I've suggested a new theory called quantised inertia (or MiHsC) that assumes that inertia is caused by relativistic horizons damping quantum fields. This simple theory predicts galaxy rotation, cosmic acceleration & the emdrive without any dark stuff or adjustment of any kind.
My Plymouth University webpage is here, I've written a book called Physics from the Edge and I'm on twitter as @memcculloch

Wednesday, 18 January 2017

The core of MiHsC / quantised inertia / horizon mechanics*, is the idea that the property known for centuries as inertia is caused by an asymmetry in Unruh radiation (an asymmetric Casimir effect). I have already discussed the evidence for Unruh radiation itself here (Fulling-Davies-Unruh radiation), but many people have asked how can a process based on the zero point field, so weak in the Casimir effect, could have such a large effect on matter that it produces inertia. How can it be?

Well, it can be! This can be shown with simple maths and the schematic below. The black circle is a Planck mass. Let us say that for some reason it is accelerating to the left (purple arrow), so a combination of quantum mechanics and relativity says that it sees a warm bath of Unruh radiation (orange colour). Relativity then says that information from far to the right (from the black zone) is limited to the speed of light and so cannot reach the mass, so this is its 'unknowable space'. A Rindler horizon forms to separate that space from the known space. Now as far as the mass is concerned, there is no space beyond the horizon and waves need space to wiggle in. So this horizon damps the Unruh waves on the right, creating a colder Unruh bath there (blue area). The gradient in the Unruh radiation means that more thermal energy bangs into the Planck mass from the left than from the right and so it is pushed back against its initial acceleration. Another way to think about this is that energy is now extractable from the difference in (virtual) heat.

Maths helps us to be specific. The wavelength (L) of the Unruh radiation seen by a mass of acceleration 'a' is

L = 8c^2/a

The c is the speed of light, a huge number, so that the c^2 in the numerator makes the Unruh wavelength usually very long. A sperm whale falling in Earth's gravity would see Unruh waves a lightyear long, but probably wouldn't last long enough (a year) to measure one passing by. The energy in the Unruh field on the left is then

E1 = hc/L = hca/8c^2 = ha/8c

The energy in the Unruh field on the right is

E2=0

Using normal physics, the force on the mass is the energy gradient from left to right across the diameter of the mass

F = dE/dx = ((E1-E2)/d = ((ha/8c)-(0))/d

F = ha/8cd

This looks suspiciously like Newton's second law: F=ma, and suggests that m=h/8cd

For a Planck mass d is the Planck length so the predicted mass is m=1.7x10^-8 kg. The accepted Planck mass is 2.2x10^-8 kg. In other words, at least in this case of the Planck mass, the Unruh effect is strong enough to produce inertia. It predicts the accepted numbers quite well even in this simple analysis which leaves out a lot of detail. As I said in my 2013 paper on this (see below): to make this process work for larger particles, you can't just put in a larger diameter d. You have to add up the effect of each Planck mass.

References

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

--
Horizon mechanics* = A new name suggested to me by J.M. Dorman.

Tuesday, 10 January 2017

A Taste of Kafka

Well, before I start I should say that most journals I have dealt with have been fair, but I'm having a bad month it seems, and every so often one is entitled to a rant. It's therapeutic for me and I think it is illuminating, maybe, for people to see the agonizing effort I'm making to try and squeeze my papers through peer review.

I've written a paper that gives good observational evidence that quantised inertia / MiHsC models 153 galaxies in the SPARC dataset without dark matter and without any adjustment of any kind. I've discussed this comparison on this blog too. I've submitted the paper on it to four journals so far. I've just received this frustrating reply from the editor of the 4th one:

Dear Dr. McCulloch:

I am writing to you with regard to your manuscript cited above, which you recently submitted to the (name of journal). I regret to tell you that we are not able to undertake further consideration of your submission for publication in the (name of journal group).

In case you are waiting for the scientific reason, that is the end of the message! This isn't the only meaningless response I've had in my career but surely science can do better! The whole point of science is that an empirical, or at least rational, reason has to be given for decisions. The Royal Society decided in about 1600 that science worked better this way. Otherwise, instead of rational progress you get hidden elites deciding whatever they want in their own interests. Recently, as I have written papers that show more and more clearly that quantised inertia works far better than dark matter, I have increasingly received vague responses like this. The editor clearly is unable to find any fault with quantised inertia, and yet is unwilling to even consider it. Why? I don't mind being rejected for a rational reason, but I get a mediaeval or Kafkaesque chill when my papers are rejected for no reason at all.

My reply to the editor was:

Dear Editor,

You have to give a reason, since you represent a scientific journal.

Mike

No response. If you have any advice on which journal I can next submit myself to, please let me know. Readers Digest? I always wanted to submit there..

Friday, 6 January 2017

Emdrives, dielectrics, & the Kaporin optimisation.

In the past I've presented many comparisons between quantised inertia (MiHsC, horizon mechanics) and the emdrive thrust data, and here is another one (see the graph below) updated with the new NASA 2016 data (White et al., 2016). The ten comparisons between the thrust predicted by MiHsC/QI (this way) along the x axis, and the thrust experimentally observed, along the y axis, are shown by the open squares. Ideally, they should all lie on the diagonal line, and they are close to it, but you'll notice that the NASA thrusts (NASA2014 and NASA2016) are overestimated (too far to the right ) by anything up to a factor of ten (the scales are logarithmic), and Shawyer's first test (Shawyer1) is too far to the left.

I wondered (see the NASA shift) if it could be because NASA put a thin dielectric at the narrow end of their emdrives (Paul March confirmed they did), and Shawyer put a dielectric at the wide end of his first emdrive (Shawyer1). So I have now calculated the change this makes to MiHsC/QI since a dielectric changes the speed of light. The amended thrusts are shown on the plot with the black diamonds, and they lie closer to the diagonal 'correct' line, which is encouraging and some evidence that MiHsC/QI is the right explanation (but let's see if the reviewers of my new paper, to be submitted, agree with the way I've calculated the effect of the dielectric). Here is the same data in table format:
I'm also very grateful that, just before Christmas, Professor Igor Kaporin of the Russian Academy of Science, Moscow, told me he'd taken equation 14 from my paper (see the first reference below), which predicts the emdrive thrust, and optimised it to predict the emdrive shape likely to give maximum thrust. It is silly I didn't do that, since I've done it many times in other contexts (eg: least squares matrix algebra) and it is quite easy to do. You differentiate the MiHsC thrust equation (eq. 14) with respect to L and set the result equal to zero and what comes out after a few lines of algebra is that the maximum thrust occurs when L=4*(ws*wb)^0.5, where L = cavity length, wb & ws are the big and small end widths. I should point out that eq. 14 is approximate and doesn't include the effects of cut-offs within the cavity or the effect of dielectrics, but I will publish the dielectric-capable formula soon, and I will be sure to optimise this time!

References

McCulloch, M.E., 2015. Testing quantised inertia on the emdrive. EPL, 111, 60005. Preprint

White, H., P. March, J. Lawrence, J. Vera, A. Sylvester, D. Brady, P. Bailey, 2016. Measurement of impulsive thrust from a closed rf cavity in vacuum. AIAA J. of Propulsion and Power.

Saturday, 17 December 2016

The New Physics

It's often said that when offering new ideas, it best not to attack the old stuff, but to build the new. So here is a deliberate attempt to do that and show what a MiHsC-ian (quantised inertia) world would look like. Just a warning: I am thinking far ahead here.

I'll start with the obvious. The gravity well would be broken because it would become possible to launch objects fuelessly into space by making a gradient in the zero point field. This is, according to MiHsC, what the emdrive does. The launches will be far safer as well, no huge explosions would be needed to blast atoms downward to get Newton's momentum accountant to move the rocket the other way. You just need to put some meta-materials (a metal structure that bends electromagnetic waves) above or in your satellite or human-rated capsule to damp the wavelength of Unruh waves that are likely to form above it, and it'll glide slowly into space. Similarly it would revolutionise satellite station-keeping, as the Chinese have already recognised. Ground transport would also be revolutionised: no wheels would be required: put metamaterials above cars and they will be pulled up by the Unruh-void and glide along frictionlessly. Want a floating house? Floating city? No problem, given a big enough damper above. The problem is to have a metal structure of the right size to damp the Unruh waves that are likely to form. For terrestrial accelerations these are a light year long! In the emdrive, photon accelerations are huge so the Unruh waves are as short as the cavity, so its small size can do the job.

Energy. No longer will big companies own the means of energy production, huge oil or nuclear installations, and be able to charge up to the limit. Energy will be obtainable by everyone at home, by putting horizons in the zero point field in a way that makes rotational movement, for example using a nano-construction like this.

Physics will not be taught in the same schizophrenic way: as quantum mechanics for the small and relativity for the fast or large. MiHsC shows that the two halves link up if you consider the effect of relativistic horizons on the quantum fields as I discuss here. The assumption of smooth fields will go too, the cosmos is broken up into reference-frame dependent information cliffs (horizons). Dark matter and dark energy are not needed in the MiHsC-ian framework so we can close the dark matter detectors down and divert the millions in funding to horizon engineering (some reading this will fear for their funding - they will have to change topic, that's all). Dark matter, like the Michelson and Morley experiments, will be regarded as a null result.

String theory, and its 11 dimensions, will also be out, but will get some credit for its discovery of the holographic principle, and the EPR paradox will be solved because in MiHsC, time does not exist for quantum systems that are not able to perceive it, so quantum systems have no sense of time and this means the future is known to them.

No longer will engineering just involve sticking bits of existing matter to other bits. We will be able to create matter by setting horizons up for photons. In MiHsC, matter or particles are just confined photons so this will make Star Trek technology like the holodeck or food replicators possible. Another name for MiHsC or quantised inertia is 'Horizon mechanics' (this name was suggested to me by John Dorman, and I like it: it's more general). Horizon mechanics will replace the whole of present engineering.

The philosophy of MiHsC is that if something can't be seen in principle, then it does not exist, so you can delete space and step over it. This was the basis for my sci-fi novel (yes, OK, I've been told to "stick to physics", but the ideas in it are valid). Also, we previously assumed that mass->energy and the cosmos ends up in a depressing heat death. MiHsC makes it clear that the heirarchy is information->mass->energy, and information is always being created. So the cosmos can grow instead of die. Which brings us on to biology. Do organisms make use of MiHsC? Why are cells the size they are? Are they precluding Unruh waves longer than they are and so regulating their temperature?

Coming back to space, the galaxy will be open to human colonisation. The emdrive, explained by MiHsC as just being a metamaterial (metal structure) that creates a gradient in the zero point field, doesn't need to carry fuel with it and so, although it accelerates very slowly, it will get us as close as we like to the speed of light, so that we could get to Proxima Centauri in four or so years of Earth time, and less time for those in the ship (given that special relativity still applies and slows time down for the travellers).

Who could possibly give anything else a second of their time, given the fact that quantised inertia / MiHsC / horizon mechanics is unbelievably simple, works perfectly to explain the data in the galaxy rotation problem for all galaxies, and galaxy clusters, cosmic acceleration and predicts many other anomalies as well (see the 12 journal papers that I have published), and it predicts all of the above applications?

References

Video clip to provide serious background: Mary Poppins flies in on her metamaterial .. sorry, umbrella: https://www.youtube.com/watch?v=5BHoDW9f7vY

Thursday, 15 December 2016

Game over for dark matter

Back in 2006 when I had not yet published MiHsC / quantised inertia, I went to an evening seminar at Exeter University by someone who'd been sitting in the Boulby Mine in Yorkshire for ten years, isolated from cosmic radiation, looking for (hoping to detect) dark matter. Afterwards, being the tactful person I am, I went up to him and said that I had an alternative to dark matter. It is a tribute to the centuries of civilisation we stand on, that he didn't go for my throat, and we discussed things in a rational manner. Back then, I already believed, somehow, that quantised inertia would replace dark matter, but I did not have solid observational proof. I now have a lot of evidence, including this plot:

The plot shows the expected Newtonian rotational acceleration of stars orbiting in galaxies on the x axis, and that observed on the y axis. The line predicted by Newton is of course the diagonal dotted one (expected=observed). The data, binned from 153 galaxies in the SPARC catalogue, that was sent to me recently by Prof Stacy McGaugh, is shown by the grey squares. It shows that at low accelerations (at the outer edges of galaxies, left hand side of the plot) the acceleration is higher than expected: the squares are above the diagonal line. This means that galaxies spin too fast for Newtonian gravity and they should explode with centrifugal force. This would be a cool, but brief, sight to see, but they don't explode. They just sit there, anomalously spinning too fast. The old solution to this of course is to arbitrarily add dark matter to the galaxies to hold them in by gravitational force, rather as governor Tarkin tried to hold The Empire together by force, but this is obviously bogus because you have to add a different arbitrary amount of dark matter to each galaxy.

The solid line in this plot shows the predictions of MoND, which has been fitted to the data by varying its adjustable parameter a0, so it's not that big a deal that it fits. It has been made to fit by that adjustment, and without a physical reason, but it is at least less adjustable than dark matter.

The dashed line shows the prediction of quantised inertia (MiHsC) using only the visible matter, the co-moving diameter of the cosmos, and the speed of light: all well-known parameters that are unadjustable. Quantised inertia (MiHsC) therefore beats dark matter and MoND in fitting this data without any adjustment at all. This is why I claim dark matter is finished, and why I claim that quantised inertia explains the empirical relation that was MoND. A paper on this is now going though review, but really it is only a slight update to the paper I published back in 2012 (see references). The title of this paper (Testing quantised inertia on galactic scales) had a pun (double meaning) that I was proud of, but no-one seemed to notice (galactic scales could imply size, or weighing scales for inertial mass. Ho ho ho!). Hopefully the new paper will be published soon and noticed, and all that dark matter funding can be put to better use, and that guy down the mine, who usefully got a null result, can finally get some vitamin D.

References

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. ApSS, 342, 2, 675. http://arxiv.org/abs/1207.7007

Thursday, 8 December 2016

Notes on EMdrive and MiHsC

Here are some notes that I made (to anticipate likely questions) to prepare for a radio interview on the EMdrive and how MiHsC explains it, that was recorded yesterday (on 'Hotel Mars' with John Batchelor and David Livingston). The audio interview is available here (this version has better audio) and The Space Show here.

What is the emdrive?

The emdrive is a truncated-cone made out of a copper shell with microwaves resonating within it. A bit like a microwave oven built into a metal megaphone. Roger Shawyer from Britain & Guido Fetta from Italy discovered that such a thing moves slightly towards its narrow end. The thrust is tiny: ~1mN per kW so the acceleration is on the order of 0-60 mph in 3 days, so it won't be on The Grand Tour anytime soon, but the crucial thing is that it accelerates without expelling propellant, an ability that gets rid of the need to carry heavy fuel and therefore revolutionises the prospects for interplanetary/interstellar flight.

Why is it controversial?

It is the equivalent of moving your car by sitting in it and pushing on the dashboard. Physics disallows this because if you push forward on the dashboard, your backside pushes back on the seat and the two forces cancel. This is due to the conservation of momentum, which has never been seen to be broken before. Physics says you can’t move unless you leave something behind. If you throw your shoe out of the back of the car then the car (if the brake is off) will move forward, because you expelled something. That is how rockets work. The emdrive does not expel anything so physics says it shouldn’t move.

Why is it important?

It violates a central part of physics (the conservation of momentum) which has never failed before, so if it is confirmed physics will need a radical change (see below). Also, the applications are huge: hovercars, launching without rockets, new energy sources from apparently ‘nothing’, and interplanetary and interstellar travel becomes practical because this engine works without having to carry heavy fuel.

How many groups have tested it?

UK. Shawyer, 1999-. Many experiments have been done. Several reports have been published on the SPR website.
China. Juan et al., 2012. They got a larger thrust than Shawyer, but later found an error, and their recent results are null, but consistent with the other results since their apparatus is unable to measure the likely thrust.
US. Guido Fetta, 2014. The Cannae drive has a much flatter shape, but they also found positive thrust.
Germany. Tajmar et al., 2015. They also saw a thrust, but the emdrive also thrusted when upright, which needs to be looked into.
US. NASA, 2014. Tested positive for thrust, but in air.
US. NASA, 2016. Tested positive in vacuum and published a peer reviewed paper.

What is different about the new NASA paper?

1. NASA tested the emdrive in a vacuum. One of the earlier criticisms was that the thrust was being caused by air currents. This is obviously now ruled out since they saw the same thrust in a vacuum.
2. It is a peer reviewed, checked by other scientists. Most of the experimental papers on it before this have been conference reports, not subject to the same rigour. It was apparently a very long and difficult process too, so Dr Harold G. White of NASA should be commended for having the courage to do this in the first place, and for his hard work through peer review.
3. It is NASA, so it has raised the profile of the emdrive.

The NASA emdrive results (see the recent paper) are interesting because they get weaker thrusts than everyone else so far, and also they tend to put dielectrics in the narrow end of their cavity. Quantised inertia predicts that the dielectric should thrust the other way, cancelling the force due to the taper of the cavity. I need to look into this in more detail.

I can use an analogy with ships at sea. Usually waves hit ships from all around so they don’t push them on average, but if you put two ships together there’s a sheltered zone between them, so suddenly more waves hit the ships from outside then from between them, so they move together. If the crew don’t know about the waves they’ll think it odd, like physicists think the emdrive is odd.

Quantum mechanics predicts there’s a quantum sea all around us called the quantum vacuum and the Casimir effect and Lamb shift have proven its existence. Relativity predicts that when objects accelerate, information horizons appear in the opposite direction to the acceleration vector, since information cannot catch up to the object from behind that horizon, and relativity has been tested. I’ve suggested that relativistic horizons damp the quantum vacuum, just as the ships damp the sea waves, making a void that pulls the objects back against their acceleration. This model, called quantised inertia or MiHsC, predicts the old property of inertia (which suppresses accelerations). It also predicts galaxy rotation exactly without dark matter or any adjustment and cosmic acceleration. I have published 12 papers on this and a book called ‘Physics from the Edge’.

Quantised inertia can model the emdrive too because it allows more quantum waves to exist at the wide end of the cavity so microwave photons that go to that end gain inertial mass, they’re heavier. This is like a rocket expelling mass at the wide end. Another way to think about it is that the microwaves’ centre of mass is continually being shifted towards the wide end, so the emdrive cavity itself moves towards its narrow end to conserve momentum.

An analogy is a person on a ship who keeps walking from the front to the back. Every time he goes to the back he picks up a weight from the deck. This moves the centre of mass of the ship backwards, so the ship has to move forwards slightly to conserve momentum.

What is MiHsC/QI in a nutshell?

A summary: quantised inertia says that relativistic horizons damp the quantum vacuum, making it non-uniform, creating new forces.

A poem: Go to the right, the left’s out of your sight. A horizon appears, damps zero point fields, dragging you back. Inertia is that!

What has been the response of the scientific community to MiHsC?

They have mostly ignored it, so far. Two criticisms they have made are that the Unruh radiation (quantum vacuum) I’m using has not been seen, but it is a widely-accepted prediction akin to Hawking radiation and may have been seen in experiments recently. The second criticism is that I’m varying the speed of light in the vacuum, but this is not so serious since special relativity only demands that light is emitted at a constant speed, c. Apparent speed of light changes happen in general relativity all the time but are explained away with bent space. Also, NASA tests may have shown light changing speed (space bending) in the cavity.

Interest is growing and a few people are now working with me: including Dr Jaume Gine who recently worked with me on this paper, and Prof Perez-Diaz who is a very capable experimenter. He recently visited me and we designed some experiments, including the LEMdrive, that he is now doing.

What other theories are there?

Many people have said there must be an experimental error, but no one has suggested an error that fits the data. For example, the heating/expansion of the cavity can offset the centre of mass and make the cavity move to conserve momentum, but that and other errors were calculated in the NASA paper and found to be too small.

Roger Shawyer has a theory that uses special relativity to explain it, and while I respect him for the experimental emdrive discovery, I don’t accept his theory because relativity should also obey the conservation of momentum. The emdrive does not.

Grahn, Annila and Kohlemainen from Finland have an interesting idea that photons in the emdrive are pairing up and cancelling each other out, so they can leave the emdrive undetectably through the wide end, pushing it towards the narrow end. However, this theory relies on many assumptions and ‘invisible stuff’ and I haven’t seen a comparison with data yet.

In their new paper, NASA propose that the particles in the quantum vacuum are ‘real’ (a non-standard view due to David Bohm) so that sound waves can exist in the quantum vacuum and it can act as a momentum sink. An interesting approach, but again it is adjustable and complex so it’s easy to get the right answer for the wrong reason. Also, I’ve not seen a comparison with the emdrive thrusts.

What’s Next for the Emdrive?

It has been given a boost by the positive NASA test, and I admire the NASA Eagleworks people, eg: Dr Harold G. White, Paul March and others, for having the curiosity and courage to test it.

The next step is that universities need to get involved and perform rigorous tests, and do some crucial experiments, that those who have theories can suggest.

There should also be a test in space. The Earth is a messy environment, and you never know what electromagnetic forces might be around. In space, it’s cleaner. Guido Fetta aims to test an emdrive in space using a 6U cubesat (small satellite), possibly in 2017. It’ll have a solar panel to power it and be pointed narrow end up, so if it stays in orbit longer than expected that’ll be a sign that it is thrusting upwards. If it works, it’ll change the satellite industry completely.

Also, the quality factor of the cavity is a crucial parameter. This is the number of times microwaves can bounce around inside without being absorbed. So Guido Fetta and Roger Shawyer are now trying out emdrives coated inside with a superconducting layer, because they have much better Q factors: far more photon bounces.

Cannae has also proposed a deep space probe, that uses 10 em-/Cannae-drives powered by RTGs to accelerate at 8.66x10^-3 m/s^2 from low Earth orbit to Sol escape velocity in 2 months. It could travel 0.1 light years in 15 years (1.35% c). This could be the first interstellar probe. To do this with a rocket you would need to carry a Ceres-sized amount of fuel.

Isn’t there a suggestion that dark matter can predict the emdrive?

Someone wrote a blog saying it could be dark matter. But, dark matter is an awful hypothesis. It has been forgotten that in 1980 or so physics failed to predict the newly-observed galaxy rotation: they rotate so fast they should explode, but don’t. Instead of changing the theory, they added ten times as much dark mass to galaxies as there is visible mass, to hold them in by gravitational force, but they have to add it by hand to each galaxy differently. Some galaxies are 92% dark, some are 99.3% but there’s no reason behind these numbers, and dark matter is not falsifiable: if your multimillion pound experiment can’t find it, you can say “OK, maybe it’s in this other more difficult regime” and that can go on for ever. In the same way you can glibly say "dark matter drives the emdrive" but until you point out a specific process that can be tested or falsified it is meaningless hand waving. In contrast quantised inertia predicts all galaxies (and the emdrive) without any adjustment, and Unruh radiation is something that can be looked for in one place and is either there or not. It is falsifiable.

Is the emdrive a warp drive?

Well, it’s not based on Alcubierre’s warp theory, but I’m suggesting that the speed of light changes within it. This can happen in relativity if you bend spacetime to make sure the change in c is not measurable to an observer, say a bug inside the cavity, so maybe space-time is bending in there. NASA found something like that when they fired a laser through, but couldn’t quantify.

Do you think the emdrive is really anomalous?

Yes. Of course there is always doubt in science, but as Captain Kirk says in the film Star Trek: Generations "You have to take some risk if you want to sit in that chair", and the emdrive has now been successfully repeated in 4 independent labs. So you have to pay attention to that. It's vital in science to value new observations over old theories.

Concluding thought?

It’s a time to be excited: anomalous observations such as galactic rotation, cosmic acceleration, the flyby anomaly, the emdrive and many others are forcing a rethink of physics. In my opinion they are all telling us that mass-energy can be created from information horizons, this is the basis of quantised inertia, and the theoretical and practical implications are huge. I’m hoping now that universities will get involved in tests.

Monday, 28 November 2016

Emdrives & dielectrics: the NASA shift

The NASA paper further supporting the previous emdrive experiments (in which a microwave-filled conical cavity moves towards its narrow end without expelling anything, as standard physics says it just shouldn't do) has finally been published. Apparently Eagleworks had a terrible time publishing it, so well done to them.

It is interesting that all the NASA results are anomalous in comparison with results from the other teams: Shawyer's, the Cannae group and Tajmar's. The plot below shows the thrust predicted by quantised inertia (MiHsC) on the x axis, and the y axis shows the thrusts observed in the lab. It would be great if all the diamonds representing the different emdrive experiments were along the diagonal line (a perfect agreement). The Shawyer, Cannae and Tajmar experiments are, but the NASA experiments are all shifted rightwards. This shows that MiHsC over-predicts the thrust for NASA's tests by a factor that can be as much as ten.
I may have an explanation for this. MiHsC predicts the emdrive's thrust by saying that the inertia of the microwave photons is caused by Unruh radiation (a radiation you only see if you accelerate). At the wide end of the cavity more Unruh wavelengths fit within, and are 'allowed', due to the bigger space available, but at the narrow confined end fewer are allowed (as for the Casimir effect). Thus, MiHsC is continually shifting the photons' collective centre of mass towards the wide end so that to conserve momentum the cavity has to shift the other way, as indeed it does, but more slowly as it is far more massive than the microwaves (more detail).

A new possibility to explain NASA's anomaly within an anomaly (the NASA shift) is as follows. Most of the NASA experiments, including the latest one, put a dielectric at the narrow end of the cavity. A dielectric means that Unruh waves will be slower and have shorter wavelengths, and so more of them will fit at the narrow end. MiHsC therefore predicts that having a dielectric at one end is rather like widening that end, and if you put it at the narrow end, then you reduce the taper and reduce the thrust.

I've already worked out some of the maths for dielectrics, after I read an interesting, but inconclusive, 2016 report by a group at CalPoly (Kraft and Zeller, 2016) who tested a cylindrical emdrive with a dielectric at one end. I just need to account now for both a dielectric and taper and see if the numbers fit the NASA shift.

References

McCulloch, M.E., 2015. Testing quantised inertia on the emdrive. EPL, 111, 60005. Preprint

K. Zeller and B. Kraft, 2016. Investigation of a partially-loaded resonant cavity. CalPoly research report.

White, H., P. March, J. Lawrence, J. Vera, A. Sylvester, D. Brady, P. Bailey, 2016. Measurement of impulsive thrust from a closed rf cavity in vacuum. AIAA J. of Propulsion and Power. Online