I’m taking a short break from this blog for health reasons (concentrating on the other one).
The plan is to relaunch this one in September from another location.
I’ll post here when the new blog is available and going to be regularly updated.
em2: formulating the impossible
Big Al was puzzled by many things.
For instance whenever he asked his scientist and mathematician friends what they meant by coordinates on a graph they would tell him not to be silly, graphs and coordinates were obvious.
Not to Al they weren’t. His uncertainty was one of the starting points for discovering relativity theory.
He also did a lot of what most teachers won’t allow you to do in lessons: he daydreamed. For instance he tried to imagine what it would be like travelling through the universe seated on a beam of light. Pathetic. Get a life, Al. Don’t give up the day job.
Big Al in 1921
He kept thinking, and talking, and daydreaming, and thinking, and in 1905 while in his mid twenties he published some extraordinary scientific papers1.
One of them asserted that space and time have to be symmetrical. A necessary conclusion is that mass and energy, which appear to be so different, must just be versions of the same thing. This was illustrated nicely when the first atomic bomb worked.
So what is the c in e = mc2 ? It’s the speed of light. It is a very, very, very large number. I used to wonder why something as apparently irrelevant as the speed of light could possibly be involved in a formula about mass and energy, but I was getting my ideas backwards. Al found there must be a very special fixed number which he called c. One application of this weird number is that stuff in our universe has to be in just one of two groups. Either it has mass at normal speeds but cannot travel faster than c, or it can only exist when it is travelling at c. Examples are the electron and the photon. Electrons have mass but will not travel as fast as photons2. Photons are kind of what light is, so light travels at c.
Another application for c is in that energy-mass thing e = mc2 . We’ll dismantle it in the next post.
1 1905 was later called Einstein’s Annus Mirabilis. He published four scientific papers which were to shake the world in more ways than one. You really want to know? Okay, here they are:
- The one about the photo-electric effect (ie how solar power works) asserted that light wasn’t just a wave motion but was also made up of chunks now called photons. This was of course impossible. It also seems to be true.
- The one about Brownian motion used statistics to show that those implausible things called atoms that some people were talking about probably existed.
- The third one was called ‘On The Electrodynamics of Moving Bodies’. It was about Special Relativity, the ‘easy’ bit of relativity theory that leaves out gravity and acceleration.
- Finally came ‘Does the Inertia of a Body Depend Upon Its Energy Content?’ which introduced e = mc2.
2 If you want to know a bit more about this kind of stuff keep following this blog – and if I forget then do nag me.
energetic maths 1: the gadget works
16th July 1945, Alamogordo, New Mexico, just 16 milliseconds after 'The Gadget' was triggered. The fireball is already larger than an Olympic stadium.
e = mc2 has to be the most famous whatever it is in the world, but what is it?
Who cares!
It’s fun, and it is better than stuff like C = 2πr because it doesn’t use weird symbols like that thing between the 2 and the r.
Einstein came up with it. Everyone knows that.
Several decades later a bunch of scientists packed it into a device the size of a bloated fridge-freezer. They called it the ‘gadget’. They put it twenty metres up a tower in the desert. At fifteen seconds before half past five in the morning they set it off.
Bets amongst the scientists ranged from a mere ‘fizzle’ all the way through to the world’s atmosphere being ignited and killing all life on earth. I guess the person betting on that last option didn’t expect to collect his winnings.
In fact the result was somewhere in between. Windows were rattled as far away as the distance between Leeds and London – three hours drive at the speed limit. The nearest observers ten miles away from the gadget reported feeling for a few seconds as if they were in an oven. The surrounding mountains were lit up far more brightly than they ever were by mere sun light. The gadget left a crater deep enough to hide in standing up, and several football pitches across.
The desert sand was turned into glass.
In response to enquiries – well you would be asking what the hell was going on if you lived anywhere nearby – the local air base issued a press release saying that ‘a remotely located ammunitions magazine containing a considerable amount of high explosives and pyrotechnics exploded’. Actually the amount of really explosive stuff (plutonium) in the gadget was barely the size of a small apple1, though rather heavier. Only a fifth of it properly ‘exploded’, and less than a gram was actually converted into light, heat, sound and pressure waves.
That gram, that grain of plutonium is the m in e = mc2.
The light and heat felt many tens of miles away, and the pressure waves rattling windows hundreds of miles away, that was the e in e = mc2.
So less than a gram m of plutonium can be turned into the same amount of explosion e as twenty thousand tons of normal explosive.
Wow!
c must be a very large number. We’re multiplying an insignificant m by it, and then by it again, and we’re getting something vast beyond understanding.
(Up next will be em2: formulating the impossible)
1 Everything is backwards in atomic bombs. The gadget held just 6 kg of plutonium, but bringing that material together in the right way at the right time required several tons of normal explosive and a seriously complicated box of electronics. Another weird factor is that it’s not making the plutonium go critical that’s the real problem, although that is hard enough. The catch is getting the plutonium, which only occurs naturally in minute quantities. You need a nuclear reactor powered by uranium to make plutonium. Before that you have to mine the uranium, purify it, and then get rid of most of the unhelpful 238 strain. The rest of the bomb is cheap compared with how much it costs to make the plutonium!
ufmt : 001
What use is a math teacher? You'd be surprised.
cartoon devised by one of subrambler’s students during a boring lesson, drawn by miriam
