The Supposed Black Hole Information Paradox and the Idolatry of Mechanism
For a while now, physicists have been talking about their perplexity at what they call the black hole information paradox. The paradox comes about when you combine general relativity with quantum mechanics.
Matter, composed of particles, falls into a black hole. Theoretically speaking, you can trace the particles' paths as they enter the back hole. These positions and momenta represent information that, according to a classical theory like general relativity, should be preserved; if you could look inside the black hole, you should in theory be able calculate the particles' original paths from their present state (positions, momenta). Since we can't see inside black holes (light cannot escape), this naïve belief can't apparently be falsified.
But then enter Stephen Hawking. He famously used quantum mechanics to show that black holes slowly radiate their mass/energy away, which is to say that we can, after a fashion, "see inside" black holes. What we see come out of black holes is a thermal radiation field (i.e., black body spectrum). The radiation is the same no matter what falls into the hole (depending only on bulk parameters of the hole like its mass), so the "information" about the particles that went into the black hole has apparently been destroyed. The paradox is, as Sabine Hossenfelder puts it, "If you combine gravity with quantum theory, it seems you get a result that's inconsistent with the quantum theory you started from." Well, as we'll see, "inconsistent with the quantum theory you started from" is not that simple and requires some explanation.
To any normal person looking at this situation, the idea of the particles' paths being preserved inside the black hole sounds ridiculous. Even from the classical paradigm, everything that goes in to a black hole ends up at the singularity at the center, a place of infinite pressure and density: how can any "information" survive that? But then you add in quantum theory, with its famous uncertainty principle that makes it impossible to know both position and momentum with exact precision in principle, and then you expect to be able to know how to trace the particles' paths backward? Absolutely ridiculous!1
In reality there are two parts to quantum theory. First there's the "unitary" part described by Schrödinger's equation and the like that describes how the wavefunction evolves deterministically. Secondly, there's the "reductive" part that happens during a measurement; we have no mathematical description of how this works, but this is the part that appears "random"; out of all the possible outcome states the wavefunction describes, only one is the outcome after the measurement. Since many states are (apparently without deterministic cause) reduced to one state, our science won't allow us even in principle to figure out the pre-measurement state. So even according to quantum mechanics, we can't figure out the particles' original paths given their present state: "information" is lost.
Roger Penrose describes how many physicists for some reason still believe the information is preserved (the "store" and "return" alternatives), when the information "loss" alternative is more reasonable:
The reader might wonder why people feel the need to go to the lengths required for store or return, when the most obvious alternative would appear to be loss. The reason is that loss seems to imply a violation of unitarity, i.e., of the operation of U. If one's philosophy of quantum mechanics demands that unitarity is immutable, then one is in difficulty with loss. Hence we have the popularity, among many (and apparently most) particle physicists of the possibilities of store or return, despite the seemingly contrived appearance of these alternatives.
Penrose is right. The reason so many physicists are still hung up on the unitary part of QM is a philosophical commitment. It is in fact part of the founding, extra-scientific (in fact scientistic) faith of Cartesian, Galilean physics given birth by Newton: that reality is completely intelligible and controllable by human reason. At core this commitment, the mechanical philosophy, is the assumption that the human mind stands over and distinct from the world of matter in a transcendent, God-like posture. Laplace precisely stated the metaphysical commitment this way:
We ought to regard the present state of the universe as the effect of its antecedent state and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. The perfection that the human mind has been able to give to astronomy affords but a feeble outline of such an intelligence.
Physics will continue to fail in its quest to understand nature as long as it abides by this disproven idea.
Notes
1. It sounds as if there's a sort of hidden-variable assumption behind the idea that position and momentum information is preserved.
Roger Penrose The Road to Reality: A Complete Guide to the Laws of the Universe (New York: Alfred A. Knopf, 2005), § 30.8, 840.
Pierre Simon de Laplace, Théorie analytique des probabilités (1812).
