November 08, 2011

Relativity-12: David Hume and causality

(For previous posts in this series, see here.)

Suppose that the claim that neutrinos can travel faster than light holds up. What are the implications?

As I said earlier in the series, this does not mean that Einstein's theory of relativity is overthrown, since it always allowed for faster than light particles, though we had never observed them. But it does mean that Einstein causality, the idea that if two events are causally connected by a signal that travels from one event to the other, then all observers' clocks will agree that the signal left the source before it arrived at the other end, will have to go.

How hard would it be to keep the theory of relativity but abandon the idea of Einstein causality? It is not impossible. The idea that if A causes B, then A must occur before B is, after all, just another hypothesis subject to empirical testing. As Victor Stenger points out, long before Einstein came along, the whole idea of causality, that we can know that one event causes another, was challenged by philosopher David Hume (1711-1776).

Wikipedia has a nice synopsis of Hume's views on the relationship of the problem of induction to that of causality:

First, Hume ponders the discovery of causal relations, which form the basis for what he refers to as "matters of fact." He argues that causal relations are found not by reason, but by induction. This is because for any cause, multiple effects are conceivable, and the actual effect cannot be determined by reasoning about the cause; instead, one must observe occurrences of the causal relation to discover that it holds. For example, when one thinks of "a billiard ball moving in a straight line toward another," one can conceive that the first ball bounces back with the second ball remaining at rest, the first ball stops and the second ball moves, or the first ball jumps over the second, etc. There is no reason to conclude any of these possibilities over the others. Only through previous observation can it be predicted, inductively, what will actually happen with the balls. In general, it is not necessary that causal relation in the future resemble causal relations in the past, as it is always conceivable otherwise; for Hume, this is because the negation of the claim does not lead to a contradiction.

Next, Hume ponders the justification of induction. If all matters of fact are based on causal relations, and all causal relations are found by induction, then induction must be shown to be valid somehow. He uses the fact that induction assumes a valid connection between the proposition "I have found that such an object has always been attended with such an effect" and the proposition "I foresee that other objects which are in appearance similar will be attended with similar effects." One connects these two propositions not by reason, but by induction. This claim is supported by the same reasoning as that for causal relations above, and by the observation that even rationally inexperienced or inferior people can infer, for example, that touching fire causes pain. Hume challenges other philosophers to come up with a (deductive) reason for the connection. If that the justification of induction cannot be deductive, then it would beg the question for induction to be based on an inductive assumption about a connection. Induction, itself, cannot explain the connection.

In this way, the problem of induction is not only concerned with the uncertainty of conclusions derived by induction, but doubts the very principle through which those uncertain conclusions are derived.

What Hume pointed out is that what we actually observe is always just a sequence of events and just because in the past we have always seen one event preceding another does not mean that it will always do so in the future or that the first event is the cause of the second. The past is not a predictor of the future, something known as the problem of induction. Just because our neighbor has, even since we have known him, picked up the morning paper from his driveway in his bathrobe does not mean that he will do so tomorrow. He may appear in a tuxedo. This is true even for events that we consider to be driven by natural laws. Just because the Sun has come up every day of our lives does not allow us to infer that it will do so tomorrow. Just because when I release my pen it falls and hits the ground, and this happens over and over again, does not allow me to conclude that it will do so the very next time I try it. Because inductive thinking is so appealing, we have developed laws that explain correlated sequential phenomena in terms of cause and effect. But just because such laws are so successful does not mean that we can ignore the fact that causality is merely an inference based on an idea of induction that has not been a priori justified.

Hume argued that our ideas of causality suffer for the same reasons that induction does. Going back to our shooting example, if person A fires a gun and the bullet enters person B and causes B to die, we say that A's actions caused the death of B. But all that we actually observed is that there was a temporal sequence of events in which the gun was fired, and the bullet then traveled and entered B who died and so we impute causality to the process. Our belief in causality is so strong because we have constructed laws that explain those temporal correlations in behavior that enable us to predict that if the first event is repeated, the second will too. So A shooting B in the same way will always result in the death of B. But what Hume says is that we cannot be sure of this. Maybe the next time A shoots at B, the bullet will, like a boomerang, stop half way and go back and hit A.

If we view a film and see a bleeding person lying on the floor and blood flowing back inside him followed by the person standing up and a bullet emerging from his body and going back into a gun held by another person, we would conclude that the film was being run backwards because all these things seem to violate causality. If we looked at the clock readings at the locations of the two events, we would expect to find that the clock reading with the man lying on the floor would be later than the clock reading in which the bullet was in the gun even when the film was run backwards. But can we be sure of this?

Hume's idea that causality is merely an assumption that may not always hold true received support in modern physics when it was found that the basic laws of physics are (almost always) time-reversal invariant. This means laws of physics are such that if one looked at a film showing reactions between elementary particles, one would not be able to deduce whether the film was being run forwards or backwards, because the basic laws of physics do not discriminate between the two. The only exception we have to date that violates this conclusion is the decay of an elementary particle known as the neutral kaon.

Furthermore, modern physics has shown that not every effect need be associated with a cause. For example, the decay of a radioactive nucleus appears to be totally spontaneous and unpredictable. Nothing causes it, it just happens. So if we can have acausal events and cannot even in principle assign a causal connection between two events, then Einstein causality may turn out to be just one of those convenient assumptions that seemed at one time to be self-evidently true but that we now need to outgrow and replace with a more sophisticated way of thinking, just like we grew out of assuming that the Earth was flat or that it was at the center of the universe.

Not that doing so will be easy. Causality, like the belief in free will, is so deeply ingrained on our psyches that abandoning it will be difficult.

Next: Some concluding thoughts


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Ok, this is a little technical and off topic, but are you including time-reversal negating (like magnetic field) as time-reversal invariant? I don't have a strong theoretical background, but I have been given to understand from talks that I have attended that many things break time-reversal symmetry on the microscopic scale.

Posted by Jared A on November 8, 2011 11:16 AM


I think that is incorrect. Time-reversal symmetry used to be considered a universal property until very recently. James Cronin and Val Fitch won the 1980 NObel Prize for their discovery in 1964 of time-reversal symmetry. Until then, there were thought to be no violations.

Theirs is a fascinating story and a Google search will give you lots of interesting stuff about their work.

Posted by Mano on November 8, 2011 02:56 PM

Karl Popper addresses the problem of induction. I think you should do a segment on his solution to the problem.

Posted by Robert Allen on November 8, 2011 03:42 PM


I touched on Popper's role on induction in my series on the logic of science here and did not want to go into it again here.

Posted by Mano on November 8, 2011 04:18 PM

Mano, just curious—how would you respond to the argument that acausal events, possibly augmented by chaotic/nonlinear effects, could provide an avenue for divine intervention?

Posted by Paul Jarc on November 10, 2011 01:27 PM

Thanks for the reference, Mano, I will look into Cronin and Fitch's work sometime.

By the way, the talks I am referring to are on topological insulators, which is rapidly growing thing in condensed matter physics as I bet you already know.

Even in the wikipedia article they talk about "local perturbations that break the time reversal symmetry". It must be shorthand for something else.

Posted by Jared A on November 10, 2011 02:31 PM


Even acausal events like radioactive decay follow statistical laws, so they are not idiosyncratic. And chaotic systems are deterministic in that the same initial conditions lead to the same outcomes.

Diving intervention is presumably not subject to any laws.

Posted by Mano on November 10, 2011 02:39 PM


I understand now what you were referring to.

When you look at macroscopic systems, there can be a directionality to time, even though the fundamental laws of science as applied to microscopic systems are time-reversal invariant.

Take for example take the behavior of a gas. If you look at the collisions of individual gas molecules, they are time reversal invariant in that you cannot tell which way time is flowing by looking at any individual collision.

But if you take a macroscopic system of the entire gas, then you can say which way time is flowing by measuring the entropy of the entire ensemble of molecules and seeing if it is increasing or decreasing.

This also happens in phase transitions between two states of a system, as the article you linked to deals with. If you see a piece of ice on a table melting, that's ok. But you never see water on a table coalescing to form an ice cube. Time seems to flow only one way, which is an example of time-reversal symmetry breaking. But if you looked at any single molecule of water up close, you could not tell if it was part of an ice cube becoming water or of water becoming an ice cube.

It is the symmetry of the fundamental laws that we think represent the symmetries of nature.

Posted by Mano on November 10, 2011 02:52 PM

Thanks, Mano, that actually makes a lot of sense.

Posted by Jared A on November 10, 2011 04:20 PM

Acausal events follow statistical laws, but individual cases are still unpredictable. Chaotic effects are deterministic, but they are highly sensitive to those individual details. So if one radioactive nucleus decays right now instead of another, could that lead to substantially different macroscopic effects later on? It doesn't allow for total omnipotence, but it still seems to allow some degree of intervention.

Posted by Paul Jarc on November 11, 2011 10:27 AM


Yes, it would be possible to conceive of god intervening in some acausal events and then intervening in others too to make the statistics come out right.

This would be like those prayer studies that show no effect. People could argue that god does answer the prayers of some people but deliberately opposes the prayers of others so as to make the results come out to be compatible with random chance.

This is really the argument that god for some reason wants to intervene in the world but at the same time wants to leave no traces.

You can always salvage any proposition if you surround it with sufficient auxiliary propositions.

Posted by Mano on November 11, 2011 10:41 AM