
Books and publications on the
interaction of systems in real time by A. C. Sturt 


Radioactive Clocks 

A Basis for the Absolute Measurement of Time by
A. C. Sturt 


Summary.
Variations in the wavelength of electromagnetic radiation observed on Earth
are a well established phenomenon. Increases of wavelength have variously
been ascribed to the recession of the emitters (stars), time dilation
(satellites’ clocks) and gravity (the Einstein redshift). On the other hand
reductions occur when light travels through transparent media such as
liquids, because frequency is maintained while velocity is reduced.
At the
same time wavelengths are used to define universal standards of time and
length i.e. the second and the metre. The assumption is that the conditions
in which measurements are made can be standardised, so that extraneous
variations do not occur. But, however unlikely it is, the possibility of
ambiguity must remain.
This
note suggests that it might be possible to make a clock based on
radioactivity which provides a unit of time that is certainly invariable and
totally independent of all other phenomena i.e. an absolute unit of time. In
principle it can be as accurate as patience permits, comparable to the
caesium133 clock
or 1 in
10^{10}, 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. 
Unit interval of
radioactive time N_{1} Successive absolute
units of time Calculation of λ
the absolute radioactive decay constant Calculation of
successive time periods E. Confounding of Units
of Time and Length Unit interval
of radioactive time N_{1} Successive
absolute units of time Calculation
of λ the absolute radioactive decay constant Calculation
of successive time periods 

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.
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.
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?


electromagnetic
definition radioactive time interval number  homogeneous
through time

Copyright A. C. Sturt 27 September 2001 

Churinga
Publishing 