Is there a place for causal reasoning in physics?

1. Is there a place for causal reasoning in physics? Mathias Frisch University of Maryland College Park

2. On the one hand… :Bertrand Russell • "The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm"

3. Russell and the Neo-Russellians • Russell: causal notions play no role in physics and should therefore also be excluded from other domains of discourse. • ‘Neo-Russellians’: • Huw Price: “Causation reflects the distinctive perspective of a creature who takes herself to have the ability to intervene in her environment.” • The source of the causal asymmetry is the temporal orientation of deliberation (deliberationaction) • ‘Neo-Russellian’ arguments for why causal notions could not be part of the scientific image or the detached perspective of physical theorizing. • Bas van Fraassen, Richard Healey, Huw Price, Hartry Field, James Woodward, Chris Hitchcock, Jennan Ismael

4. On the other hand… • David Griffiths: The principle of causality is “the most sacred tenet in all of physics.” (Introduction to Electrodynamics)

5. My plan: • Examine a number of neo-Russellian arguments. • Assert that in order to make progress in addressing the Neo-Russellian’s claim it is crucial to investigate role of putatively causal constraints in actual examples of theorizing: • Two examples of apparently causal reasoning in physics • Remarks about potential metaphysical implications.

6. Preliminary remarks • ‘Well-established theories’: any theory currently on the books. • What methodological place does causal talk occupy? • Integral component of theorizing: causal assumptions as part of the toolbox of physics • Part of informal commentary • Integral component of applied science • Which dimensions/aspects of causal notions play a role in physics? • Determinism • Locality • my focus here: Asymmetry • Connection to causal ‘oomph’?

7. Neo-Russellian arguments “The dynamical laws are expressed by differential equations defined over the universal phase space. They don’t describe local relations between particular events, they have no intrinsic direction, and they have no exceptions. Causes, by contrast, are asymmetric relations between localizable events, e.g., the striking of a match and the appearance of the flame. They depend on background conditions, and they are full of exceptions. The difference between the two notions was so great that Russell famously recommended that we do away with the notion of cause and replace it with that of a dynamical law.” (Jennan Ismael)

8. Neo-Russellian arguments • time-reversal invariance vs. temporal asymmetry. • Precisely defined states vs. vague causal relata. • Complete initial value surfaces vs. cause/background distinction. • (Global models vs. causal systems with outside.)

9. 1. time-reversal invariance • Causal relations are temporally asymmetric. • The physical laws of our well-established theories have the same character in both the forward and backward temporal directions. • Therefore, there is nothing in our well-established theories of physics to ground a temporal asymmetry. • Therefore, there is nothing in our well-established theories of physics to ground causal relations.

10. 1. time-reversal invariance Causal assumptions can’t be part of theory: • Hidden assumption: • Identification of content of a theory with its dynamical laws. • Causal relations cannot be part of the content of physical theory. • But: one can mathematically represent a causal interpretation of a theory by introducing causal structures as additional structure over state space models: • Define a transitive and non-circular partial ordering over the set of states x, y, z∈S: <x, y> • (1) if <x;y> and <y;z> ,then <x;z>, ∀x, y, z∈S (transitivity); • (2) if <x;y> and <y;x> then x = y∀x, y∈S (non-circularity). Compare: causal set approach to quantum gravity. (Sorkin) Epistemologically ‘grounded’: • Causal asymmetry might be inferred from asymmetry in prevailing initial or boundary conditions.

11. 2. Vague causal relata vs. precision of dynamical models • Danger of confusing relations in models with model-world relations: • For both causal and dynamical models • relations within model precise (causal Bayes nets) • model-world relation imprecise/vague. • Woodward: Causal “coarse-grained variables may fail to completely partition the full possibility space from the point of view of an underlying fine-grained micro theory.” • this is true for dynamical models of any but the most fundamental theory as well

12. 3. Distinction ‘causes/background conditions’ cannot be drawn in physics • Distinction merely pragmatic? • A core notion of cause that is purged from pragmatic elements? • But Woodward’s worry (see also Hartry Field): If entire backward light cone is cause, the connection between causation and manipulation is lost: • Consider the following events: • (E) my headache’s going away • (A) my taking aspirin at t, 30 min. before (E) • (W) my wishing at t that headache disappears • (S) my neighbor’s sneezing at t. • Fine-grained specifications (E*), (A*), (W*), and (S*) of the micro states realizing these events.

13. 3. Distinction between causes and background conditions (contd.) • Woodward’s worry: • Since (E*) also depends on (S*), sneezing (S) turns out to be a cause of my headache going away (E). • But we don’t think that manipulating neighbors’ sneezings is an effective strategy for making headaches disappear. • Thus, the connection between manipulation and causation appears lost. • Two interpretations of the worry: • It simply follows from the fact that S* is a cause of E* that S is a cause of E as well. • Once we grant that E* depends on S*, we have to worry about ‘extreme fillings’ for the values of the variables characterizing S* (e.g. neighbor’s shriek!)

14. 3. Distinction between causes and background conditions (contd.) Two replies to Woodward’s worry: • There can be fine-grained causal dependence without coarse-grained dependence: • Interventions on (S*) that affect (E*)butdo not affect (E) • Thus, the relation between intervention and causation is preserved • To the extent that we take extreme fillings to be possible, they offer means of manipulations. • Whether we consider such fillings is a pragmatic issue.

15. 4. ‘Small’ vs. ‘Large’ Worlds • Judea Pearl: “if you wish to include the whole universe in the model, causality disappears because interventions disappear.” • Christopher Hitchcock: “how to find or even understand causation from within the framework of a universal theory is one of the very deep problems of philosophy.”

16. 4. ‘Small’ and ‘Large’ Worlds • Problem arises within interventionist framework: notion of causation intimately linked to that of hypothetical intervention. • But: intervention a formal notion; we can define notion of intervention without appeal to outside: • intervention on the variable X =def remove the structural equation for X from the causal model and replacing it by an equation that fixes the value of X to a non-actual value x. (Pearl)

17. 4. ‘Small’ and ‘Large’ Worlds • Epistemological worry: how to find causal relations? • Begin with ‘small-world’ models of our theories, which by assumption can be interpreted causally • Embed these models into ever larger models. • Causal interpretation will be preserved in embedding model, as long as embedding variables remain within invariance range of the embedded model. • Causal models of suitably fundamental theory have unlimited range of invariance. • Why should causal model disappear at very last step?

18. Causal assumptions at work (I):causal constitutive relations • General framework: a system on which a (generalized) external force/field F is acting. Response function L(t1, t2) links the system’s response B to the force. • Posit most general linear time-translation invariant relation between response and force: dB(t1)=L(t1-t2)F(t2)dt2 • Posit causal constraint: t1>t2

19. Causal constitutive relations • Adding together the influences due to the external field at all times gives: • The response at t is given by the force at all prior times and the causal memory function. • Contrast with anti-causal response function:

20. Causal constitutive relations • One can then derive certain properties of system (such as dispersion relations, or relations for transport coefficients) from causal assumption. • General strategy widely applied: • derivation of dispersion relations in scattering theory • electric circuit theory • fluid dynamics.

21. Causal constitutive relations Denis Evans (ANU) and Debra Searle (Brisbane): “Causality, response theory and the second law of thermodynamics” (Phys. Rev. E 53, 6), discussing the response of a fluid to strain: • Begin by stating: “We live in a universe where cause precedes effect.” • Then show that causal response is overwhelmingly probable to satisfy the second law of thermodynamics; • And that anti-causal response will with overwhelming probability violate the second law! • Conclude: “We have thus shown that there is a deep connection between causality and the second law of thermodynamics.”

22. Causal assumptions at work (II):the radiation asymmetry • The pattern of correlations between fields and sources exhibits a temporal asymmetry: • Field sources, such as oscillating electric charges, are accompanied by coherent radiation fields diverging from the source. • We don’t observe coherent fields converging on a source. • A standard explanation of this asymmetry, given in physics literature: field sources produce or cause field disturbances that propagate away from the charge.

23. Radiation asymmetry: a non-causal explanation? “Suppose that a radio antenna broadcasts into empty space so that the outgoing radio waves travel to spatial infinity. It would seem nearly miraculous if the time reverse of this scenario were realized in the form of anti-broadcast waves coming in from spatial infinity and collapsing on the antenna. The absence of such near miracles might be explained by an improbability in the coordinated behavior of incoming source free radiation from different directions in space. Or it might be explained non-probabilistically by a prohibition against any truly source free incoming radiation.” (John Earman)

24. Radiation asymmetry • But: Earman’s two ‘explanations’ are guilty of a ‘temporal double standard’ (Price): • Why is coordinated behavior of incoming source free radiation from different directions in space improbable but not coordinated outgoing radiation? • Why should there be a prohibition against any truly source free incoming radiation but not against outgoing source free radiation? (i. e. prohibition against radiation that is not centered on past sources, but not against radiation that is not centered on any future sources) • analogy: a gas in a box with a small hole in the box • Possible answer: because of the causal constraint! • Note: dynamical laws are of no help here.

25. Causal Metaphysics? • My claim: Price’s (and Healey’s and van Fraassen’s and Ismael’s) appeal to deliberative asymmetry cannot explain the successful appeal to causal principles in these cases. • But: explanations appealing to causal constraints on their own are metaphysically (almost) neutral: • Exclude only that causal principles are ‘more perspectival’ than other components of scientific image. • Compatible with a metaphysically ‘rich’ notion of causal production (Tim Maudlin?) • Compatible also with a broadly Lewisian picture!

26. A pragmatic, broadly ‘Lewisian’ account of causal constraints • Causal constraints are part of the best system for beings like us. • David Albert’s audience with God: • God could give Albert the complete fundamental laws together with precise initial conditions, but that would take much too long and be too cumbersome. • Instead: God gives him the Maxwell equations plus the causal constraint. • Allow us to know much about the field in presence of charges without detailed knowledge of initial conditions.

27. The End • Thank you!