NO OTHERNESS

Abstract

A resolution of the measurement problem is crucial not only for quantum mechanics but also for practical applications in technology such as quantum computing and quantum cryptography. We present here a framework that explains the transition from quantum states to classical outcomes.

Introduction 

The measurement problem is a longstanding issue in quantum mechanics, especially regarding the collapse of the wave function upon measurement. This paper develops a comprehensive solution that encompasses two famous paradoxes: Schrödinger’s Cat and Wigner’s Friend. We illustrate how environmental interactions and information processing cause the seeming collapse of the wave function.

Understanding the Problem

1. Quantum Superposition and Collapse

— Superposition: A quantum system can exist in multiple states at once, represented by a wave function. This leads to phenomena that defy classical intuition. For example, a particle can be in multiple locations at once until measured.

— Collapse: Measurement appears to cause the wave function to collapse to a single eigenstate, yielding a definite outcome. This is often viewed as a fundamental change, but the apparent collapse through decoherence is an appearance without a physical mechanism.

2. Issues

— Physical Mechanism: What is the physical process that causes the wave function to seemingly collapse upon measurement?

— Nature of Reality: What is the ontological status of a quantum system before observation, and how does it transition to a classical state?

Quantum Decoherence

— Understanding Decoherence: Decoherence is the process through which interactions with the environment cause quantum superpositions to lose their coherence. This leads to the formation of classical mixtures of states rather than pure superpositions. 

— Environmental Interactions: When a quantum system interacts with its environment, the superposition states become entangled with environmental degrees of freedom, causing the loss of coherence among the superposed states.

— Effective Collapse: Decoherence explains the wave function’s apparent collapse, while conserving the unitary evolution governed by the Schrödinger Equation. Instead of an actual physical collision, we observe a transition from quantum behavior to classical-like behavior because of the overwhelming influence of the environment.

Implications

— Classical Outcomes: Decoherence explains why we observe definite outcomes in experiments, despite the underlying quantum descriptions remaining coherent.

— Measurement as Decoherence: The act of measurement itself can be framed as a form of decoherence. As it engages the system with the environment, measurement creates classical outcomes.

Information Theory and Measurement

— Information Gain: Measurement pertains to the acquisition of information about a quantum system, which reduces the system’s entropy and offers insights into its state post-measurement.

— Thermodynamic Cost: Landauer’s principle posits that erasing information incurs a minimum thermodynamic cost. The energy consumption during measurement reflects this.

— Entropy Change: The entropy before measurement is high because of  uncertainty in the system’s state. Post-measurement, entropy decreases as the system transitions to a definite state, embodying the information gained.

— Information Theory Framework: Quantum information theory provides a framework for showing how information is processed during measurement and its effects on a system’s state and entropy.

Resolution 

— Decoherence as Collapse: Decoherence serves as a physical explanation for the effective collapse of the wave function, describing how quantum superpositions appear to collapse into classical states without an actual mechanism for collapse.

— Role of the Environment: Recognizing the environment’s role yields a practical explanation for the classical behavior observed in macroscopic systems.

— Measurement and Entropy: The entropy change associated with measurement closely aligns with information theory principles. Measurement reduces uncertainty about a system’s state, leading to a decrease in entropy.

— Thermodynamic Costs: The thermodynamic costs associated with measurement reinforce the connection between information and entropy, showing the energetic nature of information gain during quantum measurements.

— Insights: Quantum information theory contributes to the analysis of how measurements and entanglement influence a system’s state and entropy. Entanglement with the environment, followed by decoherence, provides a robust explanation for the classical outcomes that emerge from measurement processes.

Wigner’s Friend Paradox

This scenario, conceived by physicist Eugene Wigner in 1961, posits that a friend of Wigner’s conducts a measurement on a quantum system in a sealed laboratory and observes a definite outcome. According to quantum mechanics, the friend’s measurement entangles the system with the lab environment. However, from Wigner’s perspective, this presents a paradox. While his friend inside the lab observes a definite outcome, Wigner remains unaware of the measurement and according to his description the quantum system should still be in a superposition of states.

Wigner’s relative lack of information explains the paradox. His friend’s measurement entangles the quantum system with the environment, leading to a classical outcome that Wigner will not observe until he measures the system himself.

Schrödinger’s Cat Paradox

Schrödinger’s Cat Paradox is a thought experiment proposed by physicist Erwin Schrödinger in 1935. In it, a cat is placed in a sealed box with a radioactive atom, a Geiger counter, a hammer, and a vial of poison. The decay of the radioactive atom is random and triggers the Geiger counter, which in turn releases the hammer to break the vial of poison, potentially killing the cat. Until the box is opened and the cat is observed, does it exist in a superposition of both alive and dead states?

The cat’s fate—alive or dead—becomes entangled with the behavior of the radioactive atom. Decoherence prevents the realization of this superposition at a macroscopic level, as environmental interactions disrupt the coherence necessary for the superposition to persist. This results in a classical mixture of outcomes that align with our everyday experiences.

Empirical Validation

The framework in this paper has strong empirical support from a range of experimental findings and technological advances.

1. Cavity Quantum Electrodynamics: Studies involving coherent interactions between light fields and trapped atoms have shown that environmental interactions lead to decoherence. Experiments in controlled environments, such as those by Haroche and Kleppner, have demonstrated that superpositions can rapidly lose coherence after coupling with external fields.

2. Quantum Dots and Photonic Systems: Experiments with quantum dots have confirmed the principle of decoherence, where the interference patterns observed in quantum dot systems degrade because of their interactions with the environment.

3. Quantum Key Distribution (QKD): The implementation of QKD protocols, such as BB84, demonstrates how quantum measurements can be viewed through the lens of information theory. Experiments in QKD have shown how information gain during measurement directly correlates with securing communication channels against eavesdropping, reflecting the connection between information processing and entropy reduction.

4. Quantum Erasure Experiments: By manipulating which-path information, researchers have demonstrated that entangled photons can exhibit interference patterns contingent on the availability of data. This shows that measurement is a process of information gain and entropy reduction, and it depicts the pivotal role of the observer.

5. Thermodynamic Measurements: Empirical studies have confirmed Landauer’s Principle, as teams have measured the minimal energy dissipation involved during information erasure in computational systems. This illustrates the thermodynamic implications of measurement.

6. Quantum Error Correction: The development of quantum error correction codes, such as Shor’s and Steane’s, illustrates how understanding decoherence and measurement permits the design of robust quantum systems that mitigate errors.

7. Quantum Sensors: These exploit principles of superposition and entanglement to achieve unprecedented sensitivity in measurements. The effects of decoherence and information gain are critical in such applications.

Conclusion

Decoherence explains the effective collapse of the wave function, driven by environmental interactions. Information theory describes the role of measurement in a system while incurring thermodynamic costs, reflecting fundamental principles of information processing. Quantum information theory further illustrates how measurements and entanglement influence a system’s state and entropy, reinforcing this resolution’s broader context.

Measurement not only reveals the state of a system but also fundamentally alters it by reducing the entropy associated with uncertainty. Information gain is connected to thermodynamic principles, with each observation incurring both physical and informational costs.

Philosophically, the resolution of the measurement problem encourages a broad inquiry into the nature of reality and the role of observation in it.

References

– Zurek, W. H. (2003). Decoherence, Einselection, and the Quantum Origins of the Classical. Reviews of Modern Physics, 75(3), 715-775. doi:10.1103/RevModPhys.75.715
– Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.
— Landauer, R. (1961). Irreversibility and Heat Generation in the Computing Process. IBM Journal of Research and Development, 5(3), 183-191. doi:10.1147/rd.53.0183
– Wigner, E. P. (1961). The Problem of Measurement. In Quantum Theory and Measurement (pp. 169-190). Princeton University Press.
– Schrödinger, E. (1935). Die gegenwärtige Situation in der Quantenmechanik.Naturwissenschaften, 23(48), 807-812. doi:10.1007/BF01491891
– Haroche, S., & Kleppner, D. (2005). A Trapped Atom as a Quantum Bit. Physics Today, 58(11), 26-31. doi:10.1063/1.2131256
– Bennett, C. H., & Brassard, G. (1984). Quantum Cryptography: Public Key Distribution and Coin Tossing. Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, 175-179.
– Scully, M. O., & Drühl, K. (1982). Quantum Eraser: A Proposed Photon Correlation Experiment Concerning Observation and “Delayed Choice”. Physical Review Letters, 65(22), 2201-2204. doi:10.1103/PhysRevLett.65.2201
– Toyabe, S., et al. (2010). Experimental Demonstration of Information-to-Work Conversion and Thermodynamic Cost in the Measurement Process. Nature Physics, 6(2), 188-192. doi:10.1038/nphys1740
– Shor, P. W. (1995). Scheme for Reducing Decoherence in a Quantum Computer. Physical Review A, 52(4), R2493-R2496. doi:10.1103/PhysRevA.52.R2493