I've suggested (& published in 21 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

## Sunday, 9 August 2020

### Minding One's Ps and Qs

I am impressed with the six quantised inertia experiments that are going on around the world. The spirit of science and curiosity is being brilliantly represented by the people who agreed to be part of my DARPA project, and by some of those I met at conferences or on twitter. It is exciting to see the number of experiments growing every month. To recap, all you need to do is to get light to accelerate enough (bounce around, circulate) inside an asymmetric metallic setup.

However, there is a learning process due to my lack of experience in experimental design .. and telling people what to do! The aim is to prove or disprove quantised inertia in a lab test. To do that, we have to be able to make a specific enough prediction that the lab tests can detect or rule it out. With QI this is uniquely possible since, in its simplest form, the expected thrust is F=PQ/c. The power of the light used (P) is known, so is the speed of light c. What is difficult to know is the Q factor, which is crudely the number of times the light bounces around / circulates in the cavity before dissipating as heat. What thrusts the cavity in QI is not the force from the photons (F=P/c) but the metal cavity making a gradient in the Unruh radiation pushing on the cavity (F=PQ/c).

So far, in all the tests done by, for example, the lab in Dresden, we have not known the Q factor of the cavity. In Dresden this is because Tajmar could only determine that Q was "greater than 19" and also because, as a quick and dirty approach, he used a system (an open cavity) that our cavity model could not cope with. What has proved to be a better experiment is the fibre-optic loop being tested in Madrid. The great advantage of this setup is that the Q is simply the number of times the light goes around the loop - a sort of electromagnetic version of a Formula One race. Orderly & quantifiable!

From now one we need to make sure that in all experiments both Power P and Q are known. I should have listened to my mother who always used to tell me to "mind my Ps and Qs".

Jimmy Johnson said...

Mike,

The standard procedure for determining cavity "Q" at microwave frequencies it to excite the cavity while sweeping across frequencies and observe the frequency response. A spectrum analyzer provides an easy way to perform this measurement. The quality factor "Q", which is equal to 2*Pi* Energy Stored/Energy Dissipated per cycle (i.e. the Energy Stored/Energy Dissipated per radian) is calculated by the resonant peak frequency divided by the 3dB bandwidth of the response curve. The response curve is easily seen on the spectrum analyzer and the resonant value of "Q" is visually obvious.

Since the physics of the issue is the same at optical frequencies, an optical spectrum analyzer should provide the same information for an optical cavity. Note also that while a cavity has a fixed "Q" for every resonant frequency, the "Q" that is normally measured is only relevant at that resonant frequency. If you drive a cavity off resonance, then the effective "Q" value will be less. The higher the "Q" the more reduction of effective "Q" for being off frequency.

Shawyer, in his decades long endeavors with the Emdrive, seems to be quite aware of the more practical but crucially important engineering issues. One of the very important issues is maintaining frequency lock between the source of electromagnetic power and the resonant frequency of cavities when the Emdrive starts to move. For a high "Q" cavity Doppler shifting creates a big problem. Although he has written of this issue, and even patented a potential solution, it appears that most people do not understand this issue. It also appears that many of the researchers working on optical cavities similarly do not understand the significant relationship between a cavity "Q" and the frequency of the source.

Jimmy Johnson

Unknown said...

Mike, In the previous post you mention only 5 experiments. What about the sixth?

Thanks

Oscar Martin

Simon Derricutt said...

Mike - it may be relevant that PxQ relates to the actual EM field intensity inside the cavity. As Jimmy says, being off-frequency from the actual resonance will reduce the effective Q and will reduce the actual field-strength achieved, so at higher Qs we need to be more careful about getting a feedback to control the frequency put in in order to hit that peak resonance frequency. That frequency lock is pretty important, especially as the cavity changes size with temperature.

If I'm correct about the field providing the force (and CoM being a result of normally using constant or significantly-constant fields to generate a force) then the currents in the cavity walls will react against the fields produced within it. Though these forces will be balanced in a symmetrical cavity, they will be likely unbalanced in a non-symmetrical cavity. Thus in a generalised strategy, we want PxQ as high as possible and to ensure that the reactions between the wall currents and the fields produce a net force in one direction. Could be a reason for the Bart cavity to work well. In the design of this, I'd suggest that the multiple reflections within the conical (or wedge-shaped) "hair" spikes should produce a plane wave out for a plane wave in at the frequency used, and that the "head" part should be a multiple of half-wavelengths. Thus the angle and precise shape of the "hair" spikes may take some thought. There may be some relevant designs in horn reflectors, though a corner reflector would certainly provide a plane wave out without problems (but I'm not certain about the wall currents in that case, and how they react against the resonant fields). Might be worth testing out a tetragonal cavity made from 3 right Isosceles triangles and one equilateral triangle, fed at the apex at the resonant frequency, so the plane wave is parallel to the equilateral face. May not be the best, but at least the dimensions are easier to calculate than a full conical, conical frustrum, or exponential horn. Height of the apex from the equilateral base would be multiples of half a wavelength, I think, and it would be possible to add extra rectangular walls in an equilateral prism on the base in half-wavelength sections if wanted. Also possible to make a Bart by using an array of these corner reflectors. If the "hair" section was a half-wavelength high, then the increased volume to surface area ratio should improve the Q at the design frequency in the Bart design whilst reducing it for the fundamental frequency of that volume of cavity.

Feeding a single tetragonal cavity could maybe be done by a half-wavelength wire (or a shorter one with a quarter-wave impedance transformer in the coax) running from the apex towards the centre of the equilateral side. For a Bart array, only one of the spikes would need that feed. Suggestions welcome on this - I don't think a loop feed would work well enough.

Obviously, these are ideas put out to spark ideas from others, and I won't know whether they are actually good ideas until I've tried them.