"I used to be in two minds about Quantum Uncertainty, but now I'm not so sure..."
Much like the particle.
But how can our friendly particle be in two places at the same time, I hear you cry? (He’s at it again with the talking to himself, I also hear you whisper amongst yourselves.) Well, that is precisely what I’m going to discuss here. Things may get a little heavy as we go on, but stay with me (please, I get ever so lonely). This is all just information that feeds into the play, not the actual play itself. Yes, Heisenberg and the Bohrs talk of interpretations and nuclear orbits and radioactive bombardment, but they are just the items of discussion; the real meat of the play is how the three players interact, the truths they reveal, the secrets they harbour, and moments of doubt and pain and hurt and anger and isolation and joy and laughter – and dealing with them all at the same time. I will discuss more of this myriad of emotions that the characters experience as we get into the rehearsals.
So, if this all seems a bit complicated, which it can be (it is physics after all), don’t let it put you off the show. I love Castle and Drop Dead Diva[1] but know next to nothing about writing a novel[2], criminal law, being a lawyer or matching heels with a power suit[3]; it really doesn’t impact on my enjoyment of the narrative. It’s like watching the documentary about Blade Runner before you see the film: when certain bits turn up and scenes play out, you can see all the subtext and subtle links shine through, only adding to a brilliant movie.
I repeat in big important letters: THIS ISN’T THE SHOW – JUST SUPPORTING INFORMATION THAT WILL ONLY ADD TO YOUR ENJOYMENT. Honest.
So, let’s start with a tank of water.
The water is still, nothing is moving. We are at one end and a large blank screen is submerged at the other. A light shines across the surface of the water. Just for fun, we drop a pebble into our tank to watch the ripples spread across the surface towards the other side. Assuming the tank is wide enough the undulating wave with its peaks and troughs strikes the far screen without any side ‘echoes’. As the wave hits the wall we take a snapshot of the screen. With the light across the surface being disturbed by the waves, we can see a pattern form on the screen: at the centre of the screen, the light is completely blocked by the wave. As you look away from this central point, towards the sides of the screen, more light is visible. Let’s invert this image and imagine the water wave is light hitting a wall. Due to it’s curved nature spreading out from the dropped pebble, the amount of energy, demonstrated by the height of the wave, as it hits the flat, incurving wall decreases the further you get from the middle of the screen, directly opposite the dropped pebble/ imagined light source.
Let’s do it again. The water is calm; the light is shining across the screen. Now, we have two pebbles. We drop them at t he same time, at the same end of the tank, about a third of the way in from the sides. Now we have two sets of expanding ripples. Two ripples that begin to interact with each other[4]. One wave built of peaks and troughs begins to multiply the other. If two peaks meet, then the resulting wave is twice its starting height. If a trough meets another trough, it becomes a trough of twice its starting depth. If a peak meets a trough, then they cancel each other out. As this merging of energies surges across the surface, we again pause, take a snapshot and observe the screen. As before we have a gradient of light (we’ll cut to the chase here with the inversion of the image) peaking in the middle ands disappearing at the ends, but due to the crossing ripples, the smooth pattern is broken into stripes.
Shadow
Light.
Shadow.
Brighter light.
Shadow.
Very bright light.
Shadow.
Brilliant bright light.
Shadow.
Very bright light.
Shadow.
Brighter Light.
Shadow.
Light.
Shadow.
The two waves have produced an Interference Pattern.
Right hold that thought. Waves coming from two close sources will produce an interference pattern.
At the other end of the garage we have another screen, a vertical plank of wood with a slit in it, and a small automatic tennis ball server. Now the slit is just wide enough for a tennis ball through. And we have already marinated our tennis balls in paint (for that extra special flavour). Let’s fire it up!
For an hour or so we fire tennis balls at the plank. Those that get through splat against the screen, creating a lovely stripe of paint. Great. Pretty. Would take forever to paint the room.
So let’s double our chances of finishing the room: two slits in the plank.
As expected, we now get two parallel stripes.
Hold that thought, too. Tennis balls, our physical particles, make two lines when passed through two slits.
Okay, still with me – groovy. Let’s go small. Let’s change the tennis ball for an electron, a tiny particle of matter. If we scale down the plank of wood to electron size, we can fire the electrons through. And yes, we get a single line pattern from the single slit plank.
So far, so straight forward. Let’s try it with two slits. Twang, twang, Dakka-dakka-dakka. Feel free to add your own machine gun noises. And voila, the perfect example of two parallel – wait! What’s this? An Interference Pattern? Like the wave from the tank! Freaky.
But could it be the stream of electrons are colliding with each other, deflecting their path, and producing this weirdness? Let’s make it simple. Let’s fire one electron at the plank at a time. But no! Even with an isolated projectile, the Interference Pattern is still emerging after several shots at the wall. From this, and some highfalutin mathematics, it seems that the particle was passing through the slits as waves of potential and interfering with itself[5]. But the maths at this point makes this even stranger: As the electron leaves the launcher and before it hits the screen, the particle has:
Gone through one slit
Gone through the other slit
Gone through both slits
Gone through neither
…all at the same time!
This overlapping of potential positions is called Superposition, and it is the first part of Heisenberg’s Uncertainty Principle.
So far we’ve looked at the particle launcher and the screen – let’s study the slit to see what is happening down there. But oh the calamity! As we watch the particle leave the launcher, the electron will only do one of the four events listed above. This, over time, will only produce the two stripe pattern associated with matter going through the slits. If we shut the camera down, removing the observation, and run the experiment again, the Interference Pattern returns. It seems that by observing the experiment we are changing what the electron does and which pattern is produced.
Heisenberg theorised that we can’t know exactly how the particle will behave without destroying the wave nature of its movement and eradicating the Interference Pattern. By extrapolating this, he proposed that the more accurately we know the position of a particle, the less accurately we know its velocity, and vice versa[6]. All we can discover is the probability of where a particle may be, or at what velocity is travelling, not both.
So, particles in two places at once: Making Christmas easier a quantum at a time[7]. Now I’m off to scrape tennis ball paint of my garage walls, but next time we’ll have a look at Schrödinger and his zombie cat.
[1] Oh the shame. Manliness out of the window. My name is Kevin, and I’m a Drop Dead Diva fan. And Castle has Nathan Fillion and Stana Katic in it, which is enough for anyone.
[2] As anyone who is reading this blog will tell you.
[3] Stop that sniggering.
[4] Ooh. And most definitely, Er.
[5] Nope. Not doing that joke, it’s juvenile.
[6] Copenhagen by Michael Frayn, page 150, Methuen Drama Edition, 2003.
[7] For more on light through slits, have a look at Young’s double slit experiment http://physics.about.com/od/lightoptics/a/doubleslit.htm
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