[ExI] Deriving The Born Rule

[John Clark]

*I am resending this, the first time it got bounced for some reason. *

On Tue, Jul 21, 2026 at 9:20 AM BillK via extropy-chat <
extropy-chat at lists.extropy.org> wrote:

*> Gemini 3.5 Flash AI Extended Thinking Wrote: This comment is a
> remarkably sharp, well-informed summary of the modern debate in quantum
> foundations. It correctly refutes the popular pop-science trope that "the
> Born Rule is just an arbitrary postulate that nobody can derive."*
>

*Thank you Mr. Gemini. *

> > *Gemini**:* *Gleason’s theorem proves the uniqueness of the Born Rule,
> but it doesn't explain its physical origin.* *It assumes probability from
> the start: Gleason begins by assuming a probability measure exists and acts
> on projection operators. It doesn't answer why deterministic quantum
> evolution should give rise to probability in the first place.*
>

*I did admit that the big mystery is why we need probability at all when
Schrodinger's equation is 100% deterministic, and Gleason says nothing
about that. *


> *> Gemini: Non-contextuality is a heavy assumption:** While
> non-contextuality sounds innocent, theories with hidden variables (like de
> Broglie–Bohm mechanics) explicitly violate Gleason's non-contextuality
> assumption to explain measurement outcomes deterministically.*
>

*Yes but in de Broglie–Bohm pilot wave theory those hidden local variables
can NOT be local. But the primary reason I dislike the pilot wave
interpretation is that it adds needless complications; it** keeps
Schrödinger's equation but adds another very
complicated equation that describes the behavior of something
called a "pilot wave" which has some very unusual properties. The pilot
wave is extremely non-local, it has to take the state of the entire
universe into account in order to know if it should guide an electron
through the right slit or the left slit in an experiment, and influences
can be instantaneous, and distance does not diminish effects. And **the
pilot wave can affect an electron BUT an electron cannot affect the pilot
wave, it can NOT push back. This sort of one-way causation has never been
observed before. *

*And no one has found a pilot wave equation that is compatible
with Special Relativity. *

*At the end of the day all the pilot wave does is provide a little arrow
that points at a particle and says "this is the real particle, ignore all
others", the purpose of all the increased complexity, like adding an
entirely new equation, is to get rid of those universes that pop up
automatically unless additional steps are taken to get rid of them.  T**hat's
is why detractors of pilot wave theory have called it " the
disappearing worlds theory" or "Many Worlds theory in denial".  *


> *> Gemini**:* *Critics (such as Tim Maudlin or Adrian Kent) push back on
> two fronts:*
>
>    1.
>
>    *Timing of uncertainty: Self-locating uncertainty explains ignorance
>    after the split has happened, but decision-making usually happens before
>    the measurement.*
>
> *I don't see the relevant difference between making a decision before a
split happened, and making a decision before you know that a split has
happened.  Subjectively the two things are identical, and explaining our
subjective experience is what this is all about.*


> *> Gemini: Hidden assumptions. **To get the exact ∣ψ∣2 weighting—rather
> than, say, assigning equal probability to every branch regardless of
> weight—the Epistemic Separability Principle must be invoked. Critics
> contend that ESP secretly smuggles in the mathematical structure of the
> Born measure under the guise of an "intuitive symmetry."*
>

*Assigning equal probability to every branch regardless of weight would be
equivalent to just counting branches to determine the probability of you
seeing something, but it's easy to show that won't work. Suppose you're
about to measure the spin of a previously unmeasured electron in the
vertical direction, "you" know there is a 50% chance "you" will see spin up
and a 50% chance "you" will see spin down, and the world splits into 2, and
counting branches seems to work. BUT before "you" did any measurement "you"
decided that if "you" got spin down then "you" would do nothing but if
"you" got spin up then "you" would wait one hour and then measure that same
electron in the horizontal direction. In that case "you" would know there
is a 50% chance "you "would see spin left and a 50% chance "you" would see
spin right.*

*So now there are 3 branches on the spin up branch but only 1 on the spin
down branch. So if "you" used branch counting then "you" would have to
conclude that in the first original measurement there was now only a 25%
probability of seeing spin down not 50% as there was one hour ago. BUT it
makes no sense that a measurement made in another world that "you" could
never see could have affected the probability of a measurement that
occurred in "your" universe an hour ago!*

*That's why the analogy I use to think about it is measuring the thickness
of a world as determined by the amplitude of the wave function (or
alternatively measuring the weight). Some worlds are thicker than others
(that's why they're more probable) but the total thickness of all the
worlds added up never changes.*

*Another way I think about it is that even though the universe splits
because there is a difference, sometimes that difference is so small it
does not make a noticeable impact in my conscious experience; for example I
never realized that a particular butterfly in Brazil flapped its wings
three times instead of twice. *

*> Gemini: The critical nuance: *The Deutsch-Wallace proof is widely
> considered one of the most rigorous derivations available, but it stands or
> falls on its rationality axioms—specifically *Branching Indifference*: Branching
> Indifference posits that an agent should not care if a branch splits into
> two identical sub-branches, provided the total weight (∣ψ∣2) remains
> unchanged.*The Catch:* Is Branching Indifference a neutral requirement of
> pure logic, or is it a tailored physical assumption designed specifically
> to yield the Born Rule? Skeptics argue that defining "rationality" in a way
> that respects wave function amplitudes already commits you to the Born Rule
> from the start.
>
*I think "rationality" means using the best way to achieve what you want to
achieve, in this case to win a bet. Suppose somehow I knew for a fact that
Everett style universe branching did occur, would I then expect it be
possible to make exact predictions even at the sub microscopic quantum
scale? No I would not expect that!  And if it turned out it was possible
then that would be a profound mystery that I didn't have even a hint of an
idea how to explain.  *

*John K Clark*
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