by Richard Obousy

Physicist Richard Obousy here takes a look at an intriguing new paper by Mike McCulloch, a researcher at Plymouth University. In addition to his work in theoretical physics and warp drive possibilities, Obousy is current project leader and primary propulsion design lead for Project Icarus, a joint venture between the British Interplanetary Society and the Tau Zero Foundation to re-think the original Project Daedalus starship design. In the review below, Obousy places McCulloch’s work on the Pioneer anomaly in the context of current thinking on dark matter, dark energy and the nature of mass. Does the Higgs field explain inertial mass, or are there alternatives? Read on.

Few areas of research have garnered as much attention from both the public and scientific communities as those of dark energy and dark matter – and for good reason. Both terms stem from observations of the physical universe that, simply put, don’t belong within the well-understood framework of known physics. Another phenomenon discovered in the nineties concerns an anomalous acceleration of the Pioneer probes. These ostensibly unrelated observations may, in fact, be connected to each other by an intriguing line of research currently being investigated by Mike McCulloch, a researcher at the University of Exeter. Before exploring McCulloch’s research, a brief review of dark energy, dark matter, and the anomalous Pioneer acceleration will be presented.

Dark matter is a proposal put forward to explain the observations first made by Zwicky in 1933 that galaxies were too energetic to be held together by observable matter. Zwicky originally proposed the existence of an unseen form of baryonic matter that provided the necessary gravitational force to hold the galaxies together. Due to constraints imposed by modern cosmology, the idea has evolved to assume this form of matter is non-baryonic (not made of quarks); however, the fundamental idea has remained unchanged. After decades of searching for dark matter, none has been directly detected, but a number of experiments are ongoing.

Dark energy stems from the truly astounding observation made originally by Riese and Perlmutter in the late 90’s that the rate of cosmological expansion, long thought to be either static or decelerating, is actually accelerating. For this to be happening, it is commonly believed that the universe is filled with a ubiquitous and exotic negative pressure field that drives the accelerated expansion. Although we can give this energy a name, and predict what it will do, dark energy as a ‘real’ physical field has never actually been measured in the lab, and today, dark energy remains somewhat of an enigma.

As if dark energy and dark matter haven’t dealt theoreticians enough of a blow, cracks began to appear in our understanding of gravity due to the observation made by Anderson et al in 1996 that both Pioneer 10 and 11 are experiencing an anomalous acceleration of 8.74±1.33×10-10 m/s2 directed approximately towards the sun. It is precisely this anomaly that is studied by Mike McCulloch in his recent publication in Europhysics Letters called Minimum Accelerations from Quantized Inertia (reference below). McCulloch’s work addresses the Pioneer anomaly, and within the framework of his model, one could perhaps come to a deeper understanding of dark matter and dark energy thanks to a novel idea known as MOND, or Modified Newtonian Gravity.

The basic idea that McCulloch explores is the nature of mass, and the possibility that inertial mass, in fact, changes slightly under certain conditions. It has been known since the time of Newton that all bodies attract all other bodies in the universe with a force that is proportional to their mass. This type of mass is what is known as gravitational mass. It is also known that when one applies a force to an object, it accelerates at a magnitude that is proportional to its mass. This type of mass is known as inertial mass. It is commonly assumed that gravitational and inertial mass are identical, and this has been verified by our highest precision instruments to date.

The fundamental nature of inertial mass is not precisely known and is an issue that has been pondered at least since the time of Mach. Recent efforts to codify inertial mass into the Standard Model (SM) of particle physics have resulted in the famous Higgs field, which is a ubiquitous field that bestows mass upon matter via a process known as spontaneous symmetry breaking. Although the Higgs field has not been experimentally detected, many physicists are confident that it will be found at the Large Hadron Collider.

Despite the widespread acceptance in the existence of the Higgs field, there have been alternative attempts to uncover the nature of inertial mass. One paper, Inertia as a Zero Point Lorentz Force, written in 1994 by Rueda, Puthoff and Haisch (RPH), represents a stalwart effort to model inertia as a back-reaction of matter to the quantum vacuum similar to the Unruh field. Despite not gaining widespread acceptance in the theoretical community, the paper galvanized interest in the possibility that the quantum vacuum and inertial mass may be related. The basic premise of the paper was that matter, modeled as a ‘Parton’, interacts with the quantum vacuum in such a way that any acceleration generates a Lorentz-type back-reaction to the vacuum which manifests itself macroscopically as a resistance to acceleration or, more simply, as inertial mass.

The RPH paper was not the first to suggest that accelerated matter is effected by the quantum vacuum. In 1976, Unruh showed that a body undergoing an acceleration in the vacuum sees a thermal radiation of temperature T that is related to its acceleration. Wien’s displacement law tells us that, for a given temperature, there will be a dominant wavelength which, via the Unruh effect, is inversely proportional to the acceleration – namely, as the acceleration gets smaller, the radiation wavelength gets bigger. As the acceleration decreases, this wavelength reaches a limiting value: the wavelength of the observable universe. Milgrom, in 1994, speculated that at this point, there would be a ‘break in the response to the vacuum’ and the Unruh radiation would be unobservable. He further speculated that this could have an effect on inertial mass. Herein lies the crux of this line of thinking – that matter’s response to the vacuum is what generates inertia.

McCulloch further develops the idea of Milgrom by allowing for a more natural development in the Unruh radiation spectrum. In the original idea by Milgrom, only the dominant wavelength was considered. McCulloch, however, develops what he calls a Hubble-Scale Casimir effect, where a range of wavelengths are allowed based on the boundary conditions of the size of the observable universe.

“The new assumption is that this Unruh radiation is subject to a Hubble-scale Casimir effect. This means that only Unruh wavelengths that fit exactly into twice the Hubble scale (harmonics with nodes at the boundaries) are allowed, so that a greater proportion of longer Unruh waves are disallowed, reducing inertia in a new, more gradual, way for low accelerations.”

Using this model, McCulloch is able to develop an equation which illustrates the modification of inertial mass for low accelerations. Put in simpler terms, as the Pioneer probes depart our solar system they experience a force due to the gravitational attraction of the sun. This force generates an acceleration which, due to its extremely small value, modifies the inertial mass of the pioneer probe. Because of this modification, the Pioneer probes, seemingly now less massive, feel a greater acceleration due to the sun than that predicted by Newtonian mechanics, creating the anomalously large acceleration.

How does this all relate to dark energy and dark matter? The answer is in the relationship between certain natural scales that occur in physics. The basic building block is the scale that characterizes the cosmological constant. We call this scale R and it is the distance scale over which the cosmological constant curves the universe. R is about 10 billion light years and is 1040 times the size of an atomic nucleus – the scale where the standard model of particle physics is applicable). R is also 1060 times the Planck scale – the scale at which we believe in GUT’s (Grand Unified Theories), where all the forces in nature behave identically. It is therefore pragmatic to wonder whether this scale R might be indicative of some new physics.

Hints at new physics at the scale R manifest themselves in the cosmic microwave background (CMB) – thermal radiation left over from the Big Bang. This radiation has been cooling as the universe expands, and is now at a fairly uniform temperature of 2.7 degrees Kelvin. Fluctuations in this temperature exist to a level of a few parts per 100,000, and the patterns of these fluctuations provide us with clues to the physics of the early universe.

Analysis of the temperature fluctuations over the last decades illustrate how much energy is contained in this radiation as a function of wavelength. It appears that the CMB is dominated by a single large peak, followed by a number of smaller peaks. It also appears that there is very little energy in the longest wavelength. This data can be interpreted as indicative of a ‘cutoff’, above which the thermal modes are less excited. What is particularly remarkable is that this cutoff occurs on a scale R which we associate with the cosmological constant.

This cutoff is somewhat puzzling from the perspective of inflation theory, which was developed by Alan Guth of MIT and, originally, by Alexei Starobinsky of the Landau Institute for Theoretical Physics in Moscow. According to the theory of inflation, the early and rapid expansion of the universe created huge regions of the cosmos with relatively uniform properties. This region is thought to be much larger than the observable universe. The cutoff indicates that, at the scale R, inflation stopped just at the point where it created a region as large as we now currently observe. If, in fact, inflation ‘switched off’ just at the point where it created the cosmos as large as we currently observe, then some physical mechanism must have been responsible for selecting this unique time to stop. This seems incredibly improbable, since nothing in the physics of inflation says anything about scales on the order of 10 billion light years.

Said another way, if inflation produced a largely uniform universe, then it likely produced uniformity on scales much larger than we observe. Thus, the patterns produced by inflation, the small fluctuations, should be visible beyond the present size of the universe. Instead – what the data indicate is that these fluctuations stop above the scale R.

Another indication that new physics may occur at scales on the order of R is an apparent asymmetry in the distribution of hot and cold spots in the CMB dubbed the ‘Axis of Evil’. This observation was first made in 2005 by Kate Land and Joao Magueijo of Imperial College London. A number of independent studies have confirmed this apparent alignment of anisotropies in the CMB.

There are additional phenomena associated with the scale R that are worth discussing. One way we can explore R is to combine it with additional constants of nature. An interesting place to start is to combine it with the speed of light, c, to give us R/c. Dimensionally, R/c gives us a time, and that time corresponds to the present age of the universe. Taking the reciprocal of this, c/R, gives a frequency, a profoundly low ‘note’ which has completed one oscillation in the entire lifetime of the universe.

Going one step further, we can explore c2/R which, dimensionally, gives us the units of acceleration. Remarkably, this number is the acceleration produced by the cosmological constant. This is the same acceleration that we currently believe dark energy is responsible for and is on the order of 10-10 m/s. This also happens to be the roughly the same anomalous acceleration that the Pioneer probes are currently experiencing!

The c2/R also crops up when we examine rotational velocity of orbiting stars in galaxies. Recall that stars are seen to rotate at a velocity that would, according to Newtonian Mechanics, be too fast for them to be held in a stable orbit. The contemporary fix for this problem is to introduce dark matter. This is not the only fix, however. For spiral galaxies, in which stars move in circular orbits, anomalous velocities (orbital velocities that, according to Newtonian Mechanics, should not be possible) are only apparent beyond a certain orbit. Within this ‘special’ orbital distance Newtonian gravity works perfectly. Because stars move in a circular orbit they experience an angular acceleration which is related to their velocity (a=v2/r). The breakdown of Newtonian gravity occurring at this ‘special’ orbital distance occurs when the stars are rotating with an angular acceleration of 1.2×10-10 m/s2, almost identical to the scale c2/R. This is thoroughly fascinating, and this string of relationships which appear to be related to the scale R represent tantalizing hints at physics beyond what is currently studied and practiced within the mainstream academic community.

Today, nobody knows for certain what this new physics is (if it really is new physics), and nobody has written down a theory codifying its behavior. Mike McCulloch, however, is arguably helping to increase momentum within this curious and remarkable area of research.

The paper is McCulloch, “Minimum accelerations from quantised inertia,” Europhysics Letters Vol. 90, No. 2 (20 May, 2010). An abstract is available, with full text here. The paper by Rueda, Haisch and Puthoff is “Inertia as a Zero Point Lorentz Force,” Physical Review A, Vol 49, No 2 (February 1994), pp.678-694.