I've suggested (& published in 18 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 July 2017

QI and Emdrive: dc/dt=0.

I've had some complaints that my explanation for the emdrive violates a central tenet of special relativity: that the speed of light cannot change. Well, there were reasons not to be worried so much about that, but as it happens I've just published a paper in EPL that shows that the results I derived in 2016 do not imply a speed of light change in the cavity anyway. The new derivation is based on an insight I had one night when I was walking into the local TESCOs (not too often associated with scientific inspiration, but times change): what quantised inertia says is that more Unruh waves (assumed to cause inertia) can exist at the wide end of the cavity, and this simply shifts the centre of inertial mass of the input microwaves continually towards the wide end of the cavity. The cavity then has to move the opposite way, towards its narrow end. This more simply reproduced the same results I had before, but without the need for a change in light speed, so there is no possibility of relativistic violation.

In this new paper I also investigate what happens when you put a dielectric in the cavity. Dielectrics are insulators, so electrons do not move through them freely, but the electrons can shift slightly. So, like people in unions, who can organise to resist forces from above, the electrons can re-arrange en-masse to create a counter field to resist an applied electric field. Air is a dielectric, so are glass and all plastics. Dielectrics really do reduce the speed of light in a way that is well accepted, and since the frequency of light stays the same, the wavelength of the light has to shorten and this means that the Unruh waves can also be expected to shorten in the dielectric, meaning that more of them fit into the cavity at the end with the dielectric.

So, according to quantised inertia, adding a dielectric to a cavity end is rather like widening that end. If you add a dielectric to the wide end you can expect an enhanced emdrive thrust since it boosts the existing surplus of Unruh waves there. Conversely, if you add a dielectric to the narrow end, it should reduce the thrust since it reduces the effective 'taper'. As you can see in the paper, the best-documented NASA tests all used dielectrics, and considering them in the theory improves the predictions of QI considerably. Unfortunately for the first Shawyer test it worsens the prediction considerably, such that the thrust is now equal but opposite to that observed. The observed and predicted emdrive thrusts are shown in this table:


McCulloch, M.E., 2017. Testing quantised inertia on emdrives with dielectrics. EPL, Vol. 118, 34003. Journal paper, now open access! Full text also here.


Brian Moore said...

Using rough numbers what kind of size/geometry/setup would be necessary to make an EM-drive with a thrust of 1+ Newtons, as estimated by your formula?

ShardPhoenix said...

Under this theory, could see an em-drive effect in a non-tapered cylinder with a dielectric at one end?

Jimmy Johnson said...

I think it is important to point out that based upon Mike's quantized inertia (MiHsC) formula for thrust (as well as Shawyers original formula) the quality factor, Q, can have a much greater effect on the thrust produced than the effect of dielectrics or cavity taper. The force produced according to the above mentioned formulas increases in direct proportional to the value of Q. The practical effect of an optimized cavity taper with or without taking into account the presence of dielectrics is likely to be less than 10.

To get an estimate of how large the quality factor effect can be, it is possible to achieve a quality factor of greater 10^5 in standard metal cavities, and greater than 10^10 in superconducting cavities at a few gigahertz. While some low loss ceramic dielectric resonators can have a quality factor of more than 10^5, the type of plastic dielectric loaded RF cavities used by Shawyer, NASA, and others have a quality factor closer to 10^3. The Q multiplier was Shawyer's main reason for moving away from dielectric loaded cavities and focusing on superconducting cavities.

While the mathematical path is clear, the practical engineering problems of working with extremely high Q cavities is not. Matching an RF source to a high Q cavity is extremely challenging. Only that portion of the RF spectrum that falls within the cavity resonance will excite the cavity. The typical bandwidth of most gigahertz RF sources is very much wider than the bandwidth of moderate to high Q cavities. The oven magnetrons used in many of the cruder emdrive experiments are probably the worst choice from the standpoint of coupled power. It is unlikely that more than a few percent of the 1000 watt magnetron output couples to a well constructed typical Shawyer conical cavity. A typical oven magnetron output spectrum can be viewed here: https://www.nextbigfuture.com/2015/04/magnetron-powered-em-drive-construction.html

Because only that portion of the RF source power that actually falls within the cavity bandwidth can be used to excite the RF cavity, evaluating experimental results using formulas based upon the power of the RF source is likely to give severely inaccurate results. The RF source frequency and the RF cavity acceptance frequencies (bandwidth) change during operation due to thermal effects further complicating the problem. Under stationary operation, all of the usable power from the RF source is turned into heat within the resonant cavity. This is a major issue with superconducting cavities which require cryogenic cooling to work.

An example will help to clarify the some of the issues.

Given: a niobium superconducting cavity with a Q= 5 X10^9 resonant at 5 gigahertz and a 5 watt driving source is ideally matched in frequency and bandwidth to the cavity.

* The cavity and the source will have a bandwidth (3dB) of 1 hertz (BW = Freq/Q).
* The power circulating in the cavity will be several billion watts with an appropriately large electric and magnetic fields.
* 5 watts will be dissipated on the cavity walls which must be kept below 1.8 Kelvin.
* If the source or Rf cavity frequencies drift as much as a few hertz from one another coupling will drop to a few percent.

* Because resonant cavity frequency and physical dimension are essentially inversely proportional maintaining a resonant frequency within 1 hertz at 5 GHz requires maintaining physical dimensions to 1 part in 5 X 10^9 under thermal, magnetic, and electric field stress. For such a cavity 50 cm long a change in length of 1 micron would likely cause a shift in frequency of 10 KHz

The reason for bringing up the practical issues in this forum is primarily twofold. First it helps in understanding the degree of uncertainty that is likely present in the reported experimental data. Second, it allows better understanding of just the source cavity matching difficulty of performing emdrive experiments.

Jimmy Johnson

Mike McCulloch said...

Brian: There are several possible answers. For example, one combination of parameters that produces a 1N force would be: P=1kW, Q=200,000, L=0.16, wb=0.16, ws=0.1, nb=6 (a dielectric at wide end) and ns=1. There are many others varying, Q, P, aspect ratios and refractive indices (n) that you can play around with.

Mike McCulloch said...

ShardPhoenix: Yes, as I say in my paper, you can have an viable emdrive that is a cylinder (no taper) with a dielectric at one end. The best results come from having both a taper and a dielectric.

Brian Moore said...
This comment has been removed by the author.
Brian Moore said...

Mike: Thanks. Those numbers don't actually seem that unreasonable. I'd be nice if they built one that powerful, to actually determine if the darn thing works or not.

Jimmy Johnson: that was an excellent writeup. There was a paper that just came out a few weeks ago, where scientists have claimed to have discovered the time-bsndwidth product limitation of waveguides to not exist, or at least be much, much higher. They claimed they already improved it by a factor of 1000 on their test platform.

To me this sounded interesting and even groundbreaking, but waveguides aren't my area of expertise.


(Link to paper in article)

Would this discovery significantly expand how much energy you could get to couple with the RF source? Or would their method interfere with how the EM drive is supposed to function?

If it significantly improves the energy you could get to couple with a high q factor, the timing of the discovery seems serendipitous to say the least.

Jimmy Johnson said...


Thanks for the reference to the breakthrough in cavity energy storage.

My back of the envelope estimates of the RF source to cavity matching issue barely touches the tip of the iceberg with respect to practical Emdrive RF issues. I did not mention the fact that only the RF power in the correct one of the many available cavity modes counts. Even if the correct mode is excited there is always mode competition for power in a multimode RF cavity.

Another significant problem at high Q is electrical breakdown in the cavity due to the enormous electric fields. Even in vacuum the fields can be large enough to rip electrons out of the metal resulting in arcing and multipactor losses. The energy stored in the electric field in a cavity is the integral of 1/2 D dot E over the volume. The energy stored in the magnetic field is 1/2 B dot H. The cavity resonance is associated with the transfer of energy between the energy in the electric and magnetic fields. Higher circulating power in an RF cavity always entails higher electric fields. In high power accelerators like Fermi and others the engineers spend weeks aging, degassing, and working their high Q resonant cavities up the power scale.

I am very interested in the outcome of Emdrive experiments. If Mike's (or other) theory give working formulas then the practical engineering work can begin. My rule of thumb from many years in technology is that it takes about 2 billion dollars to turn a valid concept into usable hardware, and about 10 times that to get that technology to a mature state. When you see articles from critics which say, "If the Emdrive works, how come we do not have working hardware" you know they have no clue how much development work is required to make working hardware. I doubt that as much as 50 million dollars has been spent on all EMdrive testing. If the Emdrive is a valid concept then from my rule of thumb it is less than 2.5% (50^10^6/2*10^9) of the way to working hardware and .25% toward product level hardware.

Jimmy Johnson

Mike McCulloch said...

Jimmy: Many thanks for your input. I am a theorist, but one very keen to apply theory to practical systems, systems that I lack practical experience with, so it is gr8 to get your technical comments.

Interesting that you say in the experiments done so far only a few % of the input power couples to the right mode, suggests room for improvement, and yet the quantised inertia formula uses the total input power and gets a reasonable result (no systematic overestimate at least).

Do you have any experience in flooding these cavities with dielectrics such as ammonia? I've been contacted by two people (Mohan Ahad and Robert Virkus) who have suggested using BECs.

Frank Becker said...

Mike, Jimmy,

Concerning the energy as far as I understand not the energy is relevant which excites and resonates within the cavity (which has losses).
Rather the energy is the basis for the quantity of the events (per second) of mass is passing through the Unruh bath gradients (and being reflected).
The mass is continuously (re-)supplied and per Mike’s method (also per Franck’s dynamic standing wave methodology) this accounts for ‘Q’.
Basically the Q factor (as determined) from my present understanding should account for the “event” of mass (or here better photon) travel.
In other words the supplied power provides a more or less stable supply of number of photons into the system.
We could say this is the number of event simultaneously (and statistically) could occur e.g. within a duration of one second (with one bounce minimum).
The ‘Q’ factor is the multiplier of the number of events which could happen in a frame of time (multiplier per bounces).
Therefore the actual losses which do exists, but which would not reduce the Q-factor or the photons inside the frustrum could be disregarded.
Let us rewrite F=dE/dx for this scenario and consider dE is proportionally multiplied to the power P.
F=dE/dx*N*Q with N=P/Ep with (energy of one photon) Ep=f*h*c
This would suit the number of events (per timeframe) a single photon would be under the situation to pass through a horizon (dE) gradient.
I am not a expert and do not know much about resonance cavities, but from my perspective the important parameters is to take care of ‘Q’ and ‘P’.
But ‘P’ mainly to supply photon, if those do disappear by the frustrum design, this would be accounted already into (reduced) ‘Q’.
Perhaps I am too simply in this visualization of the resonance cavities, but this may explain why Mike is stating that power reduction appears not to affect.

Jimmy Johnson said...


I have made an attempt to outline in imprecise and very general terms some of the issues associated with the RF source and resonant cavity issues. The reason for being imprecise and general is that a treatment of the detailed problem is far more complex than could be explained in this forum and frankly beyond that which I am competent to discuss. Having said that I will try to clarify some of my previous comments so that I do not mislead.

Bandwidth of the Source that can Couple into the Cavity

If the source bandwidth is smaller than the cavity resonant bandwidth then it is possible with the correct RF launch to transfer all of the RF source into the cavity. If the RF source bandwidth is wider than the cavity bandwidth then only that portion of the source that overlaps the cavity resonance is available for coupling.
A very useful RF engineering formula is that 3 dB bandwidth of a resonant cavity (dF) is equal to the resonant frequency(F) divided by the quality factor (Q). The higher the Q the narrow the bandwidth of the cavity. Very high Q resonant cavities require very stable spectrally pure RF sources.

For example if a typical Shawyer conical copper wall cavity resonant at 2.45 GHz has a Q of 1x10^4 then it has a resonance bandwidth of 245 kHz. If you look at the spectral power output of a free running 2.45 GHz oven magnetron between 2.4 and 2.5 GHz you would see what looks like the back of a porcupine across most of that bandwidth. The spikes would be moving around in time under thermal and mechanical perturbations. Only those frequencies that fall into the 245 kHz cavity resonance will be useful power. The poor spectral quality of a magnetron makes it a poor source for a high Q resonator. Other RF sources which have much better spectral purity would be better choices. There are techniques to narrow the bandwidth of RF sources.

Competent RF engineers like those at NASA are aware of this and have almost certainly taken this into account in their reported RF power. I would not assume that this is the case for all of the reported experiments however.

Gas as a dielectric is generally not a good choice in any high Q resonant cavity because it will invariably break down at even low RF input power. At high power, high Q ,so muck as a scratch on the cavity wall or an oxide inclusion can cause catastrophic electron avalanche breakdown even in vacuum.

Magnetron Spectrum: https://www.nextbigfuture.com/2015/04/magnetron-powered-em-drive-construction.html

Excellent RF Cavity Discussiion:

Jimmy Johnson

Unknown said...

while power transfer is more efficient if it's a resonant cavity, does anything in the theory require that it be resonant?

Mike McCulloch said...

Unknown: Resonance is required for the high Q factor: to get the photons to bounce back and forth repeatedly, rather than just be absorbed by interactions with the walls. Resonance and high Q sets up the QI process. If no resonance, then the effect would be negligible.

Laurence Cox said...

Reading Jimmy Johnson's useful comments made me wonder whether the GHz frequency range is the best for demonstrating the effect. Yes, the RF sources are easily available and superconducting cavities are used in particle acclerators, so that technology is easily transferable, but the cavities themselves are not much larger than the wavelength.

So the thought occurred to me, why not do the experiments at a much higher frequency in the optical region. The effects of diffraction would be much less because the physical size of the cavity would be similar but the wavelength much shorter than for microwaves. Also, lasers can be made with very narrow linewidths and stable frequencies. An optical cavity design with one concave mirror and one convex mirror could mimic the conical microwave cavity (these are already used in high-power lasers). Mirrors with reflectances of up to 99.9998% have been made and are used in cavity ring-down spectroscopy.

Phil Delltablet said...


You may like to have a listen to this (http://www.bbc.co.uk/programmes/b08wn9mb), the "Infinite Monkey Cage".

I was on a business trip and the podcast arrives on my phone, so I would have been more prompt. The words uttered "our theory of gravity might be incomplete" , when esteemed academics were put on the spot by the comedian (of the duo).



Mike McCulloch said...

Phil: Amusing show, and you're right: when pushed they actually started to sound like me, doubting dark matter (comedy has a way of cutting to the core) and they do realise that their collective opinion that everything 'fits together' depends on the framework they assume. This is good. I just wish I could tell them about quantised inertia which provides a simple solution to galaxy rotation and cosmic acceleration with no tuning and on a piece of paper (you don't need a telescope on the far side of the Moon, just a bit of thought). It is a bit frustrating because despite publishing 19 papers on quantised inertia now, I still can't get to speak at conferences, and the arxiv are still putting my papers in the 'general physics' section that no-one looks at. Anyway, thank you for this that gives me a little bit of hope that the log-jam is breaking.

tyy said...

Your theory is completely crank in nature, so there is actually nothing to complain about it. Just to ignore.

joesixpack said...


Have you ever been published in EPL? No?

Marek Korbel said...

Dear Mike,

This article made me thing how could qi be associated to the speed of light limit, im not a physicist, but the way I understand it is, that a rindler horizont forms on the left when an observer is accelerated to the right, then more zpf waves hit the right side, since some portion of zpf waves cant reach it from the left and this causes inertia..

but for very slow accelerations this horizont exists behind hubble horizont so the observer would experience no inertia and so he would be able to move faster than light (?), if it was true we could just forget 80 years of physics.. the other option is there is a minimal acceleration in the universe which could be the dark energy which seems to be true, the question i have is what happens if you try to accelerate the observer under this limit? Does he just stay in place and do nothing without reaction? This on the other hand would be against newtons laws and we could forget 300 years of physics :D Maybe my questions are stupid, but both versions in this thought experiment seem to have unacceptable result for me.. Could you please correct me?

Thank you,


mikenyc said...