Following an article by John von Neumann on infinite tensor products [1], we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of  representations,  stops  working  when  countable  infinities  of  particles  (or  degrees  of freedom)  are  encountered.  This  is  because  the  dimension  of  the  corresponding  Hilbert space  becomes  uncountably  infinite,  leading  to  the  loss  of  unitary  equivalence,  and  to sectorisation.  By  interpreting  physically  this  mathematical  fact  [2],  we  show  that  it provides a natural way to describe the “Heisenberg cut”, as well as a unified mathematical model  including  both  quantum  and  classical  physics,  appearing  as  required incommensurable facets in the description of nature [3].
 
 [1] J. von Neumann, “On infinite direct products”, Compositio Mathematica 6, 1-77 (1939).    
http://www.numdam.org/item?id=CM_1939__6__1_0
[2] M. Van Den Bossche and P. Grangier, “Contextual unification of classical and quantum physics”, Found.
Phys. 53:45 (2023) [arXiv:2209.01463].
[3] M. Van Den Bossche and P. Grangier, “Revisiting Quantum Contextuality in an Algebraic Framework”,
https://arxiv.org/abs/2304.07757

Coffee and pastries will be served at 11:00 in the hall.