Explaining MiHsC: Whirling a Ball around on a String

Imagine you are standing there in your garden with a ball tied to a string. Slowly you whirl the ball around you so it is pulled outwards. What it pulling it outwards? No one understands the mechanism, but this effect is called inertia. The idea is that objects tend to keep going in the same direction at the same speed until something pushes on them. The ball has inertial mass so it wants to go in a straight line, but you and the string are pulling it towards you. A balance is reached: an orbit, until you let go of the string and send your friends running for cover.

Zooming out by a factor of a million million million, galaxies are similar. Balls of fusion (stars) mutually orbiting, with inertia pulling them apart and gravity pulling them together. The problem is that galaxies spin around so fast that the inertia as we know it, should win over gravity and tear the galaxies apart. Yet galaxies remain stably intact. The small amount of matter we can see lit up in fusion (ie: stars) seems to hold all the stars together. How?

In the 1930s a Swiss called Fritz Zwicky proposed that matter that we cannot see is responsible: dark matter. This sounds fair enough, but the 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 predictive or falsifiable. Given any galaxy you can add dark matter wherever you want to fit your predicted rotation curve to the one observed.

If we come back to you whirling a ball around in the garden for a minute. Imagine you could whirl the ball so fast it becomes a blur. Surely the string would break under the inertial pull outwards. What if it didn't? Well, you could conclude that the string was made of strong carbon fibre so it can pull inwards without breaking (just like extra matter in a galaxy provides extra inwards pull), or otherwise you could conclude that the ball is hollow and has less inertial mass than you thought. This means it is less inclined to follow a straight line and zoom off, and more easily bent into a curved orbit even by an ordinary string.

Similarly, instead of adding extra gravitational mass to the galaxy, can we reduce the inertial mass of its stars? There is a way to do this using what is called: "Unruh radiation". This is similar to the Hawking radiation you get in a gravitational field, but you see Unruh radiation only when you accelerate. You also see inertia only when you accelerate, so maybe inertia is linked to Unruh radiation.

Unruh radiation is a wave with a wavelength that depends inversely upon the acceleration. At the edge of galaxies the acceleration is tiny and the Unruh waves become so long that a smaller proportion of them can be measured, and Ernst Mach once said that if you cannot measure something you should discard it, and this kind of thinking led Newton to discard Descartes' vortices and led Einstein to discard the aether, so let us say that if the Unruh waves cannot be seen, then they cannot contribute to inertia, so galactic edge stars lose inertial mass in a new way. On galactic "scales" they have lost mass (forgive the pun). 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.

To cut a long story short, such a model, called MiHsC or quantised inertia, works and fits galaxy rotation curves without dark matter (see the paper below). It also does this without adjustable parameters, which means it gives only one answer, and that happens to be the right one.

McCulloch, M.E., 2012. Testing quantised inertia on galactic scales. Astronomy and Space Science. Vol. 342, No. 2, 575-578.
Journal paper: http://www.springerlink.com/content/1778177x0570j647/

Preprint: http://arxiv.org/abs/1207.7007

QI & MoND vs the data: new figure.

Someone helpfully suggested that I should redo the Figure that I published in this paper (in Astrophysics and Space Science) using a vertical log scale, and the result is much clearer and is shown below. This Figure shows the baryonic mass of the astronomical system in Solar masses along the x axis, from the light dwarf galaxies, through gas discs and spiral galaxies and up to galaxy clusters. The vertical log axis shows the rotation speed of the system in km/s. The black circles are the observations (from McGaugh et al., 2010).

MoND predicts the two dotted lines, but to do this you must "tune" its adjustable parameter (a0) by hand to be 1.2x10^-10 m/s^2 or 2x10^-10 m/s^2. Quantised inertia (MiHsC) predicts the dashed line without any adjustable parameters. See here or the preprint for more details. So both MoND and MiHsC agree with the data within its uncertainty but MoND has to be "tuned" to fit, whereas MiHsC works as it is.

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.