Hello, and welcome to August’s Lost in Space-Time, your dispatch from the infinite realms of the cosmos. Not that we know how big the cosmos is (or at least, how fast it is expanding) – or, bizarrely, what size infinity is. Those are just two of the themes we’ll delve into this month, but first: an astrophysical problem that is, well, elementary.
Where do the chemical elements come from?
Nucleosynthesis – now there’s a word to set the pulse racing. Well, for many cosmologists it is, anyway, as they cast a beady eye all the way back to the big bang. The first instants of the universe’s existence were a roiling furnace that, though many details of its first sub-instants remain unresolved, had a clear, very consequential outcome for the further history of the universe and in particular the creation of the first stable, light atomic nuclei (which, let’s face it, is what we really care about, as otherwise we wouldn’t be around to stroke our chins about the early universe in the first place).
Measurements of the abundance of things like helium in the early universe through analysis of the cosmic microwave background, the afterglow of the big bang, pretty much agree with measurements of their abundances in stars and galaxies today. I remember that was one of the things cosmologist Jim Peebles – who not only pioneered the study of the cosmic microwave background, but more or less built our standard cosmological model on the back of it – highlighted as a success when he wrote about that model for New Scientist last year.
In other words, our ability to predict what sort of nuclei exist in the cosmos is one of the things that has convinced us that we’re on the right track with a model that says our entire universe began in an infinitesimal pinprick of unbelievable heat and density some 13.8 billion years ago. That’s a statement that doesn’t lose any of its “wow” power as you knead it around in your brain.
Granted, there are problems with that model (I’ll get on to a recent favourite, the Hubble tension, later in this newsletter). As far as big bang nucleosynthesis goes, for example, a long-standing niggle is that we don’t see even half as much lithium, the third-lightest element after hydrogen and helium, back in the early universe as we’d expect, given how much of it there is around today.
A recent New Scientist feature highlights another gap in our understanding, however. Once you’ve made hydrogen and helium, you can pretty much understand how all the heavier elements up to iron were made either in the furnaces of stars or in the cataclysmic supernova explosions that occur when they die.
But once you get to elements heavier than iron, there is a hard stop. Nuclear fusion just doesn’t work to make these elements, such as gold. Where did they come from?
The astronomer Fred Hoyle – a notorious sceptic of the big bang, incidentally, who coined the term in disparagement, only to find it caught people’s imagination – provided an answer with a process called r-process neutron capture. This allows atoms under certain circumstances, in certain special environments, to hook in extra free neutrons as they whizz past, growing first into heavier, unstable isotopes of the same element, and then changing by radioactive decay into stable isotopes of things like gold.
But there are serious questions as to whether that is the right answer – with recent developments casting new doubt on whether, when it comes to the heaviest elements in the cosmos, we have any true clue how they are made. I’ll spare you the details – do read the feature for those. But our confusion when it comes to such a basic question is a stunning reminder both of how far we have come, but also how far we still have to go.
Supernovae like the one that left the remnant Cassiopeia A make heavy elements - but only up to iron. Credit: NASA/ JPL-Caltech
A new size of infinity?
How far do we have to go to understand the nature of infinity? There’s quite an obvious answer to that: I find it fascinating to think about how we have invented a concept that it is simply not within our brain’s power to grasp.
I once asked the mathematician Ian Stewart how he set about envisaging infinity. His reply was: “I generally think of it as: (a) very big, but (b) bigger than that.” I characterised this at the time as an easy, but not particularly helpful, way of thinking about it – a judgement I stand by.
Why am I going on about this? Well, basically because of rumblings recently that what’s known as the “continuum hypothesis” might have been disproved. This hypothesis, established by the mathematician Georg Cantor in the 19th century, is rooted in another bizarre fact about infinity: that there are many different sizes of it.
That might sound utterly weird, but you can justify the existence of at least two different sizes of infinity reasonably intuitively. One is the size of infinity you get by counting how many countable whole numbers there are: 1, 2, 3, 4… and so on. Another is the size of infinity you get by totting up all the “real” numbers – the whole numbers plus all the other numbers in between with as many decimal places as you like, things like 0.1, 0.01, √2, π and so on.
It’s a reasonable assumption that this second “continuum” infinity is bigger than the first “countable” infinity. For once intuition doesn’t let us down – mathematicians have proved just that. Cantor’s continuum hypothesis basically says that these are the two lowest levels of infinity there are – there’s not another one in between them.
That assumption has now been dealt a blow with a new result published in May in the Annals of Mathematics. It unites two axioms underlying set theory – the theory of manipulating numbers – showing one follows from the other, increasing the likelihood that both are true. A corollary of that is that the continuum hypothesis is more likely to be false. There could be a new level of infinity out there to be discovered within the realm of numbers that we can just about grasp – although quite what that would correspond to, I for one am struggling to grasp. In fact, I’m thinking of commissioning a feature for New Scientist to answer just that question. You heard it here first…
Time to turn to my monthly stab at answering a question from the more than 1000 sent in by readers to our “Your Physics Questions Answered” live event in March. This month: do protons decay?
Short answer: we very much hope not.
To back up with a bit of particle physics: protons and neutrons, the constituents of the atomic nucleus, are the two lightest “hadrons” we know about. Hadrons are particles that can be thought of as being made up (principally) of three quarks, particles we think are fundamental: the proton with two “up” and one “down” quark, and the neutron with one “up” and two “down” quarks. I say principally, as according to the theory of quantum chromodynamics, composite particles like the proton and neutron are complex, roiling broths of these quarks, plus a whole load of other quarks and the particles that bind them popping into and out of existence from the quantum vacuum… but anyway.
The point is that the slight difference in the make-up of the proton and the neutron also makes the neutron slightly heavier than the proton. And I mean slightly: in the units that particle physicists use, the neutron weighs in at 939.6 megaelectronvolts and the proton at 938.3 megaelectronvolts, making for a difference of just 0.14 per cent.
This tiny difference means that, under certain circumstances, a neutron can spontaneously decay into a proton – a process known as beta decay. The reverse can also happen, but only when a proton-rich nucleus gets an extra energy kick when it captures a passing electron, forcing the transformation of a proton to a neutron. If you take a proton on its own, it will never decay.
Did I say never? Of course, there’s the fundamental dictum that absence of evidence is not evidence of absence. All we can say is that, despite looking very, very hard at a very large number of protons, we’ve never seen one decay. With a bit of statistical sleight of hand, what we come out with is a minimum value of the proton’s half-life of the order of 10^34 years. That’s about a thousand billion billion billion times the lifetime of the universe.
And that, my friends, is a good thing. It’s the proton’s stability that makes atomic matter possible, and that means you and I are here to ask the question. So, I for one will take the answer as a “no”.
Have we solved the universe's expansion?
My foray onto the physics arXiv preprint server this month concerns a paper that came out just after I’d written my last newsletter, and my colleague Leah Crane has written about for New Scientist.
It’s called “Measurements of the Hubble Constant: Tensions in Perspective ” and it’s by the cosmologist Wendy L. Freedman. It’s about the Hubble tension I mentioned earlier, and that I’ve mentioned in previous newsletters as one of the greatest challenges to our current model of cosmology. This is the fact that we have two conflicting values for the current rate of expansion of the universe. One is the value we get directly from observations of the present-day universe: measuring how far away things are and how quickly they appear to be receding from us. The second is the value we get by measuring the rate of expansion of the early universe, something we can read off the cosmic microwave background, and using our cosmological model, wind that through to the present day. If the model’s right, the two values should agree – but they don’t.
Cepheid variables are part of the "cosmological ladder" we use to estimate distance in the universe - but measurements based on them might be skewed. Credit: NASA/JPL-Caltech/Science Photo Library
Freedman’s contention is both simple and controversial: that dust might have obscured the brightness of stars known as Cepheid variables that we use as part of what’s known as the “cosmological distance ladder” to measure distance in our local universe, and therefore skewed our estimations of the expansion rate, in the present day. Freedman and her colleagues have used a different type of star, called the tip of the red giant branch stars, with the result – just a suggestion at the moment that needs to be confirmed – that there might be no tension after all.
Two musings on that. First, if Freedman’s result is confirmed, it’s another stark reminder of the problems of dust and other intervening detritus in skewing astronomical measurements. People with long memories may remember the BICEP2 experiment, which reported that it had seen primordial gravitational waves – “ripples from the big bang” – back in 2014. That turned out to be the result of rather more local dust in the Milky Way skewing the measurement.
Second, a positive confirmation will leave us with a huge problem. Yes, the Hubble tension will have gone away – but we’ll have no clue about what to probe to make progress beyond our current model which, though wildly successful, posits those weird unknowns like dark matter and dark energy that we’re no closer to understanding. And so we stumble on…
Unlock more world-class physics content when you subscribe to New Scientist. Subscribers receive full access to newscientist.com, our archive of over 30 years of content, 200+ talks in the New Scientist video library, iOS and Android apps plus exclusive access to subscriber only events.
1. In my newsletter in May, I mentioned Chiara Marletto and her programme to recast the whole of the laws of physics in terms of can/can’t statements. If you didn’t get the full significance of the idea from my telling, you can hear about it from Marletto herself in a New Scientistlive event on 2 September and subsequently on demand. Sign up now!
2. Our regular columnist Chanda Prescod-Weinstein’s latest contribution is on the theory of eternal inflation, and whether it truly is eternal. Worth checking out, whatever branch of the multiverse you’re in.
3. Can physics explain consciousness? It’s one of my favourite questions ever, and one I’ve written about myself in the past. Find out the latest on that and a whole load of other mind-benders in our special on consciousness, out last month.
That’s it for now. Thank you for reading! If you have any comments or questions, you can let me know by emailing me at lostinspacetime@newscientist.com and I’ll try to answer them in an upcoming newsletter. If you know someone who might enjoy Lost in Space-Time, please forward it on. If you haven’t yet, you can sign up to get it in your inbox every week here.
Registered Office: 25 Bedford Street, London, WC2E 9ES Registered in England under Company No. 10644366 Australian mailing address: PO Box 2315, Strawberry Hills, NSW 2012, Australia Registered in Australia under ABN 22 621 413 170
