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 Books and publications on the interaction of systems in real time by A. C. Sturt Economics, politics, science, archaeology. Page uploaded 25 November 2004.

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# Radioactive Clocks

A Basis for the Absolute Measurement of Time

by A. C. Sturt

# or 1 in 1010, but this depends on the development of a suitable standard of radioactive decay.

Such a clock would provide a way of investigating variations in units of time which are measured using other bases: ephemeris, sidereal, electromagnetic etc. It could also be used to elucidate the effects on light of other natural phenomena, such as gravity, distance travelled through space, velocity and so on, as it approaches its limit i.e. the relativistic effects.

A. Introduction

# A. Introduction

Radioactive decay is used to date the formation of naturally occurring materials and the manufacture of artefacts from the distant past. The basis of the method is the decay of radioactive atomic species with time. Residual radioactivity emitted per unit time is measured with a detector and a clock, and the age of the sample can then be calculated from the decay equation using the known parameters for that element. The age is therefore expressed in terms of clock units i.e. seconds, though these may be transformed into months or years etc. It must therefore contain any uncertainty in or local influence on the physical phenomenon on which the clock is based e.g. the wavelength of electromagnetic radiation. These are inherent in the standardised conditions referred to above.

However, the process of radioactive decay may itself form the basis of measurement of elapsed time. A radioactive clock need not depend on the measurement of time by using another natural phenomenon, such as electromagnetic radiation. The unit of “radioactive time” may therefore respond differently at velocities approaching the speed of light, when other clocks slow down, according to the Theory of Relativity.

If radioactive time were found to behave differently under extreme conditions, it would have profound implications for the SI Units of time and distance i.e. the second and the metre, and all that flows from them.

Clocks conventionally rely on phenomena which involve continuous repetition of events in series long enough to run in parallel with the events which are being timed e.g. the vibrations of quartz crystals, the frequencies of electromagnetic radiation, the cycles of astronomical phenomena etc to time races, processes, orbits and so on.

Repetition in the proposed radioactive clock lies in the unchanging probability of decay of a radioactive nucleus. Radioactive elements decay by a change of state of the individual atom from which a quantum of radiation is emitted. Each quantum of radiation can be made to produce a scintillation or “spark” in a detector, so that it can be individually counted. Using statistical concepts this provides the means of measuring time spark by spark in large populations of radioactive nuclei, expressed solely in terms of number i.e. the number of decay events.

Number, unlike physical phenomena, must unquestionably be constant throughout time and hence space. It must always have been constant, because it is a definition. There is no other possibility.

# B. Assumptions

A number of assumptions need to be made about the process of radioactive decay. However, they are all assumptions which can be tested independently under laboratory conditions. They relate to the decay of nuclei both as individual entities and en masse.

1. Individual nuclei

1. The decay of the individual nucleus is independent of other nuclei. There is no interaction between them.

1. The presence of products of decay does not influence the decay of an individual nucleus. It is not an equilibrium process.

1. Radioactive decay is stochastic. The decay of any single nucleus is not a predictable event.

1. Populations of nuclei

a.       However, decay in a population of radioactive nuclei i.e. in large quantities of a radioactive element is both extremely predictable and characteristic of that element. The term “population” is used in the statistical sense of a very large number of the species, such that its behaviour encompasses that of all smaller numbers or “samples” of the species. In effect it overrides the stochastic variations of the individuals of which the population is composed.

b.       The number of radioactive nuclei in a population which decays during an interval of time is proportional to the number of radioactive nuclei present in the instant before each decay event. Decay in a population is therefore an exponential decline with respect to time.

1. Characteristics of the phenomenon

a.       The process of decay of an individual radioactive nucleus is homogeneous through time, and hence space. It has always been the same everywhere.

b.       The rate of the process depends only on the nature of the radioactive element.

c.       As far as we are aware, no other natural phenomenon affects the probability of decay of an individual nucleus. It is not influenced by temperature, pressure or gravity etc. In particular, it is not affected by acceleration, or by velocity in the way that mass is predicted to be affected in the Theory of Relativity.

# C. Time Dilation

The Theory of Relativity predicts time dilation which becomes apparent as the speed of light is approached. Units of elapsed time, conventionally seconds, are predicted to become longer as velocity increases. This is accompanied by changes in all the parameters which form the framework of physics: length, mass and everything derived from them.

If time dilation occurred with radioactive decay, it could only mean that the interval between events or sparks increased with the velocity of radioactive material. This would raise a fundamental question, which could be asked in various forms as follows:

1.       How could a nucleus know about the time interval between its own decay and that of its neighbours, since there is no interaction between them?

1. How could time dilation be reconciled with a process which is measurably a sequence of stochastic events? The sparks themselves are the events. If the interval between events occurring in the mass is dilated, by what principle can this occur?

1. If in spite of these objections time is still considered to be dilated in radioactive decay, what exactly does this mean, since “time is nothing without an event to mark it” (Einstein), and there are no events between sparks ?

radioactive decay rate uses SI time interval

electromagnetic definition

external influences?

radioactive time interval

profound implications

conventional clock events

radioactive clock based only on number of ‘sparks’

number - homogeneous through time

radioactive decay assumptions

individual nuclei

populations of nuclei

homogeneity through time

characteristic of species

no external influences

Relativity

time dilation

problem with the concept

 Copyright A. C. Sturt 27 September 2001

 Churinga Publishing