Tom Kibble (1932-2016)

Featured image: From left to right: Tom Kibble, Gerald Guralnik, Richard Hagen, François Englert and Robert Brout. Credit: Wikimedia Commons.

Sir Tom Kibble passed away on June 2, I learnt this morning with a bit of sadness that I’d missed the news. It’s hard to write about someone in a way that prompts others either to find out more about that person or, if they knew him or his work, to recall their memories of him when I myself would like only to do the former now. So let me quickly spell out why I think you should pay attention: Kibble was one of the six theorists who, in 1964, came up with the ABEGHHK’tH mechanism to explain how gauge bosons acquired mass. The ‘K’ in those letters stands for ‘Kibble’. However, we only remember that mechanism with the second ‘H’, which stands for Higgs; the other letters fell off for reasons not entirely clear – although convenience might’ve played a role. And while everyone refers to the mechanism as the Higgs mechanism, Peter Higgs, the man himself, continues to call it the ABEGHHK’tH mechanism.

Anyway, Kibble was known for three achievements. The first was to co-formulate – alongside Gerald Guralnik and Richard Hagen – the ABEGHHK’tH mechanism. It was validated in early 2013, earning only Higgs and ‘E’, François Englert, the Nobel Prize for physics that year. The second came in 1967, to explain how the mechanism accords the W and Z bosons, the carriers of the weak nuclear force, with mass but not the photons. The solution was crucial to validate the electroweak theory, and whose three conceivers (Sheldon Glashow, Abdus Salam and Steven Weinberg) won the Nobel Prize for physics in 1979. The third was the postulation of the Kibble-Żurek mechanism, which explains the formation of topological defects in the early universe by applying the principles of quantum mechanics to cosmological objects. This work was done alongside the Polish-American physicist Wojciech Żurek.

I spoke to Kibble once, only for a few minutes, at a conference at the Institute of Mathematical Sciences, Chennai, in December 2013 (at the same conference where I met George Sterman as well). This was five months after Fabiola Gianotti had made the famous announcement at CERN that the LHC had found a particle that looked like the Higgs boson. I’d asked Kibble what he made of the announcement, and where we’d go from here. He said, as I’m sure he would’ve a thousand times before, that it was very exciting to be proven right after 50 years; that it’d definitively closed one of the biggest knowledge gaps in modern theoretical particle physics; and that there was still work to be done by studying the Higgs boson for more clues about the nature of the universe. He had to rush; a TV crew was standing next to me, nudging me for some time with him. I was glad to see it was Puthiya Thalaimurai, a Tamil-language news channel, because it meant the ‘K’ had endured.

Rest in peace, Tom Kibble.

'Infinite in All Directions', a science newsletter

At 10 am (IST) every Monday, I will be sending out a list of links to science stories from around the web, curated by significance and accompanied by a useful blurb, as a newsletter. If you’re interested, please sign up here. If you’d like to know more before signing up, read on.

It’s called Infinite in All Directions – a term coined by Freeman Dyson for nothing really except the notion behind this statement from his book of the same name: “No matter how far we go into the future, there will always be new things happening, new information coming in, new worlds to explore, a constantly expanding domain of life, consciousness and memory.”

I will be collecting the links and sending the newsletter out on behalf of The Wire, whose science section I edit. And so, you can trust the links to not be to esoteric pieces (which I’m fond of) but to pieces I’d have liked to have covered at The Wire but couldn’t.

More than that, the idea for the newsletter is essentially a derivative of a reading challenge a friend proposed a while ago: wherein a group of us would recommend books for each other to read, especially titles that we might not come upon by ourselves.

Some of you might remember that a (rather, the same) friend and I used to send out the Curious Bends newsletter until sometime last year. The Infinite in All Directions newsletter will be similarly structured but won’t necessarily be India-centric. In fact, a (smaller than half) section of the newsletter may even be consistently skewed toward the history and philosophy of science. But you can trust that the issues will all be contemporary.

Apart from my ‘touch’ coming through with the selection, I will also occasionally include my take on some topics (typically astro/physics). You’re welcome to disagree (just be nice) – all replies to the newsletter will land up in my inbox. You’re also more than welcome to send me links to include in future issues.

Finally: Each newsletter will not have a fixed number of links – I don’t want to link you to pieces I myself haven’t been able to appreciate. At the same time, there will be at least five or so links. I think The Wire alone puts out that many good stories each week.

I hope you enjoy reading the newsletter. As with this blog, Infinite in All Directions will be a labour of love. Please share it with your friends and anybody who might be interested in such a service. Again, here is the link to subscribe.

A universe out of sight

Two things before we begin:

  1. The first subsection of this post assumes that humankind has colonised some distant extrasolar planet(s) within the observable universe, and that humanity won’t be wiped out in 5 billion years.
  2. Both subsections assume a pessimistic outlook, and neither projections they dwell on might ever come to be while humanity still exists. Nonetheless, it’s still fun to consider them and their science, and, most importantly, their potential to fuel fiction.

Cosmology

Astronomers using the Hubble Space Telescope have captured the most comprehensive picture ever assembled of the evolving Universe — and one of the most colourful. The study is called the Ultraviolet Coverage of the Hubble Ultra Deep Field. Caption and credit: hubble_esa/Flickr, CC BY 2.0
Astronomers using the Hubble Space Telescope have captured the most comprehensive picture ever assembled of the evolving universe — and one of the most colourful. The study is called the Ultraviolet Coverage of the Hubble Ultra Deep Field. Caption and credit: hubble_esa/Flickr, CC BY 2.0

Note: An edited version of this post has been published on The Wire.

A new study whose results were reported this morning made for a disconcerting read: it seems the universe is expanding 5-9% faster than we figured it was.

That the universe is expanding at all is disappointing, that it is growing in volume like a balloon and continuously birthing more emptiness within itself. Because of the suddenly larger distances between things, each passing day leaves us lonelier than we were yesterday. The universe’s expansion is accelerating, too, and that doesn’t simply mean objects getting farther away. It means some photons from those objects never reaching our telescopes despite travelling at lightspeed, doomed to yearn forever like Tantalus in Tartarus. At some point in the future, a part of the universe will become completely invisible to our telescopes, remaining that way no matter how hard we try.

And the darkness will only grow, until a day out of an Asimov story confronts us: a powerful telescope bearing witness to the last light of a star before it is stolen from us for all time. Even if such a day is far, far into the future – the effect of the universe’s expansion is perceptible only on intergalactic scales, as the Hubble constant indicates, and simply negligible within the Solar System – the day exists.

This is why we are uniquely positioned: to be able to see as much as we are able to see. At the same time, it is pointless to wonder how much more we are able to see than our successors because it calls into question what we have ever been able to see. Say the whole universe occupies a volume of X, that the part of it that remains accessible to us contains a volume Y, and what we are able to see today is Z. Then: Z < Y < X. We can dream of some future technological innovation that will engender a rapid expansion of what we are able to see, but with Y being what it is, we will likely forever play catch-up (unless we find tachyons, navigable wormholes, or the universe beginning to decelerate someday).

How fast is the universe expanding? There is a fixed number to this called the deceleration parameter:

q = – (1 + /H2),

where H is the Hubble constant and  is its first derivative. The Hubble constant is the speed at which an object one megaparsec from us is moving away at. So, if q is positive, the universe’s expansion is slowing down. If q is zero, then H is the time since the Big Bang. And if q is negative – as scientists have found to be the case – then the universe’s expansion is accelerating.

The age and ultimate fate of the universe can be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterised by values of density parameters (Ω_M for matter and Ω_Λ for dark energy). Caption and credit: Wikimedia Commons
The age and ultimate fate of the universe can be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterised by values of density parameters (Ω_M for matter and Ω_Λ for dark energy). Caption and credit: Wikimedia Commons

We measure the expansion of the universe from our position: on its surface (because, no, we’re not inside the universe). We look at light coming from distant objects, like supernovae; we work out how much that light is ‘red-shifted’; and we compare that to previous measurements. Here’s a rough guide.

What kind of objects do we use to measure these distances? Cosmologists prefer type Ia supernovae. In a type Ia supernova, a white-dwarf (the core of a dead stare made entirely of electrons) is slowly sucking in matter from an object orbiting it until it becomes hot enough to trigger fusion reaction. In the next few seconds, the reaction expels 1044 joules of energy, visible as a bright fleck in the gaze of a suitable telescope. Such explosions have a unique attribute: the mass of the white-dwarf that goes boom is uniform, which means type Ia supernova across the universe are almost equally bright. This is why cosmologists refer to them as ‘cosmic candles’. Based on how faint these candles are, you can tell how far away they are burning.

After a type Ia supernova occurs, photons set off from its surface toward a telescope on Earth. However, because the universe is continuously expanding, the distance between us and the supernova is continuously increasing. The effective interpretation is that the explosion appears to be moving away from us, becoming fainter. How much it has moved away is derived from the redshift. The wave nature of radiation allows us to think of light as having a frequency and a wavelength. When an object that is moving away from us emits light toward us, the waves of light appear to become stretched, i.e. the wavelength seems to become distended. If the light is in the visible part of the spectrum when starting out, then by the time it reached Earth, the increase in its wavelength will make it seem redder. And so the name.

The redshift, z – technically known as the cosmological redshift – can be calculated as:

z = (λobserved – λemitted)/λemitted

In English: the redshift is the factor by which the observed wavelength is changed from the emitted wavelength. If z = 1, then the observed wavelength is twice as much as the emitted wavelength. If z = 5, then the observed wavelength is six-times as much as the emitted wavelength. The farthest galaxy we know (MACS0647-JD) is estimated to be at a distance wherefrom = 10.7 (corresponding to 13.3 billion lightyears).

Anyway, z is used to calculate the cosmological scale-factor, a(t). This is the formula:

a(t) = 1/(1 + z)

a(t) is then used to calculate the distance between two objects:

d(t) = a(t) d0,

where d(t) is the distance between the two objects at time t and d0 is the distance between them at some reference time t0. Since the scale factor would be constant throughout the universe, d(t) and d0 can be stand-ins for the ‘size’ of the universe itself.

So, let’s say a type Ia supernova lit up at a redshift of 0.6. This gives a(t) = 0.625 = 5/8. So: d(t) = 5/8 * d0. In English, this means that the universe was 5/8th its current size when the supernova went off. Using z = 10.7, we infer that the universe was one-twelfth its current size when light started its journey from MACS0647-JD to reach us.

As it happens, residual radiation from the primordial universe is still around today – as the cosmic microwave background radiation. It originated 378,000 years after the Big Bang, following a period called the recombination epoch, 13.8 billion years ago. Its redshift is 1,089. Phew.

The relation between redshift (z) and distance (in billions of light years). d_H is the comoving distance between you and the object you're observing. Where it flattens out is the distance out to the edge of the observable universe. Credit: Redshiftimprove/Wikimedia Commons, CC BY-SA 3.0
The relation between redshift (z) and distance (in billions of light years). d_H is the comoving distance between you and the object you’re observing. Where it flattens out is the distance out to the edge of the observable universe. Credit: Redshiftimprove/Wikimedia Commons, CC BY-SA 3.0

A curious redshift is z = 1.4, corresponding to a distance of about 4,200 megaparsec (~0.13 trillion trillion km). Objects that are already this far from us will be moving away faster than at the speed of light. However, this isn’t faster-than-light travel because it doesn’t involve travelling. It’s just a case of the distance between us and the object increasing at such a rate that, if that distance was once covered by light in time t0, light will now need t > t0 to cover it*. The corresponding a(t) = 0.42. I wonder at times if this is what Douglas Adams was referring to (… and at other times I don’t because the exact z at which this happens is 1.69, which means a(t) = 0.37. But it’s something to think about).

Ultimately, we will never be able to detect any electromagnetic radiation from before the recombination epoch 13.8 billion years ago; then again, the universe has since expanded, leaving the supposed edge of the observable universe 46.5 billion lightyears away in any direction. In the same vein, we can imagine there will be a distance (closing in) at which objects are moving away from us so fast that the photons from their surface never reach us. These objects will define the outermost edges of the potentially observable universe, nature’s paltry alms to our insatiable hunger.

Now, a gentle reminder that the universe is expanding a wee bit faster than we thought it was. This means that our theoretical predictions, founded on Einstein’s theories of relativity, have been wrong for some reason; perhaps we haven’t properly accounted for the effects of dark matter? This also means that, in an Asimovian tale, there could be a twist in the plot.

*When making such a measurement, Earthlings assume that Earth as seen from the object is at rest and that it’s the object that is moving. In other words: we measure the relative velocity. A third observer will notice both Earth and the object to be moving away, and her measurement of the velocity between us will be different.


Particle physics

Candidate Higgs boson event from collisions in 2012 between protons in the ATLAS detector on the LHC. Credit: ATLAS/CERN
Candidate Higgs boson event from collisions in 2012 between protons in the ATLAS detector on the LHC. Credit: ATLAS/CERN

If the news that our universe is expanding 5-9% faster than we thought sooner portends a stellar barrenness in the future, then another foretells a fecundity of opportunities: in the opening days of its 2016 run, the Large Hadron Collider produced more data in a single day than it did in the entirety of its first run (which led to the discovery of the Higgs boson).

Now, so much about the cosmos was easy to visualise, abiding as it all did with Einstein’s conceptualisation of physics: as inherently classical, and never violating the principles of locality and causality. However, Einstein’s physics explains only one of the two infinities that modern physics has been able to comprehend – the other being the world of subatomic particles. And the kind of physics that reigns over the particles isn’t classical in any sense, and sometimes takes liberties with locality and causality as well. At the same time, it isn’t arbitrary either. How then do we reconcile these two sides of quantum physics?

Through the rules of statistics. Take the example of the Higgs boson: it is not created every time two protons smash together, no matter how energetic the protons are. It is created at a fixed rate – once every ~X collisions. Even better: we say that whenever a Higgs boson forms, it decays to a group of specific particles one-Yth of the time. The value of Y is related to a number called the coupling constant. The lower Y is, the higher the coupling constant is, and more often will the Higgs boson decay into that group of particles. When estimating a coupling constant, theoretical physicists assess the various ways in which the decays can happen (e.g., Higgs boson → two photons).

A similar interpretation is that the coupling constant determines how strongly a particle and a force acting on that particle will interact. Between the electron and the electromagnetic force is the fine-structure constant,

α = e2/2ε0hc;

and between quarks and the strong nuclear force is the constant defining the strength of the asymptotic freedom:

αs(k2) = [β0ln(k22)]-1

So, if the LHC’s experiments require P (number of) Higgs bosons to make their measurements, and its detectors are tuned to detect that group of particles, then at least P-times-that-coupling-constant collisions ought to have happened. The LHC might be a bad example because it’s a machine on the Energy Frontier: it is tasked with attaining higher and higher energies so that, at the moment the protons collide, heavier and much shorter-lived particles can show themselves. A better example would be a machine on the Intensity Frontier: its aim would be to produce orders of magnitude more collisions to spot extremely rare processes, such as particles that are formed very rarely. Then again, it’s not as straightforward as just being prolific.

It’s like rolling an unbiased die. The chance that you’ll roll a four is 1/6 (i.e. the coupling constant) – but it could happen that if you roll the die six times, you never get a four. This is because the chance can also be represented as 10/60. Then again, you could roll the die 60 times and still never get a four (though the odds of that happened are even lower). So you decide to take it to the next level: you build a die-rolling machine that rolls the die a thousand times. You would surely have gotten some fours – but say you didn’t get fours one-sixth of the time. So you take it up a notch: you make the machine roll the die a million times. The odds of a four should by now start converging toward 1/6. This is how a particle accelerator-collider aims to work, and succeeds.

And this is why the LHC producing as much data as it already has this year is exciting news. That much data means a lot more opportunities for ‘new physics’ – phenomena beyond what our theories can currently explain – to manifest itself. Analysing all this data completely will take many years (physicists continue to publish papers based on results gleaned from data generated in the first run), and all of it will be useful in some way even if very little of it ends up contributing to new ideas.

The steady (logarithmic) rise in luminosity – the number of collision events detected – at the CMS detector on the LHC. Credit: CMS/CERN
The steady (logarithmic) rise in luminosity – the number of collision events detected – at the CMS detector on the LHC. Credit: CMS/CERN

Occasionally, an oddball will show up – like a pentaquark, a state of five quarks bound together. As particles in their own right, they might not be as exciting as the Higgs boson, but in the larger schemes of things, they have a role to call their own. For example, the existence of a pentaquark teaches physicists about what sorts of configurations of the strong nuclear force, which holds the quarks together, are really possible, and what sorts are not. However, let’s say the LHC data throws up nothing. What then?

Tumult is what. In the first run, the LHC used to smash two beams of billions of protons, each beam accelerated to 4 TeV and separated into 2,000+ bunches, head on at the rate of two opposing bunches every 50 nanoseconds. In the second run, after upgrades through early 2015, the LHC smashes bunches accelerated to 6.5 TeV once every 25 nanoseconds. In the process, the number of collisions per sq. cm per second increased tenfold, to 1 × 1034. These heightened numbers are so new physics has fewer places to hide; we are at the verge of desperation to tease them out, to plumb the weakest coupling constants, because existing theories have not been able to answer all of our questions about fundamental physics (why things are the way they are, etc.). And even the barest hint of something new, something we haven’t seen before, will:

  • Tell us that we haven’t seen all that there is to see**, that there is yet more, and
  • Validate this or that speculative theory over a host of others, and point us down a new path to tread

Axiomatically, these are the desiderata at stake should the LHC find nothing, even more so that it’s yielded a massive dataset. Of course, not all will be lost: larger, more powerful, more innovative colliders will be built – even as a disappointment will linger. Let’s imagine for a moment that all of them continue to find nothing, and that persistent day comes to be when the cosmos falls out of our reach, too. Wouldn’t that be maddening?

**I’m not sure of what an expanding universe’s effects on gravitational waves will be, but I presume it will be the same as its effect on electromagnetic radiation. Both are energy transmissions travelling on the universe’s surface at the speed of light, right? Do correct me if I’m wrong.