I've suggested a new theory for inertia (called quantised inertia or MiHsC) that assumes that inertia is caused by relativistic horizons damping quantum fields. This simple theory predicts galaxy rotation and cosmic acceleration without any dark stuff or adjustment of any kind.
My Plymouth University webpage is here, I've written a book called Physics from the Edge and I'm on twitter here: @memcculloch

Thursday, 8 December 2016

Notes on EMdrive and MiHsC

Here are some notes that I made (to anticipate likely questions) to prepare for a radio interview on the EMdrive and MiHsC that was recorded yesterday (it was Hotel Mars with John Batchelor and David Livingston). Most of these I did not use. I will post the podcast here when it comes out.

What is the emdrive?

The emdrive is a truncated-cone made out of a copper shell with microwaves resonating within it. A bit like a microwave oven built into a metal megaphone. Roger Shawyer from Britain & Guido Fetta from Italy discovered that such a thing moves slightly towards its narrow end. The thrust is tiny: ~1mN per kW so the acceleration is on the order of 0-60 mph in 3 days, so it won't be on The Grand Tour anytime soon, but the crucial thing is that it accelerates without expelling propellant, an ability that gets rid of the need to carry heavy fuel and therefore revolutionises the prospects for interplanetary/interstellar flight.

Why is it controversial?

It is the equivalent of moving your car by sitting in it and pushing on the dashboard. Physics disallows this because if you push forward on the dashboard, your backside pushes back on the seat and the two forces cancel. This is due to the conservation of momentum, which has never been seen to be broken before. Physics says you can’t move unless you leave something behind. If you throw your shoe out of the back of the car then the car (if the brake is off) will move forward, because you expelled something. That is how rockets work. The emdrive does not expel anything so physics says it shouldn’t move.

Why is it important?

It violates a central part of physics (the conservation of momentum) which has never failed before, so if it is confirmed physics will need a radical change (see below). Also, the applications are huge: hovercars, launching without rockets, new energy sources from apparently ‘nothing’, and interplanetary and interstellar travel becomes practical because this engine works without having to carry heavy fuel.

How many groups have tested it?

UK. Shawyer, 1999-. Many experiments have been done. Several reports have been published on the SPR website.
China. Juan et al., 2012. They got a larger thrust than Shawyer, but later found an error, and their recent results are null, but consistent with the other results since their apparatus is unable to measure the likely thrust.
Italy. Guido Fetta, 2014. The Cannae drive has a much flatter shape, but they also found positive thrust.
Germany. Tajmar et al., 2015. They also saw a thrust, but the emdrive also thrusted when upright, which needs to be looked into.
US. NASA, 2014. Tested positive for thrust, but in air.
US. NASA, 2016. Tested positive in vacuum and published a peer reviewed paper.

What is different about the new NASA paper?

1. NASA tested the emdrive in a vacuum. One of the earlier criticisms was that the thrust was being caused by air currents. This is obviously now ruled out since they saw the same thrust in a vacuum.
2. It is a peer reviewed, checked by other scientists. Most of the experimental papers on it before this have been conference reports, not subject to the same rigour. It was apparently a very long and difficult process too, so Dr Howard White of NASA should be commended for having the courage to do this in the first place, and for his hard work through peer review.
3. It is NASA, so it has raised the profile of the emdrive.

The NASA emdrive results (see the recent paper) are interesting because they get weaker thrusts than everyone else so far, and also they tend to put dielectrics in the narrow end of their cavity. Quantised inertia predicts that the dielectric should thrust the other way, cancelling the force due to the taper of the cavity. I need to look into this in more detail.

So what is your suggestion?

I can use an analogy with ships at sea. Usually waves hit ships from all around so they don’t push them on average, but if you put two ships together there’s a sheltered zone between them, so suddenly more waves hit the ships from outside then from between them, so they move together. If the crew don’t know about the waves they’ll think it odd, like physicists think the emdrive is odd.

Quantum mechanics predicts there’s a quantum sea all around us called the quantum vacuum and the Casimir effect and Lamb shift have proven its existence. Relativity predicts that when objects accelerate, information horizons appear in the opposite direction to the acceleration vector, since information cannot catch up to the object from behind that horizon, and relativity has been tested. I’ve suggested that relativistic horizons damp the quantum vacuum, just as the ships damp the sea waves, making a void that pulls the objects back against their acceleration. This model, called quantised inertia or MiHsC, predicts the old property of inertia (which suppresses accelerations). It also predicts galaxy rotation exactly without dark matter or any adjustment and cosmic acceleration. I have published 12 papers on this and a book called ‘Physics from the Edge’.

Quantised inertia can model the emdrive too because it allows more quantum waves to exist at the wide end of the cavity so microwave photons that go to that end gain inertial mass, they’re heavier. This is like a rocket expelling mass at the wide end. Another way to think about it is that the microwaves’ centre of mass is continually being shifted towards the wide end, so the emdrive cavity itself moves towards its narrow end to conserve momentum.

An analogy is a person on a ship who keeps walking from the front to the back. Every time he goes to the back he picks up a weight from the deck. This moves the centre of mass of the ship backwards, so the ship has to move forwards slightly to conserve momentum.

What is MiHsC/QI in a nutshell?

A summary: quantised inertia says that relativistic horizons damp the quantum vacuum, making it non-uniform, creating new forces.

A poem: Go to the right, the left’s out of your sight. A horizon appears, damps zero point fields, dragging you back. Inertia is that!

What has been the response of the scientific community to MiHsC?

They have mostly ignored it, so far. Two criticisms they have made are that the Unruh radiation (quantum vacuum) I’m using has not been seen, but it is a widely-accepted prediction akin to Hawking radiation and may have been seen in experiments recently. The second criticism is that I’m varying the speed of light in the vacuum, but this is not so serious since special relativity only demands that light is emitted at a constant speed, c. Apparent speed of light changes happen in general relativity all the time but are explained away with bent space. Also, NASA tests may have shown light changing speed (space bending) in the cavity.

Interest is growing and a few people are now working with me: including Dr Jaume Gine who recently worked with me on this paper, and Prof Perez-Diaz who is a very capable experimenter. He recently visited me and we designed some experiments, including the LEMdrive, that he is now doing.

What other theories are there?

Many people have said there must be an experimental error, but no one has suggested an error that fits the data. For example, the heating/expansion of the cavity can offset the centre of mass and make the cavity move to conserve momentum, but that and other errors were calculated in the NASA paper and found to be too small.

Roger Shawyer has a theory that uses special relativity to explain it, and while I respect him for the experimental emdrive discovery, I don’t accept his theory because relativity should also obey the conservation of momentum. The emdrive does not.

Grahn, Annila and Kohlemainen from Finland have an interesting idea that photons in the emdrive are pairing up and cancelling each other out, so they can leave the emdrive undetectably through the wide end, pushing it towards the narrow end. However, this theory relies on many assumptions and ‘invisible stuff’ and I haven’t seen a comparison with data yet.

In their new paper, NASA propose that the particles in the quantum vacuum are ‘real’ (a non-standard view due to David Bohm) so that sound waves can exist in the quantum vacuum and it can act as a momentum sink. An interesting approach, but again it is adjustable and complex so it’s easy to get the right answer for the wrong reason. Also, I’ve not seen a comparison with the emdrive thrusts.

What’s Next for the Emdrive?

It has been given a boost by the positive NASA test, and I admire the NASA Eagleworks people, eg: Dr Howard White, Paul March and others, for having the curiosity and courage to test it.

The next step is that universities need to get involved and perform rigorous tests, and do some crucial experiments, that those who have theories can suggest.

There should also be a test in space. The Earth is a messy environment, and you never know what electromagnetic forces might be around. In space, it’s cleaner. Guido Fetta aims to test an emdrive in space using a 6U cubesat (small satellite), possibly in 2017. It’ll have a solar panel to power it and be pointed narrow end up, so if it stays in orbit longer than expected that’ll be a sign that it is thrusting upwards. If it works, it’ll change the satellite industry completely.

Also, the quality factor of the cavity is a crucial parameter. This is the number of times microwaves can bounce around inside without being absorbed. So Guido Fetta and Roger Shawyer are now trying out emdrives coated inside with a superconducting layer, because they have much better Q factors: far more photon bounces.

Cannae has also proposed a deep space probe, that uses 10 em-/Cannae-drives powered by RTGs to accelerate at 8.66x10^-3 m/s^2 from low Earth orbit to Sol escape velocity in 2 months. It could travel 0.1 light years in 15 years (1.35% c). This could be the first interstellar probe. To do this with a rocket you would need to carry a Ceres-sized amount of fuel.

Isn’t there a suggestion that dark matter can predict the emdrive?

Someone wrote a blog saying it could be dark matter. But, dark matter is an awful hypothesis. It has been forgotten that in 1980 or so physics failed to predict the newly-observed galaxy rotation: they rotate so fast they should explode, but don’t. Instead of changing the theory, they added ten times as much dark mass to galaxies as there is visible mass, to hold them in by gravitational force, but they have to add it by hand to each galaxy differently. Some galaxies are 92% dark, some are 99.3% but there’s no reason behind these numbers, and dark matter is not falsifiable: if your multimillion pound experiment can’t find it, you can say “OK, maybe it’s in this other more difficult regime” and that can go on for ever. In the same way you can glibly say "dark matter drives the emdrive" but until you point out a specific process that can be tested or falsified it is meaningless hand waving. In contrast quantised inertia predicts all galaxies (and the emdrive) without any adjustment, and Unruh radiation is something that can be looked for in one place and is either there or not. It is falsifiable.

Is the emdrive a warp drive?

No, it’s not based on Alcubierre’s warp theory, but I’m suggesting that the speed of light changes within it. This can happen in relativity if you bend spacetime to make sure the change in c is not measurable to an observer, so maybe space-time is bending in there. NASA found something like that when they fired a laser through, but couldn’t quantify.

Do you think the emdrive is really anomalous?

Yes. Of course there is always doubt in science, but as Captain Kirk says in the film Star Trek: Generations "You have to take some risk if you want to sit in that chair", and the emdrive has now been successfully repeated in 4 independent labs. So you have to pay attention to that. It's vital in science to value new observations over old theories.

Concluding thought?

It’s a time to be excited: anomalous observations such as galactic rotation, cosmic acceleration, the flyby anomaly, the emdrive and many others are forcing a rethink of physics. In my opinion they are all telling us that mass-energy can be created from information horizons, this is the basis of quantised inertia, and the theoretical and practical implications are huge. I’m hoping now that universities will get involved in tests.

Monday, 28 November 2016

Emdrives & dielectrics: the NASA shift

The NASA paper further supporting the previous emdrive experiments (in which a microwave-filled conical cavity moves towards its narrow end without expelling anything, as standard physics says it just shouldn't do) has finally been published. Apparently Eagleworks had a terrible time publishing it, so well done to them.

It is interesting that all the NASA results are anomalous in comparison with results from the other teams: Shawyer's, the Cannae group and Tajmar's. The plot below shows the thrust predicted by quantised inertia (MiHsC) on the x axis, and the y axis shows the thrusts observed in the lab. It would be great if all the diamonds representing the different emdrive experiments were along the diagonal line (a perfect agreement). The Shawyer, Cannae and Tajmar experiments are, but the NASA experiments are all shifted rightwards. This shows that MiHsC over-predicts the thrust for NASA's tests by a factor that can be as much as ten.
I may have an explanation for this. MiHsC predicts the emdrive's thrust by saying that the inertia of the microwave photons is caused by Unruh radiation (a radiation you only see if you accelerate). At the wide end of the cavity more Unruh wavelengths fit within, and are 'allowed', due to the bigger space available, but at the narrow confined end fewer are allowed (as for the Casimir effect). Thus, MiHsC is continually shifting the photons' collective centre of mass towards the wide end so that to conserve momentum the cavity has to shift the other way, as indeed it does, but more slowly as it is far more massive than the microwaves (more detail).

A new possibility to explain NASA's anomaly within an anomaly (the NASA shift) is as follows. Most of the NASA experiments, including the latest one, put a dielectric at the narrow end of the cavity. A dielectric means that Unruh waves will be slower and have shorter wavelengths, and so more of them will fit at the narrow end. MiHsC therefore predicts that having a dielectric at one end is rather like widening that end, and if you put it at the narrow end, then you reduce the taper and reduce the thrust.

I've already worked out some of the maths for dielectrics, after I read an interesting, but inconclusive, 2016 report by a group at CalPoly (Kraft and Zeller, 2016) who tested a cylindrical emdrive with a dielectric at one end. I just need to account now for both a dielectric and taper and see if the numbers fit the NASA shift.


McCulloch, M.E., 2015. Testing quantised inertia on the emdrive. EPL, 111, 60005. Preprint

K. Zeller and B. Kraft, 2016. Investigation of a partially-loaded resonant cavity. CalPoly research report.

White, H., P. March, J. Lawrence, J. Vera, A. Sylvester, D. Brady, P. Bailey, 2016. Measurement of impulsive thrust from a closed rf cavity in vacuum. AIAA J. of Propulsion and Power. Online

Monday, 21 November 2016

Experiments with balls: the mystery of big G

I've written a few blogs of late, showing how quantised inertia (MiHsC) predicts galaxy rotation and other things perfectly without adjustment, but to avoid sounding like a advert I also want to talk about the new things I am puzzling over. So this blog entry will be a bit messier, but perhaps more fruitful.

I've mentioned before that the gravitational constant (big G) is in trouble. Well, it still is. I recently read an interesting paper on this by Norbert Klein (see references) who analysed two of the recent experiments to measure big G in light of the galaxy rotation problem. The experiments typically measure G using a development of the Cavendish experiment. For example Quinn and Speake (2014) suspended four 1.2kg masses arranged in a circle radius 120mm (see the 4 small balls in the diagram below) from a fibre (the vertical line) and then put four much larger masses (11 kg) on a 214 mm radius circle around them, and then rotated this outer circle by 18.9 degrees so that the tiny gravitational force between the four pairs of masses twists the inner arrangement, so that they can work out from the twist what the force is. Since they know the masses M and m, the force F and the distance (r) very well they can work out G from Newton's gravity law: F=GMm/r^2.

The trouble is that the two different values of G they found disagree by more than the uncertainty in the experiments! Which they just can't do, unless something 'unknown' is going on. Schlamminger measured G=6.674252x10^-11 m^3kg^-1s^-2 and Quinn and Speake found G=6.67545x10^-11 m^3kg^-1s^-2. The observation that got me excited was that Norbert Klein, in his paper, points out that in the Schlamminger experiment (the low G value) the gravitational acceleration between the two balls (if they'd be free to move) was relatively high, but in Quinn and Speake's experiment (the high G value) it was very low.

This agrees with quantised inertia since a low acceleration should mean the small ball has lower inertial mass and so is more sensitive to the large ball, so it should 'appear' that G is bigger, as indeed Quinn and Speake found. I have done a rough calculation assuming the mutual acceleration is four times the gravitational acceleration between each pair of balls (there are four pairs), and quantised inertia predicts that the apparent change in G divided by G (dG/G) should be 11.3x10^-4 whereas Quinn and Speake measured a change from the standard value of G of dG/G=3x10^-4.

The prediction is a factor of 3.8 out, but there are large uncertainties in the calculation. For example, what is the correct acceleration to plug into MiHsC/QI? Is it, as I have assumed, the along-inner-circle component of the acceleration that the small mass would have towards the bigger one, times four? Does the rest of the environment contribute? How about the curve of the ball around its circle as it moves? That is an acceleration too. Also, what is the 'raw' value of G, that MiHsC/QI predicts should only be seen at high accelerations? This affects dG. It's something interesting to think about anyway.

My family must think I'm training for a boxing match since I can often be found these days walking round the house holding my fists up to represent two balls and mumbling to myself.. Saying that, maybe I should learn to box: given some of the online responses to MiHsC/QI, if I ever attend another conference, such a skill might be needed!


Quinn, T., C. Speake et al., 2013. Phys. Rev. Lett., 101102. Link

Schlamminger, S., 2014. Phil. Trans. Roy. Soc., 372, 20140027. Link

Klein, N., 2016. Are gravitational constant measurement discrepancies linked to galaxy rotation curves? https://arxiv.org/abs/1610.09181

Saturday, 12 November 2016

Critique of Verlinde's Gravity

People have been sending me Verlinde's new emergent gravity paper wanting me to comment on it. I started reading it and I'm afraid I stopped at the sentence 'code subspace in microscopic bulk Hilbert space'. I skimmed the rest. He focuses on gravity, and just assumes inertia, and is proposing a new force that starts to appear at large scales. Although there are similarities to MiHsC in that he uses the Unruh temperature formula and information, there are many observations that falsify Emergent Gravity:

1) Emergent gravity predicts an anomalous effect that occurs only on large scales, and so it is falsified by the many tiny globular clusters and small satellite galaxies that show even more of an anomalous rotation effect than big galaxies (MiHsC is successful with these minnows too because it predicts anomalies at low accelerations, instead of just large scales). Emergent Gravity also cannot deal with many other anomalies like the cosmic acceleration, the flybys and the emdrive. MiHsC explains all of these.

2) Emergent Gravity has been falsified by experiments in which uncharged neutrons were confined in the vertical direction by making them bounce off a mirror below, and allowing gravity to pull them down. It was found that, in agreement with quantum mechanics, the neutrons did not move continuously along the vertical direction, but jumped from height to height like mountain goats. Entropic gravity predicts the wrong heights (see the Kobakhidze reference).

3) Emergent Gravity relies on something called code subspace, which is something we cannot directly see, so it is another kind of informational dark matter that is difficult to test for directly.

It is strange people that people are considering Emergent Gravity and are not discussing MiHsC / quantised inertia which is far simpler, requires less new physics, is based only on observable things, and predicts far more. To summarise:

1. MiHsC/quantised inertia is deliberately based only on things we can see: visible matter, the speed of light, the cosmic diameter, and Unruh radiation that was already predicted and is at least observable, and may have been seen already (relevent blog).

2. MiHsC is simple. Emergent gravity is complex and Byzantine, and needs more untestable assumptions (like code subspace) than you can shake Occam's razor at, MiHsC needs only one new assumption and 6 lines of maths to predict galaxy rotation and many more anomalies on a huge range of scales.

3. The new assumption in MiHsC: that quantum mechanics (the zero point field) and relativity (horizons) interact on all scales via the uncertainty principle simply gets rid of the dark sector and unifies physics.

4. The same mathematics that leads to MiHsC, also predicts gravity, so MiHsC predict both gravity and inertia.

5. MiHsC predicts the many anomalies that have been seen in recent years (29 or so of them), but also makes very specific predictions for new things that can be looked for (eg: early galaxies span faster at the same visible mass, the emdrive can reverse if you change its aspect ratio..)

Of course, Verlinde should be applauded for at least trying to solve galaxy rotation without vague dark matter, but he is still suffering from the excess-baggage problem of theoretical physics. He had to start from general relativity and try to add invisible elements to it so that it fit the galaxy data. The result is complex and contrived.

Quantised inertia / MiHsC is far simpler because you don't have to add anything unobservable. All you have to do is admit that quantum mechanics and relativity interact via horizons and the uncertainty principle (summary).


Kobakhidze, A., 2011. Once again gravity is not an entropic force. arXiv

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. arXiv

Verlinde, E., 2016. Emergent gravity and the dark universe. arXiv

Friday, 11 November 2016

Based on Leonard Cohen's Hallelujah - Hallowed Data

Just for fun I've just written this, based on Leonard Cohen's song "Hallelujah", but with a science/MiHsC theme.

Hallowed Data

Thales of Miletus, in Ancient Greece
said the Gods were not the keys
and we should only assume things we can see, yeah.
Putting data first
gave us gravity
and Einstein's relativity.
Humanity was rising towards the stars with Hallowed Data.

Hallowed data
Hallowed data
Hallowed data
Hallowed data

Their faith was strong, but they needed bread.
They went for funding, lost their head.
The beauty, & the aura, overthrew them.
She tied them up
in darkness then
and broke Occam's razor, when
they threw out that essential hallowed data.

Hallowed data
Hallowed data
Hallowed data
Hallowed data

They say I aspire far too high
but I just want to pierce the sky,
and if I did, well really, what's it to you?
MiHsC was born
outside the herd.
It doesn't matter what you heard.
It's simply and surely based on Hallowed data.

Quantised inertia
Quantised inertia
Quantised inertia
Quantised inertia

I did my best, it wasn't much.
I couldn't join, but I tried to push.
I've told the truth, I didn't come to fool you.
And even though
I'm on the edge
I'll stand before the garden hedge,
with nothing on my tongue but Hallowed data.

Hallowed data
Hallowed data
Hallowed data
Hallowed data.

Sunday, 30 October 2016

A Test using Redshift

Galaxies further away from us, are moving away much faster than close ones, and therefore the light coming from them is red-shifted. So the redshift of star light is a measure of its distance, and of increasing age, since when we look far off we are also looking back in time since the light has taken aeons to reach us. Like an ice core in climatology, this gives us a record of the distant past.

The minimum acceleration predicted by Quantised Inertia / MiHsC is given by: a = 2c^2/CosmicDiameter, and 'CosmicDiameter' varies with time as the cosmos expands. This means that as we look at galaxies further away, and further back in time, the CosmicDiameter was smaller and the minimum acceleration was bigger (This might also explain the inflation of the early universe, but that's another story). The prediction then is that earlier galaxies, ones at higher redshift, have to rotate more rapidly, with the same visible mass, to remain above the minimum acceleration. I proposed this as a test in McCulloch (2007) (see paragraph 4 of the Discussion), but at the time the data did not seem to be good enough.

I was reminded of this test by various insightful people on my last blog entry and in a few emails (see the guilty names below). Thanks to them I've looked into it again and added it to the discussion of my latest paper (just submitted to MNRAS) which includes the plot below. Along the x-axis we have the log of the stellar acceleration expected given the visible matter and Newton's laws, and along the y-axis the log of the acceleration observed directly from the movement of the stars. Newton and Einstein would expect the results to lie on the dotted line. The observations, taken from McGaugh et al. (2016) are shown by the squares with their size indicating the uncertainty, and they are obviously at odds with dear Albert and Isaac. At low accelerations (on the left hand side) the stars orbit the galaxies far too fast. This is the famous galaxy rotation problem, that is usually solved by stuffing in huge amounts of dark matter wherever it's needed (the second worst hypothesis in history in my opinion, since it is unfalsifiable).

The black line shows the prediction of MoND which fits the data (the squares) and is much more falsifiable than dark matter, but despite the great respect I have for Milgrom's bold step, MoND has been adjusted to fit the data using its parameter a0, so it's not surprising that it fits. The MoND prediction also shows no dependence on time.

The coloured lines show the predictions of quantised inertia / MiHsC. Uniquely, among all the theories QI/MiHsC predicts the observations correctly without any adjustment, and, also uniquely, its prediction varies with redshift. The light blue line shows the curve for a redshift of Z=0 (nearby galaxies in this epoch). This agrees with McGaugh et al. (2016)'s data (which was for Z=0). The dark blue curve shows the prediction for Z=0.5, purple for Z=1 (for which the cosmos was half its present size) and the red curve for Z=2. As you can see the galaxy rotation problem is predicted by QI/MiHsC to have been worse when the cosmos was young (all other things being equal). If two galaxies have the same visible mass, then according to QI/MiHsC the one further away (earlier in time) should spin faster.

Does this prediction agree with the data? Well, the data still seems noisy, but earlier galaxies do seem to have faster spin, see for example Figure 6 in the Thomas et al. (2013) reference below (a paper found by airenatural). With a bit more data this could be the definitive proof that QI/MiHsC needs..


Thanks to S.S. McGaugh for sending his binned data, and R. Ludwick, T. Short, Magnus Ihse Bursie and J.A.M. Lizcano (airenatural), for advice ...and anyone else I may have forgotten.


McCulloch, M.E., 2007. The Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. https://arxiv.org/abs/astro-ph/0612599

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

Thomas, D., et al., 2013. Stellar velocity dispersions and emission line properties of SDSS-III/BOSS galaxies. MNRAS, 431, 2, 1383-1397. https://arxiv.org/abs/1207.6115

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.