by Paul Davies
I’m with Ayer in thinking that the meaning of meaning is fraught with difficulties, so let me come at this question from a different tack. When I was sixteen, I became friendly with a young lady in the same year at school. Because I was studying science and she arts, we never shared a class. The only time we saw one another was in the school library. I remember her sitting opposite me one day as I ploughed through a physics calculation. ‘What are you doing?’ she asked, frowning at my scribbles. ‘Working out the range of a ball thrown up an inclined plane,’ I replied. She thought for a moment, then said, ‘But how can you do that by writing things on bits of paper?’ At the time, I dismissed her question as silly. After all, this was my homework, so it had to make sense! But now I realize that her comment touched on something profound. Scientists and engineers can use abstract mathematics to work out in advance what will happen in the physical world because mathematics, which is a rational construct of the human mind, is also found to align with the deep order of nature.
Successful prediction is only one facet of the role of mathematics in describing nature. Another is understanding. Merely describing the world, however accurately, is not at all the same as making sense of it. Physicists often refer to ‘curve fitting’ as simply matching up data with the mathematical function that best fits, without that function having any broader linkage with a law or a deeper set of concepts. However, science is full of ‘Ah!’ moments – discoveries when things connect and fall into place. Let me illustrate this point. In the 1950s, particle accelerators were producing a host of new subatomic splinters. So many, in fact, that physicists ran out of names for them. There were pions and kaons and sigmas and lambdas, and then just a whole bunch of letters and numbers. The rapidly proliferating list of particles looked bewildering and arbitrary. Then, in 1961, Murray Gell-Mann came up with a mathematical scheme based on a branch of mathematics called group theory to bring some order to the data. All those diverse subatomic entities were, he said, made of smaller particles he dubbed quarks – three inside a proton, two inside a kaon, and so on. He produced neat-looking schematic patterns to show how it all hung together. Gell-Mann was able to predict a hitherto undiscovered particle, which rejoiced in the name of the omega minus, based on the fact that there was a gap in one of his pretty group theory patterns. In 1964, Gell-Mann’s missing particle was found. Suddenly the particle zoo ‘made sense’. And quarks are real: you can detect them jiggling about inside protons.
The list of successful predictions in theoretical physics is extensive – the Higgs boson, antimatter, black holes, gravitational waves – they all provide clear examples of things ‘falling into place’, sometimes after decades of experimental searching. It seems to me that if we can extract sense from nature, then there must be something like ‘sense’ in nature. By this I mean that nature is ‘about’ something, an interconnecting rational scheme that for some reason can be grasped by the human mind. It is what I called ‘the key to the universe’ in Chapter 2. Finding that key was by no means inevitable. For a start, there is no absolute reason for nature to have a straightforward mathematical subtext in the first place. And even if it does, there is no reason why humans should be capable of comprehending it. You couldn’t tell from daily experience that the disparate physical systems making up the natural world are linked, deep down, by a network of coded mathematical relationships.
How has this come about? How have human beings become privy to nature’s subtle and elegant scheme? Somehow the universe has engineered, not just its own awareness, but its own comprehension. Mindless, blundering atoms have conspired to spawn beings who are able not merely to watch the show, but to unravel the plot, to engage with the totality of the cosmos and the silent mathematical tune to which it dances.
In this book, I have focused on the great questions of existence viewed through the lens of science, which is my own perspective. However, it’s fair to say that the majority of scientists aren’t comfortable trespassing into philosophical questions, some of which seem to stray into theology. Challenged on whether the universe might have some sort of meaning or purpose, most would either say no or, like Ayer, dismiss the question itself as meaningless. One distinguished scientist bold enough to address the topic is Steven Weinberg, who wrote, ‘The more the universe seems comprehensible the more it also seems pointless.’ Weinberg was roundly condemned for deigning to dignify the concept of a universe with a ‘point’, even if only to deny it.
A universe that ‘just exists’ for no reason, with specific properties that ‘just are’, is correctly described, in formal logic, as ‘absurd’. But if there is no rational coherent scheme beneath the surface phenomena of nature, if things ‘just are’, if the universe is absurd, then the success of the scientific enterprise is totally enigmatic. It cannot be pursued with any expectation that the methods adopted hitherto will continue to work, that we will go on uncovering new mechanisms and processes that make sense, for how can sense be rooted in absurdity?
Some years ago, I committed these deliberations to an article in the New York Times. The editor chose the by-line ‘Having faith in science’. It provoked a furious backlash from some of my peers, who counsel against anything that blurs the boundary of science and religion, even on topics where their agendas overlap, and even though the word ‘faith’ has many shades of meaning. One of the more polite responses came from the renowned cosmologist and writer Sean Carroll, who expressed the consensus on the dependability of the laws of nature in characteristically eloquent fashion: ‘There is a chain of explanations concerning things that happen in the universe, which ultimately reaches the fundamental laws of nature and stops . . . at the end of the day the laws are what they are . . . that’s okay. I’m happy to take the universe just as we find it.’
Every scientist who opts to work on profound cosmic questions is confronted by this stark choice: either, like Carroll, take the universe for what it is – an inexplicable brute fact – and get on with the practical job of doing science, or accept that the entire scientific enterprise rests on a deeper layer of rational order. If the latter is the case, a pressing question is whether science will ever advance to the point where we can fully grasp that deeper layer. That is the biggest of all the big questions discussed in this book.
30. What’s New on the Cosmic Horizon?
Historians will look back at the last few centuries as an exceptional time in human history, when explanations of the world transitioned from magic and miracles to mechanisms. The success of the scientific method in accurately describing so much of nature is astonishing. Yet the ambitious project to explain the universe is a work in progress. There are many loose ends – plenty left for future generations to investigate, contemplate and resolve. Some of this unfinished business has been touched upon in the preceding chapters, like the cold patch in Eridanus. Nobody can say what, if anything, preceded the big bang, whether there is one universe or many, or even how many dimensions of space there may be. Was there really an inflationary phase in the very early universe and, if so, what is the nature of the inflaton field that drove it? The new discrepancy in the value for the Hubble constant (see ‘Hubble wars’, p. 18) rings alarm bells, as do the results of a mammoth survey of dark matter showing huge cosmic voids. The observations suggest that dark matter is not as clumpy as Einstein’s general theory of relativity might predict. In addition, we are in the dark about a vast slice of time, from about 400,000 years until half a billion years after the big bang – appropriately called the cosmic Dark Age. And the speed-up of the expansion rate that took everyone by surprise when it was discovered in the 1990s raises the question of whether the acceleration is constant, or is itself increasing or decreasing with time. Nothing less than the fate of the universe hangs on it.
Some of these outstanding questions will benefit from a range of new experiments. A huge system of coupled radio antennae, called the Square Kilometre Array (SKA), is being built in South Africa and Western Australia and will enable astronomers to p
enetrate the cosmic Dark Age. The James Webb optical and infrared telescope – a successor to the Hubble Space Telescope – should launch soon and will probe the very distant universe in far greater detail. To investigate whether dark energy is changing with time, the European Space Agency is due to launch a special satellite called Euclid in 2022, while NASA is planning a Wide Field Infrared Survey Telescope that should also cast light on the problem. Both will garner precision data over billions of years of cosmic history to determine more accurately how the expansion rate has changed. Gravitational wave detectors will be refined and improved in the coming years, providing an abundance of data on the most violent cosmic events, especially those involving black holes.
Because microcosm and macrocosm – the very large and very small – are so intimately linked, unresolved issues in particle and quantum physics also have a bearing on cosmology, such as the crucial asymmetry between matter and antimatter that isn’t completely explained. The nature of dark matter and dark energy remains enigmatic, but it’s possible that any day a dark matter particle detector will get a positive signal. Something unexpected may be found in cosmic rays, or in the large underground neutrino experiments. New particles may yet be created in an upgraded LHC or in one of its mooted successors.
Theoreticians also have a long list of open questions. There is no fully unified theory of the forces of nature, and supersymmetry, which has been part of the theoretical physicists’ armoury for decades, remains unconfirmed. A quantum theory of gravity, crucial for explaining the earliest moments after the big bang, the end state of black hole evaporation and the paradox of missing information, is still not definitive, although string theory remains a popular contender. These difficulties suggest that we still do not possess the complete set of fundamental physical laws. The Standard Model of particle physics is clearly an approximation to something that might turn out to be very different in form. There could even be totally new kinds of laws to be uncovered. On top of these specific technical problems, there are foundational open questions, such as whether quantum physics can be applied to the universe as a whole and what determined the cosmological initial conditions. Another profound question concerns the status of the laws of physics: are they immutable, or can they vary from one cosmic region to another, or one bubble universe to another, or even change with time within our universe? Can the laws of physics themselves actually be explained, or will they for ever lie outside the scope of the scientific method?
In the previous chapter I argued that science goes beyond just explaining the physical world; it also provides a basis for understanding it. A fully satisfactory scientific explanation is one that ‘makes sense’ and can be incorporated into a broader rational account of existence. The catalogue of loose ends I listed above indicates that there is much we do not understand about the universe. Sometimes when scientists encounter a deep problem it is solved by a new discovery or by working harder at the theory. But when there is a real dead end, the reason why we are stuck is often because scientists are thinking about the problem the wrong way. The theory of relativity resolved many troubling issues of physics by abandoning the natural assumption that space and time provide a fixed scaffold in which matter moves about; instead, space and time need to be treated as flexible and dynamic. Quantum mechanics rescued microphysics by relinquishing the intuitive notion that the atomic domain is just a scaled-down version of the everyday world, with electrons and protons behaving like little billiard balls obeying the usual rules of cause and effect. Both relativity and quantum theory succeeded by fundamentally altering the entire conceptual framework of the subject matter.
I suspect that some of the problems faced by physicists and cosmologists today will likewise require a radical overhaul of existing concepts. I have explained how the key to the universe came with the realization that the physical world is mirrored by a mathematical world. Mathematics is, of course, a limitless ocean of forms and relationships. The mathematical structures employed in theoretical physics, however, are actually of a very special nature, often selected on grounds of simplicity and even beauty. There is no guarantee that restricting ourselves to this specific limited class will always yield results in physics. To make the latter point explicit, the theories I have discussed in this book – general relativity, quantum mechanics, electromagnetism, the weak and strong forces, Newtonian mechanics and gravitation – are all what we might call bottom-up theories. They are cast in terms of what happens at each point of space and time, focusing on the simplest level. Physicists refer to these as ‘local’ laws. Adopting this standard approach, complexity in physical systems is regarded as a secondary or derivative quality that emerges in some large systems, such as living organisms, and not something to be built into the basic description – an example of reductionism (see p. 94). There is also an assumption that the laws are fixed, immutable and universal. All of these assumptions can be challenged.
Let me illustrate a possible alternative way forward. Sometimes our wonderful and much-loved theories lead to bizarre predictions. In Chapter 16 I mentioned how the laws of electromagnetism can describe radio messages going back in time. Is that reason to throw out the whole theory as absurd? No, because it turns out that reversed-time radio waves are not impossible, just very improbable, like shuffling cards back into numerical order. More seriously, I also discussed how general relativity permits time travel into the past, arguably undermining the rational basis of cause and effect. Does that suggest general relativity should be discarded in favour of a theory of space, time and gravitation that is paradox-free? Similar causality issues arise if singularities can form by gravitational collapse without being trapped inside black holes. If these so-called naked singularities form, or could be engineered, they could emit influences that lie completely outside the ambit of rational inquiry because cause and effect break down at singularities.
One way to avoid such unpalatable scenarios is to start with certain overarching principles, as Einstein did when formulating the theory of relativity, or Mach did when trying to attribute the origin of centrifugal force to the structure of the universe. Adopting this ‘top-down’ approach, one might use the opportunity to rule out certain philosophically repugnant or outlandish possibilities, of the sort I touched on in the earlier chapters. Many scientists regard duplicate worlds, duplicate beings, or Boltzmann brains, as unacceptable. Should we invent a new principle of nature to ban them, and place it alongside the laws of physics, requiring us to rule out any cosmological models that predicted them? Similar ‘no-go theorems’ have been invoked for other unpalatable scenarios, such as perpetual motion, naked spacetime singularities and time travel – recall Hawking’s Chronology Protection Hypothesis. Science has long been informed by the Principle of Sufficient Reason, first articulated by Leibniz, which says there should be reasons for why things are the way they are. Perhaps we need a Principle of Sufficient Reasonableness too? One could use that as a starting point to identify appropriate mathematical structures, rather than setting out with the standard bottom-up theories and hoping they never predict absurdity. The requisite mathematics might involve novel features, such as non-local laws, or laws that vary across space and time or within systems above a certain level of complexity. Perhaps they will have a form that nobody has yet thought of. What it needs is the proverbial ‘next Einstein’ to pull some of these ideas together into a fully worked-out theory.
Such is my hope and vision. It could be that the golden age of cosmology has been a lucky streak, a dream run of discoveries and theoretical advances that may not last. After all, there is no guarantee that the human intellect has the ability to complete the glorious programme of explanation and unification I have described in this book. The precious cosmic key we have in our possession may serve to unlock the outermost box containing the secrets of nature, but the inner sanctum may for ever elude us. I fervently believe, however, that, while the scientific method continues to deliver results, humanity must persevere in its quest for th
e ultimate prize.
Notes
5. Where is the Centre of the Universe?
* Or, rather, clusters of galaxies are moving away from other clusters. Within clusters, galaxies mill about and occasionally bump into each other. The local group of galaxies includes Andromeda, which is actually flying towards us at 110 km per second (its light is blue-shifted, and was first measured by our unsung hero Vesto Slipher, no less) and will eventually smash into the Milky Way. This awesome encounter won’t happen for a few billion years, however, and even when it does it is unlikely to result in stars actually colliding.
18. A Theory of Everything?
* In April 2021, it was announced that the magnetic field of the muon – the electron’s heavier cousin – seems to deviate by a tiny amount from the Standard Model prediction, again hinting at new physics.
19. Fossils from the Cosmic Dawn
* Balloon lovers take note: most of the industrial helium used today comes from radioactive decay in the Earth, not from the big bang.