of wavelength, on the x-axis. See the peak at 900 nm). Beversluis et al. proposed a complex 3-stage process to explain it but also stated that each step was implausible.

Enter Smolyaninov (2008) who claimed that their suggested 3-step process for explaining this 900 nm radiation was indeed implausible, and showed how the conversion of 780 nm laser light to 900 nm photoluminescence could be due to Unruh radiation instead. It works as follows: the 780 nm laser light impacts the gold surface and creates 'plasmons' (quantised waves of free electrons) which zoom around the sharp bend at the tip (this is well known). The plasmons' acceleration generates Unruh waves of wavelength L = 8c^2/a = 8000 nm. The newly-incoming laser photons excite the gold molecules and normally they'd then drop back to the ground energy state and emit the same frequency photon (Rayleigh scattering), but the ground state is now higher because of the Unruh excitation so the molecules don't lose as much energy as they gained, and the light they emit now has a lower energy (a longer wavelength). In more typical, non-Unruh, cases this is called Raman scattering and is usually undetectable, but for rough surfaces it can be enhanced (a well-known process called Surface Enhanced Raman Scattering, discovered first by Martin Fleischman in 1973, well before he co-discovered cold fusion / LENR). So the emitted light has a lower energy and frequency as follows:

f(emitted) = f(laser) - f(Unruh)

Replacing frequencies with wavelengths, L, given f = c/L

c/L(emitted) = c/L(laser) - c/L(Unruh)

L(emitted) = 1/(1/L(laser)-1/L(Unruh)) = 864 nm.

This predicts the emission of light of wavelength 864 nm (or above, from the less curved parts of the nanotip), which agrees with the observed anomalous photoluminescence seen by Beversluis et al. of around 800 nm and above (see figure) and so this is good evidence that Unruh radiation has been indirectly seen, since other explanations have been implausible, so far.

This interests me not only because it provides more direct evidence for Unruh radiation, but also that it implies that Unruh waves, seen only in the reference frame of the accelerated object, can cause directly testable effects in the laboratory frame, and this makes me wonder about sonoluminescence (which MiHsC predicts) and LENR (which it doesn't yet, but might if high accelerations are involved).

One way to confirm that this experiment shows Unruh radiation would be to vary the curve of the nanotip and see if the emitted wavelength varies as expected (for example, a spherical nanotip, of uniform curvature, with a cylindrical stem should show a narrower Unruh-peak). Another more direct test of MiHsC (quantised inertia) itself would be to try to interfere with these shorter Unruh waves by shielding them, to see if the plasmons' inertia (trajectory) is affected.


Beversluis, M.R., A. Bouhelier, L. Novotny, 2003. Continuum generation from single gold nanostructures through near-field mediated intraband transitions. Phys. Rev.B., 68, 115433.

Smolyaninov, I.I., 2008. Photoluminescence from a gold nanotip in an accelerated reference frame. Preprint

Wednesday, 14 September 2016

MiHsC: from Hubble scale to Emdrive

A comment on my previous blog entry (by qraal) pointed out something that is obvious to those familiar with MiHsC, but needs to be more widely known: MiHsC does not just predict galaxy rotation like other models (eg: MoND and MOG) but, as I've shown in my papers, it can explain many other eclectic (varied) anomalies that have been seen, from cosmological scales right down to the lab scale (emdrive).

As an introduction for those who are new to this blog. Unruh radiation is like Hawking radiation but is predicted to be seen only by accelerating objects. Its wavelength gets longer as accelerations reduce. MiHsC says that the long-taken-for-granted property of inertial mass is caused by the relativistic Rindler horizon that opens up behind objects when they accelerate. This horizon then damps the Unruh waves on that side but not in front, thus making a radiation pressure that resists the original acceleration and causes humans to say 'that's inertial mass'. This force is also weakened when objects have tiny accelerations because the Unruh waves get long enough to be damped by the spherically symmetric Hubble horizon leading to a new prediction: a weakening of inertia at very low accelerations. MiHsC is encapsulated by the equation below, which is an approximation to the real process of Unruh waves being deselected by horizons

where mi is the inertial mass, mg is the gravitational mass, c is light speed, |a| is the magnitude of the acceleration of the mass and the Theta is the Hubble scale (2.6x10^26 metres). The good thing about this equation is that it is inevitable, being based on an intuitive physical model and all these quantities are well defined and known, so any agreement with data that I talk about here has not occurred because I've 'tuned' the model. The model can only make one prediction, which happens to agree with nature.

On cosmic scales MiHsC correctly predicts the recently observed cosmic acceleration. This drops straight out when you put the above formula for mi into Newton's 2nd law and gravity law. You can try it yourself! At the same scale MiHsC predicts the recently-observed unexpected smoothness of patterns in the Cosmic Microwave Background (the so called low-L CMB anomaly). The Hubble horizon is damping long waves.

MiHsC predicts the rotation of all galaxies from tiny dwarfs, through discs to galaxy clusters, and just from the equation above, whereas MoND has to be 'tuned' by parameter a0, and dark matter has to be packed-in differently for each galaxy to make the rotation curve fit general relativity. MiHsC also predicts why the oddities start when accelerations go below a particular value: the Hubble horizon then starts deselecting the long Unruh waves (see diagram below).

MiHsC predicts the Pioneer, Galileo and Ulysses anomalies, with its weakening of inertial mass at low accelerations. The Pioneer anomaly has been also explained by a complex thermal model, but the emphasis here being on complex.. I distrust complex adjustable models. MiHsC predicts the flyby anomalies, close, but not perfectly, as being due to the weakening of inertia since mutual accelerations between passing spacecraft and the spinning Earth are lower near the poles, reducing the inertia mass of the craft and by conservation of momentum (mass times speed) boosting their speed.

It predicts the anomalous effects seen by Tajmar when he spun a supercooled disc and noted that a nearby accelerometer moved slightly with the disc (with no frictional contact).

It predicts the Emdrive, a truncated metal cavity with microwaves inside, which, In MiHsC, is rather like joining a big cosmos (the wide end) which allows more Unruh waves (more inertia) to a small cosmos (allows fewer waves, less inertia) so that objects, microwave photons in this case, going from the small end to the big end gain mass (ie: the mass shifts rightwards, see diagram) so to conserve momentum (mass x speed) the cavity has to go the other way, as it does. The numbers agree with the data quite well.

This list represents successes from a cosmic scale of 10^26 metres, right down to the lab scale of a 0.1m! I'm now working on the proton radius anomaly which may give me another 10 orders of magnitude of scale. I should say also, that MiHsC reduces to the standard model for high accelerations (in the equation above hen a is huge then mi = mg, the famous equivalence principle) so it is not contradicted by any empirical data.

MiHsC can also be called quantised inertia, which is a more accessible name. Another possible name is 'horizon mechanics', which was suggested recently by someone who's read my book: John Michael Dorman. More theoretically, it is another step consistent with the history of science, which has always progressed by debunking invisible quantities, like the Greek gods (Thales), epicycles (Newton), the aether (FitzGerald, Einstein). Now we can jettison dark matter (well, most of it). MiHsC also links together relativity and quantum mechanics in a natural way.

Mathematically, MiHsC is not complete, instead of the equation above, it ideally needs a formula to describe exactly how Unruh waves are allowed or disallowed by horizons of a complex shape, and then how the remaining Unruh waves push the object around. There lots of scope for mathematicians here..

Experimentally, the best way to prove MiHsC would be to try and accelerate an object so much that the Unruh waves it is assumed to see, become small enough (they're usually light years long) to be interfered with by our technology. For example if you set up a spinning disc or resonate light within a cavity, and then block the Unruh waves on one side only, MiHsC predicts the object should move towards the blockage.

Tuesday, 6 September 2016

A marriage of relativity & quantum mechanics

I'm often accused of being a radical, but I'd like to point out that MiHsC is actually far less radical than dark matter. Consider dark matter. Its supporters believe that 96% of the universe is in the form of a new and invisible form of matter and energy that has a weird structure, as dark matter for example must cling to the edges of galaxies and stay away from their centres, so it needs an entirely new dark-sector physics to explain it.

In the meantime, MiHsC says only that we need to fully accept both relativity and quantum mechanics and therefore the horizons and Unruh waves that they have already predicted and, here's the crucial new bit: assume that inertial mass (never understood before, and Higgs only predicts 0.01% of it) is caused by the Unruh waves being modified by the horizons. The result is a dynamics far better than the usual one since it predicts all dwarf galaxies, spirals and clusters without any tuning, whereas the dark matter hypothesis needs a new type of matter and its physics to be added, and a different amount for each galaxy. This is why it is strange that dark matter-ists accuse MiHsC of being a weird theory out of the blue. The pot calling the kettle black.

MiHsC is simply a particular marriage of relativity and quantum mechanics that happens to predict inertial mass. Of course, people have been trying to marry these two theories off for a long time and have failed because they didn't want to break the equivalence principle or they worried about non-locality, but these breaks are theoretical and not necessarily forbidden by experiment.

The bride (quantum mechanics) and groom (relativity) were first introduced to each other by Hawking, Fulling, Unruh and Davies who predicted Hawking-Unruh radiation. People like Jennison, Milgrom and Haisch and Puthoff offered hints but without a plausible method. I disliked the complexity of the arrangement and suspected there was actually a baby coming (a better model of inertial mass), got my shotgun and rammed the two theories together, and damn the consequences. I've been able to continue because all the consequences that were feared for decades turn out not to disagree with experiment and in fact they predict many of the anomalies that the dark sector was invented to fudge. It just shows that sometimes you just have to suck it and see.

To make this point even more simple mathematically than before, I've recently submitted a paper showing I can derive MiHsC (with an annoying factor of 1.26 probably caused by my simplification of the shape of the Rindler horizon) in 10 lines just from Heisenberg's uncertainty principle and special relativity, similar to my approach to gravity in 2014 (see ref). So I'm just waiting patiently for the standard first rejection...


McCulloch, M.E., 2014. Gravity from the uncertainty principle. A&SS, 349, 957-959. Video