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.
Bell’s Inequality: The End of Local Realism
Bell’s theorem focuses on Local Realism. This is the combination of two intuitive ideas:
Locality: No physical influence can travel faster than the speed of light.
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 > | 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:
Particles do have definite positions and properties (Realism).
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?"
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John K Clark