I've suggested (& published in 15 journal papers) a new theory called quantised inertia (or MiHsC) that assumes that inertia is caused by relativistic horizons damping quantum fields. It predicts galaxy rotation, cosmic acceleration & the emdrive without any dark stuff or adjustment.
My Plymouth University webpage is here, I've written a book called Physics from the Edge and I'm on twitter as @memcculloch

Tuesday, 30 June 2015

Critique of Shawyer's emdrive theory

While I do believe, cautiously, that the thrust Shawyer found in the emdrive is real (emdrive: a microwave oven shaped as a truncated cone) and that Shawyer and then Juan et al & NASA should be respected for finding and testing it respectively, I'd like here to criticise Shawyer's theory of it, which I believe is confused. I'll try to do this in an accessible way, and briefly discuss my alternative MiHsC explanation.

In a New Scientist article on the emdrive Shawyer said: "Key is the fact that the diameter of a tubular cavity alters the path - and hence the effective velocity - of the microwaves travelling through it. Microwaves moving along a relatively wide tube follow a more or less uninterrupted path from end to end, while microwaves in a narrow tube move along it by reflecting off the walls. The narrower the tube gets, the more the microwaves get reflected and the slower their effective velocity along the tube becomes. Shawyer calculates the microwaves striking the end wall at the narrow end of his cavity will transfer less momentum to the cavity than those striking the wider end (see Diagram). The result is a net force that pushes the cavity in one direction. And that's it, Shawyer says." (from New Scientist: the end of wings and wheels).

I think there is a lot wrong with Shawyer's explanation, and for once I'm not alone on this! For example he uses special relativity for an accelerating system and his explanation wrongly indicates a thrust towards the wide end of the cavity, but I'll focus here on the asymmetry in force he claims to exist between the large end plate and the small. I haven't seen an accessible refutation of this, so here goes. Referring to the quote above, he does not seem to consider that the photons 'reflecting off the side walls' will exert a pressure force on those walls, which will have a component towards the narrow end. The schematic below shows a simplified setup for ease of explanation: first of all an equilateral triangle which can be generalised to a 3-d cone by an integration using a rotation around the central axis of symmetry (the horizontal line) without changing the conclusions, so this is a nice accessible way to do it.

In the diagram on the left the microwave photons bouncing around inside the cavity make a force (F, per unit area) that pushes outwards on all three faces equally (the blue arrows). Assuming that the length of the sides are equal (l) it's easy to show that the left-right components of force balance:

Force right = Fl
Force left=2Fl.sin(30)=Fl

In the diagram on the right I've truncated the triangle/cone halfway down its sides to represent the truncated cone of the emdrive, and again the result can be generalised to a 3-d emdrive by integrating things in rotation around the axis of symmetry (dashed line) without changing the conclusion. So now we have:

Force right = Fl
Force left = 2*left force on side walls + left force on flat end
                = 2F(l/2).sin(30)+F(l/2)
                = Fl

Again the forces balance in contradiction to what Shawyer said in his interview (which may have been an over-simplification on his part that he needs to address). This, and his use of special relativity for an accelerating system, and the wrong direction of his predicted thrust indicates that his theory is confused.

I have suggested an alternative, which is perhaps less confused, but requires new physics. The schematic below represents the MiHsC explanation of the emdrive. The brighter colours on the right are meant to indicate that more modes of the zero point field can exist at the right hand, wider, end of the cavity. That means that the mechanism MiHsC uses to produce inertial mass from an asymmetry in Unruh radiation caused by a Rindler horizon (an asymmetric Casimir effect, see McCulloch, 2013) is more effective on the right hand side. So, as photons go right (lower arrow) they gain inertial mass (arrow thickness) and as they go left they lose it (upper arrow), so to conserve overall momentum the cavity is predicted to move left (left hand arrow). The predictions from MiHsC fit the data, reasonably well (see McCulloch, 2015), but not yet such good agreement that I'm writing to Nature about it..

McCulloch, M.E., 2015. Can the emdrive be explained by quantised inertia? Progress in Physics, 11, 1, 78-80. Link

McCulloch, M.E, 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001. Link

Sunday, 28 June 2015

Asking nature for directions

Standard physics now assumes that gravity is caused by matter making a curvature in space (general relativity) and microscopic behaviour is caused by quantum mechanics. This theoretical duality is ugly: there should only be one model.

Einstein in his later years thought that model should be a field theory like general relativity. I much prefer quantum mechanics which has passed every test (it has even passed a crazy test, given Bell's anomaly) whereas general relativity has been well tested at high accelerations, but in my view has failed at low accelerations. For example, it didn't predict galaxy rotation and needs a huge dark matter fudge, and it didn't predict cosmic acceleration and needs another dark energy fudge. Gravitational waves haven't been found either. So I like quantum mechanics and I've been trying to build everything from that (specifically the zero point field and Unruh radiation) with a dash of special relativity (specifically Rindler horizons) added.

The resulting model for inertia, MiHsC, makes successful predictions that general relativity cannot do by itself, eg: galaxy rotation, cosmic acceleration and others. Buoyed by this I've tried for many years to get gravity from several MiHsC-compatible schemes. One based on the GPS carrier phase method (that I teach), one invoking the uncertainty principle (dp.dx~hbar) and one involving the sheltering of Unruh radiation by massive bodies. All are intriguing, but all have problems. For example, for the latter, it is unclear to me how opaque matter is to Unruh radiation, and I don't want to incorporate an uncertain quantity.

How to proceed? The way I approached things with MiHsC is with some imagination, but also having the humility to ask nature for directions, and by that I mean: finding an anomaly that tells me which of the many possible theories I can imagine is actually the right one. Luckily, there is one gravity anomaly that is bugging me: an anomalous variation in the gravitational constant (G) that I have discussed before, that appears to have a 5.9 year period (Anderson et al., 2015) and seems to coincide with an increase in the length of day.

To paraphrase H.L. Mencken: one good anomaly is worth 10,000 syllogisms.


Anderson, J.D., G. Schubert, V. Trimble, M.R. Feldman, 2015. Measurements of Newton's gravitational constant and the length of day. EPL, 110, 10002. Paper

Friday, 19 June 2015

Nothing doing

Our civilisation is based on extracting work from heat. This is what steam engines, cars, rockets do. In the steam engine fire boils water, expansion pushes a piston which turns a wheel which rolls. The engine turns heat into useful motion. Amazingly, the Greeks and Romans could have had such technology at the time of Christ if they'd have thought a little more about the aeolipile of Hero of Alexandria, which was indeed an embryonic steam engine. What they missed at the time was a theory of heat to suggest wider applications for it and better efficiency, but by then Greek science had become too metaphysical to bother with experimental anomalies, and the chance was lost.

It is my belief that we are in a similar situation now, but instead of heat and the aeolipile, mainstream physics is now ignoring the zero point field (ZPF) and a long list of anomalies, because it's chasing unfalsifiable hypotheses like dark matter and strings.

The zero point field (ZPF) was proposed by Einstein and Otto Stern in 1913 to better explain the behaviour of hydrogen gas at low temperature, and you can imagine it as a hidden sea of mass-energy everywhere. It is a sort of heat you can't feel, and that's because it is generally uniform everywhere and therefore, just as for a uniform temperature field, work was not thought to be extractable.

Then along came Casimir in 1948 and proposed that if you put two conducting plates very close together you damp the ZPF within the plates so the ZPF left outside pushes the plates together. The force is so tiny it took until 1997 for it to be measured and the significance of this has been lost because it is not a useable effect (just like the aeolipile). However, if a door is even slightly ajar, it can be pushed open, and what the Casimir effect is doing is tapping into a huge source of hidden energy, the ZPF, by forcing the waves in the ZPF to have nodes at 'horizons': in this case the parallel plates so some of them are disallowed and the ZPF becomes non-uniform and therefore it can effect the real world and become useful.

I've used this to extend physics so that it pays attention to the ZPF and how, when you put horizons in it, you can get new energy out (this is the basis of MiHsC). For example, the energy you get when you accelerate and a Rindler horizons forms behind you produces in MiHsC (via Unruh radiation) the energy needed for what we always called inertia, but never understood. Also, MiHsC predicts that the far-distant Hubble horizon produces cosmic acceleration and the galaxy rotation anomaly, and the predictions fit the data. The most controllable and repeatable example yet is the emdrive, which may be our aeolipile. MiHsC suggests that the asymmetry of its cavity makes a ZPF (Unruh radiation) gradient within it (the ZPF being supercharged by all the energy put in) and the cavity then rolls down that ZPF gradient (MiHsC predicts the emdrive fairly well, but not perfectly, see the paper below).

MiHsC is not complete yet, and I'd like to ask other physicists to help. At the moment what they are doing is trying to rescue an old paradigm from embarrassing new data, with the unfalsifiable hypotheses of dark matter and energy. This is unscientific. MiHsC offers a new paradigm which agrees more simply with the new data that Einstein could not have known about, brings the ZPF and horizons fully into physics and offers a way out of a civilisation based on heat, which is damaging our planet. It's quite elegant too.


McCulloch, M.E., 2015. Can the emdrive be explained by quantised inertia? Progress in Physics, 11, 78-80. Link.

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

Monday, 15 June 2015

MiHsC & the Equivalence Principle.

One of the complaints I often get is that MiHsC violates the equivalence principle, which says that the inertial and gravitational masses are equal. This principle forms the basis of general relativity (GR) and has been well tested, so you might say that to suggest a theory that disagrees with it takes some balls.

Speaking of balls, legend has it that Galileo first demonstrated equivalence by dropping two of them of different mass off the leaning tower of Pisa, and showed that they hit the ground together. This occurs because, although the heavier ball has more gravitational mass and is attracted by the Earth more, it also has more inertial mass, so finds it harder to accelerate. The cancellation of these two effects is the equivalence principle. These days people do the same experiment far more accurately using a torsion balance: a couple of balls of different masses at either end of a rod in a dumb-bell like arrangement. The rod is suspended from its mid point by a wire whose resistance to twist is known. The differential horizontal 'falling' of the two balls of different mass towards distant objects like the Sun or the galaxy, is determined from the twist in the wire. No violation of equivalence has been observed down to unfeasibly tiny accelerations.

The reason this does not disprove MiHsC is clear, but subtle. MiHsC predicts that inertial mass is caused by Unruh radiation and for normal accelerations such as those on Earth or in the inner Solar system it predicts the standard inertial mass. MiHsC starts to deviate from normal when accelerations become ridiculously small, for example for the slowly curving stars at the edges of galaxies, because then the Unruh wavelengths the stars see, and that MiHsC says cause their inertia, get extremely long and a lesser proportion of them fit exactly within the Hubble scale. As a result logic says they cannot be observed (we have to assume there's no space outside the Hubble sphere for them to wiggle in) and therefore they cannot exist. This means that MiHsC predicts that the stars' inertia reduces in a new way for low accelerations, and a new acceleration appears which is 'independent of the objects' mass' and of size: 2c^2/(Hubble scale). This is intriguingly the same size as the cosmic acceleration and also fixes the galaxy rotation problem.

The crucial point is that no matter at what tiny acceleration equivalence is tested using the balls, the effects of MiHsC will not be seen, because the extra MiHsC acceleration is independent of the mass, meaning that Galileo's two balls, or the balls in the torsion balance, will still 'fall' equally, so there will be no twist in the wire and equivalence will appear to be unbroken. The difference is that with MiHsC the two balls both fall very slightly faster. What this says about the relationship between MiHsC and general relativity (which was build on equivalence) I do not yet know.

Having told you how MiHsC cannot be seen, it's only fair to tell you how it could be seen. One method is discussed here. Another interesting method would be to take the MiHsC acceleration: a=2c^2/(Hubble scale), and reduce the Hubble scale from its usual value of about 10^27 m (as big as it gets, so it makes the MiHsC effect tiny), by instead creating a closer horizon using a metamaterial structure (as I suggested in the last section of the first reference below, please ignore the first part which has been superceded by a later paper). Such a structure, or cavity, would boost the new MiHsC acceleration. The emdrive may be doing this, since MiHsC predicts the observed thrust quite well (see the second reference below) and this blog entry.


McCulloch, M.E., 2008. Can the flyby anomalies be explained by a modification of inertia, JBIS, 61, 373-378. ArXiv link (please see only section 4!).

McCulloch, M.E., 2015. Can the emdrive be explained by quantised inertia? Progress in Physics, 11, 78-80. Link

Tuesday, 2 June 2015

What you can see is what you get

Far from MiHsC being antagonistic to (special) relativity, what I am doing with MiHsC is going back to an attitude that you might call 'What can't be seen, doesn't exist' or 'What you can see is what you get' (WYCSIWYG) that has produced most of the great leaps forward in physics, including Einstein's special relativity.

The first example of this attitude was Thales way back in 600 BC who rejected ancient Greek mythology and insisted on modelling nature with something that could be seen. OK, he came up with "Everything is water" which was easily falsified, but this is the crucial point: the idea was falsifiable, and so Thales started the scientific process (dark matter and string theory are not easily falsifiable and are not good science).

Newton used this attitude when he rejected Descartes' model of gravity which used unobservable vortices, and when he derived his theory of gravity he focussed on things that could be measured like masses and distances and refused to hypothesise about what gravity might actually be since he couldn't think of anything that could be tested. However, he faltered when he introduced the invisible entities of absolute space and time which can't in principle be seen, and was later critised for that by Gottfried Leibniz, Bishop Berkeley and most especially Ernst Mach. This idea of focussing on 'observables' or things that can be seen is sensible, in the same way that crossing a river using the most solid-looking stones is sensible.

Einstein had read Mach's criticism of Newton's unobservable space and time and decided to devalue them and focus on something that could be seen and tested like the properties of light. This had consequences. For example, if you have a couple of mirrors and you get a photon to bounce up and down between them, then this makes a sort of clock. Now if you happen to see this clock moving sideways past you, then from your point of view the light has further to travel because it has to move along a diagonal path, but Maxwell's equations say that the speed of light is always the same, and this has been experimentally confirmed, so the clock now must tick slower as it takes longer for the light to go along the diagonal. Some might say this is just an 'appearance' of slowness. Einstein was happy to say that time has really slowed down, because time is not a thing you can measure well from a distance anyway, whereas the constant speed of light had been well measured, so it made sense to believe in the properties of light and be flexible with time. This implies then that physics is determined by what you can see (and this does not mean by us as individuals, but what you can 'in principle' see). This was confirmed experimentally by Hafele and Keating (1972) who took one clock on a plane trip round the world and showed it slowed down relative to a clock they left at home.

MiHsC is based on this same observable attitude, but now applied to the new discovery of information horizons. You can make such a horizon if you suddenly accelerate, say, to the right. Then, information from a certain distance to your left can never catch you up, being limited to light speed. The boundary between what you can and can't see is called the Rindler horizon. There is also a cosmic horizon, because objects at the Hubble edge are traveling away from us at the speed of light and we can't see them, or what lies beyond.

So with this attitude we must assume that from the point of view of someone accelerating there can be nothing beyond the Rindler horizon they see behind them, because they can in principle see nothing there. Also from the point of view of someone within the cosmos, there can be nothing outside the cosmic horizon. This includes fields, so all fields must have a node (zero value) beyond the horizon (fields can't wiggle in nothing) and also on the horizon. In this way the cosmos is like a drum in that all waves on it must close at the boundary and only some vibration patterns or 'notes' are allowed.

In MiHsC I assume that inertia is caused by Unruh waves, and so this attitude means that these waves too can only exist if they have nodes at the horizons.

It turns out that if you do assume this, then with the Rindler horizon MiHsC predicts the standard inertial mass to within 29%, and also with the Hubble horizon it predicts a subtle deviation from the standard inertial mass that agrees with the anomalous rotation of galaxies, galaxy clusters and the recently observed cosmic acceleration. It also predicts the low-l CMB anomaly, an anomalous suppression of patterns seen on the longest cosmic scales, and several other anomalies, including emdrive.

My general point is that whenever science has focused in on things that can be 'in principle' seen, it has leaped forward. Whenever it has lost discipline and used non-falsifiable things like epicycles, vortices, strings, extra dimensions or dark matter, it stagnates. MiHsC represents a new era of focusing on observables, like the period from 1899 to 1930, and sure enough it predicts anomalies that other theories can't reach, without having to invent invisible stuff.


Hafele, J.C. Keating, R.E., 1972. Around-the-World Atomic Clocks: Predicted Relativistic Time Gains. Science, 177 (4044): 166–168.