## Monday, February 13, 2012

### Physics and causality

In some previous posts, I discussed the notion of causality.  I talked about how difficult causality is to prove, and how the very concept of causality breaks down in some situations.  For example, if a particular trend has two causes, there is no objective way to define the relative importance of those two causes.

In my humble opinion, the fact that "causality" breaks down in some situations indicates that it is not a fundamental property of the universe.  If causality were fundamental, it would apply in all situations.  You are free to disagree.  I think it's an arguable point.

Some readers may think that this is dissonant with my other views.  I'm a physicist after all.  Isn't the whole of physics based on the idea of cause and effect?  In fact, you might even say I have it all backwards.  On an everyday level, we have to deal with these free-acting humans, who appear to defy cause and effect.  But the reductionists among us know that the free will is an illusion, and that on a fundamental level, it's all cause and effect.  Right?

(Image not original; found all over the 'net.)

But let me tell you what physics really says.  The fundamental laws of physics never mention cause and effect.  It looks a little more like this:

|Ψ> represents the universal state at some point in time.
U(t) represents the time-evolution operator.
U(t)|Ψ> represents the universal state after a length of time t.  t may be positive or negative.

Where do you see causality here?  Let's break it down.
• What if the universe were different?  If instead of |Ψ>, we had |Φ> (that is, if the universe were in a different state), then it is indeed true that after time t, the universe would still be different.  Changing the initial state changes the outcome.  Sounds a little like causality!  So perhaps we could say that |Ψ> causes U(t)|Ψ>.
• The past causes the future.  Not the other way around.  Therefore, if t is positive, we would say |Ψ> causes U(t)|Ψ>, but if t is negative, we would say U(t)|Ψ> causes |Ψ>.
• Is the present caused by all stages of the past?  If we say |Ψ> causes U(1)|Ψ>, should we also say that U(-1)|Ψ> causes U(1)|Ψ>?  Should we say U(-2)|Ψ> also causes U(1)|Ψ>?  We might conclude that any given universal state has an infinite number of causes, corresponding to all the universal states preceding it.
• Are the laws of physics also a cause?  We could also talk about U(t)|Ψ> being caused by the nature of U(t).  That is, we could talk about the state of the universe being caused by the laws of physics which govern how it changes over time.  But this seems to be a distinct sense of causation.  U(t) does not cause U(t)|Ψ> the same way |Ψ> causes U(t)|Ψ>.
• What about objects within the universe?  It is very clunky to restrict causality to the state of the entire universe.  We would have to add more machinery in order to speak of one small part of the universe causing another small part of the universe.  In fact, this is possible.  Because of relativity, no information travels faster than light.  And so the events at one point can only be caused by past events which are a finite distance away.  The further back in the past we look, the further away the cause may be.
The past light cone is a way of illustrating what events at what distance could have caused an event at one point in space and time.  Image from Wikipedia.
• Each event has infinite causes.  I already suggested that the universe at any point in time is caused by all previous stages in the past.  This is also true of each individual event within the universe.  Additionally, at any particular past point in time, there are infinite points in space which might be considered causes.
• Are you caused by faraway stars?  Betelgeuse is a star that is 640 lightyears away, meaning that the state of Betelgeuse 640 years ago may have "caused" my present state.  But I usually see Betelgeuse as having no significance to my life.  And yet, if we are considering all possible states of the universe |Ψ>, there must be one in which the state of Betelgeuse was different 640 years ago, and where this has an effect on my life.  For instance, if 640 years ago, Betelgeuse went supernova, and released a gamma ray burst that killed me, then Betelgeuse would have "caused" my death.  Why do we say a supernova has an effect on me, while an absence of a supernova does not?  Is it because supernovaes which harm life on earth are rare, while absence is common?
The picture is additionally complicated by the fact that there is more than one way to view the same physical laws.  In the Lagrangian formulation of physics, we start with an initial state A and a final state B.  The Lagrangian formulation tells you what path the universe must take to get from A to B.  In this view, causation is an alien concept.  I've discussed this years ago, opining that it is meaningless to ask whether the universe is governed by cause and effect.  If causation appears in one formulation of physics, but not in another, and if each formulation predicts the same results in every experiment... that means a universe with causation and a universe without causation could look exactly the same.

I do not wish to convince the reader that there is no such thing as causality.  I argue that the concept of causality is not contained within physics.  To the degree that physics does contain causality, it does not entirely match our colloquial understanding of "cause".

Of course you won't find many physicists going around saying that there is no such thing as cause and effect.  To a physicist, it is obvious that our everyday lives are quite different from the world of subatomic particles and fundamental physics.  It is clear that baseball exists, even if it is not contained within fundamental physics.  If baseball can exist, why not causality?  For that matter, why not free will?

Other posts in this mini-series:
Colds and Causality
Women and Causality
Responsibility and Causality
Nature/nurture and Causality
Physics and Causality
Math and Causality

#### 1 comment:

Larry Hamelin said...

A couple of quibbles:

I don't think your example is illustrative of a "breakdown" of causality. If a trend has two causes, then the conjunction of the two causes is the cause of the trend. This is no more a breakdown of causality than (A and B) implies C is a breakdown of deduction.

Second, I would quibble about terminology. If something applies in all situations, it is universal. If something cannot be reduced to components or elements, it is fundamental.