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:  

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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.

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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.

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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."

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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.

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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.

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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.

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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?"

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John K Clark

[Stuart LaForge]

On 2026-03-23 07:23, John Clark via extropy-chat wrote:
> 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:
>
> ===
>

> 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.
>

> -------------------------

Well that is what the wavefunction is, isn't it? A hidden signal that
coordinates particle properties in a definable pattern? I would imagine
that quantum states from multiple systems that become entangled with one
another during decoherence would share some global or universal hidden
variable; a distinct master phase shift, for example, that could
distinguish one Everett branch from another in a well-ordered manner.

>
> LEGGETT’S INEQUALITY: THE ATTACK ON REALISM

>
> 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.

Yes, the effect is even more pronounced and "unrealistic" when 3 or more
particles are entangled together. Take the Greenberger–Horne–Zeilinger
(GHZ) triplet state. If we prepare a set of three particles using a
Gerlach-Sterns device to be in a GHZ-state with all their spins aligned
in the same z-orientation, then the three particles displays the
following spin correlations when all are measured in the x orientation
or when one is measured in the x-orientation and the other two are
measured in the y-orientation:

{Ax}{Bx}{Cx} = -1
{Ax}{By}{Cy} = +1
{Ay}{Bx}{Cy} = +1
{Ay}{By}{Cx} = +1

Here Ax is the spin of particle A in the x-direction and can be +1 for
spin up and -1 for spin down. Similarly for the other variables. In
experiments, the products of their spins always follows the given
pattern as predicted by QM. The four equations above are true.

Now let's assume reality in the sense that the spins of particles A, B,
and C in the x and y-directions are "real" and fixed in a definite state
of spin up or spin down before they are measured.

If you pay close attention to those equations, then you will notice that
there is no way to pre-assign spin states to A, B, C in the X and Y
directions to make all three equations true at the same time.

For example, let's say that you preassign A, B, and C to spin down in
the x-direction leading to the first of the only two possible scenarios.
Substituting -1 in for Ax, Bx, and Cx yields:

{-1}{-1}{-1} = -1 for the first equation and for the rest we get
{-1}{By}{Cy} = +1
{Ay}{-1}{Cy} = +1
{Ay}{By}{-1} = +1

Dividing all the equations by -1 on both sides yields:
{-1}{-1} = +1
{By}{Cy} = -1
{Ay}{Cy} = -1
{Ay}{By} = -1



Here you can clearly see that the spins of all three particles in the
y-direction must be simultaneously be different (opposites) from one
another, but that is not possible when you only have the two states of
up or down to choose from. You can't have three numbers that are all
inverses of one another without two of them being the same number. This
contradicts out starting premise all three spins were down in
x-direction.

So what about the second possible scenario with two of A, B, and C being
spin up in the x-direction and only one of them being spin down in x.

{-1}{+1}{+1} = -1
{-1}{By}{Cy} = +1
{Ay}{+1}{Cy} = +1
{Ay}{By}{+1} = +1

Dividing out the factor {+1} as redundant gives

{-1}{+1} = -1
{-1}{By}{Cy} = +1
{Ay}{Cy} = +1
{Ay}{By} = +1

So now we divide both sides of equation 2 by {-1} to yield
{-1}{+1} = -1
{By}{Cy} = -1
{Ay}{Cy} = +1
{Ay}{By} = +1

And we can clearly see that the spins {By} and {Cy} must be different
from one another, but simultaneously the same as the spin {Ay}. Another
contradiction.

One can see that by symmetry arguments, it would not matter which
particle A, B, or C was the one that started out spin down in the
x-direction, each and every time, a contradiction is reached.

Therefore the assumption of the spins of particles having a real value
prior to measurement is proven false by contradiction.

Q.E.D.

Stuart LaForge