Re: Gy and Sv = J/kg

[Jack Couch <jgcouc@planetx.bloomu.edu>]

In article  rkathren@tricity.wsu.edu (Ron L. Kathren) writes:
>Sorry to question my old (but not elderly!) mentor Wade Patterson, but I
>note that the dose equivalent quantities as expressed in rem and Sv are not
>necessarily numerically equal to J/kg. The equality only holds for absorbed 
>dose.
<snip>

Louis Iselin:
I must disagree.  Wade has expressed an idea that I have been uncomfortable 
with ever since I was introducted to dosimetry units in Chuck Roessler's 
Radiation Dosimetry class.

In all of science, except for health physics, when a quantity is mulitplied by 
a conversion factor that changes the units, the conversion factor has units of 
its own that tell you how the original quantity will be modified.  Only the Gy 
to Sv conversion is different.  Stupid might be a better description.
<snip>

There are other examples, such as Circumference = 2 pi Radius. Looked 
at dimensionally, one concludes that 6.28 m = 1 m (a mathematical 
absurdity) for a radius of 1 m. Not unlike the way we say 20 J/kg = 1 J/kg 
for a Q of 20 in the familiar H = QD.  

In the first case, we invent the radian to be the (dimensionless) ratio 
of circumference-to-radius for a circle, which is numerically 2 pi. By 
analogy, the dimensionless ratio of H-to-D is the numerical value we assign 
to Q. I don't know why we (I include myself) are uncomfortable with 
H = QD but perfectly at ease with C = 2 pi R. Maybe its because we 
have the word "radian" to cling to. 

David Golnick* offers a nice solution to those (including my students) 
who agonize over this point. He endows Q with the "units" Sv/Gy, which 
is of course dimensionless (like the radian associated with 2 pi). My 
students like multiplying 5 Gy by 20 Sv/Gy to get H = 100 Sv. This 
of course breaks both with tradition and the formal definition of Q, 
where Q carries no units.

*Ref. Basic Radiation Protection Technology, 3rd edition (Pacific 
Radiation Corporation, Altadena, CA, 1994).

This issue was discussed at length through an exchange of letters in the 
HP Newsletter about a decade ago. As I recall, the letters were very 
informative. Maybe someone on the list can cite the references. 

Jack Couch
Bloomsburg University