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.

Saturday, 28 February 2015

Shooting relativistic fish in a rational barrel

I need to take a breather from grant writing, which is consuming almost every waking hour in between all of the other things that I still need to do. So see this post as a cathartic exercise.

What makes a scientist? Is it the qualification? What you do day-to-day? The association and societies to which you belong? I think a unique definition may be impossible as there is a continuum of properties of scientists. This makes it a little tricky for the lay-person to identify "real science" from "fringe science" (but, in all honesty, the distinction between these two is often not particularly clear cut).

One thing that science (and many other fields) do is have meetings, conferences and workshops to discuss their latest results. Some people seem to spend their lives flitting between exotic locations essentially presenting the same talk to almost the same audience, but all scientists probably attend a conference or two per year.

In one of my own fields, namely cosmology, there are lots of conferences per year. But accompanying these there are another set of conferences going on, also on cosmology and often including discussions of gravity, particle physics, and the power of electricity in the Universe. At these meetings, the words "rational" and "logical" are bandied about, and it is clear that the people attending think that the great mass of astronomer and physicists have gotten it all wrong, are deluded, are colluding to keep the truth from the public for some bizarre agenda - some sort of worship of Einstein and "mathemagics" (I snorted with laughter when I heard this).

If I am being paid to lie to the public, I would like to point out that my cheque has not arrived and unless it does shortly I will go to the papers with a "tell all"!!

These are not a new phenomenon, but were often in shadows. But now, of course, with the internet, any one can see these conference in action with lots of youtube clips and lectures.

Is there any use for such videos? I think so, as, for the student of physics, they present an excellent place to tests one knowledge by identifying just where the presenters are straying off the path.

A brief search of youtube will turn up talks that point out that black holes cannot exist because
is the starting point for the derivation of the Schwarzschild solution.

Now, if you are not really familiar with the mathematics of relativity, this might look quite convincing. The key point is this equation

Roughly speaking, this says that space-time geometry (left-hand side) is related to the matter and energy density (right-hand side, and you calculate the Schwarzschild geometry for a black hole by setting the right-hand side equal to zero.

Now, with the right-hand side equal to zero that means there is no energy and mass, and the conclusion in the video says that there is no source, no thing to produce the bending of space-time and hence the effects of gravity. So, have the physicists been pulling the wool over everyones eyes for almost 100 years?

Now, a university level student may not have done relativity yet, but it should be simple to see the flaw in this argument. And, to do this, we can use the wonderful world of classical mechanics.

In classical physics, where gravity is a force and we deal with potentials, we have a similar equation to the relativistic equation above. It's known as Poisson's equation
The left-hand side is related to derivatives of the gravitational potential, whereas the right-hand side is some constants (including Newton's gravitational constant (G)) and the density given by the rho.

I think everyone is happy with this equation. Now, one thing you calculate early on in gravitational physics is that the gravitational potential outside of a massive spherical object is given by
Note that we are talking about the potential is outside of the spherical body (the simple V and Phi are meant to be the same thing). So, if we plug this potential into Poisson's equation, does it give us a mass distribution which is spherical?

Now, Poisson's equation can look a little intimidating, but let's recast the potential in Cartesian coordinates. Then it looks like this

Ugh! Does that make it any easier? Yes, let's just simply plug it into Wolfram Alpha to do the hard work. So, the derivatives have an x-part, y-part and z-part - here's the x-part.
Again, is you are a mathphobe, this is not much better, but let's add the y- and z-parts.

After all that, the result is zero! Zilch! Nothing! This must mean that Poisson's equation for this potential is
So, the density is equal to zero. Where's the mass that produces the gravitational field? This is the same as the apparent problem with relativity. What Poisson's equation tells us that the derivatives o the potential AT A POINT is related to the density AT THAT POINT! 

Now, remember these are derivatives, and so the potential can have a whole bunch of shapes at that point, as long as the derivatives still hold. One of these, of course, is there being no mass there and so no gravitational potential at all, but any vacuum, with no mass, will above Poisson = 0 equation, including the potential outside of any body (the one used in this example relied on a spherical source).

So, the relativistic version is that the properties of the space-time curvature AT A POINT is related to the mass and energy AT A POINT. A flat space-time is produced when there is no mass and energy, and so has G=0, but so does any point in a vacuum, but that does not mean that the space-time at that point is not curved (and so no gravity).

Anyway, I got that off my chest, and my Discovery Project submitted, but now it's time to get on with a LIEF application! 

Sunday, 25 January 2015

The Constant Nature of the Speed of light in a vacuum

Wow! It has been a while, but I do have an excuse! I have been finishing up a book on the fine-tuning of the Universe and hopefully it will be published (and will become a really big best seller?? :) in 2015. But time to rebirth the blog, and what a better way to start that a gripe.

There's been some chatter on the interweb about a recent story about the speed of light in a vacuum being slowed down. Here's oneHere's another. Some of these squeak loudly about how the speed of light may not be "a constant", implying that something has gone horribly wrong with the Universe. Unfortunately, some of my physicsy colleagues were equally shocked but the result.

Why would one be shocked? Well, the speed of light being constant to all observers is central of Einstein's Special Theory of Relativity. Surely if these results are right, and Einstein is wrong, then science is a mess, etc etc etc.

Except there is nothing mysterious about this result. Nothing strange. In fact it was completely expected. The question boils down to what you mean by speed.
Now, you might be thinking that speed is simply related to the time it takes for a thing to travel from here to there. But we're dealing with light here, which, in classical physics is represented by oscillations in an electromagnetic field, while in our quantum picture it's oscillations in the wave function; the difference is not important.

When you first encounter electromagnetic radiation (i.e. light) you are often given a simple example of a single wave propagating in a vacuum. Every student of physics will have seen this picture at some point;
The electric (and magnetic) fields oscillate as a sin wave and the speed at which bumps in the wave move forward is the speed of light. This was one of the great successes of James Clark Maxwell, one of the greatest physicists who ever lived. In his work, he fully unified electricity and magnetism and showed that electromagnetic radiation, light, was the natural consequence. 

Without going into too many specific details, this is known as the phase velocity. For light in a vacuum, the phase velocity is equal to c.

One of the coolest things I ever learnt was Fourier series, or the notion that you can construct arbitrary wave shapes by adding together sins and cos waves. This still freaks me out a bit to this day, but instead of an electromagnetic wave being a simple sin or cos you can add waves to create a wave packet, basically a lump of light.

But when you add waves together, the result lump doesn't travel at the same speed as the waves that comprise the packet. The lump moves with what's known as the group velocity. Now, the group velocity and the phase velocity are, in general, different. In fact, they can be very different as it is possible to construct a packet that does not move at all, while all the waves making up the packet are moving at c!

So, this result was achieved by manipulating the waves to produce a packet whose group velocity was measurably smaller than a simple wave. That's it! Now, this is not meant to diminish the work of the experimenters, as this is not easy to set up and measure, but it means nothing for the speed of light, relativity etc etc. And the researchers know that!

And as I mentioned, understanding the difference between phase and group velocity has been known for a long time, with Hamilton (of Hamiltonian fame) in 1839, and Rayleigh in 1877. These initial studies were in waves in general, mainly sound waves, not necessarily light, but the mathematics are basically the same. 

Before I go, once of the best course I took as an undergraduate was called vibrations and waves. At the time, I didn't really see the importance of of what I was learning, but the mathematics was cool. I still love thinking about it. Over the years, I've come to realise that waves are everywhere, all throughout physics, science, and, well everything. Want to model a flag, make a ball and spring model. Want to make a model of matter, ball and spring. And watch the vibrations!

Don't believe me? Watch this - waves are everywhere.