I hope that some of the folks (Mike, Howard, Patrick, Robin) who have engaged in the other threads [1][2][3] on outcome counting (ie Patrick's APP) see this thread.(adsbygoogle = window.adsbygoogle || []).push({});

Starting with the Feynman path integral formulation of ordinary quantum mechanics, it is pretty straightforward to derive Hamilton's action principle, as discussed in [4][5]. Since Hamilton's principle is equivalent to Newtonian mechanics, we have (with the caveat of msg #8 by abszero in [4]):

QM (FPI) ==> Hamilton's principle <==> Newtonian mechanics

In a perhaps analogous manner, quantum field theory yields an action principle from which we may derive general relativity:

QFT ==> action principle ==> GR

The derivation of GR from QFT is more problematic than the derivation of Newtonian mechanics from standard QM, as pointed out by Physics Monkey in msg #12 in [4].

Note that in both steps, we start outassumingquantum mechanics in one form or another. Now recall that the whole idea of outcome counting is to modify the MWI by replacing the Born rule with an alternate "probability rule," ie one where each branch is equally likely. The immediate question, discussed at length in [1][2][3], is whether it is possible to introduce some further modification so that the Born rule emerges as a valid coarse-grained approximation.

But a second question has occurred to me. Suppose we modify QFT by replacing the Born rule with outcome counting. Can we still derive GR, along the lines of the above prescription?

Now it is not entirely clear to me how, technically speaking, one might modify QFT by assuming outcome counting in place of the Born rule. QFT is just not "built" like that. I mean QFT is not like an automobile, where you can just open up the hood, take out the "Born-rule-erator," and replace it with an "outcome count-erator," like so many spark plugs. But there must be some sort oflogically equivalentmodification that would amount to the same thing. (I'm trying to get up to speed on QFT, so maybe I'll have more to say later.)

Now I have argued in [1][2][3] that outcome counting isontologicallysuperior to the Born rule; indeed, that it might be considered asymmetry principle. But it's really only justified to call it a symmetry principle iff it somehow provesmathematicallysuperior to its alternatives. As I said above, the derivation of GR from QFT is a bit problematic. So this leads to my wondering:if we (somehow) modify QFT via outcome counting, might this remove some of the difficulties inherent to the derivation of GR from QFT?

David

[1] my paper on the born rule

https://www.physicsforums.com/showthread.php?t=95585

[2] are world counts incoherent?

https://www.physicsforums.com/showthread.php?t=101339

[3] attempts to make the Born rule emerge from outcome counting

https://www.physicsforums.com/showthread.php?t=101982

[4] QM and action principles

https://www.physicsforums.com/showthread.php?t=112257

[5] a democracy of spacetimes?

https://www.physicsforums.com/showthread.php?t=112556

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# Outcome counting, the action principle, and GR

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