Contrary to the ''linear no threshold hypothesis,'' which implies that
''any amount, however small'' of radiation energy is a serious cancer
threat, it is shown here that only relatively quite large amounts of
such energy can pose such a threat to a person or population. Key to d
oing this is to make a sharp distinction between the actual amount of
the radiation agent imparted energy, epsilon, which must be expressed
in units of joules, and the average concentration or density of energy
, epsilon/m (i.e, absorbed dose), which is expressed in units of Gy. W
ith any cellular system, ag., in tissue culture, one can easily adjust
the numbers of cells used at each dose point so that a clearly signif
icant number of radiation-induced quantal responses (e.g., mutations,
chromosome aberrations, malignant transformations, cell death), in the
absorbed dose range of about 0.7 to 3 or more Gy, can be observed. Ho
wever, if the number of cells is held constant as the absorbed dose is
progressively reduced, a point is reached at which no significant exc
ess is observable. This situation is frequently ''remedied'' by includ
ing more cells at that point, which, of course, can increase the numbe
r of malignant transformations sufficiently to render the excess stati
stically valid. However, because both axes are expressed in relative t
erms, the data point, despite having gained statistical significance,
remains at the same location on the graph. This gives the false impres
sion that no more of the agent energy was added or needed to achieve s
ignificance. However, if both coordinates are put in absolute terms, i
.e., the actual number of quantal responses vs. imparted energy, and t
he same exercise of ''improving the statistics'' at low exposures is a
ttempted, it then becomes evident that any point thus rendered signifi
cant must be relocated at a substantially higher energy point on the g
raph. This demonstrates unequivocally the fallacy in the proof of the
'linear hypothesis'' which is based on agent concentration response cu
rves and not agent amount, It shows that the smaller the agent concent
ration (absorbed dose; epsilon/m), the larger the amount of radiation
energy that must be added to the system in order to demonstrate a radi
ation-induced response. This suggests a minimum average energy require
ment for production of a radiation-attributable cancer. It is conclude
d that the 'linear hypothesis'' should be abandoned as the cornerstone
of radiation protection and practice.