Sunday, August 7, 2011

Causality: a footnote on temporal abnormalities

[continued from this]

I bracket off this sub-subtopic from the main trunk, since it differs in that it seems to lack a scientific or a moral dimension, but rather plays with paradox  in a sandbox of its own making.  Accordingly, parting momentarily from my usual Victorian-gentleman courtliness, I shall treat of these subtopics in a rollicking spirit of satire and abuse.
(Thus, to begin: for "sandbox", read:  kitty-litter box.)

(1)  Michael Dummett,  in “Can an Effect Precede its Cause?” (1954) calls causality into question, not in the sort of detailed empirical way that quantum or chaos theorists did, but in the sort of I-wonder-do-I-actually-have-hands style of philosophers.  He begins:

On the ordinary Humean view of cause, a cause is simply a sufficient condition:  it is merely that we have observed that, whenever A happens, B follows. 

I think he means “follows” in a logical or empirical, rather than a temporal sense; though if so, then, given the context, it’s an unfortunate choice of words.  Anyhow, he goes on:

But obviously we can also observe that an event of a certain kind  is a sufficient condition for an event of another kind; and why should we not then call the later event the ‘cause’ of the earlier?

Aristotle actually did go some ways towards covering the case, with his notion of ‘final cause’ (Τέλος -- basically, purpose conceived as one of several types of enabling conditions);  but that seems not to be what Dummett has in mind;  in any case the matter of ‘final cause’ is not addressed.

Why should we lay down temporal precedence as a defining property of a cause?

Why indeed, so long as we are doubting the existence of our own hands. -- Somehow I am reminded of such other latitudinarian grand gestures as “Why, after all should marriage be defined as between a woman and a man -- rather than, say, between a gentleman-pig and a baby boy?”  -- To both these questions, we reply as did Mr. Bingly, to the question whether it would not be more rational for balls to feature conversation to the exclusion of dancing: "Much more rational, but much less like a ball."   -- Or, less delphically:    Whenever you meet an integer that is an even prime, you will invariably discover that that same integer is twice unity;  and vice versa.  These are invariable concomitants, but we don’t call the one the cause of the other.  And why not?   Because that is just not the way we talk, and if you stretch the term to cover such cases, you have modified the language, nay the very ‘speech community’, much as you have done when two grooms exchange rings.

Finally he settles down with:

Causes are simultaneous with their immediate effects, but precede their remote effects.

In other words:  “Never mind.”

(2)  Cosmology itself is not exempt from what can be considered a causal paradox, ever since Gödel discovered temporal-loop solutions to the equations of general relativity.  Now, Gödel himself (one of the heroes of this blog) did not draw any meretricious philosophical or televisable conclusions from this calculational oddity;  he just said, “Tiens!  A loop solution to the Einstein equations,” and went back to his real work.
The reason I resist including this case among the more substantive, is that, whenever time itself is held to differ either topologically or algebraically from a directed linear segment, it would seem you have worse problems on your hands than niceties of causality -- as though worrying whether falling into a black hole might muss your hair.   The point at which physics-porn purveyors start jabbering of time-travel and wondering whether we might just jolly pop round and strangle our infant great-grandfather in the crib, is the point at which I bail, and go read something more level-headed and believable, like Father Brown or the Gospels.

Anyhow, let’s listen in on a passage from a distinguished contemporary mathematician, Roger Penrose (in The Road to Reality, 2004).  We learn that “the null cones are more fundamental than the metric;  in particular, they determine the causality properties of spacetime.”  Then (p.  408):

The null-cone structure defined by this [metric] g  specifies E’s [Einsteinian spacetime] causality structure, must as was the case for Minkowski space.  Locally, the differences are slight, but things can get decidedly more elaborate when we examine the global causality structure of a complicated Einsteinian spacetime.  An extreme situation arises when we have … causality violation, in which ‘closed timelike curves’ can occur, and it becomes possible for a signal to be sent from some event into the past …!

Disturbing, doubtless.  Still, don’t lie awake worrying about it.

(3)  There also exists a proposal for backwards-causation that does not depend on any hypothetical cosmological exotica, put forward by two quite celebrated physicists:  Wheeler and Feynman’s “Classical Electrodynamics in Terms of Direct Interparticle Action” (1949) -- “direct”, that is, as opposed to the usual retarded forces of electrodynamics.  Mario Bunge (Causality 1963) comments thus:
The chain of action and reaction can be completed so as to satisfy functionalism, if advanced forces are introduced alongside retarded ones.  Such advanced forces behave in a ‘premonitory’ way … they represent the action of a still unborn future on the present.

In the face of such dizzying ideas, I can only retreat to my simple peasant faith.

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