Taking a break from the vicissitudes of trying to find evidence of
discrete self-similar order in exoplanet systems, which is a much more difficult
problem than I initially expected, I went to the library and chanced
to find the latest issue of Publications of the Astronomical Society
of the Pacific.
Therein, Fu et al have a paper [PASP, 121, 251-259, March 2009] on the
SX Phoenicis star DY Pegasi, and it struck me that this star might
have the right qualities for a possible test the discrete fractal physics of Discrete Scale Relativity. Below are the results of the test.
DY Pegasi has a mass of about 1.45 solar masses, and a high amplitude
radial oscillation frequency of about 13.713 cycles/day, or about
1.587 x 10^-4 sec^-1.
Discrete Scale Relativity predicts that one can identify a discrete
self-similar analogue on the Atomic Scale and test this by predicting
its oscillation frequency uniquely.
In DSR, 1 stellar mass unit (SMU), a scaled analogue to atomic mass
units (amu), is equal to 0.145 solar masses. Therefore 1.45 solar
masses corresponds to 10 SMU, and DSR predicts that we are dealing
with an analogue to a 10 amu atom, with the most likely candidate
being a Boron atom.
Given the P(n) = nP(0) relation that is known to apply to atoms, DSR
can be invoked to predict that the most likely value for n, given the
oscillation frequency of DY Pegasi and the scaling rules of DSR, is
n
= 4.
Since the oscillation of DY Pegasi is a fundamental radial
oscillation, DSR predicts that
l ~ 0.
DSR predicts that if you divide the 13.713 d^-1 frequency of DY Pegasi
by 5.2 x 10^17, in order to scale it to the Atomic Scale, and
carefully convert the frequency into a wavenumber, you get
2752.869
cm^-1 and this should be the corresponding wavenumber of the discrete
self-similar Atomic Scale transition frequency.
So, we have a simple test: if you go to your Atomic Data Tables and
look up Boron will you find a likely self-similar analogue to the DY
Pegasi oscillation frequency? Luckily Boron is a fairly simple atom
with a 1s^2 2s^2 nl spectrum.
(1) Do we find a transition with a wavenumber of about 2752 cm^-1?
We
do! We find a transition with a wavenumber of 2776.826 cm^-1, which
agrees at the 99.13% level. Note that ambient EM fields, temperatures,
pressures, etc. can shift the Stellar Scale periods and unfortunately
we cannot take stars into the lab to control these influences.
(2) Is the uniquely identified transition primarily an low l
transition?
Yes! It is a p [l=1] to s [l=0] transition.
(3) Is the uniquely indentified transition associated with n = 4?
Yes! The uniquely identified transition is a 1s^2 2s^2
4p to 1s^2 2s^2
4s transition.
(4) Do any other Boron transitions match our requirements?
No! No
other transition provides an acceptable quantitative/qualitative fit.
So I suppose one could just say that by coincidence I just happened to
notice a particular Stellar Scale system and it just happened that by
coincidence it's properties matched up remarkably well with a uniquely
indentified Atomic Scale analogue. But I would suggest that there is a
simpler and more likely explanation, albeit one that implies that
nature has a mighty big surprise in store for us: nature has a discrete fractal organization with
discrete Scales [i.e., subhierarchies like the Atomic Scale and the Stellar Scale]
that are exactly self-similar to one another, as described by
Discrete Scale Relativity.
Yours in science,
Robert L. Oldershaw
www.amherst.edu/~rloldershaw http://independent.academia.edu/RobertLOldershaw