U-238 spacings and Zeta function zeroes?

[houlahound]

I read some old unpublished student notes where the student in an undergrad project was looking at general patterns in QM results.

Seemed arbitrary to claim anything but the student did show that spacings in EV between transitions in U238 followed the same general form of zero spacings in the Zeta function. There was no attempt to look at other nucleus or explain why.
Assuming the student work is correct is there a research field that would cover this or is anyone aware of this particular match between energy spacings in nucleus and the spacing of zeroes in the Zeta function?

 

[hilbert2]

I've seen several fringe theories that try to fit some data into a simple mathematical formula, for example the Heim theory "formulae" for the masses of elementary particles. If someone examines the spectral data of all atoms for which it's available and then tries to fit all of them one at a time into a large number of mathematical rules, it's likely that they will eventually find something that seems to be a good fit but is actually a random occurrence with no physical significance.

https://en.wikipedia.org/wiki/Correlation_does_not_imply_causation

 

[houlahound]

Yeah I was dubious on those grounds. The paper/report seem to be a primer to justify further research...reeks a bit of numerology under the pretence of physics.

Pretty neat just the same it matches with Zeta zeroes. whole thing sounds cool and spooky, prolly why I hung onto it from years ago. I guess I can clear that space out now.

One interesting thing I did get out of it was a series called;

"The Thue-Morse Series".

Seems a cool set of numbers, in the process if googling it. Hope its legit.

ETA; ya, seems legit, not sure what a s[n] function is tho;

https://www.google.com.au/amp/m.wikihow.com/Generate-the-Thue-Morse-Sequence?amp=1

 

[hilbert2]

Some people may try to assign some kind of mystical significance to the zeta function, mostly because the related Riemann hypothesis is so difficult to prove. Some mathematical physicists have tried to approach the problem by attempting to construct a quantum operator that has a spectrum that consists of the imaginary parts of the zeta function zeroes, but that probably doesn't have much to do with uranium.

There are some strange coincidences related to physical constants, such as that found by Dirac , which may have some actual unknown meaning, but it takes quite a lot of statistical intuition to see what coincidences are important and which ones aren't.

 

[houlahound]

I can see the appeal, makes for great chatter at a cocktail party...how much productive physics is involved I don't know.

Makes me question what all the hoopla is about re global patterns in complex systems yadyada.

Thanks for link, be an interesting read I am hoping.

 

[Vanadium 50]

but the student did show that spacings in EV between transitions in U238 followed the same general form of zero spacings in the Zeta function.

I'm looking at both now, and they don't look anything like each other.

 

[houlahound]

I reread the report, it is a bit misleading. It took spacing between peaks and plotted them in bins 9eV wide and showed the frequency of how many peaks were in the 9 EV bins. ie;

0-9 2
9-18 8
18-27 7
27-36 5
36-45 3

The Zeta function is shoe horned into the text via results from a paper by Montgomery in the 70's the reference cited as;

Barry Copra, Prime formula Weds Number Theory and Quantum Physics, Science vol 274, 20 December 1996 pp 2014-2015.

I don't have access to this paper. the student claims the freeman Dyson said

"Freeman Dyson saw Montgomery's work ...zeroes of the Zeta function behaved like the solutions that physicists were using to calculate energy levels in large nuclei..."

paraphrased for brevity.

The more I read the report the more I don't like it. Not worth the time. I wouldn't mind reading the Montgomery paper tho but it is only indirectly referenced via above source.