:: Article

on the foundations of physics

Tim Maudlin interviewed by Richard Marshall.

Tim Maudlin is the Tekken Revolution of the philosophy of physics. He is forever brooding on why there is no deep fissure between philosophy and science, the brilliance of Einstein and John Stewart Bell, about how to work out how the world is, about how to solve the liar paradox, on issues regarding metaphysics and physics, on time passing, on the way mathematics can mislead physicists, about relativity and why calling Einstein’s theory that is a bad idea, about why there is no quantum theory that can be interpreted, and why he finds the idea that nothing is fundamental possible but implausible. All so Huckleberry!

3:AM: What made you become a philosopher?

Tim Maudlin: As an undergraduate, I pursued a joint degree in physics and philosophy. In both fields, the attraction stemmed from a desire to get down to the most foundational level of the things, to have all the basic concepts laid out to view. But each field also had its own drawbacks, at least to my mind. Much of the effort in physics was devoted to learning mathematical techniques for solving particular problems, which often does not provide much in the way of deep insight into the physics. And philosophy can have the tendency to become detached from clear and contentful questions about the nature of the world. Foundations of physics, which occupies most of my attention, always keeps fundamental questions in view.

3:AM: You’re working in the area of philosophy of physics and science. This hasn’t been an altogether happy relationship and recent spats have broken out that suggest that physicists don’t think they need to heed philosophy and philosophers think physicists are inept at interpreting their own theories. You tend to be in this latter camp don’t you, and have been pretty vociferous in arguing that there is a role for philosophy in understanding physics. How do you diagnose the problem – and how come it is philosophy that tends to be sober in their interpretations and the scientists who seem more content with paradoxes and contradictions and expensive ontologies like multiverses?

TM: I don’t think that the spats between physicists and philosophers are more heated, or of a different kind, then the spats that break out among philosophers or among physicists; they just get more public attention. Disputes in foundations of physics typically cannot be settled by observation or experiment, so argumentation has to come to the fore. And the analysis and evaluation of arguments requires a certain fastidiousness about terms and concepts that can be fostered by a background in philosophy.

That said, though, I do not see any deep fissure that runs between the two fields. In my view, the greatest philosopher of physics in the first half of the 20th century was Einstein and in the second half was John Stewart Bell. So physicists who say that professional philosophers have not made the greatest contributions to foundations of physics are correct. But both Einstein and Bell had philosophical temperaments, and Einstein explicitly complained about physicists who had no grounding in philosophy. The community of people who work in foundations of physics is about evenly divided between members of philosophy departments, members of physics departments and members of math departments. Many of us on all sides are trying to open and broaden channels of communication across disciplinary boundaries. And I don’t see that there is much correlation between disciplinary affiliation and sobriety: no one is more sober than Bell and Einstein were, or more cavalier (at times) than Bohr or John Wheeler. A more salient division in contemporary foundations is between those, like myself, who judge that Bell was basically correct in almost everything he wrote and those who think that his theorem does not show much of interest and his complaints about the unprofessional vagueness that infects quantum theory are misplaced.

3:AM: It seems that running through all your work – from the liar paradox work through to your latest book on the philosophy of physics – that there’s a key idea which grounds your approach that might be summarized as the proposition ‘the world is some way or other.’ Is this why you take issue with Bohr who ducked this issue and encouraged physicists since the twenties to avoid its implications and just get on with their calculations?

TM: Your comment is very interesting to me, because on the one hand it is true that I always work from the proposition that the world is some way or other (and our task is to figure out, or get the best evidence we can, about how it is), but on the other hand I have never thought of this as a “key idea” but as a triviality. I really can’t understand how anyone can deny it. I don’t think that Bohr would deny it, although he would deny that the microscopic world is anschaulich, or “intuitive”. If you put that phrase in the context of a Kantian background, in which space and time are considered to be just forms of human sensible intuition, then you get the conclusion that the concepts of space, time, and causation cannot be applied to the quantum realm. That is not to say that the world isn’t some way or other, but that the way it is cannot be grasped intuitively. Of course, in a certain sense even a four-dimensional space-time cannot be “intuited”, so that particular demand has generally been abandoned by physics, with good reason.

I don’t think that Bohr is the source of the “shut up and calculate” zeitgeist in physics. If anything, Bohr’s writings are overstuffed with (often rather poor) philosophy. It was later generations of physicists, who could not understand what Bohr was saying and who had nothing else to replace it with, that fell into instrumentalist slogans. Bell and Einstein both insisted that physics aspire to more than just instrumental and predictive accuracy.

3:AM: It might strike people as surprising that a logical, semantic paradox like the liar paradox could be solved, or even thought to be solved, by relating to this idea of there being an objective world which is some way or other. But that’s what you have done isn’t it? Can you say something about your idea here and why it took you so many drafts – and long ones at that – before you came to your preferred solution?

TM: Perhaps what was slightly unusual about my approach to the Liar was to focus not just on the semantics (the account of what truth values there are and how sentences get them) but also on the purely syntactic question of valid argument forms. It is easy to see that adding the T-Inferences (roughly, the inferences from “P is true” to P and vice-versa) to the inferences of standard logic yields disaster: every sentence becomes a theorem. So one has to ask, quite independently of the semantics, how to modify the logic to avoid the disaster. That technical problem looks a little different in a natural deduction setting rather than an axiomatic setting, so maybe a slightly new slant arose from thinking in terms of natural deduction. What led to so many drafts was the fact that there are many, many ways to block the bad inferences, and it took a while to investigate what other consequences they had. On the semantic side, I do think that all true and false sentences are made true or false by a non-semantic world, which has a particular structure, so that sentences that do not make proper contact with that world (such as the Liar) cannot be true or false (even if they have the syntactic form of a “logical truth” or “contradiction” in standard logic). Eventually the inferential structure harmonized with the semantics and everything came together.

3:AM: Is it an implication of your argument that truth is rooted in non-semantic facts and it follows that maths truths are also linked to the world? Does this imply that you take a naturalistic, even materialistic, view of maths rather than see it as a counterexample to naturalism and even materialism?

TM: Philosophy of mathematics is a large and fascinating area about which I have had nothing at all to say. I am a mathematical Platonist in the simple sense that I believe clear, unambiguous mathematical propositions (e.g. Goldbach’s conjecture or the Axiom of Choice) to be either true or false independently of whether or not they can be proven. Indeed, it seems obvious to me for many different reasons (including, of course, Gödel’s theorems) that infinitely many mathematical truths are not theorems of any intuitively acceptable proof system. So I believe in a “world” of mathematical fact in virtue of which clear mathematical propositions are either true or false. But I do not take these mathematical facts to be materialist or naturalistic in any interesting sense. I would not, myself, regard this as a “counterexample” to naturalism or materialism, because I never thought of those doctrines as making any claims about mathematics. But perhaps I am idiosyncratic in that regard.

3:AM: You’re skeptical of metaphysics that doesn’t look to scientific practice, and when looking at the metaphysical questions of ontology you say philosophers should look to physics don’t you? Perhaps a parade case of the kind of metaphysics you’re objecting to is that of Humean Supervenience – the idea that all we have is an arrangement of qualities – named after Hume and developed by David Lewis. So can you take us through what this is and say why it’s a mistake?

TM: The relation of metaphysics—the most general inquiry into what exists—to physics strikes me as obvious: one big part of metaphysics concerns itself with physical entities, and that part had better be informed by physics. That part may have no interesting implications for other sorts of fact, for example mathematical fact or facts about objective moral values. But Humean supervenience as Lewis proposed it is focused on physical existence in any case.

My own approach to physical existence can be characterized, at least initially, as quite naïve: I begin with a sense of basic physical ontology that comes out of studying physics. There are some things that are presented as fundamental in a physical theory and standing in need of no further analysis. Among those are the basic dynamical laws of the theory. We are told, for example, that Newtonian dynamics postulates that F = mA. Taken at face value, the equation implies that there are physical facts about what forces there are in the world, and what masses, and what accelerations, and how these are related to each other as a matter of physical law. Some of these things, such as accelerations, are not taken as primitive but are rather defined in terms of the space-time structure. Some, such as forces, seem to have different status in different presentations of the theory and so become objects of philosophical inquiry. But the physicist never feels it necessary to further analyze the notion of lawhood itself: that is taken as clear enough.

Lewis, of course, thought that lawhood itself needed to be analyzed, and offered a sort of Best Systems theory. What is basic, according to Lewis, is just the Humean Mosaic: the distribution of purely local physical characteristics throughout space-time. Insistence on a reduction of everything else to the Humean Mosaic is certainly not recognized by physical practice, and I just cannot see any independent plausible motivation for it. Quantum states are not simply matters of local fact, nor are laws just convenient summaries of local fact. What I have tried to do is distill from physics a collection of fundamental physical entities in terms of which everything else receives a natural analysis. That has not led to the Humean Mosaic, so I regard Lewis’s strictures as unjustified.

3:AM: Philosophers like Huw Price argue that time’s arrow isn’t real and that our best physics agrees with this. Why do you disagree? And how come causation isn’t foundational like time given that the two often seem linked?

TM: I sometimes remark that we live in an astonishing world: I can actually put food on the table by going around giving talks defending the radical view that time passes! Part of what characterizes the passage of time—and what many philosophers and physicists dispute—is that the temporal structure of the world, independently of its material contents, has an intrinsic directionality. The later states of the world arise from, are produced from, the earlier states. This is independent of, e.g., the direction in which entropy increases. Even if the world were at thermal equilibrium, with constant entropy, still the later states would be produced from the earlier states in accord with the fundamental laws of physics.

Sometimes it is difficult to make the dispute clear, but one clue is that many physicists and philosophers like to say that the passage of time is an “illusion”. In my account of things, it is not at all illusory: time passes from past to future by its intrinsic nature. Further, the fundamental laws of nature are exactly physical constraints on what sorts of later states can come from earlier states. Parmenides, of course, also argued that time and motion are illusions. I think I understand what he was claiming, and think it is just flatly false. I don’t see the modern defenders of the “illusion” claim as in any better position than Parmenides was.

I further believe that physicists have been misled by the mathematical language they use to represent the physical world. Temporal structure is part of (maybe all of!) the geometry of space-time, and the standard mathematical description of geometrical structure was developed with purely spatial structure in view. Space, unlike time, has no directionality and the mathematics developed to describe spatial geometry does not easily or naturally represent directionality. The project I have been working on for the past few years involves replacing that mathematical language (standard point-set topology) with a new mathematical language called the Theory of Linear Structures. In the Theory of Linear Structures the possibility of an intrinsically directed geometry arises naturally. If one rewrites Relativistic physics in this mathematical language, the intrinsic directionality of time stands out.

As for causation, everyday causal locutions are highly context-sensitive and subject to pragmatic considerations. One does not want any foundational physical concepts to have these features, so at least everyday causal locutions cannot be translated cleanly into basic physical terms. Furthermore, physics gets on fine without mention of causation: dynamical law does all the work. So there is no need to admit some new irreducible notion of causation to make sense of physics. A deterministic physics might endorse a claim like “earlier global physical states cause later global physical states”, but that claim is of little use for everyday talk of causes.

3:AM: You challenge Ockham’s razor – is this because it offers a spurious a priori principle to oppose a rich ontology given by physics and therefore disregards the science for a sort of aestheticism?

TM: If one interprets the razor as a blanket prima facie preference for smaller rather than bigger ontologies then I can’t think of any justification for it. There is one obvious piece of methodological advice: if someone proposes that some entity exists, ask what grounds there are for believing in it and what grounds for believing in rival ontologies. Of course, there will be disputes about what constitute “good grounds” for credence in any entity. There are more straightforward empirical grounds, and more general sorts of superempirical grounds, which often go by names like “simplicity”, “elegance”, etc. Those names often point at features that can be given a sharper, and more compelling, characterization. But I don’t think anything at all convincing comes from just counting entities or types of entities. For example, the empirical evidence for the electromagnetic field all comes down to the observed behavior of charged matter such as electrons and protons. A theory that denies the existence of the field but postulates that electrons and protons behave as if there were such a field obviously has a smaller ontology. But I don’t see that as counting in its favor in the least.

3:AM: Relativity and quantum physics seem very strange when physicists unpack them for us. So we’re used to being told that a cats’ life is dependent on being observed, that a person going into a black hole will burn up when observed from outside the hole but from inside nothing happens to her, Entanglement seems to say particles that are miles apart are still connected somehow, that there isn’t time and space but a four dimensional spacetime block universe instead. Is the reality as strange as all this suggests, or are we just messing up interpreting the theories very badly?

TM: The list you give is a very, very mixed bag, so the immediate moral is not to adopt any default attitude about what physicists say. No clear, exact understanding of quantum theory implies that the health of a cat is dependent on being observed, and the claim about so-called “black hole complementarity” is just as nonsensical as it seems. Nonlocality in the physical world (which seems to be produced in part by entanglement in the quantum state) is proven by observed violations of Bell’s inequality, so we have to take that on board. And the four-dimensional space-time structure, properly understood, is perfectly clear and even geometrically simpler than Newton’s theory of space-time structure. Each case has to be approached individually, with an open mind, and also with a healthy dose of skepticism.

3:AM: You have recently presented the first half of a philosophy of physics that fleshes out how you think we should think about physical reality. In this first volume you’re looking at space and time and spacetime and so deal with theories of relativity. What are the key philosophical confusions that arise when trying to conceptualise physical reality using these theories?

TM: The theory of Relativity is a theory of space-time structure. According to the theory that structure, the geometry of space-time, is perfectly objective and rather different from the space-time structure postulated in classical physics. In the General Theory, the geometry is dependent on the distribution of matter and energy. Relativity is intrinsically perfectly clear, but often presented more obscurely than it need be. Sometimes this is because it is presented in terms of coordinate systems, and coordinate systems are not physically real. The first step in understanding the theory is to learn a coordinate-free presentation, and to think in terms of pure geometrical structure.

The history of mathematical physics over the last three centuries is one of favoring numerical and algebraic presentations over geometrical ones. And in the history of mathematics proper, Dedekind set about to remove all reference to geometry from the analysis of numbers. I am interested in the other side of the coin: removing all reference of numbers from the analysis of geometry.

Numerical methods were introduced into geometry by means of coordinate systems. This can be extremely powerful as a mathematical tool, but it can also obscure the physical structure under analysis. If my own presentation of Relativity has any virtue, it is this relentless focus on geometrical structure independently of coordinate systems and numbers generally.

3:AM: How do you conceptualise relativism so that we don’t misunderstand the theories and are there aspects of your interpretation that will perhaps surprise many of us?

TM: It has often been remarked that “The Theory of Relativity” is a very bad name for Einstein’s theory. One is told, for example, that in his theory simultaneity is “relative” to an observer or to a reference system. What is correct is that simultaneity is nonexistent in the theory: there just is no such physical relation among events. “Simultaneity in a coordinate system” is just a matter of how we (more or less arbitrarily) attach numbers to events, and has no intrinsic physical interest.

The Relativistic account of space-time geometry makes the light-cone structure of space-time a fundamental part of its geometry. This, rather than the “constancy of the speed of light” lies at the heart of the theory. Indeed, all reference to the “speed” of anything, including light, is either about “speed in a coordinate system” (and so is as much about coordinates as about physical reality) or else a completely inappropriate throwback to Newton’s theory of Absolute Space and Time (in which things do have unique objective speeds). Phrases like “clocks go slower as they approach the speed of light” are multiply misleading: accurate clocks do not “slow down”, they always record the objective length of their trajectories, and there is no such objective state as “approaching the speed of light”. Clocks never have objective speeds at all. All of these inappropriate and misleading phrases can be avoided. Relativity postulates an objective geometrical structure to space-time and accurate clocks measure that structure, i.e. the proper time along their trajectories.

3:AM: Quantum mechanics is even weirder. Physicists delight in telling us that I’ve got to accept that reality is dependent on our observations and that rejecting that proves an ignorance of science. This seems mystical and Idealist. How do you see the relationship between quantum mechanics and common sense? Have we got a good philosophical grip on this science yet? Will we ever?

TM: The situation with respect to quantum theory is completely different from that with respect to Relativity. Properly speaking, there is no such thing as “quantum theory” that can be “interpreted”. A physical theory should make clear postulates about what physically exists and how it behaves. What is in physics books is not a theory in that sense, but rather a (somewhat imprecisely formulated) recipe for making certain sorts of predictions, which is (nonetheless) extremely accurate. What is called “interpreting quantum theory” is really a matter of constructing clear and precise physical theories that return these same predictions, or nearly the same. There are several different general ideas for how to construct such theories that have been fleshed out in the non-Relativistic domain. None of these clear theories makes physical behavior dependent on observation as such. Indeed, the so-called “measurement problem” is just the problem of articulating a physics in which the sorts of experiments called “measurements” are treated as physical interactions just like any other. The exact nature of those interactions depends on the detailed physics proposed, but the physical analysis of these interactions according to the theory should validate the quantum prediction recipe.

That is not to say that these exact quantum theories do not shock “common sense”. Bell’s theorem implies that one way or another the physics should implement some form of non-locality, which is not going to comport with common sense. The “Many Worlds” approach obviously violates common sense even more. But no physical theory should have to accommodate common sense any more than to explain why effective “common sense” ways to interact with the world are as effective as they are. Physics should aspire to clarity and precision, and the main complaint about textbook “quantum theory” is that it has neither.

3:AM: I think you say that some of the difficulties are caused by physicists using the wrong math? Is that right? And can maths be explained by physics, and if it can, wouldn’t that make all physics theories viciously circular?

TM: Mathematics is the language of mathematical physics, and physical theories can appear to have different implications depending on the language in which they are written. So one thing that can be meant by “the wrong math” is “an inappropriate mathematical language”. As I said above, I think that the standard mathematical tool used for describing geometrical structure hides the intrinsic directionality of temporal structure, and the new language I have developed makes it manifest.

In fact, the difference between standard topology and the Theory of Linear Structures runs a bit deeper. In order to form a space-time out of a set of point events, the events must be somehow organized into a structure. Standard topology postulates that the foundational organization is provided by “open set” structure: you specify the topology of a space by specifying which collections of points in the space form open sets. The Theory of Linear Structures postulates that the most basic geometrical organization is specified by indicating which collections of points constitute continuous lines or directed lines. These are alterative accounts of geometrical structure, and so when employed by mathematical physics they suggest different claims about physical structure. In a Relativistic setting (but not a classical setting), one can maintain that the ultimate physical source of directed lines in space-time is time: the ordering of the events is exactly time order. Thus, space-time structure is reduced to pure temporal structure. There is no similar way to give a physical account of the organization of events into open sets.

It is not a matter of “explaining” math by physics. Think of mathematics as providing various tools, representational tools, for the use of mathematical physicists. Physicists represent physical structure by means of mathematical tools. The deep question of why a given mathematical object should be an effective tool for representing physical structure admits of at least one clear answer: because the physical world literally has the mathematical structure; the physical world is, in a certain sense, a mathematical object. This seems absurd for numerical representations: the world is not made of numbers. But it never seemed absurd for geometry: physical space was long taken to be a three-dimensional Euclidean space. Once one thinks of mathematics as providing representational tools, then it opens the possibility of some tools working more smoothly, the way a screwdriver works more smoothly for getting a screw into wood than a hammer does. That is explained by the structure of the screw and the wood, and the way the screwdriver works. Similarly, some mathematical tools can work better for doing physics, and that might be explained by the structure of the physical world.

3:AM: What do you make of someone like James Ladyman who argues that everything thing must go, in that our notion of thingyness is no longer underwritten by physics and that what we have instead are relationships between structures? And he also disputes the idea that there are any fundamentals anywhere, and that so long as we recognize that different scales require different ontologies everything is explained?

TM: The term “thingyness” does not convey anything of use to me. In a certain sense, as soon as one gets used to thinking in terms of space-time events the usual notion of a “thing” gets left behind. Physics is none the worse for it. But spatio-temporal relationships among events are not, in any clear sense, “relationships between structures”. Indeed, I don’t see how one can have structures without some sorts of entities that are so structured. The entities (like events, or quantum states, or fields, or particles) may or may not be “things” in the everyday sense, but that hardly seems worrying.

The idea that nothing is fundamental is one I find comprehensible but not plausible. In one clear sense, the physical description of a situation is more fundamental than the chemical or biological or economic or psychological description of the same situation. Chemistry, for example, can get along well using simple laws about valence electrons to make predictions about atomic bonding, but the description in terms of electron shell structure is both more detailed and more accurate. And physical descriptions themselves can be more or less detailed. I believe that there should be a fundamental, maximally detailed physical description, but it is logically possible that one can always go to further and further levels of detail and accuracy.

One sense in which physics is more fundamental than other sciences is illustrated by the “Wernher Von Braun Principle”. The lyrics to a wonderful Tom Lehrer song run: “Once the rockets are up, who cares where they come down? “That’s not my department”, says Wernher von Braun”. There are many events in space-time for which the biologist or economist or psychologist can say “That’s not my department”: stellar collapse, for example. But every actual event that the biologist or economist or psychologist tries to account for also falls under the purview of physics. There is nothing in space-time about which the physicist can say “That’s not my department”. In this sense, physics underlies all of biology and economy and psychology. In this sense, the physical description is more ontologically fundamental.

Nonetheless, disciplines other than physics can provide insight or understanding of phenomena that are not given by the physical analysis alone. In this sense, the special sciences can be explanatorily (but not ontologically) autonomous from physics. Here’s a simple example. A particular physical system, which happens to be a computer, sits on my desk displaying a little clock whose hands go round and round. This must be explicable from a purely physical analysis of the system: electricity runs through the wires and chips in certain patterns that yield the image of the clock. The computer scientist can provide a different sort of insight into the phenomenon: she notices that my program has a loop in it. Interpreting the little clock as an indication that the algorithm is still running, she predicts that the clock with go round forever without knowing anything at all about the physics of the machine except that it somehow instantiates the computer program. If one only had the physical description, one would miss this insight into the phenomenon.

Still, the physical treatment is in one sense more fundamental. The computer scientist says that unless something intervenes to change the programming, the clock will go round forever. The physicist says that unless something intervenes physically, the screen will go black in exactly 34.7 minutes, when the battery runs out. The physicist, if he has done his job properly, will make the correct prediction, and must modify the physical theory if the prediction fails. The computer scientist can say, when the question of battery life comes up, “That’s not my department”.

So I would say that while phenomena can require, for their most complete understanding, different sorts of conceptual descriptions, these are not really different ontologies. The ontology is all, at the most fundamental level, a physical ontology. And I believe that physics itself has a most fundamental level. That is the level physicists themselves are seeking.

3:AM: And other than your own books, are there five others you could recommend to help us delve further into this extraordinary world?

TM: For anyone interested in foundations of physics, I would only half in jest recommend getting John Bell’s Speakable and Unspeakable in Quantum Mechanics and reading it five times. But for variety and inspiration, I always find it refreshing to go back to Einstein’s Autobiographical Essay in Albert Einstein: Philosopher-Scientist. Two excellent books for those trying to puzzle out quantum theory are David Albert’s Quantum Mechanics and Experience and GianCarlo Ghirardi’s Sneaking a Look at God’s Cards: Unraveling the Mysteries of Quantum Mechanics. And one (to my mind) neglected masterpiece in the methodology of science is Imre Lakatos’ delightful and profound Proofs and Refutations.


ABOUT THE INTERVIEWER
Richard Marshall is still biding his time.

First published in 3:AM Magazine: Friday, July 5th, 2013.