I can't help warming to Carlo Rovelli, he is such an enthusiast, for his subject of course but also for life, for experience, for poetry and architecture and beauty and music and ideas. I love it that he quotes Dante and Shakespeare and Dostoevsky (even if he mucks up his quotation of the Brothers Karamazov – this really should have been picked up by his publisher!)
I also love a passage where he asks when does somebody's life really begin – when their mother first starts to dream of them? at conception? at birth? when they first recognise their own name or start to speak in their own words? It's beautiful and it is also part of his exploration of how we understand things and grow in knowledge, by interaction and not by prescription.
The summaries of the development of cosmological thought over time are extremely helpful for a lay person like me to get a sense of how ideas have grown and evolved from previous insights. He's really good on the personalities of the scientists and thinkers involved as well – though in his polemic against the Church as a dysfunctional system of knowledge, starting from a priori beliefs rather than the examination of what is before us, he fails to acknowledge just how many of the pioneering physicists to whom he attributes so much advancement were passionate and committed believers: Copernicus, Newton, Faraday, Maxwell, Cavendish and so on. At least he doesn't try to hide Lemaitre's faith from us!
I think his distrust of the Church relates to the Roman Catholics and their Magisterium, not to the Reformed Churches where people are expected to think for themselves and to explore God's world in accordance with the command in Genesis 1. The passion of these believing scientists was drawn from their conviction that they were exploring God's world, thinking God's thoughts after Him, and taking delight in what He has done. I don't think this was a straitjacket for them, more like a spur.
Basically Rovelli is arguing for the predominance of quantum mechanics over other understandings of the universe such as general relativity. He does this by asserting that gravity is not a continuum as in relativity but must be made of quanta in the same way that electro-magnetic fields turn out to be made of photons. The importance of this is that gravity in Einsteinian relativity is the outcome of the space-time continuum. If there are gravitational quanta then they are also quanta of space-time itself. Thus gravitational particles are in fact spatial particles. This means that all phenomena are quanta, every part of the universe is granular, and the disciplines of relativity and quantum mechanics are unified. In this unity quanta become everything and fields – such as the space-time continuum – have no place.
The enormous attractiveness of this is that a theory that explains lots of things is clearly much more powerful than one that explains fewer things. This is the driver behind the quest for a Theory of Everything which has been motivating so much of physics for a while now and has led to the development of string theory, brane theory and multiverse theories among others. It's surprising in fact that Rovelli doesn't specifically mention theories of everything.
The potential problems for theories of everything, and therefore for Rovelli who clearly belongs in this field, are twin. First is the multiplication of invisible and untestable entities which artificially expand explanations to cope with the complexity of what it is sought to explain. Examples include the requirement for a dozen or more additional invisible dimensions to get string theory to work, or the invention of large numbers of unverifiable extra universes to produce a multiverse. These all fall foul of the principle known as Occam's Razor: that a simple explanation is more likely to be true that one that requires the multiplication of hypotheses.
The second of the twin problems for theories of everything is the reductionism that tries to sweep away awkward aspects of reality by stating that they are "nothing but" some less awkward phenomenon. I'm going to argue that Rovelli resorts to this in presenting his ideas about quantum particles of gravity.
I hope the above is an accurate summary of the position Rovelli is moving towards. As a layman I can't claim to grasp every aspect of spin-foam and loop theory, especially the mathematical bits. But I can see that he is looking for a theory of everything even if he doesn't use the name. I also see that there is a problem with the invention of quanta of gravity whose only property is extension. I think I am right in saying that other particles have properties including mass, energy and charge. This makes them amenable to experimentation and observation. A particle whose only property is extension however seems to me to be one that is very close to untestability. How will we ever be sure they are there when we cannot observe them, weigh them etc etc? We seem to be in danger of a very close shave with Occam's Razor…
To my mind Rovelli's biggest difficulty concerns time. I am suspicious of any position that denies the reality of time as he does. Everything in the universe is conditioned by time. Rovelli can't escape this by pretending it's not a problem, asserting that there is no such thing as time, things just happen. But if there is no time, things can't happen. Every event from the Big Bang through the expansion of the universe to the fluctuations of quanta and the waves of energy that he describes constantly pulsating through the universe requires that there was a time before the event happened, a time when it happened and a time after it happened. To assert that there is no time is to assert that none of the events he describes can happen.
I think the source of Rovelli's embarrassment is that time does seem (to me as a non-specialist) to be ineluctably a continuum. It therefore conflicts with his primary assertion that everything in the universe is granular. It's very hard to see, at least in a dull commonsense way, what meaning granularity could have when applied to time.
In fact we know that time is fundamental to the universe because of the velocity of light. Velocity is meaningless without time. It means – doesn't it? – that an object, say a photon, is at one place at one moment and moves continuously until it reaches another place after a measurable passage of time. Since the whole universe is dependent on its relativity to the speed of light, time cannot just be brushed away as an inessential – can it?
When it comes to gravity, isn't time even more essential because gravity describes the acceleration of one mass towards another in metres per second per second? No time = no seconds = no acceleration = no gravity = no universe and no gravitational quanta either?
I think this is why Rovelli makes such heavy weather of his refutation of the ancient problem of Achilles and the tortoise. An object travelling close to the speed of Usain Bolt – say 10 metres/sec – will always catch up with and overtake an object whose speed is a mere 1/10 metres/sec. Repeated observation and experimentation will always demonstrate this. So when Zeno proposes that it is impossible for Achilles to catch the tortoise, all he tells us is that he has formulated the problem incorrectly. What Zeno has failed to do is to take time seriously. If the tortoise has a 10m head start, Achilles reaches the point where the tortoise was in one second, but the tortoise has moved 10cm forward. However after two seconds Achilles has travelled 20 metres and the tortoise is 9.8 metres behind having travelled a mere 20 centimetres (give or take a few microns because Achilles is travelling closer to the speed of light than the tortoise)
So why does Rovelli labour what should be a simple piece of empiricism over several pages? Because, like Zeno, he fails to acknowledge the reality of time. Zeno creates an artificial problem by halving the length of each unit of time compared to the previous one, so that very soon each unit of time is cut down to a quasi-infinitesimal degree. Zeno is therefore denying the passing of time and so denies the velocity of both Achilles and the tortoise, since velocity is the measure of distance over time. Zeno commits an absurdity by setting forth a problem about time while dismissing the role of time.
Unfortunately Rovelli accepts Zeno's premise instead of rebutting it. He has to get right down to the granularity of the universe on the scale of the Planck constant to let Achilles win: he states that this granularity means that in the end you can't keep subdividing the distance covered forever. He really makes it sound as though it's all but a dead heat and Achilles only wins out by the width of a couple of quanta! But all we need to do is to accept that Zeno has mis-stated the problem by failing to grasp that speed is a correlation of distance and time to find that Achilles wins every time. Rovelli's distaste for the concept of time is the cause of his difficulties here.
Another area where Rovelli appears to labour unnecessarily is his demonstration of the curvature of space. He spends several pages explaining why two-dimensional Euclidian geometry doesn't successfully describe three dimensional surfaces. Perhaps this is where he believes most of his lay readership is at. Perhaps he intends it as a metaphor – since three-dimensional curves cannot be described using solely two-dimensional descriptions, how can we grasp four-dimensional space when we only perceive three dimensions?
But if this is what he is trying achieve he doesn't succeed very well. Frankly it reads more as though he is trying to describe the difficulties of three-dimensional geometry than as though he is demonstrating the curvature of space. Isn't it a fact of the Einsteinian universe that space time must be curved through this fourth dimension? Isn't this what gravity as a distortion of space time, the rubber sheet model, is indicating to us?
I think we have hit upon another problem with quanta of gravity here. These quanta are three-dimensional. Their only property is extension and this extension appears in the text to be in three dimensions only. Curvature through another dimension starts to look as though it is bringing in the dreaded Einsteinian continuum again.
Here is a thought experiment by which I personally feel convinced of the curvature of space through an additional dimension which we are unable to perceive:
- Get the most powerful telescope available and survey the universe as far out towards its edge as it will reach. As you gaze upon the most distant observable galaxies, be aware that the light has taken billions of years to reach you on planet Earth. Therefore you are seeing the universe as it was billions of years ago… But that universe was different to the one we inhabit now. Recall that the universe is expanding rapidly – so the universe when those galaxies emitted the light we now see it was much smaller… the galaxies were much closer together… in fact we are not only looking out to the edge of the universe but must simultaneously also be looking in towards its centre. How can the same act of observation be directed both towards the edge of the universe and towards its centre? Only if space is curved through a dimension we don't perceive.
It gets even stranger when we call to mind that those galaxies which are all rushing away from us so fast that the light they emit is red-shifted must also in some sense be rushing towards that centre at the same time? Can this be right? I think it must be because of the residual radiation from the Big Bang. How can this be spread fairly evenly across the universe as it has apparently been shown to be, when the Big Bang, having its origins at a single point, ought to be localised in some particular direction in three dimensional geometry? Only if there is a curvature through some other dimension.
I'm pretty sure my guesses, which I acknowledge to be under-informed, must be faulty, but I'd love to discuss them with someone who knows more. Nonetheless I suspect that Rovelli hasn't done justice to the issues here and I guess it's because they don't really sit well with his gravitational quanta.
A few briefer observations and then I'm done:
• I was puzzled by a passage somewhere where Rovelli says in passing that electrons don't all have the same charge. But surely a particle with a different charge or a different mass isn't an electron, is it? I'm probably showing a really pedestrian grasp of quantum fundamentals, but if there is the least element of randomness in the charge or the mass of electrons (or protons or neutrons) then atomic and molecular structures would be impossible – wouldn't they? And the universe we know and love could not then exist. In fact one of the questions I long to put to physicists is, how do we account for the regularity of these particles? They all arose from a Big Bang, so how did they manage to coalesce in such a regular way? I also speculate that perhaps dark matter and energy are particles which are not regular and so simply cannot be an observable part of the universe?
• Rovelli comments on Newton's description that the void of space is "God's Sensorium," saying that it is hard to know what Newton is getting at and speculating that Newton himself probably didn't know. I think he underestimates the extent to which Newton was an ardent believer in the literal truth of every word of Scripture. My guess is that Newton was thinking of a Scripture such as Hebrews 1:3, which states that the Lord "sustains all things by His word of power." The nature of space is therefore that which is known and sustained by God. It solves the Newtonian problem of "ether," that is, how can waves of energy such as light be transmitted through a vacuum when all other waves are motions in some kind of substrate. So there must be an "ether" or immaterial substance through which these waves pass. Quantum mechanics overcomes the difficulty by asserting that electro-magnetism works by particles. It's interesting that Rovelli has brought back a species of ether by asserting the existence of spatial particles.
• Odd to see the "Big Bounce" has bounced its way back into this book. I thought the Bounce had been discredited by the discovery that the universe is expanding too energetically for it to be possible for gravity to pull it all back again into a Big Crunch. If a previous universe had the same mass and same energy as ours it could not have gone into a Crunch or a Bounce. If it had less energy, where did the extra energy come from? If it had more mass, where the mass go? Stephen Hawking posited the universe arising out a singularity in 1986 in A Brief History of Time – but dropped it from The Universe in a Nutshell. Presumably the singularity was expected to be the remnant of a previous universe and research into the above difficulties had in Hawking's mind shown that the concept was improbable as above.
Unfortunately I seem to have written far more in criticism of this book than in commendation. This gives a wrong impression – I loved it! My comments are not because I think I know more about cosmology than Rovelli, which is absurd. Instead they are my attempts to explore the questions he has raised in my mind in this most stimulating work.
Colin Gibson January 2018
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