Air traffic control and radiobiology

Despite their superficially disparate nature, there is a striking formal similarity between air traffic control, and the processes studied in radiobiology.

In air traffic control, the objects of attention are the aircraft flight paths across a bounded region of airspace, called a sector. In radiobiology, the objects of attention are the energetic particle tracks across the bounded region of space occupied by a biological cell.

In air traffic control, there is a relationship between the number of flights passing through a sector, and the workload of an air traffic controller, and this relationship is given by a linear-quadratic function. In radiobiology, there is a dose-response relationship between the dose of radiation inflicted on a cell, and the biological response of interest, which may be the number of chromosome aberrations, DNA mutations, or the probability of cell death. For radiation of a fixed type and energy, the dose inflicted on a cell essentially corresponds to the number of particle tracks crossing the cell. Hence, the dose-response relationship is a relationship between the number of particle tracks crossing a cell, and the biological consequences. In the case of so-called chromosome translocations, a response crucially related to the probability of subsequent carcinogenesis, the dose-response relationship is given by a linear-quadratic function.

Let us elaborate on these linear-quadratic relationships a little in order to understand the reasons for such formal similarity. In the case of air traffic, the linear component of controller workload is due to (i) the number of routine flight level and airspeed instructions issued per aircraft, and (ii) the communication required with other controllers, when an aircraft is received from, or transferred to another sector. This component of controller workload is independent of the flow-rate, the number of aircraft passing through the sector per hour.

The quadratic component of controller workload is that associated with aircraft conflict-prediction and resolution; there are regulatory separation minima between aircraft, which must not be infringed. Each aircraft could be in potential conflict with any other aircraft in that same sector in the same time-window, hence this component of workload squares with the number of flights. This component of workload is clearly flow-rate dependent; at times of very low flow-rate, it will vanish.

In radiobiology, it is generally acknowledged that in those circumstances where there is a linear-quadratic dose-response relationship, the linear component arises from intra-track mechanisms, whilst the quadratic component arises from inter-track mechanisms. For example, chromosome translocations occur when genetic material is exchanged between two different chromosomes. It is generally thought that such chromosome aberrations occur because the two separate chromosomes both suffer double-strand breaks; i.e., the double-helix of DNA is thought to be broken in two separate chromosomes. The fragments from the two broken chromosomes are then exchanged, rather than spliced back to the correct chromosomes from which they originated.

There is a linear-quadratic relationship between radiation dose and the number of chromosome translocations in an irradiated cell. The linear component is due to individual particle tracks breaking two separate chromosomes. In contrast, the quadratic component is thought to be due to independent particle tracks breaking two separate chromosomes. This component squares with the dose because a break caused by one particle has a chance of interacting with a break caused by any other particle which passes through the cell within the same time-frame, (a period determined by the cycle of cellular repair processes). This component of the dose-response relationship is therefore dose-rate dependent; at low dose-rates it vanishes.

As yet, however, there appear to be no textbooks for those wishing to jointly specialise in air traffic control and radiobiology.

Published in: on April 17, 2010 at 12:06 pm  Leave a Comment  

Nuclear physics in other universes

The anthropic principle claims that the universe we live in is finely-tuned to permit the existence of life. According to current mathematical physics, there are many aspects of our physical universe which are contingent rather than necessary, and these include such things as the values of the numerous free parameters in the standard model of particle physics, and the parameters which specify the initial conditions in general relativistic models of the universe. The values of these parameters cannot be theoretically derived, and need to be determined by experiment and observation. The anthropic principle is based upon analysis which shows that if the values of any one of those parameters were to be changed, only slightly, then the universe would be inhospitable to life.

There is, however, some recent theoretical work which suggests that the fine-tuning claim which supports the anthropic principle may be just a little glib.

One of the favourite parameters used in anthropic arguments is the cosmological constant Λ. This appears to have a very small, but non-zero value. It is the cosmological constant which is driving the accelerated expansion of the universe discovered in 1998. If Λ were very much larger, it is argued, then the universe would have expanded far too quickly for any stars and galaxies to form. However, this argument tacitly assumes that the value of all the other parameters of physics are held constant. As Lee Smolin points out in Scientific alternatives to the anthropic principle, one can also vary the amplitude Q of the density fluctuations (which seed the formation of galaxies). If the value of Λ is increased, and the expansion of the universe is accelerated, then one can increase Q to compensate: “one can have stars and galaxies in a universe in which both Q and Λ are raised several orders of magnitude from their present value.” Modern cosmologists hypothesize that the amplitude of the density fluctuations is a consequence of inflation, the short period of exponential expansion in the early universe’s history, which was driven by a scalar field called the inflaton. As Smolin points out, Q therefore depends upon the parameters which define the inflaton potential energy function, parameters such as the mass and self-coupling, which are free parameters.

The existence of life in our universe is also dependent upon nuclear physics, in the sense that life appears to require the existence of hydrogen, carbon and oxygen, and these chemical elements can only exist if the nuclear physics of a universe permits the stable existence of atomic nuclei of electric charge equal to 1 (hydrogen), 6 (carbon) and 8 (oxygen), and if the nuclear physics of a universe facilitates the fusion of carbon and oxygen from primordial hydrogen.

Recent research, summarised by Alejandro Jenkins and Gilad Perez in the January issue of Scientific American, suggests that these criteria can be satisfied by universes with a nuclear physics quite different from our own.

The first case considered is a so-called ‘weakless universe’. Our own universe has four forces (gravity, electromagnetism, the strong nuclear force, and the weak nuclear force). A weakless universe has only three forces, being deprived of the weak force. This is a significant omission as far as nuclear physics is concerned, because the weak force is required for neutrons to transform into protons and vice versa.

A proton consists of two up quarks and one down quark, whilst a neutron consists of one up quark and two down quarks. If one of the down quarks in a neutron emits a W particle, (one of the so-called gauge bosons of the weak force), it will transform into an up quark, and the neutron will transform into a proton. This is called beta-decay. The W gauge boson then decays into an electron and an anti-electron-neutrino, the conventional radioactive products of beta decay. Conversely, if one of the up quarks in a proton emits a W+ gauge boson, it will transform into a down quark, and the proton will transform into a neutron.

The latter process is required for the nuclear fusion which takes places within the stars in our own universe. The so-called PPI chain requires pairs of protons to fuse together, and for one of the protons to transform into a neutron. The result is a nucleus with one proton and one neutron, called deuterium. Further protons then fuse with such deuterium nuclei to form helium-3 nuclei, and pairs of helium 3 nuclei then fuse into helium-4, spitting out two surplus protons in the process.

Remove the weak force, then, and stellar nuclear fusion can’t get started, can it? On the contrary, this conclusion only holds if all the other parameter values are held fixed. Harnik, Kribs and Perez argue in A universe without Weak Interactions, that if the level of asymmetry between matter and anti-matter in the early universe is also varied, then universes without the weak force can still synthesize the atomic nuclei required to support life. If the so-called baryon asymmetry is reduced, then a sufficient proportion of deuterium nuclei will be left over from big-bang nucleosynthesis, for the fusion of heavier elements to proceed within stars. Such stars will be colder and smaller than our own stars, but will still support a zone of habitability for planets orbiting at just the right distance.

The second case considered is that in which the masses of the quarks are varied. In our own universe, only the two lightest quarks, the up and the down quark, combine to form stable baryons: the proton and the neutron. The other quarks are too massive to form such baryons, hence they do not participate in the physics of atomic nuclei. The down quark in our universe is heavier than the up quark, hence the neutron is slightly heavier than the proton. Jaffe, Jenkins and Kimichi argue in Quark Masses: An Environmental Impact Statement, that universes with other combinations of quark masses could support the existence of life.

If, for example, the up quark is set to be heavier than the down quark, and protons are therefore set to be heavier than neutrons, then whilst hydrogen itself would be become unstable, the heavier isotopes of hydrogen, such as deuterium and tritium, would act as stable substitutes.

Another potential life-supporting universe is one in which the mass of the strange quark is reduced to a value close to that of the up quark, and the down quark is given a much lower mass than either of them. In such a universe, the sigma minus baryon Σ, consisting of two down quarks and one strange quark, functions as a substitute for the proton, and can combine with neutrons to form stable isotopes of hydrogen, carbon and oxygen.

As Perez and Jenkins comment, “Physicists in such a universe might be puzzled by the fact that the up and strange quarks would have almost identical masses. They might even imagine that this amazing coincidence has an anthropic explanation, based on the need for organic chemistry. We know, however, that such an explanation would be wrong, because our world has organic chemistry even though the masses of the [up] and strange quarks are quite different.”

Published in: on April 2, 2010 at 12:29 am  Leave a Comment