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February 2013 Archives

 While generally speaking I'm very pleased to hear physics words appear in everyday conversation, I would prefer for them to be used approximately correctly. 'Exponentially' is a case in point - it gets used for something that keeps getting bigger, regardless of how exponential it really is. 

So, while 'nanotechnology' is a good word to hear (because that's what it is, technology on the scale of nanometres), 'megamilk' or 'mitre 10 mega' is not. What is there that's a million times more in megamilk than normal milk? Is mitre 10 mega a million times bigger than a mitre 10. I think not. 

With data storage abilities of gadgets growing exponentially (and I mean exponentially here) we are rapidly traversing the prefixes for large things: kilo (a thousand - remember when 64k RAM was a big deal?) mega (a million), giga (a billion, or ten to the power 9) and now tera (ten to the power 12) is beginning to be a household prefix. Next comes peta (10^15) and exa (10^18), zetta (now that's a cool sounding one, 10^21) and yotta (10^24), though I admit to having looked up the last three. 

I wonder when we'll see 'zetta-' things go on sale, at zetta-stores?

Going the other way, we have milli (a thousandth), a micro (a millionth), a nano (a billionth) and then pico, femto, atto, and beyond.  I came across this article today about mobile phone networks. The idea of a microcell is old hat. They're already in the realm of  femto cells - tiny little mobile cells at airports etc (a totally mangled definition of femto if you ask me) - and people are beginning to talk about attocells - e.g. every lightbulb in your house becomes a transmitter in a separate 'cell'. 

Actually, the article is really interesting to read, highlighting some of the problems with exponentially (again!) demand for data bandwidth. I propose we go to zeptocells, where each limb on your body is a cell. 

 

 

 

 

 

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One of the things I frequently bleat about is that physics isn't synonymous with stuffing numbers into formulae. Therefore, it's with some horror that I've watched through my attempts at doing the 2012 NZQA Scholarship Physics exam and seen myself stuffing numbers into formulae. At least, that is how many of the videos come across to me. I'm left thinking why. I mean, I know you can't answer a scholarship physics exam if you think it's about plugging-and-chugging. You need to know your physics to know what mathematical relationships may or may not be required, and how to use them.

I think the problem with these videos is that they haven't captured what I have been thinking. WHY have I chosen to use a particular expression to relate X and Y? What sometimes comes across is that I'm picking the relationships out of thin air. HOW do I know they are the 'right' ones to use? That I've often not made clear. I think some viewers might be frustrated here - they can do the solve the equations and plug-and-chug bit at the end, what they can't do and need help on is identifying exactly what needs solving and plugging. That skill is really hard to teach. Partly, I think, this is down to being an 'expert' in the area. It is really hard to explain thought processes when they are second-nature to you. Perhaps more powerful would be to give the paper to a couple of good first year students and get them to work through it.

Or, maybe more powerful still, give some 'experts' some yet tougher problems to work through. Things that really stretch their thinking. A quick survey of some of the PhD projects going on here would, I'm sure, unearth a number of really tough problems that need some solutions. Give one of those problems to a small group of physicists (and, realistically, other flavours of scientist) and get them to discuss it together. Now, there's an idea for some more videos.

If you want to see some physics-without-the-equations taking place, here's a Walter Lewin lecture on rainbows that came to my attention recently. There's a teeny-weeny amount of maths in it, but you can really ignore that if you want to. It's a long lecture but really good. Much better than the usual Friday night television. http://www.youtube.com/watch?v=FJVvtOy-ukE .Enjoy. As for me, I'm off to the swimming pool.

 

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Yesterday Sam and I finished filming my attempts to do the 2012 Physics Scholarship exam. There were some tough questions in there.  I got on top of them, I think, with some careful thinking through the principles involved, which is a very good way to start when you are bemused by a question.

I'm sure Sam will get the movies uploaded onto physicslounge soon, to join the others. Hopefully some of you will find them useful.

Next, the calculus one.  No! - only joking.

 

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One of baby Benjamin's books has a storyline that goes like this. (Not wishing to fall foul of the Copyright Act I shall not quote directly from it - any sensible quote is about 10% or greater of the work!)

There's an animal that's being chased by another animal. This second animal is being chased by a third. The third by a fourth. And so on. The seventh animal is being chased by the first... One can picture the scene of seven animals trouping round in a circle. And that's it. Enough to entertain a seven-month old. (Though I think it's the colours, Daddy's voice and the fact that he can chew it that leads to most of the entertainment, rather than the nuances of the text and storyline.)

Anyway, the book reminded me of a lecture I had as an undergraduate looking at characteristics in differential equations (don't worry about those) and shock fronts. The lecturer wanted to use an example of a physical system where velocity increases with density of the things doing the moving. The example he chose? (and he admitted this was a bit naff): A infinite line of people interspersed with tigers. When there is a large separation of the members of this line, it moves slowly. But when the tigers are close at the heels of the people, everyone moves quickly. It's the opposite of more common physical systems where things slow down at high density, such as with traffic flow. High traffic density causes traffic jams, not high speed driving.

The tigers and people line has an interesting property of being able to generate a shock-front. Here there is a discontinuous change in the density of the system. A more reasonable example that does something similar is a hydraulic jump. When flowing water experiences a sudden change in depth (and therefore velocity), there can be shock-fronts formed.  I remember experiencing a strange example of this (or something similar) when sailing along the south coast of England several years ago. We sailed over a sand bank that had a strong tidal current flowing over it - and at the edge where the depth changed quickly, the water transitioned from very calm to choppy. The change was extremely sudden. Right at the edge of the front, there was a set of very well formed standing waves. It would have been good to have had a video camera to record the action.

I had a look on Youtube for some movies of hydraulic jumps. Here's a nice one for you surfers. Fancy being a designer on this - it would make your engineering degree well worth while.

 

 

 

 

 

 

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I've been having some discussion with a collaborator in Sydney regarding a numerical model that we are developing. It concerns the response of the brain to pulses of magnetic field, but for the purposes of this blog entry, that is immaterial. One thing that we've been grappling with is 'dealing with infinity'. Basically, in physical processes, what is happening now depends on a sum of everything that's happened previously. Processes are causal. To understand the present, we look at the past (not the future). How far back in the past do we have to look? That depends on the problem, but, technically speaking, we have to look infinitely far back in the past. There is not cut-off time. Sure, there comes a point where what happened X seconds (or hours, years, millennia ago) isn't going to make much of a difference, but where we take this cut-off is usually arbitrary. So often we physicists simply say 'start from a time of minus infinity', which means consider all things in the past, no matter how far back they happened.

What we get are integrals that run from minus infinity to now in time. And that, in the case of the model that I've been looking at, causes some conceptual problems. We end up with an infinite result. But that doesn't actually turn out to be a physical problem. That's because what we actually want to know involves integrating this result over another infinite time range, which generates an infinite sum of infinities. But here's the neat bit. Some of these are positive infinities and some are negative infinities, and they cancel and divide out to something sensible and finite. It sounds odd, but mathematically it is all quite reasonable.

There are a few examples of this kind of thing in physics. Perhaps the most significant is renormalization in particle physics. Here, when one calculates using quantum electrodynamics how electrons and photons interact, the calculations are full of infinities. But the infinities, if considered carefully can be shown to cancel out. The positive infinities cancel with negative infinities. It was a major conceptual leap forward to accept that this sort of thing was reasonable.

I first came across the idea with my PhD - looking at how electrons interact with each other in solids. Here, there is a seminal paper by Gell-Mann and Bruekner (1957) which shows that while perturbation theory gives an infinite sum of infinite integrals, the infinities can be dealt with and a finite result remains. After a bit of on-line hunting I tracked it down here. It's rather neat (if you're a physicist).

The moral of all this for the non-mathematician is to be careful with the idea of infinity. Don't treat infinity as 'the biggest possible number'. There is no such thing. If you think you've found it, let me know and I'll prove you wrong by adding one to it.  It's simply a short-hand for 'and keep going...'

 

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