Visualization as a Tool for

Scientific Understanding

Henk W. de RegtLorentz Fellow, NIAS 2009-2010

Faculty of Philosophy, VU University Amsterdam

Lorentz Workshop Understanding and the Aims of Science

Leiden, 4 June 2010

Schrödinger on Heisenberg

“I naturally knew about his theory, but was discouraged, if not repelled, by what appeared to me as very difficult methods of transcendental algebra, and by the lack of Anschaulichkeit.”

Heisenberg on Schrödinger

“The more I think of the physical part of Schrödinger’s theory, the more abominable I find it. What Schrödinger writes about Anschaulichkeit makes scarcely any sense, in other words I think it is crap.”

Outline

1. Introduction

2. The loss of visualizability in atomic physics

3. The debate about Anschaulichkeit

4. A theory of scientific understanding

Classical physics and Anschaulichkeit

C.F. von Weiszäcker (1979):

“Physicists identify anschaulich with ‘classical’ because classical physics describes all physical phenomena as states of quantities in three-dimensional, Euclidean space and as changes of these states in one-dimensional, objective time.”

Bohr’s atomic model (1913)

A partially visualizable, semi-classical model:– discrete electron orbits visualizable– ‘quantum jumps’ non-visualizable

The waning of visualizability

• Wave-particle duality– of light (Einstein 1905) and matter (De Broglie

1923)– no unambiguous visualization

• Reality of electron orbits disputed– Pauli’s fourth quantum number (1924)– atoms completely non-visualizable

Two new quantum theories

• Heisenberg’s matrix mechanics (1925)– only relations between observable quantities– no (visualizable) model of atomic structure

• Schrödinger’s wave mechanics (1926)– atomic structure is complex wave phenomenon– no quantum jumps; no wave-particle duality– a promise of visualization

Visualizing Schrödinger’s atom

Schrödinger on Anschaulichkeit

“The aim of atomic research is to fit our empirical knowledge concerning it into our other thinking. All of this other thinking, so far as it concerns the outer world, is active in space and time.”

“We cannot really alter our manner of thinking in space and time, and what we cannot comprehend within it we cannot understand at all.”

The epistemic power of visualization

Examples:

• Wave mechanics yielded many more applications than matrix mechanics.

• Electron spin (Goudsmit and Uhlenbeck, 1925): visualizing Pauli’s fourth quantum number.

• After WW II: Feynman diagrams

Electron spin

Wolfgang Pauli

(1900-1958)

Pauli on Anschaulichkeit

“We should not want to clap the atoms into the chains of our preconceptions […] but we must on the contrary adjust our ideas to experience.”

“Even though the demand […] for Anschaulichkeit is partly legitimate and healthy, still this demand should never count in physics as an argument for the retention of fixed conceptual systems. Once the new conceptual systems are settled, then also these will be anschaulich.”

Heisenberg’s 1927 paper: Über den anschaulichen Inhalt der quanten-

theoretischen Kinematik und Mechanik

• Reinterpretation of Anschaulichkeit

“We believe we understand [anschaulich zu Verstehen] a physical theory when we can see its qualitative experimental consequences in all simple cases and when at the same time we have checked that the application of the theory never contains inner contradictions”

• Uncertainty relations: Δp.Δq ≥ ½(h/2π)

Outcome of the debate

• Schrödinger’s attempted visualization of atomic structure failed

• Heisenberg admitted visualizable concepts

• Result: new ‘quantum mechanics’ that combined both theories

Conclusions of case study

• Visualizability problematic in quantum domain can’t be a necessary condition for intelligibility.

• But visualization remained a useful tool for understanding, even in the quantum era.

The epistemic significance of intelligibility

• Thesis: intelligibility is epistemically significant.

• Intelligibility = pragmatic understanding of theory, ability to work with the theory.

• Explanations (understanding of phenomena) require intelligible theories.

Explanation and pragmatic understanding

• Deductive-nomological (Hempel)– Example: flying jets– Deductive reasoning requires skill

• Model-based (Cartwright)– No deduction, but tinkering (approximation,

idealization)– Skills and judgment needed

Intelligibility

Positive value that scientists attribute to the cluster of theoretical qualities that facilitate use of the theory– No intrinsic property, but related to skills

context-dependent

– Examples of valued qualities: visualizability, causality, unifying power, simplicity, etc.

A possible test for intelligibility (esp. physical science)

A scientific theory is intelligible for scientists if they can recognize qualitatively its characteristic consequences without performing exact calculations.

Conclusion: understanding as a means and an end

• Epistemic aim of science: explanations that provide understanding of phenomena.

• Understanding phenomena requires understanding theories – intelligibility!

• Intelligibility: not a matter of ‘feeling good’ about a theory, but of being able to use it.

If you want more:

H.W. de Regt, S. Leonelli & K. Eigner (eds), Scientific Understanding: Philosophical Perspectives. University of Pittsburgh Press, 2009.

H.W. de Regt & D. Dieks, ‘A contextual approach to scientific understanding’, Synthese 144 (2005) 137-170.

H.W. de Regt, ‘Making sense of understanding’, Philosophy of Science 71 (2004) 98-109.