Original post at superposer.substack.com/p/no-classic...

Thanks! I've updated my post. I think we're both saying the same thing in different ways, but I don't think locality is the issue here, because classical fields can't mediate entanglement even if they're non-local.

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I think there are several differences but indeed the non linearity is due to this back reaction and feedback. There are observable consequences eg share.google/dmi6mVvwkdCA...

And visa versa, both systems act and react to each other. This follows from two of the axioms.

Crucially, the quantum state remains pure at all time, conditioned on the classical trajectory. No decoherence! One world, not many. Both systems trace a single definite (but unpredictable) path through their configuration spaces. 5/5

Now here's the remarkable part: we just apply standard classical probability theory to the classical system.
Using a change of measure (standard tool from finance/probability), and the Born rule ( |ψ|²)emerges automatically. No measurement postulate needed. No many worlds. 4/5

A natural candidate for the classical system? Spacetime itself. Quantum field theory appears to require a classical spacetime to be well defined. E.g. we demand [φ(x),φ(y)]=0 for spacelike separated points. But "spacelike" presupposes a definite causal structure—a classical spacetime metric.
3/5

Joint work with Isaac Layton and Zachary Weller-Davies.

We propose a few simple axioms:
- A classical system exists.
- Quantum systems evolve linearly.
- Their interaction may be stochastic.
- The interaction depends on the current quantum state.
- No preferred basis.
2/5

Renyi divergences emerge when agents bet (or "invest" as some people call it), over a finite number of rounds. In the limit of an infinite number of bets we recover the Kelly Criterion, given in terms of Relative entropy distances (KL divergences). Such a fun project! 4/4

And it allows us to extend gambling into other settings (like thermodynamics) and into the quantum domain where we use it to quantify what it means for competing agents to know more in a quantum world. 3/

scirate.com/arxiv/2510.08418 and scirate.com/arxiv/2510.0... with Renato Renner, Takahiro Sagawa, and Philippe Faist. We find a risk–reward trade-off governed by Rényi divergences. The resource theory framework unifies gambling, utility theory, and hypothesis testing. 2/