Understanding and explanation in physics

Dennis Dieks

History and Foundations of Science

Utrecht University

Plan

• Unity or disunity of science?• A confusion: does the question pertain to the

universal (or not) validity of basic scientific theory; or is it about the use of scientific theory?

• Understanding has often to do with our skills in using theory and modeling situations–it is here that plurality reigns. But this does not conflict with the universal nature (and possible universal validity) of the equations of fundamental theory.

Unity versus Disunity

• Unity. The traditional “reductionist” account: at least within physics, higher-level descriptions can be understood on the basis of more fundamental descriptions/theories, by means of some logical relation between them (often involving a limit). On the basic level there is one universal physical theory.

• Disunity. Even within one domain there may be several mutually inconsistent theories (e.g., Feyerabend)

• “Theories are successful where they are successful, and that is that”

• “Nature is governed by different systems of laws not necessarily related to each other in any systematic or uniform way”

• “I suppose this is metaphysical pluralism”

However,…

There is strong inductive evidence for the universality of basic physics (in the sense of universally applicable mathematical equations).

For example, quantum theory “extends its dominion” ever further into territories intuitively thought to be purely classical

• omnipresence—in principle—of superpositions

• (almost-)macroscopic Schrödinger cat states

• atomic systems of few electrons, once cited as important problems for fundamental quantum treatment, have long proved to be very accessible—the ground state of helium can now be calculated to 15 digits

• etcetcetc

what is true is that the relations between theories at different levels

can be complicated, needing case-by-case approaches

• For example, classical mechanics does not automatically follow from QM “in the limit of large quantum numbers”

• Nor does CM automatically follow from ћ0

Moreover: treatment by fundamental laws is not necessarily profitable for all purposes,

even if it is feasible; in particular, subsumption under a mathematical scheme

need not give us understanding of phenomena

The patchwork of descriptions and approximations is to be located in this striving for understanding. This does not reflect a disunity of fundamental

theory; but it shows non-uniqueness of methods of achieving understanding

• If explanation is taken to relate to subsuming phenomena under true laws

• And if understanding is taken to relate to the skill of “seeing through” phenomena in the sense of being able to deal with them successfully by applying some intuitively acceptable conceptual scheme

• Then understanding and explanation are two relatively independent subjects; and understanding rather than explanation is the domain of plurality and disunity.

Understanding

Conceptual toolkitTheory

Phenomenon

One possible tool: causal notions

• Newtonian theory: F=m.a; F= Gm1m2/r2

• History shows that Understanding for many is only achieved if F, the force, is considered the cause of the acceleration, emanating from the central mass, etc.

Fermions repelling each other

• Pauli principle in QM: “Fermions are antisocial and bosons gregarious. There is an effective repulsion between two fermions, called the exchange force, that keeps them spatially separated.”

But, in fact, what is at stake is a symmetry property of the total wave function that is completely unrelated to dynamical considerations; Ψ = √(1/2!) {ψφ - φψ}

Fermions/Bosons

In the (anti-) symmetrical states the average distance between measurement results is less/greater than in a product state:

“Processing” this formal result with causal concepts in some contexts helps physical intuition, by bringing it in line with other, well-known cases. But in other contexts it may well confuse, and it has no fundamental validity.

22 | | | |not symm x

Individuality

In symmetrical states like √(1/2!) {ψ1φ2 + φ1ψ2}each index “gets an equal share” of each one-particle state (here: ψ , φ). The same “state” is assigned to each index, here: W = ½ |ψ><ψ| + ½ |φ><φ|

(“partial tracing”)

Consequently, the indices in the formalism are really unable to represent the different particles we can so easily imagine!

But this no-go result is more often than not ignored

• The conceptual tool of individual particles is applied nevertheless, as if indices corresponded to them

• This leads to an understandable picture in the case of non-overlapping wave packets φ, ψ—and although literally taken false, it leads to the right expectation values and provides a visualizable, intelligible picture

The Visual Quantum Mechanics project, funded by the National Science Foundation, introduces quantum physics to high school and college students who do not have a background in modern physics or higher-level math. To reach these students, the instructional units integrate interactive computer programs and digital multimedia with inexpensive materials and written documents in an activity-based environment.

The Quarks to Quasars Story

Colliding Beams

                                                                        

                                  

Watch the beams of protons and antiprotons collide in the Tevatron and produce a spray of

particles. The Collider and D0 detectors, located where the arrows appear, record the

events.

Particles

• In the case of non-overlapping packets this helps to understand the situation

• But in other cases the discrepancy with the fundamental theory shows itself, and instead of understanding confusion results

Discussions about the fundamental metaphysical status of different “identical quantum particles” that have all physical properties in common (Do they violate Leibniz’s Principle? Do they possess “haecceity”?) miss the point:

These particles do not “live” on the level of fundamental theory, but constitute conceptual “intelligibility” tools, applicable to restricted contexts

conclusions

• There is disunity on the level of scientific understanding

• Nevertheless, there is every reason to assume unity on the level of basic physical theory

• Basic physical theory is formulated mathematically

• Understanding uses conceptual tools like causality and vizualizability, with limited applicability

• It is a category mistake to seek a universal metaphysical status for these intelligibility tools