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

Saturday, 12 December 2015

Testing MiHsC in Dwarf Galaxies

The best test of MiHsC is to find circumstances where it is likely to appear - that is, in systems in the deep of space with very low accelerations. I've recently been looking into some ideal candidates: Milky Way dwarf spheroidal galaxies. The Milky Way has lots of these tiny systems orbiting around it and some of them are so wispy that they should show up MiHsC, and they do. The plot below shows the five wispiest cases I could find that also have observations of their stars' orbital velocity. In the figure the x-axis shows the visible mass of the system (in Solar masses) and the y-axis (black squares) shows the velocity (km/s), for the dwarfs Segue-1, Triangulum-II, Bootes, Coma Berenices and Ursa Major 2. The error bars (uncertainties) are also shown.

The first thing that can be done is to calculate the maximum orbital speed that Newton would allow without the systems becoming gravitational unbound given their visible mass (general relativity predicts similarly). These maximum Newtonian velocities are shown with crosses and are much smaller than the stars' observed speed which implies that the dwarfs should explode centrifugally (inertially) because of the inability of their visible mass to bind them gravitationally. However, they look bound. Dark matter enthusiasts will no doubt say "Just add dark matter", but in the case of Segue and Triangulum-II you have to add 2600 and 3600 times as much dark matter as the visible matter, which makes the dark matter hypothesis look ridiculous.

Another possibility is to use MoND, Milgrom's empirical formula that modifies gravity or inertia, and the results of that are shown in the Figure by the triangles. MoND uses an adjustable parameter a0 of 1.8x10^-10 m/s^2 and also predicts too low a maximum velocity: outside the uncertainties in the observed velocities in all but one case: Coma Berenices, but it is much better than Newton, or 'naked' GR.

Finally, the predicted maximum velocity of MiHsC is shown by the diamonds (using the same method I used for full scale galaxies in the reference below). MiHsC is the closest to the observations and agrees, given the error bars, with all but one of the observations (Triangulum 2). It certainly performs the best, which is impressive given that, unlike dark matter and MoND it has no adjustability. My goal now is to emulate Gandalf and collect a few more dwarfs, the lighter the better.


McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. A&SS, 342, 2, 575-578.  Preprint

Sunday, 6 December 2015

Comparison of GR, MoND, MiHsC

One of the great advantages MiHsC has, and that doesn't seem to be appreciated, is that it fits a lot of data without needing adjustment, so here is a table to emphasize that. In the left hand column I've listed eleven anomalies and in the other columns I've used a colour code to show how the theories listed at the top (General Relativity, MoND and MiHsC) fit the data. If the theory can't fit the data because it would need ridiculous amounts of adjustment then I've coloured the square red. If the theory can fit with an adjustment that needs more than one arbitrary number to define it (eg: the addition of dark matter) I have coloured the square orange. If the theory needs adjustment with only one arbitrary number the box is green, and if it needs no adjustment at all the box is blue.

It is inevitably a vague comparison, but general relativity produces a lot of orange (it fits, but with a lot of adjustment) because of its flexibility, aided by huge numbers of scientists with computers, arbitrarily adding dark matter and energy. MoND, which is simpler and has only one adjustable parameter shows more green, but also some red, because it has less flexibility and, for example, it cannot cope with galaxy clusters, nor the new data coming from labs, like the Tajmar effect and Shawyer's emdrive. 

MiHsC performs well without needing adjustment at all (lots of blue). This is because I have designed it from the ground up with some of these anomalies in mind from the start. This is how science should be done: working from the data to a theory, not, as is done with general relativity, by fudging a revered theory to fit the data. The details of this table are open to debate, but MiHsC obviously performs best on this measure, and more generally: scientists should try to propose theories that produce a conclusive red or blue, not orange.

Sunday, 29 November 2015

Dark Matter Jumps the Shark

Mainstream theoretical physics needs to take a long hard look at itself. I've just read an article about Lisa Randall's new suggestion that dark matter killed the dinosaurs and after collapsing in a tangled heap of laughter I realised that this perfectly captures the attitude of mainstream theoretical physics: the extrapolation of untested and possibly untestable hypotheses into a regime where you are unlikely ever to be proven wrong, like the interior of black holes, the first millisecond after the big bang or the age of the dinosaurs. It is the physics of the unimaginative and cowardly.

Dark matter is like a universal plaster for any anomaly. For galaxies stick the invisible stuff freely onto your equations in a halo. For the flyby anomalies put it in a thin disc, for the dinosaurs it is a layer (I refuse to look at the details, like I refuse to read up on ghostology). There's a useful idea called Russell's teapot (pointed out to me by DaKangaroo on twitter). Bertrand Russell said that if someone claims there's a teapot orbiting the sun between Mars and Jupiter the onus is on them to prove it, certainly before expecting people to believe anything else deduced from it (By the way, I'm not saying dark matter can't exist at all in some minor form, just not as it is taken by the mainstream as a panacea for all their problems).

In contrast to dark matter's arbitrary flexibility, MiHsC is unadjustable. This means that, unlike the dark side, I can't cheat. MiHsC only predicts one possibility, and yet that possibility correctly models the observed anomalies I've tried it on: galaxy rotation, cosmic acceleration, the orbit of Proxima Centauri, the spin of extreme dwarf galaxy Triangulum II, the Pioneer and flyby anomaly, the Tajmar experiments and the emdrive. Meanwhile the mainstream is messing around with the insides of black holes, the early universe and the dinosaurs, confident no-one can disprove them.

But there is hope. In the fifth season of the TV series Happy Days ratings were falling so that the writers wrote in a scene where Fonzie jumped over a shark on skis. Ever since then a useful phrase has entered the English language: to 'Jump the Shark' meaning to use shock tactics to retain dying interest. There's now a similar term 'Nuke the Fridge' based on Indiana Jones 4. With Randall's dinosaur demise the dark matter bandwagon has just jumped the shark, so things may now get interesting.

Sunday, 22 November 2015

Evidence for MiHsC: Triangulum II

The usual balance in systems such as galaxies is between gravity which holds them in (keeps them bound) and the inertial centrifugal force that tries to explode them. In all the systems we see today these two forces must be balanced, or we wouldn't still see them. Writing this balance mathematically gives

G*M*mg/r^2 = mi*v^2/r

where G is the gravitational constant, M is the galaxy's mass within a radius r, mg is the gravitational mass of a star at radius r, v is its orbital speed and mi is the star's inertial mass (usually it is assumed that mg=mi, the equivalence principle). For the amazingly low accelerations in deep space MiHsC proposes that mi is much less than mg so that a gravitationally bound system should appear to have stars orbiting too fast, this is indeed the case. This is because MiHsC reduces the centrifugal force breaking them apart, allowing them to spin faster without exploding. Therefore, to prove MiHsC, a good plan would be to look for galaxies with mindbogglingly low accelerations, ie: low mass ones.

The most extreme such system has just been found by Laevens et al. (2015). Triangulum II is a dwarf galaxy, one of many orbiting our Milky Way galaxy, with very little visible mass in it: only 450 times the light output of the Sun, so the equivalent of 877 Suns in mass (Assuming star type K0 - thanks to Javier Freire Venegas for putting me right on the mass/light ratios) and it is only 34 parsecs in radius.

As expected, both Newton's and Einstein's models (General Relativity, GR) have a problem with this dwarf galaxy because they predict that any rotation speed above 0.34 km/s would blow it up (v=(GM/r)^0.5). But, Kirby et al. (2015) have just seen the stars zooming around it at 5.1 km/s! (with an error bar meaning that the speed is somewhere between 3.7 and 9.1 km/s). Assuming that this system is stably bound (something probable, but still debated) then to keep Newton and Einstein happy and stop it exploding you'd need to add 3600 times more invisible dark matter to it than the visible matter present. This is clearly becoming ridiculous.

MoND does a slightly better job. The MoND formula, which is v=(G*M*a0)^0.25 predicts an orbital speed of 2.1 km/s, but MoND relies on an adjustable parameter a0 which must be set by hand to be typically 1.8x10^-10 m/s^2 and MoND has nothing to say about where this number comes from.

MiHsC does an even better job, and it contains no convenient adjustable parameters. The MiHsC formula, v=(2GMc^2/Theta)^0.25, predicts a rotation speed of 3.0 km/s (in this formula c is the speed of light and Theta is the Hubble diameter). This Table summarises the observed speed and the various predictions:

  Observed     = 3.7-9.1 km/s (range of possible velocity dispersions)
  Newton/GR  = 0.34 km/s
  MoND          = 2.1 km/s
  MiHsC         = 3.0 km/s

Whether or not MiHsC agrees with the observation depends on the error bars in its prediction, and so I need to know what the uncertainty of the mass given for Triangulum II is (I'm writing a paper so will have to look closely at all the error bars), but the MiHsC prediction is clearly the best in the Table. As for the dark matter hypothesis, the amounts needed for this particular case are clearly ridiculous.


Kirby et al., 2015. Triangulum II: possibly a very dense ultra-faint dwarf galaxy. Astrophysical Journal Letters, 814: L7. Pdf

Laevens, B.P.M. et al., 2015. Astrophysical Journal Letters, 802: L18.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics & Space Science, 342: 575-578. Preprint

Saturday, 14 November 2015

A Case for Human Spaceflight

I spoke at a debate at Exeter University's debating society yesterday in favour of human, as opposed to robot, space exploration. Here is roughly what I said:

I would say that human spaceflight and settlement off-world is as inevitable and natural as the first fish crawling out of the sea, or humans leaving Africa, and this is why:

It is already possible, given the will: Six humans are living in space on the ISS which is already providing a dividend in showing Americans and Russians that they can co-operate. For this reason the ISS has been suggested for a Nobel prize. The Moon and Mars are settle-able in the next few decades, the Moon being the obvious first choice.

Even interstellar travel is more possible than you might think because special relativity says that time slows down aboard a spaceship moving very fast. So if you have an engine powerful enough to get you close to the speed of light, you can travel anywhere in the galaxy in the lifetime of a human on the ship, just not in the lifetime of people back on Earth. This gets rid of the need for generation-ships or suspended animation and reduces galactic colonisation from something that most people think is an impossibility, to merely a extremely difficult engineering problem (you have to accelerate and decelerate at 1g, 9.8 m/s^2, for a year, and then cruise).

New physics is coming, since general relativity has difficulty with galaxies (needing arbitrary dark matter), with cosmology (needing dark energy) and is inconsistent with quantum mechanics, and there are experimental problem like the EPR-Bell tests and other anomalies. I have suggested MiHsC to fix these problems.

Where do we go? Well, this is the time and place to ask that. Many exoplanets are now being discovered, some will be like the Earth, and one of the main centres for exoplanet research is here at Exeter University.

So if it is possible, is it a good idea? I would argue yes as follows:

Insurance: Humans have had a long and painful struggle to civilise (well, partially anyway) and we have something unique to say. It would be a shame if that was lost. Off-world colonies are essential so that if the Earth is damaged by an asteroid, nuclear war or climate change, humanity will endure and our long history will not be in vain.

Finite planet: Earth's resources are finite, and yes, we should learn to be sustainable, this will also help us with space travel and settlement, but even with sustainable policies, resources will eventually run out on the finite Earth. Space offers infinite or at least mind-boggling resources.

The need for challenge: humans have an innate need for challenge, and the challenges on Earth are running out and in these circumstances there is the danger of degenerating into a stagnant heirarchical society where a few try to make money off the rest. We need a collective and hopeful project, like Project Apollo, to bind our society together and give everyone hope of a better future. Hope is important. Also, the failures of a system can often only be seen by looking at it from the outside, that is increasingly difficult in our connected world.

Cultural diversity: The culture of Earth is becoming more uniform and this is a shame since it leads to sterility. There is very little option now to try radical new ideas on Earth, but if some people left the planet they could start radically different societies and experiment with them, just as the Pilgrim fathers did and devised a better constitution, and other brilliant inventions, eg: pizza.

The imperative: If we look at plants & animals we see the huge resources they put into reproduction, for example Salmon return over whole oceans to their birth place to reproduce. Evolution has made them that way since the ones who couldn't be bothered left no offspring. Lovelock has suggested that the Earth is an organism. If so, then it is logical to say it intends to reproduce. Is it developing us, a space-faring species, to do that?

Exploration by proxy is shallow: History tells us that if you send people to new environments, in this case other planets, they'll invent things we'd never dream of. One example is Charles Darwin who went to the Galapagos Islands and noticed the animals varied from island to island and thought of evolution. Robots are not yet creative like this. A robot on the Moon may be the eyes for someone back on Earth, but that someone is still on the Earth sat on a chair. If the person was on the Moon, they would think in a different way and could be a new Thomas Jefferson or Darwin, inventing a better society or a better way to generate energy.

The importance of human exploration is instinctively understood: almost no-one remembers the first probe to the Moon (Luna 2) but everyone remembers the first human. You can’t predict the ideas space settlers will have, but you can help it to happen by voting for human spaceflight today.

Tuesday, 10 November 2015

How can MiHsC be applied to a hot star?

Peter Reid just asked me this following question: 'For one of those stars near the edge of a galaxy, wouldn't its individual particles still be accelerating quite a bit, since they are part of a seething ball of plasma? It seems like that should make the minimum acceleration not apply to the individual particles, and so not apply to the star as a whole. How do you account for this?'

This is a good question because MiHsC usually only produces anomalies for things at very low accelerations, so how can it predict anomalies for stars with huge thermal accelerations inside? The diagram below explains how. It shows a star (the yellow circle) orbiting the galaxy (the centre of which is to the left), with an orbital speed shown by the arrow pointing up. The schematic shows five hot, highly-accelerated particles inside the star (the red circles) and their acceleration vectors (the black arrows). Each particle has a large acceleration and so a Rindler horizon forms close by in the opposite direction (the black curves) and this horizon affects the particle's own inertial mass due to MiHsC, but since there are a lot of particles and they are moving randomly in the plasma, the black Rindler horizons are distributed randomly around the star and they therefore have no effect on the star as a whole (we'll forget the star's spin for now, which is a small acceleration in comparison). In this schematic there are only five particles, so it may not look like the black horizons quite average out, but in a star there are a very large number so the average will be very good.

Each particle within the star also has a tiny acceleration that it shares with all the other particles due to the orbit of the star in the galaxy. In the diagram this is shown by the light blue arrows, which are all pointing at the galactic centre to the left. The Rindler horizons associated with these smaller accelerations are much further away because the orbital acceleration is ridiculously smaller than the thermal, and these horizons must be far off to the right hand side, something I can't represent well on the diagram (see the blue curves surrounded by the dashed circle). This circled pack of horizons is the composite horizon that MiHsC applies to stars, or any object, as shown in the previous blog. If you consider an object as a whole, you can ignore its particle's individual horizons which average out, and just consider the composite horizon due to its combined acceleration, and figure out how Unruh waves hitting it are sheltered by that.

I've been asked other insightful questions recently, so I'll answer those in following blogs...

Tuesday, 27 October 2015

MiHsC with horizons, no waves.

Here are some schematics to show how MiHsC explains inertia, for the first time, in a mechanistic way, and also the observed cosmic acceleration. This explanation is equivalent to my previous explanations using Unruh waves fitting into the cosmic horizon, but uses Rindler and cosmic horizons only, no waves, for simplicity.

Imagine a spaceship in deep space (the black central object, below). It sees a spherical cosmic horizon, where objects are diverging away from it at the speed of light (the dot-dashed line). This line is an information horizon, so the people on the spaceship can know nothing about what lies behind it. This horizon produces Unruh radiation (orange arrows) that hit the ship from all directions. The spaceship is firing its engines (red flames) and accelerates to the right (black arrow), so information from a certain distance to the left can never catch up with the spacecraft, so a Rindler information horizon appears behind it to the left, and MiHsC says that the Rindler horizon damps the Unruh radiation from the left (the orange arrows disappear) so more radiation hits from the right and a leftwards force appears that opposes the rightwards acceleration. This predicts inertial mass (McCulloch, 2013) which has never before been explained, only assumed.

Now imagine the spaceship starts to run out of fuel, so that its acceleration rightwards decreases (smaller red jet, smaller black arrow, see below). Now the Rindler horizon moves further away (the distance to it is c^2/a, where c is the speed of light and a is the acceleration). Now a bit more Unruh radiation can arrive from the left so the net Unruh radiation imbalance and the inertial force is weaker, to mirror the lower acceleration:
Now the engine dies completely, and you would expect there to be no acceleration at all. The Rindler horizon is just about to retreat behind the cosmic horizon, but before it does the ship now feels Unruh radiation pressure almost equally from all directions, so its inertial mass starts to collapse..

As its inertia collapses the spacecraft becomes suddenly very sensitive to any external force, including from the gravitating black dot in the bottom right of the picture, so it is now accelerated towards that (the lower inertia makes the gravitational attraction seem stronger than expected, as an aside: this fixes the galaxy rotation problem without the need for dark matter) and a new Rindler horizon appears near the top of the picture to produce an Unruh field that opposes the acceleration
It turns out that in order for the Rindler horizon to be disallowed from retreating behind the cosmic horizon, there is a minimum acceleration allowed in MiHsC which is 2c^2/Theta where Theta is the Hubble diameter (the width of the observable cosmos). This acceleration is similar in size to the recently observed cosmic acceleration, and explains it without the need for dark energy.


McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect, EPL, 101, 59001. http://arxiv.org/abs/1302.2775

Friday, 9 October 2015

MiHsC from Bit

The concept of information has been skirting around the borders of physics for over a century, trying to get in. It first started causing trouble when Maxwell (1867) devised a thought experiment with a rectangular box separated into two by a partition, with molecules in it moving around at various speeds (see the red dots, Fig.1). The partition has a door at the bottom, beside which stands a 'Demon' (in blue). Every time a faster-moving molecule approaches the door going right, the demon opens it and lets it through, so that eventually all the fast molecules are on the right hand side of the partition. This implies that if you have detailed information about the molecules, then you can violate the second law of thermodynamics because the entropy of the box has decreased: where the temperature was uniform, there is now a gradient. This was a big problem, because the 2nd law is a pretty big law to violate.

Leo Szilard (1929), with a more practical bent, then showed that you should be able to get energy out of information in this way (Szilard's engine). Fig.2 shows a cylinder with a partition, one molecule bouncing around inside it. If you have a bit of information telling you which end of the cylinder the molecule is in, say it is in the right hand side, then you can put down the partition trapping the molecule there, advance the left hand piston (frictionlessly and without resistance from the molecule), remove the partition and allow the molecule to push the left hand piston back. Thus you have generated energy to move the piston solely from the information you had about the molecule's position. If you have one bit of information it turns out you can get kTlog2 Joules of energy out, where k is Boltzmann's constant and T is the ambient temperature. Szilard's Engine has recently been realised experimentally (see Toyabe et al., 2010).

As an aside, I have an amusing (to me), version of this, that I thought of when watching a comedy routine by Dudley Moore and Peter Cook (One Leg Too Few, 1964). If you happen to have a one-legged chicken, and you have information about which leg is missing, then you can attach a string to the appropriate side and generate energy as it falls down.. apologies to chickens everywhere.

The huge problem of the violation of the 2nd law in these scenarios was finally resolved by Landauer (1961) who was a computer scientist, very familiar with information. He realised that the memory system of a computer is also a physical system, so the 2nd law should apply. A computer uses binary digits, eg: 010011, but in fact the 0s and 1s correspond to real physical attributes in the solid state memory, so when computer memory is erased (changing it from say 010011 to 000000) this represents a very real elimination of physical patterns and therefore a reduction of entropy, violating the second law of thermodynamics. To preserve the 2nd law Landauer proposed that enough heat must be released to increase the entropy of the cosmos, to more than offset the decrease in entropy of the memory storage device. This implies that any deletion of information must lead to a release of heat and this is now called Landauer's principle.

All this makes clearer something I've been trying to do for a long time: to show that another way of thinking about MiHsC is to regard it as a conversion of information to energy, and that what is being conserved in nature is not mass-energy, but EMI (energy+mass+information). I've recently managed to show that when an object accelerates, information of a particular kind is deleted and the amount of energy released looks very much like MiHsC. I'm unwilling to say more now because I've just submitted a paper on this (McCulloch, 2015), but this is an exciting new development, bringing information theory into the mix, and it's nice to be able to derive MiHsC in two different ways: 1) from the fitting of Unruh waves into horizons and 2) from information loss.


Landauer, R., 1961. Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5 (3): 183–191.

Toyabe, S., T. Sagawa, M. Ueda, E. Muneyuki, M. Sano, 2010. Information heat engine: converting information to energy by feedback control. Nature Physics 6 (12): 988–992. arXiv:1009.5287

McCulloch, M.E., 2015. Inertial mass from information loss. Submitted to EPL..

Moore, D., P. Cook, 1964. One Leg Too Few. https://www.youtube.com/watch?v=lbnkY1tBvMU

Monday, 28 September 2015

Resisting the end of physics

Things go in cycles, they say. Maybe more in history than in physics. In 600 BC Thales started an era of scientific thought by rejecting the idea that nature is driven by the Greek Gods and argued that it was made of water. This idea was more incisive than it seems at first sight, because unlike every theory that preceded it, it was testable. This great tradition of Greek science continued for seven centuries and included such greats as Aristarchus who suggested the Sun-centred Solar system and Hero with his steam engine (AD 100).

The death blow for Greek astronomy occurred seven centuries after Thales, when Ptolemy in 150 AD used the new tool of geometry, to make a complex Earth-centred model using many oscillating circles (epicycles) which worked well enough to fit planetary motion, for the wrong reasons, as it is easy for complex systems to do. After Ptolemy 1200 years of intellectual darkness descended (despite a few brief flashes in the dark). Of course, it was not all poor Ptolemy's fault since the zeitgeist was moving away from science as well, he was more like a symptom than a cause, but the effect of the epicycles on human thought was dulling.

Scientific enquiry started again 1200 years later around 1300 AD when William of Occam realised that complex models are false friends, and can easily be right for the wrong reason, and proposed Occam's razor (keep it simple). 'Roger' Bacon (thanks qraal) then supported the importance of experimental evidence. Humankind was finally self-correcting and after people like Kepler, Galileo and Newton applied logic (maths) to this reawakened scientific mindset a revolution soon followed.

Now seven hundred years after Occam and Bacon, physics is in danger once more. This time from dark matter, which is just as insidious as Ptolemy's epicycles: a complex fudge to allow an old theory to fit new data. Physicists have used data from galaxy rotation and the new tool of computers to work out what ad hoc complex distributions of invisible stuff will allow the old theories to fit the newly-observed galactic rotation and in so doing have backed themselves into a dark corner it'll be hard to get out of. Specifically, it is unsatisfactory because:

1. Dark matter is ad hoc. It is added to the cosmos by definition to make general relativity predict the data, so, like the epicycles, it inverts the scientific method of changing theories to suit facts, and changes uncheckable 'facts' to suit the theory.

2. It is complex. Rather like the epicycles, it has so many versions and so much flexibility that it is possible for it to appear to work, and yet be absolute rubbish.

3. Mainstream astrophysics must now claim that 95% of the cosmos is made of dark stuff and their model therefore predicts only 5% of the cosmos. If the Met Office only had a 5% success rate I think they'd be revising their model.

4. Dark matter is often presented in the articles I read as doubtless fact, always a danger sign.

5. Popper: any theory that is not falsifiable is not scientific. Dark matter is not falsifable. If they don't find any tomorrow they'll ask for funding to look in a different regime, as has happened many times.

My point is that if dark matter is allowed to absorb almost all the physics funding, then it will stop progress in the same way that Ptolemy's epicycles killed Greek astronomy. It is right on cue as well, roughly seven centuries after Roger Bacon and William of Occam restarted the scientific process. We need to look back at the mindset they had: take no-one's word for it, keep it as simple as possible, look at the data without prejudice, disregard received opinion. The opposite to today's mainstream.

Observations used by Galileo to prove the Sun-centred theory which could have saved Aristarchus' model much earlier, are the phases of Venus. In Ptolemy's Earth-centred Solar system model, Venus could never be behind the Sun, so could never be fully illuminated (see the first reference below). It should have always shown a crescent. In reality, Venus shows phases, sometimes full, sometimes crescent, supporting a Sun-centred model. These phases are just about visible to the naked eye and had been noticed, it is thought, by the Babylonians (Venus has horns they said). Aristotle was sensibly susceptible to data: he had decided the Earth was round by looking at the curved shadow of the Earth during a lunar eclipse. Just imagine if he'd studied the phases of Venus? Being swayed by observation he may well have opted for a heliocentric theory and erased 1200 years of human stagnation. We might be settling Tau Ceti now..

More to the point, what observations in our time unambiguously discredit dark matter? The problem is that dark matter's adjustability (like the epicycles) means it is not easily falsifiable, but there are some data that embarrass it, eg: the anomalous spin of globular clusters which are too small to have dark matter, the alignment of quasars, the critical acceleration in galaxies, the overall agreement of lots of anomalies with MiHsC. Acceptance of these observations at this point may well save us from a 1200 year dark age.

Send any further such observations to the Seldon project, planet Terminus, or, failing that, post a comment below :)


Venus reference: http://astronomy.nmsu.edu/geas/lectures/lecture11/slide02.html

Asimov, I., 1951. Foundation. Gnome Press.

Friday, 18 September 2015

The Magellanic Clouds and MiHsC

The Large and Small Magellanic clouds (LMC and SMC) are galaxies just outside the Milky Way, named after the explorer Magellan. These minor galaxies appear to be gravitationally bound to our Milky Way galaxy because they have left a trail of debris behind them, called the Magellanic stream, that curves around in a way that seems to show that they are orbiting our galaxy, see the schematic below:

However, as for almost every orbit on a cosmic scale (galaxy clusters, disc galaxies, dwarf galaxies, globular clusters, Proxima Centauri) the observed orbital velocity is so high that the orbiting mass should break free and zoom off to infinity. The observed orbital velocity of the LMC around the Milky Way is 378 km/s (Kallivayalil, 2013). If we assume Newtonian physics and that the Milky Way has only baryonic (normal) matter, this predicts an orbital speed v = sqrt(GM/r), where G is Newton's gravitational constant, M is the Milky Way's mass and r is the radial distance. This predicts that the maximum orbital velocity that the LMC can have without breaking away is 75 km/s. Oops. So, the LMC should have broken away, but the Magellanic stream suggests it hasn't.

If we assume the usual amount of dark matter in the galaxy, so boost the galactic mass by a factor of ten by adding an invisible and unexplained new kind of matter, then this predicts a maximum orbital velocity before breakaway of 237 km/s, so the LMC should still break away in contradiction to the Magellanic Stream.

MiHsC says that because of its low acceleration outside the galaxy, the LMC has lost some inertial mass and it predicts the following orbital speed, the second term being due to MiHsC:

v = sqrt(GM/r + 2c^2r/Theta)

where c is the speed of light and Theta is the Hubble scale. The MiHsC maximum speed for LMC boundedness is

v = 967 km/s

The observed orbital velocity of the LMC is 378 km/s, so from these examples you can see that MiHsC predicts that the LMC is bound to the Milky Way and is consistent with the observation of the Magellanic Stream that seems to show a bound past trajectory for it. Of course, you can mess around with dark matter arbitrarily till you get the answer you want, but that arbitrariness is deeply abhorrent.


Kallivayalil et al., 2013. http://arxiv.org/abs/1301.0832

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. Space Sci., 342, 575-578. http://arxiv.org/abs/1207.7007

Saturday, 12 September 2015

Singularities forbidden?

I usually avoid discussing things like the invisible interiors of black holes, since any predictions are not directly testable, but there is one component of black holes that has been solidly observed and is unexplained: relativistic jets, and these past few days I've realised that, as well as a minimum, MiHsC predicts a maximum acceleration that might get rid of black hole singularities in a way that could be tested by predicting these jets.

I've already shown that MiHsC predicts a minimum acceleration for nature similar to the size of the observed cosmic acceleration (McCulloch, 2010). To recap: MiHsC assumes that inertial mass is caused by Unruh radiation (a radiation seen by objects that accelerate) and that only Unruh waves that fit exactly into the Hubble scale are allowed (since partial waves would reveal what lies behind the horizon: a logical impossibility). The wavelength (L) of the Unruh radiation seen increases as an object's acceleration reduces, and is given by L = 8c^2/a, where a is the acceleration. At tiny accelerations the Unruh wavelengths stretch so that a greater proportion of the waves do not fit within the cosmos (width of cosmos W = 2.6x10^26 metres wide), and at an acceleration of a = 8c^2/W ~ 7x10^-10 m/s^2 no Unruh waves can fit at all. The point is that before an object moving out into deep space manages to achieve this tiny acceleration the MiHsCian collapse of its inertial mass boosts its acceleration. The result is that its acceleration (relative to other matter) can never drop below 7x10^-10 m/s^2. This explains the recently-observed cosmic acceleration.

The Hubble scale is one horizon beyond which we cannot see, another obvious one is the tiny Planck scale (1.6x10^-35 m), so it makes sense to say that Unruh waves shorter than the Planck scale cannot exist (again using Mach's philosophy that only things that can be seen in principle can exist) and so it should be impossible in MiHsC for accelerations to be so large that the Unruh waves are shorter than the Planck scale (lp). Since the Unruh wavelength = 8c^2/a > lp this means that a < 8c^2/lp so a < 4.5x10^52 m/s^2.

The great Sakharov (1966) predicted a similar maximal acceleration, also using Unruh radiation, but without connecting it to inertial mass. Also Caianiello (1984) predicted a similar size of maximum acceleration in a very different way: starting from the uncertainty principle. This maximum may be testable on Earth: Papini (1995) have suggested that light resonating in cavities might be used to generate accelerations this large and that type-I superconductors could experience accelerations as large as this already.

Now back to the black holes. Non-rotating black holes have the problem that general relativity embarrassingly predicts that they have infinite-density singularities at their centres. MiHsC changes this dramatically because it suggests that at soon as the acceleration reaches the maximum near the centre the inertial mass will collapse. I can't picture what such a collapse would do yet, but it is interesting because the physics will somehow have to adjust to keep the acceleration below the maximum (smoothing the singularity) and the energy released could power the unexplained relativistic jets.


Caianiello, E.R., 1984. Lett. Nuovo Cimento, 370.

McCulloch, M.E., 2010. Minimum accelerations from quantised inertia. EPL, 90, 29001. arXiv

Papini G., A. Feoli, G. Scarpetta, 1995. Phys. Lett. A., 50.

Sakharov, A.D., 1966. JETP Lett., 3, 288.

Thursday, 3 September 2015

Two body thought experiment

Imagine there are two masses, alone in the cosmos. We could call them A and B but I'm tired of Alice and Bob, so let's call them Amy and Sheldon and let's assume, that Ernst Mach was right and that they cannot deduce their acceleration relative to that unmeasurable concept 'absolute space', and can only deduce their acceleration with respect to each other. How romantic! Here they are, and I'm assuming they're wearing futuristic transparent plastic shields (a la Galaxy Quest) to keep them alive in space:

Now let's imagine that Sheldon has a jet pack. It's just the kind of thing Sheldon would have in such a circumstance. Now he fires it and accelerates to the right with respect to Amy. Physics sees this relative acceleration and decides to form a Rindler horizon to Sheldon's left and according to MiHsC this damps the Unruh radiation on the left side of him so he feels more radiation pressure from the right than the left and that pushes him back a little against his acceleration to the right. "Oh, yes", drawls Sheldon, "that's Mike's quaint little explanation for inertia isn't it? I deduce that Mike's writing this story". Very clever Sheldon, but what about Amy? Physics sees Amy accelerating to the left with respect to Sheldon and puts a Rindler horizon to Amy's right which damps the Unruh radiation there and drags her to the right. Oddly enough, Amy is now following Sheldon's motion! "This is very annoying" thinks Amy since she's trying to play hard to get (difficult enough with Sheldon already!), but she is willing to admit, being a member of the fair sex, that this is logical in the MiHsCian world.

What all of this means is that when you consider Mach and MiHsC, and you have two bodies side by side in an empty universe. If you move one, the other will move to follow it. If you have three bodies though, it won't be the same since the mutual accelerations are now more complex, so that if Howard and his turtleneck was there as well, then Amy would be less sensitive to Sheldon's movements and could play hard to get more successfully. This is what is predicted by MiHsC for this contrived situation.

So where's the evidence? Well, in our far more complex world it is difficult to set this experiment up, but in my opinion an inkling of this occurred when Martin Tajmar span his supercooled disc and a nearby accelerometer moved with the disc without frictional contact, rather similar to the way that Amy moved with Sheldon in the thought experiment. Indeed MiHsC predicts these Tajmar results pretty well (McCulloch, 2011). This effect is likely to be more obvious on a cosmic scale, since objects in deep space are closer to being lone masses, and it has been found recently for example that quasar and galaxy spins are aligned.


McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 39002. arXiv

Monday, 31 August 2015

Why MiHsC is Compelling

One of the things I'd most like to convince physicists of is that MiHsC is fantastically compelling compared to theories like dark matter, dark energy and, say, string theory. To see why, consider the most famous anomaly in physics: the galaxy rotation problem. The outer edges of disc galaxies spin too fast to be held in by the gravity of the small amount of visible matter we can see in the middle. What is not well known, and which was first pointed out by Milgrom, is that the misbehaviour of the stars always starts at the radius from the galactic centre where the rotational acceleration of the stars falls below a critical value, about: 2x10^-10 m/s^2. This critical radius is different for each galaxy, but the critical acceleration is always the same, for globular clusters too (which cannot contain dark matter, by the way) and this is unlikely to be a coincidence.

There is no physical reason why invisible (dark matter) should suddenly appear at this critical acceleration and so it has to be added arbitrarily rather like the aether of the 19th Century or Descartes vortices of the 17th, but if you assume that inertia is caused by Unruh radiation, as MiHsC does, then this all makes sense, because at just this critical acceleration the Unruh waves get long enough (they get longer as accelerations decrease) to be disallowed because they do not fit exactly within the Hubble scale. In MiHsC the cosmos is modeled like a drum, in that only certain wavelengths can exist in it, those with nodes (where the waves' amplitude is zero) at the edge (this is because partial waves would allow us to infer what lies beyond the Hubble horizon, a logical absurdity). In a disc galaxy this means that Unruh waves for stars at the galactic edge are too long to fit, and those stars loose inertial mass because of MiHsC, so that the centrifugal force that would otherwise blow the galaxy apart reduces, and the stars stay nicely bound despite the apparent lack of gravitating matter.

It's always good if theories that have been designed to fix one problem, also fix other ones for free, and MiHsC does that: it predicts the cosmic acceleration discovered in 1999 by Riess and Perlmutter et al without needing any arbitrary dark energy to be added. It also explains a whole plethora of other embarrassing anomalies that have been brushed under the carpet recently, such as the flyby anomalies, the Pioneer anomalies, the Podkletnov and Tajmar effects, the anomalous decrease of power in the cosmic microwave background at large scales, the Tully-Fisher relation and the emdrive, and these are only the anomalies I've managed to publish papers on. There are many more that I suspect can be explained by MiHsC but haven't managed to prove yet, eg: galactic jets, globular clusters.

So to conclude: MiHsC is simple, has a logical philosophy to it, is compelling in the way mentioned above, and agrees with more data than does the standard model (without invisible matter having to be added). I would ask physicists to consider these points without prejudice. There is a lot of scope in MiHsC for development, and they could certainly improve on the mathematical/computational techniques that I have used so far.

Tuesday, 18 August 2015

So hard to create, so easy to destroy

One of the sadnesses in suggesting something new is people trying to erase or forbid it. I've already been blacklisted by the arXiv, as have many others I believe, for nothing more than daring to think differently, and now there's an minor online MiHsC-war going on with some people adding very well-written wikipedia pages on MiHsC (not necessarily believing MiHsC, but motivated to present the full range of ideas), and others trying to delete all mention of it, always anonymously and without citing any experimental counter-evidence. In response I said this on twitter recently: "To online deletors of ideas: what'll you say in the retirement home? Will you boast of the thoughts you silenced? The possible futures you erased?"

It is possible for a paradigm to survive not because it is more successful, but because it deletes the alternatives, and this is what an unscientific minority of dark matter supporters are doing. One of the safest criteria by which to identify the wrong side in any period of history is to see who is erasing information (burning books) because they can't engage in debate. Information creators always win in the long term.

Friday, 7 August 2015

The Emdrive Energy Paradox

As always, treat this blog entry with due skepticism: I'm thinking aloud in the hope of constructive feedback.

The emdrive energy paradox was found and is discussed nicely by frobnicat (from the NSF forum) in the emdrive wiki reference below. The problem is as follows. The rate of electrical energy input to the emdrive is constant so the total energy put in goes up linearly with time, but the kinetic energy (KE) stored and available for extraction from the emdrive's motion is: KE = 1/2mv^2 and since the acceleration is constant, v is a linear function of time so KE depends on t^2. Eventually, at high enough speeds, the KE exceeds what we put in! Therefore there must be a new source of energy here, one which provides more energy at higher speed. How is this possible?

It's not possible using standard physics, but is using MiHsC which considers the zero point field. The force or thrust predicted by MiHsC is like an inertial force (in fact, I claim it is the inertial force, see McCulloch, 2013) and a characteristic of inertia is that no matter what the speed of an object is, its resistance to acceleration, its inertia, is the same (This fits with special relativity's insistence that the laws of physics should be independent of speed, which is a relative thing). The MiHsC/inertial force is then also like whatever force is driving the emdrive, since no matter what the emdrive's speed is, the force on it seems always the same. This last point is an increasingly solid observation: as frobnicat's points out on the NSF reference below, the emdrive has been tried in different places and times and if its behaviour depended on something so meaningless (after Einstein) as 'speed' then it would have given very different results at different times since the Earth is moving with respect to everything else, and spinning.

So where does this new energy come from? To be more mechanistic about it, the MiHsC paradigm says that the asymmetric structure of the cavity makes a gradient in the density of Unruh radiation (zero point energy) and that this gradient is the new source of energy. For more detail see here or  here. New sources of energy always cause an uproar, but in just this way MiHsC predicts inertial mass, galaxy rotation, cosmic acceleraton & the emdrive quite well. I did suggest a more direct test for the mechanics of this (if applied on the nanoscale) here.


Emdrive wiki: http://emdrive.wiki/Energy_Conservation

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

McCulloch, 2015. Energy from swastika-shaped rotors. Progress in Physics, 11, 2, 139-140. pdf

Monday, 3 August 2015

Observations that dark matter can't explain

Someone recently told me there's a new contender for dark matter, a 'new kind of pion', as well as the WIMPs and axions and assorted possibilities that have been suggested before and haven't been seen, so I thought I'd explain why I don't believe there is any form of exotic dark matter in the amounts needed to hold galaxies together.

First, as we all know by now, the rotational velocities of stars around galaxies are too great for them to be held in by the gravity of the mass we can see in them, hence the ad hoc addition of 'dark' matter. Anything ad hoc is bad science in the first place, but the crucial observation here is that this discrepancy always starts at the galactic radius where the stars' rotational acceleration drops below a critical acceleration of 2x10^-10 m/s^2 (Milgrom, 1983). It is difficult to hypothesize any type of matter that would suddenly appear at a specific low acceleration like this, but it is easy to hypothesize a direct link with Hawking-Unruh radiation because at just that crucial acceleration the waves of this radiation become equal to the Hubble scale. This is a fascinating agreement out of which arises MiHsC theory.

Second, globular clusters are smaller, bound, collections of stars usually located in a sphere around the centre of the galaxy (last week I spent some time searching the sky for them when I was on holiday in Cornwall) and wide binaries are bound stars very far apart. Both of these types of system show the same odd behaviour as the much larger galaxies that surround them: at radii where their stars fall below an acceleration of 2x10^-10 m/s^2 they start to rotate around the systems too rapidly for standard physics (Scarpa et al., 2006, Hernandez, 2012). The crucial point here is that in these cases dark matter cannot be used to fix the anomaly since it must be smooth on these scales to allow it to work on galactic scales, so you can't pack a lump of it into the globular cluster or binary system to bind it gravitationally. This implies that whatever effect is happening in globulars (ie: not dark matter!) also applies to the similarly-misbehaving galaxies (MoND theory also fails for globulars which are close to the galactic centre and so the 'external' acceleration is larger than 2x10^-10 m/s^2).

There are also more philosophical reasons for disliking dark matter: science always progresses by presenting old theories with embarrassing new data, so that those theories can be improved. What the dark matter paradigm is doing is defending an old theory by changing the 'observations' (adding unseen mass) which is a complete reversal of the scientific process and more resembles the machinations of the dark ages.

The solution, as ever, is to use crucial observations to force old entrenched theories to make themselves so complex that they collapse in ridicule under the weight of their own convolutions: I hope globular clusters and wide binaries can be useful in this respect.

"You see, the thing that really finishes a Boggart is laughter. What you need to do is force it to assume a shape that you find amusing." - J.K. Rowling (Harry Potter & the Prisoner of Azkaban).


Milgrom, M., 1983. A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. Astrophys. J., 270, 365.

Scarpa et al, 2006. Globular clusters as a test for gravity in the weak acceleration regime. Proceedings of the 1st crisis in cosmology conference. http://arxiv.org/abs/astro-ph/0601581

Hernandez, X., M.A. Jimenez, C.Allen, 2012. Wide binaries as a critical test of classical grvaity. http://arxiv.org/abs/1105.1873

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. Space Sci., 342, 575-578. http://arxiv.org/abs/1207.7007

Tuesday, 14 July 2015

MiHsC and EmDrive: Clarification

It seems, after several comments I've received, that the way MiHsC (may) work on the emdrive is easily misunderstood (including by me, so I've just rewritten this blog again!). Anyway, here is an attempt to clarify it and explain why I think you get a push consistently towards the narrow end from MiHsC and why, although new physics, it is at least perfectly self-consistent. This is based on the maths in my published paper (see the reference below).

Imagine a microwave photon bouncing from end to end of the emdrive cavity (see the diagram below). As the photon goes from the narrow end to the wide end (see the lower arrows) the number of allowed Unruh waves increases because of MiHsC (more are allowed on the right because the cavity is wider) so the photon's inertial mass increases (so the right hand arrow is thicker). This means that MiHsC has disturbed momentum conservation, which can only be satisfied by applying a leftwards force to slow the photon down (its speed is represented by the arrows' length).
As the photon bounces off the right end plate and goes leftward again (upper arrows) it looses inertial mass by MiHsC (the upper left hand arrow is thinner) so the only way to satisfy momentum conservation is again to apply a leftward force to speed the photon up (the left hand arrow is longer). In both cases, to satisfy both MiHsC-induced mass changes and the conservation of momentum, a new force must appear towards the narrow end. Since the momentum at both ends is the same, the photon pressure on the end walls cancels (see this previous post). This new thrust predicted by MiHsC agrees quite well with the emdrive data (see the reference below).


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

Tuesday, 7 July 2015

Ode to MiHsC

A more lighthearted summary of MiHsC, occasionally veering into a Yorkshire accent:

Inertia means you coast along, no-one ever explained the why,
but when you accelerate, a horizon opens behind you as you fly.

The horizon's like a black hole's, so it gonna be damn hot.
You'll see Unruh-heat, if accelerating, but nowt at all if not.

Heat is waves, and MiHsC theory says: they must fit from you to the horizon
because partial waves would let you see behind Mach's forbidden curtain.

So from behind you, horizonward, there'll be fewer waves impacting
The waves in front'll push you back, just as inertia's long been acting

OK so far, but can MiHsC say why in deep space physics fails?
In that slow realm the waves are as long as Hubble's cosmic scales.

So there MiHsC disallows more waves and inertial mass collapses.
Quite a shock, but maybe welcome if you've 'et too many biscuits.

Galaxies spin so fast the centrifugal force should explode 'em all.
MiHsC reduces this inertial force just right: it's really on the ball.

Cosmic acceleration is predicted since before accelerations disappear,
the Unruh waves grow too long to fit into Hubble's sphere.

Dark matter is like Ptolemy's epicycles on steroids, by computer.
MiHsC works with just a few lines, on a piece of paper.


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.

Sunday, 31 May 2015

MiHsC & emdrive: a new approach.

In previous work I've offered an explanation for emdrive in terms of MiHsC operating on the light within the emdrive cavity (see McCulloch, 2015), and I have not abandoned this photon based approach (I'm now convinced it is better, but might benefit from the diagram below). However, in the past couple of days I've wondered whether I can do it, probably with the same maths, by looking at the cavity instead and forgetting about the light, except as a source of vibration. This schematic shows what I have been considering.

It shows, on the left, a cubic cavity (black box) accelerated left (upper panel) and right (lower panel) by the microwaves in the cavity. In each case a Rindler horizon (red curve) appears in the opposite direction to the acceleration and MiHsC then damps the Unruh radiation more on that side (see the red dashed line which shows the decrease of power in the Unruh spectrum going towards the horizon, ie: the red line trends down). This gradient in the Unruh spectrum then pushes the cubic cavity in the opposite direction to whatever acceleration it had and thereby gives it inertia (McCulloch, 2013).

Now look at the emdrive cavity (right hand side). Again we accelerate it left and right, and again the Unruh radiation spectrum decreases towards the horizon making a force that counters the initial acceleration, but now the cavity itself, assuming it's like a horizon and MiHsC applies, also damps the Unruh radiation more at the narrow end (see the green dashed line, which shows decreasing power towards the narrow end). This then, for both left and right acceleration pushes the emdrive towards its narrow end. The acceleration is essential, because without it you wouldn't have the Unruh field and the cavity wouldn't be able to make it asymmetric.

This is a different way of thinking about it than using photons, but it uses MiHsC in the same way and cuts out having to worry about light which is difficult to visualise. Comments welcome!


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

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

Friday, 22 May 2015

Emdrive: whence motion?

Imagine an object in empty space accelerating rightwards. Now information from beyond a certain distance to its left, limited to light speed, can't catch up so there is an  information horizon, and the volume to the left of that horizon can never be seen by the object. A radiation like Hawking radiation comes off this horizon (Unruh radiation).

The first new contribution of MiHsC is that it says Unruh radiation is damped between the object and the horizon. Ernst Mach said, 'what can't be seen, can't exist', so from the point of view of the object all fields beyond the horizon must be zero, so they must be zero on the horizon too. Therefore, only waves with nodes at the horizon can be allowed. This cuts out many Unruh waves on the left side but not on the right, so more Unruh radiation hits the object from the right, slowing its acceleration. This correctly models what we call inertia, which has never before been explained. In general the horizon makes the zero point field, hitherto hidden, suddenly vary in space and able to push on real objects (see reference McCulloch, 2013, below).

The second part of MiHsC is that the Unruh radiation is also damped slightly by the far off Hubble horizon which cuts out some long wavelength Unruh radiation. This weakens the part of MiHsC described above, and so weakens inertia slightly in a new way. This makes more difference for low acceleration objects (which see long Unruh waves) and in this way MiHsC correctly models galaxy rotation without dark matter, and cosmic acceleration without dark energy (McCulloch, 2012).

Now to the emdrive: the photons in the cavity have inertial mass (photons in a mirrored box do) so MiHsC should apply. If we assume that the cavity walls are like the cosmic horizon in MiHsC then they will damp some Unruh radiation and make inertia weaker, but less so at the wider end. So the photons at the wide end have more inertia, and photons gain mass going from the narrow to the wide end. You'll note that mass-energy is not conserved in the usual way here because the horizon causes the zero point field to become real: just as black hole horizons cause virtual particles to become real (Hawking radiation). To conserve momentum the cavity has to move towards the narrow end. This predicts the emdrive results quite well, see here.

The application of MiHsC to the emdrive is summarised and derived properly (mathematically) in the paper below (McCulloch, 2015) and I'm mentioning it here in the hope of stimulating much needed debate.


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

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. and Space Sci., 342, 2, 575- Link

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