I've suggested (& published in 15 journal papers) a new theory called quantised inertia (or MiHsC) that assumes that inertia is caused by relativistic horizons damping quantum fields. It predicts galaxy rotation, cosmic acceleration & the emdrive without any dark stuff or adjustment.
My Plymouth University webpage is here, I've written a book called Physics from the Edge and I'm on twitter as @memcculloch

Friday, 7 August 2015

The Emdrive Energy Paradox

As always, treat this blog entry with due skepticism: I'm thinking aloud in the hope of constructive feedback.

The emdrive energy paradox was found and is discussed nicely by frobnicat (from the NSF forum) in the emdrive wiki reference below. The problem is as follows. The rate of electrical energy input to the emdrive is constant so the total energy put in goes up linearly with time, but the kinetic energy (KE) stored and available for extraction from the emdrive's motion is: KE = 1/2mv^2 and since the acceleration is constant, v is a linear function of time so KE depends on t^2. Eventually, at high enough speeds, the KE exceeds what we put in! Therefore there must be a new source of energy here, one which provides more energy at higher speed. How is this possible?

It's not possible using standard physics, but is using MiHsC which considers the zero point field. The force or thrust predicted by MiHsC is like an inertial force (in fact, I claim it is the inertial force, see McCulloch, 2013) and a characteristic of inertia is that no matter what the speed of an object is, its resistance to acceleration, its inertia, is the same (This fits with special relativity's insistence that the laws of physics should be independent of speed, which is a relative thing). The MiHsC/inertial force is then also like whatever force is driving the emdrive, since no matter what the emdrive's speed is, the force on it seems always the same. This last point is an increasingly solid observation: as frobnicat's points out on the NSF reference below, the emdrive has been tried in different places and times and if its behaviour depended on something so meaningless (after Einstein) as 'speed' then it would have given very different results at different times since the Earth is moving with respect to everything else, and spinning.

So where does this new energy come from? To be more mechanistic about it, the MiHsC paradigm says that the asymmetric structure of the cavity makes a gradient in the density of Unruh radiation (zero point energy) and that this gradient is the new source of energy. For more detail see here or  here. New sources of energy always cause an uproar, but in just this way MiHsC predicts inertial mass, galaxy rotation, cosmic acceleraton & the emdrive quite well. I did suggest a more direct test for the mechanics of this (if applied on the nanoscale) here.


Emdrive wiki: http://emdrive.wiki/Energy_Conservation

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

McCulloch, 2015. Energy from swastika-shaped rotors. Progress in Physics, 11, 2, 139-140. pdf


TheTraveller said...

Hi Mike,

We don't really know what the dynamic, under acceleration, power usage of the EMDrive is.

In Shawyer's published rotary test, the power consumed by the magnetron dropped as the velocity increased.


Here I inverted the velocity curve and placed it under the dropping power curve. Sure doesn't look like power stayed constant but it was only a 80 sec test.

My planned rotary tests should generate a lot more data over a much longer acceleration time as the table accelerates from 0 rpm to 120 rpm.

All the best,

The Half Baked Blogger said...
This comment has been removed by the author.
WarpTech said...


I've had quite a bit of difficulty understanding this paradox from the beginning. But from what I've come to understand is that this paradox is there for "Any" propellantless propulsion device that has greater thrust than a photon rocket. So it is not unique to the EM Drive or the frustum geometry. So your conjecture that energy is being extracted from the ZPF may not be applicable across the board to resolve this paradox.

Also, the amount of energy extracted would quickly become enormous at speeds greater than breakeven, Eout = Ein. Do you really believe your theory predicts unlimited energy extraction from the ZPF?

Another point, the frame of reference is not consistent in the problem. The thrust-to-power ratio is measured in the proper frame of the accelerating vehicle. The kinetic energy, E = (mv^2)/2 is measured in the external frame of "rest", which is an inertial frame. So it's not exactly comparing apples to apples in this regard. From the perspective of someone on-board the vehicle, the fuel is being spent to accelerate. It is not refilling the fuel tank once it exceeds the breakeven velocity. On-board, the velocity of the vehicle is always 0, and whatever is causing the propulsion is always moving at v < c.


qraal said...


Can you unpack this part of your comment a bit for us:

"On-board, the velocity of the vehicle is always 0, and whatever is causing the propulsion is always moving at v < c."

How so?


Eirinn Mackay said...


Because the velocity according to an onboard observer is always 0, the ship always has 0 kinetic energy and there's indeed no CoE violation there. We only need to consider the external frame, and the CoE violation is very clear there.

You're correct that this applies to any propellantless engine, which is why those things are typically considered to be impossible. The only other example I can think of off the top of my head is the Woodward device, which supposedly alters the Mach effect to induce acceleration. The zero-point field has also been proposed as the energy source for that acceleration.

The ZPF is astronomically large but not infinite, and extracting energy from it does not violate CoE.

qraal said...

Dr Woodward would have an apoplectic seizure to be mentioned in the same breath as the ZPF. He's adamant that his device conserves BOTH energy and momentum, and is merely pushing against the Universe via gravitational back-reaction. Only Paul March has suggested otherwise.

Mike McCulloch said...

WarpTech: Re: infinite energy. I suspect it's not as easy as all that :) but MiHsC does allow a huge amount of new energy to appear under the right circumstances as it predicts that when horizons appear they make gradients in the zpf, making that energy accessible. For example, MiHsC speeds up galactic spin and also predicts cosmic acceleration. The amount of energy needed to do those things is mind-boggling.

Mike McCulloch said...

Hi TT: True, we need more data on the power input, but the acceleration in your plot looks fairly constant and the reduced power input actually strengthens the argument that for this to work as stated, then new energy from somewhere is needed.

Ramachandra Gopal said...

Hi Mike
I have been a lurker in EMdrive forums and your blog. I am particularly impressed with your paper on the MiHsC analysis of Emdrive effect. I had suggested to use your calculations as specified in the excel sheet in Emdrive.wiki with these values

Input Reference Value
Big Diameter 28
Small Diameter 1
Cavity Length 100
Q 5000
Frequency 2.45
Power 1000
Big Radius 14
Small Radius 0.5

mN Force 1608.75
mN Force 1081.08
mN Force 1025.45

I was told that you had mentioned that large length/diameter ratios are bad for actual thrust. I am not sure why.
(I also have a hunch that a Horn loudspeaker kind of design of the frustum could be even more powerful in thrust)

Second question.
How do you think the Alcubierre calculations would be impacted if MiHsC were introduced in them?


Mike McCulloch said...

Dear Ramachandra, The formula I published, and that you are using, was an approximation that assumed the Unruh waves can only resonate perpendicular to the emdrive's cavity axis. This is an approximation because the Unruh waves can also resonate along the axis, and in diagonal directions. If you had a pointed cone, this formula would then predict no waves at all at the pointed end, and an infinite thrust since Wsmall=0, but in the real emdrive Unruh waves would still be able to exist at the small end by resonating along the length of the axis. This limitation of the formula is not so bad for the emdrive because it is a truncated cone, but a better formula is needed and I've been trying to calculate the exact analytic formula to take account of resonance in all directions. In lieu of that I've developed a simple formula that does take account of resonance along the axis. It is:

F = 6PQL/c * ( 1/(L+4wb) - 1/(L+4ws) )

L=axial length. You can also see my discussion of this formula here:


To answer your second question: Alcubierre's work used general relativity, and MiHsC violates (infinitesimally, and usually undetectably) the equivalence principle that GR is based on, so MiHsC is fundamentally different. However, MiHsC tentatively suggests that the speed of light may be exceeded in a different way. I discuss this a little here:


Alain Coetmeur said...

Dear Mike,
just agains a naive question, to open a door that I cannot get through myself.

when you imagine a perfect emdrive, you have an energy source, which transform mass into energy, and feed a microwave source.

then this energy is transformed partially depending on the Q into heat, which vould be radiated by a sphere in which the Emdrive is hidden.

the rest of the energy in Shawyer model is consumed to increase kinetic energy (what for MiHsC?), through detuning of the cavity...
an idea to balance the equation of energy or momentum could be to account for the energy and momentum that disappear, and thus the mass lost by the vehicle during energy production.

maybe it can help to solve some paradox?

many question... for example if energy is lost through detunig, maybe this mean all energy is lost as heat in the cavity...
but if it is disappearing "magically" from symmetries effects then something inertial may change ?

is that a meaningful idea?

Eirinn Mackay said...

The problem with the shawyer model of a cavity becoming "detuned" at high speed (and thus needing more electrical energy to generate a force) is that it implies a universal reference frame. It solves the paradox by opening up a much bigger one. There's also no evidence for it...

Julien Geffray said...


Did you know about that 1998 paper by Smolyaninov?

Smolyaninov, Igor I. (8 September 2008). "Unruh effect in a waveguide". Physics Letters A (Elsevier) 372 (37): 5861–5864. arXiv:physics/0606072. doi:10.1016/j.physleta.2008.07.033.

Mike McCulloch said...

Dear Alain. Eirinn's point about Shawyer's dependence on speed by 'detuning' is a good one. There can be no dependence of the process on speed because as Einstein showed (after Michelson & Morley's expt) the laws of physics can't depend on something like speed, which is different for every observer. It can't be right that we could define the emdrive's speed relative to Roger Shawyer, to the Sun, to the Andromeda galaxy and predict a different behaviour.

Your question about energy is the crux of the matter. The energy MiHsC brings in, is independent of speed and dependent on the acceleration of the microwaves, and is new. One way to think about it to say that the resonating and accelerating microwaves are setting up a horizon that is closer at the narrow end, making a gradient in the zpf which is supercharged by the power input and the emdrive is being pushed down that gradient. The effect of this horizon is not recognised by standard physics, hence the anomaly. This note is too short to be easily understood, so I will try to write another blog entry to explain my point of view..

Mike McCulloch said...

Dear Julien. I like Smolyaninov's work. I hadn't seen this one, but it's quite a relief to see someone else talking about the acceleration of photons :) and the experiment to detect Unruh radiation looks easier than the other suggestion that I did see from Smolyaninov which was to accelerate plasmons around a gold nanotip: http://arxiv.org/abs/cond-mat/0510743 Thank you.

Jim said...

You mention a lot about how the edges of galaxy rotate faster because of MiHsC. Some other physicists claim it is because of dark matter. My favorite explanation is from Randell Mills where he claims that dark matter is just another form of hydrogen, which he called a hydrino. He is capable of producing this new state of hydrogen in his lab. This hydrino is smaller than hydrogen and is difficult to detect.

Mike McCulloch said...

While obviously I think that MiHsC is the solution to galaxy rotation, I'm always willing to look at bold theories like the hydrino, provided that they correctly predict the standard experiments and the anomalous data without 'tuning parameters'. It may be that Mills' is better than dark matter in this sense (it can't be worse, can it?) because at least he proposing a particular single particle. Can he predict the data? Has he published a peer reviewed paper?

qraal said...

There are plenty of dark matter candidates. The problem is finding experimental reasons for choosing between them.

Jim said...

Mills has over 90 published papers including a peer reviewed one in the prestigious, "Journal of Physics D: Applied Physics". He has some papers, which may or may not have been peer reviewed, that mention that there is evidence that dark matter consists of hydrinos. If I get the chance I will look for them. There are a few universities and research labs which have replicated his experiments.

conundrum said...

Some folks are suggesting building a 24 GHz EMDrive and flying it on a CubeSat.

I've had much the same idea, in my case the plan was to get it to maybe 105K feet, launch a rocket to get it near orbit then turn on the solar powered drive.

By comparing a control satellite launched at the same time with the equipped satellite, it would be very obvious if the drive was working correctly.

Mike McCulloch said...

There may be other advantages of space testing that I haven't thought of (?) but the problem is that it's expensive, and there are effects (Solar radiation pressure, residual friction, gravity due to uncertainties in the geoid, difficulty of positioning..) that are difficult to quantify and subtract from the data.

A vacuum test on Earth is cheaper, can be controlled, and is easier to measure, and that is the kind of data needed to conclusively demonstrate or refute the emdrive.

Mike McCulloch said...

One way to make the emdrive easier to test in space (though still more difficult than in a vacuum chamber on Earth) would be to use two emdrives side by side, facing the opposite way, and look for an accelerating spin. Spin is easier to measure than drift.

Alain Coetmeur said...

Cubesat is a good idea, and this could interest both crowd funding and tycoons.

one things to please the skeptics is also reversal.

spin seems good idea, but it is also important to make it change direction

I see a 4 Emdrive setup in square:


you could switch them to spin, in both direction, and to thrust in both directions

the problem is that the skeptics will moan on artifacts on each emdrive, and on the switching system, but the rest of the setup could not be accused.
One way to avoid question could be to put power and distribution at the center of the square.

anyway if you make a closed cube of anything, just powered by solar energy, and you are able to make it spin and accelerate in both directions wherever is the sun shining, for long time enough, you make your point.

I imagine a cubesat powered from solar face.
the internal program says it spin clockwise one day, then anticlockwise the day after, and that for 1 year.

it can eliminate the possibility of newton-compatible artifact.

Michael xChaos Polák said...

to Alain: I am afraid, that results obtained low-power, 24 Ghz baby-EmDrives are negative so far (this attracted attention of makers in hackerspaces, because it is small enough to be 3D printed, which on the other hand I am afraid is not precise enough technology for small resonant cavities...). Of course, higher frequences would make it easier to fit in Cubesats, but it can be quite opposite - that the microwave oven frequencies are just on the edge, and that lower frequences in really huge cavities with unrealistic surface properties may be needed to demonstrate it conclusively (think lower radio frequencies and huge ultra-polished and at the same time structurally ultra-rigid and superconducting cavity - not "baby emDrive" - which may be theoretically possible, but impractical because we will just don't have materials for that, just like we don't have it for space elevator)

to Mike:
(there is already obvious emDrive anthem of very British origin, by the way: https://www.youtube.com/watch?v=hBjkkYgD8iw - remix of good old 80's "we gotta install ..." :-)) somehow it seems, that now we gotta deliver custom kitchens in space... which reminds me of "black kitchens", laboratories of alchemic era... I live just few kilometers away from the site where alchemists live on the court of Rudolf II and where "black kitchens" are tourist attraction now... just having such associations - non conspiracy, non-crank, not-believing in anything, just having the feeling - makes it quite easy in local online communities to get labeled as crank....)

Mike McCulloch said...

Thanks for the remix, Mark Knopfler is my favourite contemporary musician (Dylan's my favourite lyricist) and Alchemy is a brilliant album.

You're right that crank is a favourite label to beat people with these days, but it's amusing to remember that the greatest scientist we ever had: Sir Isaac Newton, was an alchemist, a 'crank' of his day. The Newton-alchemy link is no coincidence since to be a creative scientist you have to actively seek out those areas where data appears to conflict with the old theory. Of course, the experiments may be flawed, but you have to look there to check. This takes courage because the majority always support the old theory, but new data counts more than old words. The Royal Society of Newton's time had a great phrase 'Nullius in Verba' by which they meant: "an expression of the determination of Fellows to withstand the domination of authority and to verify all statements by an appeal to facts determined by experiment" (Royal Society website).

I like your suggested twin-probe test, the Royal Society would approve :) so I'm going to do a few calculations and get back to you..