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A Possible Solution to the Problem of Time in Quantum Cosmology
By Stuart Kauffman and Lee Smolin

Lee Smolin, Murray Gell-Mann, Julian Barbour, Stuart Hameroff, Philip Anderson, Murray Gell-Mann (2), Lee Smolin (2), John Horgan, Lee Smolin (3), Stuart Hameroff (2), John Baez, Stewart Brand, John Baez (2), George Johnson, Stuart Hameroff (3), Lee Smolin (4), Kevin Kelly, Stuart Kauffman, Julian Barbour (2), John Horgan (2), Kevin Kelly (2), John Maddox, Lee Smolin (5), Piet Hut, Lee Smolin (6), and Piet Hut (2) on A Possible Solution to the Problem of Time in Quantum Cosmology by Lee Smolin and Stuart Kauffman.

From: Lee Smolin
To: John Brockman

Date: 3-26-97

Dear John,

As you know, Stu Kauffman and I met each other a year ago. After an exchange of emails I invited him to Penn State to give a talk. From the moment he got off the plane he was talking, and what he wanted to talk about was how we might invent rules for knots and networks to evolve in time in such a way that they may replicate themselves and hence create autocatalytic systems. It is a true fact about Stu that he is always talking, but it is also a very interesting fact that this idea of networks replicating themselves is relevant for both the origin of life and quantum gravity. The first, because living cells consist of a myriad of chemical reactions that are collectively autocatalytic -- that is each molecule is synthesized in reactions that are catalyzed by other molecules.

The question is interesting for quantum gravity because, as Carlo Rovelli (now professor at the University of Pittsburgh) and I discovered a few years ago, the quantum states of the gravitational field-or equivalently of the geometry of space-are described by networks of a certain kind. These are called spin networks, and they were originally invented by Roger Penrose in the 1960's, but for a completely different reason. We rediscovered them as part of our search for a quantum description of space and time. These networks are graphs with integers on the edges, representing quantum mechanical spins.

Carlo and I, and then some others -- especially two very good postdocs Thomas Thiemann and Rouman Borissov -- figured out how these networks should evolve in time if Einstein's equations hold at the quantum mechanical level. But there is a problem, which is they seem unlikely to do something nice. The networks are very very tiny, a typical volume occupied by a node is 10 to the power -99 centimeters cubed (that there is a discrete scale to quantum geometry-even if very tiny, is one of the things Carlo and I discovered.) But the world seems regular, and its geometry seems Euclidean on scales much much larger than these tiny quanta of geometry. Thus, to describe the real world these networks must grow slowly and smoothly, so that they describe the geometry of the space we see. This is unlikely, just as it is unlikely that atoms organize themselves into a regular crystal such as in a metal. And this is the essence of the problem-to understand why the world is big (compared to 10 to the -33 centimeters) and the geometry of space is almost Euclidean requires that these networks that describe the quantum geometry of space organize themselves into a very regular arrangement.

I don't know what Stu knew about quantum gravity when we met -- I think he had only heard something about our knots and networks. But somehow he had intuited right away that a key problem in quantum gravity and cosmology was going to be a problem of how these networks can self-organize themselves into a regular, slowly changing state. For him this was analogous to problems of self organization as they appear in biology and other areas such as non-equilibrium statistical physics. And this is what he was talking about when he got off the plane to meet me.

I had also thought about this issue, and seen the possibility of an analogy between problems of self-organization in quantum gravity and cosmology and problems in biology. This was one reason I wanted to meet Stu. But of course I'm a physicist, this is what I do. How it is that Stu understood this I don't know, but this shared feeling of the importance of analogies between problems in fundamental physics and biology has been the basis of what quickly became a great friendship and a collaboration.

In the past year I've taught Stu a bit of quantum mechanics and in return he has taught me something about biology. So after a while it seems we have fallen into working together on both kinds of problems. I am part of a collaboration he organized to make a try at understanding the origin of life and I have also tried to formulate mathematically his notion of an autonomous agent. I also described to him a problem in astronomy I was working on -- which is to understand how spiral structure forms in galaxies. He told me about models of pattern formation biologists and chemists use, due originally to Turing, called reaction diffusion equations, which I then applied to the interactions among the stars, gas and dust in the disk of a spiral galaxy. And Stu has also gotten involved in our work on quantum gravity. This paper is one outcome of this work.

For me, this paper came from the coming together of three lines of thought. The first was a long conversation Stu and I were having about how to formalize theoretical biology. Stu is very worried that you cannot specify all the possible tasks or niches or properties that might give an organism selective advantage all at once, in advance of watching a system evolve. He is not sure that the standard model of natural selection in which there is a fitness landscape, labeled in advance by fixed properties is really useful. Instead, he has been trying to develop a notion of the adjacent possible states: that a system evolves by moving into a space of configurations that are just one step -- one new reaction or one exaptation -- away from the present state. At some point he mentioned that he was also worried about whether you could describe a complex system quantum mechanically, because it might not be possible to specify a basis for the possible quantum states of the system in advance.

I had dismissed this last point as his taking things to far -- as he sometimes does. But then all of a sudden I realized that this might in fact apply to the space of states of quantum gravity. The reason is that the mathematical structures involved, which are the networks I mentioned, might not be classifiable. This means that one might not be able to invent any test that could be guaranteed to tell any two apart in a finite amount of time.

I realized this because I was caught in an argument between two views of time. On the one side Julian Barbour, whose ideas on understanding of space and time in relativity theory have been very influential. Nonetheless, I had been unable to agree with his thinking of the last few years, in which he has come to the conclusion that in quantum cosmology time cannot be fundamental. Time, according to him, should play no fundamental role in nature.

But although I instinctively disagree with this, I have been unable to defeat the argument that leads Julian to it. Nor has anyone else. The result is a famous problem in quantum cosmology called the problem of time -- time is nowhere to be found in the fundamental equations of the theory.

On the other side I have been worrying about the meaning of some work I have been doing with Fotini Markopoulou, of the University of London. Fotini has her own strong views about time, which are very different from Julian's. In particular, she wants the notion of causality to be present at a fundamental level in quantum gravity. She is not the first to think this, Roger Penrose also argued for it a long time ago, and it was a main motivation of his twistor theory. But what is new is that Fotini proposed that it should be possible to construct a version of quantum gravity based on the spin networks, in which there is a notion of causality at the fundamental level. And in fact it is possible, and we have constructed a version of quantum gravity that works this way.

This seems right to me, but I had been bothered that I saw no way to refute Julian's argument that time disappears from the basic equations of quantum cosmology. But at some point I realized that what I had been discussing with Stu might be relevant. For if Stu is right and the space of quantum states of quantum gravity cannot be specified in advance, Julian cannot run the argument that leads to the disappearance of time from the basic equations. Instead, if the space of possible quantum states must be constructed as the system evolves, then a notion of causality, and hence of time, cannot be avoided. This is the basic idea in the paper.

I should say right away that I am not sure that this is the right solution to the problem of time. It is just the first one I've heard of that seems plausible to me and I have been thinking and writing about this problem for many years. I should say also that its not known that the states of quantum gravity can't be classified -- certain classes of knots, which are only a bit simpler, can be. Furthermore, the actual networks that Fotini and I use in our version of quantum gravity are much simpler than the ones that Carlo and I found to be the states of quantum gravity -- and these simpler set can be classified. The idea of using only these simpler states was Fotini's -- and she argued for it for an entirely different reason (in technical language these are simpler because they are described intrinsically -- they are not embedded in any prior three dimensional space). But I think Julian would be happy to say maybe she is right if in the end it allows him to keep his argument that there is no time at a fundamental level. So the only thing I would say definitely for the proposal in the paper is that it is new, it is making us think, and we are having fun with it. And I guess I would add that if it's right, it's important, but again that's what we often say about ideas in this field.

I am pleased you are emailing the paper to the Third Culture Mail List and also posting it to the Website. I hope this will be the beginning of an interesting discussion and Stuart and I look forward to comments.

- Lee Smolin

From: Murray Gell-Mann
To: John Brockman

Date: 3-26-97

Jim Hartle, in papers published during the last few years and based in part on our collaborative work on quantum mechanics, has greatly clarified the issue of how time is to be treated in quantum cosmology. The authors whose work you are distributing seem to be unaware of this clarification, although they do refer to some other papers by Jim. It may well be that Hartle's approach makes it unnecessary to invent all this ponderous machinery.

From: Julian Barbour
To: John Brockman

Date: 3-26-97

Lee finds my idea that time flow does not exist "scary." This was his comment after a sleepless night following my explanation to him of the notion of time capsules: that each experienced instant of time is really a completely self contained entity, a time capsule, that gives the impression it is embedded in a flow if time solely because it is structured in a very special way. The instant is not in time. Time is in the instant. There are just lots of different nows, and the ones we experience happen to be structured in such a way that they lead us to believe in an external flow of time.

I was led to this radical solution to the problem of time in quantum gravity, which was first revealed in its full depth in 1967 by Bryce DeWitt, because all other attempts to reconcile our strong impression of the flow of time flow with the static nature of DeWitt's wave function of the universe seemed to me to smuggle in time through one illicit tacit assumption or another. The basic idea of time capsules is explained in qualitative terms in my paper in the CUP paperback Physical Origins of Time Asymmetry (edited by Halliwell, Perez-Mercader, and Zurek) and in more detail in Classical and Quantum Gravity, 11, 2853-2897 (1994).

It is very good that Stu Kauffman and Lee are making this serious attempt to save a notion of time, since I think the issue of timelessness is central to the unification of general relativity with quantum mechanics. The notion of time capsules is still certainly only a conjecture. However, as Lee admits, it has proven very hard to show that the idea is definitely wrong. Moreover, the history of physics has shown that it is often worth taking disconcerting ideas seriously, and I think timelessness is such a one.

At the moment, I do not find Lee and Stu's arguments for time threaten my position too strongly. Starting with Stu's interesting point that it seems effectively impossible to specify all at once and in advance "all the possible tasks or niches or properties that might give an organism selective advantage," I do not think a similar difficulty applies to my basic notion, which is that of the space of all possible relative configurations the universe might have. The set of possible configurations stands in correspondence, not with a set of selectively advantageous tasks, but with the set of all possible living organisms. There is a very beautiful description of The corresponding space of possible organisms is Dawkins's The Blind Watchmaker, which reminded me strongly of the configuration space of general relativity (and hence of quantum gravity in the so-called metric representation) when I read that book a year or two ago. Since living organisms are essentially defined by their DNA, I do not think that the difficulties in defining a space of tasks applies to the definition of the space of possible living organisms or the space of possible relative configurations of the universe.

Turning to the difficulties Lee raises, two points can be made: first, he suspects there may be difficulties in specifying in advance the space of quantum states of quantum gravity. However, this presupposes that the quantum mechanics of the universe as a whole has the same basic structure as the quantum mechanics of the subsystems of the universe, in particular a Hilbert space of quantum states. I doubt whether this is the case, and I think Lee must be sympathetic to my doubt, since a central argument of his forthcoming The Life of the Cosmos is our shared conviction that the physics of the complete universe will almost certainly be very different from the physics of its subsystems. My timeless proposal for quantum gravity only relies on a configuration space (which is like the space of possible vector potentials modulo gauge transformations in QED), not necessarily a quantum state space of the kind Lee and his collaborators are seeking (which is somewhat analogous to the Fock space of quantum field theory). I do not think the difficulty of specifying vector-potential configurations in a finite time (as opposed to the finite time needed to specify elements of Fock space) in any way undermines that way of looking at QED.

Second, it is not entirely clear to me that spin-networks, which (as Lee is careful to point out) have to be embedded in a prior three-dimensional space (a bare manifold), so that an uncomfortable amalgam of the definitely concrete (the network) and an intangible (the manifold) arises, represent the final definitive framework of quantum gravity. Personally, I would be much happier with the entirely intrinsically defined structures that Fotini Markopoulou advocates, which seem to me completely in the spirit of Riemann's conjecture that the metrical properties of space arise from a discrete foundation. But then there is no problem with specification, and a timeless arena for quantum physics of the universe will be available. Of course, one might still try for a timelike causal evolution within such an arena, as Fotini advocates. I shall be interested to see how that idea develops, since my strong conviction is that the deep structure of general relativity considered as a dynamical theory indicates a totally different timeless structure for the quantum theory. My guess is that Fotini and Lee will seek in vain, but no doubt there will be fun and interest along the way. I think a theory of space is more likely to arise from such work than a theory of causal evolution in time.

-Julian Barbour

From: Stuart Hameroff

Date: 3-29-97


I congratulate Stuart Kauffman and Lee Smolin for some bold thinking. In the context of my collaboration with Roger Penrose, I offer the following comments:

The flow of time is a feature of consciousness. Outside of consciousness, there may not be a flow of time. Consciousness provides the clock.

Consider Julian Barbour's time capsules. "Each experienced instant of time is really a completely self contained entity, a time capsule....The instant is not in time. Time is in the instant. There are just lots of different nows..."

This is beautiful, but requires consciousness to *experience* the instant. What is consciousness?

The model which Roger Penrose and I have put forth ("orchestrated objective reduction - Orch OR") for brain microtubules predicts conscious events which are rearrangements of fundamental spacetime geometry -- for example at the level of Planck scale quantum spin networks. If experience is a fundamental property of the universe, like mass, spin, charge (as proposed by Wheeler -- "pre-geometry", Chalmers and others) then qualia, or proto-conscious experience must be embedded at the most basic level. Quantum spin networks (first described by Penrose in 1971, and elaborated e.g. by Rovelli and Smolin in 1995) are a representation of the most basic level of reality, and therefore provide a possible "site" for proto-conscious experience. If proto-conscious experience is indeed a "funda-mental" property, where else but the Planck scale could it be embedded? So consciousness, it is proposed, is a self-organizing process at the level of quantum spin networks.

The particular self-organizing process is Penrose's "objective reduction -- OR" -- Roger's quantum gravity solution to the problem of the collapse of the wave function.

Basically, a quantum superposition which is isolated from environment and avoids decoherence will continue to evolve according to the Schrodinger equation, but only until reaching a threshold imposed by quantum gravity. It then reduces, or collapses to discrete, classical states.

The time until threshold is inversely related to the degree of superposition -- the amount of superposed mass and separated spacetime -- by E=h/T. E relates to the superposed mass, h (actually hbar) is Planck's constant over 2pi, and T is the time until reduction, or collapse. A large superposed system therefore collapses quickly, a small system only after a long time (assuming isolation in both cases). For example a one kilogram superposed Schrodinger's cat -- if isolated -- would self-collapse after only 10^-37 seconds. A single superposed atom -- if isolated -- would self collapse only after 10^6 years !! Somewhere in between these extremes are physiological brain processes in the range of tens to hundreds of milliseconds. An OR brain process in this range would require superposition of mass in the range of nanograms.

The quantum gravity threshold is the "objective" criterion for self-collapse. According to Roger it comes into play for the following reason. In quantum superposition, mass (curvature in spacetime) apparently exists simultaneously in two location, or states. Roger takes this separation seriously, and observes that the underlying spacetime geometry down to the Planck scale of spin networks also separates -- i.e. simultaneous curvatures in opposite directions. A critical degree of spacetime separation becomes unstable, and reduces, or collapses to a single geometry, or universe state. Roger claims the separation reduces ("chooses") non-computably, but only if it occurs by the OR quantum gravity process. If reduction occurs by environmental decoherence -- loss of isolation -- the classical states are chosen computably, as would generally be the case in a technological quantum computer. (The "non-constructible" process Stu and Lee mention may be Penrose's OR.)

Non-computable OR events are irreversible. A sequence of irreversible events "ratchet forward in time", creating a direction in spacetime, a subjective "flow" of time. Thus consciousness is a sequence of conscious events.

Our model proposes that OR events are coupled to neurophysiological processes, specifically at the level of microtubules in the brain's neurons and glia. Microtubule-associated proteins "tune" the quantum states, so we refer to the proposed process as "orchestrated objective reduction -- Orch OR". We have suggested that isolation and coherence are maintained by cycles of actin gelation (for example in concert with 40 Hz neural activity) and that macroscopic quantum coherence among microtubules in widely distributed neurons and glia occurs via gap junctions.

The proposed Orch OR conscious events resemble Barbour's "time capsules", and both seem similar to events which the philosopher Alfred North Whitehead described as "occasions of experience". (Abner Shimony has observed that Whitehead "occasions" are suitable descriptions of quantum events.) Discreteness in consciousness may also account for reports by meditators of "flickerings" in their consciousness, and relate to what Rodolfo Llinas has characterized as 40 Hz "cognitive quanta".

If consciousness is a sequence of discrete events, apparent aberrations in the subjective flow of time may be explained. The basketball superstar Michael Jordan, when asked to account for his astounding number of "moves" replied that when he is playing well, time (or at least the other players) seem to slow down. Accident victims often recount how time slowed down. In these cases, the number of conscious events may be increased compared to some standard frame of reference. Patients under general anesthesia have no concept as to how long they were unconscious -- or them, time did not flow.

The two main points I'd like to make:

1) The flow of time is a feature of consciousness. Outside of consciousness, there may not be a flow of time. Consciousness provides the clock.

2) The Orch OR model suggests consciousness is a sequence of self-organizing rearrangements of spacetime geometry at the level of quantum spin networks.

In closing, I wonder if Stu Kauffman would comment on the possible role of consciousness in evolution, and particularly the suggestion that the appearance of primitive consciousness at the level of small worms and urchins precipitated the Cambrian evolutionary explosion 540 million years ago.

Stuart Hameroff

From: Philip Anderson
To: John Brockman

Date: 3-31-97


I was a little disturbed that Murray did not object a little to the introduction you gave the SFI. We have been trying very hard to get the message out that we are primarily an institution which does not indulge in "ironic science", in horgperson's phrase. You made us sound a little less flaky than some journalists do, but the aspect of postmodernism does hover over the examples of our faculty you chose.

I also did want to comment that I found the Smolin-Kauffman piece extraordinarily "ironic". One needs only to substitute angels for the things they are counting and we're back in the Middle Ages. I firmly believe that science is only what is subject to empirical test, at least in some foreseeable future. Lee and Stu are very bright people but they do not seem to understand this objection to what they do, nor do they have much sesitivity to the real concerns that lead many of us to be a little ambiguous about Horgan's thesis.

From: Murray Gell-Mann
To: John Brockman

Date: 3-31-97

I didn't see the "introduction" to SFI to which Phil refers. If it presents our institute as flaky, I object very strongly. Please convey that message to Phil. We do have one or two flakes, but generally speaking our work is quite respectable as well as refreshing.

- Murray

From: Lee Smolin
To: Murray Gell-Mann, Julian Barbour, Stuart Hameroff, Philip Anderson

Date: 3-31-97

Here are my comments to the responses:

First, to Murray Gell-Mann's comment:

Of course I am aware of the work Jim Hartle, Murray and others have done on decoherence as well as its possible applications to the problem of time. At the same time, the approach we have been taking recently has some new features, that offer a different perspective on the basic interpretational issues in quantum gravity, including the problem of time.

It is true that Jim and Murray may have a right to say "I told you so" as I, as well as several others like Mike Reisenberger and Carlo Rovelli, are now using path integral methods in quantum gravity, which they have been doing for years. This puts our work, which grew out of a line of work using the more traditional canonical approach, in closer touch with theirs, which is good.

(I should explain to the readers that there are two approaches to quantum mechanics, the first based on the canonical or hamiltonian formalism, the second based on Feynman's path integral formalism. So there are correspondingly two classes of approaches to quantum gravity.)

However, our work is rather different the previous path integral work, as it has grown out of a set of results that came from canonical quantization. Of course, if all we were saying in this paper is that path integral approaches offer some way out of the problem of time in quantum cosmology that would not be available in a canonical approach we would be repeating things they wrote many years ago. But we are saying some new things, that I would hope that they pay attention to. To repeat them briefly:

  1. The kind of path integral we are contemplating has a special form, which came out of work by and with Fotini Markopoulou, in which each state goes in a finite time to a finite number of other states. This makes it possible to apply certain analogies to statistical mechanics problems like directed percolation and boolean networks, which are not available for general path integral formalisms. The particular point of the paper with Stu is that this gives us new possibilities for the construction and interpretation of the theory that were not available before.
  2. The states that are propagated by the path integral are related to those that came out of the canonical approach (these are the spin network states). We know how to measure certain observables in these states such as area and volume, thus the proposal is much more specific then before. In particular, as we know the state space, we can raise in detail problems of about the constructibility of the state space, inner product and so forth. Such problems may have been raised before in a general setting, now they are being found in a particular approach to quantum gravity based on quantization of general relativity on which many people are working.
  3. There are close connections between all the new proposals for path integrals in quantum gravity made by Reisenberger, Rovelli, Markopoulou and myself, Baez etc and an important mathematical structure, which is topological quantum field theory in four dimensions. As Louis Crane has been saying for some years (and he is the person who has been leading that field) this opens up a new approach to the interpretational issues in quantum cosmology, based on the fact that in topological quantum field theory states are assigned not to the whole of a closed universe, but to boundaries splitting the universe into parts.
I certainly appreciate that there is a history of worrying about both problems of constructibility in physics and about the problem of time in path integral formalisms that I would like to know more about. When I was an undergraduate Harold Morowitz gave me some very good advice, which was to always follow the scientific questions and be prepared to invent or adopt new techniques whenever called for, rather than to stick with one approach because one knows it. He forgot to tell me that when one does this one often finds oneself working with some ideas that are new to you, but have been the concern of other people for some time. I hope that Murray, Jim and others who have been working on path integrals for many years will see that we do have something new to contribute to this direction, both technically and in terms of the various interpretational problems. In turn I look forward to learning more from them about things I certainly missed in their work.

To Julian Barbour's comment:

Julian's influence has been extremely important for myself and others in figuring out how to think clearly about the hard issues in quantum gravity. I certainly take his point of view very seriously, and I agree with him about a great many things. But in the end I can't accept his idea that the notion that there is a flow of time is an illusion. My intuition is that a good theory of cosmology should have time and causality in it as an essential element, for reasons that I go into at length in my book. As a result, I was very interested in Fotini Markopoulou's proposal that an evolution rule be constructed for quantum gravity that has causality built in at the fundamental level, which is how this work started.

However, Julian's argument that time disappears in a theory of quantum cosmology is pretty strong. I think it can only be defeated in two ways: by attacking the assumptions of the standard approach and by constructing an alternative. In the work connected with the paper with Stu we are trying to do both. One can also understand the work of Gell-Mann, Hartle and others as an attempt to formulate a version of quantum cosmology in which time plays a role.

About the details of what Julian says: I think there may very well be a problem with constructing the whole configuration space of general relativity, because of the necessity of identifying structures which are identical under diffeomorphisms. This may very well give rise to a recognition problem for which there is no finite procedure or which is at least NP complete. But as this is a technical issue I won't go further into this here.

Certainly I agree with Julian that in the future we will know more and that getting there will be a lot of fun. That's one reason I believe in time.

To Stuart Hameroff's comments:

Whooosh, consciousness.... Let me say two things before anything else: 1) there is no scientist I admire and respect more than Roger Penrose and 2) I am far from convinced that science has advanced to the point that consciousness is a scientific problem. I think it very well may be the case that sometime in the future, after we have solved some of the problems we seem to be able to make progress on, we may very well have a language and conceptual framework adequate to address the question of consciousness. But I don't think we do now. So my attitude to the problem of consciousness is to postpone it for future scientists. I think the problems we are just now able to make progress with, such as the origin of life or quantum gravity are hard enough. I also suspect that their solution will change the way we understand the world so much that questions that are presently out of bounds like consciousness will look rather different.

I also believe strongly that we can solve problems like quantum gravity and the origin of life without having to worry about consciousness. I doubt very much that whatever consciousness is it has anything to do with the basic quantum transitions between quantum states of spacetime geometry. We seem to be able to do quite well without any such notions.

Of course this does not mean that very smart and brave people like Roger Penrose and Stuart Hameroff, or Daniel C. Dennett, or others, may not be able to say provocative things about consciousness, which may effect what they try to do in physics and mathematics. And it certainly doesn't mean that neurobiologists may not make a lot of progress understanding in detail what are the biological processes associated with consciousness. But the deep philosophical problems of "qualia" and so forth remain as far as I can tell, beyond what we can discuss scientifically.

To Phil Anderson's comment:

I have the impression Phil is complaining a bit too much. I am sure I am not doing "ironic science", and would ask Phil to look a little at the actual work and reconsider his comment. I take it that Phil refers to John Horgan notion of ironic science, which is science that has no hope of being tested experimentally. I would like to explain that the paper with Stu comes out of a line of work that has aimed at, and succeeded in, making definite experimental predictions. That paper by itself makes no predictions, I would agree, but it is aimed at providing the context within which further experimental predictions may be couched. I would ask Phil to look at the whole body of work that this paper comes from before making a judgement as to its "irony". I think I am sufficiently "sensitive" to the need to connect theory to possible experiment that I have spent much of the last ten years trying to invent ways that ideas about quantum gravity could be subject to test. I would like then to respond to Phil by explaining something about what people have been able to do to connect ideas in quantum gravity with experiment.

It is true that in quantum gravity we are dealing with questions that are both ambitious and difficult. They are ambitious because their solution may very well require modifying or replacing the basic principles of quantum theory and/or relativity. They are difficult because we cannot now do experiments at the Planck scale and one must be inventive to do things that can in principle be tested experimentally. But it is very possible to do work in quantum gravity that makes experimental predictions. I would point to several:

  1. With Carlo Rovelli and others we have predictions of discrete spectra for areas and volumes in quantum gravity. These are specific predictions of the spectra; when it will be possible to measure geometrical quantities to the accuracy of the Planck scale the theory (which rests on very generic assumptions) will be easily refutable. It should also be mentioned that the results of Rovelli and myself on the discreteness of quantum geometry have been reproduced as theorems in a mathematically rigorous formulation of quantum gravity, so they have the same status as the CPT theorem and the connection between spin and statistics in ordinary quantum field theory.
  2. In string theory there are detailed predictions as to the behavior of high energy scattering, that would easily confirm or disconfirm the theory.
  3. String theory now makes detailed predictions about scattering of radiation from certain classes of black holes, beyond the regime where previous theory was reliable. Disconfirmation of any of these would refute the theory.
  4. There are detailed predictions of violations of CPT in scattering of neutrinos in one version of quantum gravity, due to Chang and Soo.
  5. Given simple and widely discussed conjectures about what happens at the singularities of a black hole, one can make detailed predictions about astrophysical consequences of varying the parameters of low energy physics. As these are discussed in detail in my book I will not dwell on them, except to say that there are testable consequences, for example, for the upper mass limit of neutron stars. This is to say there are hypotheses about quantum gravity that would be refuted by the discovery of a 3 solar mass neutron star. Some versions of this theory are already refuted.
These are not the only examples, but I think they are enough. (for more details I have a paper on Experimental predictions from quantum gravity which can be found on the lanl.gov archive at gr-qc/9503027.) It is true that many (but by no means all) of these experiments must await improvements of technology, so that we can do experiments at the Planck scale. But to be ironic there must be no reasonable hope of ever doing such experiments and I don't think this would be a reasonable position. There are now proposals to build a satellite that will improve the resolution of measurements of the cosmic black body radiation to the point that details of inflationary models can be tested; this involves the physics of the grand unified scale which is only four or so orders of magnitude away from the Planck scale. We also now have detected cosmic rays with 10 to the 19 electron volts energy. These are both much closer to the Planck scale than one may have guessed. I don't think it is at all impossible that clever people will invent ways to deduce information about Planck scale physics from observation; there are always new ideas about how to push the limits on the testability of theory. A recent paper of Coleman and Glashow about how to use cosmic rays to test special relativity to much higher precision than previously thought is an example. I think it is reasonable to go ahead and work on quantum gravity with the expectation that some time in the next century people will be doing experiments that test predictions about Planck scale physics.

A reasonable person might wonder whether it might not be better to wait till then before attacking quantum gravity seriously. In principle they might have been right, but some of us have been going ahead any way, and what we have found is that the problem of combining the principles of general relativity and quantum field theory is constrained enough that one gets definite experimental predictions out. Thus, it seems it is possible to do good science now in quantum gravity, and collect a set of predictions that we hope will stimulate experimental physicists and observational astronomers to develop methods to check them. This is good old old fashioned science, as I understand it, nothing ironic or postmodern about it.

I can't say very much on Phil's other comments. I don't understand why people at SFI seem so worried about its image, it is clear to me, and I would think to most scientists, that it is a very impressive and exciting place. I know of a lot of good science going on there, and I've found it a very stimulating place to visit. I've learned a lot there that has helped my work in astrophysics, stimulated thoughts about directions in quantum gravity and given me a way to talk and collaborate with people about problems in theoretical biology and statistical physics. I highly approve of the place, if there are a few journalists who don't I suspect it is because they misunderstood what the place is about to begin with.

From: John Horgan

Date: 4-2-97

I was hoping that someone would apply the term "ironic science" to the piece by Lee Smolin and Stuart Kauffman, "A Possible Solution for the Problem of Time in Quantum Cosmology," which was posted in this space on March 20. I am delighted that the person to apply the ironic label was none other than Phil Anderson, who like Kauffman is a leader of the Santa Fe Institute. I coined the phrase ironic science in my book The End of Science to refer to theories that can never possibly be verified through empirical means. Such theories are ironic in the sense that they cannot, and should not, be taken literally; they are thus more akin to literary criticism, theology and philosophy than to real science. It is a truism by now that some of the most popular theories emerging from the social sciences in the past 100 years or so--Marxism, psychoanalysis, structuralism--have been ironic. What is less appreciated is that even physicists like Smolin and biochemists like Kauffman, who are supposed to be so hard-nosed, indulge in this kind of stuff. If I didn't know Smolin and Kauffman, I would have guessed that their piece was a pseudo-scientific parody like the one Alan Sokal got the hapless editors at Social Text to publish last year. But not only are Smolin and Kauffman not kidding; they are passionate about their work. I grant that their speculations are inspired by some very deep, real mysteries. Science has done an extremely good job at describing the universe, but it has done a very bad job at telling us why the universe is the way it is rather than some other way. Why do we have these laws of physics and not some other laws, this configuration of space and time and not some other configuration, this type of life and not some other type? Most of us want to believe there was something inevitable about the cosmos and our place in it--religion is a manifestation of that belief--and Smolin and Kauffman are attempting to give this belief a scientific basis. They are in good company. Many popular theories and ideas in physics and cosmology--such as superstring theory, loop-space theory, the anthropic principle, inflation, multi-universe theories--are also aimed at answering questions about our inevitability, or lack thereof. And these theories are all equally ironic in that they can never be verified by any conceivable experiment. Smolin is quite right that some of these theories make predictions and are thus "testable" in a narrow, technical sense. Superstring theory predicts supersymmetric particles,for example, and inflation predicts a specific cosmic mass-density. But other much less extravagant theories make the same predictions without postulating extra dimensions and infinitesimal string-like particles and parallal universes. These phenomena are as permanently hypothetical as, well, angels dancing on the head of a pin (to use the analogy Phil Anderson favors). What separates real science from ironic science is not just testability but verifiability; real science establishes certain facts beyond a reasonable doubt. I know this definition violates Karl Popper's view that we can never verify anything; we can only falsify theories. But Popper was obviously wrong. The existence of electrons and atoms and elements and viruses and genes and natural selection and galaxies and gravity and the expansion of the universe has been established as irrefutably and permanently as the fact that the earth is round and not flat. Like the people working on superstring theory, inflation and other ironic stuff, Smolin and Kauffman are obviously extremely smart, ambitious and creative scientists. The fact that such talented folks are engaged in such a futile exercise is to me one of the surest indicators that science has entered its twilight. By the way, Kauffman, Smolin, Anderson and I hashed out a lot of this stuff during a online debate between Kauffman and me on Hotwired last June. The address for that brouhaha is http://www.hotwired.com/braintennis/96/25/index0a.html.

John Horgan
Scientific American

From: Lee Smolin
To: John Horgan

To John Horgan's comment:

It impresses me that some of these comments - Horgan's included - fail to address any of the issues that are the actual subject of the paper I wrote with Stu Kauffman. In fact, our paper, which John and Phil feel so free to characterize, came out of a particular research program in quantum gravity (which as I will stress again below, has already let to experimental predictions.) The paper addresses a particular constellation of puzzles, raises a particular technical objection to certain proposals, and makes a new proposal. This proposal is related to a particular series of developments in quantum gravity, which the reader can find described in the papers it references, by Crane, Reisenberger, Rovelli, Markopoulou, Baez, myself and others. The proposals it criticizes are also referenced, in the papers of Barbour and others. I would have hoped that someone who felt fee to characterize the paper at least took a few minutes to understand what questions the paper is addressed to, what results it is based on, and what it says about them.

Nowhere in that paper do we say anything about the questions raised by John Horgan such as why the laws of physics are what they are, why the universe is in the state we find it, why we exist, why there is life and so forth. Instead, the paper addresses a rather different set of issues which stem from the necessity of incorporating a dynamical theory of spacetime geometry such as general relativity or string theory in quantum theory. This is no mystery, we state clearly what issues we address, and then we address them. Even if Stu or I have written a few things about the issues John mentioned it should not be assumed that anything we write - or even most of the work we do as scientists - is addressed to these issues.

I think personally that the actual issues we discuss are interesting, and might very well be of interest to non-scientists. That is why I thought it would be interesting to post the paper publically, especially as much of the literature in this subject is less accessible to non-experts.

Having said this, let me come to the issues raised by Horgan. While they have nothing to do with our paper, I don't mind addressing them, they are issues that I've thought and written about, although not here. Horgan's concerns are not stupid, science is at a very interesting point, and it is not obvious that good science can be done now about some of the key issues that confront us, concerning quantum gravity, the selection of the parameters of particle physics, the initial conditions in cosmology, as well as questions from biology such as the origin of life. But what I am contending is that in spite of the superficial reasons why one might worry that progress cannot be made on these issues, progress is in fact being made. I rest this contention not on the paper I wrote with Stu, but on the whole body of work that many of us have been contributing to in quantum gravity, string theory, cosmology etc. I would hope it is not too much to ask that anyone who wants to discuss this issue familiarize themselves to some extent with this work and the claims that it makes.

At the risk of repeating myself, let me stress some of the claims:

  1. String theory predicts many more things than the existence of supersymmetric particles. The particular features of high energy scattering predicted by the theory are quite different than those predicted by any ordinary field theory. At the same time exactly this behavior seems to be necessary to reconcile quantum theory with relativity and gravitation at the level of perturbation theory.
  1. Several very important and exciting things have happened visa via black holes recently, that lead to predictions that are in principle easily verifiable, subject only to the discovery of certain kinds of black holes.

  2. Non-perturbative quantum field theory methods applied to quantum gravity yields quite specific and robust predictions concerning the spectra of physical areas and volumes. When it is possible to make Planck scale measurements of geometry these will be tested.

  3. There are hypotheses about quantum gravity and cosmology that are easily refutable-and in some cases refuted, by astrophysical observations. There are several chapters and an appendix of my book that discuss this in detail.

Let me stress that John Horgan himself characterizes ironic science as "theories that CAN NEVER POSSIBLY be verified through empirical means." As string theory and quantum gravity make specific predictions that will be easily verifiable when the appropriate technology is developed, (and as a few predictions are even testable now) these developments are absolutely non-ironic, by his definition. Finally, let me emphasize that all of the examples I mentioned are verifiable predictions of some version of quantum gravity, in the sense that these are phenomena that could not be accounted for by any conventional quantum field theory that did not include quantum gravitational effects.

As a result of all this progress, I've come to a very different perspective from John about the future of fundamental physics. Some of this is reflected in my book, and I've tried to present there a series of arguments that lead to a very optimistic perspective for the future of fundamental physics. But whether one agrees with those conclusions or not, I do want to insist that we must discuss these issues in the spirit of the scientific tradition, which means we make arguments based on careful consideration of various kinds of evidence. We should also be willing to change our minds based on evidence and arguments, as the subject is science, and there are often new developments that belie our expectations. I know I myself have modified significantly my own views about things like inflationary cosmology and string theory, as these subjects developed. I expect that there will be things I will change my mind about in the future. I would hope that John Horgan and anyone else who has something to say about the future of science will come to the discussion with a spirit of care, openness and respect that the issue deserves.

As a last comment: the future of science does not depend at all on what any of us say in this context. It depends only on the actual results of work now being done by large numbers of smart and enthusiastic people. I doubt very much that astronomy, cosmology, string theory and quantum gravity would be attracting the efforts of a large number of incredibly impressive young people, as in fact they are, were these fields not progressing rapidly.

From: Stuart Hameroff

Date: 4-5-97

Lee Smolin said that his "attitude to the problem of consciousness is to postpone it for future scientists."

How ironic! First Philip Anderson discounts Lee and Stu Kauffman'sdelving into the Planck scale as unapproachable "angel dancing", and then Lee puts consciousness and the Penrose-Hameroff model way out of reach. I feel second-order Horganized!

But seriously, Lee's defense of the potential experimental approachability of Planck scale physics was excellent. I might add that the "Casimir force" of Planck scale quantum vacuum fluctuations was recently measured quite precisely by Lamoreaux at Los Alamos.

In 1948 the Dutch scientist Hendrick Casimir predicted that the all-pervading Planck scale quantum vacuum energy (virtual photons) could be measured using parallel surfaces separated by a tiny gap. Some virtual photons would be excluded from the gap region, Casimir reasoned, and the surplus photons outside the gap would exert pressure forcing the surfaces together. Lamoreaux's experimental surfaces were separated by a distance *d* ranging from 0.6 to 6 microns, and the measured force was extremely weak.

At the Tucson II consciousness conference, physicist George Hall of North Carolina State University presented calculations of the Casimir force on model microtubule cylinders. Hall considered the biological microtubule hollow inner core of 15 nanometers diameter as the Casimir gap d. As the force is predicted to be proportional to d^-4, Hall's models predict significant pressure on the order of atmospheres exerted by the quantum vacuum on longer microtubules. Hall adds that Casimir forces may also exert pressure in ubiquitous smaller biological spaces including intra-protein pockets. So biological systems may interact routinely with Planck scale quantum phenomena. Testable predictions abound (e.g. a paper currently in press lists 19 testable predictions of the Orch OR model). At least this approach to consciousness (right or wrong) need not necessarily wait for future scientists.

Lee also said: "I think the problems we are just now able to make progress with, such as the origin of life or quantum gravity are hard enough."

But perhaps consciousness, life and quantum gravity are related? I think life involves quantum coherence, and like consciousness is a self-organizing process in fundamental spacetime geometry.

Lee: "But the deep philosophical problems of "qualia" and so forth remain as far as I can tell, beyond what we can discuss scientifically."

Not necessarily. If Roger and I are correct, experience is a property embedded at the Planck scale. The spin networks that Lee and Carlo Rovelli describe and the experimental approaches Lee listed could tell us how qualia, or proto-conscious experience are encoded. Their spectra of geometric Planck scale volumes -- which Roger describes as having a non-local character -- could represent the essential grain of conscious experience.

This is a modern physics extension of a line of panexperiential philosophy which suggests that proto-conscious experience is "fundamental". Leibniz saw the universe as an infinite number of fundamental geometric units ("monads") -- each having a primitive psychological being (spin network geometric configurations may be "quantum monads"). Whitehead described dynamic monads with greater spontaneity and creativity, interpreting them as mind-like entities of limited duration ("occasions of experience" -- each bearing a quality akin to "feeling"). More recently Wheeler described a "pre-geometry" of fundamental reality comprised of information, and David Chalmers contends that fundamental information includes "experiential aspects" leading to consciousness.

And while we're at it, Planck scale features may also encode Platonic values. In Shadows Of The Mind Roger described a Platonic world of mathematical truths, laws and relationships, as well as aesthetics and ethics -- our senses of beauty and morality. Perhaps the Platonic world is ingrained at the most basic level of reality? Plato at the Planck scale!

From: John Baez

Date: 4-5-97

To digress slightly from the general drift of the thread thus far, I would like to talk, not about consciousness, ironic science, or the media's image of the Santa Fe Institute, but about the paper by Stuart Kauffman and Lee Smolin. The goal of their paper is to avoid the "disappearance of time" that seems to occur in background-independent theories of physics. This is a rather arcane subject, and it's also extremely confusing -- it's been the subject of heated debate for decades. So it's not surprising that the conversation has turned towards other topics. Nonetheless I think they have raised some interesting points that are worth discussing.

However, rather than launching into my views, I think I will mainly give a short sloppy summary of their paper. Hopefully this will help the non-experts see what they are on about. As for the experts, I hope they will object to all the horrible mistakes I'll make, and thus wind up clarifying various subtleties.

I won't try to define a "background-independent theory" here. It's easier to start with the main example of such a theory, namely general relativity. Normally we imagine running an experiment and timing it with a clock on the wall that ticks along merrily regardless of what's going on in the experiment. In general relativity it's known that this is not strictly true. This has to do with how gravity affects spacetime. Very roughly speaking, if you move an object, you change the gravitational field in the room and inevitably affect the rate of ticking of the clock. So if you run an experiment and ask "what did the voltage meter read when the clock said it was 5:30 pm?" you have to recognize that the experimental setup has affected not only the oscilloscope but also the clock. To put it rather floridly, you can't treat the spacetime measured by clocks and rulers as some sort of fixed grid upon which events play out while remaining loftily unaffected by these events; instead, it interacts with them.

For most purposes these effects are small enough that we can either ignore them or treat them as small corrections. The fun starts when we try to figure out how to do physics while taking them seriously. In one approach, one decides to treat everything relationally. In particular, one treats clocks as just another part of the physical world with no privileged status: instead of asking what the voltage meter reads when the clock says it's 5:30, one could equally well ask "what did the clock say when the voltage meter read 217 V?".

Taking this viewpoint to the extreme, one can argue that the laws of physics don't describe how things change "as time passes": instead, they just express correlations between various observed quantities, like meter readings. This is what's meant by the "disappearance of time" in background-independent theories.

Julian Barbour is a strong proponent of this sort of purely relational view -- though I'm surely oversimplifying his thoughts. Kauffman and Smolin seem to want a way out of this view. I'm not sure how clearly it comes through in their paper, but in conversations Smolin has made it clear that he wants to keep some notion of time in order to preserve the concept of novelty. In the purely relational view, there is no fundamental notion of the passage of time; there is simply a fixed set of ways the world can be, and laws describing correlations, like: "if X holds, then Y holds with probability P". As Barbour noted, Smolin finds this idea "scary". Personally I don't find it scary, and I am also rather suspicious about pursuing a course of research to avoid some conclusion one finds scary -- though I have no quarrel with striving to reach a conclusion one finds attractive.

Anyway, Kauffman and Smolin suggest the following way out: perhaps it doesn't really matter if there is a fixed set of ways the world can be, because we cannot tell what this set is! Here they are taking advantage of the work of Gödel, Turing and others. These folks showed that there are lots of mathematical problems for which no algorithm can provide the answer. Kauffmann and Smolin give some arguments for why determining membership in the set of "ways the world can be" might be a problem of this kind. They also try to see what physics might be like in this situation.

I'll wrap up with a few thoughts of my own. Since I'm not scared by the thing they are trying to avoid, I am not competent to judge whether their way out, if true, would be reassuring. Personally, I have other directions I want to go when exploring the issue of background-independent theories. However, the problem of "uncomputable configuration spaces" is interesting in its own right.

Their paper is not the first to suggest relations between time and computability. Even apart from background-independent theories, there is the interesting question of why, if the past determines the future, the future is still in some sense "new". One natural answer is that in many circumstances, the quickest way to compute the future knowing the present is just to wait for the future to come. (A good place to read about this is in the work of Charles H. Bennett on "logical depth".)

Another interesting question concerns the "arrow of time" and computability: sometimes it's easier to compute the future from the past than vice versa. This is related to public-key cryptography. In this form of cryptography, everyone can easily encode texts for you to read, but they are not supposed to be able to easily perform the inverse operation of decoding. Whether this is really true -- whether there really exist reversible computations that are easier to do than to undo -- is the content of the famous unsolved mathematics problem "is P = NP?"

I think that the questions Kauffman and Smolin raise would be best discussed in the context of these other ideas.

From: Stewart Brand
To: John Brockman

Date: 4-6-97

John, the fascinating thing (to me) I came across in Lee Smolin's letter introducing the piece with Kauffman on time in quantum cosmology was the apparent assumption that...

evolution means causality means time.

Did I get that right? Causality requires time? Does time require causality?

Just curious...

From: John Baez
To: Stuart Hameroff

Date: 4-6-97

You write:

"I might add that the 'Casimir force' of Planck scale quantum vacuum fluctuations was recently measured quite precisely by Lamoreaux at Los Alamos."

and conclude

"So biological systems may interact routinely with Planck scale quantum phenomena."

This is wrong. The Casimir effect we measure has no direct relation to Planck-scale physics, and there is no evidence that biological systems interact with Planck scale phenomena.

Perhaps it would help to recall what the Planck scale actually is. Max Planck cooked up a unit of length from 3 constants: the speed of light, the gravitational constant, and what we now call Planck's constant. These constants are crucial to relativity, gravity, and quantum mechanics, respectively. Thus it is natural to guess that Planck's unit of length is the distance scale at which quantum gravity effects become important. The Planck length is about 10^{-35} meters. For comparison, the radius of a proton is about 10^{-15} meters, and that of an atom is about 10^{-10} meters. No experiments have been done that yield direct information about Planck-scale physics.

The Casimir effect that has been measured in the lab has nothing to do with gravity, as far as anyone can tell. It is an electromagnetic effect, and one can calculate how it works using only the behavior of quantum electrodynamics at distance scales larger than the radius of an atom. Measuring it therefore tells us nothing about Planck-scale physics, only physics at length scales 10^{25} times larger. By the way, it was measured in 1958 by Sparnay.

From: George Johnson

Date: 4-8-97


John Horgan and I have a curiously ambiguous relationship. We admire each other's books in many ways while disagreeing completely on the nature of science and where it is going. He reviewed my book Fire in the Mind: Science, Faith, and the Search for Order in The Sciences. (You can see what he said at this address: http://www.santafe.edu/~johnson/fire.reviews.horgan.html). I've not written about "The End of Science," but I told John that I found many of his caricatures very arresting -- particularly the one skewering Karl Popper. But caricatures, by their very nature, are skin deep. I don't think anyone who knows the scientists depicted in the book will mistake John's artful cartoons for the real thing, any more than they would mistake Tom Oliphant's craft for photography.

I also think John's argument about the wheel-spinning nature of some farflung scientific enterprises is defensible, even if I am not entirely convinced. But where we really split ways is over our views of the future of science. He sees it as ending while I see it as endless. Neither view sits comfortably with many scientists. Most, I'm guessing, really do believe that science will end someday; they just don't want it to happen yet.

For all the outrage he has caused, John pays science the compliment of believing, fervidly, that it has succeeded in discovering the way the world really is. He is a hardcore Platonist, who believes that Laws of the Universe exist in some ethereal phantom zone and that our brains are miraculously attuned to resonate with them. In that regard, he and Roger Penrose belong to the same church. I argue in Fire in the Mind that this is pure mysticism. Our nervous systems evolved on this particular planet to help us find food and to keep from being eaten. It is a leap of faith as great as that taken by any religion to believe that evolution also equipped us to understand the ultimate laws. The mind is not a mirror but a tinkered-together set of filters. Are the orders we think we perceive really out there in the universe? Or are we just seeing the shadows cast by our own brains? Surely the answer lies somewhere in between, but we can't ever know where to draw the line. We are trapped in our nervous systems. Like fish up against the edge of the aquarium, we can't tell whether the shapes and colors that dazzle us are simply our own reflections distorted by the glass. The only position one can honestly take is that of the agnostic.

Since the map is not the territory, the possibility always exists that we will have to tear it all up and start over again. John and I had a good argument about this on Ira Flatow's show on NPR. (Those who want to listen in while they're crocheting spinor networks or cleaning out microtubules can find a link to a RealAudio recording at http://www.santafe.edu/~johnson.) John, displaying his Platonist colors, tried to bait me by asking if I believed in the existence of the electron. I didn't think fast enough to provide a good answer in real-time. If the debate had been on the Net, I would have thought a while and come back with something like this:

"Are you asking whether I believe there are negatively charged entities that hover around nuclei, jumping from orbit to orbit without traversing the space in between -- 'particles' that cannot be said to simultaneously have a fixed position and momentum, that act like something which can best be described as a cross between a particle and a wave (and not even a wave of matter but a wave of probability)? Do I believe (1) that such a thing really exists? Or (2) that it is a construct -- albeit a brilliant one -- of minds struggling to explain a world that will always elude them, with a science that will never end? The obvious answer is number 2."


I'd like to thank John Baez for that crystal-clear explanation of Smolin and Kauffman's paper, which I couldn't make hide nor hair of. Baez's postings on sci.physics are one of the treasures of the Internet.

-George Johnson
The New York Times

From: Stuart Hameroff
To: John Baez

Date: 4-8-97

"The Casimir effect we measure has no direct relation to Planck-scale physics, and there is no evidence that biological systems interact with Planck scale phenomena."

Thank you for your comments. I am not a physicist, and am always grateful for clarification and feedback.

As I understand it, the measurable Casimir force is a cumulative effect of Planck scale physics, perhaps like water pressure is a cumulative effect of H2O molecular interactions. So it is true that we cannot derive information about "discrete" Planck scale phenomena from presently available techniques. Lamoreaux's experiments (and earlier, less quantitative ones such as Sparnay's) merely reflect the "bulk" effect of the quantum vacuum.

My point was that as the force is proportional to d^-4, as macroscopic systems get smaller the force becomes more significant (based on original work by physicist George Hall). So nanoscale biological systems whose dynamics are delicately poised may be susceptible to influence by Planck scale phenomena. You are correct that there is no evidence for this -- it is being proposed as a theory based on calculations.

As an example, consider a neural protein whose conformational dynamics are necessary for brain activity including consciousness. It appears that quantum-level phenomena such as localization of single electrons within a protein "hydrophobic pocket" may regulate the protein conformation. Anesthetic gas molecules disrupt these phenomena by van der Waals forces which derive from quantum-level interactions similar to Casimir forces. One cubic nanometer -- the size domain of a protein pocket for example -- is equivalent to roughly 10^78 Planck scale volumes. So what I'm suggesting is that these Planck scale effects can "vote" to influence the protein state through the "lever" of van der Waals/Casimir forces. This may have profound implications not only for consciousness, but for the origin of life.

Stuart Hameroff

From: Lee Smolin

Date: 4-8-97


As usual John Baez has explained things in a way that even those whose ideas he is talking about understand them better after reading him. So I can't add much. I might just say that I don't think it is quite right to give the impression that my rejection of Julian Barbour's view of time is based on fear. I have a strong intuition that there is something real about time and also something wrong about the equivalence between space and time that is so easy in mathematical representations of physical theory. I suspect that the original scene of the crime here goes back to the use of the real number line to represent time, so that time is represented as isomorphic to space. I suspect that, despite the truth of special relativity, space and time are different, and that the right representation of time cannot be as something we can visualize: because to visualize a process occurring in time is to represent it as if it were something static in some pre-existing space. This is what we have gotten used to-we draw pictures of trajectories of particles in classical physics, but I suspect that when we get to the level of quantum gravity it must be wrong.

To get out of this, one route is to try to see if the pre-existing space of configurations in a real theory like general relativity or quantum gravity might be complex in a way that would prevent its construction mathematically. I am glad to learn from John that there are some people who have already been thinking about related questions.


Stewart Brand wrote: "the fascinating thing (to me) I came across in Lee Smolin's letter introducing the piece with Kauffman on time in quantum cosmology was the apparent assumption that....evolution means causality means time.....Did I get that right? Causality requires time? Does time require causality?"

I think "means" here is too strong. I hope that John Baez's piece makes it clearer than I did what the problem is we are struggling with. What Stewart Brand says is not a bad slogan for the idea Stu and I described in our paper.

But I must emphasize that this idea is a proposal; it may or may not be useful-or true-and therefore, I do not believe that I know that evolution "means" causality "means" time. If it is a good idea it will lead to something testable, that will distinguish it from other approaches such as that of Julian Barbour.

-Lee Smolin

From: Kevin Kelly
To: John Horgan

Date: 4-15-97

I want to thank John Horgan for a very clear statement of what he means by ironic science. I read his book The End Of Science (pretty thoroughly I thought) but didn't grasp his use of "ironic science" until this posting.

It seems to me, John, your theory of science would be more widely embraced if it didn't antagonize unnecessarily, as it does with such a heavily loaded phrase as "real science," especially when one is accused of not doing it. Perhaps science has stages, as in first falsifiability, later verification.

I also don't get it why superstring is inherently unverifiable. Would you say the same for relativity?


From: Stuart Kauffman
To: Phil Anderson

Date: 4-15-97

Hello John Brockman, Phil Anderson, Lee Smolin and others known and unknown. I join this discussion a bit late. First, as a mere biologist, I want to thank Lee Smolin for the patience he has shown in allowing me to join in the body of work he started some time ago. I find myself fascinated and delighted. And our efforts have proceeded further since the manuscript, together with Louis Crane and Fotini Markopoulou.


What Lee and I are trying to do is not ironic science. Like any other scientists, we too want testable consequences of any theory we do. It is certainly the case that the step initially taken and noted in our manuscript does not yet have any consequences that we can see. But in our further efforts we have some hope of deriving testable consequences. The move we make in the manuscript is to ask whether, in principle, there could exist a set of possible configurations which could not be finitely specified "beforehand". This issue is somewhat parallel to the question I raise in Investigations, (an SFI preprint), as to whether the emergence of evolutionary novelties called "exapations" or "preadaptations" can be finitely specified "beforehand". Here is the evolutionary issue: Darwin tells us that, roughly, the function of the heart is to pump blood. This assertion means, roughly, that the heart exists because it has been the subject of natural selection. The causal consequence of the heart for virtue of which it has been selected is its capacity to pump blood. Now the heart also has other causal consequences. It makes heart sounds. It is a resonant chamber. The function of the heart is, therefore, a subset of its causal consequences. In Investigations I discuss the intriguing feature of functions that the function of a part can only be defined in the context of the "whole" -- the organism. Now an exaptation arises when a causal consequence of a part that was not formerly a function, say the capacity to be a resonant chamber, comes to be of functional significance in an environment. For example, the resonant capacity of the heart might allow someone to feel an earthquake pretremor in Los Angeles, and do the right thing, hence survive and have children. A subspecies of homo sapiens might evolve "earthquake detectors". Thus, earthquake detectors would come to exist in the biosphere. So too did flying squirrels arise, hearing arise, etc.

The puzzle about such an exaptation is that there appears to be no finite description ahead of time of all the possible context dependent causal consequences of "parts" of organisms that might happen to be useful, hence might happen to arise in evolution. The problem does not appear to be a failure to be able, in a finite specification, to specify an infinite set of "properties". For example, the infinite Fourier basis set of cosines and sines, with all different real number wavelengths and phase relations can be finitely specified. But it does not seem, and remains to be proven, that no similar finitely specifiable but possibly infinite basis set exists of possible context dependent causal consequences that all exapation functionalities might be projected upon. Assume for the moment that this is true. Yet in evolution, novel, non-prespecifiable exapations.

Yet in evolution, novel exaptations that are not finitely prespecifiable appear to arise all the time. Such exaptations include novel molecules, morphologies, and behaviors. Thus, exaptations have genuine physical consequences for the molecular content of the Universe. This latter point can be stressed by pointing out that the number of possible proteins length 200 is so vast that the Universe will not have time and matter enough to try each such protein once on a time scale vastly longer than the current age of the Universe. Non-prespecifiable exaptations drive the unique unfolding of the Universe

One can wonder whether the above can be shown as theorems. In addition, even if shown, one can wonder how this sequence of novelties is related to Godel's theorem, if at all, or to the halting problem, if at all. In these problems one begins with a set of formal axioms or production rules, and establishes statements about a class of possible theorems derived from the axioms by the production rules: formal undecidability. In the case of exaptations, it is not clear what the failure to finitely specify a finite or infinite basis set means. In the Godel case, one can add a new axiom that allows derivation of formerly undecidable cases, but creates new ones. Yet where did this new axiom come from? We grab it from the Platonic realm or whatever our philosophy may be with regards to the foundations of mathematics. In the exaptation case, it seems something like the biosphere happening upon an opportunity that was not finitely predescribable and jumping on the opportunity. The flying squirrel arises because the owl chases a squirrel that happens to have a flap of skin in its axilla. So the unfolding of the biosphere seems creative in this sense.

In brief analogy, Lee and I wrote our manuscript in part based on the possibility that the configuration space of the space or spacetime could not be finitely prestated. Carrying out the analogy, such a universe would unfold, but not in a specificifiable configuration space. Since the biosphere seems to manage without a prespecified configuration space, perhaps the universe can as well.

Well, Phil, and all, perhaps it's just that us biologists will come along and clean up the conceptual mess in physics, while you physicists clean up the conceptual mess in biology and economics.

-Stu Kauffman

From: Julian Barbour

Date: 4-15-97



Further to John Baez's helpful comments on frame-independent theories, one way to see how they differ from theories with external frames of reference is to consider the famous three-body problem of celestial mechanics (it gave Newton headaches when he tried to consider the mutual gravitational motions of the Moon, Earth, and Sun). If, at some initial time, your were given two snapshots of the three bodies taken with a small but unknown time separation and without any background information, then in the framework of Newtonian theory it would be impossible to predict the future uniquely because one cannot tell the angular momentum of the system, which is determined by how the system as a whole is rotating in space, nor the energy, since without clock information you do not know how fast the bodies are moving apart. As a result, the future evolution of the system cannot be predicted: there is a fourfold uncertainty about what will happen. This very illuminating and powerful way of seen the defect in Newtonian theory is due to Poincare (Science and Hypothesis). Now there are theories that do not have such defects; in nonrelativistic mechanics, Bertotti and I found examples (see references in my first contribution to this discussion), and, most importantly, general relativity is a sophisticated relativistic theory of such kind. From the point of view of the dynamics of such theories, the really important thing is that it is entirely determined by structures: the dynamics is determined by the intrinsic difference between structures that the universe can have in different instants (simultaneities in relativity). There simply is nowhere to fit in a time in addition to structures. That is why time is redundant in classical physics. However, one structure still follows another, so in classical physics the notion of history survives.

But quantum mechanics must change this in a truly radical way. In ordinary quantum mechanics, Schrodinger introduced a wave function of systems in a background that was essentially absolute space and time. The systems were quantized but the background remained classical. That step already destroyed that notion of the history of an individual electron; however, because the background remained inviolate, one could still conceive the history of the wave function. In frame-dependent theories, that luxury goes out the window, simply because there never is a frame in the first place. All one has in such theories is structures, for which the so-called Wheeler-Dewitt equation simply gives static probabilities. It was to try to recover our normal sense of the passage of time from this radical stasis that I introduced the notion of time capsule.


I am well aware of Jim Hartle's work on path integrals and of his collaboration with Gell-Mann on the consistent histories interpretation of quantum mechanics. However, I simply cannot accept their point of departure: that histories are the fundamental notion in cosmology. Quantum mechanics destroys histories. I have discussed this often with Jim (in fact, discussions with him were a key influence in bringing me to my timeless ideas), and we just come to this impasse that he cannot conceive a universe not based on histories at the most fundamental level. He is in very distinguished company, but so was Ptolemy. John Bell, in his paper "Quantum Mechanics for Cosmologists" (reprinted in the paperback of his papers) saw very clearly that if the many worlds interpretation of QM is taken seriously, which is very hard to avoid in cosmology unless you follow Roger Penrose who is trying to orchestrate objective wave-function collapse, then its "really novel element" (which he thought had not been identified) "is a repudiation of the 'past,' which could be considered in the same liberating tradition as Einstein's repudiation of absolute simultaneity." Bell's paper is important support for my timeless views.


Turning to Lee's desire for a real time, evolution, and genuine novelty, I am sure the things most dear to his heart (novelty and a future that is not utterly predetermined) are perfectly available in my scheme. All I am saying is that each instant we experience corresponds to some definite intrinsic structure of the universe. By definition, all the structures are different (that is the principle of Leibniz that Lee and I like so much). Thus, experience of different instants cannot but fail to introduce novelty. Moreover, what most people call advance in time is in my view transition to richer structure. Our present experience gives us merely hints for what this richer structure, which we call our future, might be. What more do you want Lee?


From: John Horgan
To: George Johnson and Kevin Kelly

Date: 4-29-97

I just discovered, belatedly, the responses by George Johnson and Kevin Kelly to my posting here of a few weeks ago. Lest they think I was ignoring them, I'd like to respond, as briefly as possible. You know George, it must drive scientists crazy to hear you and me going at it. One guy thinks science is all over, and the other thinks it never really got anywhere in the first place. Some choice! And they work for the New York Times and Scientific American, no less! No wonder science is having so much trouble!

As for your characterization of me as a Platonist, well, I don't think that's quite right. I'd call myself a functionalist, which I define as follows. If a theory works so well that it does everything asked of it -- prediction of new phenomena and extremely accurate description of old ones -- you have to grant that it is true in a functional if not absolute sense. As it survives test after test, it becomes increasingly unlikely to be displaced by any better theory, and therefore it becomes de facto a final theory. That seems to be the case with quantum mechanics and general relativity, which are theories that you find implausibly odd, and with good reason. I don't think these mathematical formalisms are absolute truths, or "discoveries," in the same way that the existence of galaxies or cell structures or elements are discoveries, but they come close just because they work so damn well. In my review of your book (and thanks for citing that in your note, because I go through all this in much more depth there) I call them "virtual discoveries."

Kevin, I agree that my style is bumptious, excessively so, no doubt, at times. But I get frustrated (and I think George Johnson does too) by the excessively fawning stance of much science writing these days, and by books and articles that pass off philosophical speculation as science. If you don't want to take my word that superstring theory is unverifiable, in the same sense that the standard model is, read Weinberg's Dreams of a Final Theory or Hawking's Brief History of Time. They concede that the Planck scale, where superstrings supposedly dwell, can never be directly accessed through experiments.

General relativity, although not nearly as well established as quantum mechanics, has been verified by plenty of different experiments. In fact, the Global Positioning System makes relativistic corrections in calculating positions. Relativity is plain old engineering now.

-John Horgan

From: Kevin Kelly
To: John Horgan

Date 5-7-97

I like the boldness of your argument, John Horgan, but you leave me behind whenever we arrive at this central issue of your own certainty that some fashionable science theories are unverifiable. Ironic science, you call it. When I queried you about why you reject superstring theory and not relativity -- both to my mind equally abstract and out of the realm of ordinary experience -- you replied back:

If you don't want to take my word that superstring theory is unverifiable, in the same sense that the standard model is, read Weinberg's Dreams of a Final Theory or Hawking's Brief History of Time. They concede that the Planck scale, where superstrings supposedly dwell, can never be directly accessed through experiments.
Well, I don't take your word, nor theirs, on this, as much as I respect Weinberg and Hawking. This is where I depart from your very interesting hypothesis: that you offer only an ironic and not a scientific means to predict what is "unverifiable" and what is not.

By what means are we so sure superstring theory is unverifiable? Before general relativity was verified, how much certainty was there that is was verifiable? Very little at first, as a fine grained reading of the history shows. Ditto for the more extreme notions in quantum theory, which of course even Einstein had doubts about anyone being able to prove. But now that they have been verified (and shown to be verifiable) they become "fundamental" in your view, whereas any far out idea that has not been verified yet becomes "unverifiable" in your notion. This is what I would call "ironic science"; Something is ironic until it becomes fundamental. How can a theory migrate from being "ironic" to "fundamental"? Only because those terms have no exactness or meaning except in retrospect.

Here is another way to describe the confusion in the way you present your idea. As far as I can tell the only way you have of determining that a theory is verifiable is to verify it -- to prove that it is "truable" by proving it is true. This is confusing the veracity of an argument with its verifiability. You need to clarify that muddlement which pervades your book.

If you want to propose a real scientific theory about science, you'll have to come up with a way to determine apriori which notions are inherently and forever untestable, and then make some specific predictions (and ideally some unexpected predictions) about what theories are ironic and what are real. Until then, it is hard to take your arguments seriously, as intriguing as I find them.

-Kevin Kelly

From: John Maddox
To: John Brockman

Date: 6-18-97

Dear John,

First, many thanks for your kind invitation for this week-end. Sadly, I cannot make it. I have a raft of commitments starting at the week-end Û talks and things like that.

ThereĖs some gossip to pass along. I found myself panning Horgan (for reasons that will nor surprise you) and Smolin, which may be more unexpected. My objections to his argument? As you can imagine, IĖm going to welcome anybody who can dispense with the need for a single Big Bang. I have the following points:

1. Do the universes inside each black hole have the gravitational mass that shows up in our Universe: if so, the chance that they produce stars must be pretty small?

2. Presumably "our" Big Bang is the inside of some other universeĖs black hole: but you still need inflation to smooth it out, so that itĖs a much bigger event than you would think by looking in our light-cone.

3. Where do the small variations between universes come from, when a Big Bang is a Big Bang, producing the well-calculated ratio of hydrogen to helium?

4. I believe the natural selection analogy is false. (I should have chipped in on your earlier web-site argument, but I hadnĖt read the book then.) The essence of natural selection is the interaction between the changing environment and the genomes of evolving species. Here itĖs simply an optimisation problem: the universes that make the most black holes will become more common, because they reproduce each other more often.

My real worry is that Smolin leaps too lightly over the quantum gravity problem. He said at Hay that that will be solved "in a couple of years". Really? ThatĖs the old Hawking fallacy - that thereĖll be a Theory of Everything any day now, just because people recognise that itĖs become the central problem. IĖd like to know what Ed Witten and his ilk think of the outlook.

I also worry that even the flags that Smolin waves about his idea being a "speculation" will not prevent the man in the street believing that the origin of life and of the Universe are now wrapped up.

Sorry to sound so sour.

All the best,


From: Lee Smolin

Date: 6-19-97

First, I would like to say that I am very honored that a range of astronomers and biologists have found the proposals made in my book worthy of their thought and criticism. In looking for and developing the idea of cosmological natural selection I was motivated primarily to try to invent hypotheses about quantum gravity that would have testable consequences for observable phenomena. I was very happy to have found a way to do this, but I have been continually surprised that scientists who work in the realms that IĖve stolen from and trespassed onto have taken a positive interest.

Having said this, let me take up John MaddoxĖs points, in reverse order.

First, am I somehow acting irresponsibly towards "the man in the street", by discussing speculative ideas in a book meant for a wide audience? This is a point he raised also in his review in The New Statesman. I must insist that I would not have done so were it not the case that the ideas lead to a theory that is testable. Having devoted three chapters (8-10) and an appendix to explaining how the theory is to be tested, as well as having listed and discussed every objection and counter-example known to me, I think IĖve done my duty. My claim is only that the idea is genuinely testable and refutable, and could easily be refuted in the near future, for example by the discovery of a 3 solar mass black hole. Given that many recent physical and cosmological theories that have been widely discussed in the recent popular literature are not so testable, I think I am doing nothing unethical in bringing the idea forward in this way, especially as I tell the reader many times which ideas in the book are accepted science and which are new, not yet confirmed, hypotheses.

Second, am I falling for the "old Hawking fallacy - that thereĖll be a Theory of Everything any day now"? I really donĖt think so. IĖve been working on quantum gravity for about 20 years and IĖve never before believed or said that we were within a few years of real progress. My belief that we are is based on several developments. There are in fact four directions along which progress has been and is being made; black hole thermodynamics, string theory, topological quantum field theory and non-perturbative quantum gravity. In each of these there have been dramatic developments in the last two years, capping many years of frustratingly slow (but steady) progress. In both string theory and non-perturbative quantum gravity we are now able to make specific and robust physical predictions about Planck scale phenomena. It is very tempting to believe that these four directions represent partial progress towards a single theory, in the same way that the developments of the first 15 years of the century in the thermodynamics of radiation, low temperature physics and atomic physics represented each partial progress towards quantum mechanics. Most importantly, in several different ways these different approaches are now being connected to each other. I personally believe that in the next years we will see a convergence of these four directions that will lead to a real quantum theory of gravity.

Of course, it is possible to disagree about this. We place our bets by investing our time and effort, and I am happy to leave it to the future to see how it turns out. But certainly it is true that in the last year a sense of excitement and optimism has been expressed by many people in these areas, especially string theory and topological quantum field theory.

4. Is the natural selection analogy false? As I explain in Chapter 7, there is a precise mathematical analogy between how cosmological natural selection works and the standard mathematical model of a species evolving by natural selection on a fixed fitness landscape. We can quibble about the meaning of words; I would agree that "the interaction between the changing environment and the genomes of evolving species" is crucial for the history of life and is not present in the cosmological theory I discuss. Whether or not this, or the optimization of numbers of surviving offspring, represents "the essence of natural selection" is a semantic question that in any case I donĖt have the authority to decide.

Actually, I think the interesting question is to what extent the standard mathematical model of a single species evolving on a fitness landscape is a reasonable representation of real biology. It is clear that it captures part of the truth, but it also leaves out the possibility of collective effects involving many species. Such effects are discussed by biologists over the whole spectrum from Dawkins to Margulis. Mathematical models by Bak, Sneppen, Paczuski, Kauffman and others seem to show that the existence of such effects is perfectly compatible with the basic postulates of neo-Darwinism.

3. This seems to be two questions:

"Where do the small variations between universes come from...?" The original point was to ignore this question, give our ignorance about Planck scale physics, and just to postulate that there is some source of variation. This is what Darwin had to do, as he was equally ignorant of molecular biology. However, given the progress in string theory, we can try to answer the question. Probably the best hypothesis is that it comes from transitions between different string vacua, of the sort discussed last year by Strominger and others.

"....when a Big Bang is a Big Bang, producing the well-calculated ratio of hydrogen to helium?" . As I explain in detail in Chapter 8 and in the appendix, the ratio of hydrogen to helium is under the control of several parameters, the most important one of which is the strength of the weak interaction. Assuming this varies like the other parameters, its present value, and hence the present ratio of hydrogen to helium, must be set in such a way that it maximizes the production of black holes. As I discuss in the appendix, (p 311.) this leads to a possible direction for testing the theory.

"2. Presumably "our" Big Bang is the inside of some other universeĖs black hole: but you still need inflation to smooth it out, so that itĖs a much bigger event than you would think by looking in our light-cone. "

I agree that inflation is likely needed to explain the flatness problem. The combination of inflation and cosmological natural selection leads to several more tests of the theory, as I discuss in the appendix (309-310.) It should be noted that inflation is about to be subject to rather severe test, from the data about inhomogeneities in the cosmic black body radiation that the Planck and Map satellites are expected to bring in. In particular we will know if Omega is really equal to one, as the simplest inflation models predict, or if it is less, as the astrophysical data so far seems to suggest. If Omega is less than one additional parameters must be finely tuned, which could be more work for cosmological natural selection, and lead to more tests of the theory.

"1. Do the universes inside each black hole have the gravitational mass that shows up in our Universe: if so, the chance that they produce stars must be pretty small?"

This is a standard question, I believe that Alan Guth has an appendix devoted to a careful answer to it. The essence is that as gravitational potential energy is negative, it can cancel positive contributions from matter, so that a universe with zero total energy (or mass) can be arbitrarily big and have arbitrarily many stars in it.

May I make a last remark? For me, the most important argument of the book is not connected with the specific proposal about universes "reproducing" through black holes. It is instead an argument I make in the last half of the book about the connection between theories of space and time and the questions of how the laws of nature were chosen so that our universe is full of structure and variety. The conclusion of this argument is that the relational point of view about space and time, which is realized in classical general relativity, needs to be joined to some mechanism of self-organization such as natural selection in order to complete the unification of general relativity with quantum theory. The reason, in brief (the argument is given in the last two Parts of the book), is that a relational theory of space and time, such as general relativity or any reasonable theory of quantum gravity, requires a complex world if space and time are to have their usual meanings. But, given the second law of thermodynamics, the laws that govern the physics of large scales must have certain characteristics if the world is to be permanently full of structure and complexity, and avoid equilibrium. Thus, the line of thought from Leibniz, Mach and Einstein must be joined to the discovery that there are physical processes that can produce structure and complexity, as we learn from Darwin and contemporary biologists, if it is to lead in the end to a coherent theory.

When taken together with the apparent lesson of recent developments in string theory, which is that the problem of unifying quantum theory with general relativity does not have a unique solution, this argument leads me to conclude that some historical processes analogous to natural selection must have played a role in our past to choose the laws of nature from a larger possible set, leading to a world with the structure and complexity of ours. I am not at all sure that the particular theory described in the book, involving black holes and "many universes" will survive. It is just the only theory like it IĖve been able to devise that was not easy to rule out by comparison with observation, while at the same time remaining genuinely vulnerable to falsification by plausible observations, such as three solar mass black holes.

Let me then end by coming back to the first point. What I think I have shown is that one way to wrest real falsifiable predictions from quantum gravity and string theory involves taking advantage of this last argument to posit that historical process analogous to those that built up structure in the biosphere have taken place on cosmological scales. If this is in fact right, then I believe it has huge implications for a whole range of philosophical issues from the methodology of the sciences to the foundations of mathematics to, perhaps, theology. Because I believe this is very possibly the direction that science will take, I thought that it was fitting to bring the argument to the attention of a wide audience of scientists, philosophers, intellectuals and people in general. It is because of this, and not to try to pull something over on "the man in the street" that I have tried to write for a wide audience, while at the same time trying to communicate honestly the real uncertainties and difficulties involved.

From: Piet Hut

Date: 6-25-97

I like Stu Kauffman's and Lee Smolin's idea of resisting the one-way-street program of reducing biology to physics, by looking for ways in which biology might provide insights useful for physics. Much as I enjoy their cosmological speculations, I wonder whether we can allow full two-way traffic, by looking for applications squarely within established physics as well.

A few years ago, reflecting on the notion of path integrals, related to the principle of least action, I realized that quantum mechanics can be described as selecting the `fittest' path from along a `population' of paths, resulting in a behavior that looks law-like in the classical limit.

In classical mechanics, a particle follows the path it does as the result of its inertia propelling it forwards while external forces act to bend its path. In quantum mechanics, in constrast, a particle goes literally every which way, simultaneously, but most paths interfere destructively with each other. The actual trajectory emerges as the result of active and ongoing competition in an enormous field of competitors. The properties of the `winner' can be directly derived from this process of competition.

Here is an example of a `trait' that nature selects within the population of all possible paths: smoothness. We know from experience that throwing a tennis ball makes it fly through a smooth path, without abrupt changes of direction. Why are there no sudden kinks in its trajectory? Newton invoked a property called inertia, `propelling' the ball along a smooth path. In quantum mechanics, however, inertia is not put in by hand, but arises as an emergent property. Here is how it works.

For every orbit with a kink, there are neighboring orbits with a somewhat larger or somewhat smaller kink. Each of these orbits have a very different phase, and as a result they interfere destructively. In contrast, a kink- free, smooth orbit has at least a chance that its nearby orbits have almost the same phase, resulting in constructive interference. Which smooth orbit is selected by nature depends on the system under consideration, but the point is this: nature has no preference for smooth, rather than kinky orbits. In fact, in the shimmering realm of quantum mechanics, there where actuality and potentiality mingle, kinky orbits are equally present with equal status as smooth orbits. As soon as we make the transition to larger scales, we can see how the whole population of kinky orbits collectively self-destructs, leaving only smooth orbits behind in the classical limit.

It would be an interesting project to write a physics text book from a biological point of view, from scratch. Instead of starting with classical mechanics, and then going to quantum-mechanical wonderland, we could look through the other end of the actuality-potentiality telescope. Starting with the fundamental contingency associated with measurements in quantum mechanics, we could arrive at our normal field of experience as the result of a form of natural selection.

From: Lee Smolin
To: Piet Hut

Date: 7-10-97

Piet's idea is pretty interesting and imaginative. I've often wondered whether there could be something like self-organized critical behavior that naturally accounted for the existence of the classical limit from path integrals in quantum gravity or even ordinary quantum field theory. This would be analogous to the way that equilibrium critical phenomena like second order phase transitions are mathematically analogous to the continuum limit in what is called Euclidean field theory, which is quantum field theory with the modification that the time dimension is treated exactly like space, so spacetime is just an ordinary four dimensional Euclidean space.

I'm not sure whether the ordinary process in which the classical limit emerges from the path integral through interference effects is really analogous to natural selection. For natural selection to be applied there needs to be reproduction, variation and selection. Ordinarily I don't think we have these components. True there are the many paths, and their actions do vary, but I think this is still not really analogous to the schema of natural selection. But still, what Piet writes is worth thinking about, and it may lead to something interesting.

From: Piet Hut
To: Lee Smolin

Date: 7-17-08

Lee, thanks for your comments. This is a fun topic, which I talked a lot about with Stu Kauffman and Brian Goodwin, at the Santa Fe Institute last week. I hope they will join in here as well.

You wondered whether my biological analogy of path integrals extends to all three aspects of natural selection: reproduction, variation, selection. I think it does. In fact, it even maximizes both reproduction and variation (as you might expect from a fundamental theory; nothing half-way here).

  1. reproduction is taken care of by Huygens' principle: each point in a wave front reradiates the wave in all possible directions. At each next moment, all possible next steps are taken in any direction.
  1. variation is taken care of by the `democracy of histories', as John Wheeler likes to call the fact that all paths are equally traversed; in this sense variation is the global counterpart of point 1).

  2. selection is taken care of by the superposition principle, that weeds out the whole lot to arrive at the final probability for a path to be taken.
So in each moment everything possible is being reproduced; together all this provides maximal variation in the sense that all possible histories contribute; and superposition thus has the maximum possible play ground within which to select through interference.

There are interesting historical aspects to both sides of this physics/biology metaphor. Darwin provided a causal mechanism for seemingly teleological results. Similarly, quantum mechanics provides a causal mechanism for why the principle of least action works, a principle that smells teleological, the way it is formulated classically.


Back to A Possible Solution to the Problem of Time in Quantum Cosmology by Lee Smolin and Stuart Kauffman

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