I'm always saying to my students that "The best way to learn is to do", and I always enjoy scribbling back-of-the-envelope calculations (in the manner of Hans Bethe and Enrico Fermi) so here's a quick MiHsC-emdrive calculation I did recently. Note that it is not as rigorous as my paper, it is a heuristic simplification.

It is important to have a real experiment as a basis, so I've used Shawyer's first experimental setup, with a cavity Q = 5900, power input P = 850W, cavity length L = 0.156m, wide end width = 0.16m, narrow end = 0.1275m, and I've assumed a mass of 10 kg (as you'll see this last is unimportant as it cancels out).

The time for a photon to dissipate, given Q is

T = distance/c = QxCavityLength/c

T = 5900x0.156/3x10^8 s

T = 3.1x10^-6 s

Energy input into the cavity in this time is

E = PowerxT = 850x3.1x10^-6 = 0.0026 J

The mass (m) of the microwave energy is

m = E/c^2 = 0.0026/(3x10^8)^2 = 2.9x10^-20 kg.

The new effect predicted by MiHsC is that photons' centre of mass is continually shifted towards the wide end. Normally, as in my paper, I would calculate the photon mass change implied by MiHsC as more Unruh waves are allowed at the wide end, increasing photon mass there in a new way. Here, in order to point out the wider connection with MiHsC-cosmology, I'm going to take a short cut and calculate photon behaviour by noting that in MiHsC, a volume (sphere) bounded by a horizon must have a minimum acceleration of

a = 2c^2/L

where L is the diameter of the sphere. If you put in the Hubble volume L = 2.6x10^26 metres, then MiHsC predicts the recently-observed cosmic acceleration (usually attributed arbitrarily to dark energy) and it also predicts the acceleration below which galaxies misbehave and their rotation (usually attributed to arbitrary dark matter). We can regard each end of the cavity as being a little Hubble sphere (introducing an error of probably a factor of two) but the acceleration of the photons along the length of the emdrive cavity is then the difference between the accelerations at the wide end (the big cosmos) and narrow end (small cosmos), which is:

a = 2c^2/Lwide - 2c^2/Lnarrow = 2x(3x10^8)^2 x (1/0.16 - 1/0.1275)

a = 2.87x10^17 m/s^2

As the microwave photons are shifted rightwards by MiHsC (see the red arrows in the Figure) the cavity must shift left to conserve momentum (see the black arrow).

We can calculate the acceleration of the cavity, much smaller due to its greater mass, by differentiating the conservation of momentum:

Acceleratn of cavity x CavityMass = Light Acc x MicrowaveMass

Ac x Mc = Al x Mm

Ac = Al x Mm / Mc = 2.87x10^17 x 2.9x10^-20 / 10

Ac = 0.00083 m/s^2

So F = ma = 10x0.00083 = 8.4 mN (The observed force was 16 mN for this case).

I always enjoy the closure and elegance of this sort of calculation and I believe that the ability of a theory to predict something openly on a single sheet of paper speaks well for it, in contrast to theories that require adjustable parameters hidden in labyrinthine computer programs or in the small print of complex derivations. There are no such parameters here.

It is important to have a real experiment as a basis, so I've used Shawyer's first experimental setup, with a cavity Q = 5900, power input P = 850W, cavity length L = 0.156m, wide end width = 0.16m, narrow end = 0.1275m, and I've assumed a mass of 10 kg (as you'll see this last is unimportant as it cancels out).

__Step 1. Calculate the mass of light in the cavity__The time for a photon to dissipate, given Q is

T = distance/c = QxCavityLength/c

T = 5900x0.156/3x10^8 s

T = 3.1x10^-6 s

Energy input into the cavity in this time is

E = PowerxT = 850x3.1x10^-6 = 0.0026 J

The mass (m) of the microwave energy is

m = E/c^2 = 0.0026/(3x10^8)^2 = 2.9x10^-20 kg.

__Step 2. The MiHsC-acceleration of photons in the cavity__The new effect predicted by MiHsC is that photons' centre of mass is continually shifted towards the wide end. Normally, as in my paper, I would calculate the photon mass change implied by MiHsC as more Unruh waves are allowed at the wide end, increasing photon mass there in a new way. Here, in order to point out the wider connection with MiHsC-cosmology, I'm going to take a short cut and calculate photon behaviour by noting that in MiHsC, a volume (sphere) bounded by a horizon must have a minimum acceleration of

a = 2c^2/L

where L is the diameter of the sphere. If you put in the Hubble volume L = 2.6x10^26 metres, then MiHsC predicts the recently-observed cosmic acceleration (usually attributed arbitrarily to dark energy) and it also predicts the acceleration below which galaxies misbehave and their rotation (usually attributed to arbitrary dark matter). We can regard each end of the cavity as being a little Hubble sphere (introducing an error of probably a factor of two) but the acceleration of the photons along the length of the emdrive cavity is then the difference between the accelerations at the wide end (the big cosmos) and narrow end (small cosmos), which is:

a = 2c^2/Lwide - 2c^2/Lnarrow = 2x(3x10^8)^2 x (1/0.16 - 1/0.1275)

a = 2.87x10^17 m/s^2

__Step 3 - By conservation of momentum__As the microwave photons are shifted rightwards by MiHsC (see the red arrows in the Figure) the cavity must shift left to conserve momentum (see the black arrow).

We can calculate the acceleration of the cavity, much smaller due to its greater mass, by differentiating the conservation of momentum:

Acceleratn of cavity x CavityMass = Light Acc x MicrowaveMass

Ac x Mc = Al x Mm

Ac = Al x Mm / Mc = 2.87x10^17 x 2.9x10^-20 / 10

Ac = 0.00083 m/s^2

__Step 4 - The Predicted Force__So F = ma = 10x0.00083 = 8.4 mN (The observed force was 16 mN for this case).

I always enjoy the closure and elegance of this sort of calculation and I believe that the ability of a theory to predict something openly on a single sheet of paper speaks well for it, in contrast to theories that require adjustable parameters hidden in labyrinthine computer programs or in the small print of complex derivations. There are no such parameters here.

## 16 comments:

Do you have any references on existing microwave cavity designs with high Q? For example, if someone wanted to use MiHsC's formulae to build an emdrive in their basement with as high a thrust as possible, how high a thrust could feasibly be made out of real-world, existing parts?

Most of the complaints about the EmDrive seem to focus on the violation of momentum, but isn't the real question of what is balancing the momentum? Isn't the logical explanation that there is EM-radiation emitted opposite to the thrust? OR is the problem really that this radiation has such a long wavelength that it's impossible to detect?

I loved your book, by the way. One thing that struck me: If an object in geostationary object sees only gravitational attraction to the earth, because the Earth appears stationary, wouldn't this reduce inertial mass and necessitate an unexpected orbital corrections?

This is nice calculation - but it's not based on Unruh radiation, but on photon dissipation - i.e. the effect, which can be modeled with the water surface analogy.

https://www.reddit.com/r/Physics_AWT/comments/4gjz1p/testing_quantized_inertia_theory_on_the_emdrive/d36ujzq

If the mass of photons dissipates along their path in EMDrive, it will also lead into some acceleration - or not? Why to consider some esoteric Hubble horizons and giant Hubble volumes, after then?

Zephir: it is based on Unruh radiation. The change in mass of the photons is because more Unruh waves are allowed at the wide end. I just took a short cut via the resulting acceleration, rather than calculate the masses directly, because I wanted to make the connection to cosmic acceleration.

Dear Francis: What I'm trying to say with MiHsC is that there is a source of mass-energy that we did not formerly recognise: information horizons. If you put such a horizon into the zero point field you can get unexpected mass-energy out, so that it looks like momentum conservation is being violated. What is conserved instead is mass+energy+information. I'm trying to get a paper discussing this published.

Francis: Interesting point about geostationary satellites that I had not considered. I'll look into it.. Thanks also for your positive review of my book on amazon.

An object in any orbit should be totally unaffected by the rotational speed of the primary (with the ultra-small exception of Einsteinian frame-dragging). "Geostationary" is only geostationary because of a particular rotational speed of the Earth. The geostationary satellite is balanced by centrifugal force, just like all satellites.

KAP: That is what the old Newtonian text books say. MiHsC says different.

If inertial mass is affected by nearby relative accelerations, then geostationary orbit is interesting because the Earth appears to be stationary.

Also of interest is the constant added to the centripetal acceleration, which may be detectable in higher orbits? (It makes me wonder exactly how GM is measured.)

The photon mass would not be evenly distributed in the cavity. Some modes (frequencies) have most of the photon density in the middle of the cavity, some modes have it bunched at the big end, and some have it bunched at the little end. However, I do not think that the theory that you have sketched out here would be affected by this.

Why would Unruh waves be affected by the walls in a way that would allow more in at one end. Both ends of the cavity are equally effective at blocking electromagnetic radiation, as are the curved walls. Does Unruh radiation interact with the curved walls differently than it interacts with the end walls?

Frank: Re, your second comment. It is not that the walls allow more Unruh waves 'in', the Unruh waves are formed in the cavity. The cavity enforces an acceleration, and a horizon with it, that is coincident with the walls so that a photon at the wide end 'sees' an apparent Hubble volume that is larger and so allows more Unruh waves. Interaction with the walls is the same, but the walls' separation is different.

Hi Mike

Interesting preprint: http://arxiv.org/abs/1605.09229

End of a Dark Age?

W.M. Stuckey, Timothy McDevitt, A.K. Sten, Michael Silberstein

We argue that dark matter and dark energy phenomena associated with galactic rotation curves, X-ray cluster mass profiles, and type Ia supernova data can be accounted for via small corrections to idealized general relativistic spacetime geometries due to disordered locality. Accordingly, we fit THINGS rotation curve data rivaling modified Newtonian dynamics, ROSAT/ASCA X-ray cluster mass profile data rivaling metric-skew-tensor gravity, and SCP Union2.1 SN Ia data rivaling ΛCDM without non-baryonic dark matter or a cosmological constant. In the case of dark matter, we geometrically modify proper mass interior to the Schwarzschild solution. In the case of dark energy, we modify proper distance in Einstein-deSitter cosmology. Therefore, the phenomena of dark matter and dark energy may be chimeras created by an errant belief that spacetime is a differentiable manifold rather than a disordered graph.

...which makes me wonder if your theory can be rewritten in terms of GR as modified above?

Have you seen the CalPoly results? Also, what are your thoughts about how quickly the emdrive will move into a commercial environment? http://www.slideshare.net/BrianKraft2/investigation-of-anomalous-thrust-from-a-partially-loaded-resonant-cavity

Michael. Thanks. I had not seen these CalPoly results. MiHsC predicts that a cylindrical microwave cavity with a dielectric at one end will show a thrust. Given the parameters they gave in their paper: P=950W, Q=306, L=0.2m (my guess), Width=0.1m (guess), and with a plexiglass dielectric (ri=1.5) MiHsC predicts a thrust of 2.2mN (observed=2.4 mN)..

How does this paper relate, if at all, to MiHsC?

http://scitation.aip.org/content/aip/journal/adva/6/6/10.1063/1.4953807

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