NZ government funds new Science Centre

The University of Canterbury (UC), my undergraduate institution, is struggling financially following the 2010/11 Christchurch earthquakes that left the university with damaged infrastructure and reduced student numbers.

The government recently made some announcements that they will give much-needed financial support to UC to build a $212m “Canterbury Regional Science and Innovation Centre” and to upgrade its engineering facilities. The Science/Engineering bias is in accordance with government agenda and any support for other areas will have to come from funding within the university.

I was asked by the UC media consultant to answer some questions relating to this announcement. I tried to be optimistic about the support for science, whilst emphasising that it’s important that other academic areas are supported in the university–lest UC becomes a technical institute.The resulting article is here, but I’ll paste my full answers below:

How exciting this is for the future of UC Science–and why? How this will really raise the value, integrity and status of UC Science?

This is tremendously exciting for the future of UC Science. If post-quake UC is to be a competitive science research and teaching institution that attracts students and leading researchers, then it needs upgraded infrastructure and a distinctive brand.

There is a unique opportunity for us to learn from our earthquake experiences and to plan strategically for the future as we rebuild; the proposed Canterbury Regional Science and Innovation Centre (CRSIC), which is made possible due to this government support, is representative of the type of ambitious long-term thinking that UC and Canterbury needs.

However, it is important to remember that people are a university’s most valuable asset. New infrastructure alone does not create a thriving university, although it can certainly help to attract world-class academics and foster research. In addition, a healthy and diverse intellectual climate requires that we give adequate support to non-STEM subjects.

How exciting this is for prospective UC students–and why?

Future students can look forward to having modern, open science facilities. Well-designed spaces can make a huge difference to one’s university learning and social experiences—something I have recently experienced first-hand at Oxford in the vibrant atmosphere of the new Mathematics Institute. Such spaces also encourage collaboration and the transfer of ideas through casual interactions amongst academics and students, both within and across disciplines—such interdisciplinary collaboration will be needed to solve complex problems such as climate change. The new science facilities should help to improve students’ learning experiences and to equip them to tackle such important future problems, as well as to thrive in modern collaborative workplaces.

How this will help attract Year 12 and 13 high school students to UC?

Modern facilities will naturally attract students, but also the improved outreach ability that UC Science will have will strengthen connections with local schools. Hopefully this will expose some young people to the excitement of science when they might not have had the opportunity otherwise, and perhaps it will even encourage them to pursue science at university.

How this proposal will help graduating Science students get jobs?

[I don’t really have anything meaningful to say here.]

The new facilities will be designed to encourage collaboration with industry. This will be an important component of making graduates more employable and fostering innovation in the region.

Any over overall comments would be great.

Overall, the type of support that the government is giving UC Science is vital if we are to be globally relevant in science education and research in the future. It is important that we not only invest in long-term structural foundations, but that we leverage this financial support to attract and retain leading researchers so that we can move forward also on a strong intellectual foundation.

The Unabomber

I had only a passing knowledge of the Unabomber episode when I came across this book in a Phnom Penh bookshop a few weeks ago, but the prospect of finding out more about this mathematician-turned-bomber was enough temptation for me to buy it and find out more. I was given extra impetus to write about this topic when I woke up this morning to the developing news story about the bombing of the Boston marathon, which is vaguely yet disturbingly reminiscent of Ted Kaczynski’s semi-random bombings during the last quarter of last century.

Ted Kaczynski, aka the Unabomber, was a clever mathematician on his way to earning tenure when, two years into an assistant professorship at UC Berkeley, he suddenly quit and became a recluse living in a remote Montana cabin without electricity or running water. After a few years he started mailing bombs to people and organisations. Over a twenty year period he sent a total of 16 bombs across America, killing three people and injuring 23–he seemed to target universities and airlines, hence the name “Unabomber” given to him by the media. In 1995, toward the end of his bombing campaign, his manifesto was published, at his request with the promise to stop sending bombs, by the New York Times and the Washington Post. The gist of his manifesto, Industrial Society and Its Future, and his justification for killing people, is that he thinks that industrialisation inevitably causes individuals to lose their freedom and that a violent revolution is needed to prevent a future in which human life becomes unnatural and meaningless because of our dependence on technology.

The Unabomber’s 35,000 word manifesto is included in the book and I found it interesting enough to read it in full, if only because it gave an insight into how political ideology can motivate an intelligent person to kill people. In fact, there are parts of the manifesto in which it’s surprisingly difficult to disentangle the rational, reasonable ideas from the absurd ones. There’s a particular section titled (something like) “Motivations of Scientists”, which I found intriguing. Kaczynski argues that the common claims by scientists’ that they do science “out of curiosity”, or “to help people”, are fallacious since specialised scientific questions could not satisfy any natural kind of curiosity and that “science marches on blindly, without regard to the real welfare of the human race”. This is meant to degrade science for it is merely a “surrogate activity” that promotes the pursuit of “artificial” goals, rather “real” goals, like hunting and scavenging. My view is that Kaczynski’s argument is mostly bollocks; that curiosity is a legitimate reason to pursue science; and that, in the modern world, science is one of the most meaningful pursuits that one can undertake. Of course, my point of view is exactly what Kaczynski would expect from a budding “Leftist” (to use Kaczynski’s terminology) scientist and therefore it’s probably true that our points of view are irreconcilable.

The book itself is quite unremarkable, probably since it was hastily put together so that it could be published when the story was most topical. I would guess that someone has since written a more eloquent account of the Unabomber episode, but this one does a good enough job of conveying the essential information.

As for the relation of this to the recent bombing of the Boston marathon mentioned earlier, I think it’s plausible that this event is also the result of a rogue individual motivated by a fringe political ideology–although this is completely unfounded speculation.

Questions and Some Attempted Answers on General Relativity

I’ve been reading A. Einstein’s popular book “Relativity, the Special and the General Theory”, translated by R. Lawson. Reading this has reminded me of how much I enjoy this area of physics and also how rusty is my understanding of it. I had some questions that I could not immediately answer so, at the risk of exposing my ignorance, I thought that I’d write them down here, possibly together with some of my own or Einstein’s attempted explanations. I’ve also included some verbatim quotes (italicised) that I particularly liked. Corrections are welcomed.

First of all, the following comment puzzled me and I still have no explanation:

“The general theory of relativity renders it likely that the electrical masses of an electron are held together by gravitational forces.”

I suspect this is related to some (now) outdated attempt at unification by Einstein and/or some old model of the electron.

“…the law of the constancy of the velocity of light in vacuo…cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position…We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena.”

This is not a point that I’ve considered much before: light rays curve in the presence of a gravitational field and therefore the velocity of light is not constant with respect to a non-inertial system of coordinates. The principle of the constancy of the speed of light is replaced by the more general law that light rays follow null geodesics in spacetime–of course the latter can be suitably interpreted as saying that light rays follow “straight lines” and have a constant speed c (with respect to a local system of inertial coordinates).

Question: I know that the general principle of relativity puts all coordinate systems on an equal footing, but what does that have to do with gravity?

Answer: The fundamental idea, which is explained elegantly in the book, follows from the equivalence of inertial and gravitational mass–the fact that gravity acts on masses irrespective of construction or composition. The idea is that a reference frame which is accelerated with respect to an inertial reference frame can legitimately be regarded, by a comoving observer, as being “at rest” since any forces on some object due to its inertial mass (as viewed from the inertial reference frame) can be attributed, by a comoving observer, to the action of a (possibly time-varying) gravitational field on that object’s gravitational mass. This is only possible thanks to the equivalence of inertial and gravitational mass.

This next one is just a quote that I quite liked.

“No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case.”

I wonder when general relativity will rightly inherit its fair destiny?

Question: How does the mathematical formulation of general relativity incorporate the general principle of relativity?

Short answer: By formulating the laws of nature in terms of tensor equalities.

Longer answer: We want all coordinate systems to be equivalent, insofar as any observer can deduce the same general forms for the laws of nature. Thus, the relevant conceptual framework should represent physical quantities by coordinate independent geometrical objects. It turns out that tensors are just such suitable geometrical objects: they are mathematical objects defined on the tensor bundle of a differentiable manifold and have sufficient complexity to represent things of interest to physicists, such as energy-momentum and curvature. So, if we write down our physics equations in terms of tensors, then we automatically satisfy the general principle of relativity.

Caveat: From a quick google search, it looks as if the matter is much more complicated than my attempted answers make out. There’re all sorts of relativity principles and they aren’t all necessarily realised in general relativity. This free online book dedicates a large amount of space to the issue. Possibly a future blog post will try to sort this out properly.

Question: Are the laws of special relativity tensorial?

In special relativity there are a special class of observers, the inertial observers, who observe the laws of nature in their simplest form. Different coordinate systems corresponding to different inertial observers are related by the Lorentz transformations. It is not true in special relativity, unlike in general relativity, that observers in coordinate systems related by arbitrary transformations will derive the same form for the laws of nature. That is, the laws of nature are not required to be generally covariant. Since it is general covariance that tensorial laws embody, the laws of special relativity are not necessarily tensorial. We do, however, require the laws to be invariant under arbitrary Lorentz transformations, which we do by expressing physical quantities as Lorentz invariant scalars.

Question: In general relativity coordinates are unphysical; why is this? Does this hold in special relativity, or is some intrinsic physical meaning then attached to coordinates?

Question: Is a spacetime devoid of matter and fields the only possible physical realisation of a strict Euclidean (Minkowski) space?

Question: What is the nature of time in general relativity?

Answer: “Clocks, for which the law of motion is of any kind, however irregular, serve for the definition of time. We have to imagine each of these clocks fixed at a point on the non-rigid reference-body. These clocks satisfy only the one condition, that the ‘readings’ which are observed simultaneously on adjacent clocks (in space) differ from each other by an indefinitely small amount.”

Question: General relativity is a special example of a gauge field theory. In what exact mathematical sense is this true and what, if any, consequences does this have in quantum gravity?

Partial Answer: A gauge theory means that the Lagrangian is invariant under a group of local transformations. Another way of looking at gauge invariance is to say that there is some redundancy in the mathematical description of a physical system i.e. the map from conceptual framework to physical reality is not injective, although this redundancy does have physically implications. In general relativity the redundancy is that many coordinate systems describe the same physical system–the descriptions of laws are generally covariant. My understanding is that the gauge, or symmetry, group is special because it is infinite dimensional, whereas, for example, the standard model gauge group U(1)xSU(2)xSU(3) is finite dimensional.

Oxford bound!

I got an acceptance letter today for my application to the Oxford D.Phil program in Theoretical physics. Yay! I haven’t got a definite supervisor or project yet, but this means that I can now worry about those details when I begin studying this October. I’ve had some contact with Pedro Ferreira and Jo Dunkley, whilst still waiting for other potential supervisors to reply to my emails…