Tim Maudlin's right and (more often) muddled opinions about physics

Vincent has asked me what I thought about an interview with philosopher of physics Tim Maudlin at 3:am,

On the foundations of physics.

Regular TRF readers remember Maudlin as the main villain in the 2011 story about Tom Banks and anti-quantum zealots which was ignited by a discussion at Preposterous Universe (well, it was at Cosmic Variance at that time).

Yesterday, Maudlin mostly said the same wrong things as he did 1.5 years ago but let me discuss them again.




At the beginning, he's asked why he became a philosopher. As an undergrad, he dreamed about kibitzing about the fundamental issues in Nature but he didn't want to go through the hard exercise of learning what is needed for this kibitzing to be meaningful – so he inevitably ended with a "compromise" which meant to become a philosopher of physics.




Maudlin thinks that the spats between philosophers of science and scientists are no different than spats between scientists themselves. There's one difference, however: scientists, even when they disagree with each other, usually agree that the right answers should be found by the scientific method. Philosophers including Maudlin disagree about this very first rule – they want philosophical prejudices to be the most powerful players.

Some fruitless discussion is dedicated to the Liar Paradox, i.e. even more futile attempts to assign a truth value to the sentence "this sentence is false". This sentence can't be false because then its negation would have to be right and the negation would imply that the sentence is true; and vice versa. It can't be true and false at the same moment which means that it can't be attributed any particular truth value.

I think that most intelligent schoolkids understand the previous paragraph. On top of that, one may add some adults' interpretations. First of all, there's nothing wrong about a proposition's having an undefined truth value. Meaningless sentences can't be assigned truth values. That's the case when the fail to obey some rules of grammar or syntax. But even if they do, they may fail to obey other conditions, conditions linked to the "beef" of our axiomatic system.

This contradiction is avoided in any consistent framework to assign truth values to some propositions because any such consistent framework does forbid – has to forbid (in order to be consistent) – such sentences. These requirements are reflected by special refinements such as the GB or ZF set theory that overcome a similar paradox due to Bertrand Russell in Georg Cantor's naive set theory (which allowed a set \(M\) of all sets \(X\) such that \(X\notin X\) which makes the question whether \(M\notin M\) equally paradoxical).

Most trivially, axiomatic frameworks in physics avoid the Liar Paradox because the allowed propositions talk about external objects and don't legalize self-referring propositions at all.

The sequence of several paragraphs above really exhausts everything one may say about the Liar Paradox and some of the comments are "related applications" rather than aspects of the paradox itself. Maudlin hasn't even said the things above – still, he has "studied" (?) this kindergarten problem for years. It's just stupid to study such a triviality for years especially if the result is that he is still totally muddled when it comes to rather closely related questions.

(Later, I realized that it may not be the best idea for a guy called Motl to build on the similarity between the words Maudlin and muddled but I won't revise the text because of that!)

And be sure that he is muddled. When they discuss philosophy of mathematics, he claims that the Axiom of Choice must be either true or false. He thinks that the validity of the Axiom of Choice is on par with the validity of Goldbach's conjecture (an unproven but almost certainly true claim about integers: every integer above 2 may be expressed as a sum of two primes). However, their status isn't the same at all. Only the Axiom of Choice has been proven to be undecidable in conventional axiomatic set theory. It means that you may add it as an axiom but you may also add its negation – it is independent – and these two choices are equally allowed, equally "true". This has been proven. There can be no mathematical proof bringing some asymmetry between AC and non(AC). There can't be any physical experiments, either, because physics prohibits experiments with arbitrary infinite sets. The relevant complicated systems of sets really can't be realized physically; physics doesn't build on the mathematics of arbitrary extensive sets and sets of sets. It's picking other, more specific and continuous-number-based portions of mathematics. AC and non(AC) will forever be equally valid and equally invalid.

Nothing like that has been proven about Goldbach's cojecture which is just another not-yet-settled problem in number theory. It is sort of unbelievable that Maudlin seems to be unaware of this difference. He may call himself by pompous words such as "mathematical Platonist" but if he isn't aware of the fact that it's been proven that the Axiom of Choice and its negation are equally true – undecidable – then he is just ignorant about basic results that should dictate the philosophy of mathematics. If one builds a "philosophy of mathematics" by ignoring the rigorously proven theorems, he is bound to end up in a cesspool.

That's also where one ends up if he builds a "philosophy of physics" while ignoring or denying key scientifically demonstrated results in physics. And Maudlin does that, too.

He says some incoherent things about the arrow of time. But a few paragraphs later, he clarifies why his text had to be incoherent when he says

I further believe that physicists have been misled by the mathematical language they use to represent the physical world.

Another math hater. He believes that the maths used by physicists isn't capable of attaching a directionality (sign) to timelike intervals in the spacetime. Be sure that it is possible to equip the spacetime with this structure because the set of nonzero timelike vectors isn't connected (it is composed of the future light cone and the past light cone) and physicists are fully aware of this trivial fact.

Maudlin also rejects Occam's razor, the preference for simpler theories with fewer (independent) defining concepts and laws. There are ways to use such a "razor" incorrectly but Maudlin is clearly throwing the baby out with the bath water. Some usage of the razor is inevitable in science because one must always abandon explanations that become too contrived. Quantitatively speaking, such contrived or fudged explanations with many ad hoc choices should be eliminated because they should be assigned a tiny prior probability in the Bayesian inference – because they have to share the prior probability with many similarly contrived but inequivalent hypotheses. If one weren't able to reject any "fudged" or "too contrived" hypotheses at all, for their being "fudged" or "too contrived", we couldn't have made any progress in physics. Or any science, for that matter. We would be overwhelmed by posthumous children (ad hoc mutations) of hypotheses that were ruled out in the past. We wouldn't notice that something is wrong about this whole dynasty's DNA (whether the mutation is added or not) and more than a small mutation is needed to get the right picture.

Finally, he is asked about relativity and especially quantum mechanics. Maudlin says:

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.

The problem is that Maudlin fails to adopt the results of physics not only immediately but he fails to learn them even many years after he began to "be" a philosopher of science, whatever it means (it surely doesn't mean to possess any expertise on physics, as he demonstrates by his own example).

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.

Whether a physical system such as the cat (or, more fundamentally, an electron) may be assigned an objective property before it is observed doesn't depend on a philosopher's mood or feelings, on philosophical prejudices, or on "interpretations". It is actually a well-defined question about the way how Nature works and the only right answer that has been demonstrated by the scientific tools is that the property can't be thought of as being "objectively decided" prior to the measurement. This follows from the fact that two generic properties of physical systems are expressed by two operators that almost never commute with each other which implies that they don't share eigenstates.

The black hole complementarity is another true manifestation of this fact that observables in quantum mechanics (in the true description of Nature) refuse to commute, unlike their classical counterparts (in the description that has been falsified, namely classical physics).

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.

No, there is no violation of locality in any situation or experiment in the Minkowski space. Locality – an exact one – follows from special relativity, a principled theory supported by nearly waterproof empirical evidence. Bell's inequality implies that the laws of Nature can't be both local and "realist", and because relativity makes it very clear that they are local, it follows that they are not "realist". So both answers by Maudlin to the questions whether Nature is local and whether it is realist are wrong.

But Maudlin says some bizarre things about relativity, too.

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.

Relativity surely doesn't make space or time or spacetime any more "objective" than they were in classical physics. What it is doing is that it is forcing us to treat space and time in a unified way, as a spacetime, because the spacetime's separation or projection to space and time is not objective, as relativity shows. It is subjective, more precisely dependent on the inertial system (a rather transparent, innocent version of subjectivity, but quantum mechanics brings more intrinsically subjective aspects to physics).

So the identification "what is space" and "what is time" is something that relativity makes subjective or relative, just like the length of objects, duration of processes, and simultaneity of events. That's a good reason why relativity is called "relativity". Some concepts that used to be absolute are simply made relative. Nevertheless, this new apparent "vagueness" doesn't imply any genuine loss of predictivity because the viewpoints of the inertial observers are linked to each other by rigid principles – by the Lorentz transformations that preserve certain "invariants". That's a reason why Einstein has proposed an "opposite" name for relativity, "Invariantentheorie", as well. Because of the invariants, the different observers' answers are not "arbitrary". The truth about everything isn't relative or subjective. Only some numbers etc. – components of vectors and tensors – have to be rotated into each other.

As the name "relativity" correctly indicates, certain questions – such as the simultaneity of two events – do become observer-dependent in relativity. Others, such as whether a bomb exploded in a city, remain observer-independent and "absolute" because these properties are functions of "invariants".

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.

There is nothing wrong about a description in terms of coordinates and in fact, it is pretty much needed when we want to calculate pretty much anything – or at least a sufficiently general and complex problem. The fact that the choice of coordinates isn't unique isn't a lethal disease of coordinates as a concept in any sense. It just means that certain aspects or intermediate results are observer-dependent or relative or subjective, if you wish. One may still extract some properties that are observer-independent.

Maudlin's mysterious "purely geometric structure" is mathematically nothing else than the situation as seen in a coordinate system modulo all Poincaré transformations that identify "equally looking situations" with it. Such a quotient, something using the word "modulo", is omnipresent and increasingly omnipresent in physics (especially when we consider theories that are naturally formulated using gauge symmetries, BRST formalism, and so on). There's nothing wrong about it. It's so important that one should better learn how to work with it and to learn why there's nothing wrong with it – instead of promoting a completely misguided philosophy that physics should only work with the observer-independent concepts (e.g. that it should even ban coordinates). Just to be sure, I am not telling you that you can't like a description of a subset of problems that avoid the explicit coordinates or numbers. I am just telling you that you will have a hard time to find a similar description for other contexts – and the problems will be increasingly severe as you converge towards state-of-the-art physics because redundancy has simplified many things and physicists don't even know how to work without it.

After all, the "purely geometric structure" isn't a well-defined concept before we begin to define it using something that does use a mathematical representation of a space – and a space is defined as a set of \(n\)-tuples of real numbers. There's no versatile enough "constructive" mathematical definition of geometric objects that would completely avoid numbers and coordinates.

One could say that Maudlin's misguided commandment that a scientific theory should avoid all not uniquely determined concepts and quantities and all quantities that are subjective or observer-dependent is also the root cause of his inability to comprehend quantum mechanics correctly. It's a fundamental postulate of quantum mechanics in general that the statements that quantum mechanics may answer are intrinsically subjective observations or "perceptions" if I use a word that emphasizes the non-classical and in this sense "non-materialist" character of Nature as quantum mechanics discovered it.

Maudlin criticizes the name "relativity":

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.

It's not true that simultaneity has no intrinsic physical interest. What is true is that it is observer-dependent, it is relative. But something's being relative doesn't mean that it has no intrinsic physical interest. As I said, every meaningful and natural enough description of every sufficiently general and complex situation has to work with quantities that are observer-dependent.

Maudlin's statement that simultaneity is unphysical is wrong and completely different from the right statement that simultaneity is relative. By his desire to outlaw relative i.e. observer-dependent quantities, he is denying both relativity as well as pretty much all of physics because relativity is saying that some quantities that have been used in physics for centuries are observer-dependent. If you declare them "unphysical", you throw the baby out with the bath water. You just shouldn't do such things unless you are a moron. Physics is composed of quantities such as time, space, energy, momentum, mass, electric fields, and so on. They're surely not unphysical but they're observer-dependent.

A related fact is that he is distorting the "degree of arbitrariness" that the Lorentz or Poincaré transformations bring to the coordinate description of physics. These coordinates aren't attached "almost arbitrarily"; there's just a 6- or 10-dimensional group so the inertial systems only form a 6-dimensional or 10-dimensional set. If you have 1006 or 1010 coordinates of many objects, 6 or 10 of them may be used to isolate the inertial system and the remaining 1000 coordinates tell us some objective, Lorentz-invariant information about the system. So the "attachment of the numbers" called coordinates is as far from "arbitrary" as you can get: a vast majority of the coordinate information about a complex enough system (everything except for 6 or 10 numbers) is the opposite of "arbitrary".

His attempt to criticize all notions that depend on the inertial system leads to some comical assertions – well, at least I couldn't resist to laugh out loud when I was reading the following stupidities:

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”.

It makes a perfect sense to approach the speed of light. That's what the LHC has done with several quadrillion protons before they were collided. Their velocity – relatively to the soil in Switzerland or relatively to the Sun, the difference isn't really detectable here – increases up to 99.9999 percent of the speed of light. It approaches the speed of light. An observer moving by a similarly high speed relatively to the Earth may disagree but everyone else will agree that the protons are approaching the speed of light but never reach it – unless he is a moron.

And arbitrarily accurate clocks do slow down by the Lorentz factor, \(\sqrt{1-v^2/c^2}\). This just means that the number of ticks that the moving clocks make per unit time is smaller exactly by this factor than the number of ticks that the same stationary clocks do during the same unit time. This statement is true and it is how "slow down" is defined. To deny this slowdown means to be an idiot, too. It's surely one of the basic high-school-level implications of relativity.

When he denies that one can talk about the time that a tick takes or about the velocity that is increasing, it is pretty much clear that he can't talk about any physically meaningful concept, so he can't possibly understand relativity. At most, his approach may be good to prevent you from talking about non-relativistic (today incorrect) physical questions. But it will prevent you from talking about almost all relativistic (correct) questions, too. His commandments are uncorrelated with the changes that relativity brought us.

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.

Clocks don't have objective speeds because nothing has objective speeds. Speeds depend on the coordinate system. After all, they depended on the coordinate system – they were relative – already in Newtonian physics. But this relativity of the velocity doesn't make the concept of velocity unphysical or "misleading". Velocity remained as important a quantity for the description of any motion as it was in Newtonian physics.

But the full-fledged bigotry of Tim Maudlin is only uncovered when they begin to talk about quantum mechanics.

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”.

LOL. There is not quantum theory, we learn. "Quantum theory" was the term reserved for Planck's first 1900 "quantum" results about the quantization of energy carried by electromagnetic waves. That's why people began to use a different term, "quantum mechanics", for the full new framework of physics that emerged in the 1920s. We use "quantum mechanics" for all the universal postulates that were defined in the 1920s and that are obeyed by many particular "quantum theories" and for the whole class of these theories as well, whether these theories are just "mechanical" or more complicated.

Quantum mechanics not only exists but it is the main theory underlying modern science. Claiming that it doesn't exist is a sign of the utter stupidity of the speaker.

A physical theory should make clear postulates about what physically exists and how it behaves.

Quantum mechanics clearly says that the outcomes of the measurements exist – from the viewpoint of those who perceive them – and gives us tools how the probabilities of different results may be calculated assuming the knowledge about the initial state. It also clearly says that no "objective properties" exist prior to the measurement. It's as clear as it can be.

Be sure that you won't be able to prove that quantum mechanics is incomplete just because it says that "there is no objective reality prior to the measurement". To prove that such a reality actually does exist, you would have to measure it, but to measure something before the first measurement is the same contradiction as the proposition that 3 is smaller than 3. The opinion that objective reality exists prior to the measurement is not only unprovable but, as quantum mechanics shows, incorrect.

If you want to squeeze Nature into a straitjacket where Nature is "obliged" to respect your rule that "something objective must exist prior to the measurement", then your efforts are equally foolish as if you "demand" that the right theory of the origin of species must assign a day of the week to every species to indicate when it was created by God. The right theory simply doesn't obey this condition, OK? Life didn't arise in this way. And the refusal of the theory to assign the days of the week isn't a flaw. Instead, it is your flaw if you demand such a thing because such a "demand" you are articulating shows that you are ignorant about something really basic about science. You may scream your "demands" loudly and seemingly authoritatively but that only shows how big a jerk you are.

The case of the "objective reality that physically exists" is identical. It just doesn't exist at the fundamental level, OK? If you don't like how Nature around us works, then please f*ck off and ask for asylum in a different Nature.

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.

It's not a theory in a stupid sense but it's surely a theory in the scientific sense. The purpose of a scientific theory isn't to pay lip service to arrogant morons with invalid philosophical prejudices about Nature's inner workings. The purpose of a theory is to explain and predict the observations and experiments we have made, we are making, and we will make. That's what quantum mechanics does, too. So it is surely a theory. A paramount one.

The disrespectful word "recipe" that Maudlin offered to compare quantum mechanics in cooking doesn't show the inadequacy of quantum mechanics. Instead, it shows the inadequacy of himself as a thinker about physics. Is there any difference between a theory and a recipe? Well, the difference is arguably subtle and hard to pinpoint but there is surely a difference in the degree of respect that these words ignite. Quantum mechanics is nothing like a recipe for a single type of a pie. Instead, it is the right framework that underlies all of physics – which includes not only the behavior of all pies and kinds of pies but also all other natural sciences. From this viewpoint, the word "recipe" is inappropriate. However, a "recipe" also conveys the message that the theory/recipe tells you very clearly what you should do to derive the predictions and how they're tested etc. This specific character of the "quantum recipe" – the fact that it's not muddy – is a virtue, not a vice.

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.

Indeed, this is what is usually meant by the people when they talk about "interpretations of quantum mechanics" and that's why almost all people who are working on "interpretations of quantum mechanics" are misguided bigots. They are trying to fabricate a non-quantum explanation that pretends to be the right theory – quantum mechanics – but it's not. Of course, they can never succeed but the very effort is painful.

The research of quantum mechanics is telling us certain important things – much like heliocentric astronomy or Darwin's theory of evolution – and whoever tries to "construct" a geocentric, creationist, or classical (i.e. "realist") framework to "present" these three theories has completely missed their point. Heliocentric astronomy isn't just a minor refinement of the geocentric one; evolution isn't just a minor refinement of creationism; and – most undoubtedly – quantum mechanics isn't just a particular version of a classical theory. Revolutions have taken place in all three situations and the quantum one is arguably the most profound one. People who deny that these revolutions took place and who want to return to the old ways of thinking by "demands" that it has to happen are idiots who have learned nothing.

There are several different general ideas for how to construct such theories that have been fleshed out in the non-Relativistic domain.

It is impressive that Maudlin has noticed that these misguided efforts ultimately fail because of relativity. But he apparently doesn't care even though special relativity has been known for 108 years to be a crucial requirement that every viable theory in fundamental physics has to obey.

A chaotic segment in which Maudlin ignores relativity and uncontrollably promotes various "realist interpretations" of quantum mechanics – i.e. non-quantum, classical theories that are fudged to imitate some of the results of some quantum mechanical theories – follows. It is very clear from the text that he doesn't prefer any "approach" to this misguided enterprise. He knows that none of them is any good so all of them are "equally good for his cause". The cause, namely his totally invalid dogma that quantum mechanics is "obliged" to be translated to the framework with an "objective reality" in the classical sense, is clearly more important to him than the validity of any statement he makes.

Some muddled paragraphs use convoluted terms such as "Theory of Linear Structures" which, as far as I can say, only have the purpose to assign the directionality (sign) to timelike intervals. The name is completely inappropriate and he doesn't even seem to solve the trivial problem of assigning the signs.

Following paragraphs talk about "thingyness", whatever it is, that Maudlin rejects. And he sort of correctly points out that other scientific disciplines reduce to physics – except that he doesn't understand the basic framework in which modern physics operates. At the end, he recommends some outdated texts such as one by John Bell (well, texts that were obsolete already when they were first published) to emphasize that he hasn't learned – and he doesn't want to learn – anything about the revolution that kickstarted modern physics.

But I must end this blog entry with a praise. He has an amazing ratio of the money divided by knowledge+expertise that he is receiving for claiming to study the foundations of study. It is quite amazing that you may be paid for studying foundations of physics even though you have understood them much less correctly than an average undergraduate student.