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

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. 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 very large 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 an stagnant heirarchical society where a few try to make money off the rest. We need a collective 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). 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.

More to the point, what observations in our time unambiguously discredit dark matter? This is not easy, because it is not easily falsifiable (not due to robustness, but through adjustability), but I believe there are some data that embarrass it, eg: the anomalous spin of globular clusters which are too small to have dark matter. The critical acceleration in galaxies. The overall agreement of lots of anomalies with MiHsC. A crucial observation at this point may well wipe out in advance 1200 years of human stagnation (send any further crucial observations to the Seldon project, planet Terminus, or, failing that, post a comment below).



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