I’m not sure this dichotomy you’ve set up is quite so binary. Essentially, I agree with metaphysicist’s comment (see also rocurley’s) -- a fundamental set of laws is descriptive, but it’s also more—but I’d like to add to it.
It’s well accepted that physical laws are descriptive, in the sense that there can be multiple equivalent descriptions (consider all the different descriptions of classical mechanics). On the other hand, we expect that it is possible to find a set of laws which can be called “fundamental”, and that these are not just descriptive in the ways economic laws are, in two ways. Firstly, we expect these laws to be complete, and, secondly, actually true rather than merely approximate, so that any deviations we see are due to errors in our measurement, rather than a need to refine the laws we’fe found. Furthermore, we expect it is possible to find such a set of laws which is finite.
Note that there is no uniqueness condition here, and in that sense the laws are descriptive. Note also that the label “fundamental” only applies to sets of laws, not individual ones (although you could certainly have a fundamental singleton—just ‘and’ them all together!). When you have multiple equivalent descriptions, some of which may not include certain laws, it’s a little hard to sensibly speak of such-and-such a law causing a certain interaction (except as a manner of speaking).
There are other ways in which this does not quite work. For one thing, actually thinking “prescriptively” hardly works in a universe where there’s no universal notion of “time”. Relativity forces us to think in a block-universe fashion[0]. Honestly, I’d say just having continuous time rules out a simple prescriptive idea, because then you have to reify velocity or other derivatives, and also because solutions to differential equations are not always unique! The equations that actually come up in the fundamental laws might have unique solutions, but that’s a descriptive condition.
But on the other hand, while we don’t expect a fundamental set of laws to be prescriptive in that sense, we do still expect them to be (probabilistically / quantum / mixed-state) deterministic, in the sense that the (wavefunction of / density matrix of the) present (with respect to any fixed observer) determines the future. Note that this is purely a descriptive condition; we don’t insist that the laws somehow reach in and cause the future, just that they’re sufficient to uniquely constrain it. But it is, I suppose, a descriptive condition with some prescriptive flavor. And note that it requires a set of laws to be fundamental in the senses above—you can’t have a sensible determinism (even in the broad sense above) without actual truth; and if a set of laws is enough to uniquely constrain the future, then it’s necessarily complete.
So in actuality what we expect of a fundamental laws is descriptive rather than prescriptive, but it’s not the bare descriptivism of economic laws, e.g.; it’s a complete and truthful description. And when you take a block-universe point of view[0], or rocurley’s point of view, this is the only sensible way to interpret the notion of a prescriptive set of laws in the first place, so in that sense it can be called “prescriptive” while also being descriptive, and while not taking the ridiculous prescriptive view torn apart in the post.
[0]Tangent: Eliezer may insist on “timelessness”, but so far as I’m concerned the idea is near-nonsensical. It’s correct to the extent that it overlaps with the block-universe idea, which in terms of how it describes how you should think about time is quite a lot. Time is not ontologically special, etc. (Although it is physically special, because, you know, +1 +1 +1 −1. And the equations are different.) But insisting that actually it’s just a consequence of other things is—well, where is this linear ordering coming from, and why should it be real-valued, and how can you possibly account for Lorentz-invariance, and etc.? I’d also like to take a moment to point out that while it’s perhaps better to think of laws as describing[1] a relation between past and future, that doesn’t mean it’s wrong, as suggested in HMPOR, to think of them as describing[1] how things change over time, because these mean the same thing! Similarly, describing how things in one place are different from things in another place is describing how things change over space, and describing how hot things are different from cold things is describing how things change over temperature; time isn’t ontologically special. The only way it’s wrong to think of things changing over time is if the only way you can read that is as some ontologically special thing where the future replaces the past or something equally ridiculous. The block-universe view provides a perfectly good way of thinking about time, without having problems with physics. [1]The original wording was “enforcing a relation”, and “changing things over time”, rather than a descriptive wording; but that was describing a magic wand rather than physical laws, so maybe that was appropriate. Although it’s not clear to me that there’s a real difference.
On the completeness of physics, see my response to metaphysicist here.
As for the determinism of physical law, I’m afraid that’s not looking too good these days either. Initial value problems for the gravitational field equations satisfy existence and uniqueness conditions only within the domain of dependence of the initial data surface, and this need not extend across all of spacetime. In particular, if the spacetime is not globally hyperbolic, the initial value problem will not (in general, although there are specific exceptions) have a unique solution. Global hyperbolicity fails if, for instance, there are naked singularities (singularities without event horizons). It is for this sort of reason that Penrose came up with the cosmic censorship conjecture, outlawing naked singularities.
Unfortunately, the conjecture seems to be in tension with what we know about quantum gravity. Consider Hawking radiation, the process by which black holes gradually evaporate away. If (and this is a pretty big if) the evaporation can be described by a classical general relativistic spacetime, then it must eventually result in a momentarily naked singularity, violating cosmic censorship (and global hyperbolicity).
There are also problems involving quantum mechanics, even if you don’t adopt a collapse interpretation. There are configuration spaces that possess singularities. In the classical case, these singularities are usually protected by a potential barrier, preventing the system from falling into them. But in the quantum case, it is possible for the system to tunnel through the barrier, leading to non-unitary evolution. Mathematically, this corresponds to a Hamiltonian operator that is not essentially self-adjoint (its closure is not self-adjoint). This problem would arise if we were doing quantum mechanics on a spacetime with a timelike or naked singularity.
There are also interesting issues related to the failure of narratability in relativistic quantum theory, discussed in this cool paper.
While I put consideration of the “block-universe” concept and directly-related statements until I understand them (and what you mean by them) properly, I find the rest of this post to be a very good description* of my own current model of nature.
I’d like to know more about this “block-universe” concept, though. I’m not sure if it would clash with my own model of relativity interactions, and if so, I want to know how. My understanding of relativity is, admittedly, rather limited and untrained/uneducated, so any non-trivial evidence at this point is very much worth it. If you could point me to a paper or book on the subject, that would be even better.
* (insert immature pun along the lines of “I rule!”)
I’m not sure this dichotomy you’ve set up is quite so binary. Essentially, I agree with metaphysicist’s comment (see also rocurley’s) -- a fundamental set of laws is descriptive, but it’s also more—but I’d like to add to it.
It’s well accepted that physical laws are descriptive, in the sense that there can be multiple equivalent descriptions (consider all the different descriptions of classical mechanics). On the other hand, we expect that it is possible to find a set of laws which can be called “fundamental”, and that these are not just descriptive in the ways economic laws are, in two ways. Firstly, we expect these laws to be complete, and, secondly, actually true rather than merely approximate, so that any deviations we see are due to errors in our measurement, rather than a need to refine the laws we’fe found. Furthermore, we expect it is possible to find such a set of laws which is finite.
Note that there is no uniqueness condition here, and in that sense the laws are descriptive. Note also that the label “fundamental” only applies to sets of laws, not individual ones (although you could certainly have a fundamental singleton—just ‘and’ them all together!). When you have multiple equivalent descriptions, some of which may not include certain laws, it’s a little hard to sensibly speak of such-and-such a law causing a certain interaction (except as a manner of speaking).
There are other ways in which this does not quite work. For one thing, actually thinking “prescriptively” hardly works in a universe where there’s no universal notion of “time”. Relativity forces us to think in a block-universe fashion[0]. Honestly, I’d say just having continuous time rules out a simple prescriptive idea, because then you have to reify velocity or other derivatives, and also because solutions to differential equations are not always unique! The equations that actually come up in the fundamental laws might have unique solutions, but that’s a descriptive condition.
But on the other hand, while we don’t expect a fundamental set of laws to be prescriptive in that sense, we do still expect them to be (probabilistically / quantum / mixed-state) deterministic, in the sense that the (wavefunction of / density matrix of the) present (with respect to any fixed observer) determines the future. Note that this is purely a descriptive condition; we don’t insist that the laws somehow reach in and cause the future, just that they’re sufficient to uniquely constrain it. But it is, I suppose, a descriptive condition with some prescriptive flavor. And note that it requires a set of laws to be fundamental in the senses above—you can’t have a sensible determinism (even in the broad sense above) without actual truth; and if a set of laws is enough to uniquely constrain the future, then it’s necessarily complete.
So in actuality what we expect of a fundamental laws is descriptive rather than prescriptive, but it’s not the bare descriptivism of economic laws, e.g.; it’s a complete and truthful description. And when you take a block-universe point of view[0], or rocurley’s point of view, this is the only sensible way to interpret the notion of a prescriptive set of laws in the first place, so in that sense it can be called “prescriptive” while also being descriptive, and while not taking the ridiculous prescriptive view torn apart in the post.
[0]Tangent: Eliezer may insist on “timelessness”, but so far as I’m concerned the idea is near-nonsensical. It’s correct to the extent that it overlaps with the block-universe idea, which in terms of how it describes how you should think about time is quite a lot. Time is not ontologically special, etc. (Although it is physically special, because, you know, +1 +1 +1 −1. And the equations are different.) But insisting that actually it’s just a consequence of other things is—well, where is this linear ordering coming from, and why should it be real-valued, and how can you possibly account for Lorentz-invariance, and etc.? I’d also like to take a moment to point out that while it’s perhaps better to think of laws as describing[1] a relation between past and future, that doesn’t mean it’s wrong, as suggested in HMPOR, to think of them as describing[1] how things change over time, because these mean the same thing! Similarly, describing how things in one place are different from things in another place is describing how things change over space, and describing how hot things are different from cold things is describing how things change over temperature; time isn’t ontologically special. The only way it’s wrong to think of things changing over time is if the only way you can read that is as some ontologically special thing where the future replaces the past or something equally ridiculous. The block-universe view provides a perfectly good way of thinking about time, without having problems with physics.
[1]The original wording was “enforcing a relation”, and “changing things over time”, rather than a descriptive wording; but that was describing a magic wand rather than physical laws, so maybe that was appropriate. Although it’s not clear to me that there’s a real difference.
On the completeness of physics, see my response to metaphysicist here.
As for the determinism of physical law, I’m afraid that’s not looking too good these days either. Initial value problems for the gravitational field equations satisfy existence and uniqueness conditions only within the domain of dependence of the initial data surface, and this need not extend across all of spacetime. In particular, if the spacetime is not globally hyperbolic, the initial value problem will not (in general, although there are specific exceptions) have a unique solution. Global hyperbolicity fails if, for instance, there are naked singularities (singularities without event horizons). It is for this sort of reason that Penrose came up with the cosmic censorship conjecture, outlawing naked singularities.
Unfortunately, the conjecture seems to be in tension with what we know about quantum gravity. Consider Hawking radiation, the process by which black holes gradually evaporate away. If (and this is a pretty big if) the evaporation can be described by a classical general relativistic spacetime, then it must eventually result in a momentarily naked singularity, violating cosmic censorship (and global hyperbolicity).
There are also problems involving quantum mechanics, even if you don’t adopt a collapse interpretation. There are configuration spaces that possess singularities. In the classical case, these singularities are usually protected by a potential barrier, preventing the system from falling into them. But in the quantum case, it is possible for the system to tunnel through the barrier, leading to non-unitary evolution. Mathematically, this corresponds to a Hamiltonian operator that is not essentially self-adjoint (its closure is not self-adjoint). This problem would arise if we were doing quantum mechanics on a spacetime with a timelike or naked singularity.
There are also interesting issues related to the failure of narratability in relativistic quantum theory, discussed in this cool paper.
While I put consideration of the “block-universe” concept and directly-related statements until I understand them (and what you mean by them) properly, I find the rest of this post to be a very good description* of my own current model of nature.
I’d like to know more about this “block-universe” concept, though. I’m not sure if it would clash with my own model of relativity interactions, and if so, I want to know how. My understanding of relativity is, admittedly, rather limited and untrained/uneducated, so any non-trivial evidence at this point is very much worth it. If you could point me to a paper or book on the subject, that would be even better.
* (insert immature pun along the lines of “I rule!”)