TAKE a bucketful of subatomic particles. Put them together one way, and you get a baby. Put them together another way and you’ll get a rock. Put them together a third way and you’ll get one of the most surprising materials in existence: a high-temperature superconductor. How can such radically different properties emerge from different combinations of the same basic matter?
The history of science is replete with investigations of the unexpected qualities that can arise in complex systems. Shoals of fish and ant colonies seem to display a collective behaviour that one would not predict from examining the behaviour of a single fish or ant. High-temperature superconductors and hurricanes offer two more examples where the whole seems to be greater than the sum of its parts. What is still hotly disputed is whether all such behaviour can ultimately be derived from the known laws of physics applied to the individual constituents, or whether it represents the manifestation of something genuinely new and different – something that, as yet, we know almost nothing about. A new factor could shed light on this most fundamental question. And it comes from an entirely unexpected quarter: cosmology.
The standard scientific view, known as reductionism, says that everything can ultimately be explained in terms of the “bottom level” laws of physics. Take the origin of life. If you could factor in everything about the prebiotic soup and its environment – and assuming you have a big enough computer – you could in principle predict life from the laws of atomic physics, claim the reductionists.
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What has become increasingly clear, however, is that many complex systems are computationally intractable. To be sure, their evolution might be determined by the behaviour of their components, but predictive calculations are exponentially hard. The best that one can do is to watch and see how they evolve. Such systems are said to exhibit “weak emergence”.
But a handful of scientists want to go beyond this, claiming that some complex systems may be understood only by taking into account additional laws or “organising principles” that emerge at various levels of complexity. This point of view is called “strong emergence”, and it is anathema to reductionists.
The debate is often cast in the language of “Laplace’s demon.” Two centuries ago, Pierre Laplace pointed out that if a superintelligent demon knew at one instant the position and motion of every particle in the universe, and the forces acting between them, the demon could do a massive calculation and predict the future in every detail, including the emergence of life and the behaviour of every human being. This startling conclusion remains an unstated act of faith among many scientists, and underpins the case for reductionism.
Laplace’s argument contains, however, a questionable assumption: the demon must have unlimited computational power. Is this reasonable? In recent years, there has been intense research into the physical basis of digital computation, partly spurred by efforts to build a quantum computer. The late Rolf Landauer of IBM, who was a pioneer of this field, stressed that all computation must have a physical basis and therefore be subject to two fundamental limitations. The first is imposed by the laws of physics. The second is imposed by the resources available in the real universe.
The fundamental piece of information is the bit. In standard binary arithmetic of the sort computers use, a bit is simply a 1 or a 0. The most basic operation of information processing is a bit-flip: changing a 1 to a 0 or vice versa. Landauer showed that the laws of physics impose limits on the choreography of bit-flips in three ways. The first is Heisenberg’s uncertainty principle of quantum mechanics, which defines a minimum time needed to process a given amount of energy. The second is the finite speed of light, which restricts the rate at which information can be shunted from place to place. The third limit comes from thermodynamics, which treats entropy as the flip side of information. This means a physical system cannot store more bits of information in its memory than is allowed by its total entropy.
“The concordance between the numbers derived from cosmology and those derived from experimental biology is remarkable”
Given that any attempt to analyse the universe and its processes must be subject to these fundamental limitations, how does that affect the performance of Laplace’s demon? Not at all if the universe possesses infinite time and resources: the limitations imposed by physics could be compensated for simply by commandeering more of the universe to analyse the data. But the real universe is not infinite, at least not in the above sense. It originated in a big bang 13.7 billion years ago, which means light can have travelled at most 13.7 billion light years since the beginning. Cosmologists express this restriction by saying that there is a horizon in space 13.7 billion light years away. Because nothing can exceed the speed of light, regions of space separated by more than this distance cannot be in causal contact: what happens in one region cannot affect the other. This means the demon would have to make do with the resources available within the horizon.
Seth Lloyd of the Massachusetts Institute of Technology recently framed the issue like this. Suppose the entire universe (within the effective horizon) is a computer: how many bits could it process in the age of the universe? The answer he arrived at after applying Landauer’s limits is 10120 bits. That defines the maximum available processing power. Any calculation requiring more than 10120 bits is simply a fantasy, because the entire universe could not carry it out in the time available.
“Some physicists have long speculated that the laws of physics might not be fixed”
Lloyd’s number, vast though it is, defines a fundamental limit on the application of physical law. Landauer put it this way: “a sensible theory of physics must respect these limitations, and should not invoke calculative routines that in fact cannot be carried out”. In other words, Landauer and Lloyd have discovered a fundamental limit to the precision of physics: we have no justification in claiming that a law must apply – now, or at any earlier time in the universe’s existence – unless its computational requirements lie within this limit, for even a demon who commandeered the entire cosmos to compute could not achieve predictive precision beyond this limit. The inherent fuzziness that this limit to precision implies is quite distinct from quantum uncertainty, because it would apply even to deterministic laws.
How does this bear on the question of strong emergence – the idea that there are organising principles that come into play beyond a certain threshold of complexity? The Landauer-Lloyd limit does not prove that such principles must exist, but it disproves the long-standing claim by reductionists that they can’t. If the micro-laws – the laws of physics as we know them – cannot completely determine the future states and properties of some physical systems, then there are gaps left in which higher-level emergent laws can operate.
So is there any way to tell if there is some substance to the strong-emergentists’ claims? For almost all systems, the Landauer-Lloyd limit is nowhere near restrictive enough to make any difference to the conventional application of physical laws. But certain complex systems exceed the limit. If there are emergent principles at work in nature, it is to such complex systems that we should look for evidence of their effects.
A prime example is living organisms. Consider the problem of predicting the onset of life in a prebiotic soup. A simple-minded approach is to enumerate all the possible combinations and configurations of the basic organic building blocks, and calculate their properties to discover which would be biologically efficacious and which would not.
Calculations of this sort are already familiar to origin-of-life researchers. There is considerable uncertainty over the numbers, but it scarcely matters because they are so stupendously huge. For example, a typical small protein is a chain molecule made up of about 100 amino acids of 20 varieties. The total number of possible combinations is about 10130, and we must multiply this by the number of possible shapes the molecule can take, because its shape affects its function. This boosts the answer to about 10200, already far in excess of the Landauer-Lloyd limit, and shows how the remorseless arithmetic of combinatorial calculations makes the answers shoot through the roof with even modest numbers of components.
The foregoing calculation is an overestimate because there may be many other combinations of amino acids that exhibit biological usefulness – it’s hard to know. But a plausible guesstimate is that a molecule containing somewhere between 60 and 100 amino acids would possess qualities that almost certainly couldn’t have been divined in the age of the universe by any demon or computer, even with all the resources of the universe at its disposal. In other words, the properties of such a chain simply could not – even in principle – be traced back to a reductionist explanation.
Strikingly, small proteins possess between 60 and 100 amino acids. The concordance between these two sets of numbers, one derived from theoretical physics and cosmology, the other from experimental biology, is remarkable. A similar calculation for nucleotides indicates that in DNA, the properties of strings of more than about 200 base pairs might require additional organising principles to explain their properties. Since genes have upwards of about this number of base pairs, the inference is clear: emergent laws may indeed have played a part in giving proteins and genes their functionality.
Biologists such as Christian de Duve have long argued that life is “a cosmic imperative”, written into the laws of nature, and will emerge inevitably and naturally under the right conditions. However, they have never managed to point to the all-important laws that make the emergence of life “law-like”. It seems clear from the Landauer-Lloyd analysis that the known laws of physics won’t bring life into existence with any inevitability – they don’t have life written into them. But if there are higher-level, emergent laws at work, then biologists like de Duve may be right after all – life may indeed be written into the laws of nature. These laws, however, are not the bottom-level laws of physics found in the textbooks.
And while we are looking for phenomena that have long defied explanation by reductionist arguments, what about the emergence of familiar reality – what physicists call “the classical world” – from its basis in quantum mechanics? For several decades physicists have argued about how the weird and shadowy quantum micro-world interfaces with the concrete reality of the classical macro-world. The problem is that a quantum state is generally an amalgam of many alternative realities, coexisting in ghostly superposition. The macro-world presented to our senses is a single reality. How does the latter emerge from the former?
“Landauer and Lloyd have created a limit to the precision of physics”
There have been many suggestions that something springs into play and projects out one reality from many. The ideas for this “something” range from invoking the effect of the observer’s mind to the influence of gravitation. It seems clear, however, that size or mass are not relevant variables because there are quantum systems that can extend to everyday dimensions: for example, superconductors.
One possible answer is that complexity is the key variable. Could it be that a quantum system becomes classical when it is complex enough for emergent principles to augment the laws of quantum mechanics, thereby bringing about the all-important projection event?
To find where, on the spectrum from atom to brain, this threshold of complexity might lie, we can apply the Landauer-Lloyd limit to quantum states of various configurations. One such complex state, known as an entanglement, consists of a collection of particles like electrons with spins directed either up or down, and linked together in a quantum superposition. Entangled states of this variety are being intensively studied for their potential role in quantum computation. The number of up-down combinations grows exponentially with the number of electrons, so that by the time one has about 400 particles the superposition has more components than the Landauer-Lloyd limit. This suggests that the transition from quantum to classical might occur, at least in spin-entangled states, at about 400 particles. Though this is beyond current technology, future experiments could test the idea.
For 400 years, a deep dualism has lain at the heart of science. On the one hand the laws of physics are usually considered universal, absolute and eternal: for example, a force of 2 newtons acting on a 2-kilogram mass will cause it to accelerate by 1 metre per second per second, wherever and whenever in the universe the force is applied.
On the other hand, there is another factor in our description of the physical world: its states. These are not fixed in time. All the states of a physical system – whether we are talking about a hydrogen atom, a box full of gas or the recorded prices on the London stock market – are continually moving and changing in a variety of ways.
In our descriptions of how physical systems behave, these states are as important as the laws. After all, the laws act on the states to predict how the system will behave. A law without a state is like a traffic rule in a world with no cars: it doesn’t have any application.
What the new paradigm suggests is that the laws of physics and the states of the real world might be interwoven at the deepest level. In other words, the laws of physics do not sit, immutable, above the real world, but are affected by it.
“Any calculation requiring more than 10120 bits is simply a fantasy”
That sounds almost heretical, but some physicists – most notably John Wheeler – have long speculated that the laws of physics might not be fixed “from everlasting to everlasting”, to use his quaint expression. Most cosmologists treat the laws of physics as “given”, transcending the physical universe. Wheeler, however, insisted the laws are “mutable” and in some manner “congeal” into their present form as the universe expands from an initial infinitely dense state. In other words, the laws of physics might emerge continuously from the ferment of the hot big bang.
It seems Wheeler’s ideas and the Landauer-Lloyd limit point in the same direction. And that means the entire theory of the very early universe could be back in the melting pot.
