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, 30 October 2016

A Test using Redshift

Galaxies further away from us, are moving away much faster than close ones, and therefore the light coming from them is red-shifted. So the redshift of star light is a measure of its distance, and of increasing age, since when we look far off we are also looking back in time since the light has taken aeons to reach us. Like an ice core in climatology, this gives us a record of the distant past.

The minimum acceleration predicted by Quantised Inertia / MiHsC is given by: a = 2c^2/CosmicDiameter, and 'CosmicDiameter' varies with time as the cosmos expands. This means that as we look at galaxies further away, and further back in time, the CosmicDiameter was smaller and the minimum acceleration was bigger (This might also explain the inflation of the early universe, but that's another story). The prediction then is that earlier galaxies, ones at higher redshift, have to rotate more rapidly, with the same visible mass, to remain above the minimum acceleration. I proposed this as a test in McCulloch (2007) (see paragraph 4 of the Discussion), but at the time the data did not seem to be good enough.

I was reminded of this test by various insightful people on my last blog entry and in a few emails (see the guilty names below). Thanks to them I've looked into it again and added it to the discussion of my latest paper (just submitted to MNRAS) which includes the plot below. Along the x-axis we have the log of the stellar acceleration expected given the visible matter and Newton's laws, and along the y-axis the log of the acceleration observed directly from the movement of the stars. Newton and Einstein would expect the results to lie on the dotted line. The observations, taken from McGaugh et al. (2016) are shown by the squares with their size indicating the uncertainty, and they are obviously at odds with dear Albert and Isaac. At low accelerations (on the left hand side) the stars orbit the galaxies far too fast. This is the famous galaxy rotation problem, that is usually solved by stuffing in huge amounts of dark matter wherever it's needed (the second worst hypothesis in history in my opinion, since it is unfalsifiable).

The black line shows the prediction of MoND which fits the data (the squares) and is much more falsifiable than dark matter, but despite the great respect I have for Milgrom's bold step, MoND has been adjusted to fit the data using its parameter a0, so it's not surprising that it fits. The MoND prediction also shows no dependence on time.

The coloured lines show the predictions of quantised inertia / MiHsC. Uniquely, among all the theories QI/MiHsC predicts the observations correctly without any adjustment, and, also uniquely, its prediction varies with redshift. The light blue line shows the curve for a redshift of Z=0 (nearby galaxies in this epoch). This agrees with McGaugh et al. (2016)'s data (which was for Z=0). The dark blue curve shows the prediction for Z=0.5, purple for Z=1 (for which the cosmos was half its present size) and the red curve for Z=2. As you can see the galaxy rotation problem is predicted by QI/MiHsC to have been worse when the cosmos was young (all other things being equal). If two galaxies have the same visible mass, then according to QI/MiHsC the one further away (earlier in time) should spin faster.

Does this prediction agree with the data? Well, the data still seems noisy, but earlier galaxies do seem to have faster spin, see for example Figure 6 in the Thomas et al. (2013) reference below (a paper found by airenatural). With a bit more data this could be the definitive proof that QI/MiHsC needs..


Thanks to S.S. McGaugh for sending his binned data, and R. Ludwick, T. Short, Magnus Ihse Bursie and J.A.M. Lizcano (airenatural), for advice ...and anyone else I may have forgotten.


McCulloch, M.E., 2007. The Pioneer anomaly as modified inertia. MNRAS, 376, 338-342. https://arxiv.org/abs/astro-ph/0612599

McGaugh, S., F. Lelli, J. Schombert, 2016. The radial acceleration relation in rotationally supported galaxies. Phys. Rev. Lett., (accepted).

Thomas, D., et al., 2013. Stellar velocity dispersions and emission line properties of SDSS-III/BOSS galaxies. MNRAS, 431, 2, 1383-1397. https://arxiv.org/abs/1207.6115


Andrew Jaremko said...

Mike - you have a great bunch of readers and commenters here. I wasn’t quick enough to add my two cents worth about QI’s prediction varying with redshift, which is to say with the Hubble diameters (or Hubble parameters, HPs) in the past. I want to get some additional thoughts in here ahead of some of the others… All of what I summarize here needs a lot of elaboration, obviously.

The Hubble horizon and Casimir horizons have been phrased as information horizons. I have begun to think of them as causation horizons (CHs): there is no information without causation. (And no observation without causation, as well.) These horizons are mediated by electromagnetism (EM): call them an ECHs .

There’s a third causation horizon, mediated by gravitation: the event horizon of what’s called a ‘black hole’. This is the gravitational causation horizon, GCH. Nodes of EM are ‘pinned’ to be zero at CHs, and NO causation can occur across CHs. Causation is mediated by EM, and if no causation happens across CHs, then photons don’t cross the GCH and black holes don’t evaporate. Therefore the picture of anything ‘falling into a black hole’ is simply wrong. I note that Lawrence Krauss’s explanation of Hawking’s original derivation of an event horizon’s temperature doesn’t involve photons ‘falling into a black hole’. I read this explanation in Krauss’s book A Universe From Nothing.

The minimum acceleration applies to all particles and specifically to quarks and leptons and therefore to everything built from them. It means that the accelerations that masses have as they vibrate have a minimum value - they can’t get rid of their energy and vibrate more slowly. This implies that the lowest energy anything can have - photon or particle - is determined by the current Hubble parameter. Which means that the lowest temperature anything can have - absolute zero - is a function of the HP. (!) This has serious implications for small values of the HP at the earliest times after an HP reset.

An HP reset happens (I think) when a GCH forms with the formation of a ‘black hole’. The GCH most likely happens across a Planck time interval, which pulls the CH in from the Hubble radius to (potentially) a Planck distance in a Planck time, disallowing a lot of photon wavelengths and hence photon energies.

This could give physicists a starting point for thinking about what happens when a GCH forms. As well as what happens on our side (the proximal side) of the GC AND the far (distal) side of the GC.

QI and the HP could determine a lot of what’s happening in the universe. Together they throw a major monkey wrench, or spanner, into a lot of physics thinking. It could be the thing ‘hiding in plain sight’ that Lee Smolin is looking for, as referred to in his various books including Time Reborn and The Singular Universe.

I have no idea whether these observations make any sense whatsoever. I think you can tell that I’m an amateur, but at least I haven’t been excessively trained to think in the current paradigm, as you discuss in your book Physics From the Edge. The ideas have given me some sleepless hours over the last few nights. I offer them to the community to see what you all can make of them. Is QI in Nobel Prize territory? Or IgNobel? Time will tell...

Roy Lofquist said...

The speed of light, c, is a constant FAPP. FAPP is an acronym for "For All Practical Purposes" coined by John Bell of inequality fame. But is it? A constant?

We have no way of measuring the speed of light from extra-galactic sources. When the Hubble shift was discovered it was attributed to "the expansion of space" because there was no known mechanism to impede the propagation of light in vacuo. But that was before we discovered that the interstellar, and presumably intergalactic, media are pervaded by magnetic fields as revealed by the Voyager probes.


So, what does that do? The Faraday Effect, caused by a magnetic field, slows EM radiation.

"Faraday rotation is an important tool in astronomy for the measurement of magnetic fields, which can be estimated from rotation measures given a knowledge of the electron number density.[10] In the case of radio pulsars, the dispersion caused by these electrons results in a time delay between pulses received at different wavelengths, which can be measured in terms of the electron column density, or dispersion measure."


So, how come we don't see a dispersion in the spectra of distant sources? It is too small to be detected by our instruments. We are trying to measure the delta v of quanta who's delta wavelength is proportionally very small. In electrical talk we call that low Q.

What does all this mean? Maybe Maxwell rather than Einstein holds the key. Maybe we replace tensor calculus with high school algebra. Oh Nos!!

airenatural said...

A line to recognize the comments of qraal on Fulvio Melia publications, extremely interesting and probably could be combined in MiHsC model for very high redshifts, because it can affect the very early universe (maybe wider than the inflation model proposes, as far I can understand). Mike, you are creating a research group, or at least supporters that try to help. All the best for you and we wish your theory one day is recognized by the mainstream physics, there are too many evidences…

Let me present another experimental fact I found that can be interesting to check. I suspect that MiHsC has something to say to this finding that “dark matterists” are hiding from some years on. Please have a look to these articles… specially the first one:


Rotation velocities in the galaxies are generally asymmetric, and these asymmetries correlate with distance and ORIENTATION from neighbour galaxies. This effect in not explained by MoND neither Dark Matter…

Specifically the firs paper states: “The potential energy transferred is at a maximum if the neighbour galaxy is in the target galaxy's plane and at a minimum if the neighbour galaxy is along the polar axis of the target galaxy.”

Does this ring a bell to you?

Dan's Test Blog said...

Mike, I have a question. Do massless particles such as light receive the MiHsC c^2/ø acceleration bonus, for example when they travel around a gravitational lens? Thank you!

Mike McCulloch said...

airenatural: Thanks for the CERN paper. I have just emailed the authors.. The asymmetry differences they saw could just be caused by the greater expected asymmetry of the potential gradient supplied by a galaxy off-axis. What interests me more is the falling rotation curve they saw when a galaxy had a neighbour. This could well be due to QI/MiHsC, since a spinning neighbour would increase the inertial mass of the edge stars and make the curve more Newtonian (ie: falling).

Mike McCulloch said...

Dan: Yes, light should also be affected by QI/MiHsC. It's rest mass is zero, but not its inertial mass. I assumed this in this paper: https://arxiv.org/abs/1604.03449 and it seems to predict well.

Andrew Jaremko said...

Mike - thanks for your reply to Dan. In it you've answered a question that I posed in an earlier comment when I asked about gravitational lensing in galaxy clusters and whether QI could predict it and its distribution. I note that lensing would also be affected by changes in the size of the Hubble causality horizon. This suggests to me yet another thing to look for to test QI, and that I need to go and actually read your papers. Carefully. ;-)

Mike McCulloch said...

Andrew: An intriguing suggestion re lensing. Good luck, & do let me know how it goes.

Dan's Test Blog said...

Mike, if light is accelerated by c^2/ø towards the nearest galaxy (or in whichever direction in the field) it's implied that there is some radius around a galaxy (r = v^2/a) by which the equations balance -- (c^2 / (c^2/ø)) = ø. Thus light energy cannot leave the universe and simply circles the radius if it tries...I guess you touched on that in your book.

RG said...

I'd be interested to read your 'review' of the new paper by Professor Subir Sarkar of Oxford University's Department of Physics et al which unravels the scarce supernova case for dark energy. It seems that astrophysics really is more of a cult of personality than a science as evidenced by the Nobel and other prizes hastily awarded 5 years ago for what now is evidenced to be a spin-mastering job on old dogma.

duane oldsen said...

What is the minimum possible sensible scale for a horizon?

How would this compare to known "fundamental" particles?

Mike McCulloch said...

Dan: That is right for a photon in an empty MiHsCian cosmos. You need to add gravity to that, since you mentioned a galaxy.

Mike McCulloch said...

RG: I try not to get too focused on cosmological tests, since the data is so indirect and it may not be clear what we are seeing. It is better to focus on tests closer to home, eg: galactic spin or lab tests. The supernova result needs to be decided by the data and the statisticians: lots more data is coming soon. MiHsC predicts an acceleration..

Mike McCulloch said...

Duane: The minimum possible scale (area) for a horizon would be the Planck length (Planck area). Given this, MiHsC predicts a maximum acceleration of about 10^52 m/s^2, and that the acceleration should be quantised close to this limit as the horizon changes its area in a series of Planck area jumps. I haven't managed to link this to the menagerie of particles yet, though I made a start in my latest paper.

qraal said...

I'm inclined to believe in anti-gravity being a thing... Look at Donald Trump's hair!

Mike McCulloch said...

qraal: It sure is Unruh-ly :)

Alain Coetmeur said...

did you study the position of ethan siegel on darkmatter, proiven, not disproven by recent paper observing darmatter follows normal matter (he says thi is just what model demand)


this article is more balanced...

Mike McCulloch said...

Alain: The first article is typically misleading. First of all the 5 evidences they mention are not independent, and 2-5 are meaningless since dark matter is just added ad hoc to make things fit. It is a bit like saying "Every year invisible fairies pull the leaves off the trees" and then being smug every autumn. We should be doubly skeptical if, as in this new paper, newly collected data contradicts the model so they make it even more complex. They claim they are adding nothing, but they actually are, and how many extra adjustable parameters have they set in their more complete simulation? Have they done a Monte-Carlo test?

In contrast, MiHsC has zero flexibility and still fits the McGaugh data using only a piece of paper. This is the equivalent to linking autumn to the changing seasons, which can also be measured.

airenatural said...

In the second reference cited by Alain there is a link to the latest article by McGaugh


He addresses some criticisms posed by dark matter supporters, by adding in this new study more types of galaxies and more range of masses. Some interesting conclusions:

“The radial acceleration relation describes the local link between baryons and dynamics in galaxies, encompassing and generalizing several well-known galaxy scaling laws. This is tantamount to a Natural Law: a sort of Kepler law for galactic systems. A tight coupling between baryons and DM is difficult to understand within the standard DM cosmology. Our results may point to the need for a revision of the current DM paradigm”.

And also for the first time, he, as a mainstream physicist, speaks about Modified Inertia Theories, as a variation on MoND:

“MoND can be viewed either as modifed gravity (MG) by changing the Poisson's equation or modified inertia (MI) by changing the Second Law of Newton”

Tom Short said...

Shifting gears again, here's an interesting paper discussing the modified-inertia interpretation of MOND and differences in recent measurements of the gravitational constant.


At low accelerations, one experiment measured higher G that was in the range of MOND values. I didn't track down the experimental paper.

Anyway, it might be something to look at for QI.

Mike McCulloch said...

Tom: Thanks again for this link. I've just made contact with Prof Klein....

Unknown said...

slashdot is running a story saying that NASA is confirming that EMdrive works


Leaked NASA Paper Suggests The 'Impossible' EM Drive Really Does Work (sciencealert.com) 83
Posted by BeauHD on Monday November 07, 2016 @10:30PM from the subject-to-external-verification dept.

A source close to NASA Eagleworks has leaked the test results of the 'impossible' EM Drive. While it's important to note that the results that have been leaked haven't been published in an academic journal, they do suggest that the system works and is capable of generating force of 1.2 millinewtons per kilowatt in a vacuum. ScienceAlert reports:

The paper concludes that, after error measurements have been accounted for, the EM Drive generates force of 1.2 millinewtons per kilowatt in a vacuum. That's not an insignificant amount -- to put it into perspective, the super-powerful Hall thruster generates force of 60 millinewtons per kilowatt, an order of magnitude more than the EM Drive. But the Hall thruster uses fuel and requires a spacecraft to carry heavy propellants, and that extra weight could offset the higher thrust, the NASA Eagleworks team conclude in the paper. Light sails on the other hand, which are currently the most popular form of zero-propellant propulsion, use beams of sunlight to propel them forward rather than fuel. And they only generate force up to 6.67 micronewtons per kilowatt - two orders of magnitude less than NASA's EM Drive, says the paper. The NASA Eagleworks team measured the EM Drive's force using a low thrust pendulum at the Johnson Space Centre, and the tests were performed at 40, 60, and 80 watts. They were looking for any sign that the thrust could be a result of another anomaly in the system, but for now, that doesn't appear to be the case. "The test campaign included a null thrust test effort to identify any mundane sources of impulsive thrust, however none were identified," the team, led by Harold White, concluded in the paper. "Thrust data from forward, reverse, and null suggests that the system is consistently performing with a thrust to power ratio of 1.2 +/- 0.1 millinewtons per kilowatt." But the team does acknowledge that more research is needed to eliminate the possibility that thermal expansion could be somehow skewing the results. They also make it clear that this testing wasn't designed to optimize the thrust of the EM Drive, but simply to test whether it worked, so further tweaking could make the propulsion system more efficient and powerful.

qraal said...

You might have some competition from the Emergent Gravity theory - though I suspect your idea and Verlinde's are akin:


Emergent Gravity and the Dark Universe

Erik P. Verlinde

(Submitted on 7 Nov 2016)

Recent theoretical progress indicates that spacetime and gravity emerge \break together from the entanglement structure of an underlying microscopic theory. These~ideas are best understood in Anti-de Sitter space, where they rely~on~the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional `dark' gravitational force describing the `elastic' response due to the entropy displacement.

We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale a0=cH0, and provide evidence for the fact that this additional `dark gravity~force' explains the observed phenomena in galaxies and clusters currently attributed to dark~matter.

Dan's Test Blog said...

Dan: That is right for a photon in an empty MiHsCian cosmos. You need to add gravity to that, since you mentioned a galaxy.

Suppose a photon leaves a distant galaxy, en route to our telescopes, and reaches a point far enough away from it that another galaxy becomes the dominant gravitational force; then beyond that another does; etc. MiHsC says that the photon should wiggle a little more? How much would such a thing influence our picture of the sky -- or would it all average out, since there ought to be roughly equal pull in all directions as it travels? Finally, as the photon finally approaches Earth, surely the extra acceleration could not induce it to travel faster, could it?