4 ms·
"Prior to the new work, mathematicians had wondered whether they could get away with approximating infinite-dimensional matrices by using large finite-dimension
by potiuper 7y ago
"Prior to the new work, mathematicians had wondered whether they could get away with approximating infinite-dimensional matrices by using large finite-dimensional ones instead. Now, because the Connes embedding conjecture is false, they know they can’t." Your question is like asking if limits actually exist. It might be answered by first proposing what continuity holds for the quantum system.
- n4r9 7y agoI'm not sure what you mean by "proposing what continuity holds for the quantum system". There are a number of results about how measurements of an individual infinite-dimensional quantum system can be approximated to arbitrary degree by an arbitrarily large finite-dimensional system. This new result seems to suggest that for joint entangled systems there's a "buffer" between measurement results obtained by having arbitrarily many dimensions, and by having infinite dimensions. I was wondering how practical it could be to actually do an experiment and verify that the buffer line is crossed.
- AstralStorm 7y agoThe other version of this is to define or find a problem where the difference is smallest. (we know it's not vanishingly small)
- phkahler 7y agoI think the parents question is whether the real world follows the finite vs infinite model.
- mikorym 7y agoTo me the question has always been: Does infinity exist in nature? Infinitely small things (even infinitely small nothingness) is to me the relevant question as we may have it within our reach. Infinitely large things are more of a perpetual argument that I don't know whether one can argue about physically (although mathematically one could try). To me the difference between QM and relativity is exactly continuity. This is the key question.