There is a difference between a future that is "determined but nonexistent" and a future that "exists." In the latter case for example, the Geroch quote applies, but not in the former.
I don't know anything about "infinite time histories," so I can't comment there :-)
You need the settings that go with the outcomes (not the settings a nanosecond before or after), so both pieces of information are "there" in the future together.
If information about the future measurement settings exists at the emission event where and when the particles are emitted, then the future exists. If the future exists, no thing is moving in spacetime, no information is "being sent" anywhere. Here is a good quote from Geroch:
Therefore, the...
We wrote an entire book arguing for adynamical explanation over dynamical explanation ("Beyond the Dynamical Universe," Oxford UP, 2018) and I have written many Insights along those lines. However, I think the easiest way to view adynamical constraint-based explanation is via "principle"...
Ken is the editor of a special issue of Entropy “Quantum Theory and Causation”:
https://www.mdpi.com/journal/entropy/special_issues/causation
I think the reason retrocausality hasn’t gained more converts is that it doesn’t get you a classical ontology as hoped. Here is a paper in that special...
Foundations is not viewed favorably within the physics community as a whole. Quantum computing/information (QI) was only granted its own section heading for the APS March Meeting three years ago. Foundations of physics is included in QI for presentations at the APS Meeting. The plenary talks for...
There are many experiments in foundations of physics. I have two explained in these Insights: https://www.physicsforums.com/insights/weak-values-part-1-asking-photons/
https://www.physicsforums.com/insights/weak-values-part-2-quantum-cheshire-cat-experiment/
This Insight references one by...
It's clear something we cherish has to go (free will or causality or locality or realism or objectivity, etc.), since QM works. So, each interpretation is based on a property of Nature the author can live without :-)
Physics has largely accepted that SR is a principle theory, as you note. We're trying to build on that fact by suggesting it's time to accept QM as a principle theory as well. In fact, they're both based on the same principle. That's the point, but this discussion is not relevant to the OP, so...
The point of the addendum to my post about principle explanation is in response to ’t Hooft’s complaint that QM only gives averages. He thinks that fact entails that something is missing from QM. Our paper shows that average-only conservation is necessarily the best the conservation principle...