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

Sunday, 26 October 2014

MiHsC vs Emdrive: updated table

I have updated the Table comparing the predictions of MiHsC with the available, fully-documented, emdrive experimental results, including a 6th result that I've just found online: that of the Cannae drive of G. Fetta (I take it as an emdrive because the grooves cut into it were found by NASA to make little difference). I've shown the predictions of the 1-dimensional MiHsC formula (which is preliminary) which assumes that accelerations are produced by the radio frequency oscillations:

F = PQ/f * ((1/w_big)-(1/w_small))              MiHsC1

where P is the input power, Q is the Q factor, f is the input frequency, w_big and w_small are the widths of the end plates. I have also shown the predictions of an alternative formula (MiHsC 2) that assumes that the accelerations are caused by photons bouncing at the cavity ends, and includes the cavity length (s) and speed of light (c):

F = PQs/c * ((1/w_big)-(1/w_small))            MiHsC2

See the new table below. The first column shows the experiment (S=Shawyer, C=Cannae and B=Brady), the other columns show the diameters of the big and small (two estimates) cavity end plates, the Q factor, power input, frequency, and the last three columns compare the predictions of MiHsC1 and MiHsC2 with the observed force (in bold):

Expt     Q       Power     Freq'   w_big   w_small      s     MiHsC1  Observed  MiHsC2
                      Watts      GHz       cm        cm          cm      (--------milliNewtons--------)
S a      5900     850       2.45       16        12.750   15.6     3.26         16            4.15
S b    45000   1000       2.45       28        12.890   34.5   76.90      80-214    216
C a     1.1e7       10.5    1.047     22        20            3.0   50.14       8-10           5.25
B a      7320       16.9    1.933     39.7     24.4       33.2     0.10       0.0912       0.22
B b    18100       16.7    1.937       "           "          33.2     0.25       0.0501       0.53
B c    22000         2.6    1.88         "           "          33.2     0.05       0.0554       0.10

MiHsC1 underestimates the Shawyer (2008) experiments (S), predicts five times the Cannae result (C), and agrees with the NASA / Brady et al. (2014) a and c results, but not case b where it overestimates by a factor of five. The Cannae drive (C) has a very different geometry to the others (the width is 22cm, the length is 1cm) and this difference is useful for testing. MiHsC2 is perhaps comparable in success, but does less well for the NASA results (the most accurate?) which may be because of the 1-d limitations of my approach, or it could mean that it is the radio frequency oscillation that is driving the acceleration that causes the Unruh radiation (MiHsC1) rather than the microwave photons physically bouncing between the plates (MiHsC2).

Thanks to Dr J. Rodal for correcting my cavity dimensions again! The source of the Cannae experiment geometry and results is:  http://web.archive.org/web/20121104025749/http://www.cannae.com/proof-of-concept/design see also the experimental results section.

Friday, 24 October 2014

MiHsC: motion from logic.

The advantages of MiHsC are that it is simple, it follows logically from very few assumptions and it predicts anomalies no other theory can without needing the infinite adjustability of dark matter (in fact MiHsC has zero adjustability).

Understanding MiHsC is simple: consider an object, say Spock in a spacesuit, in a vacuum. Everywhere around him is the zero point field, a sea of virtual particles predicted by Heisenberg's uncertainty principle and whose existence Spock notes has been proven by experiments on the Casimir effect. Pairs of these virtual particles are always forming and recombining quickly. The zero point field usually has no effect on Spock in a vacuum because it is usually weak and uniform in space and so virtual particles bang into Spock from all directions equally so there is no net force.

Now imagine Spock fires a back pack rocket motor and accelerates forward. He might then look behind him and tell McCoy on the static Enterprise that logically he can now never see things more than a certain far distance away because information from that far away traveling at the speed of light will never catch up to him as he accelerates. At this distance, then, is a horizon, which only exists in Spock's reference frame, so McCoy on a static Enterprise would look for the horizon, not see it, and tell Spock grumpily that he's getting  carried away by his own logic again. Nevertheless, at that distant horizon virtual particle pairs that form can now be separated because one of them goes away from Spock and is lost forever behind the horizon and one will come towards him. The virtual particles that would have recombined, now never will, and Spock will see particles and radiation all around him: Unruh radiation, just like the Hawking radiation from black hole horizons, but caused by acceleration not gravity.

Radiation is a kind of wave so its waveform must 'fit' exactly within the cosmos. Why? Well, because if the wave didn't fit exactly then it would go through the horizon and we'd then be able to know something about what lies behind the horizon, so it wouldn't be a horizon anymore. So some of the Unruh waves in front of Spock are disallowed by the cosmic horizon and disappear in a puff of logic and Spock raises his eyebrow approvingly. This is only a small effect though, and it makes a big difference only if accelerations are tiny, as they are at the edges of galaxies (this part of MiHsC correctly accounts for galaxy rotation without needing dark matter). Now behind Spock the waves must fit between Spock and the new horizon, which is much closer than the cosmic edge, so more waves are disallowed by logic behind him. This means more Unruh radiation hits Spock from in front than from behind, and this makes a force that opposes his acceleration and predicts the phenomenon we know as inertia (see the references below for more detail).

This is the basis of MiHsC, & I think Spock would love it, because is shows how quantum mechanics (that provides the zero point field), relativity (that makes the horizon) and his beloved logic (that disallows non-fitting waves) can work together in a new way to make something as fundamental as inertia, and also solve a few problems that the old physics cannot.


McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001. http://arxiv.org/abs/1302.2775

McCulloch, M.E., 2014. Physics from the edge. World Scientific.

Sunday, 19 October 2014

EmDrive, MiHsC & horizon physics

The small anomalous acceleration of the emdrive (which is like a microwave oven built into a copper cone) towards its narrow end, may or may not be a real effect, but is proving to be a lot of fun to think about. I've written before about 'thinking in the context of a real experiment' and I think that is lacking in mainstream theoretical physics where people incessantly drop objects into imaginary black holes. Looking for new physics one must look for 'direct' observations that disagree with the old physics, and the emdrive is a great example of that, and one that has been reproduced in three different labs. It turns out that MiHsC predicts it quite well (see this entry, and for MiHsC, see McCulloch, 2013, 2014, references below). Specifically MiHsC predicts a force of

F = PQ/f * ((1/w_big)-(1/w_small))     (1)

where P is power input (Watts), Q is the number of photon 'bounces' before they are absorbed, f is the input microwave frequency (Hz) and w_big and w_small are the diameters (metres) of the big and small emdrive end plates. Last night I worked out how to prove this formula from first principles so I'm now much happier about it. I've also tried replacing f with c/CavityLength=c/s, where c is the speed of light. This is because in the derivation the f is the frequency of Unruh radiation seen by the photons, and this is determined not by the microwave frequency, but by the cavity length which forces the microwave photons to change direction back and forth, and it is this that does the accelerating. This gives the similar formula

F = PQs/c * ((1/w_big)-(1/w_small))     (2)

Now, you may be saying 'for photons the rules are different', but ultimately, causes must be universal and photons do have inertial mass, the source of radiation pressure (it is only the photons' rest mass that is zero) and if they have inertia, then according to MiHsC this is caused by Unruh radiation (which is more than just em radiation) and for the huge accelerations of these photons as they bounce between the ends of the cavity the Unruh waves are short enough to 'see' the cavity and be damped by its walls (as electrons move to cancel the field there). They will be more damped at the narrow end, meaning they will have less inertial mass at that narrow end. This means that, for each photon bounce, more mass goes from the narrow to wide end than the other way around, and so to balance the books the conservation of momentum demands a force towards the narrow end of a size as in Eq. 1 or Eq. 2. The best defense of this model is that it works quite well. For the results of Eq. 1 see two blogs back, and Eq. 2 predicts the following for the five experiments for which complete information is available (excluding the Chinese experiments whose geometry is unknown). Table:

Experiment                P              Q         s        w_big    w_small     Observed    Predicted
(see refs)                  W             dl         m           m             m           (mN)          (mN)
Shawyer (expt)       850          5900    0.156     0.16       0.11            16                7
Shawyer (demo)   1000        45000    0.345     0.28       0.17          147            123
Brady et al. A            16.9       7320    0.332     0.397     0.244            0.09           0.22
Brady et al. B            16.7     18100    0.332     0.397     0.244            0.05           0.53
Brady et al. C              2.6     22000    0.332     0.397     0.244            0.06           0.10

The table shows that the MiHsC predictions (the last column) agree quite well with the data (the second to last column), except for the second Brady et al. (2014) experiment. More experimental data is urgently needed, but this suggests tentatively that MiHsC can be applied to light in cavities, and this opens up a whole new area for testing. I have submitted a paper on this, so let's see what the reviewers say. Note: Thanks to Dr Jose Rodal, aero & John Fornaro (NSF forum) for clarifying the emdrive geometry.


Brady, D., et al., 2014. Anomalous thrust production from an RF test device measured on a low-thrust torsion pendulum. Conference proceedings, see Table page 18. Link

Shawyer, R., 2008. Microwave propulsion - progress in the emdrive programme. See section 6, page 6. Link

McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001. http://arxiv.org/abs/1302.2775

McCulloch, M.E., 2014. Physics from the Edge, published by World Scientific. Link

Saturday, 11 October 2014

In support of empiricism

I find it strange that those who support theories like dark matter, dark energy and string theory always respond to MiHsC by saying that it needs more evidence, as if they had some irrefutable evidence tucked away in a drawer somewhere! They have none. They are putting dark matter into galaxies because they blindly trust general relativity (GR), and they want it to predict the right rotation curve given the stars they can see, but they have absolutely no reason to trust general relativity here, because it has never been tested at low accelerations, only at high accelerations, for example with Gravity Probe B, orbiting binary pulsars and the perihelion of Mercury. The acceleration of a star at a galaxy's edge is more than ten orders of magnitude lower. The last time someone tried to extrapolate a theory ten orders of magnitude was when they tried to apply classical physics to the atom, and that went well...

It is clear to me how proper physics was done by the people I admire: Strato of Lampsacus, Galileo, Newton, the early-Einstein, 'Back of the Envelope' Fermi, Stommel & dear old Feynman and partly because of this, and my background in the more testable physics of the ocean, I have developed MiHsC consciously by looking directly at the observations (empiricism), particularly interesting anomalies, and deliberately avoiding the mainstream hypotheses and fashions, because to be frank they are vague, unimaginative, overly-complex and untestable.

As a result of this data-driven approach I can model the Pioneer anomaly well (yes, controversial), the flyby anomalies fairly well, the Tajmar effect well, dwarf galaxy, spiral galaxy and galaxy cluster rotation without dark matter, cosmic acceleration without dark energy, and the low-wavelength CMB anomaly. It seems all the mainstream can do is patch GR using dark matter in increasingly bizarre shapes and forms: they may as well attribute it all to 'God's stirring spoon' and join the clergy. Revered theories die hard, especially if there is no evidence for them!

Sunday, 5 October 2014

MiHsC vs EmDrive data: 1

This is not yet complete, it is a mathematical exploration using MiHsC, and I'm not sure of it, but I'm including it here to stimulate or support discussion (updated, 18/10/1014).

Assume an asymmetric resonant cavity, with microwave photons bouncing around inside it. They carry a force F=2P/c, where P is power and c is the speed of light, due to the inertial mass of light (light does have an inertial mass, or Solar sails wouldn't work). Including the Q factor (number of photon 'bounces') gives F=2PQ/c. Now MiHsC says the inertial mass is caused by Unruh radiation, and so it is affected by the Hubble horizon since Unruh waves must fit exactly within this horizon. In MiHsC the inertial mass (mi) is modified as mi=m(1-L/4T) where m is the unmodified mass, L is the Unruh wavelength determined by the acceleration, and T is the Hubble distance (see McCulloch, 2007, eq. 8) so for the low accelerations seen in deep space, hence long Unruh waves which 'feel' the Hubble horizon, inertia decreases in a new way which fixes the galaxy rotation problem (McCulloch, 2012).

What if the resonant cavity walls acted like a Hubble horizon, especially for Unruh waves of a similar length (as they are in this case)? Then the inertial mass of the photons would increase towards the cavity's wide end, since more Unruh waves would fit there, since mi=m(1-L/2w), where w is the cavity width. The force carried by the photons then increases by this factor as they go from the narrow end (width w_small) towards the wide end (width w_big). The force difference between ends is

dF = (PQ/c)*((L/w_big)-(L/w_small)) = (PQ/f)*((1/w_big)-(1/w_small)).

The leap is that the only way to conserve force (or conserve momentum) is to have an equal force pushing the whole system the other way towards the narrow end.

The Table below compares the predictions of MiHsC with the available data. The columns show, from left to right: the data source, the widths of the large and small ends of the cavity used, the Q factor, the power applied, the frequency applied, the thrust predicted by MiHsC and the observed thrust. The sources are Shawyer (2008) and Brady et al. (2014) (see their table on page 18). Dr Jose Rodal has provided some data for the Juan (2012) experiment (rows 3-4, italic), but their cavity geometry is unknown, so I've calculated the range of possible predictions due to MiHsC, given the range of geometries in the two Shawyer experiments (see red colour). The table:

Experiment               w_big   w_small    Q       Power in      Freq'      MiHsC    Observed
                                     cm        cm                      Watts         GHz          (milliNewtons)
Shawyer (2008) a          16        11            5900     850          2.45          5.8          16
Shawyer (2008) b          28         17          45000    1000         2.45        44             80-214
Juan (2012) TE011        16/28  11/17       32000    1000         2.5           30-36     214
Juan (2012) TE012        16/28  11/17       50000    1000         2.45        47-58     315
Brady et al. (2014) a      24.75  16.5         7320    16.9          1.933         0.129        0.0912
Brady et al. (2014) b       "           "           18100   16.7          1.937         0.315        0.0501
Brady et al. (2014) c       "           "           22000     2.6          1.88           0.061        0.0554

The MiHsC predictions vary in the same proportion, but typically underestimate the observations significantly (I don't know what the error bars on the observations are). An increase in cavity size, power input and Q factor usually increases the observed force as predicted. Case 6 is a bit worrying. Here Brady et al. (NASA) increased the Q factor which according to the prediction, and Shawyer's previous results, should have boosted the force, but the observed force was smaller (but note that MiHsC-inertia also depends on whether the Unruh waves fit exactly into the cavity and this can change with slight changes in frequency, for a discussion, see McCulloch, 2007, link below, the first paragraph of the Discussion).

Thanks: The data for the 5th case and several mistakes in geometry kindly pointed out by aero & Dr Jose Rodal on an NSF forum and the comments section below.


Brady, D., et al., 2014. Anomalous thrust production from an RF test device measured on a low-thrust torsion pendulum. Conference proceedings, see Table page 18. Link

Juan, W., 2012. Net thrust measurement of propellantless microwave thrusters. Acta Physica Sinica, 61, 11. 

McCulloch, M.E., 2007. Modelling the Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. Link.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophys. & Space Sci., 342, 575-578. Link

Shawyer, R., 2008. Microwave propulsion - progress in the emdrive programme. Link. (see section 6, page 6).