### Interlude

Kuhn begins his essay The Function of Measurement in Modern Physical Science with a quote from Lord Kelvin

If you cannot measure, your knowledge is meager and unsatisfactoryWhat Kuhn discusses, in his waffly style, is the observation that quantitative progress in physics usually requires first a lot of qualitative wandering in the dark. Moreover, it is often very difficult for proponents of a new idea to present evidence, because empirical data never matches theory exactly, and there are more subjective criteria in determining a best fit, when alternative theories are available, than many scientists would be happy to admit. He argues that all scientists, on all sides, may be considered rational, because they each use a large set of criteria in determining their position. At some times, however, when ideas begin to converge, the subjective differences become more apparent amidst the ocean of converging evidence.

## 6 Comments:

In 1874 the same Lord Kelvin with P.G. Tait published a paper claiming that the speed of light was slowing. Since so many big names have wondered about c over time, one wonders why it is so violently opposed today.

Speaking of convergence of ideas I have good news.

1. Number theoretical braids are indeed analog of Feynman diagrams.

a) The realization that the strands correspond to minima of Higgs potential (auxiliary quantity) led to the realization that number theoretic braids describe also fusion of strands and their decay. I just missed this crucial observation earlier and was frustrated.

b) As a conseqeuence each light-like partonic 3-surface contains generalized braid diagram and functional integral over 3-surfaces corresponds to a sum over

this kind of diagrams.

2. One can however wonder what use one has for a perturbation expansion giving vanishing net result.

a) Radiative correction vanish for quantum critical value of Kahler coupling strength is necessary for number theoretical universality.

b) For finite measurement resolutions (inclusions, Connes tensor product) one expects that the sum reduces only to a finite number of generalized braid diagrams so that one would have connection with QFT cutoff description. The sum is non-vanishing since the vanishing of radiative corrections does not take place term by term.

c) Finite number of terms is number theoretically ok and one obtains non-trivial radiative corrections and their non-vanmishing does not reflect approximate calculation but finite measurement resolution.

d) The hierarchy of Jones inclusions comes in powers of 2 for time scale associated with zero energy state so that p-adic length scale evolution based on primes near powers of 2 emerges.

Rather nice convergence of ideas indeed! The crazy intuition about generalization of braid diagrams was correct!

Measurements rely on some kind of theory about measurement. Quantum measurement theory is usually regarded as an ugly appendix of the real theory involving such awkward and poorly defined notions as measurement resolution and conscious observer. For a real macho physicist consciousness of course belongs to the realm of pseudoscience.

Basic courses of quantum theory hardly mention quantum measurement theory. All that is said that measurement projects into an eigenstate of measured observables. For some funny reason - must reflect kind of zeitgeist- students have decade after decade swallowed all this without realizing that it is just a handy hypothesis cooked up in order to get rid of interpretational problems and to get into calculations.

It would be ironic if quantum measurement theory would be the ugly ducling transforming to a beautiful swan. And if this ugly notion of finite measurement resolution were the key to the understanding of fundamental interactions.

Hi Matti,

your comment on quantum measurement is intriguing. Indeed, there is a logical jump somewhere that I never figured out very well...

But I'm an experimentalist, and an old one at that. And old dogs, as they say, hardly learn any new tricks...

Cheers,

T.

Dear Tommaso,

it is very difficult to learn the new way to see the things. I have been fighting hardly for years to see in the new manner and found that existing formalisms do not help much. Quite a painful trial and error process and no hope of mechanical Feynman rules before everything is understood conceptually (and some analytic genius loses his/her patience with my long explanations and decides to make it ;-).

Each morning has however something new in store (besides the discovery of the errors of yesterday;-) and in the typical overoptimistic mood I declare in this beautiful morning that I really undestand

*how Connes tensor product realizes the notion of finite measurement resolution as a neglect of quantum fluctuations interpreted as addition of zero energy states of shorter time scale to positive/negative energy part of the state.

* how Connes tensor product automatically implies discrete coupling constant evolution in time scales coming as powers of two so that one can also understand p-adic length scale hypothesis stating that p-adic primes near powers of 2 are in a special role.

* how one obtains non-trivial radiative corrections as a sum over maxima of Kahler function labelled by generalized braid diagrams having a structure of Feynman diagrams although radiative corrections vanish for the functional integral around a given maximum by quantum criticality.

For an attempt to explain this coherently see the latest posting at my blog.

Best,

Matti

Hi all. That's great, Matti! It is frustrating knowing how clear everything has to be before the computational tools can be sorted out. And I see Tommaso is showing off his mastery of English, as usual.

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