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

Thursday, 14 July 2016


It would be good to test MiHsC directly with an experiment. One proposal I made in a paper in 2013 (see reference) was to try to damp Unruh waves on one side of an object so that the Unruh waves that impact it on the other side push it along. The problem is that Unruh waves are lightyears long for normal low accelerations, and you'd have to accelerate/spin a disc very fast to make Unruh waves short enough so they can be damped by standard technology. Accelerating heavy discs is problematic.

Since then I've shown that MiHsC seems to predict the emdrive fairly well, and this implies that MiHsC also modifies the collective inertial mass of photons (McCulloch, 2016). The logical conclusion is, instead of using heavy discs, why not rotate light in a similar way? The method would be as follows: put photons into a fibre-optic loop (see the white loop in the diagram) and put a metal baffle on one side (the grey rectangle).

The photons will circle around the loop at light speed so that their acceleration will be huge and the Unruh waves they see will be of a similar size to the loop, and their electromagnetic component might therefore be damped by putting a metal shield on the left of the loop (the grey rectangle). That means there will be more Unruh waves hitting the fibre-optic loop from the right (more orange colour) than from the left (less orange) so the loop should move left. It rolls down a gradient in the Unruh radiation field.

I've done a simple calculation, and shown that if 2 Watts of power is put into the loop as photons, and if the loop has a Q factor of 10^6 then the thrust should be something like 21 mN multiplied by the efficiency of the damper in damping Unruh radiation (which I do not know, but the emdrive suggests might be close to one). This would be a kind of emdrive using light, not microwaves. A LEMdrive?


McCulloch, M.E., 2013. Inertia from a asymmetric Casimir effect, EPL, 101, 59001. Preprint

McCulloch, M.E., 2016. Testing quantised inertia on the emdrive. EPL, 111, 60005. Preprint

Monday, 4 July 2016

MiHsC and Gravity from Uncertainty?

I've always liked Heisenberg's uncertainty principle, and a few years back I managed to derive something that looks like gravity from it (see references). This approach is very appealing: it feels somehow like the open channel, and over the weekend I managed to derive something that looks like MiHsC inertia from it (with caveats, see below). I won't go into details before publication, but to explain vaguely: the uncertainty principle says that the uncertainty in momentum of an object (Dp=D(mv)) times the uncertainty in position of it (Dx) is equal to the reduced Planck's constant (hbar), see the equation in the diagram:

This is pure quantum mechanics, but what happens if now we apply it on the macroscale where it is not supposed to be valid, and add relativity? When any object (the blue arrows in the diagram) accelerates, say, to the left (black arrows), a relativistic Rindler horizon forms to the right (the black curves) and blocks a huge chunk of space since information can no longer get from beyond that horizon to the object. With greater acceleration the horizon comes closer (see the diagram). Why not say that this horizon reduces the uncertainty of position, Dx? (the red arrows). It obviously does since the 'knowable space' shrinks. If we assume that and apply the uncertainty principle, then the momentum (or energy/c) uncertainty goes up and this becomes available to produce the inertial force to oppose the original acceleration (blue arrows).

I did the maths over the weekend, and the inertial mass predicted this way looks like that predicted by MiHsC (which explains galaxy rotation without dark matter and cosmic acceleration.. etc) My previous derivations are actually equivalent, but this way is rather elegant. There is a 27% difference though, which can be explained by the crudity of the model I've used so far: I have assumed the horizon is spherical.

What is becoming clearer is that MiHsC is inevitable if you take seriously both relativity and quantum mechanics, and allow an interaction between them on large scales.


McCulloch, M.E., 2014. Gravity from the uncertainty principle. Astrophys. and Space Sci., 349, 957-959.

Friday, 24 June 2016

MiHsC & Interstellar Travel

I've been asked to summarise what MiHsC has to say about the potential for faster than light travel which I discussed towards the end of my recent radio appearance on The Space Show (link). This is of course of great interest scientifically, philosophically and practically for interstellar travel. It is also at the heart of MiHsC, which relies on local dynamics being affected by the far off Hubble edge. I cannot summarise it all in one blog, and the subject is even more on the edge than normal for me, so the tone of this blog will be more like a varied update on work in progress than the surer, didactic blogs I've tended to write recently.

It is well known that special relativity predicts that as an object or spacecraft approaches the speed of light, its inertial mass, as seen by a stationary observer, increases to infinity, forbidding further acceleration and enforcing a constant maximum speed somewhere below light speed (c) dependent on the power of the spacecraft's engine. Now (re: qraals comment below) I realise that faster than light travel is possible for those on the ship due to time dilation, but here I'm looking to resolve larger issues. MiHsC has a tiny correction to make to the usual picture: it says that a constant speed (zero acceleration) cannot be allowed because Unruh waves would then exceed the Hubble scale. So, even as the mass approaches infinity in relativity, and the acceleration reduces towards zero, the inertial mass will start to dissipate due to MiHsC. A tiny relativity-proof acceleration remains: 2c^2/HubbleScale = 6.9x10^-10 m/s^2.

Is there any observational evidence for this prediction? Yes: 2c^2/HubbleScale is close to the cosmic acceleration that was recently found using distant supernovae. Also see galactic jets. This also solves a paradox in that stars just inside the Hubble horizon are moving at just less than c, just beyond it they are moving just above c (relative to us) and so cannot be seen (this is one reason why the night sky is black). In relativity this transition should require infinite energy. Some say this is because space itself is expanding, but I dislike the use of undetectable entities like space in this way. In MiHsC this can be explained naturally by the minimum acceleration.

The huge import of this aspect of MiHsC (a=2c^2/HubbleScale) is that the relativity-proof acceleration is inversely proportional to the size of the Hubble horizon. If we could make a small shell-horizon we might be able to boost this acceleration. I mentioned this in a paper in 2008 and talked about all this at the 100 Year Starship symposium in 2010. I am returning to this subject now, because you can derive the emdrive results from MiHsC by assuming that the emdrive cavity is making such a shell, asymmetrically (see this blog entry) and NASA did detect a change in the speed of light inside the cavity which immediately interested me, but they did not pursue...

One huge problem with all this, also hard to think about, is how might faster than light propagation be reconciled with causality? This is the heart of the problem and so is a good place to start. The diagram below shows space along the x axis, and time (ct) along the y axis for two stationary observers (S1 and S2, light blue lines). It also shows the new skewed spacetime axes (dashed lines) seen by two moving observers (M1 and M2, dark blue lines). With this diagram we can look at the implications of allowing faster than light travel.
Imagine S2 at spacetime point P2 tells a passing M2 that he's just hit his own thumb with a hammer and we allow M2 to send this information to co-moving M1 instantaneously (along their moving x axis: see upper red arrow). M1 just happens to be passing the stationary S1 who he tells about the accident. S1 can now instantaneously tell S2 at the earlier time of P1 about the hammer and S2 can hire handyman Harrison Ford to do it and this changes the future. This paradox arises for instantaneous communication, and also for any communication faster than light speed, but there is something missing from this picture that has forced people like Novikov and Hawking to set up 'Chronology Protection Conjectures' that demand that this sort of thing can't happen. This seems to me a cheat. It should come out of the physics. MiHsC might model this more naturally by bringing in information. Sending information from P2 to P1 destroys a future and there is an energy cost to that, that would preclude this in most macroscopic cases, but maybe not for special quantum cases.

For example, the Einstein-Podolsky-Rosen paper and Bell's tests have shown that spooky action at a distance or future-past interaction probably does occur for quantum systems and I have written a paper (not accepted yet) showing how this can be allowed for quanta since there are only tiny exchanges of information between future & past. I think that time is porous and allows information through in small doses.

Coming back to more practical matters. How might you design a MiHsC-Shell? It would be an array of metamaterials (metal structures) surrounding a spaceship which damp the em-component of Unruh waves likely to be seen by it, at whatever acceleration it is undergoing. If the ship accelerated at 9.8 m/s^2 for example, the Shell would need to deselect em waves of length 7x10^16 m (forgetting relativistic effects for now). If you could do that then the spaceship would have less inertial mass and would be easier to accelerate, and then you'd need to change your tuning to accommodate that change in acceleration. It could also be done by damping more Unruh waves at the front of the ship than the back, for example.

MiHsC offers a tiny chink of light to those wanting interstellar travel, in helping getting to speeds close to c by inertial control (Tau Ceti in a human lifetime), and maybe more, but thinking about space and time is difficult because they are so fundamental. It is rather like trying to rebuild the floor of a tree house while you're standing on it! It's best done with experiments to light the way and for now, I would like to see the great NASA Eagleworks try some more of those emdrive interferometer experiments and publish the results.


Bennet, G.L., H.B. Knowles, 1993. Boundary conditions on faster than light transportation systems.

McCulloch, M., 2008. Can the flyby anomalies be explained by a modification of inertia? JBIS, 61, 373-378.

Monday, 20 June 2016

The Pull of the Distant Horizon

MiHsC (the first model that explains inertia) works using horizons, which are boundaries in space between areas that can get information to us at light speed, and areas which can't, like black hole event horizons. If you accelerate away from a region of space fast enough it means that information there suddenly cannot get to you and an information horizon forms cutting it off. In MiHsC this horizon damps the zero point field on the side opposite to your acceleration vector, so you roll down a gradient in the zpf towards the horizon, and this models inertial mass. I wrote a twitter-poem to summarise this:

  If you move to the right,
  the left's out of your sight.
  so a 'horizon' appears,
  damps zero point fields,
  pulling u back.
  Inertia is that!

The idea of information horizons may seem abstract, but this model explains a lot (eg: galaxy rotation without dark matter) and there is one big clue that is obviously MiHsC-like. The biggest object we can ever hope to see is the Hubble horizon. Distant stars are moving away from us at faster than the speed of light, so their information is lost to us. This causes the Hubble horizon surrounding the sphere of the visible universe.

The other interesting observation, made by Reiss and Perlmutter in 1999, is that the entire universe is accelerating away from itself. This phrase is easy to say, but the universe is a pretty big thing. You may have tried to push a car which is maybe 1000 kg in weight, and if you're like me, you'll have had difficulty. The cosmos is 10^49 times heavier than that, and yet something is accelerating it! Modern physics just glibly invents this so called 'dark energy' but suggests no origin for it. The amount of energy involved here would be very useful if we could understand and therefore control it.

MiHsC provides the right amount of energy straight away. It can be explained using Unruh waves as I have before, and also in a simplified mechanistic way by the diagram above. The Hubble horizon is shown by the black circle. The red is the zero point field (energy usually unavailable to us, because it is spatially uniform). MiHsC means that the ZPF is damped between the yellow stars and the Hubble edge (see the orange areas) so that more energetic virtual particles hit the stars from the cosmic centre, then from the other direction accelerating the stars outwards towards the Hubble horizon. Note that the acceleration of the stars is due to their apparent vicinity to the Hubble horizon from our point of view. from their point of view it would be us near the horizon, and us accelerating. MiHsC predicts the cosmic acceleration very well.

Can gravity also be modeled this way? Could it be due to objects making sheltered regions in the zero point field (see the narrow orange corridors)? I have not yet managed to show the mathematically.

Cosmic acceleration is the biggest clue (in size and mass-energy) we've ever been given by nature, and it points clearly to MiHsC. What if we could produce such an gradient in the ZPF in a lab? We could get new energy out. In my opinion, this is what the Casimir effect and the emdrive are doing.

Saturday, 11 June 2016

A Smoking Gun in Every Galaxy

Why am I so confident that MiHsC / quantised inertia is right? There are as many reasons as there are pieces of data I've tested it on, a lot, but one particularly compelling reason is illustrated by the schematic below. It shows a typical disc galaxy. In the inner part, in yellow, the stars are always well-behaved and all orbit the galactic centre just as they should according to Newton (or general relativity), but in the outer orange part madness ensues as they orbit far too fast for Newton.

It was noticed by Milgrom (1983) that the transition yellow to orange always occurs at an orbital acceleration of 2x10^-10 m/s^2. This is also true by the way of globular clusters that dark matter cannot be applied to. The wavelength of Unruh radiation depends on acceleration (a) as follows: wavelength~8c^2/a. For stars in the yellow the orbital acceleration (a=v^2/r) is high, so the Unruh wavelength is short (shown by the bottom red sine wave). As you go radially outwards, the orbital acceleration drops, so the Unruh waves lengthen (see the second red wave from the bottom). Near the point where the stars start to misbehave the Unruh waves become as long as the Hubble scale (see the two upper red curves). Milgrom noticed this telling link between dynamics and cosmology but could not explain it in his MoND model (this critical acceleration has to be input by hand) and if you try the numbers: wavelength = 8c^2/(2x10^-10) = 36x10^26m you'll see the predicted Unruh wavelength is 14 times larger than the Hubble scale which is 2.6x10^26 m.

MiHsC specifically explains this dynamics-cosmology link, and although it predicts a different critical acceleration (a=6.9x10^-10 m/s^2), the point is: it predicts it! MiHsC says that the inertial mass of objects is caused when they accelerate and an information horizon forms damping Unruh radiation, making it vary in space, and so able to push to oppose the initial acceleration. However, only Unruh waves that fit exactly (resonate) within the Hubble horizon are allowed (those with nodes at the horizon, see the diagram). The logic is that partial waves would allow us to infer something outside the horizon (that part of the wave) which would defeat the purpose of the horizon. So, as the Unruh waves lengthen, a lesser proportion of them are allowed (it is rather like a Hubble-scale Casimir effect) so the outer stars' Unruh-radiation-induced inertial mass collapses, they feel less centrifugal force, and so they can orbit much faster without the galaxy exploding. In this way MiHsC predicts galaxy rotation, with no dark matter needed.

The fact that the Unruh wavelength stars see when they start to misbehave in galaxies is equal to the observed distance to the Hubble horizon, is a direct indication of MiHsC. A smoking gun in every galaxy. Something that the ad hoc dark matter hypothesis can never hope to achieve.


Milgrom, M., 1983. ApJ, 270, 365.

McCulloch, M.E., 2007. MNRAS, 376, 338-342. https://arxiv.org/abs/astro-ph/0612599

Sunday, 22 May 2016

We learn by doing, MiHsC, emdrive

I'm always saying to my students that "The best way to learn is to do", and I always enjoy scribbling back-of-the-envelope calculations (in the manner of Hans Bethe and Enrico Fermi) so here's a quick MiHsC-emdrive calculation I did recently. Note that it is not as rigorous as my paper, it is a heuristic simplification.

It is important to have a real experiment as a basis, so I've used Shawyer's first experimental setup, with a cavity Q = 5900, power input P = 850W, cavity length L = 0.156m, wide end width = 0.16m, narrow end = 0.1275m, and I've assumed a mass of 10 kg (as you'll see this last is unimportant as it cancels out).

Step 1. Calculate the mass of light in the cavity

The time for a photon to dissipate, given Q is
T = distance/c =  QxCavityLength/c
T = 5900x0.156/3x10^8 s
T = 3.1x10^-6 s
Energy input into the cavity in this time is
E = PowerxT = 850x3.1x10^-6 = 0.0026 J
The mass (m) of the microwave energy is
m = E/c^2 = 0.0026/(3x10^8)^2 = 2.9x10^-20 kg.

Step 2. The MiHsC-acceleration of photons in the cavity

The new effect predicted by MiHsC is that photons' centre of mass is continually shifted towards the wide end. Normally, as in my paper, I would calculate the photon mass change implied by MiHsC as more Unruh waves are allowed at the wide end, increasing photon mass there in a new way. Here, in order to point out the wider connection with MiHsC-cosmology, I'm going to take a short cut and calculate photon behaviour by noting that in MiHsC, a volume (sphere) bounded by a horizon must have a minimum acceleration of
a = 2c^2/L
where L is the diameter of the sphere. If you put in the Hubble volume L = 2.6x10^26 metres, then MiHsC predicts the recently-observed cosmic acceleration (usually attributed arbitrarily to dark energy) and it also predicts the acceleration below which galaxies misbehave and their rotation (usually attributed to arbitrary dark matter). We can regard each end of the cavity as being a little Hubble sphere (introducing an error of probably a factor of two) but the acceleration of the photons along the length of the emdrive cavity is then the difference between the accelerations at the wide end (the big cosmos) and narrow end (small cosmos), which is:
a = 2c^2/Lwide - 2c^2/Lnarrow = 2x(3x10^8)^2 x (1/0.16 - 1/0.1275)
a = 2.87x10^17 m/s^2

Step 3 - By conservation of momentum

As the microwave photons are shifted rightwards by MiHsC (see the red arrows in the Figure) the cavity must shift left to conserve momentum (see the black arrow).

We can calculate the acceleration of the cavity, much smaller due to its greater mass, by differentiating the conservation of momentum:
Acceleratn of cavity x CavityMass = Light Acc x MicrowaveMass
Ac x Mc = Al x Mm
Ac = Al x Mm / Mc = 2.87x10^17 x 2.9x10^-20 / 10
Ac = 0.00083 m/s^2

Step 4 - The Predicted Force

So F = ma = 10x0.00083 = 8.4 mN (The observed force was 16 mN for this case).

I always enjoy the closure and elegance of this sort of calculation and I believe that the ability of a theory to predict something openly on a single sheet of paper speaks well for it, in contrast to theories that require adjustable parameters hidden in labyrinthine computer programs or in the small print of complex derivations. There are no such parameters here.

Sunday, 15 May 2016

Clearer Explanation of MiHsC & EMdrive

Last night I drove to the big out of town TESCO on a mercy mission to buy some fish food and I was glad I did because while walking in the fresh air into the shop, what I have been thinking about, and doing messy calculations on, over the past few days, suddenly became clear. It is a clearer way to explain my MiHsC-emdrive paper. I laughed out loud in the entrance to TESCO, but luckily they didn't lock me up.

In the emdrive the magnetron puts microwaves into the cavity. MiHsC allows more Unruh waves (greater photon inertial mass) at the wide end, so as new microwave energy is put into the cavity its centre of mass is continually being shifted by MiHsC towards the wide end (see diagram). To conserve momentum the cavity has to move the other way towards the narrow end (note: this needs new physics, MiHsC, not standard).

But hang on!: MiHsC is causing a huge acceleration of the microwaves of 10^18 m/s^2 (~c^2/L). The cavity is not accelerating that much the other way? Why?

Because the cavity is so much more massive. The microwaves in the cavity have a mass (given m=E/c^2) of 10^-20 kg (roughly), whereas the cavity may be 10 kg, so the acceleration of the cavity to conserve momentum can be 10^-21 times smaller, which is about 10^-3 m/s^2, implying a force (F=ma) of a few microNewtons. This is the same process as in my paper but this explanation is different and hopefully much clearer.

An analogy to this would be a small 'magic' boat that everyone is puzzled about, because when it rains it always moves forwards. How is this possible? If you look at the boat from a different angle, from the side, you become aware of the slope in its bottom which pushes rainwater to the back and moves the boat forwards. Similarly, look at the emdrive with MiHsC and the slope is a gradient in the zero point field.

The moral of this piece is clear - when I get rid of the flu I should go for more walks!