Saturday, 13 August 2016

For the love of Spherical Harmonics

I hate starting every blog post with an apology as I have been busy, but I have. But I have. Teaching Electromagnetism to our first year class, computational physics using MatLab, and six smart talented students to wrangle, takes up a lot of time.

But I continue to try and learn a new thing every day! And so here's a short summary of what I've been doing recently.

There's no secret I love maths. I'm not skilled enough to be a mathematician, but I am an avid user. One of the things I love about maths is its shock value. What, I hear you say, shock? Yes, shock.

I remember when I discovered that trigonometric functions can be written as infinite series, and finding you can calculate these series numerically on a computer by adding the terms together, getting more and more accurate as we add higher terms.

And then there is Fourier Series! The fact that you can add these trigonometric functions together, appropriately weighted, to make other functions, functions that look nothing like sines and cosines. And again, calculating these on a computer.

This is my favourite, the fact that you can add waves together to make a square wave.
But we can go one step higher. We can think of waves on a sphere. These are special waves called called Spherical Harmonics.

Those familiar with Schrodinger's equation know that these appear in the solution for the hydrogen atom, describing the wave function, telling us about the properties of the electron.

But spherical harmonics on a sphere are like the sines and cosines above, and we can describe any function over a sphere by summing up the appropriately weighted harmonics. What function you might be thinking? How about the heights of the land and the depths of the oceans over the surface of the Earth?

This cool website has done this, and provide the coefficients that you need to use to describe the surface of the Earth in terms of spherical harmonics. The coefficients are complex numbers as they describe not only how much of a harmonic you need to add, but also how much you need to rotate it.

So, I made a movie.
What you are seeing is the surface of the Earth. At the start, we have only the zeroth "mode", which is just a constant value across the surface. Then we add the first mode, which is a "dipole", which is negative on one side of the Earth and positive on the other, but appropriately rotated. And then we keep adding higher and higher modes, which adds more and more detail. And I think it looks very cool!

Why are you doing this, I hear you cry. Why, because to make this work, I had to beef up my knowledge of python and povray, learn how to fully wrangle healpy to deal with functions on a sphere, a bit of scripting, a bit of ffmpeg, and remember just what spherical harmonics are. And as I've written about before, I think it is an important thing for a researcher to grow these skills.

When will I need these skills? Dunno, but they're now in my bag of tricks and ready to use.

Sunday, 5 June 2016

A Sunday Confession: I never wanted to be an astronomer

After an almost endless Sunday, winter has arrived with a thump in Sydney and it is wet, very, very wet. So, time for a quick post.

Last week, I spoke at an Early Career Event in the Yarra Valley, with myself and Rachel Webster from the University of Melbourne talking about the process of applying for jobs in academia. I felt it was a very productive couple of days, discussing a whole range of topics, from transition into industry and the two-body problem, and I received some very positive feedback on the material I presented. I even recruited a new mentee to work with. 

What I found interesting was the number of people who said they had decided to be a scientist or astronomer when they were a child, and were essentially following their dream to become a professor at a university one day. While I didn't really discuss this at the meeting, I have a confession, namely that I never wanted to be an astronomer. 

 This will possibly come as a surprise to some. What I am doing here as a university professor undertaking research in astronomy if it was never my life dream? 

I don't really remember having too many career ideas as a child. I was considering being a vet, or looking after dinosaur bones in a museum, but the thought of being astronomer was not on the list. I know I had an interest in science, and I read about science and astronomy, but I never had a telescope, never remembered the names of constellations, never wanted to be an astronomer myself.

I discovered, at about age 16, that I could do maths and physics, did OK in school, found myself in university, where I did better, and then ended up doing a PhD. I did my PhD at the Institute of Astronomy in Cambridge, but went there because I really liked physics, and the thought of applying physics to the universe. With luck and chance, I found myself in postdoctoral positions and then a permanent position, and now a professor. 

And my passion is still understanding the workings of the universe through the laws of physics, and it's the part of my job I love (one aspect of the ECR meeting was discussing the issue that a lot of the academic job at a university is not research!). And I am pleased to find myself where I am, but I didn't set out along this path with any purpose or forethought. In fact, in the times I have thought about jumping ship and trying another a career, the notion of not being an astronomer anymore never bothered me. And I think it still doesn't. As long as the job is interesting, I think I'd be happy. 

So, there's my Sunday confession. I'm happy being a research astronomer trying to understand the universe, but it has never been a dream of mine. I think this has helped weather some of the trials facing researchers in the establishing a career. I never wanted to be an astronomer.

Oh, and I don't think much of Star Trek either. 

Thursday, 26 May 2016

On The Relativity of Redshifts: Does Space Really “Expand”?

I've written an article 'On the Relativity of Redshifts: Does Space Really "Expand"?' which has appeared in Australian Physics (2016, 53(3), 95-100). For some reason, the arXiv has put the article on hold, so you can download it here.

I like it :)

Sunday, 15 May 2016

How Far Can We Go? A long way, but not not that far!

Obligatory "sorry it's been a long time since I posted" comment. Life, grants, student, etc All of the usual excuses! But I plan (i.e. hope) to do more writing here in the future.

But what's the reason for today's post? Namely this video posted on your tube.
The conclusion is that humans are destined to explore the Local Group of galaxies, and that is it. And this video has received a bit of circulation on the inter-webs, promoted by a few sciency people.

The problem, however, is that it is wrong. The basic idea is that accelerating expansion due to the presence of dark energy means that the separation of objects will get faster and fast, and so it will be a little like chasing after a bus; the distance between the two of you will continue to get bigger and bigger. This part is correct, and in the very distant universe, there will be extremely isolated bunches of galaxies whose own gravitational pull overcomes the cosmic expansion. But the rest, just how much we can explore is wrong.

Why? Because they seem to have forgotten something key. Once we are out there traveling in the "expanding universe" then the expansion works in our advantage, increasing the distance not only between us and where we want to get to, but also between us and home. We effectively "ride" expansion.

So, how far could we get? Well, time to call (again - sorry) Tamara Davis's excellent cosmological work, in particular this paper on misconceptions about the Big Bang. I've spoken about this paper many times (and read it, it is quite excellent) but for this post, what we need to look is at the "conformal" picture of our universe. I don't have time togo into the details here, but the key thing is that you manipulate space and time so light rays trade at 45 degrees in the picture. Here's our universe.

The entire (infinite!) history of the universe is in this picture, mapped onto "conformal time". We're in the middle on the line marked now. If we extend our past light cone into the future, we can see the volume of the universe acceptable to us, given the continued accelerating expansion. We can see that encompasses objects that are currently not far from 20 billion light years away from us. This means that light rays fired out today will get this far, much, much larger than the Local Group of galaxies.

But ha! you scoff, that's a light ray. Puny humans in rockets have no chance!

Again, wrong, as you need to care about relativity again. How do I know? I wrote a paper about this with two smart students, Juliana Kwan (who is now at the University of Pennsylvania)  and Berian James, at Square. The point is that if you accelerate off into the universe, even at a nice gentle acceleration similar to what we experience here on Earth, you still get to explore much of the universe accessible to light rays.

Here's our paper 
 The key point is not just about how far you want to get, but whether or not you want to get home again. I am more than happy to acknowledge Jeremy Heyl's earlier work that inspired ours.

One tiny last point is the question whether our (or maybe not our) decedents will realise that there is dark energy in the universe. Locked away in Milkomenda (how I hate that name)  the view of the dark universe in the future might lead you to conclude that there is no more to the universe than ourselves, and it would appear static and unchanging, but anything thrown "out there", such as rocket ships (as per above) or high velocity stars, would still reveal the presence of dark energy.

There's plenty of universe we could potentially explore!

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.