So what's quantum amplitude made up of? Well, I'm not sure that is a coherent question. It just sort of is.
It makes perfect sense to ask what "quantum amplitude is made of", if not quite in those terms. It just turns out that further reduction appears to be unusually hard. Could be strings, or quantum spin foam, or something else. Maybe the LHC will provide some hints, some time this decade or next.
Reductionism is more the idea that reality is made of a single level, that is made of simple stuff obeying mathematical laws. And that everything else, especially the "complicated" things like stars, planets, planes, molecules, human beings, ... can be reduced to that unique underlying level.
And that's what we do, when we reduce the fall of an apple and the movement of planets to the single force of gravity, when we reduce fire, breathing and rust to the same chemical reaction (oxydation), when we reduce all of matter to configurations of neutrons, protons and electrons, and so on.
Reductionism doesn't claim "you can always split things into smaller components", it claims "you break every macroscopic, complicated system to the same limited set of small components".
Using an analogy : reductionism is like lego. You can reduce all legos (starships, castles, firetrucks) to the same set of basic building bricks. Reductionism doesn't need to say what these bricks are made of - if all the more or less complicated Lego construction can all be reduced to the same set of small components, it's reductionism.
This seems to be an extremely naive answer, because everything we once thought was a microscale component turned out to really be a macrosystem made up of smaller things, all the way down to configurations of quantum amplitudes. This answer is exactly the thing I'm trying to address. If it wasn't clear in my post, I totally understand what "reductionism is" -- I'm more interested in how to explain our state of the art understanding of giving a reductionist account of actual physics, which seems to terminate at questions about the ontological status of quantum amplitude.
I'm more interested in how to explain our state of the art understanding of giving a reductionist account of actual physics, which seems to terminate at questions about the ontological status of quantum amplitude.
The next step below quantum amplitude, if there is one, is Tegmarkian multiverses, which are a reduction fixpoint (they reduce to themselves). (There might be one intermediate in between - I have a strong suspicion that quantum amplitudes are a continuous approximation of something discrete). However, there is pretty good reason to believe that we cannot gather evidence about them, even in principle.
I understand the concept of Tegmarkian multiverses, but could you explain how they "reduce to themselves"?
Let me amend that slightly. I understand that if you're given observations which indicate that X is composed of something more basic called Y, then reductionism suggests you should believe that X only exists by virtue of being made up of Y. But my questions is, what about the claim "Everything that exists only exists by virtue of being made up of something else that's more basic." Why would this overstep reductionism? How does this claim mesh up with what we theorize or know about quantum configurations?
Your claim: "Everything that exists only exists by virtue of being made up of something else that's more basic" is inadequate.
A better formulation would be: Everything except the most fundamental components, whatever they ultimately turn out to be, exists only by virtue of being made up of something else that's more basic.
Right, but I'm specifically talking about those most fundamental components, whatever they happen to be. It seems that we cannot give an account of what quantum amplitude is made up of, pending some highly speculative theories. And, in fact, large swaths of physicists and philosophers suggest there is good reason to think that quantum amplitude may indeed be that fundamental concept.
I use the term "ontologically basic" to refer to what you call the "most fundamental concept." Basically, an eigenvector of the "decompose into smaller parts" operation, with eigenvalue 1. I am curious whether inside of physics we can have reason to think we have found such an ontologically basic concept (quantum amplitude).
Is it falsifiable to claim that X is ontologically basic yet really does exist, for some X? If X = the Christian God, for example, we say that with high probability the answer is no and we can ignore it. And because any anticipated experience yielded by this ontologically basic God doesn't constrain experience, we can have a real evidence-based way to reject that X exists. But what if X=quantum amplitude?
I can't believe that nobody's mentioned the mathematical universe hypothesis yet...
More helpfully, there is one prediction of reductionism that you can distinguish from any sense of "the bottom level": the notion that, for any two phenomena, there is a lower level of description that explains both of them. Indeed, this is what people typically deny when they deny reductionism- they believe that (for example) matter is explained by one kind of rules, and consciousness is explained by another, and there's not a single explanatory level below both.
I think it reasonably likely that there will turn out to be a bottom level, but even if it's turtles all the way down, there's at most one turtle-tree.
This was a very helpful answer, and you're right. It isn't so much that we can't currently explain whether something underlies amplitude that bugs people. It's more that they want some way to rationalize that it is plausible for their favorite phenomena to also be like amplitude in the sense of not having an as-of-yet-describable lower level explanation. Then they think separate magisteria allows them to claim that the inexplicability of their favorite phenomena has equal footing as the inexplicability of quantum amplitude.
I see reductionism as "everything is made out of the same stuff, and that stuff invariably obeys mathematical regularities." If, millenia ago, it had turned out that everything really was made of earth, water, fire, and air; that they were ontologically basic and that you could analyze other substances by breaking them into the four elements or combine the four to create new ones; I would still call that reductionism.
I had hoped it was clear that I knew at least that much already (the "same stuff" being quantum amplitude). This doesn't help resolve ontological questions about quantum amplitude though. I'm asking for reductionism applied to our best state of the art under standing of physics.
See the comment above for a hopefully more clarified restatement of the question.
The short version of reductionism is not, "everything is made up of smaller parts". I would phrase it this way: "Only simple things exist ontologically. Everything complex is made out of arranging those simple things in particular ways."
I really feel like this is just a restatement of what I already said. I must have said it badly. Look, I understand this, but the regress of figuring out what the simple, ontological things are can be addressed physically, and many claim that quantum amplitude is the place where the buck stops. I am asking for help in understanding how one can make such a claim, what are its merits and pitfalls, and what are the state of the art aspects of physics that address this question. Do we have reason to suspect that quantum amplitude is the simple thing that exists ontologically or not, and if not, why not?
It is a tricky issue. Really, the only reason to suspect that quantum amplitude is the simple thing that exists ontologically, is that we have no hints (that I know of) that there exists something on an even lower level. It may be that there is something else (and maybe figuring out what this is will help us unify physics) but for the moment, since we don't have any evidence to suggest that any particular thing is there, we conclude (pending further investigation) that there isn't anything else there. But, I assign a fairly low probability to this statement, given the history of physics.
Yes, thank you for clearing up your point. I think that @orthonormal hit the nail on the head. What I meant to get at was not that my conversation partners care very much whether we can conclusively say that something does/doesn't underlie amplitude. It's more that they have their own favorite phenomena which they want to have similar status as quantum amplitude. It could be the power of prayer, the rightness of a political ideology, etc. They engage in the regress of "well what's that made out of" only so that when I hit something at the bottom (currently amplitude), then they can say that separate magisteria allows them to claim with equal validity that their favorite phenomena are just like amplitude and are ontologically basic.
Really this about looking at any two phenomena we can observe and saying that there is some finer level that underlies them both and explains them. Many who dispute that want to press you about whatever the limits of knowledge are in physics and then argue that this justifies their metaphysical views that some other thing cannot be reduced.
On a tangent, this makes me wonder what has been said about mathematical models of the levels of abstraction/semantic resolution of reality. Is there any kind of meaningful total ordering of these levels? Could the different levels of reductionism be partially ordered? Are they observer-dependent. These are interesting questions.
Also, see billswift's comment above where he suggests that my statement of exactly this claim is inadequate: (link)
My way of phrasing it is "everything that exists does so by virtue of being made up of simpler constituent things", obviously pending whatever is "ontologically basic", which is what my whole problem is.
Given that amplitude is a mathematical device that allows calculation of probability, and probability describes my ignorance about the world
Quantum measure can be called probability, and expectations given partial information can also be called probability. But quantum measure is not uncertainty, so no, ignorance is not built into the universe.
I think one ought to think about reductionism slightly separately from the particulars of the universe we actually live in. I think of it as rather like the opposite of a curiosity-stopper - instead of assuming that everything is ontologically basic and doesn't have underlying parts, we should assume that there may be underlying parts, and go look for them. Of course in our own universe that approach has been exceptionally fruitful.
The other part that works well is Occam's razor - the simplest explanation of any data set is not only the most lightweight way of explaining the facts, it's also the optimum way of expressing your state of ignorance as well. The simplest explanation is also the most compact way of explaining what you do know. That again arises purely out of the nature of information, and would be true in any universe, not just the noticeably elegant one we actually live in.
On the other hand, there may well be a final set of underlying parts that experiment actually points to, and there's nothing wrong with that as long as it covers your experimental data.
reductionism = (reduce until you have good reason not to);
I think this is a good construction for pragmatic reductionism. It feels like there is some connection to ockham's razor, using an excessively complex model ends up binding up computational resources that you are likely to need for some time sensitive problem. I think this is what is going on in your description of the thought chain you get bound up in. It's fine for fun to think about how relatively or quantum mechanics relate to some problem that is easily solved (or approximated quite accurately) with newtownian mechanics, but if you have some actual reason to solve that problem, it's best to take the easy answer and move on.
How do you explain to people that reductionism = (reduce until you have good reason not to); am I even right to say that or is this a harmful oversimplification?
Understand Solomonoff induction and you will at least understand what constitutes good reason in theory.
I have spent a lot of time studying Solomonoff induction, Kolmogorov complexity, and the universal prior. But that doesn't seem to lend itself to understanding why we're allowed to think we have good reason to suspect that some aspect of reality is finally truly elementary. How can there possibly be evidence for such a claim? It's one thing to say that, thus far, we cannot detect any substructure (in, say, an electron), but it's quite another to then say, "well, it seems quantum amplitude must actually really be real then"
Various approaches to string theory indicate a limit to reductionism in the sense of looking for smaller and smaller parts: T-duality makes small distances in one string theory into large distances in an equivalent, dual theory. Matrix theory doesn't even use space. The whole concept of "oscillating strings" is probably a naive and mathematically inefficient representation of the true physical content of the theory, though until we get something better, we can only limp along with the math and the concepts that we have. But already it looks like the beginning of the end.
I have read the sequences on reductionism and quantum physics some time ago now and I was hoping for some help finding the right places to go back and re-read there to address a question. If the way I describe my question reveals other ignorance on my part, please feel free to add comments above and beyond sequence references.
When trying to talk a little about reductionism, most (non-LW) people I speak to seem to want to play the following game:
What's an airplane made out of? Molecules and atoms that comprise materials like metal, plastic, glass, rubber, etc. What are molecules and atoms made out of? Well, molecules are collections of atoms bonded together, and atoms are made up of three basic particles: protons, neutrons, and electrons. What are basic particles made out of? Well, here things start to get a little more dicey. Some of the basic particles are known to be made up of even smaller sub-atomic elementary particles, such as quarks, leptons, and bosons. Some of the basic particles are examples of these elementary particles. Well, what's an elementary particle made of? Well, that's a pretty tough one, but basically there's this sort of fabric of stuff underlying everything called quantum amplitude, and a certain configuration of quantum amplitude corresponds to an elementary particle. So what's quantum amplitude made up of? Well, I'm not sure that is a coherent question. It just sort of is. A ha! I've caught you. So ultimately way down at the bottom of it all, you're telling me that some something "just exists" (i.e. is ontologically basic). But then why do you call it reductionism if it ultimately boils down to a Platonistic ideal of quantum amplitude (no one actually says this, but it's my translation of the objections I tend to face).
Is it more or less right to say that, as far as we can tell, the only reasonable thing to which we can attribute ontologically basic status is quantum amplitude? Given that amplitude is a mathematical device that allows calculation of probability, and probability describes my ignorance about the world (i.e. my best guess as to what the territory is, as opposed to the actual territory), do we view quantum amplitude as some sort of pre-states-of-knowledge concept? How does that mesh up with "what is an elementary particle made of?" It makes me want to call it "the residue of intrinsic uncertainty" or something, but why would that "really exist?" I don't think that my uncertainty about tomorrow's weather "really exists" in any Platonistic way.
How do you explain to people that reductionism = (reduce until you have good reason not to); am I even right to say that or is this a harmful oversimplification?