Schroedinger's principle eliminates the EPR-locality paradox

This paper argues that by applying a principle derived from Schrödinger's 1935 work and assuming wave-packet collapse, the EPR-locality paradox is resolved within the Copenhagen interpretation, even for simple entangled spin states and despite objections regarding the locality of spin measurements.

The Gist

The Big Picture: Solving a 90-Year-Old Mystery

Imagine a famous puzzle that physicists have been arguing about for nearly a century. It's called the EPR paradox (named after Einstein, Podolsky, and Rosen). The puzzle asks: How can two particles, separated by vast distances, instantly "know" what the other one is doing?

Einstein thought this was impossible because it seemed to violate the rule that nothing can travel faster than light. He called it "spooky action at a distance."

This paper, written by Walter F. Wreszinski, argues that the puzzle isn't actually a paradox at all. The author claims that the solution was actually hidden in plain sight in a paper written by Erwin Schrödinger (the same guy who had the famous cat) back in 1935. The paper suggests that if we look at the rules of quantum mechanics correctly, the "spookiness" disappears.

The Setup: The "Magic Coin" Game

To understand the problem, imagine a game with two people, Alice and Bob, who are standing on opposite sides of the world.

1. The Setup: A third person, Charlie, creates a special pair of "magic coins." These aren't normal coins; they are entangled. This means they are linked in a way that they don't have a definite "Heads" or "Tails" until someone looks at them.
2. The Separation: Charlie sends one coin to Alice and the other to Bob.
3. The Measurement: Alice flips her coin and sees "Heads."
4. The Paradox: Because the coins were linked, the moment Alice sees "Heads," she instantly knows Bob's coin must be "Tails."

The Problem: If Bob is on the other side of the galaxy, how did Alice's coin "tell" Bob's coin to flip to "Tails" instantly? That would require a signal traveling faster than light, which physics says is impossible.

The Author's Solution: Schrödinger's Principle

The author says the confusion comes from how we describe the coins. We tend to think of Alice's coin as one object and Bob's coin as another object.

The paper introduces Schrödinger's Principle, which says:

Once two things interact and become entangled, they stop being two separate things. Even if you pull them apart by miles, they remain one single object described by one single "wave function" (a mathematical description of their state).

The Analogy: The Single Suitcase
Imagine Alice and Bob each have half of a single, giant suitcase.

• The Old (Wrong) Way of Thinking: You think Alice has her own suitcase and Bob has his own. When Alice opens hers, she magically sends a message to Bob's suitcase to change its contents. This feels like magic and breaks the speed-of-light rule.
• Schrödinger's Way: There was never two suitcases. There was only one suitcase that was cut in half. Alice holds the left half, and Bob holds the right half. They are still part of the same object.

When Alice opens her half and sees "Heads," she isn't sending a message to Bob. She is simply discovering the state of the whole suitcase. Since the suitcase is one object, finding out what's on one side instantly tells you what's on the other side, no matter how far apart the halves are. No signal had to travel; the information was always there in the single object.

The Two Rules That Make It Work

The author argues that this solution relies on two specific rules of quantum mechanics:

1. The Speed Limit (Lieb-Robinson Bound): The paper mentions that in the real world, information cannot travel infinitely fast. There is a "group velocity" (a speed limit for signals). The paradox only seems to exist if you ignore this speed limit.
2. The "Collapse" (The Snap): The paper assumes that when a measurement happens, the "wave function" collapses.
   • Before the flip: The system is a fuzzy mix of possibilities (Heads/Tails and Tails/Heads).
   • After the flip: The moment Alice looks, the whole system "snaps" into a definite state.
   • The Result: Alice doesn't learn anything new about Bob's coin that required a signal. She simply learns the state of the entire system she is part of. She realizes, "Ah, the whole system is now in the state where I am Heads and Bob is Tails."

Why This Matters

The author claims that for decades, people thought Schrödinger's explanation was vague or incomplete. This paper says, "No, it was actually complete."

The author is essentially saying:

• We don't need to invent new physics to solve the EPR paradox.
• We just need to stop thinking of entangled particles as two separate friends sending text messages to each other.
• Instead, we must treat them as a single entity that happens to be stretched out over a large distance.

Summary

The paper claims that the "EPR-locality paradox" (the idea that quantum mechanics allows faster-than-light communication) is an illusion caused by a misunderstanding of how entangled systems work. By applying Schrödinger's Principle—which treats separated entangled particles as a single, indivisible system—the paradox vanishes. Alice's measurement doesn't send a signal to Bob; it simply reveals the state of the single system they both share.

Technical Summary

Technical Summary: Schrödinger's Principle and the EPR-Locality Paradox

Problem Statement
The paper addresses the status of the Einstein-Podolsky-Rosen (EPR) locality paradox within the Copenhagen interpretation of quantum mechanics. While the centenary of Schrödinger's 1926 papers prompts a re-examination of quantum axioms, the author notes that the EPR paradox—specifically regarding nonlocal measurements of entangled states like spin components or photon polarizations—often appears unresolved or vague in standard treatments. The core issue is the apparent contradiction where an observer (Alice) measuring one part of an entangled system seems to instantaneously deduce the state of a distant observer (Bob), potentially violating the finite group velocity ($v_g$) constraints imposed by the Lieb-Robinson bound, which limits the speed of information propagation in quantum systems.

Methodology
The author employs a rigorous axiomatic approach based on the Wigner-Dirac formulation of quantum mechanics, focusing on systems with a finite number of degrees of freedom (specifically, two spin-1/2 particles). The methodology relies on:

1. Algebraic Framework: Defining states as positive, normed linear functionals on observable algebras ($A(\Lambda)$) and distinguishing between separable (product) states and entangled states (specifically Bell states like $\Psi_{B,-}$).
2. Dynamical Constraints: Utilizing the Lieb-Robinson bound to establish a finite group velocity ($v_g$) for correlations in quantum spin systems, ensuring that physical effects decay exponentially outside a light-cone defined by $|x| < v_g |t|$.
3. Schrödinger's Principle: The paper isolates and formalizes a specific principle implicitly contained in Schrödinger's 1935 paper [Schr35]. This principle asserts that once two physical systems interact and form an entangled state, they can no longer be described by individual wave functions, even after they are completely separated.
4. Collapse Assumption: The analysis assumes that any measurement results in the instantaneous collapse of the wave-packet.

Key Contributions and Results
The paper's primary contribution is the demonstration that the EPR-locality paradox is "well-posed" but ultimately dissolved within the Copenhagen interpretation when Schrödinger's principle is explicitly invoked alongside the wave-packet collapse.

• Formalization of the Paradox: The author proves the paradox is well-posed under two assumptions: (1) measurements occur in finite time $T$, and (2) wave-packet collapse occurs at the moment of measurement. Under these conditions, a contradiction arises between the instantaneous deduction of Bob's state by Alice and the finite propagation speed ($v_g$) dictated by the Lieb-Robinson bound.
• Resolution via Schrödinger's Principle: The paper argues that the paradox disappears because Schrödinger's principle dictates that the entangled pair constitutes a single, indivisible physical system. When Alice measures her spin (e.g., finding it "up"), the collapse of the global wave function $\Psi_{B,-}$ to a product state (e.g., $|-\rangle_1 \otimes |+\rangle_2$) is a global event.
• Elimination of "New Information": Consequently, Alice does not acquire "new information" about Bob's distant particle that violates the finite group velocity. Instead, she learns the state of the entire two-spin system. The correlation is not a signal traveling from Bob to Alice; it is a consequence of the pre-existing entangled structure of the single system. The apparent nonlocality is thus a feature of the system's description, not a violation of relativistic causality or the Lieb-Robinson bound.

Significance and Claims
The paper claims a modest but precise objective: to complete the steps in Schrödinger's original analysis that were previously left implicit. The author asserts that:

• The solution to the EPR-locality paradox was already present in Schrödinger's 1935 work but has been obscured by a lack of explicit formulation in the simplest contexts (two spins).
• The "vague" impression of Schrödinger's approach is corrected by rigorously defining his observation of entanglement as a fundamental principle governing the formation of tensor products.
• This resolution is consistent with, and equivalent to, recent probabilistic interpretations (such as those by Griffiths) and algebraic approaches (Haag, Fewster, and Verch), but achieves the result using the standard Wigner-Dirac framework of states and observables without requiring new probabilistic axioms.
• The work emphasizes that the core issues of quantum nonlocality arise even in finite-dimensional systems governed solely by the superposition principle and tensor product construction, without needing the complexities of infinite quantum field theories.