### Time Machine

Although it caused quite a stir in the press and on the blogosphere, I didn't take much notice of the Time Machine paper until today, when I realised it was written by Irina Aref'eva and Volovich, who happen to work on p-adic strings and the quantization of the Riemann zeta function. Ultimately, they are simply speculating about new kinds of objects, related to classical causality violation, that may be visible at the LHC, and the catchy title is simply a gimmick without which it is difficult these days to get papers posted on the arxiv.

In this paper, the authors discuss some pretty hairy mathematics, in the physicist's characteristic shockingly hand-wavy manner. To quote:

By the spectrum they are referring to their analysis, inspired by the non trivial zeroes of the Riemann zeta function, which correspond to $m^{2}$ values in Klein-Gordon operators. In other words, the zeta function is defined not on numbers, but as a pseudodifferential operator. The Hypothesis says that the zeta field is given by a sum of such Klein-Gordon Lagrangians.

Note that in M Theory, we prefer to replace $\Lambda$ with the heirarchy of Planck scales, but this idea is basically present in their work.

In this paper, the authors discuss some pretty hairy mathematics, in the physicist's characteristic shockingly hand-wavy manner. To quote:

[this lends] additional support to the proposal that the Beilinson conjectures on the values of L-functions of motives can be interpreted as dealing with the cosmological constant problem ... in section 6 we shall discuss an approach of how to use a Galois group and quantum L-functions instead of SUSY to improve the spectrum.

By the spectrum they are referring to their analysis, inspired by the non trivial zeroes of the Riemann zeta function, which correspond to $m^{2}$ values in Klein-Gordon operators. In other words, the zeta function is defined not on numbers, but as a pseudodifferential operator. The Hypothesis says that the zeta field is given by a sum of such Klein-Gordon Lagrangians.

Note that in M Theory, we prefer to replace $\Lambda$ with the heirarchy of Planck scales, but this idea is basically present in their work.

## 2 Comments:

Irina Arefeva happens to be familiar to me too. She invited me to two conferences around 1990+epsilon held in Soviet Union, first in Shotshi, second in Kazan in honour of Lobatchevksi's bi-centennial.

At the time of Kazan conference Soviet Union was breaking down and the the return travel was a real adventure for a person who did not even understand Russian.

There was a lot of interest in TGD at that time: probably because it had become clear that super string model does not work and M-theory had not emerged as believed-to-be saviour. During the time of the Kazan conference the Empire in Finland however stroke back and I got the reputation of a crackpot. The second visible main character (there was also at least one invisible one) behind the dirty operation had visited in Kazan and I was told that he had done a lot of blackmailing.

Oh dear, Matti! (I am indeed fortunate to live in a geographically isolated country.) Perhaps now is the time to renew your acquaintance with Aref'eva.

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