A recent essay in the New York Times by Dennis Overbye has managed to attract quite a bit of attention around the internets — most of it not very positive. It concerns a recent paper by Holger Nielsen and Masao Ninomiya (and some earlier work) discussing a seemingly crazy-sounding proposal — that we should randomly choose a card from a million-card deck and, on the basis of which card we get, decide whether to go forward with the Large Hadron Collider. Responses have ranged from eye-rolling and heavy sighs to cries of outrage, clutching at pearls, and grim warnings that the postmodernists have finally infiltrated the scientific/journalistic establishment, this could be the straw that breaks the back of the Enlightenment camel, and worse.
Since I am quoted (in a rather non-committal way) in the essay, it’s my responsibility to dig into the papers and report back. And my message is: relax! Western civilization will survive. The theory is undeniably crazy — but not crackpot, which is a distinction worth drawing. And an occasional fun essay about speculative science in the Times is not going to send us back to the Dark Ages, or even rank among the top ten thousand dangers along those lines.
The standard Newtonian way of thinking about the laws of physics is in terms of an initial-value problem. You specify the state of the system (positions and velocities) at one moment, then the laws of physics tell you how it will evolve into the future. But there is a completely equivalent alternative, which casts the laws of physics in terms of an action principle. In this formulation, we assign a number — the action — to every possible history of the system throughout time. (The choice of what action to assign is simply the choice of what laws of physics are operative.) Then the allowed histories, the ones that “obey the laws of physics,” are those for which the action is the smallest. That’s the “principle of least action,” and it’s a standard undergraduate exercise to show that it’s utterly equivalent to the initial-value formulation of dynamics.
In quantum mechanics, as you may have heard, things change a tiny bit. Instead of only allowing histories that minimize the action, quantum mechanics (as reformulated by Feynman) tells us to add up the contributions from every possible history, but give larger weight to those with smaller actions. In effect, we blur out the allowed trajectories around the one with absolutely smallest action.
Nielsen and Ninomiya (NN) pull an absolutely speculative idea out of their hats: they ask us to consider what would happen if the action were a complex number, rather than just a real number. Then there would be an imaginary part of the action, in addition to the real part. (This is the square-root-of-minus-one sense of “imaginary,” not the LSD-hallucination sense of “imaginary.”) No real justification — or if there is, it’s sufficiently lost in the mists that I can’t discern it from the recent papers. That’s okay; it’s just the traditional hypothesis-testing that has served science well for a few centuries now. Propose an idea, see where it leads, toss it out if it conflicts with the data, build on it if it seems promising. We don’t know all the laws of physics, so there’s no reason to stand pat.
NN argue that the effect of the imaginary action is to highly suppress the probabilities associated with certain trajectories, even if those trajectories minimize the real action. But it does so in a way that appears nonlocal in spacetime — it’s really the entire trajectory through time that seems to matter, not just what is happening in our local neighborhood. That’s a crucial difference between their version of quantum mechanics and the conventional formulation. But it’s not completely bizarre or unprecedented. Plenty of hints we have about quantum gravity indicate that it really is nonlocal. More prosaically, in everyday statistical mechanics we don’t assign equal weight to every possible trajectory consistent with our current knowledge of the universe; by hypothesis, we only allow those trajectories that have a low entropy in the past. (As readers of this blog should well know by now; and if you don’t, I have a book you should definitely read.)
To make progress with this idea, you have to make a choice for what the imaginary part of the action is supposed to be. Here, in the eyes of this not-quite-expert, NN seem to cheat a little bit. They basically want the imaginary action to look very similar to the real action, but it turns out that this choice is naively ruled out. So they jump through some hoops until they get a more palatable choice of model, with the property that it is basically impotent except where the Higgs boson is concerned. (The Higgs, as a fundamental scalar, interacts differently than other particles, so this isn’t completely ad hoc — just a little bit.) Because they are not actually crackpots, they even admit what they’re doing — in their own words, “Our model with an imaginary part of the action begins with a series of not completely convincing, but still suggestive, assumptions.”
Having invoked the tooth fairy twice — contemplating an imaginary part of the action, then choosing its form so as to only be relevant where the Higgs is concerned — they consider consequences. Remember that the effect of the imaginary action is non-local in time — it depends on what happens throughout the history of the universe, not just here and now. In particular, given their assumptions, it provides a large suppression to any history in which large numbers of Higgs bosons are produced, even if they won’t be produced until some time in the future.
So this model makes a strong prediction: we’re not going to be producing any Higgs bosons. Not because the ordinary dynamical equations of physics prevent it (e.g., because the Higgs is just too massive), but because the specific trajectory on which the universe finds itself is one in which no Higgses are made.
That, of course, runs into the problem that we have every intention of making Higgs bosons, for example at the LHC. Aha, say NN, but notice that we haven’t yet! The Superconducting Supercollider, which could have found the Higgs long ago, was canceled by Congress. And in their December 2007 paper — before the LHC tried to turn on — they very explicitly say that a “natural” accident will come along and break the LHC if we try to turn it on. Well, we know how that turned out.
But NN have an ingenious suggestion for saving us from future accidents at the LHC — which, as they warn, could endanger lives. They propose a card game with more than a million cards, almost all of which say “go ahead, no problem.” But one card says “don’t turn on the LHC!” In their model, the nonlocal effect of the imaginary part of the action is to ensure that the realized history of the universe is one in which the LHC never turns on; but it doesn’t matter why it doesn’t turn on. If we randomly pick one out of a million cards, and honestly promise to follow through on the instructions on the card we pick, and we happen to pick the card that says not to turn it on, and we therefore don’t — that’s a history of the universe that is completely unsuppressed by their mechanism. And if we choose a card that says “go ahead,” well then their theory is falsified. (Unless we try to go ahead and are continually foiled by a series of unfortunate accidents.) Best of all, playing the card game costs almost nothing. But for it to work, we have to be very sincere that we won’t turn on the LHC if that’s what the card says. It’s only a million-to-one chance, after all.
Note that all of this “nonlocal in time,” “receiving signals sent from the future” stuff is a bit of a red herring, at least at the classical level. We often think that the past is set in stone, while the future is still to be determined. But that’s not how the laws of physics operate. If we knew the precise state of the universe, and the exact laws of physics, the future would be as utterly determined as the present (Laplace’s Demon). We only think otherwise because our knowledge of the present state is highly imperfect, consisting as it does as a few pieces of information about the coarse-grained state. (We don’t know the position and velocity of every particle in the universe, or for that matter in any macroscopic object.) So there’s no need to think of NN’s imaginary action as making reference to what happens in the future — all the necessary data are in the present state. What seems weird to us is that the NN mechanism makes crucial use of detailed, non-macroscopic information about the present state; information to which we don’t have access. (Such as, “does this subset of the universe evolve into the Large Hadron Collider?”) That’s not how the physics we know and love actually works, but the setup doesn’t actually rely on propagation of signals backwards in time.
At the end of the day: this theory is crazy. There’s no real reason to believe in an imaginary component to the action with dramatic apparently-nonlocal effects, and even if there were, the specific choice of action contemplated by NN seems rather contrived. But I’m happy to argue that it’s the good kind of crazy. The authors start with a speculative but well-defined idea, and carry it through to its logical conclusions. That’s what scientists are supposed to do. I think that the Bayesian prior probability on their model being right is less than one in a million, so I’m not going to take its predictions very seriously. But the process by which they work those predictions out has been perfectly scientific.
There is another reasonable question, which is whether an essay (not a news story, note) like this in a major media outlet contributes to the erosion of trust in scientists on the part of the general public. I would love to see actual data one way or the other, which went beyond “remarkably, the view of the common man aligns precisely with the view I myself hold.” My own anecdotal observations are pretty unambiguous — the public loves far-out speculations like this, and happily eats them up. (See previous mocking quote, now applied to myself.) It’s always important to distinguish as clearly as possible between what is crazy-sounding but well-established as true — quantum mechanics, relativity, natural selection — and what is crazy-sounding and speculative, even if it’s respectable speculation — inflation, string theory, exobiology. But if that distinction is made, I’ve always found it pretty paternalistic and condescending to claim that we should shield the public from speculative science until it’s been established one way or the other. The public are grown-ups, and we should assume the best of them rather than the worst. There’s nothing wrong with letting them in on the debates about crazy-sounding ideas that we professional scientists enjoy as our stock in trade.
The disappointing thing about the responses to the article is how non-intellectual they have been. I haven’t heard “the NN argument against contributions to the imaginary action that are homogeneous in field types is specious,” or even “I see no reason whatsoever to contemplate imaginary actions, so I’m going to ignore this” (which would be a perfectly defensible stance). It’s been more like “this is completely counter to my everyday experience, therefore it must be crackpot!” That’s not a very sciencey attitude. It certainly would have been incompatible with all sorts of important breakthroughs in physics through the years. The Nielsen/Ninomiya scenario isn’t going to be one of those breakthroughs, I feel pretty sure. But it’s sensible enough that it merits disagreement on the basis of rational arguments, not just rolling of eyes.