Quantised Inertia: From Anomalies to New Physics

Michael McCulloch Hammers Out A New Theory

“Something weird is going on at the fringes of known space.”

That would make a good introduction to a science fiction thriller, but Mike McCulloch’s Quantised Accelerations: From Anomalies to New Physics is science fact, not fiction.

At the edge of many of the galaxies and globular clusters, we observe stars orbiting faster than either Newton or Einstein say they should.

Typical rotation curve of a globular cluster (simplified). From McCulloch’s Quantised Inertia.

They call it the problem of “Dark Matter:” the mysterious missing matter that has to be there to account for the disconnect between the amount of observable matter and the rotational acceleration at the perimeter of galaxies.

Is the problem really one of “Dark Matter?” Or have we jumped to a potentially erroneous conclusion? An examination of the history of science may be of help, because, believe it or not, we’ve been here before.

Nineteenth Century Dark Matter

In the nineteenth century, astronomers noted an anomalous perihelion advance of the planet Mercury. Similar orbital anomalies had recently led to the discovery of Neptune, both validating Newton’s theory of universal gravitation and the approach of inferring the existence of hitherto unknown planets from perturbations in the orbits of known planets. The culprit, therefore, had to be an unknown planet within the orbit of Mercury responsible for the perturbations. That was the inevitable conclusion of well-settled science.

This unknown planet, dubbed “Vulcan” (because of its toasty orbit close to the Sun), could easily have been overlooked due to the difficulty of spotting such a small planet close proximity to the Sun. Vulcan was literally “dark matter.” The search for Vulcan was conducted by carefully observing the solar disk for the transit of a dark spot that would indicate the presence of a tiny planet blocking a small portion of the Sun’s light. As the fruitless search continued, astronomers placed tighter and tighter limits on the size of the supposed planet Vulcan until it became obvious no such planet of the size necessary to perturb Mercury’s orbit could possibly exist.

The solution? A new theory of gravity, Einstein’s Theory of General Relativity, was able to explain Mercury’s anomalous perihelion advance. Might the anomalous observed accelerations at the edges of galaxies be due to some similarly new physics?

That’s what Mike McCulloch thinks.

Quantized Accelerations

In Quantised Accelerations: From Anomalies to New Physics, McCulloch explores 54 anomalies difficult or impossible to explain using conventional physics. He proceeds to explain them with his hypothesis of “Quantised Inertia” or “QI,” spelled in the archaic English fashion with an “s” instead of a proper American “z.”

McCulloch’s Theory

Here’s a brief summary of McCulloch’s idea.

In the theory of relativity, it is possible to have a “Rindler Horizon,” beyond which information may not be exchanged because any interaction would require faster than light travel. In the space-time diagram below, an observer at the origin cannot perceive or interact with events in the pink shaded area past the black-dashed speed-of-light lines.

A Rindler Horizon on a space-time diagram. Courtesy, Wikipedia.

McCulloch argues that the uncertainty principle must be applied asymmetrically to all accelerating matter. On one side, a distant cosmic horizon; on the other side a closer Rindler Horizon. This asymmetry in uncertainty of position requires an inverse uncertainty in momentum, and therefore a net force corresponding to the relative difference in momentum in the two directions.

The asymmetrical horizons of an accelerating particle. From McCulloch’s Quantised Inertia.

Here’s how McCulloch explains it.

In quantised inertia the new assumption is that the uncertainty in position ∆x is the distance to a horizon. So if ∆x is small then ∆p (which I interpret as jitter) is large. In the schematic above we can see that the Planck mass has a horizon close by on its left and one far-off to its right. This implies it will have more uncertainty in momentum (jitter) to the left (see the comparative size of the light grey arrows) and so it will tend to drift leftwards, against its initial acceleration (dark arrows). This predicts what we know as inertia, with a tiny difference that happens to predict galaxy rotation and many other anomalies without needing dark matter or dark energy.

The result is a minute correction to Newton’s second law - imperceptible under most everyday circumstances - but sufficient to explain many of these outstanding physical paradoxes.

McCulloch’s work builds upon some earlier (but sadly overlooked) physical speculation from Dirac and others that the microscopic realm of particle physics may be linked to the large-scale structure of the cosmos. The large numbers hypothesis opens up fascinating new physics in which so-called physical constants, like the gravitational constant, are actually time-varying properties of the cosmos. See for instance, Alexander Unzicker’s Einstein’s Lost Key: How We Overlooked the Best Idea of the 20th Century.

McCulloch also appeals to the interactions of Unruh waves with the particle and the respective horizons to explain the effect. This bothers me, because the wave properties required do not appear consistent with the properties of conventional electromagnetic waves. His explanation requires an appeal to hitherto unknown or poorly understood wave phenomena (particle waves? quantum waves?) behaving in hitherto unknown fashions to account for the effect he describes. As in good science fiction, we generously allow the author one free wild speculation, but as additional speculations are required to justify the narrative, our skepticism is aroused.

Students of physics will recall how Newton was unable to successfully explain his remarkably powerful universal law of gravitation, either. That Newton’s theory made correct predictions was justification enough. So also with McCulloch. A persuasive narrative of how the QI phenomenon arises is not required to appreciate and apply the relationship McCulloch has identified.

A Master Class in How Physics Should Be Done

Quantised Accelerations is a master class in how physics should be done. McCulloch meticulously describes a host of physical anomalies that demand explanation. If not McCulloch’s well-thought-out-and-presented theory, then what would you propose? His book is well-referenced for serious investigators who might wish to use it as a starting point for their own investigations.

Highly recommended.

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