Quantised inertia in galaxies

This is a short summary of a paper I have just published in Astrophysics and Space Science (here). Galaxies and galaxy clusters have been seen to rotate so fast that the (inertial) centrifugal forces should tear them apart. Yet, they sit there obviously a stable collection of bound stars. Therefore, the small amount of matter we can see lit up in fusion (ie: stars) seems to hold them together. How?

Some have proposed that matter that we cannot see is responsible: dark matter. This sounds fair enough, but dark matter is needed only in the outer edges of galaxies, and no particles have been detected that could provide the very specific new physics, and the extended distribution (the halo), needed to account for the observed galactic rotations. Dark matter is also not a satisfying theory because it is not falsifiable. Given any galaxy you can add dark matter wherever you want to fit your predicted rotation curve to that observed.

Instead of increasing the gravitational mass in the galaxy to hold it in by force, one can also decrease the inertial mass of the stars in it to make them more easily bind. I have suggested a model called "Modified inertia due to a Hubble-scale Casimir effect" (MiHsC), or quantised inertia (QI) for short, that does this. In QI the inertial mass decreases in a specific new way for low accelerations. Stars at the edge of galaxies have low accelerations, so QI predicts they have less inertial mass, for the same gravitational mass. A lower inertial mass means the stars can be more easily bent into a bound orbit, even by the small amount of stellar mass we see in the galaxy. In the paper I have shown that QI predicts the rotation speeds of galaxies and galaxy clusters without needing any fitting parameters or dark matter. QI also predicts the change from the Newtonian behaviour in the galactic centre, to the anomalous rotation near the edge.

The main controversy with QI is that it violates the equivalence principle (very slightly), but as I have discussed in another paper (in the discussion of the paper here) this violation could not have been detected by the torsion balance experiments that have been used to test this principle so far.

The journal paper is here, and an arxiv preprint is here.

Quantised inertia on galactic scales

I'm pleased that my paper (Testing quantised inertia on galactic scales) has just been accepted by the journal Astrophysics and Space Science. I used the data published by McGaugh, Schombert, de Blok and Zagursky (2006) listing the baryonic mass and circular velocity of dwarf galaxies, spiral galaxies and galaxy clusters. In the paper I show that MiHsC (quantised inertia) predicts the observed circular velocity of all these structures (within the uncertainties) from their baryonic mass only (ie: without dark matter).

In more detail: MiHsC overestimates the circular velocity of galaxies (but still agrees within the error bars) whereas MOND agrees better with galaxies, if you set its adustable parameter (a0) correctly. On the other hand MiHsC agrees better with large galaxy clusters, where MoND has always had trouble, and a very important advantage of MiHsC is that it doesn't have any adjustable parameters. The paper is on the arxiv here.

Beyond the Pail: Mach's Principle

If you spin a bucket (pail) of water, initially only the bucket spins, the water remains static and its surface flat. Soon, because of friction, the water spins too, and piles up around the edges, because inertia means it moves in a straight line, and outwards from the spin axis. Eventually, a concave water surface and a pressure gradient forms that balances the inertial tendency outwards. What does this inertial force depend upon? Not, noticeably, on motion relative to the bucket wall, because at first when the fluid was moving relative to the wall there was no curve in its surface. Newton concluded that there was only a curve when the water was moving relative to absolute space. Later, Berkeley and Mach said there was no such thing as absolute space (Einstein based relativity on this) and that the spin has to be measured relative to something observable like the fixed stars, so that a pail spinning in endless emptiness would not experience inertial forces at all. Einstein called this idea Mach's principle: inertia here is due to masses there. Considering the fixed stars also allowed Mach to wonder what would happen if Newton's bucket was static, but the fixed stars span around it. He said: "no one is competent to say how this experiment would turn out." (Bradley, 1971). Would the surface of the water curve or not?

MiHsC works in a similar way to Mach's Principle and states that the inertia of an object here increases with its acceleration relative to other masses there. It is predictive, so it has something new to say about Newton's bucket: if the fixed stars were whirled around it, there would be the same mutual acceleration between, each part of, the water and the stars, that occurs when the water spins and the stars are fixed. So, according to MiHsC, the inertial mass of the water would increase in the same way in both cases. By MiHsC & the conservation of momentum, in the bucket-spin case the initial spin would be slowed by the gain in inertia, and in the fixed-stars-spin case the water would start to rotate following the stars.

For observational evidence I can cite the flyby anomalies and the Tajmar experiment. With the flyby anomalies, small observed jumps in flyby spacecraft speed can be explained by MiHsC as being due to changes in the inertia of the craft as they accelerate relative to all the matter in the spinning Earth (McCulloch, 2008). In Martin Tajmar's experiments, a ring (instead of the fixed stars) was spun around a gyroscope (in a cold environment to purge all other accelerations), and the gyro followed the rotation of the ring (slightly), just as predicted by MiHsC: the gyro gains inertial mass when the ring accelerates, and to conserve momentum it has to spin with the ring (McCulloch, 2011). In Tajmar's experiment, there was also a parity violation which is predicted by MiHsC as being due to the Earth's spin relative to the fixed stars. The success of MiHsC in predicting these cases, shows that in low acceleration environments (cold or deep space) Mach's Principle may have been glimpsed.

Bradley, J., 1971. Mach's philosophy of science. The Athlone Press.

McCulloch, M.E., 2008. Modelling the flyby anomalies using a modification of inertia. MNRAS, 389(1), L57-60. http://arxiv.org/abs/0806.4159

McCulloch, M.E., 2011. The Tajmar effect from quantised inertia. EPL, 95, 39002. http://arxiv.org/abs/1106.3266

Cosmic acceleration from MiHsC

Newton's first law, the inertial one, says that the default acceleration is zero, so, in a vacuum, objects move happily along at constant velocity until something external pushes on them.

MiHsC or quantised inertia (see the references below) predicts something slightly (usually undetectably) different: that the default acceleration is non-zero and equal to 2c^2/Theta where c is the speed of light and Theta is the Hubble scale, so 2c^2/Theta = 6.9*10^-10 m/s^2. This is tiny, but is equal to the recently-observed cosmic acceleration that some have attributed to 'dark energy', and model by grotesquely adding a cosmological constant term to Einstein's field equation. I'll try and explain here how MiHsC predicts the observed cosmic acceleration using just its two assumptions, which are:

1) Inertia is caused by Unruh radiation (a kind of wave) and..

2) ..these waves must fit exactly into the Hubble scale (like a Hubble-scale Casimir effect or cosmic seiche).

The thing about Unruh waves is that as an object's acceleration decreases the Unruh waves it sees get longer. With a boundary this becomes significant. If you make small waves in a bath with, say, an electric toothbrush, then most of the little waves will propagate, but if you make large waves with a paddle, then you'll have to get the wavelength exactly right or the waves won't fit. The point is that for longer wavelengths, a smaller proportion of the waves are allowed because of the boundary condition: this resonant behaviour is called a seiche in oceanography and happens a lot with waves in lakes and harbours. This implies straight away that Newton's first law (default acceleration = 0) won't quite work in MiHsC, because if the acceleration is zero, or close enough to zero, the Unruh waves are as large or larger than the observable universe, ie: unobservable, and as Mach said: if it can never be observed, forget it! (to paraphrase).

In MiHsC, the same process as in the bath works with objects moving into deep space. As they move away from other gravitating matter their acceleration drops. Therefore, the Unruh waves they see lengthen, and a greater proportion are disallowed, so that the inertia of the object eventually decreases very fast, making it easier to accelerate even with a distant gravitating mass, and this stabilises the acceleration at a minimum of 2c^2/Theta. Happily, this is the acceleration that has been seen in the deep cosmos. It has been attributed to the vague concept of dark energy, and modelled by adding the cosmological constant term (an adjustable parameter) to Einstein's field equations, but MiHsC predicts it far more easily, and without any adjustable parameters.

References:

McCulloch, M.E, 2010. Minimum accelerations from quantised inertia. EPL, 90, 29001. http://arxiv.org/abs/1004.3303

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

Globular clusters: crucial experiments?

I think that the way to approach physics is not to aim to invent beautiful theories, but to look for the data that shows the way. One of the sign-post papers that happened to influence me in this way was: Scarpa, Marconi and Gilmozzi, 2006, although I've read similarly clear ones by, eg: M. Milgrom, S. McGaugh & X. Hernandez.

Scarpa et al. make the point in their introduction that Newton's laws have never been tested at the tiny accelerations that exist at the edge of galaxies and that "deviations from Newtonian dynamics are always observed when, and only when, the gravitational acceleration falls below ~10^-10 m/s^2 as computed considering only baryons". They go on to state that it is agreed that dark matter cannot affect things on the small scale of globular clusters (dark matter haloes are large and smooth), so they looked at three globular clusters and showed that, indeed, below the critical acceleration (from the mass in the cluster) they deviate from Newton, just like larger galaxies. This suggests the presence of new physics rather than dark matter.

They also make the point that the external gravitational field, from the larger galaxy, acting on the globular clusters is above the critical acceleration, but the non-Newtonian behaviour is still seen. This points away from MoND where dynamics depend on the total acceleration, and points towards MiHsC where it is the local mutual accelerations that matter.

Scarpa et al. isn't perfect, only three globular clusters were analysed, but I'd like to express my appreciation to all those, like them, who risk unpopularity to base their conclusions on direct observations of nature, eg: M. Milgrom, S. McGaugh, X. Hernandez, J. Anderson, M. Tajmar, CERN (especially the OPERA team).... Observing new regimes is hugely risky, but is the only way to get to new physics.

Hartle, Hawking & Hertog's first sentence.

I should say first, that I have found Hawking's earlier work to be useful (ie: Hawking-Unruh radiation). However, I do not agree with the attitude to science represented by his recent attempt, with colleagues Hartle and Hertog, to make 11-dimensional string theory compatible with a very abstract version of reality, by adding even further complexity to string theory (they add a so-called Escher space). See: arxiv:1205.3807v2 (Accelerated expansion from negative Lambda, Hartle et al., 2012).

To make my point I can start with the first statement they make in their abstract: "Wave functions specifying a quantum state of the universe must satisfy the constraints of general relativity". The implication is that general relativity (GR) is the truth, and everything else must be measured against it. Well, whether or not GR is the final truth, and I am pretty sure it is not, what should have been said is something like: theories specifying the state of the universe must satisfy the constraints of observational data. This seems like nit-picking, but is not. It is fundamental that the data must always come before the theories.

GR only agrees with galaxy rotation data if, typically, 10 times as much matter as can be seen is added ad-hoc in an unphysical way to the galaxies to make it fit. This seems to me to be an example of theorists adding complexity to a theory (adding dark matter and the new physics needed for it) in a desperate attempt to save it (like Ptolemy's epicycles were invented to help geocentric theories fit the observed planetary ephemerides). Sure, the idea of dark matter worked in the case of Neptune, whose existence was postulated to fit the motion of Uranus to Newtonian gravity, but this was the addition of a small amount of normal matter in the plausible shape of a planet, whereas dark matter needs the addition of 10 times as much matter as is seen, in a new form and with new physics to go with it to explain its bizarre halo-like configuration.

The physicist's focus should always be on the data and not the theory, which is why I am so keen to critise the first sentence of Hartle et al.. In contrast, MiHsC is not a finished theory yet, but I have developed it from the bottom up, by looking at messy anomalous observations and disregarding most of the existing top-level theories. As a result, MiHsC is simple and can explain cosmic acceleration, dwarf and disc galaxy rotation (I've just submitted a paper on this), the flyby anomalies, the Pioneer anomaly (although so can Turyshev et al.'s complex thermal model), and the Tajmar effect (albeit unrepeated experimentally), without the need for adjustable parameters, extra dimensions, or Escher space.

Against Dark Matter: needs new mass and new laws

To me, the dark matter hypothesis seems to be rather like Ptolemy's epicycles, Descartes invisible Vortices or the aether: a fudge. One question is: if so-called dark matter only feels gravity, then what keeps it from collapsing in on itself? The collapse under gravity of ordinary matter can be arrested because, to give one example, as matter is squeezed, temperatures rise, fusion begins, and an outward pressure appears (the exchange of momentum is due to the electromagnetic, EM, force) and a balanced system, a star, is formed. This could never happen with dark matter (DM) since it does not feel the EM force and so it can't be held up by pressure (but despite this, they say it can still lose kinetic energy, and collapse inward, via three-particle collisions). To allow general relativity to predict galaxy rotation curves correctly huge amounts of dark matter must be assumed to remain in an uncollapsed state in a huge sphere (halo) around a galaxy's visible matter. The gravitation forces on this halo would be ten times that due to the baryonic matter and the halo is not spinning to provide inertially-supportive forces (no flattening) so the dark matter should have collapsed quickly. To be held out there, gravity must be assumed to be balanced by some outward force.

This force can't be assumed to be the EM force (pressure) or the strong force because DM can't possibly feel them (if it did, experiments would have seen it) and the weak force is limited to very short ranges of ~10^-17 metres.

What keeps the proposed DM in an uncollapsed state? The physics does not exist to do it. People often refer to MiHsC as "exotic" physics, but it seems exotic physics is unavoidable. Either invent a new kind of invisible (dark) matter and new physics to go with it, or (neater & simpler) keep matter unchanged and modify only the physics. MiHsC is an example of the latter approach, and models galaxy rotation like this.