My preprint “*Interacting quantum field theories as relativistic statistical field theories of local beables*” has just appeared on arxiv. Fortunately, even with the few bold claims that I made, I have not been flagged so far by the algorithmic crackpot detector and my paper went through without difficulty. As I had emphasized in the previous post, for once it is a work I am very proud of. I do not know if every single detail will hold closer scrutiny, but at least I am confident that the main message is correct and should be of interest to people working in quantum foundations (on the pure theory and phenomenology sides).

Last week, I had the pleasure to be visiting Lajos Diosi in Budapest. We made some progress on the semi-classical gravity front and on the quantum feedback front which will probably materialize in the form of preprints in the not so distant future. It was a great but tiring trip: discussing physics non-stop, from dawn to dusk, is really mind wrecking.

As an aside, I went from Munich to Budapest and back in bus (*Flixbus*) and it is a quite smart way to travel. Sure, it’s long, 8h30. But most of the time is productive. The bus had power outlets and excellent wifi and I thus managed to work, answer emails, watch movies. On my way to Budapest, I took the night option and slept almost all the way through, effectively teleporting myself instantly. It is also cheap and does not pollute much, so I would definitely recommend. In France, long distance bus lines have been authorized for only a few years which is why I have only realized this option existed recently. They were previously forbidden to provide SNCF with a monopoly. I think the argument was that a railway is essentially operated at fixed cost and, as a result, it may be optimal to nudge or even force people to use train to reach the point where the cost per passenger drops bellow that of all other means of transportation. This global optimum can be reached for fast lines (TGV) between Paris and big cities (France railway network is a star graph) but it is clearly impossible for two medium sized cities that are far from each other (say, Rennes and Toulouse). In that case, the railway monopoly was arguably harming the mobility of people. I think the situation is now closer to an optimum with two networks: a (mostly) star graph of fast TGV connections with Paris in its center, and a slower but fully connected graph of bus lines between medium sized cities.

Before going to Budapest, I spent two days in Paderborn, invited by Martin Kolb, a probabilist. He has been recently specializing in the study of one of the concepts of stochastic calculus I find the most subtle: *the local time *. It is the time the Brownian motion spends at a given point (typically 0). Of course, it is defined appropriately, as a rescaled limit of the time spent from 0 so that the result is not trivial. This is a concept I had been introduced to during my thesis when I was studying quantum spikes with Michel Bauer and Denis Bernard and I still find its properties quite counter-intuitive and sometimes mysterious ( is a Levy process, so weird stuff happens when switching from real time to local time). Martin showed me interesting results on Brownian motions conditioned through constraints on its local time. The corresponding paper is published in *Annals of Probability* (also on arxiv), and the reader interested in probability theory should have a look.

Now back in Munich and with my long-term work on foundations now packaged in a preprint and online, I hope to work a bit on subjects closer to the main interests of the group. My objective is to understand better tensor network methods in the continuum. The dimension 1 is very simple but has been widely studied already so I would like to attack the 2 dimension case. Brute force generalization of the discrete case is possible but super formal and does not seem to allow to compute anything, but maybe one can be smarter and construct continuous ansatz that have no discrete counterparts. In an unrelated subject and back in foundations, I am also thinking about writing a note on Lorentz invariant noise. It seems to me that there exists no article on what are the properties of Gaussian processes and point processes that have a Lorentz invariant probability distribution. I think I now have a crude classification of what one can get and so it might be helpful to write a short note about it. If anyone can provide existing references about this kind of stuff, a comment would be most helpful.