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

## Wednesday 19 December 2018

### Towards Propellant-less Propulsion

The Journal of Space Exploration has just accepted my latest paper in which I focus far more on applying quantised inertia to propulsion, and which also shows an even simpler way to derive and understand QI, just from the uncertainty principle and relativity. This is a path I've been tending towards for a long time (see references). Werner Heisenberg showed, for a quantum object, the uncertainty in its momentum (dp) times the uncertainty in its position (dx) always has to be larger then Planck's constant divided by two Pi (hbar), over two (aka hbar/2). So: dpdx > hbar/2.

The assumption of quantised inertia is that you can apply quantum mechanics on the macroscale, if you take account of relativistic horizons. So, imagine we have a highly-accelerated system that excites the quantum vacuum (another way to say that is to say it sees Unruh radiation). For example, this might be a cavity with microwaves or a discharge spark inside. Imagine we now increase 'hbar' to represent the energy in this macroscopic system - bringing quantum mechanics to the macroscale. Now make the cavity asymmetrical so that the Unruh waves on the left side are blocked by a shield but those on the right side are not. Since you are blocking information from the left from getting to the system you are decreasing dx on the left side (the uncertainty in position in space is decreased because so far as the system knows there is no space beyond your shield), and so dp must increase to the left. This means that the normal quantum jitter (dp) usually very weak, is now magnified by the large accelerations (Unruh radiation) and also must be larger towards the left hand side. The system on a statistical average will move towards the left. As I show in the new paper, this predicts, to the right order of magnitude, the thrusts seen in the emdrive, the Woodward drive and also some intriguing results from asymmetrical capacitors.

The thrust of the argument :) is that quantum mechanics may not just apply to the small, and relativity to the fast: quantised inertia implies that at very high accelerations they join up to produce observable, and very useful, behaviour. Thrust without propellant means much lighter (cheaper) launch systems, and the possibility of interstellar travel in a human lifetime.

References

McCulloch, M.E., 2013. Gravity from the uncertainty principle. Astrophy & Space Science, 349, 957-959 Preprint

McCulloch, M.E., 2016. Quantised inertia from relativity and the uncertainty principle. EPL, 115, 69001 Preprint

McCulloch, M.E., 2018. Propellant-less propulsion from quantised inertia. J. of Space Exploration (in press). Preprint

## Wednesday 31 October 2018

### Bozeman, Montana or TU-Dresden?

This is a summary of the visit I have just made to Prof Martin Tajmar's esteemed Institute fuer Raumfahrttechnik at the Technische-Universitat-Dresden (TU-Dresden). I arrived on time at 10am. One of his students met me and took me to his office and then after a short chat, I gave a one-hour talk on quantised inertia (QI) to him & his research group of 30 or so. Martin Tajmar asked a few questions, eg:
1. How does the cosmic horizon interact with local dynamics in QI given the speed of light limit? (Answer: there is no relativistic speed limit for monochromatic waves).
2. Your assumption of an average acceleration of photons in the emdrive is wrong, they accelerate only when they rebound (Answer: true, but my assumption now has more backing, see below).
3. What is the degree of shielding of Unruh radiation by matter? Won't that introduce an adjustable parameter to QI? (Answer: Maybe).

After the talk we all went for a meal at the nearby canteen, and I made it clear, as I tried to do in my talk, that I am very confident about quantised inertia on a galactic scale, but I need Tajmar and his team's world-class experimental expertise to bring it down to the lab scale.

Then he gave me a tour of his labs, in which he seems to be testing most of the anomalies I have heard of. I saw the equipment he used for the 'Tajmar effect' that I tried to explain in a paper in 2011 (see refs). It is still embedded in its concrete well. I held his small emdrive. He also has a massive wind tunnel for more mundane aeronautical experiments. At one point he said "And here is my Stargate..". I looked through a window and saw a huge room in which he is building something that looks like the fictional stargate (it's not).

Back in his office, a student who has just started a PhD devoted to the emdrive gave a talk on recent progress. They have applied 3-10 Watts to an emdrive and measured a thrust of two microN, but it disappears when they subtract thermal changes due to an asymmetrical expansion of the cavity and the resulting changes in the centre of mass. Note that this is a thrust ten times smaller than the thrust NASA JPL was getting for a similar power and this work is still in progress.

We talked about Travis Taylor's mirror proposal. It may not be possible to build as originally proposed, due to the dielectric and mirrors not being able to fit together - manufacturing limitations. So they suggested a simpler arrangement where the dielectric and mirrors do not touch.

Martin then said "We are physicists, let's play" and started writing on a white board, asking me for the relevant QI formulas to put in, and this way, we derived the maximum acceleration of a photon of given frequency. The result was interesting because it means that for visible light bouncing off a mirror the Rindler horizon will be so close that a shield will not effect it, but it also shows that for microwaves the horizon is cavity-sized, so they can see the emdrive shape, or a shield.

The most unexpected thing that Martin said to me was in the evening while socialising (I had some delicious Saxische Sauerbraten and dumplings, and rather more than my usual amount of beer). He criticised most of the well-known lab anomalies as being debatable due to often sloppy technique, and yet showed some interest in an anomaly I thought had been wildly discredited: Hutchison's. I thought I'd had too much beer.. Good physics is of course predictive, but the profession itself is not!

References

McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 3. http://iopscience.iop.org/article/10.1209/0295-5075/95/39002/pdf

## Monday 22 October 2018

### Quantised Inertia Needs You!

It was not long ago that I myself was trying to get a full time post, now, not only do I have one but I am offering a post-doctoral position. So, if you are good at the numerical modelling of the interaction between em radiation and physical systems, preferably using COMSOL/Java, you fully understand what is behind the terms Unruh radiation and Rindler horizons, and you are keen to help with the conquest of space by helping to develop an 'electric rocket' for much safer, cheaper launch and propellant-less thrust in space (ie: saving both the planet and the human race) then this job advert is for you:

-- x --

Research Fellow in Modelling Propellantless Thrust, University of Plymouth, UK.

We are seeking an enthusiastic postdoctoral researcher with excellent skills in physics & numerical modelling, to develop a predictive model based on a ground-breaking theory called quantised inertia. The numerical model will be used to design a new kind of thruster.

The new theory suggests that inertia is caused by an interaction between Unruh radiation and matter. It explains, for example, galaxy rotation without dark matter, but in order to enable accurate experimental tests of the theory, it must be fully coded into a numerical model that can predict exactly how Unruh radiation will push on any given configuration of matter. Your role will be to do this coding.

You must have a PhD in physics, experience in translating physics into numerical models, an understanding of the interaction between radiation and matter, quantum mechanics and relativity. Experience of COMSOL and java will be an advantage.

You will work with Dr Mike McCulloch. The post includes short trips to Dresden (Germany) and Madrid (Spain) to liaise with groups who are setting up experiments.

-- x --

It's not every day you get a well-paid chance to make history.

## Monday 24 September 2018

### Wide Binaries 2.0

As I have repeated many times on this blog, galaxies spin far too fast to be bound by their visible matter. This anomaly disagrees with standard physics and yet it has not only been brushed under the carpet, but it has been forbidden in many places to even admit that there is a carpet. A serious flaw (floor) in the mainstream attitude :) The carpet is the dark matter that has been invented to cover this up and save general relativity (which may be fine for high acceleration, but does not work for low).

There are two cases though, in which the dark matter fudge cannot be applied 1) globular clusters (see Scarpa et al., 2008 below) and 2) wide binaries which are even better (discussed earlier here). Wide binaries are twin star systems that orbit with a separation of more than 7000 AU and they show the same impossibly fast orbits that larger galaxies do. Dark matter cannot be used to fudge them because in order for dark matter to predict galaxy rotation it must stay spread out and therefore it cannot be squeezed into little wide binary systems. So wide binaries are the astrophysics equivalent of testing the emdrive in a vacuum which rules out air currents - wide binaries rule out dark matter.

I have started looking a wide binaries again, going back to a paper of Hernandez et al. (2014) who processed a lot of data on them. The data is shown in the Figure by the blue and red crosses. The x axis shows the separation of each pair in parsecs and the y axis is their orbital speed (km/s). I've shown the uncertainty in the data crudely by the blue and red coloured areas around the crosses, so you can see that the SDSS data (blue) is far less accurate then the Hipparcos data (red). To be deemed successful a theory has to predict within the blue and red areas.

I have added to the plot the predictions of general relativity (the dotted curve) which lies outside the coloured areas for all separations greater than about 0.03 parsecs. Therefore, because dark matter cannot be applied in these cases (unless they add more bells and whistles to it) we can say that general relativity has been falsified. This is a strong indication that it is wrong in galaxies as well, since the anomalies are very similar.

The other curves show Modified Newtonian dynamics (MoND, the dashed curve)  and quantised inertia (the solid curve). Both theories predict the data, but MoND has been tuned to work by arbitrary adjustment of its free parameter. Quantised inertia predicts the data all by itself, without any tuning, an advantage which shows it is deeper, more predictive (it can predict the change in the systems' rotation with cosmic time too) and also simpler. Occam's razor cannot be repealed. Note that the acceleration used for QI here includes that due to their mutual spin and their movement around the galaxy.

The next steps are to submit this to MNRAS, and try to shrink the blue and red areas of uncertainty in the data using the new GAIA dataset. This is an elegant way to debunk general relativity at these low accelerations, dark matter too, and demonstrate the advantages of QI - better data is needed though.

References

GAIA dataset: http://cdn.gea.esac.esa.int/Gaia/ (Thanks to F.Zagami for the link).

Hernandez X., A. Jimenez, C. Allen,2014. Gravitational anomalies signaling the breakdown of classical gravity. Astrophysics and Space Science Proceedings 38, 43. https://arxiv.org/abs/1401.7063

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

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astrophys. & Space Sci. 362, 149. Link to open access paper

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

## Saturday 1 September 2018

### Horizon drives / quantum rockets

Sorry for the gap in blog entries, but I have been traveling a lot, explaining to groups in Germany, exotic Hampshire, and the US, how quantised inertia predicts thrust. As you may know, I now have significant funding to do tests, and will report on these as openly as I can - this is important to me since I value feedback and comments and they help to progress the work.

So how does quantised inertia predict thrust? My explanation of this is becoming more streamlined as time goes on, so here is the latest (see, for background, McCulloch, 2016). QI says that all masses move because of the quantum 'jitter' that can be made anisotropic by horizons (barriers to information). The bold assumption in QI is that horizons are real and are able to reduce the 'dx' in the uncertainty principle, so that dp increases in that direction and the quantum jitter moves the object horizon-ward (see here). These horizons can be either relativistic, or solid conductors (as in the Casimir effect). If the quantum vacuum is more intense, you get more push. The quantum vacuum becomes more intense for accelerated objects because of the enhancement due to Unruh radiation. So the QI recipe for launch, so far, looks like this:

Step 1: Make something that accelerates very fast so that the quantum (Unruh) waves intensify and also shorten so much that they are short enough to interact with a metal structure. For example, to interact with a structure of size 1m, the acceleration of the core has to be about 10^18 m/s^2. This accelerating core could be a spinning object, resonating microwaves (as for the emdrive, which QI predicts) or a hyper-vibrating piezoelectric (as in the Woodward devices, which QI also predicts).

Step 2: Damp the Unruh waves on one side of the core more than the other. If the acceleration of the core (circle) is big enough, this can be done by putting a thicker conductor, say, above it (see the left schematic), or having an asymmetric cavity (see middle) or a patterned structure whose mesh size is bigger in one direction than another (see the figure on the right). All these structures would damp Unruh radiation (orange) more above the core (darker shade) moving them up.

Step 3: Watch the core accelerate towards the more shielded side. Be patient because at the present level of technical development (thrusts of about 1 microN) it would take 11.6 days for it to accelerate to 1 m/s (for a 10 kg setup), but now QI gives us hopefully an understanding of what is going on, it suggests ways to boost this force, and launch should one day be possible. It costs \$62M to launch a SpaceX Falcon 9. At the moment, given the funding budget I've just had to submit, I'd estimate a potential factor of 100 reduction in cost for the kind of thruster QI should allow.

References

McCulloch, M.E., 2016. Quantised inertia from relativity and the uncertainty principle. EPL, 115, 69001, https://arxiv.org/abs/1610.06787

## Monday 25 June 2018

### Does QI Predict The Woodward Effect?

James Woodward in the US has been boldly experimenting with capacitors which appear to show thrust since the 1990s. I was recently reading about one of them, and to me it looks very much like the emdrive. Also, as I will show tentatively below, the thrust from it can be predicted quite well by quantised inertia, in a far simpler way to Woodward's own explanation which mis-predicts the thrust by several orders of magnitude (ie: I admire his experiments, but I do not accept his theory).

Woodward's thrusters or Mach Effect Thrusters (see Mahood, 1999, Tajmar, 2017) typically look like the image below. An AC current is input into a capacitor (the vertical black lines) making an EM field. There is a dielectric in between (yellow) or sometimes to the side, which is a piezo-electric material (PZT) that vibrates when the EM field is applied. The setup is asymmetric because there is a heavy reaction mass (plate), here shown on the left.

Quantised inertia predicts that this contraption should move towards the end with the large brass plate (just as it is observed to do) just as the emdrive moves towards its narrow end, because in both cases Unruh waves are more damped at the end with the massive plate, so photons of the em field will always gain mass on going towards the wide end or the end with less metal, and so, to conserve momentum, the thruster itself must thrust left. The above also looks similar to the horizon drive.

So, let's get a bit more quantitative. A simplified version of the QI thrust formula is

F=(PQL/c) x ((1/w1)-(1/w2))

where F is the thrust towards the end with the massive plate, P is the power input, Q is the quality factor, L is the length and w1 and w2 are the 'widths' of the cavity at the two ends (which affects the amount of Unruh-damping). Now, how can we model exactly the damping of the Unruh waves by the two end caps' thickness? I cannot yet do it in detail, but one way to do it, to predict the maximum thrust obtainable would be to assume that the thin brass cap on the right does not damp the Unruh waves, so the photon can see the cosmos and w2 = the Hubble scale. The other end, being thicker, does damp the Unruh waves so the width (w1) there is roughly the distance between the centre of the dielectric and the middle of the brass end plate. The particular experiment I will look at is Mahood (1999) for which L=0.025m and P=145 W. To estimate Q, I have had to use the dissipation constant of 2% given for another thruster in a report by March and Palfreyman (2006). So Q=2pi x 100%/2% = 314. The thrust toward the large plate end is then predicted (in a very crude way) by QI to be

F = (145 x 314 x 0.025 / 3x10^8) x (1/0.025 - 1/huge)

F = 15x10^-5 N

The observed thrust was 5x10^-5 N (Mahood, 1999) so the prediction by QI is not bad, and far better than Woodward's model which was several orders of magnitude out (according to Mahood, 1999). As expected from the assumptions, the QI prediction overestimates the thrust. This is obviously a very crude calculation, which is why I'm spouting it here, and not in a journal yet, but it is interesting that QI predicts this Mach Effect Thruster, and also of course the emdrive, galaxy rotation, cosmic acceleration...etc. The thruster may allow a new way to test QI, and could be an example of the horizon drive. I do need to look at the other thrusters because I believe some of them were not asymmetric, and build up a more statistically-significant results list for comparison with the predictions of QI.

References

Mahood, Thomas L. (February 1999). "Propellantless propulsion: Recent experimental results exploiting transient mass modification". AIP Conference Proceedings. Space Technology and Applications International Forum-STAIF 2000, Albuquerque, New Mexico. 458. American Institute of Physics. pp. 1014–1020. Link

Tajmar,M., 2017. Mach-effect thruster model. Acta Astronautica, 141, 8-16.

March, P. and A. Palfreyman, 2006. The Woodward effect: math modelling & continued experimental verifications at 2 to 4 MHz. CP813, STAIF-2006.

## Friday 15 June 2018

### Visit to Julich Supercomputing Centre

I was recently invited by Prof. Dr. Dr. Lippert to give a talk about quantised inertia at his Computing Centre in Julich, Germany, and it has proved to be very stimulating. Most of mainstream physics is still in 'shunning' mode, so this was a great chance to talk to some highly-qualified physicists.

After my talk, I chatted with Prof Lippert and an astrophysicist. Their first comment was on precision. In my talk I showed three ways to derive QI. One using Unruh radiation, the second using the uncertainty principle and the third using information and Landauer's principle. There is a fourth thermodynamical way, but I skipped that. The point I was trying to make was that if there are four closely-related ways to derive QI it is a good thing - if all roads lead to the same place, then it is probably somewhere important, like Rome, and this indicates that there is a deeper, unifying, derivation. Prof Lippert made the good point that it would be better to present the best derivation only.

He also said that I should make the point more often that QI provides an explanation for MoND. MoND (Modified Newtonian Dynamics, devised by Moti Milgrom) is an empirical theory (an effective theory) that predicts galaxy rotations but has to use an adjustable constant (a0) to do it. QI predicts MoND behaviour without the adjustable constant, so QI provides a basis and a physical underlying reason for MoND. Instead of the free parameter a0, QI has the unadjustable '2c^2/cosmic_scale', where c is the speed of light, so QI predicts things that MoND cannot, for example: changes of galaxy rotation in the distant past when the 'cosmic scale' was smaller. Also QI can predict MoND but MoND cannot predict QI. Prof Lippert's point was that emphasising the connection to MoND means I can claim all the successes that MoND has had, and also gain allies among the MoNDians who might welcome a physical basis for it (but they may also get annoyed). The bridge here may be Prof McGaugh who has shown interest in QI but is doubtful that Unruh radiation is strong enough (I have shown it is here).

Another useful comment related to my simplified approach. For example, the spin of a solid object would produce a whole range of accelerations since the solid-body acceleration a=v^2/r changes with radius. So to properly model it I need to consider a whole family of Unruh spectra. That sounds like a job for a simulation, and Julich is the place for that. I was shown the supercomputer they have, an impressive setup capable of several Petaflops of processing power. Useful for galaxy modelling or modelling the interaction between Unruh waves and matter (QI) at a more detailed level.

The Julich, JSC is an impressive place. Situated in a beautiful forest, populated by about 6000 staff, several supercomputers, and with a physicists' cafe whose pizzas are all quantised. I wasn't allowed a slice, it was all or nothing. Planck would have loved it.

Vielen dank Prof. Dr. Dr. Lippert. I look forward to many collaborations with you in the future.

References

The abstract for my talk: Link

Website of the Julich Supercomputing Centre: https://www.fz-juelich.de/ias/jsc/EN/Home/home_node.html

If you wish to support my work a little, you can do so here:
https://www.paypal.me/MikeMcCulloch

## Thursday 24 May 2018

### Emdrive Trial by Media

You may have noticed that some of the mainstream scientific media are attempting to debunk the emdrive based on Tajmar's new result, but the data suggests that Tajmar does not yet even have a working emdrive and is looking at some sort of Lorentz force.

To demonstrate this, here is a plot showing Tajmar's newly measured thrust in comparison to the other ones. The thrust predicted by quantised inertia is shown on the x axis and the thrust observed is shown on the y axis. The diamonds show the comparison between the predictions and the data. Most of the diamonds line up along the diagonal line, meaning that QI does a good job of predicting the results (as does the Shawyer equation that also uses power times Q). One point to note is you can predict the thrust from the characteristics of the cavity (eg: Q, length, widths) not the cables. Tajmar's new thrust is way below the line (see the label: Tajmar2018). The thrust expected by QI for his setup was 0.19mN and his observed thrust was 0.004mN. This is almost fifty times smaller! If you have a car that is going 50 times slower than expected, then you can probably conclude that the engine is off. So it seems that Tajmar is not testing an emdrive yet, but is looking at some other, much smaller, effect.

This is further supported by comments from Phil Wilson who has pointed out that the cavity Tajmar is using does not have a resonance at 1.865GHz (the frequency he is inputting) and his results look very much like something else is resonating.

Also, what has been forgotten is that NASA were well aware of the potential problem of a Lorentz force, and showed their thrust was not from that. In their 2017 paper (see below, page 838, top right column) they said "The [cavity] was tested in forward, reverse and null orientations, but dc power cabling, routing & orientation was the same for all three configurations". What this means is that the NASA emdrive's thrust direction followed the cavity orientation and not the cable orientation. Therefore for a real working emdrive, it is the cavity and not the cables that make the thrust.

This is not a criticism of Tajmar, who I have the greatest respect for, but for the media response to his preliminary tests:

References

White et al., 2017. Measurement of Impulsive Thrust from a Closed Radio-Frequency Cavity in Vacuum. Journal of Propulsion and Power, Vol. 33, No. 4 (2017), pp. 830-841 https://arc.aiaa.org/doi/10.2514/1.B36120

If you wish to support my work a little, you can do so here:
https://www.paypal.me/MikeMcCulloch

## Saturday 28 April 2018

### A whole new industry

I had a friend at York University who was always responding to my comments by saying "Well, how does that put petrol in my tank?" and although I tend to drift off into theoretical realms I have always been surrounded by practical engineers (my dad and my wife) so I always eventually get reminded that science has to be useful.

OK, the most direct, and the one I have now won \$1.3 million of funding for (subject to negotiation) is thrust. Quantised inertia (QI) predicts that if you stick a horizon in the vacuum, that is: you use an arrangement of metal to bend light and stop information transfer across a surface of space, then you damp the local vacuum field (Casimir effect like) and nearby objects will move towards the damper in a new way. This form of propulsion is fuel-less. Or, if you like, the fuel is the vacuum/nothing which is freely available everywhere. It won't be technically easy, but it should be possible to launch into space without rockets this way. Also, with standard physics, travel to the nearest star in a human lifetime is not possible: you have to take a planet-sized amount of fuel! With QI it is possible since the fuel is empty space and there's lots of that out there. So, with quantised inertia, the more empty your car tank is, the more fuel you have! There you go Jason.. The evidence for the thruster is in this paper.
The second application is energy production. Quantised inertia predicts that you can get energy out of the vacuum by forming a tiny closed information space. To put it simply: since dp x dx ~ hbar/2, if you squash dx (ie: a closed space), you get new momentum and energy out. The evidence for this is that this assumption produces quantised inertia (reference) and all the agreements with data I have published, and it may help to explain cold fusion, which occurs in small spaces.

The next application would save as much money initially as the first one. Huge amounts of imaginary dark matter are put into disc galaxies because, to put it crudely, general relativity has not predicted one single galaxy rotation ever (except for one found recently, which looks to be an subsampling error). QI explains galaxy rotation without dark matter, and also explains cosmic acceleration, so a huge amount of research money could be redirected from dark matter searches and dark energy theorists to the thruster applications above.

The fourth application is more speculative, but I am beginning to see that quantised inertia predicts that matter is only the interaction of photons and information horizons, which means that we can form any type of matter from light and horizons: cue the Star Trek replicator. This is similar to the work of Jennison who predicted the electron from photons in a cavity. QI says the cavity is a horizon.

What I'm trying to say is that quantised inertia is the seed for a huge new physics and engineering industry that will dwarf Manchester's graphene breakthrough and eventually dwarf everything else as well. I have evidence to back this: I've published 21 papers now on it, evidence included. I now need this newfound funding to test it, so I hope it does not get torpedoed..

If you wish to support my work a little, you can do so here:
https://www.paypal.me/MikeMcCulloch

## Monday 23 April 2018

### Inertia & Gravity from Conservation of EMI

I'm always looking for ways to simplify quantised inertia since it is not the easiest concept to get across, and also simplification usually leads to a deeper understanding. My usual argument using Unruh waves and horizons is equivalent to what follows below, but there is now a simpler way to frame quantised inertia, which I published in 2016. First of all, just as Einstein assumed that physics should not be frame-dependent, quantised inertia assumes that physics should not be scale-dependent. To explain: a huge entity the size of a galaxy (say) should agree with us on the physics it sees. Therefore, Heisenberg's uncertainty relation (below) should apply to stars too

dp.dx~hbar/2

This is illustrated by the diagram which shows a large object (black ball) and its uncertainty in position (solid envelope) and momentum (dashed envelope). Since hbar must be kept constant, then the more an object knows its position (dx smaller, the solid line is closer to the ball) the more it does not know its momentum (dp is bigger, the dashed line is further from the ball).
Now let us forget for a moment that quantum mechanics and relativity usually get on like two cats in a bag, and combine them. If the object accelerates to the left (red arrow) then information from far to its right can never catch up and a relativistic horizon (like a black hole event horizon) appears at a distance of

d=c^2/a

in the rightward direction (see the solid right-angle). So the uncertainty in position is reduced since the object's space has been curtailed from the cosmic scale to a scale 'd'. As a result, the uncertainty of momentum to the right is increased (the dashed line is far from the ball) and the ball will jiggle more rightwards: against its original acceleration. This predicts the inertial force (blue arrow) in the modified form needed for quantised inertia, and so it predicts galaxy rotation without dark matter and cosmic acceleration without dark energy. QI is, simply put, the quantum and relativistic equations shown above rammed together in the way shown in the diagram. To put it more physically: new mass-energy (dp) appears if information about space (dx) is curtailed. Put another way: what is conserved in nature is not mass-energy, but M-E plus information (conservation of EMI).

Now imagine putting a large mass next to an object. To some extent this mass will block information from that direction, reduce dx in the uncertainty principle and increase the momentum (or quantum jitter) that way. The two objects will then jitter-themselves together. This looks very much like gravity, and in the 2016 paper I show that you get Newtonian gravity from it. To get something like general relativity (in a QI form) the same derivation will have to be done fully relativised.

Now imagine that instead of putting a large mass next to the object, we put an information horizon there that reduces 'dx' in that direction and increases the quantum jitter (dp). The object should see a thrust. Since quantum waves are partly electro-magnetic, a conducting metamaterial should do. In my opinion this has already been seen in the emdrive, since QI predicts it well, and everything I have published over the last 11 years implies that this new thrust is possible. Can it be powerful enough to oppose gravity? I think so. Good news: solid lab tests are coming.

References

McCulloch, M.E., 2016. Quantised inertia from relativity and the uncertainty principle. EPL, 115, 69001. https://arxiv.org/abs/1610.06787

If you wish to support my work a little, you can do so here:
https://www.paypal.me/MikeMcCulloch

## Monday 5 March 2018

### A paper on QI & cold fusion

I've just published a paper on cold fusion, in Progress in Physics which is a nice open access journal that has the laudable goal of encouraging research that challenges the standard paradigm.

As I described in more detail in a previous blog, the phenomena known as cold fusion or LENR (Low Energy Nuclear Reactions) is a process that appears to produce fusion by packing deuterium atoms (hydrogen atoms whose nucleii have an extra neutron) into palladium metal, which acts a bit like a sponge when it comes to deuterium. When this is done, in certain circumstances, unexpected heat is given off, more than can be explained by normal chemistry, so the argument goes (and as arguments go, this one has lasted decades!) it must be fusion, but how is this possible when these deuterons are both positively charged and so they repel very strongly? Normally you need temperatures of over 100 million Kelvin to get them to collide and fuse, and hence the 25 billions dollars spent so far on reproducing the centre of the Sun on Earth (eg: with huge fusion reactors like ITER). Cold fusion appears to do it in a test tube, at room temperature and without emitting harmful radiation and the phenomena has been repeated often (see Storms, 2006). It offers the possibility of cheap energy for all, but as so often, it doesn't agree with the standard model so very few dare to investigate it (see an interesting article by Huw Price, link).

Well, as many of those who read my blog know, nature doesn't agree very well with the standard model either, but quantised inertia (or MiHsC) does rather better and one prediction of it, is that in tiny, closed informational spaces the temperature should increase. So what about tiny cracks or defects in the palladium? They do exist as both Ed Storms (who prefers cracks, see his report below) and Russ George have told me (the latter told me about very effective Japanese 'Samurai' palladium, full of defects). If the defects are of a size 28 nm then quantised inertia predicts a temperature of 27,000K.

This is not enough to initiate fusion, but now imagine two ships in a choppy sea. Waves hit them from all around, but there will be a sheltered region between them and therefore fewer waves will push them outwards from between them, than are pushing them inwards. The result is that the ships will move together in a way not dependent on the usual physics (at sea this phenomenon is called the Maritime Casimir effect, you can guess what it is called in dry physics).

If you now think similarly about two deuterons in a palladium defect or crack then they will be pushed together in the same way by the thermal waves in the crack, as I described here. I showed in the paper (see here, or the link below) that if the crack/defect is less than 28 nm in width then this new force is strong enough to push the deuterons together through their Coulomb repulsion and they will fuse.

So, does this explain cold fusion? It is maybe a start but there are some problems. First of all, when predicting things it is best to have a observed number to test the theory on. For testing quantised inertia on galaxy rotation the test data is the observed speed of the stars. For the emdrive it is the measured thrust. With cold fusion all I have done so far is predict that defects of 28 nm width are needed. What size are the cracks in palladium where the fusion occurs? I don't know!

The other problem is that, whereas this process might possibly explain the lack of neutron emissions in cold fusion experiments (they may also be subject to the mutual sheltering effect) it does not obviously explain the lack of gamma emission observed. This radiation may be absorbed by the lattice as suggested by others, but there is certainly a lot of work to do yet.

All the same, this explanation is a simple and visualisable process, it needs no adjustment, and links cold fusion with lab scale (emdrive) and astrophysical (galactic) anomalies, so it is at least a good addition to the debate, and should help to broaden it and embed it in wider new physics.

References

McCulloch, M.E., 2018. Can cold fusion be explained by quantised inertia? Progress in Physics, 14, 2, 63-65. Open access pdf.

Storms, E., 2012. A students' guide to cold fusion. http://lenr-canr.org/acrobat/StormsEastudentsg.pdf

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## Saturday 20 January 2018

### Cold Fusion and Hot Soup?

Since I have just submitted a short paper on this, I'd like to explain how I think cold fusion might be happening. The following makes a nice story, but still could be wrong. We'll see. It is also dangerous ground, but it is necessary to keep pushing into such territory, because that is where the new physics is (partly because very few people have dared to go there yet).

I've been thinking about LENR (ie: cold fusion) since before Christmas, ever since Bob McIntyre on twitter noted that my earlier paper on quantised inertia and the proton radius anomaly [ref 1 below] might apply to it. It is also pretty clear that QI predicts that an earlier, much smaller, universe would have been hotter [ref 2] and you can see this without QI, simply from the uncertainty principle: dp.dx>hbar, where hbar is the reduced Planck's constant. If you shrink the 'known space' of an object (dx), then its uncertainty in momentum must increase, and therefore its temperature.

I've been reading a lot of Ed Storms' papers and the comment he made that impressed me was that the common factor in all the successful LENR experiments are nanoscale cracks or gaps in the palladium or other metals. In my space- and horizon-obsessed mind these are just mini-universes. See the schematic below of a crack (the white area) inside an area of red-hot palladium metal.

Coming back to the uncertainty principle: in cracks, the uncertainty in position (dx) is small, so dp and hence the temperature of the walls must be high (the red area). For the nanoscale cracks in palladium, the predicted temperature is still not hot enough for fusion, which needs temperatures of 100 MK, but recently I was cooking soup and noticed that the walls of the pan were hot and the soup was moving towards the centre. This is a different convective process, but it gave me the idea that the crack walls might be radiatively pushing the deuterons together (see the red arrows in the schematic). I've scribbled through the maths and it turns out that if the cracks are smaller than 86 nm, then the crack's walls are hot enough, and the radiation pressure, is strong enough to push the positively-charged deuterons together over their mutual repulsion and cause fusion. It might also account for sonoluminescence: light emission from small bubbles. So what do you think? Physics from the kitchen?

(Note: Argh! I have found an error in my derivation :( Thank goodness for dimensional analysis, so I will leave this blog entry here to record my blunder, and get back to the drawing board. Apologies. Correction No.2: I've decided now it was right all along, so have resubmitted it.).

References

McCulloch, M.E., 2017. The proton radius anomaly from the sheltering of Unruh radiation. Progress in Physics, 13, 2, 100-101. Link

McCulloch, M.E., 2014. A toy cosmology using a Hubble-scale Casimir effect. Galaxies, 2, 81-88. Link

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## Sunday 14 January 2018

### How QI gets rid of dark matter

Many people have asked me for a simple, graphical explanation of how quantised inertia (QI) gets rid of the awful dark matter, so here it is, for them. We start off with a schematic of a galaxy (see below, in yellow). Outer stars have been observed to have a rotational speed (the red arrow) so big that the inertial (centrifugal) forces (white arrow) should be much greater than the gravitational forces from all the matter we can see (the black arrow) and so, if it had any decency, the galaxy ought to fly apart. The problem is that galaxies are showing no decency at all, and do not fly apart. Why? Mainstream astrophysicists add arbitrary dark matter to boost the gravity arrow and achieve balance that way. Quantised inertia shrinks the inertial arrow instead.

To explain quantised inertia I will start with an oceanographic analogy (see below). A ship is parked at a dock. Lots of ocean waves can exist and hit it from the seaward side (the wavy line), but no waves can fit within the gap between the ship and the dock, they don't resonate in that space, so on average the ship is pushed by the waves towards the dock. If the crew of the ship were unaware of the waves they would say "It is a magic force moving us towards the dock!".

There is another sea. One predicted by quantum mechanics. It is a sea of quantum particles, and we have only recently detected it because Hendrik Casimir showed that if you put two plates very close together, like the ship and the dock, the plates will move together. That has now been confirmed (in 1996) so this invisible sea really does exist. Now consider an object accelerating to the right (black circle, white arrow below). It will see the quantum sea, actually an enhanced version of it (Unruh radiation). Relativity now says that in the opposite direction to the acceleration, information will not be able to catch up with the object. So there will be a horizon, like a black hole event horizon (see the black crescent). In quantised inertia this horizon is treated just like the dock wall in the analogy. it damps the waves between the object and itself. As in the analogy the object sees more waves from the right and is pushed back, always against its acceleration. This 'asymmetric Casimir effect' predicts what we always assumed before to be a 'magical' inertial mass, because we couldn't see these quantum waves (which only exist in the object's reference frame).

Information also cannot get to us from beyond the Hubble horizon, since stars there are moving away from us at the speed of light. So this horizon damps the Unruh waves equally all around the object, and so it damps the waves on the right side (there already aren't any on the left) - see the change from the dashed waves to the solid waves, below. This reduces the effect of the aCe process detailed above, and the resistance to acceleration, the inertial mass. This reduction is more serious for the longer Unruh waves that occur for low accelerations,since these 'feel' the cosmic boundary more.

The prediction then is that inertial mass is lowered for stars at the edge of galaxies, since they orbit in a slow curve and have a very low acceleration. This reduces the centrifugal (inertial) force outwards (see the change from the dashed to the solid white arrow, below) and the inertial force now balances the gravitational force - quantised inertia predicts the balance exactly for these edge stars, using only the visible matter, the speed of light and the Hubble scale, so that no arbitrariness or dark matter is needed.

I hope you can appreciate the beauty and simplicity of this theory. It has not yet been tested on the insides of galaxies, I'll need a galaxy model for that, but it does predict a lot of other observations as well such as the cosmic acceleration and the emdrive.

References

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astrophys. & Space Sci. 362, 149. Link to open access paper

If you wish to support my work a little, you can do so here:
https://www.paypal.me/MikeMcCulloch