On Thursday, November 13, 2014 3:20:45 PM UTC-5, Craig Markwardt wrote:
On Sunday, November 9, 2014 4:32:54 AM UTC-5, Robert L. Oldershaw wrote:
Here is how I compare the predicted and observed total masses.

2.6134 - 2.61 divided by 2.61 times 100 = 0.34 relative error.

100 - 0.34 = 99.66% relative agreement.

This is not a fair comparison. I will create a scenario to see why. In
my scenario the measured mass is 145.0725 +/- 0.0001 solar masses. By
your argument, there would be 99.95% agreement with quantization.
Eureka, right? And yet, the quoted mass is exactly between 1000x and
1001x multiple of 0.145, i.e. exact counter-evidence for quantization!
Using the error bars, there is a 725 sigma exclusion of quantization
based on reported errors in the scenario. By dividing by a large
number (2.61 Msun), you artificially created "agreement" with your
hypothesis. I did the same thing in my fictitious scenario.


A measured mass of 145.0725 +/- 0.0001 is highly unrealistic. Such
narrow error bars on such a large stellar mass are hard to imagine. At
the relevant lower masses my method is able to identify general
agreement with predictions and disagreement with predictions.

The correct comparison is use the reported error bars, in which case
one finds that for J1906+0746, quantization at 0.145 Msun is excluded
with essentially 100% statistical confidence.


The measured mass for J1906+0746 has error bars that give the
precision of the measurement assuming all theoretical modeling,
observations and assumptions are perfect, and that there are no
unknown unknowns.

In terms of the actual mass of J1906+0746, I would think an accuracy
of +/- 0.01 solar mass is a reasonable uncertainty to hope for at
present.

Given the accumulation of a large enough sample of accurately measured
total masses for actual binary star systems, I maintain that my method
is capable of determining whether or not there is a preference for the
predicted peaks and an avoidance of the inter-peak gaps. Then one of
us will have to change his thinking on this and more fundamental
issues.

Also, would you prefer that I not divide by 2.61 and instead just say
the error is 0.0034 solar mass?

[Mod. note: reformatted -- mjh]