[FRIAM] A Question For Tomorrow

[Eric Smith]

> I was in a forum with a bunch of physicists last year many of whom were wedded to the notion that nature was determined by things beyond experience that we would never know.  That's both a tautology AND an oxymoron.  

I think this requires care.  Never wanting to defend the positions of people I don’t know in a conversation I wasn’t in, it would be helpful to know what topic the conversation was about, in the terms the participants applied to it.


Since physics has existed as a mathematical science (let’s say, since Newton?), it has employed a notation of “state” of a system.

Also since that time, it has employed a notion of the “observable properties” (shortened to just “observables”) somehow associated with the system’s states.

In classical physics, the concept of state was identical to that of a collection of values assigned to some sufficiently complete set of observables, and which observables made up the set could be chosen without regard to which particular state they were characterizing.

aka in common language, anything inherent in the concept of a state was just the value of an observable, meaning something knowable by somebody who bothered to measure it.


In quantum mechanics, physics still has notions of states and observables.

Now, however, the notion of state is _not_ coextensive with a set of values assigned to a complete (but not over-complete) set of observables, which one could declare in advance without regard to which state is being characterized.

To my view, the least important consequence of this change is that the state may not be knowable by us, even in principle, though that is the case.  (To many others, this is its most important consequence.  But the reason I shake that red cape before a herd of bulls is so that I can say…)

The important consequence of this understanding is that we have mathematical formalizations of the concept of state and of observable, and they are two different kinds of concept.  It is precisely that both can be defined, that the theory needs both to function in its complete form, and that the definitions are different, that expands our understanding of concepts of state and observable.  A state still does the main things states have always done in quantitative physical theories, and in the sense that they characterize our “attainable knowledge”, observables do what they have always done.  Before, the two jobs had been coextensive; now they are not.


I assume Shakespeare wrote the “There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy” line about the same phenomenon as the thing that makes the Copernical revolution a revolution: people fight to give up importance they believed they had, or control they believed they had.  Once the fight is in the culture, there may not be that emotional motive in all the combatants; they may believe they have a logical problem with the revolution.  But how can there be a logical problem with the Copernican revolution?  It is a statement about the alignments of beliefs and facts.  Likewise the concepts of state and observable in quantum mechanics.

It feels like a Copernican revolution to me, every time physics shows that new operational understandings are required, and tries to give us new language habits in which to coordinate our minds (singly or jointly) around them, to pose the question how this was known all along in our folk language and thus can be logically analyzed with its categories.  There is only very limited reason for our folk language to furnish “a description” of the nature of the world.  It is a collection of symbols that are part of “the system of us”, which when exchanged or imagined mediate coordination of our states of mind (and yes, I know this term can be objected to from some behaviorist points of view, but it seems to require much less flexibility to use provisionally than the state of a quantum system, even though it is also much less well-understood at present).  If a collection of robot vacuum cleaners exchange little pulse sequences of infrared light to coordinate, so they don’t re-vacuum the same spot, we might anticipate that there is a limited implicit representation of the furniture of the room and its occupants in the pulse sequences, but we would not expect them to furnish a description of the robots’ engineering, or the physical world, or much else.  Human language is somewhat richer than that, but it seems to me the default assumption should be that its interpretation suffers the same fundamental hazard.  Signals exchanged as part of a system should not be expected to furnish a valid empirical description _of_ the system.

Common language is fraught with that hazard in unknown degrees and dimensions; technical language can also be fraught, but we try to build in debuggers to be better at finding the errors or gaps and doing a better-than-random job of fixing them.

The fluidity and flexibility with which the mind can take on new habits of language use, and the only-partial degree to which that cognitive capability is coupled to emotional comfort or discomfort in different habits, seems important to me in trying to understand how people argue about science.

Eric