(3/3) Its true that its a bit cumbersome mathematically to prove that both formalisms are equivalent (i.e. give the same mathematical predictions), but that's not relevant for its actual use.
(2/3) My only minor comment is that our real-number formalism is arguably not more cumbersome than the conventional complex-number formulation. Although I myself thought it was at 1st too, so I can't blame Sabine for thinking the same thing.
(1/3) If you've missed Sabine's @skdh recent take before the holidays on my co-authored work w/ Timothee Hoffreumon on why Quantum Theory doesn't need complex numbers, here it is www.youtube.com/watch?v=OPer... I think it's quite accurate (both our work and that of the Germans).
A t-shirt that reads "I have a proof for P not equal to NP, but it's hard to verify"
Nice surprise in the mail: just got a cool new t-shirt from the @simonsinstitute.bsky.social!
We added that the issue is unfortunately even deeper in our opinion.
Just to add: they both also asked us (Tim & I) if we think your observations are correct: we said we agreed with your analysis & think it raises a good point & while we realised it (due to it following readily from McKague et al paper), it seemed not to be widely realized by the community.
Here is the link: scirate.com/arxiv/2504.0... Thanks for pointing it out.
However, we showed that there is another representation of the tensor product which does work, thus leading to consistency with the postulates.
This was thought impossible, because it doesn't work for the Kronecker-product representation of the tensor product, which leads to nonlocal representations, which is inconsistent with the postulates.
quantamagazine.org/physicists-tak… Quanta covers our work scirate.com/arxiv/2504.028��& that of the German team's showing that quantum theory doesn't need complex numbers. In addition to the discussion here, we show that quantum theory based on real numbers is consistent with the postulates!
Dear Craig, just like we pointed out to you that your results follow readily from the McKague et al paper in our email correspondence, we also told the Quanta author Dan and later brought it up with a fact-checking Quanta editor (Anna Schier), but they never changed a thing.
This is useful. Now following the list. I'd appreciate it if I could be added too :-)
I used to be more active on twitter (now X) but a lot of scientists left so not many people to interact with now. If a lot of scientists were here, I'd be more active here
Yes, was nice! But why do I have such an awkward pose... 😶🌫️
