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The big breaking physics news is the detection of gravitational waves. These waves are distortions in space-time, caused by a large mass doing something spectacular (two colliding black holes in this case)  that propagate across the universe and create tiny changes in space when they reach us. The commentary here describes what goes on. Essentially, things change their length/width. When a gravitational wave passes through my office (say ceiling to floor) one can imagine the length of the office increasing slightly, coupled with a decrease in the width of the office, followed by the reverse - a decrease in the length and an increase in the width.  But its not just that the bricks that make up the room vibrate (e.g. as in a seismic wave) - its the whole of space that does it. 

These waves were predicted by Einstein in 1916, just after the publication of his theory of General Relativity. Their discovery is further evidence for the theory. But it's not just about Einstein. Gravitational waves provide another way of observing the universe - 'seeing' what's going on. Up to now, we've been stuck with light-based observations (be it visible light, infra-red, microwave - they all are electromagnetic waves). There are neutrino observations too, but these aren't exactly easy. But gravitational waves are something else - it's like seeing AND hearing something, rather than just seeing it. 

So how are they detected? The concept is rather simple, as explained in the commentary. Build a (large, meaning 4 km in the case of LIGO) interferometer with two arms. Pass light up and down each arm. The light from the two different paths will interfere - such interference could be constructive (if a peak from one arm comes at the same time as a peak from the other) or destructive (if a peak comes with a trough). If everything is stable, the interference is stable. But when a gravitational wave passes, the arms change their lengths. Not by much. The light takes longer to pass up and down one arm, and shorter to pass up and down the other. Now the timings of the peaks and the troughs change, and the interference signal changes. We detect a gravitational wave. 

The difficulty to now has been detecting the tiny signals amongst larger 'noise' signals, but a recent upgrade to the LIGO detector has done its job. Well done LIGO team!





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Alison Campbell alerted me to the following: Physicist Andreas Wahl shoots himself with a gun underwater - and proves a point about drag force. 

For the record - I won't be repeating this. Physics or no physics, the guy is crazy. 

BUT, what I have done, is a quick post-hoc analysis from the safety of my own office. There's a little bit of maths involved, but the gist of it is this. The drag force on an object (in turbulent conditions - which this most certainly is), is given by the equation c rho A v2 where c is the 'drag coefficient', rho is the density of the fluid in which the object moves, A its cross-sectional area and v its speed. If we equate this to the objects mass times acceleration (Newton's second law) we get an expression for the acceleration of the object in terms of some physical parameters. Solving the equation (integrate it!) gives an exponential decay relationship between the velocity of the object and the distance it travels. Thismeans there's a characteristic length-scale, d, given by:

d = rho_bullet x b / (c rho_liquid)  

where b is the length of the bullet.  Broadly speaking, d gives you an indication over what distance the speed will decay over. We can now stuff some numbers in. Let's assume the density of the bullet is about five times the density of the water (note how it's only the ratio of the two that matters) and that the bullet is about 2 cm long. The drag coefficient will be quite low, given its a streamlined object; say about 0.1. That gives a distance scale of around a metre. How far does the bullet travel? From the video, I'd say something around a metre. 

So, what's the difference between water and air? It's the density of the fluid. Air has a density around 1 kg per metre cubed (rather than water's 1000 kg per metre cubed). Fire the bullet in air, and the length scale goes to one thousand metres (1 km). I'm not a gun expert, but that figure seems about right. 

I also think he was very wise to have his head out of the water. Sound travels rather well underwater.

And it's very easy to say all that without a gun pointing at your chest. 


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Don't miss the BBC poll on what is the world's most beautiful equation. Are you a fan of Einstein's field equation, or does the Riemann zeta-function hold you in raptures? There's some great commentary on the twelve candidates here

How did I vote? Well, that would be telling, but the fact that my very first publication is titled Auxiliary-field quantum Monte Carlo calculations for the relativistic electron gas [read it here! - at least if you have access to the Journal of Physics: Condensed Matter] might give the physicist readers a few clues. 


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Going back to my last post, our fancy balance proclaims that it weighs objects from 0 to 200 g with a precision of 0.001 g (that's one milligram).   And it does - put an object on and the balance gives you an attractive-looking number on its prominent display reading 184.139 g, or something similar. It is precise to 1 milligram. It's not reading 184.138 g, neither is it reading 184.140 g, it is reading 184.139 g. 

So does that mean our test object has a mass of 184.139 g? Unfortunately not. Just because the balance gives us that number that precisely, it doesn't mean that it is that accurate. University lecturers always have a good giggle when some poor unsuspecting first year student records an answer to a wildly inappropriate number of significant figures - for example she might measure a speed in the lab of 1.48392348837 m/s.   Precise, yes. Accurate, no. However, when a third year student does the same time (I've usually got the message across by then, aided by deducting marks on assignments for stupid use of significant figures), the humour turns into despair. 

So what does our test object weigh? (What is it's mass? I mean). Well, I can weigh it several times and see how the results are spread. I've done that. It's a few milligrams. On taking the object off, and putting it on again, I don't see the recorded mass change by more than three of four milligrams. If I take a lot of measurements, and work out the mean mass and its standard uncertainty (with a bit of statistics) I can get something that has a random uncertainty of only a milligram or so. 

However, that still doesn't mean our test object has a mass of 184.139 g (or whatever our calculation says). I may have accounted for random uncertainty, by weighing it multiple times, but there's certainly other systematic sources of uncertainty. These are significant. Just look at the graph. This is the mass of the test object (as recorded by the balance) over the period starting Tuesday morning this week. Our object is getting lighter! Quite a lot lighter, too. It's moved about 40 mg over three days! That's about one part in 5000. 


What's happening? One interesting thing to note is that we initially calibrated the balance with a nominal 200.000 g mass (sent with the equipment) and a completely empty pan (0.000 g). I've also been weighing the calibration mass and the empty pan over the course of the three days too. They have shown no drift at all - just a couple of milligrams of random uncertainty, as far as I can see. 

The manual suggests that the equipment is affected by temperature and humidity. Now, Monday was one of those horrible Waikato days with a warm, damp atmosphere and lots of rain. One of those days where, if the humidity got any higher, it would be raining in your office. And there was a lot of rain Monday night, before I made the measurements. On Tuesday morning, everything 'felt' damp - but we've been drying out ever since. Is it a long-term drop in humidity in the lab that's caused the change? And is it because the test object was actually heavier (maybe there was some condensation on it) or is it because the humidity has made the balance 'stick' or affected the electronics in some way. I'm not sure?

But what I am sure about is that saying I have a 184.139 g test mass is, at present, unjustified. 





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It's a New Year and there are lots of things to do at work before the students get back in any numbers. There are still summer students and research students here, and in the last couple of days I've been working with a summer student on getting a new piece of equipment running for our Experimental Physics paper - the Gouy Balance for measuring magnetic susceptibility. 

Magnetic susceptibility is a measure of how magnetically responsive a material is - how much it magnetizes when placed in a magnetic field. Materials can be categorized as diamagnetic, paramagnetic or ferromagnetic. Paramagnetism describes a material that magnetizes with the applied magnetic field - that is, it will be attracted to a region of high magnetic field. A ferromagnetic material goes beyond this - not only is it attracted to a region of high magnetic field it retains its magnetization even after being removed from the field. Iron is the obvious example - once you magnetize it it will stay magnetized. Diamagnetism is the opposite of paramagnetism - a diamagnetic material will magnetize in a direction against the applied magnetic field and therefore be repelled from a region of high magnetic field. Water is a easy-to-get-hold-of example. 

You can demonstrate the diamagnetism of water with some rather simple apparatus. Get a short stick, skewer a couple of nice, ripe tomatoes at each end, and hang the stick by a thread from its centre. Adjust the tomatoes so that the stick is roughly horizontal when you hang it. Wait for it to settle down then take a strong magnet (a rare-earth magnet is best) and move it close to a tomato. The tomato will be repelled.

The Gouy Balance measures susceptibility in a broadly similar way - by measuring the force on a sample of material when it approaches a magnet. With the equipment we have, we actually doing the opposite - we have a magnet on a sensitive balance, and we look at the change in the weight of the magnet as a sample of material is brought towards it. With a paramagnetic material, as we lower the material toward the magnet, the magnet is attracted (slightly) to the material, and the weight recorded on the balance is reduced. The size of the reduction lets us calculate the susceptibility. 

The changes aren't big - with our test sample of titanium powder this morning our magnet's measured mass changed from 184.142 g to 184.014 g as the material approached - a change of 0.128 g, or about 0.07%. One certainly wouldn't feel the difference if one were holding the magnet, but the balance is sensitive enough to pick up the change. 

It's a neat little apparatus and will be fun to play with. And it comes with a demonstration of magnetic levitation with pyrolytic graphite


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We had our departmental Christmas lunch on Tuesday, outside in the campus grounds. We had some lovely sunshine, but the wind did rather spoil things. I've certainly got used now to living in a very wind-free place - a fresh breeze is something quite unsual here. We were hanging on to our paper plates, but didn't expect to have to hang on to glass drink bottles as well. One particular gust was strong enough to take a newly opened individual-serving-sized glass bottle of lemonade and blow it over. 

So, being a physicist I had a go at estimating just how strong the gust of wind needed to be to push over a lemonade bottle. As the wind hits the bottle it has to change direction, and this causes a change in its momentum. To do that requires a force - the force being the rate of change of momentum of the air. That gives us an estimate of the pushing force in terms of the speed of the wind - specifically the density of air, times the cross section of the bottle to the wind, times the speed of the wind squared. This generates a turning moment about a point on the base - to get this you can multiply the force by the distance of the centre of the bottle from the table. 

The bottle will tip if this force is enough to overcome the turning moment due to gravity the other way. That's simply the weight times the radius of the bottle. Doing the calculation, gave an estimate of about 15 m/s or so, or a bit above 50 km/h. Not particularly high. I was a bit disappointed by the result. 

But then I got thinking about something more interesting. In this case, the bottle tipped. But what determines whether it will tip over or slide along the table? To think about this, we need to work out how strong the wind needs to be in order to slide the bottle. In this case we can equate the sideways force exerted by the wind to the maximum amount of frictional resistance that the bottle-table interface can provide. The latter is simply the bottle's weight multiplied by the coefficient of static friction between the bottle and the table. Doing the maths again, with an estimate of the coefficient of friction of around 0.5, I got something marginally larger - about 60 km/h. 

Now, the curious thing is the ratio of the force needed to slide the bottle to the force needed to tip it. Although each individual force is quite complicated to write down (so I'm not going to), the ratio turns out to be something really quite simple and elegant. Assuming a cylindrical bottle (!) the ratio of the force-to-slide to the force-to-tip is just the square root of the product of aspect ratio (height over diameter) and coefficient of static friction. This means if the coefficient of static friction is larger than the diameter over the height, it will tip rather than slide. If the coefficient of static friction is smaller than the diameter over the height, it will slide rather than tip. 

As an example, if the coefficient of friction is low (e.g. the bottle is on ice) the force to get it to slide is much less than the force to tip it. If the wind blows hard enough, the bottle will slide, not tip. Having a small height compared to diameter also favours sliding rather than tipping - a squat ginger-beer bottle is rather more likely to slide when pushed sideways rather than a slender wine bottle. 

One could potentially use this as an amusing way of measuring the coefficient of static friction. Use differently proportioned cylinders and apply a sideways force to each until they move.  The squatter ones will slide, the more slender ones will tip. Somewhere in the middle will be one that does both at once. The coefficient of static friction is then just the diameter divided by the height of this cylinder. There are simpler ways to do it, such as measuring by the angle of a slope that is just steep enough for an object to slide down. The coefficient of friction is just the tangent of this angle. 

That's it for this year, methinks. Have a Happy Christmas and enjoy the New Year. I think it's time I headed off to Seddon Park to see Mitchell Santner destroy the second-half of the Sri Lankan batting line-up. 

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Yesterday I finally managed to achieve one of the things on my 'to do' list that's been sitting there for about a year - attend a 'Have a Go' session at the velodrome in Cambridge. For those that don't know it, it's New Zealand's new (which means about two years old) world-class velodrome and now 'home' to New Zealand cycling. It's an impressive building - probably more so from the inside than the outside. 

Walking into the central area the first thing that greets you is a terrifying view of the banking on the corners. We were told it's 43.5 degrees. It's the kind of slope you'd find on a steep slide in a playground. And we're meant to cycle on it. 

But our instructor built us up gradually to this. First off, was just getting used to the bikes - large, with a high (fixed) gear, and back-pedal braking. The last of these means no free-wheeling - they need pedalling all the time. There's a nice flat area at the bottom which allowed us to do a couple of laps of the track and get used to starting and stopping, both of which are quite technical affairs. Next, we were up on the blue strip on the inside of the track. That's banked, but not as much as the main track. Once we had this sorted, we were allowed up onto the main track on the straights only, which are less steep. Then the really scary bit. The main track all the way round. 

Although scary the first time, it's really not - or at least shouldn't be - for a physicist. The key is simply to be going fast enough. With a bike that highly geared, on a smooth track, with no wind to worry about, that's not difficult. The physics isn't too tricky to do either. Cornering requires a net centripetal force (one towards the centre of the circle) to act - one that's proportional to the square of your speed. The banking ensures that this is more-or-less provided by the normal force acting from the track onto the bicycle. In fact, at the pathetic speeds we were  doing (maybe up to 30 km/h?  my forty-something year old legs didn't seem to work the way they once did...) the banking was providing more than enough centripetal force. This means there's friction acting as well, in this case an upwards force keeping us on the banking. Our bikes were certainly far from perpendicular with the track when we were going round - we were leaning outwards with relative to the track, but a spectator would have seen us leaning inwards relative to the flat.  

Go fast enough (and some quick calculations suggest this is easily in reach of a proper cyclist) and there'll be no friction required at all - and the bike should make a neat 90-degree angle with the track. From the spectator's point of view, the cyclist will be leaning over at 43.5 degrees. Faster still, and the banking won't be enough to provide that centripetal force, and friction will then be required - this time acting down the track. The cyclist will need to lean inwards relative to the track. 

Just as there's a minimum speed required in order to get around the banking (according both the instructor and my own physics calculations about 25 km/h -  and she made sure we were up to it before letting us off the blue strip), there'll also be a maximum speed possible to take the corner safely, even with that extreme banking. My quick estimate of this is around 120 km/h, which I think is beyond what a track cyclist will be able to get to. [Extra note: these calculations make an assumption of a coefficient of static friction of around 0.8. But given that  some sprinters can actually maintain a stationary postion on the banking (so they don't have to lead in the 'sprint') there's clearly more to it than that - possibly the coefficient of static friction is particularly high!]

So, overall, not so scary after all. I'm looking forward to having another go. 


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Last week I attended a seminar by Ian Hawthorn of our Maths Department. He talked about some work which he'd done with a couple of students, Matt Ussher and William Crump. The title is a bit of a mouthful "The physics of sp(2,R)"  (what does that mean?) and I have to say that I didn't follow most of it. But I did follow some of what Ian said, some of the time, in some places. 

Before I comment on what Ian said, first I need to say what dark matter is. Actually, that's quite hard, because we really don't know. It's matter that we think is in the universe, but we can't see. Why do we think it's there? We can observe the structure of galaxies, and how they move and interact, and how they bend light.  On a galactic scale, gravity dominates the other forces, and is what is responsible for galaxies. The gravitational force is generated by mass. So by observing galaxies, we can attempt at calculating the amount of mass in they contain. The problem is, when these calculations are made, there appears to be far more mass than we can account for.

This extra, unobserved mass, is labelled 'dark matter'. It's matter - it has a gravitational effect - but it doesn't interact electromagnetically - that means it does not emit visible, infra-red, radio waves etc. We can't "see" it in any electromagnetic sense. There have been various theories put forward to describe dark matter, but researching it is tricky because we can't actually see any. 

Back to Ian's talk. He used a ten-dimensional algebra to describe the universe. As well as recovering the electromagnetic interaction from it, he recovered Einstein's description of gravity - except with a 'twist'. In Einstein's description, the gravitational effect is seen as a bending of space-time casued by a mass. It's often illustrated by the mass-on-a-membrane analogy. A regular grid on the membrane is distorted by the presence of the mass. Einstein's field equations describe this in a mathematical sense. The description might be complicated but it boils down to this - mass distorts the space-time in which we live, and we perceive this as gravity. 

Now, Ian's result is a bit different. On a 'small' length scale (which actually means something pretty big) everything's the same. But on larger scales the source in Einstein's equation is itself distorted. In other words, what is bending the space-time is not the mass, but something else that is itself caused by the mass. Does this explain dark matter?  It looks as if there must be hidden mass in galaxies, but is this down to the fact that the bending of space-time isn't directly caused by the mass we see, but via some intermediate? Maybe there is no dark matter at all - it's just our description of gravity that needs modifying. 

Ian used the analogy of a car suspension. With no suspension on the car, the car feels all the bumps on the road. But put in a suspension system, and the effect felt by the car is a distorted image of the bumps. The up-and-down movement of the car is still caused by the bumps, but there's an intermediate step (the suspension). The end result is different. So, using this analogy, mass is 'suspended' - the universe feels a distorted version of it. Ian, Matt and Will conclude their commentary on this (which, for those more mathematically-trained than I, you can tackle here), with:

We have explained dark matter by concluding that there is no dark matter as such. There is only gravity behaving as though matter were present where there is none. 

Is this interpretation correct? Is there really no such thing as dark matter? Probably time will tell, but nonetheless it's certainly an interesting possibility. 


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...the United States of America, of course. Hamish Johnston, editor of, has put together a neat little piece looking at where Nobel physics laureates start and end their days. There's no surprise on the net migration front - a huge flow from everywhere to the US. You can read Hamish's piece here. What the graphic doesn't indicate is when the award winner migrated (e.g. was it before or after their prize?) and multiple migrations - he just shows where they were born, and where they died or are currently living. 

The biggest 'loser' is Germany - in fact a whopping 13 German-born laureates left Germany (11 of them for the US, including Albert Einstein, and 2 to Switzerland) although World War II accounted for many of the migrations here. 

While 30 laureates have immigrated to the US, only 2 have emigrated including the 2011 'Australian' laureate Brian Schmidt

There's been some shuffling about within Europe too, the biggest winner of this being France, but that is insignificant compared to the large, thick arrow that heads westward across the Atlantic. 




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The Institute of Physics (IOP) has recently released "Opening Doors: A guide to good practice in countering gender stereotyping in schools" (You can access the report here and read some commentary at a recent IOP conference here.) Although funded jointly by the Government Equalities Office (now I'm sure such a thing didn't exist when I lived in the UK) and the IOP, the study is not confined to physics, nor even to science. However, given the gender imbalance in physics, the IOP has a strong interest in this. Also, given the low numbers of students studying physics at Waikato, it is something I have a strong interest in too.

The report covers many areas, such as careers guidance, staff training, tackling sexist language (whether it be conscious or unconscious), use of statistical data, and so forth. But the one that caught my eye was subject equity. What is meant by this is treating all subjects on an equal footing. Often, maths and science are given a label that says 'this is a difficult subject'. For example, that can be done by teachers (and parents, older siblings and so forth) telling students that they are hard, or sometimes by setting higher entry requirements than for other subjects - e.g. to progress from GSCE to A-level physics one might need an 'A', but to progress in English one might need a 'B'. Why does this matter? Because there is an increasing body of research that suggests that when a subject is perceived as 'hard', gender sterotypes are emphasized. That is, the minority gender fears failure much more so than the majority gender and consequently does not take the subject. At the 'Opening Doors' Conference, Prof Louise Archer (King's College, London) is reported as saying:

It is taken for granted that physics is hard and masculine, and that can lead to self-censorship and self-exclusion

In other words, work on the image of physics being hard, and the gender bias may diminish. Note that it's the girls and women who are actively choosing not to do physics, rather than the boys and men actively choosing to do physics that leads to the imbalance. Fix the gender issue and we won't lose the males in our school and university classes, but we'll gain females.

Now, this is highly relevant to physics at Waikato, which has a much higher entry requirement into its first year physics papers than it has into other first year science papers. We also have a tangled web of complicated pre-requisites to do our second and third year physics papers. In other words, the information  we provide prospective and current students implicitly says "physics is harder than other sciences".  And, as the IOP report talks about, when you have the label 'hard' against something, the minority gender fears failure and doesn't engage with it. So, as a very first little step (and I would emphasize that there is a whole lot more that needs to be done with the way we offer physics here at Waikato) we can bring our entry requirements into line with those into the other sciences. If the IOP has done its research well, we should, at very least, see more women taking physics at first year. 



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