The Quantum Mechanics of Voting

Now that I’ve finished a marathon session of report-writing I thought I’d take a few minutes out this Friday afternoon, have a cup of tea and pass on a rather silly thought I had the other day about the relationship between Quantum Mechanics (and specifically the behaviour of spin therein) and voting behaviour in elections and referendums.

Gratuitous picture of a Stern-Gerlach experiment

For a start here’s a brief summary of the usual quantum-mechanical context as it relates to, e.g., electrons (rather than elections). Being fermions, electrons possess half-integer spin. This attribute has the property that a measurement of its component in any direction has only two possible values, ±½ in units of Planck’s constant. In the Stern-Gerlach experiment illustrated above, which measures the spin in the vertical direction of silver atoms emerging from a source, the outcome is either “up” or “down”, not some spread of values in between. Silver has a single unpaired electron which is why its atoms behave in this respect in the same way as an individual electron.

The way this is often described in physics textbooks is to say that the operator corresponding to spin in the z-direction has only two eigenstates  (call these ↑ and ↓) ; the act of measurement has to select one of them, not some intermediate state. If the source is thermal then the spins of individual atoms have no preferred direction so 50% turn out to be ↑ and 50% to be ↓ as shown in the cartoon.

Once such measurement has been made, a given particle remains in the same eigenstate, which means that if it is passed through another similar measuring device it will always turn out to have spin pointing in the same direction. If you like, the particle has been `prepared’ in a given state by the act of measurement.

This applies as long as no attempt is made to make a measurement of the spin in a different direction, which is when the fun starts. If we start with a particle in the ↑ state and then pass it through an experiment that measures spin (say) with respect to the x-axis instead of the z-axis then the two allowed eigenstates are then not ↑ and ↓ but ← and →.  A particle that was definitely spin-up would then be forced to decide between spin-left and spin-right (each would have a  50% probability).

Suppose now we took our long-suffering particle that began with spin ↑ after a measurement in the z-direction, then turned out to be spin → when we measured it in the x-direction. What would happen if we repeated the z-measurement? The answer is that “preparing” the particle in the → state destroys the information about the fact that it was previously prepared in the ↑ state –  the outcome of this second z-measurement is that the particle that was previously definitely ↑ now has a 50% chance of being either ↑ or ↓.

So what does all this have to do with voting? It is clear than an election (or a referendum) is very far from a simple act of measurement. During the campaign the various sides of the debate make attempts to prepare a given voter in a given state. In the case of last year’s EU referendum the choice of eigenstates was `Leave’ or `Remain’;  no other possibilities were allowed. The referendum then `prepared’ each voter in one or other of these possibilities.

If voters behaved quantum mechanically each would stay in their chosen state until some other measurement were attempted. But that’s exactly what did happen. Earlier this month there was a General Election. More than two parties were represented, but let’s simplify and assume there were only two options, `Labour’ and `Conservative’.

Now it is true that the `Leave’ camp was dominated by the right wing of the Conservative party, and the majority of Labour voters voted `Remain’, but there were a significant number of Labour Leave voters and a significant number of Tories voted Remain. While these pairs of states are therefore not exactly orthogonal, they are clearly not measuring the same thing so the situation is somewhat analogous to the spin measurement problem.

So along came the General Election result which `prepared’ voters in a state of `Labour’ or `Conservative’, with a slight preference for the latter whereas the earlier referendum had prepared a them in a state of `Leave’ versus `Remain’ with a slight preference for the former. From a quantum mechanical perspective, however, you can further argue that the General Election prepared the voters in such a way that should have erased memories of their vote in the referendum so the previous BrExit vote is now invalid.

There’s only one way to test this quantum-mechanical interpretation of voting patterns, and that is by repeating the EU Referendum…

Follow @telescoper

LISA gets the go-ahead!

Just taking a short break from examining duties to pass on the news that the European Space Agency has selected the Laser Interferometric Space Experiment (LISA) – a gravitational wave experiment in space – for its large mission L3. This follows the detection of gravitational waves using the ground-based experiment Advanced LIGO and the success of a space-based technology demonstrator mission called Lisa Pathfinder.

LISA consists of a flotilla of three spacecraft in orbit around the Sun forming the arms of an interferometer with baselines of the order of 2.5 million kilometres, much longer than the ~1km arms of Advanced LIGO. These larger dimensions make LISA much more sensitive to long-period signals. Each of the LISA spacecraft contains two telescopes, two lasers and two test masses, arranged in two optical assemblies pointed at the other two spacecraft. This forms Michelson-like interferometers, each centred on one of the spacecraft, with the platinum-gold test masses defining the ends of the arms.

Here’s an artist’s impression of LISA:

This is excellent news for the gravitational waves community, especially since LISA was threatened with the chop when NASA pulled out a few years ago. Space experiments are huge projects – and LISA is more complicated than most – so it will take some time before it actually happens. At the moment, LISA is pencilled in for launch in 2034…

Follow @telescoper

Questioning LIGO

Well. Cat, meet pigeons..

A paper appeared on the arXiv this week with the following abstract:

To date, the LIGO collaboration has detected three gravitational wave (GW) events appearing in both its Hanford and Livingston detectors. In this article we reexamine the LIGO data with regard to correlations between the two detectors. With special focus on GW150914, we report correlations in the detector noise which, at the time of the event, happen to be maximized for the same time lag as that found for the event itself. Specifically, we analyze correlations in the calibration lines in the vicinity of 35 Hz as well as the residual noise in the data after subtraction of the best-fit theoretical templates. The residual noise for the two more recent events, GW151226 and GW170104, exhibits equivalent behavior with respect to each of their time lags. A clear distinction between signal and noise therefore remains to be established in order to determine the contribution of gravitational waves to the detected signals.

I’m going to tread carefully here because (a) I have a number of colleagues at Cardiff who are directly involved in the analysis of LIGO data; (b) one of the authors of the new paper (Panel Naselsky) is a longstanding collaborator of mine; and (c) the new paper has not yet been refereed.

In fact I’m planning to visit Copenhagen in July/August and will catch up with Panel and the other authors then.

Whether or not the points raised in the new paper are correct – and I am firmly agnostic, having not done the analysis myself – I think it’s entirely reasonable of the authors to subject the LIGO data to independent analysis. That’s how science is supposed to work; the relevant data are in the public domain now. 

No doubt the LIGO consortium will respond officially in due course. Of course, if anyone would like to comment unofficially then they are free to do so through the box below.
Update: Here is a fairly detailed rebuttal post.

Follow @telescoper

Cosmological Wave Mechanics

As promised here are the slides I used for my talk yesterday at Imperial College. I stole some of them from an old presentation given by Chris Short, who was a PhD student of mine when I was at Nottingham. Chris now works for the Met Office, working on rather different application of fluid mechanics!

Follow @telescoper

Cosmology at a Crossroads – Poll

A short comment piece by Wendy Freedman has appeared in Nature Astronomy; there’s a free version on the arXiv here. It gives a nice perspective on the current debate about the value of the Hubble constant from the point of view of an expert on cosmological distance scale measurements.

The abstract is here:

We are at an interesting juncture in cosmology. With new methods and technology, the accuracy in measurement of the Hubble constant has vastly improved, but a recent tension has arisen that is either signaling new physics or as-yet unrecognized uncertainties.

For the record, I’d go for `as-yet unrecognized uncertainties’, primarily because this field has a long history of drastically underestimated error-bars!

However, the publication of this piece gives me the excuse to resurrect the following poll, in which I invite you to participate:

Follow @telescoper

The Great Dark Energy Poll

Yesterday was a very busy day: up early to check out of my hotel and head to the third day of the Euclid Consortium meeting for the morning session, then across to the Institute of Physics for a Diversity and Inclusion Panel meeting, then back to the Euclid Consortium meeting for the last session of the day, then introducing the two speakers at the evening event, then to Paddington for the 7.15 train back to Cardiff. I was not inconsiderably tired when I got home.

I had to bale out of the evening session to get the train I was booked on, but it seemed to be going well. Before I left, Ofer Lahav asked for an informal show of hands about a few possibilities relating to the nature of Dark Energy. Since today is polling day for the 2017 General Election, I thought it might be a good idea to distract people from politics for a bit by running a similar poll on here.

There are lots of possibilities for what dark energy may turn out to be, but I’ve decided to allow only six broad classes into which most candidate explanations can be grouped:

1. The cosmological constant, originally introduced as a modification of the left hand side of Einstein’s general theory of relativity – the side that describes gravity – but more often regarded nowadays as a modification of the right-hand-side representing a vacuum energy. Whichever interpretation you make of this, its defining characteristic  is that it is constant.
2.  Modified gravity,  in other words some modification of the left-hand-side of Einstein’s equations that manifests itself cosmologically which is more complicated than the cosmological constant.
3. Dynamical dark energy, i.e. some other modification of the energy-momentum tensor on the right-hand side of Einstein’s equation that looks like some form of “stuff” that varies dynamically rather than being cosmologically constant.
4.  Violation of the cosmological principle by the presence of large-scale inhomogeneities which result in significant departures from the usual Friedman-Robertson-Walker description within which the presence of dark energy is
5. Observational error, by which I mean that there is no dark energy at all: its presence is inferred erroneously on the basis of flawed measurements, e.g. failure to account for systematics.
6.  Some other explanation – this would include the possibility that the entire standard cosmological framework is wrong and we’re looking at the whole thing from the wrong point of view. If you choose this option you might want to comment through the box below what you have in mind.

Well, there are the six candidates. Make your choice:

Follow @telescoper

Cosmology beyond the Centenary of Λ

I didn’t expect to be doing anything other than listening to the talks and getting updated on the progress of the Euclid project at this meeting in London, but this morning I was roped in to introduce a public event tomorrow evening, called Cosmology beyond the Centenary of Λ:

 

This will take the form of a dialogue/discussion/debate between two leading cosmologists taking a `big picture’ view of the state of cosmology now and likely future developments. I’m sure it will be very friendly so I won’t use any form of language that suggests confrontation but it features, in the red corner, George Efstathiou of the University of Cambridge and, in the blue corner, Ofer Lahav of University College London.

Incidentally, I posted some months ago about the fact that this is the centenary year of Einstein’s introduction of the cosmological constant into the field equations of general relativity in this paper:

I recommend anyone attending this Euclid meeting and indeed anyone with a passing interest in cosmology to read that paper – it’s very different from what you might probably imagine it to be!

Follow @telescoper