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