In his article Must Evidence Underdetermine Theory? John D. Norton attempts to refute a certain version of the underdetermination thesis. He attacks the idea that all evidence necessarily underdetermines any scientific theory. In the first part of this paper, I want to call into question part of his argument in some general terms and then focus on a particular case of possible underdetermination, namely Quantum mechanics (QM) and Bohmian mechanics (BM), in order to strengthen my criticism of Norton. Norton himself does not take sides in the debate over the question whether or not QM and BM are essentially the same theory, but says the possibility that they are cannot be ruled out. I will show that Norton, both in his general argument as well as in his judgment in the ‘QM/BM case’, takes a certain notion of theory for granted that his opponents would not agree with. In addition, I will investigate further consequences resulting from his position. This part makes up the bulk of my paper. In a second part I attempt to refute Norton on his own grounds. That is, on the basis of his idea of what a theory is, I will show that one can preclude the possibility that QM and BM are the same theory. To be clear: This paper is not a defense of the underdetermination thesis, but rather a critique of Norton’s attack.
Table of Contents
1 Introduction
2 Norton’s line of argument and my criticism thereof
3 QM and BM. What they share and what they don’t
3.1 Empirical content
3.2 Ontology
3.3 Mathematical Structure
3.4 (Non)locality
3.5 QM and BM – the same theory?
4 QM and BM as physically different theories
5 Conclusion
Objectives and Topics
This paper critically examines John D. Norton’s argument against the underdetermination thesis, specifically focusing on his comparison of Quantum Mechanics (QM) and Bohmian Mechanics (BM). The author aims to demonstrate that Norton’s claim regarding the potential equivalence of these theories is flawed because it relies on a specific, narrow notion of theory that disregards essential ontological differences and fails to account for physical distinctions observable through computational complexity theory.
- Critique of John D. Norton’s "Must Evidence Underdetermine Theory?"
- Ontological and mathematical comparison between Quantum Mechanics and Bohmian Mechanics
- Analysis of the underdetermination thesis and the role of ontological structure
- Investigation into nonlocality and physical differences between QM and BM
- Application of computational complexity theory to theory differentiation
Excerpt from the book
3.2 Ontology
In QM electrons are not viewed as intrinsically being something. Rather it is stipulated that electrons sometimes behave as if they were waves and sometimes as if they were particles. And sometimes – this is what makes QM appear to be so mysterious – they behave in a new mode that is not comparable with anything we know. When the electron behaves like that, it is said to be in a superposition. This is how the double slit experiment is explained in QM: The difference between the sum of the curves one gets when first opening only hole 1 and then only hole 2 and the curve we get when both holes are open is explained by the electron being in a superposition in the latter case. The wave function in QM is not a physical entity, but merely a mathematical description of the state of the electron. In contrast, in BM the electron is always a particle with a definite position. All other properties, such as the spin properties, are contextual. Hence, the way that a property is measured determines whether or not a system possesses that property. Spin properties in BM are mathematical properties of the wave function. The wave function itself represents a physical entity that guides the motion of the electron. The surprising results of the double slit experiment are accounted for by the inference of those waves: While each electron passes through only one hole, their trajectories are guided by a wave that passed through both holes. From this short overview of the different ontologies of QM and BM, it should have become clear that they are fundamentally different.
Summary of Chapters
1 Introduction: Provides an overview of the paper's critical focus on John D. Norton's arguments regarding the underdetermination thesis and introduces the comparison between QM and BM.
2 Norton’s line of argument and my criticism thereof: Analyzes Norton's view on observationally equivalent theories and challenges his implicit assumption that excludes ontological structure from theory definition.
3 QM and BM. What they share and what they don’t: Examines the similarities and differences between Quantum Mechanics and Bohmian Mechanics, covering empirical content, ontology, mathematical structure, and nonlocality.
3.1 Empirical content: Discusses how both theories make identical predictions for certain experiments, using the double-slit experiment as a primary example.
3.2 Ontology: Contrasts the wave-function-based description in QM with the particle-based, definite-position ontology of BM.
3.3 Mathematical Structure: Explores the deterministic evolution of both theories and how their distinct ontological underpinnings are reflected in their mathematical formalisms.
3.4 (Non)locality: Investigates the different senses of nonlocality present in QM and BM, and whether these could lead to observable differences.
3.5 QM and BM – the same theory?: Argues against the realist interpretation of Norton's position, asserting that QM and BM tell incompatible stories about physical reality.
4 QM and BM as physically different theories: Proposes that using computational complexity theory establishes a physical distinction between the two theories based on their local and nonlocal characteristics.
5 Conclusion: Synthesizes the main arguments to show that the equivalence of QM and BM is difficult to maintain without significant theoretical costs and problematic assumptions.
Keywords
Quantum Mechanics, Bohmian Mechanics, underdetermination thesis, John D. Norton, ontology, empirical content, wave function, nonlocality, physical realism, computational complexity theory, local Hamiltonian, scientific theory, superposition, measurement, epistemology.
Frequently Asked Questions
What is the fundamental goal of this paper?
The paper aims to critique John D. Norton’s argument against the underdetermination thesis by showing that his treatment of Quantum Mechanics and Bohmian Mechanics as potentially equivalent theories is flawed.
What are the central themes of the work?
The central themes include the nature of scientific theories, the role of ontological structure, the debate between realism and instrumentalism, and the potential physical distinguishability of theoretically similar models.
What is the primary research question?
The research explores whether the assertion that QM and BM are equivalent can be sustained, and what consequences follow from accepting or opposing this distinction.
Which scientific methodology is employed?
The author uses a philosophical analysis of theoretical arguments supplemented by an application of computational complexity theory to assess the practical equivalence of physical models.
What is covered in the main section of the paper?
The main section investigates the empirical, ontological, and mathematical facets of QM and BM, specifically looking at how each explains phenomena like the double-slit experiment and nonlocality.
How is the paper structured?
It is divided into two parts: the first critiques Norton’s general philosophical argument and his specific comparison of QM and BM, while the second provides a new argument for their physical difference based on computational resources.
How does the author define the difference between QM and BM regarding the electron?
In QM, the electron is treated via a wave function that does not represent a physical entity, whereas in BM, the electron is a particle with a definite position guided by a physical wave.
What is the relevance of computational complexity in this paper?
The author argues that calculating solutions in a nonlocally characterized theory (BM) is computationally more demanding than in a local one (QM), suggesting a real physical difference in their operations.
Does the author defend the underdetermination thesis?
No, the author explicitly states that the paper is not a defense of the underdetermination thesis, but rather a specific critique of Norton’s attack on it.
What is the "price" the author suggests Norton pays?
The "price" refers to the philosophical costs of Norton's position, such as having to abandon realism regarding theories and accepting the assumption that ontological differences are irrelevant to a theory's validity.
- Quote paper
- Wiebke Schröder (Author), 2011, A Case for Underdetermination: Consequences of Opposing the Distinction between Quantum Mechanics and Bohmian Mechanics, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/211422
