[[Mod. note -- Conservation of energy implies that the luminosity L of
the source (units of power, i.e., energy per unit time) must equal the
total power a surface S which completely surrounds the source. And in
the absence of absorbers, this must be true for *any* such surface S.
So... on laboratory scales (where spacetime is *very* well approximated
as being flat), if we consider a surface S which is a sphere of radius
r centered on the source, then clearly the average power crossing S is
just L / (4*pi*r^2).
Can anyone refute this hypothesis? I find it very
> troubling that I myself can't!
In the time since I made this original post I have been able to
determine that I can make a simple proof of the inverse cube law and I
can not make a rigorous proof, nor find same for the inverse square
I have of course found many graphical illustrations that show that
spherical surfaces increase with the the square of the radius but of
course spherical volumes do not.
I recently went looking for experimental evidence that confirms the
square law relation and found this;
"I think the reason why the peak lux measurements do not follow the
inverse square law..."
"So, what can we learn from this exercise? Mainly, peak lux readings
for bright lights cannot be trusted at close distances. In this
example, only readings taken from greater than or equal to 3 meters
actually follow the inverse square relationship closely. If I had used
lights with larger reflectors, then I have no doubt that readings
taken at 3 meters would also fail to follow the inverse square
relation. Larger reflectors require measurements to be taken at
How much of a difference did it really make deleting the first few
points? Well, honestly not a lot. If I average the calculated peak lux
values for all of the points I end up with 112,228 lux whereas if I
only include the data from 3 to 6 meters I end up with 117,039 lux. If
I followed the convention of only measuring at 5 meters I would have
gotten a result of 121,500. This shows how averaging multiple readings
reduces error that can occur in any one measurement, especially for
bright lights at close distances."
(My comment)This last bit demonstrates that the use of the inverse
square law in this experiment overstates the source luminescence the
greater that actual distance.
I also found;
titled, "Inverse Square Law Experiment_2.txt"
"To measure and confirm the inverse square law fall off of l"
This experimental set up is better than the first example, however, in
the data analysis instructions it states, "Analysis of data: Plot the
data as a scatter plot in Excel with no line connecting the data, and
change the scale on both axis to log so it will be a log-log plot."
If the relation is k/h*h then the plot should be log / linear and not
log log. Using log log equates the square of the distance and the
inverse square of the lux. Which I believe will reduce to the fourth
rout of the proper distance. But I can only say for certain that this
method of analysis does not seem correct to me.
a deeply disturbed,