I've suggested (& published in 21 journal papers) a new theory called quantised inertia (or MiHsC) that assumes that inertia is caused by horizons damping quantum fields. It predicts galaxy rotation & lab thrusts without any dark stuff or adjustment. My University webpage is here, I've written a book called Physics from the Edge and I'm on twitter as @memcculloch. Most of my content is at patreon now: here

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