Here is a list of most of the peer-reviewed papers on MiHsC/quantised inertia (QI) so far, with brief summaries. The most conclusive ones are generally towards the end of the list:

McCulloch, M.E., 2007. Modelling the Pioneer anomaly as modified inertia. Mon. Not. Roy. Astro. Soc., 376, 338-342. https://arxiv.org/abs/astro-ph/0612599 The initial conceptual paper, explaining QI and showing that it predicts the Pioneer spacecraft anomaly, which also agrees with the cosmic acceleration and 2c^2/Cosmic_scale. Despite this clue the mainstream no longer considers it an anomaly having invented a computer-aided complex fudge for it. There are lots of other suggestions for tests of QI in the discussion.

McCulloch, M.E., 2008. Can the flyby anomalies be explained by a modification of inertia? J. British Interplanetary Soc., Vol. 61, 373-378. https://arxiv.org/abs/0712.3022. Most of this paper is now out of date, but I discuss 'how to modify inertia using metamaterials' in the discussion.

McCulloch, M.E., 2008. Modelling the flyby anomalies using a modification of inertia. Mon. Not. Royal. Astro. Soc., Letters, 389 (1), L57-60. https://arxiv.org/abs/0806.4159. Testing QI on the flyby anomalies, unexpected tiny boosts in the speed of spacecraft flying by Earth, which it predicts should be larger for slower-spinning bodies.

McCulloch, M.E., 2010. Minimum accelerations from quantised inertia. EPL, 90, 29001 https://arxiv.org/abs/1004.3303. QI explains cosmic acceleration and the minimum mass of dwarf galaxies. A test is also suggested using the LHC: accelerate particles so fast that the Unruh waves they see can be interfered with by long wave radiation.

McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 39002.

https://arxiv.org/abs/1106.3266. QI predicts tiny dynamical anomalies observed by Tajmar close to super-cooled spinning rings.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astrophysics and Space Science, Vol. 342, No. 2, 575-578. https://arxiv.org/abs/1207.7007. My first attempt to properly model galaxy rotation. QI predicts well (within the wide error bars).

McCulloch, M.E., 2013. Inertia from an asymmetric Casimir effect. EPL, 101, 59001 https://arxiv.org/abs/1302.2775. A conceptual paper, to explain the origin of inertial mass from first principles. It is also suggested that inertia can be modified, and motion can be induced, by making an artificial horizon. ****

McCulloch, M.E., 2014. Gravity from the uncertainty principle. ApSS. 349, 957-959. https://link.springer.com/article/10.1007%2Fs10509-013-1686-9. How to derive Newton's gravity law, from quantum mechanics! (the derivation is flawed at the end as you will see, but this is sorted out in a later paper, see below)

McCulloch, M.E., 2014. A toy cosmology using a Hubble-scale Casimir effect. Galaxies, Vol. 2(1), 81-88. http://www.mdpi.com/2075-4434/2/1/81. My first attempt at a QI cosmology - are we inside a black hole? The low-l CMB anomaly (an unexpected smoothness in the CMB at large scales) is also predicted.

McCulloch, M.E., 2015. Testing quantised inertia on the emdrive, EPL, 111, 60005. https://arxiv.org/abs/1604.03449. Shows that QI predicts the anomalous thrust from asymmetric microwave cavities (emdrives).****

Gine, J. and M.E. McCulloch, 2016. Inertia from Unruh temperatures. Modern Physics Letters A, 31, 1650107. http://www.worldscientific.com/doi/abs/10.1142/S0217732316501078. The first collaborative paper - with a more thermodynamic theme.

McCulloch, M.E., 2016. Quantised inertia from relativity & the uncertainty principle, EPL, 115, 69001. https://arxiv.org/abs/1610.06787. Conceptual. A better attempt at deriving gravity & QI from Heisenberg's uncertainty principle by assuming that what is conserved is mass-energy and information/uncertainty ****

McCulloch, M.E., 2017. Low acceleration dwarf galaxies as tests of quantised inertia. Astrophys. Space Sci., 362, 57. http://rdcu.be/px8h. Quantised inertia predicts parts of the cosmos that other theories cannot, dwarf galaxies.

Pickering, K., 2017. The universe as a resonant cavity: a small step towards unification of MoND and MiHsC. Adv. Astro., Vol. 2, No.1: http://www.isaacpub.org/images/PaperPDF/AdAp_100063_2017021413572668843.pdf. Models the cosmos with a better cavity model and has an interesting take on the cosmic boundary.

McCulloch, M.E., 2017. Testing quantised inertia on emdrives with dielectrics. EPL, 118, 34003. http://iopscience.iop.org/article/10.1209/0295-5075/118/34003. A further test of QI using the emdrive, taking account of the dielectrics in them.

McCulloch, M.E., 2017. Galaxy rotations from quantised inertia and visible matter only. Astrophys. & Space Sci., 362,149. https://link.springer.com/article/10.1007/s10509-017-3128-6. Shows QI predicts galaxy rotation perfectly without the need for dark matter. It also predicts that galaxies at high redshift should spin faster for the same apparent mass: a good test of QI since no other theory predicts that, and observations now tentatively show this is the case. ****

McCulloch, M.E. and J. Gine, 2017. Modified inertial mass from information loss. Mod. Phys. Lett. A., 1750148. http://www.worldscientific.com/doi/abs/10.1142/S0217732317501486. An attempt to derive QI from a conservation of information (an improved sequel is coming..).

## 7 comments:

Thanks for this. I'll try to read them all before I ask more questions here.

Hi Mike,

Do you have any idea why the observed and predicted galaxy rotation differ at Z > 2.2?

Regards,

Tamas

Tammor: I did look into those two cases, but could find no estimates of the error in the data, except that higher red-shift galaxies are more difficult to observe, of course, being much further away.

Mike,

As I don't have access to the paywalled journals, I started by reading your 24th October 2016 paper on ArXiv. I have a question for you about your derivations of the mass of the electron and the nucleon in equations 23 & 24. As the Compton wavelength of a particle is defined as equal to the wavelength of a photon whose energy is the same as the mass of the particle, multiplying its reciprocal by h/c will surely just recover the mass. It also wasn't obvious why you used the Compton wavelength for the electron, but the radius of the hydrogen nucleus for the nucleon. (If I was being pedantic, the photon needs twice as much energy to form an electron, because it must simultaneously form a positron to ensure charge conservation).

What did interest me about the derivation of the mass of the nucleon is that (rather like the universe) there is a missing mass problem. Although the rest mass of the proton is 938 MeV/c^2,the valence quarks only account for about 9 MeV/c^2 of this. QCD assumes that the virtual quarks and gluons account for the remainder. If most of the rest mass of the nucleon came from the confinement of the valence quarks, then there might be a simpler way to formulate QCD. I'm not a theoretician, so I wouldn't know how to go about this, but a more accurate calculation of nucleon mass based on a 3-dimensional rather than 1-dimensional model might be a good place to start.

Regards,

Laurence

Laurence: Thanks for your comment. Yes, eqn. 23 is well known. What I was trying to do is choose scales that are well observed in relation to those particles, but I may well have missed the ideal values. My overall point though still stands, and a better equation to look at is eqn 22 which is different to the usual one (the extra term), and may be testable if instead of the cosmic scale (Theta) we initially encase the system in a smaller horizon.

I am interested in your comment about QCD and its missing mass problem. Isn't there a quark confinement problem as well?

Mike. Yes, quark confinement comes from the force between two quarks increasing linearly with distance between them until the energy in the 'string' is sufficient to create a new quark-antiquark pair. It had occurred to me that this is equivalent to a parabolic energy potential as in the harmonic oscillator in quantum mechanics. Back in my undergraduate physics course (which I have to say was almost 50 years ago), we had to solve the one-dimensional harmonic oscillator equation, but for the quark confinement problem it would have to be the three-dimensional harmonic oscillator (which we never got as far as).

[I just looked this up on the web and it seems that the 3-D harmonic oscillator is separable into three 1-D harmonic oscillators, so easier than I thought]

Of course, if we consider the nucleon as the ground state of a harmonic oscillator, it will also have to have excited states. Conventionally, the delta particle is considered as an excited state of the nucleon and there are other excited states (also called resonances), so any harmonic oscillator model would have to predict their masses as well, but these are known. It might be worth asking if anyone has attempted to treat the quarks in a single nucleon as a harmonic oscillator.

I have spent all my career as an experimental physicist, so don't have the theoretical equipment to handle all this, but it seems to be something that might be worth looking at.

Best wishes,

Laurence

Not to nitpick, but isnt the above definition of Compton Wavelength the Planck Particle?... It's an ideal case, possibly a virtual particle only, as i understand it...

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