Monday, 25 January 2016

Journey to the Far-Side of the Sun

There was a movie, in the old days, Journey to the Far-Side of the Sun (also known as Doppleganger) which (spoiler alert) posits that there is a mirror version of the Earth hidden on the other side of the Sun, sharing the orbit with our Earth. The idea is that this planet would always be hidden behind the Sun, and so we would not know it there there.

This idea comes up a lot, over and over again. In fact, it came up again last week on twitter. But there's a problem. It assumes the Earth is on a circular orbit.

I won't go into the details here, but one of the greatest insights in astronomy was the discovery of Kepler's laws of planetary motion, telling us that planets move on elliptical orbits. With this, there was the realisation that planets can't move at uniform speeds, but travel quickly when closer to the Sun, while slowing down as their orbits carry them to larger distance.
 There has been a lot of work examining orbits in the Solar System, and you can simply locate the position of a planet along its orbit. So it is similarly simply to consider two planets sharing the same orbit, but starting at different locations, one at the closest approach to the Sun, one at the farthest.

Let's start with a simple circular orbit with two planets. Everything here is scaled to the Earth's orbit, and the circles in the figures coming up are not to scale. By here's an instance in the orbit.

It should be obvious that at all points in the orbit, the planets remain exactly on opposite sides of the Sun, and so would not be visible to each other.

So, here's a way of conveying this. The x-axis is the point in the orbit (in Earth Years) while the y-axis is the distance a light ray between the two planets passes from the centre of the Sun (blue line). The red line is the radius of the Sun (in Astronomical Units).
The blue line, as expected, is at zero. The planets remain hidden from each other.

Let's take a more eccentric orbit, with an eccentricity of 0.1. Here is the orbit
This doesn't look too different to the circular case above. The red circle in there is the location of the closest approach of each line of sight to the centre of the Sun, which is no longer a point. Let's take a look at the separation plot as before. Again, the red is the radius of the Sun.
Wow! For small segments of the planets orbits, they are hidden from one another, but for most of the orbit, the light between the planets pass at large distances from the Sun. Now, it might be tricky to see each other directly due to the glare of the Sun, but opportunities such as eclipses would mean the planets should be visible to one another.

But an eccentricity of 0.1 is much more than that of the Earth, whose orbit is much closer to a circle with an eccentricity of 0.0167086 . Here's the orbit plot again.
So, the separation of the paths between the planets pass closer to the centre of the Sun, but, of course, smaller than the more eccentric orbits. What about the separation plot?
Excellent! As we saw before, for a large part of the orbits, the light paths between the planets passes outside the Sun! If the Earth did have a twin in the same orbit, it would be visible (modulo the glare of the Sun) for most of the year! We have never seen our Doppleganger planet!

Now, you might complain that maybe the other Earth is on the same elliptical orbit but flipped so we are both at closest approach at the same time, always being exactly on the other side of the Sun from one another. Maybe, but orbital mechanics are a little more complex than that, especially with a planet like Jupiter in the Solar System. It's tugs would be different on the Earth and its (evil?) twin, and so the orbits would subtly differ over time.

It is pretty hard to hide a planet in the inner Solar System!

Sunday, 3 January 2016

Throwing a ball in a rotating spaceship

A long time ago, I wrote a post about the Physics of Rendezvous with Rama, a science fiction story by Arthur C. Clarke set on an immense alien spaceship. The spaceship rotates, providing the occupants with artificial gravity, a staple of science fiction. I mentioned in the article that I am not an immense fan of a lot of science fiction, as much of it relies on simple "magic", but Clarke knew his physics and so he knew that the "gravity" experienced in the rotating ship will differ to that on Earth, and previously I wrote about what happens if you jump off a cliff.

In the last week, there was a question on twitter (it's an internet thing) about the movie Elysium which has a spectacular rotating spacecraft with the Earth's rich abroad.
While it's a shame that the plot was not as spectacular, the question was how can such a station keep it's atmosphere.

This is an interesting question, as you might think that it would all simply zip off into space. But the key point is that the atmosphere itself is also rotating with the ship, and so "experiences gravity". But what happens to individual molecules in the air?

Well, we can do a bit of physics (yay!) and work this out. If you have done some basic physics (or chemistry) you have have encountered the ideal gas laws, relating some of the key properties of a gas, such as the temperature, volume and pressure. The derivation of these can be deceptively simple, but the equations are very powerful. And to do these derivations, you essentially assume that atoms are very bouncy balls that bounce off the walls of the vessel.

So, what about bouncing a ball inside a rotating space station? There is a nice little discussion here on the key physics, but it is very simple (if you are an undergrad who as done your classical mechanics, you should give this a go). The important point is that seen from an external observer, a bouncing ball follows a straight-line path (remember, there are no forces acting on the ball), but the view to a person inside the ship will be different. Here's a simple example.

So, this is a bouncing ball as seen by an outside observer (taking into account the motion of the ship in the collisions).
The blue is the wall of the ship (which is rotating) and the red is the path of a bouncing ball.

What about the view from inside?
Boing, boing, boing! The ball bounces off into the distance, and, if we leave it, will bounce all the way around the station and hit you in the back of the head :)

So, an air molecule will bounce in a similar fashion around the station, and so an atmosphere will be kept there too. Yay for all the rich people!!

But, being good physicists, we can start to play with the velocity and direction of our molecules (I'm playing with the velocity relative to the outside observer. It's easy to consider it relative to the velocity of the ship at the stating point).

Slowing the ball down gives the same path to the outside observer, but why does the internal observer see?
Oh... The ball bounces the other way around the ship. Cool!

What if we lob the ball into the air rather than bouncing it off the all of the shop. In fact, let's arrange for it to go straight up (again, velocity relative to the outside observer). We'll adjust the velocity so that bounce off the other side and get bak to the start position in the time it takes for a single revolution of the ship.

Again, the red is the path as seen by the outside observer, the black by the inside.
The ball arcs behind the thrower, over the top, and comes back in front of the thrower. In fact, there are several black loops present, each on top of the other.

What if we slow the ball down a little, so the observer on the ship makes two revolutions in the time it takes the ball to get over and back.
Wow!! So we see the ball bounce of the other side of the ship and do some mid-air pirouettes. Let's slow it down by a factor of two again!
And again!
Excellent. Imagine watch this ball fly through the air!

Let's instead double the speed. What do we get?
Again, think about being a being at rest watching the ball bouncing through the ship!

Doubling again!
We can see where this is going!

And if we modify the velocity across the ship so there is not a "resonance" between the bouncing and the rotation, we get
Again, the ball will perform exquisite arcs through the ship and with bounces of the wall!

How much fun is this! I've got to take a break right now, but later I will consider what happens if you want to play a ball game, like tennis, inside a rotating space ship. The rich people might get more than they are asking for!



Sunday, 13 December 2015

Academic Toolkits

First, the usual apologies! It's been an age since I have written here, but, as you know, the life of the academic is a busy one! Especially since I have just completed a book which is to be published next year. More on that journey later, but today a little post about academic toolkits.

This is something that I have written about before, and I know some of my colleagues and peers disagree with me, but that's fine as I think it illustrates that there is no single recipe for success in academia (Am I a success in academia? That's for others to judge, but I am still here after twenty years :).

What makes a "good" academic? In modern academia, we have to be specialists, focused on a generally tiny part of the immense enterprise called science. When ever I realise this, Kenneth Williams springs immediately to mind
Crossing boundaries and commenting on other areas of science that are not in your domain is met with suspicion and attack, and it's not just new ideas about cancer, but if I tried to say something deep and meaningful about, say asteroseismology, I would be met with suspicion. Part of the reason is that people would not believe that I could have absorbed the vast amount of knowledge and information that is needed to be an expert in this relatively narrow area.

But I like to try and remain as broad as possible. I have observed with optical and infrared telescopes, counting stars, taking spectra, identifying galaxies and quasars. I can do a bit of maths, and can work with the cosmological equations and general relativity. I love coding, and data modelling, and can run code on supercomputers. And I try to publish in a broad range of areas, not being too dependent upon the next telescope allocation or insight into galaxy dynamics.

To achieve this, I've had to learn a lot (like every academic does) but I have tried to keep this knowledge broad. So, as well as the tools that I need in particular areas, I have tried to learn as much as possible across a range of topics. And this means learning tips and techniques that might seem, at the time, not to have direct relevance to my research.

A little while ago I organised a session on programming GPUs at my department. There was good attendance, but I spoke to one student who decided not to attend. Their response was "When will I need to know that?" and I must admit I was disheartened. You may never need it, or it might suddenly present itself to a tricky question, or it might even be part of the selection of a possible job coming up. You just don't know!

To the case in point. Roughly two decades ago, I started playing with povray, a raytracing code for producing photo-realistic images. It's very powerful, but has a very pernickety coding language. Over the years, I have scraped up enough knowledge to be a reasonable amateur, picking up the mantle and running a little whenever I had time. But when would it be useful to me.

Well, as I mentioned at the start, I have just had a book accepted for publication (with Luke Barnes over at LettersToNature) and we needed to think of a cover design. The book is on cosmological fine-tuning and we umm'd and ahhh'd about standard astronomical images, but decided that would be just like other books out there. So we wanted to try something different, something novel. And we turned to povray. I won't go into the in's and out's, but a week or so of discussion and debate, we had a winner.
This isn't quite the finished version as someone with serious graphic design experience is going to do the text, but we made the image, and we like it :)

It wasn't too tricky a job, but a lot of trial and error, but the fact we had some povray experience meant that there was not a huge hurdle to overcome.

So, my advice to budding academics is that you should think about developing their academic toolkits, to try and build an expansive range of skills beyond the narrow range of tools you use in your day-to-day research. It will not guarantee a path to academic success, but you may never know when they will save the day.

Saturday, 8 August 2015

Is an elephant heavier than a mouse?

Wow. It's been a while since I have written a blog post. Much of this is because of work and travels, and book writing (more news on that in the near future). But I'd like to get into blog writing, so here's a little science musing.

Is an elephant heavier than a mouse?

Now, you are probably saying "well, of course". Surely event the heaviest mouse weighs less than the newest born baby elephant, so why am I asking such a stupid question.

Well, because science can never really prove that an elephant is heavier than a mouse.

I know, I've gone and put that word in, and I've written about how proof has no place in science. But let's examine this in a little more detail.

I've stressed many times before that while measurements are important in science, without an uncertainty such measurements are useless. And while professional scientists pour over papers focused on the error bars in figures, errors and uncertainties are typically waived over in undergraduate degree. Luckily, this is changing, and statistical understanding is weaving its way through courses (But still not enough in my humble opinion).

For the simple example here, we'll consider Gaussian errors. I've just grabbed this piccy off the web as it explains the situation nicely

 The top figure is the important one and shows us the characteristic "bell-shaped" curve you get with Gaussian errors. The curve represents what a scientist would see as a measurement; the peak of the curve gives us the best estimate for the measurement. But no measurement is perfect and measuring devices have limitations and noise is introduced, and any measured value will be somewhat off from "reality" (and let's not open that can of worms). The distribution shows our belief in where the true measurement lies, most probably at the peak, but a good chance of it sitting in the body of the bell, and almost certainly within the entire range shown in the figure.

For the interested, there are plenty of tables of the values of these normal distributions.

OK, back to our elephant and mouse. Let's suppose we measure the elephant by popping it on some scales, finding it to be 5000 kg. Every measurement has an uncertainty, and the scales are quite accurate, and so the width of the Gaussian is 1 kg.

We have to use a different scale for the mouse, but find it is 500 g, but an uncertainty (the width of the Gaussian) is 10 g.

Job done you think. 5000 kg is more than 500 g, so the elephant wins!

Not so fast! The uncertainties matter!!! While the Gaussian drops away from its peak value, getting smaller and smaller, it does not go to zero. This means that while we are confident that the mouse is somewhere between 495 g and 505 g, there is a small chance that it is actually 510 g, and a smaller chance that it is 600 g, and extremely small chance that it is actually 1 kg, and an absolutely minuscule chance that it is 10000 kg.

And we can play the same game with the elephant. And while we are happy its weight is around 5000 kg, there is an absolutely minuscule chance that it is actually 10 g.

Put all together, this means that we have an extreme amount of confidence that the elephant is heavier than the mouse, there is this tiny possibility from our measurements that the mouse is actually heavier than the elephant!!

Now, I know that some of my colleagues will complain about this, as distributions in the real world will not necessarily be Gaussian etc, but that's secondary for the point I am trying to get across.

Also, some will say things like once chances get below some certain level they may as well treat things as certainty, and while this is true, it is important to remember that the choices of where the dividing line is is rather arbitrary (i.e the choice of n-sigma or p-values etc). There is nothing magical about these values!

 So, what's the point of all of that? Well, clearly in the question of the elephant and the mouse, the chances of the elephant being lighter than the mouse is so ridiculously small that you can be pretty certain that the elephant is heavier.

But science is rarely about comparing a mouse's mass and an elephant's mass, but is often about making measurements at the limits of equipments' abilities. And the question of the how significant the result is becomes of critical importance.

When people claimed to have found the Higgs Boson, there was a lot of discussion around the statistics, with many struggling to explain why they thought the detection was significant (and some performed particularly badly).

But such discussions are not typically found in the medias' discussion of science findings, such as today's pears cure hangovers. And really it means that these stories are basically worthless as you cannot assess how robust the result is (oh, and the pear result is preliminary which normally means that the statistics are poor and the result could be a fluke and is likely to vanish with more data).

And all science then gets lumped into a single basket, and people view robust science, such as climate science, as being similar to statistically flakey measurements, such as red wine being good one day and bad the next.

If every journalist simply asked for an estimate of the statistical significance of a particular day's scientific press release, I think that many would not see the light of day and the overall reporting of science would undoubtedly be improved.

To be truly scientifically literate, you must be statistically literate. It's important to remember that.

Saturday, 4 April 2015

Musings on an academic career - Part 2

A long rainy Easter weekend in Sydney. And, as promised, here's some additional musings on an academic career. I thought I would tackle a big one and present the question that all ECRs and wannabe-academics should be asking themselves from day one, and it's a question that all academics should ask themselves periodically (where the period of periodically can be as short as 5 minutes). Namely, "Do I really want an academic career?"

Now, I am sure that some of you reading this, especially the more junior researchers of you, will be thinking "Well, duh! Ain't that obvious?" But, in fact, I think this goes to the heart of many of the touted problems with regards to academia, and it's a problem of our own making, and I mean all of us.

But before I start, the usual caveats apply. While this year marks two decades since I got my PhD and so I have a long history with academia, and while I am a professor at a large, prestigious university, I have limited experience of the entire world, and what I write here is a reflection of what I have seen in this time. Furthermore, a lot of what is below has accumulated over the years, and I did not get to where I am through the execution of some well developed plan; I got here through sweat, stress and lucky breaks. Of course, my experience is limited to science, physics and astronomy. It could be very different for the historians and economists out there.

So, buyer beware, although, honestly, I wish I had realised a lot of this a long time ago.

The Romantic Academic
I am pretty sure that if I did a straw-poll of researchers on why they are in this game, the answer would be very similar. When we start off as undergraduates we get a taste of research projects, thinking that we are unlocking the mysteries of the universe (without realising that we are doing research projects with training wheels attached). Research is fun, it's exciting, it's stressful and, when it works, it can be fulfilling. I love doing research. I love thinking about all sorts of different things, trying new methods, spending the afternoon with someone at the whiteboard scribbling an erasing. Hey, it may not cure cancer, but I will understand the chemical composition of clouds of gas ten billion light years away!

I don't know about everyone else reading this, but once I was bitten but the research bug, I could not let it go. I have a hard time thinking about anything else (although, I do not only research astronomy and physics - but that's for another story). I can't imagine a day where I don't learn something new. The thought of a "job" out there banging widgets, working in finance, or running a company, just strikes us as boring (although often we are making the case from ignorance as we really don't know what these jobs comprise of). Clearly, we want a career that still allows us to continue down this research word, and looking around we see the Drs and Professors of academia who supervise and employ us, and it is obvious that we need to follow the same trajectory.

However, the everything is not as it seems, but more of that in a moment.

A Life in Research
But there is a way to have a long and fruitful career in research, a career where you can do what you want, when you want, attend the conferences you want, with nobody to answer to than yourself. Such a career is the dream of virtually every academic I have ever met, and it is possible. Want to know the secret?

Well, skip the PhD and spend the twenties making your fortune. Get a few million in the bank by the time you are thirty and then live of your investments. Effectively retire into research and become a "Gentleman scientist" (and they were virtually all men) of a bygone age.

You might be spluttering on your corn flakes at this point and be thinking that I have gone mad. But think about it.

Why do you do a PhD? To learn, of course, but you don't need to do this in the context of a degree do you? You could learn the same stuff in your living room with access to the internet and a boxset of "House of Cards" in the background. Maybe you are after the title, but what is that really for? Well, it's the next step towards an academic career, but has a journal ever asked you if you have a PhD before considering your paper? To legitimise yourself as a researcher? The Dr in front of your name means little if you don't have publications to back it all up.

So, really, why do it? If you are going to fund yourself, why do you need it? If you really want one, do one after you have made your fortune, but I don't think it is really necessary.

Now you are probably thinking that you can't do that. You don't understand finances and investing and all that stuff. It all sounds very complicated. But you are supposed to be smart, and you should realise that there are many people out there who make their fortune who don't have a PhD in astrophysics or nano-photonics or whatever. What is stopping you is that you haven't learnt how it works (but, in the end, it is just more research). Yes, there is a risk that you won't make it, but risk is a topic we'll come back to later.

But after ten years of graft, you should be set up to do what you like for the rest of your life. Impossible? Not really. It does happen.

Academic SuperStar
OK, so you don't want to make your fortune and do what you want to, but you want to continue into academia and want the next best thing. You want to do research as an academic. Well, to be able to devote yourself to research, and only research, you need to either get yourself a fantastic fellowship from a grant agency (and acknowledge that these only last a limited amount of time) or get into completely research-focused departments.

Such positions can be relatively cushy, with funding for your salary, for travel, for research costs and people. You don't have complete autonomy as you will have had to written a proposal that was assessed and you will have to follow, and here will be lovely middle-management people whose roll it is to spot you spending your funds (or at least ensuring you are spending it on what you were supposed to), but it is not bad.

And, as you can guess, these are extremely competitive and you better have all of the things on your CV that people are expecting, lots of papers, lots of citations, prizes and well connected with the right people saying the right things about you. In short, you better be pretty smart and on-the-ball, especially in terms of career management. I'll choose my words carefully here, but we all know that some are better at gathering those career-boosting bits-and-pieces than others. But it takes a lot of management on top of everything else.

Of course, as well as being very competitive, such positions are also relatively rare, and even if you have all those bits and pieces you might not get one. You might have to become an everyday academic.

Everyday Academia
So this brings us to people like me, every day academics. And if you look round the world, in the web and in the new, we appear to be a quite whiney lot. Lots of complaints about workload and the lack of time. The life of a modern everyday academic is anything but hours of musing about the mysteries of the Universe, but time is consumed by administration and teaching (two things that have hard, finite deadlines that cannot be missed), plus all of these roles that we have not been trained in, including financial and people management. The reward for research success, such as attracting more grants and students, is typically more work.

And, if we go back to the start, the reason that we got into this game was research, but time for research actually becomes often vanishingly small when one gets the coveted permanent position. It is funny that I am productive in terms of output and grant success, but it is only because I have group of students and postdocs to work with (and, in fact, working with these people remains the highlight of my everyday academia).

Not only that, but I realise that I am the lucky one to get here at all, as many able researchers leave the field as the opportunities become rarer and rarer, and the competition becomes fiercer. I actually finding it funny that people who are so risk adverse that they would not really consider alternative careers or making your own fortune to support themselves continue blindly down one of the riskiest pathways of all, namely that of trying to secure a permanent position at a good university.

Wrapping it all up
I've written a lot here, but for the students and ECRs I would like you to think about the question of whether the academic career, and it is most likely going to be an everyday academic if you stay in the field, is really what you want. If not, then it is never to early to think about managing and directing your career to at least give you the best chance of what you want.

In closing, I often hear that those that leave at the various stages towards becoming an everyday academic have somehow failed, but in reality I wonder if the real failure is us successes finding ourselves locked into careers that squeeze the prospect of doing hand-on research out of the day.

Why don't I put my money where my mouth is and walk so I can spend my copious leisure time researching what I want? Maybe I will, maybe I will.

Sunday, 29 March 2015

Musings on academic careers - Part 1

As promised, I'm going to put down some thoughts on academic careers. In doing this, I should put my cards on the table and point out that while I am a full-time professor of astrophysics of the University of Sydney, I didn't really plan my career or following the musings given below. The musings come from take a hard look at the modern state of play in modern academia.

I am going to be as honest as possible, and surely some of my colleagues will disagree with my musings. Some people have a romantic view of many things, including science, and will trot out the line that science is somewhat distinct from people. That might be the case, but the act of doing science is clearly done my people, and that means all of the issues that govern human interactions come into play. It is important to remember this.

Now, there may be some lessons below for how to become a permanent academic, but there is no magic formula. But realising some of these lessons on what is at play may help.

Some of you may have heard me harp on about some of these issues before, but hopefully there is some new stuff as well. OK. Let's begin.

Career Management
It must be remembered that careers rarely just happen. Careers must be managed. I know some people hate to realise this, as science is supposed to be above all this career stuff - surely "good people" will be identified and rewarded!

Many students and postdocs seem to bumble along and only think of "what's next?" when they are up against the wire. I have spoken with students about the process of applying for postdocs, the long lead time needed, the requirement of at least three referees, all aspects of job hunting, and then, just moments from the submission of their PhD, they suddenly start looking for jobs. I weep a little when they frantically ask me "Who should I have as my third referee?"

Even if you are a brand-new PhD student, you need to think about career management. I don't mean planning, such as saying I will have a corner office in Harvard in 5 years (although there is nothing wrong with having aspirational goals!), but management. So, what do I mean?

Well, if you are interested in following a career in academia, then learn about the various stages and options involved and how you get from one to the other. This (and careers beyond academia) should be mandatory for new students, and reminded at all stages of your career that you need to keep thinking about it. What kind of things should you be doing at the various stages of your career? What experience would your next employer like you to have? It is very important to try and spot holes in your CV and fill them in; this is very important! If you know you have a weakness, don't ignore it, fix it.

Again, there is no magic formula to guarantee that you will be successful in moving from one stage to another, but you should be able to work out the kind of CV you need. If you are having difficulties in identifying these things, talk with people (get a mentor!).

And, for one final point, the person responsible for managing your career is you. Not your supervisor, not your parents, and not the non-existent gods of science. You are.

Being Strategic
This is part of your career management.

In the romantic vision of science, an academic is left to toddle along and be guided by their inquisitive nature to find out what is going on in the Universe. But academia does not work that way (no matter how much you want to rage against it). If you want an academic career, then it is essential to realise that you will be compared to your peers at some point. At some point, someone is is going to have a stack of CVs in front of them and will be going through them and will have to choose a subset who met the requirements for a position, and then rank those subset to find the best candidate. As part of your career management you need to understand what people are looking for! (I speak from experience of helping people prepare for jobs who know little about the actual job, the people offering it, what is needed etc etc).

I know people get very cross with this, but there are key indicators people look at, things like the number of papers, citation rates, grant income, student supervision, teaching experience. Again, at all points you need to ask "is there a hole in my CV?" and if there is, fill it! Do not ignore it.

But, you might be saying, how can I be strategic in all of this? I just get on with my work! You need to think about what you do. If you have a long running project, are there smaller projects you can do when waiting to spin out some short, punchy papers? Can I lead something that I will become world known in? Is there an idea I can spin to a student to make progress on? You should be thinking of "results" and results becoming talks at conferences and papers in journals.

If you are embarking on a new project, a project that is going to require substantial investment of time, you should ensure something will come from it, even if it is a negative or null result. You should never spend a substantial period of time, such as six months, and not have anything to show for it!

Are there collaborations you could forge and contribute to? Many people have done very well by being part of large collaborations, resulting in many papers, although, be aware that when seeing survey papers on a CV now as "well, what did this person contribute to the project?".

The flip-side is also important. Beware of spending to much time on activities that do not add to you CV! I have seen some, especially students, spending a lot of time on committees and jobs that really don't benefit them. Now, don't get me wrong. Committee work and supporting meetings etc is important, but think about where you are spending your time and ask yourself if your CV is suffering because of it.

How many hours should I work?
Your CV does not record the number of hours you work! It records your research output and successes. If you are publishing ten papers a year on four hour days, then wonderful, but if you are two years into a postdoc, working 80 hours per week and have not published anything, you might want to think about how you are using your time. 

But I am a firm believer of working smarter, not harder, and thinking and planning ideas and projects. Honestly, I have a couple of papers which (in a time before children) were born from ideas that crystalised over a weekend and submitted soon after. I am not super-smart, but do like to read widely, to go to as many talks as I can, to learn new things, and apply ideas to new problems.

One thing I have seen over and over again is people at various stages of their careers becoming narrower and narrower in their focus, and it depresses me when I go to talks in my own department and see students not attending. This narrowness, IMHO, does not help in establishing an academic career. This, of course, is not guaranteed, but when I look at CVs, I like to see breadth. 

So, number of hours is not really an important issue, your output is. Work hours do become important when you are a permanent academic because all the different things, especially admin and teaching you have to do, but as an early career researcher, it should not be the defining thing. Your output is. 

Is academia really for me?
I actually think this is a big one,  and is one which worries me as I don't think people at many stages of their career actually think about. Being a student is different to being an postdoctoral researcher, is different to being an academic, and it seems to be that people embarking on PhDs, with many a romantic notion about winning a Nobel prize somewhere along the way, don't really know what an "academic" is and what they do, just that it is some sort of goal.

In fact, this is such a big one, I think this might be a good place to stop and think about later musings.

Saturday, 21 March 2015

Moving Charges and Magnetic Fields

Still struggling with grant writing season, so another post which has resulted in my random musings about the Universe (which actually happens quite a lot).

In second semester, I am teaching electricity and magnetism to our First Year Advanced Class. I really enjoy teaching this class as the kids are on the ball and can ask some deep and meaningful questions.

But the course is not ideal. Why? Because we teach from a textbook and the problem is that virtually all modern text books are almost the same. Science is trotted out in an almost historical progression. But it does not have to be taught that way.

In fact, it would be great if we could start with Hamiltonian and Lagrangian approaches, and derive physics from a top down approach. We're told that it's mathematically too challenging, but it really isn't. In fact, I would start with a book like The Theoretical Minimum, not some multicoloured compendium of physics.

We have to work with what we have!

One of the key concepts that we have to get across is that electricity and magnetism are not really two separate things, but are actually two sides of the same coin. And, in the world of classical physics, it was the outstanding work of James Clerk Maxwell who provided the mathematical framework that broad them together. Maxwell gave us his famous equations that underpin electro-magnetism.
Again, being the advanced class, we can go beyond this and look at the work that came after Maxwell, and that was the work by Albert Einstein, especially Special Theory of Relativity.

The wonderful thing about special relativity is that the mix of electric and magnetic fields depends upon the motion of an observer. One person sees a particular configuration of electric and magnetic fields, and another observer, moving relative to the first, will see a different mix of electric and magnetic fields.

This is nice to say, but what does it actually mean? Can we do anything with it to help understand electricity and magnetism a little more? I think so.

In this course (and EM courses in general) we spend a lot of time calculating the electric field of a static charge distribution. For this, we use the rather marvellous Gauss's law, that relates the electric field distribution to the underlying charges.
I've written about this wonderful law before, and should how you can use symmetries (i.e. nice simple shapes like spheres, boxes and cylinders) to calculate the electric field.

Then we come to the sources of magnetic field. And things, well, get messy. There are some rules we can use, but it's, well, as I said, messy.

We know that magnetic fields are due to moving charges, but what's the magnetic field of a lonely little charge moving on its own? Looks something like this
Where does this come from? And how do you calculate it? Is there an easier way?

And the answer is yes! The kids have done a touch of special relativity at high school and (without really knowing it in detail) have seen the Lorentz transformations. Now, introductory lessons on special relativity often harp on about swimming back and forth across rivers, or something like that, and have a merry dance before getting to the point. And the transforms are presented as a way to map coordinators from one observer to another, but they are much more powerful than that.

You can use them to transform vectors from one observers viewpoint to another. Including electric and magnetic fields. And these are simple algebra.

where we also have the famous Lorentz factor. So, what does this set of equations tell us? Well, if we have an observer who sees a particular electric field (Ex,Ey,Ez), and magnetic field (Bx,By,Bz), then an observer moving with a velocity v (in the x-direction) with see the electric and magnetic fields with the primed components.

Now, we know that the electric field of an isolated charge at rest is. We can use Gauss's law and it tells us that the field is spherically symmetrical and looks like this
The field drops off in strength with the square of the distance. What would be the electric and magnetic fields if this charge was trundling past us at a velocity v? Easy, we just use the Lorentz transforms to tell us. We know exactly what the electric field looks like of the charge at rest, and we know that, at rest, there is no magnetic field.

Being as lazy as I am, I didn't want to calculate anything by hand, so I chucked it into MATLAB, a mathematical environment that many students have access too. I'm not going to be an apologist for MATLAB's default graphics style (which I think sucks - but there are, with a bit of work, solutions).



Anyway, here's a charge at rest. The blue arrows are the electric field. No magnetic field, remember!
So, top left is a view along the x-axis, then y, then z, then a 3-D view. Cool!

Now, what does this charge look like if it is moving relative to me? Throw it into the Lorentz transforms, and voila!


MAGNETIC FIELDS!!! The charge is moving along the x-axis with respect to me, and when we look along x we can see that the magnetic fields wrap around the direction of motion (remember your right hand grip rule kids!).

That was for a velocity of 10% the speed of light. Let's what it up to 99.999%
The electric field gets distorted also!

Students also use Gauss's law to calculate the electric field of an infinitely long line of charge. Now the strength of the field drops off as the inverse of the distance from the line of charge.


Now, let's consider an observer moving at a velocity relative to the line of charge.
Excellent! Similar to what we saw before, and what we would expect. The magnetic field curls around the moving line of charge (which, of course, is simply an electric current).

Didn't we know that, you say? Yes, but I think this is more powerful, not only to reveal the relativistic relationship between the electric and magnetic fields, but also once you have written the few lines of algebraic code in MATLAB (or python or whatever the kids are using these days) you can ask about more complicated situations. You can play with physics (which, IMHO, is how you really understand it).

So, to round off, what's the magnetic field of a perpendicular infinite line of charge moving with respect to you. I am sure you could, with a bit of work, calculate it with usual mathematical approaches, but let's just take a look.

Here's at rest
A bit like further up, but now pointing along a different axis.

Before we add velocity, you physicists and budding physicists make a prediction! Here goes! A tenth the velocity of light and we get
I dunno if we were expecting that! Remember, top left is looking along the x-axis, along the direction of motion. So we have created some magnetic structure. Just not the simple structure we normally see!

And now at 99.99% we get
And, of course, I could play with lots of other geometries, like what happens if you move a ring of charge etc. But let's not get too excited, and come back to that another day.