In physics, math, and computer science, the state of a system is an encapsulation of all the information you’d ever need to predict what it will do, or at least its probabilities to do one thing versus another, in response to any possible prodding of it. In a sense, then, the state is a system’s “hidden reality,” which determines its behavior beneath surface appearances. But in another sense, there’s nothing hidden about a state—because any part of the state that never mattered for observations could be sliced off with Occam’s razor, to yield a simpler and better description.
When put that way, the notion of “state” seems obvious. So why did Einstein, Alan Turing, and others struggle for years with the notion, on the way to some of humankind’s hardest-won intellectual triumphs?
Consider a few puzzles:
The puzzle about the computer is a stand-in for countless debates I’ve had with non-scientist intellectuals. The resolution, I think, is to specify a state for the computer, involving the numbers to be added (encoded, say, in binary), and a finite control unit that moves across the digits, adding and carrying, governed by Boolean logic operations and ultimately by the laws of physics. You might ask, “What underlies the laws of physics themselves?” And whatever the answer, what underlies that? But those are questions for us. In the meantime, the computer works; everything it needs is contained in its state.
The question about the qubits is a cousin of many others; for example, if the universe is expanding, then what is it expanding into? These aren’t necessarily bad questions. But from a scientific standpoint, a perfectly justified response is “You’re proposing we tack something new onto the state of the world, such as a second space for ‘our’ space to live in or expand into. So would this second space make a difference to observation? If it never would, why not cut it out?”
The question about the envelopes can be resolved by noticing that your decision on Earth to open your envelope or not doesn’t affect the probability distribution over envelope contents that would be perceived by an observer on Pluto. One can prove a theorem stating that an analogous fact holds even in the quantum case, and even if there’s quantum entanglement between the envelope contents on Earth and on Pluto: Nothing you choose to do here changes the local quantum state (the so-called density matrix) over there. This is why, contrary to Einstein’s worries, quantum mechanics is consistent with special relativity.
The central insight here—of equal importance to relativity, quantum mechanics, gauge theory, cryptography, artificial intelligence, and probably 500 other fields—could be summarized as “a difference that makes no difference is not a difference at all.” This slogan might remind some readers of the early 20th-century doctrine of logical positivism, or of Karl Popper’s insistence that a theory that ventures no falsifiable prediction is unscientific. For our purposes, though, there’s no need to venture into the complicated debates about what exactly the positivists or Popper got right or wrong (or whether positivism is itself positivistic, or falsifiability falsifiable).
It suffices to concentrate on a simpler lesson: that, yes, there’s a real world, external to our sense impressions, but we don’t get to dictate from our armchairs what its state consists of. Our job is to craft an ontology around our best scientific theories, rather than the opposite. That is, our conception of “what’s actually out there” always has to be open to revision, both to include new things that we’ve discovered can be distinguished by observation and to exclude things that we’ve realized can’t be.
Some people find it impoverishing to restrict their ontology to the state—to that which suffices to explain observations. But consider the alternatives. Charlatans, racists, and bigots of every persuasion are constantly urging us to look beyond a system’s state to its hidden essences, to make distinctions where none are called for.
Lack of clarity about the notion of “state” is even behind confusion over free will. Many people stress the fact that according to physics, your future choices are “determined” by the current state of the universe. But this ignores the fact that regardless of what physics had to say on the subject, the universe’s current state could always be defined in such a way as to secretly determine future choices; indeed, that’s exactly what so-called hidden-variable interpretations of quantum mechanics, such as Bohmian mechanics, do. To me, this makes “determination” an almost vacuous concept in these discussions, and actual predictability much more important.
State is my choice for a scientific concept that should be more widely known, because buried inside it, I think, is the whole scientific worldview.