[ExI] Many Worlds, realism and Leggett's Inequality

[John Clark]

*I asked Gemini to explain what the experimentally derived fact that
Leggett's inequality is violated tells us that Bell's Inequality does not ,
and what implications that has on the Many Worlds interpretation of quantum
mechanics. This is what he she or it said:  *

===

While Bell's inequality was the "first blow" to our classical understanding
of the world, Leggett's inequality is often seen as the one that finished
the job. If Bell's violation told us that the universe isn't both local and
realistic, Leggett's violation suggests that realism itself is the problem,
even if you’re willing to give up locality.

To understand the difference, we have to look at what each inequality was
trying to protect.
------------------------------
Bell’s Inequality: The End of Local Realism

Bell’s theorem focuses on *Local Realism*. This is the combination of two
intuitive ideas:

   1.

   *Locality:* No physical influence can travel faster than the speed of
   light.
   2.

   *Realism:* Objects have definite properties (like position or spin) even
   when we aren't looking at them.

When experiments showed that Bell's inequality is violated, it proved that *at
least one* of these must be false. Most physicists opted to ditch locality,
leading to the acceptance of "quantum non-locality" (entanglement). However,
this left the door open for "non-local realism"—the idea that particles *do*
have definite properties, but they are coordinated by some instantaneous,
hidden signal.

------------------------------
Leggett’s Inequality: The Attack on Realism

In 2003, physicist Anthony Leggett formulated a new inequality that
targeted a specific class of *non-local hidden variable theories*. These
theories concede that the universe is non-local but insist that particles
still possess well-defined individual properties (like a specific
polarization) before they are measured.

The violation of Leggett’s inequality (first observed experimentally in
2007) tells us something much more radical:

   -

   *It isn't just about speed:* Even if we allow for "spooky action at a
   distance" (non-locality), we still cannot explain the experimental results
   if we assume that particles have definite, pre-existing states.
   -

   *The "Death of Realism":* It suggests that the measurement doesn't just
   *reveal* a property; it actually helps *create* it. The idea of a
   "substance" with inherent characteristics independent of the observer
   becomes mathematically untenable in these frameworks.

Comparing the Two
Feature Bell's Inequality Leggett's Inequality
*Target Theory* Local Realism Non-local Realism (certain types)
*Core Assumption* Nothing travels > c Particles have definite states
*Violation Means...* The world is either non-local, non-realist, or both. Even
if the world is non-local, it is likely still non-realist.
*Philosophical Impact* Shook our view of space/time. Shook our view of
"objective reality."
--

Bell told us that the world is "weird" because things far apart can be
linked. Leggett told us that the world is "weird" because the things
themselves don't even have a set "identity" until we interact with them. It
pushes us toward the conclusion that the quantum wave function isn't just a
lack of knowledge on our part—it is a complete description of a reality
that is fundamentally fuzzy.

The violation of Leggett’s inequality is often viewed as a "victory" for
the *Many-Worlds Interpretation (MWI)*, primarily because it eliminates one
of MWI's biggest rivals: *Non-Local Realism* (most notably, Pilot Wave
theory or Bohmian Mechanics).

To see how MWI digests this, we have to look at how it redefines what
"real" actually means.
------------------------------
1. MWI Rejects "Outcome Realism"

Leggett’s inequality targets theories where particles have a definite
"identity" or state (like a specific polarization) before they are measured.

In MWI, a particle *does not have a single definite state*. Instead, the
particle exists as a superposition of all possible states. When a
measurement occurs, the observer becomes entangled with the particle, and
the universe "branches."

   -

   In one branch, you see State A.
   -

   In another branch, you see State B.

Because MWI never claims that a particle has one "real" hidden value to
begin with, the violation of Leggett’s inequality doesn't bother it. In
fact, MWI predicts this violation exactly because it treats the
wavefunction as the only fundamental reality.
2. Wavefunction Realism vs. Particle Realism

The "Realism" that Leggett’s inequality kills is *Particle Realism*—the
idea that individual bits of matter have fixed properties.

MWI replaces this with *Wavefunction Realism*.

   -

   *The Particle:* Is not "real" in the classical sense (it has no fixed
   properties).
   -

   *The Universal Wavefunction:* Is the only thing that is truly real. It
   evolves deterministically and locally according to the Schrödinger equation.

By shifting the definition of reality from the "result of the experiment"
to the "mathematical wave," MWI sidesteps the constraints of Leggett’s
inequality entirely.
------------------------------
3. The Blow to Pilot Wave Theory (Bohmian Mechanics)

This is where the impact is most felt. Before Leggett, many physicists who
disliked the "fuzziness" of the Copenhagen interpretation moved toward *Bohmian
Mechanics*. This theory argued:

   1.

   Particles *do* have definite positions and properties (Realism).
   2.

   They are guided by a "non-local" pilot wave that reacts instantly across
   space (Non-locality).

Leggett’s violation proves that even if you have a non-local pilot wave,
you *still* can't give particles definite properties and match experimental
results. This forces Pilot Wave theorists to make their models increasingly
complex or "conspiring" to avoid contradiction. For MWI supporters, this is
proof that trying to keep "classical realism" alive is a lost cause.
Summary of Impact
*Concept* *Impact of Leggett's Violation*
*Local Realism* Already dead (Bell).
*Non-Local Realism* Effectively "on life support." Very difficult to
maintain.
*Many-Worlds* *Supported.* MWI thrives in a world where "definite
properties" don't exist until decoherence/branching occurs.
*Locality* MWI claims to restore locality (no information actually travels
$c$) by explaining entanglement as a local divergence of branches.
------------------------------
The Philosophical Shift

For MWI, Leggett's violation is a confirmation that *information is more
fundamental than matter.* If particles don't have inherent properties, then
the universe is essentially a massive, unfolding calculation of
probabilities rather than a collection of "things."

It moves the conversation away from "How does this particle get its
properties?" to "How does the observer become part of the quantum system?"

=============================

*John K Clark*
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