Time and physics

Einstein's rejection of the notion of time as we know and experience it was squarely based in classical physics and classical mathematics. One problem with such a view is that it assumes the existence of infinite information (e.g. infinite decimal expansions).

Nicolas Gisin, a physicist at the University of Geneva, wants to reformulate standard physics in terms of intuitionistic mathematics. This approach holds the promise of resolving some of the paradoxes and confusions which have bedevilled theoretical physics for over a century.

Information is physical. We now know that there are strict limits on how much information can exist within any specific volume of space.

Nathalie Wolchover writes: "The universe’s initial conditions would, Gisin realized, require far too much information crammed into too little space. “A real number with infinite digits can’t be physically relevant,” he said. The block universe, which implicitly assumes the existence of infinite information, must fall apart."

Wolchover's non-technical article on Gisin's ideas and reactions to them by fellow physicists is well worth reading. This is how it begins:

Strangely, although we feel as if we sweep through time on the knife-edge between the fixed past and the open future, that edge — the present — appears nowhere in the existing laws of physics.

In Albert Einstein’s theory of relativity, for example, time is woven together with the three dimensions of space, forming a bendy, four-dimensional space-time continuum — a “block universe” encompassing the entire past, present and future. Einstein’s equations portray everything in the block universe as decided from the beginning; the initial conditions of the cosmos determine what comes later, and surprises do not occur — they only seem to. “For us believing physicists,” Einstein wrote in 1955, weeks before his death, “the distinction between past, present and future is only a stubbornly persistent illusion.”

The timeless, pre-determined view of reality held by Einstein remains popular today. “The majority of physicists believe in the block-universe view, because it is predicted by general relativity,” said Marina Cortês, a cosmologist at the University of Lisbon.

However, she said, “if somebody is called on to reflect a bit more deeply about what the block universe means, they start to question and waver on the implications.”

Physicists who think carefully about time point to troubles posed by quantum mechanics, the laws describing the probabilistic behavior of particles. At the quantum scale, irreversible changes occur that distinguish the past from the future: A particle maintains simultaneous quantum states until you measure it, at which point the particle adopts one of the states. Mysteriously, individual measurement outcomes are random and unpredictable, even as particle behavior collectively follows statistical patterns. This apparent inconsistency between the nature of time in quantum mechanics and the way it functions in relativity has created uncertainty and confusion.

Over the past year [...] Nicolas Gisin, has published four papers that attempt to dispel the fog surrounding time in physics. As Gisin sees it, the problem all along has been mathematical. Gisin argues that time in general and the time we call the present are easily expressed in a century-old mathematical language called intuitionist mathematics, which rejects the existence of numbers with infinitely many digits. When intuitionist math is used to describe the evolution of physical systems, it makes clear, according to Gisin, that “time really passes and new information is created.” Moreover, with this formalism, the strict determinism implied by Einstein’s equations gives way to a quantum-like unpredictability. If numbers are finite and limited in their precision, then nature itself is inherently imprecise, and thus unpredictable. [...]

On this view the future is open (rather than closed or predetermined), and time is closer to how we experience it – and so intuitively envisage it to be – than most physicists have supposed.

Lee Smolin's realism

Lee Smolin is a respected physicist who has always had strong philosophical interests and convictions. He recently articulated his realist views in a public lecture. What follows are my notes on his lecture mixed in with a few comments and observations.

Smolin is strongly opposed to postmodernists who reject the notion of objective truth and who see reality as a social or historical construct. He draws parallels between the anti-realism of postmodernists and the anti-realism of certain physicists associated with the development of quantum mechanics (QM) and the so-called Copenhagen interpretation.

Smolin claims (as Einstein did) that QM is an incomplete theory and so, in a real sense, wrong. The key problem with QM as Smolin sees it is the so-called “measurement problem”. It relates to the notion of wave–particle duality and the two laws or rules that QM provides to describe how things change over time. Rule 1 or law 1 says, in effect, that (except during a measurement) the wave evolves smoothly and deterministically (somewhat like a wave on water). This allows the system to simultaneously explore alternative histories which lead to different outcomes all of which are represented by the smooth flow of the wave. Rule 1 applies when you are not making a measurement. Rule 2 applies only when you make a measurement.

Smolin argues that the 2nd rule means that QM is not a realist theory. If we (or other observers) were not around, only rule 1 would apply.

One of the main developers of the theory, Erwin Schrödinger, was uncomfortable with the theory and its implications. He crystallized his doubts in the form of the famous live/dead cat-in-the-box thought experiment (which is explained by Smolin in his talk (starting at 39.54)).

Niels Bohr, in contrast to Schrödinger, embraced the paradoxical nature of QM, partly because it fitted in with ideas which he had developed previously. Bohr’s notion (or philosophy) of complementarity was shaped by these ideas and by the observed behavior of elementary particles. Sometimes such particles seem to behave as if they are waves, sometimes as if they are particles and, crucially, how they are observed to behave depends on the details of how we go about observing them.

Smolin takes an unequivocally negative view of Bohr’s metaphysical views as well as of the views of Bohr’s protégé, Werner Heisenberg. Here he is on the former:

“Now, of course, Bohr had a lot to say about things being complementary and in tension all the time and you always have to have two or more incompatible viewpoints at the same time to understand anything, and that especially goes […] for knowledge and truth and beauty. And he got off on the Kabbalah, of course. Anyway [long pause] … it doesn’t cut it with me.”

For Smolin, QM's incompleteness is intimately bound up with its incompatibility with realism.* QM is not consistent with realism because the properties it uses to describe atoms depend on us to prepare and measure them.

“A complete theory,” insists Smolin, “should describe what is happening in each individual process, independent of our knowledge or beliefs or interventions or interactions with the system.” He is interested in understanding “how nature is in our absence.” After all, we were not around for most of the history of the universe.

Smolin defines realism as the view that nature exists independently of our knowledge and beliefs about it; and that the properties of systems in nature can be characterized and understood independently of our existence and manipulation. Our measuring etc. “should not play a role in what the atoms and elementary particles are doing.” What he means, I think, is that our interventions should not play an essential or crucial role in the descriptions and explanations which our theories provide.

“A theory can be called realist,” Smolin explains, “if it speaks in terms of properties whose values do not require us to interact with the system. We call such properties “beables”.”

By contrast, a theory whose properties depend on us interacting with a system is called operational. Such properties are called “observables”.

Observables are defined as a response to our intervention. Beables, by contrast, are not defined as a response to our intervention. They are just there, it seems.

But how do we get to know the values of these properties unless we interact with the system? Also, there is the framework question. Properties and values arguably only exist within the context of a particular perspective or theory. In order for properties and values to be properties and values, we need to conceptualize them as such. I will ignore this broader question, however, and focus on what Smolin means by interaction.

Even ordinary observations (like seeing or hearing or recording something electronically) involve us or our measuring devices interacting in some way with the system we/they are observing/recording. Smolin appears not to be concerned with such interactions here because, although the nature of the observer’s perceptual apparatus and/or the nature and settings of the equipment being employed determine or pick out what is and what is not being observed or recorded, the results are otherwise quite independent. The type of datum is determined by the nature of the observer or the observing or recording process, but not the data themselves.

In the case of experiments with elementary particles, however, the situation is subtly – and sometimes dramatically – different. Interactions are such that they determine, or play an active role in determining, the values in question.

Arguably, ordinary cases of measurement and observation do not pose problems for the commonsense realist. But if our observations alter in a material way whatever it is which is being observed – as appears to be the case in respect of the quantum realm – problems arise.

Operationalism was first defined by the physicist Percy Bridgman (1882–1961). The book in which he elaborated his views, The Logic of Modern Physics, was published in 1927, the same year QM was put into definitive form. Bridgman’s philosophical approach has much in common with the instrumentalism which characterized the views of the majority of thinkers (physicists, logicians, philosophers) associated with logical positivism. Bridgman was in fact personally involved in the activities of the Vienna Circle.

It was the physicist John Bell who introduced the concept of beables. According to Bell – and according to Smolin – it should be possible to say what is rather than merely what is observed. This is all very well but – quite apart from philosophical arguments questioning the notion of a noumenal world – experimental results continue to come out against the realists. Experiments with entangled particles, for example, seem to exclude the possibility of any form of local realism. Some form of nonlocal realism is still very possible however.

Smolin is at his weakest when he talks history. The story he tells about the generation of physicists who grew up during the Great War is hard to swallow. It seems that they were predisposed to anti-realism by virtue of the unusual circumstances of their early lives. They had witnessed at an impressionable age the destruction of the social optimism of the 19th century, and so were skeptical of rationality and optimism and progress. They had lost older brothers and cousins and fathers and uncles and had “nobody above them ...” No wonder they didn’t believe that elementary particles etc. have properties which are independent of our interactions with them!

You would think that the fact that Niels Bohr, the father of the Copenhagen interpretation, was not a part of this generation would sink Smolin’s generational explanation from the outset. As would even a cursory knowledge of the history of 19th century thought which is shot through with various forms of idealism, anti-realism and radical empiricism. The phenomenalist philosophy of science of Ernst Mach (1838–1916) is a case in point. At the end of the 19th century, Mach articulated ideas which were later picked up by the thinkers Smolin is criticizing.

Smolin explicitly recognizes that Bohr’s main ideas were formed well before the development of quantum mechanics and that he was influenced by 19th century thinkers – including by Kierkegaard (whom Smolin clearly does not hold in high esteem).

Smolin quotes some of Bohr’s claims:

“Nothing exists until it is measured.”

“When we measure something we are forcing an undetermined, undefined world to assume an experimental value. We are not measuring the world, we are creating it.”

“Everything we call real is made of things that cannot be regarded as real.”

Heisenberg followed the same general approach:

“The atoms or elementary particles themselves are not real: they form a world of potentialities or possibilities rather than one of things or facts.”

“What we observe is not nature itself but nature exposed to our method of questioning.”

Bohr said: “We must be clear that when it comes to atoms, language can be used only as in poetry. The poet […] is not nearly so concerned [with] describing facts as [with] creating images and establishing mental connections.” What he meant, presumably, is that the normal referential function of natural language cannot be used in relation to the quantum world, and anything we say about that world (using natural language) will necessarily be a creative construct shot through with metaphor and paradox.

Maybe so. Or maybe not. It is not something we can know a priori. It all depends on how our models develop and on the results of experiments. But, until QM is subsumed into some (hypothetical) broader theory which allows us to envisage quantum processes in more intuitive or realism-friendly ways, Bohr's general views regarding the radical inapplicability of natural language and ordinary logic to quantum events or processes will remain plausible.



* There is also the question of gravity. Quantum field theory brings together QM and special relativity. QM and general relativity have yet to be satisfactorily reconciled, though a line of research associated with the so-called AdS/CFT correspondence – a string theory-based approach – has made considerable progress towards this goal.



This is a revised version of an essay published at The Electric Agora on June 4.

David Albert on science

Having previously wondered out loud about and attempted to speculate on David Albert's general perspective on science and religion, I thought I would let him speak for himself. Okay, it's just a YouTube video and it's a few years old, but Albert is impressive and direct and concise. (This is the man Lawrence Krauss called 'moronic'.)

There are allusions to a silly film Albert got involved in which pushes all sorts of New Agey ideas and which he is seeking to distance himself from. What is particularly interesting (given all the fuss about his reliance on Templeton funding and so on) is that, far from coming across as sympathetic to a religious view of the world, Albert suggests that science, which is revealing a hard and mechanistic reality quite at odds with human desires and expectations, constitutes our best hope of getting at the truth of things.

[If you're pressed for time, I suggest you come in at the 10 minute mark.]

Quantum lemonade

Seth Lloyd's popular book* on quantum computation, life and the universe impressed me when I first read it a few years ago. I had the sense that Lloyd was saying something very important for our understanding of reality, of what ultimately underlies the whole shebang.

I still think the basic thesis of the book - that the cosmos is a quantum computer - is fascinating and maybe even true. Certainly, the parallels between thermodynamics and information theory suggest that information (bits, or qubits, and their operations) is absolutely fundamental to an understanding of the world and - speaking very loosely - the basic stuff out of which we and the cosmos are made.

But this recent article by Seth Lloyd disappointed me in a couple of ways.

Lloyd's book is beautifully written, a model of popular science writing. The science is clearly and simply presented, and there is some good - if at times only tangentially relevant - autobiographical background material. (The story of the death of Heinz Pagels is unforgettable. 'Heartbreaking', one reviewer called it.)

By contrast the article is in large part a rehash of things Lloyd has said many times before (for example, about the recalcitrance of atoms and sub-atomic particles, their reluctance to do what we want them to do and the need for infinite guile and patience on the part of quantum engineers). And unfortunately the metaphors are strained and distracting, in my opinion, and just a touch condescending. I think Lloyd is trying too hard not to sound like a boffin.

But the most significant thing about this recent piece is that in it Lloyd doesn't attempt (as he might well have done) to talk up the prospects for serious quantum computers. On the contrary, the whole program to develop and build useful quantum computers, about which he was so sanguine in his book, is presented as being somewhat problematic.

He writes: "The quantum sensitivity [Nobel Prize-winner Serge] Haroche identified certainly makes quantum computers hard to build, but it's also that very sensitivity that makes funky quantum phenomena such as Schrödinger's cat states the basis for hypersensitive detectors and measurement devices... What's bad for quantum computation is good for precision measurement - if life deals you quantum lemons, make quantum lemonade."

In other words, if we can't have miraculously powerful computers of an entirely new kind, we can at least have very accurate clocks. Mmm.

Guess I was a bit naïve to believe the hype.

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Come to think of it, years ago I was quite excited about artificial intelligence. And they can't even do a convincing natural language interface yet.

Frankly, though, I don't much care about whether these technologies eventuate or not. What interests me more is the light that research into computing - digital and quantum - has thrown on some perennial questions.

The old answers to fundamental questions are just no good any more. And if some of the old answers do get a new lease on life, it will only be, I suspect, because they happened to prefigure an explanation informed by information theory, quantum mechanics and/or other recent theoretical work in physics or related sciences.

There is hype about technology and hype about basic science. But the fact is, though progress seems slow in both spheres, progress is indeed occurring.

Which is more than can be said of perhaps any other area of human life or endeavour.



* Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos (Knopf, 2006).