1.5 Wavy Particles
Electrons and other particles have wave-like properties too.
When waves meet they can’t ignore each other – you get interference between them. This can be constructive if the peaks of one wave are aligned with the peaks of the other, leading to an increased total amplitude. On the other hand, it can be destructive if the peaks of one wave are aligned with the troughs of the other, cancelling each other out and therefore decreasing the resulting amplitude.
Figure I-ii
These effects are beautifully demonstrated for visible light waves by the legendary double slit experiment devised by Thomas Young. He is one of a substantial number of genii who have contributed to our story; “but I was the only one who also made breakthroughs in translating the hieroglyphs on the Rosetta stone,” he is quick to point out. Yes, so? thinks Nefertiti. “And developing the theory of colour vision”.
A coherent light source (like a laser) is used to illuminate a parallel, closely spaced pair of slits in an opaque screen. The light arriving at the slits can be thought of as having parallel wave fronts, as shown in the figure I-iii. A wavefront is a surface connecting points of the same phase in an assembly of waves: for example, you could think of each of the lines in the diagram as marking where the wave peaks occur.
Light passing through the slits spreads out to form semi-circular wavefronts – this effect is called diffraction. The diffracted waves from the two slits interfere with one another. Along certain lines, there is systematic constructive interference while in between, the interference is destructive. The consequences of this can be visualised by allowing the light to strike a detector screen.
Figure I-iii
This, then, is quintessentially wavy behaviour. So, are you thinking what Nefertiti is thinking? If our proposition that particles might be a bit wavy has any truth to it, we should go looking for analogous interference behaviour when particles pass through a double slit arrangement.
So here’s the set-up: electrons are fired at a screen with a pair of slits in it and a detector screen is placed some distance behind. If the electrons behave as simple particles – just blobs of stuff – this is what we expect to happen:
Figure I-iv
What happens, however, is that while individual electrons arrive at specific points on the detector screen, these arrival points are not confined to the anticipated bands. Nor are they randomly distributed, however: as a large number of electron impacts are detected, a pattern emerges of alternating bands of high and low frequency of electrons arriving at the screen, echoing the bright and dark fringes in Young’s light experiment:
Figure I-v
There is just no way you can explain this in terms of particles acting as simple blobs and following Newton’s laws. Instead, it indeed suggests that the electrons behave like waves, undergoing diffraction and interference, just as the light did in the original experiment. And it’s not just electrons: very similar interference effects have now been observed for atoms and molecules too. Molecules as big as buckminsterfullerene (C60) have indeed been shown to do a good job with the double-slit trick. So wave-like behaviour seems to be a general property of particles. Nefertiti thinks ……… seabirds. She arranges a pair of narrow openings, blindfolds Cormorant and instructs him to fly repeatedly at them. In those cases where he makes it through, she records his trajectory on the other side. After many trials Cormorant is feeling pretty fed-up, especially when Nefertiti reports no evidence of interference effects, so no paper in Nature to compensate for his bruises. We will discover why this experiment was more Cormorant-breaking than groundbreaking in a later chapter.
What we will need to do is to try to understand the nature of these “matter-waves” and, crucially, to find a way to describe them mathematically. For now, though, we have successfully arrived at the beginning. We have evidence that energy levels of are quantised and we have a hypothesis that this might be because they are somehow associated with standing waves. We’ve recognised the parallel with how light behaves and we’ve added experimental evidence for the wavy nature of particles, so we can have some confidence that this is an idea worth taking forward. So now what?
Uncle Albert has a suggestion. “Why not start with the momentum of a photon?” Cormorant is embarrassed. “The old guy has finally lost it,” he thinks; “photons have no mass, so (since momentum = mass x velocity) they can’t have any momentum”. Except that they do. That’s what causes comets to have tails: the transfer of momentum from photons from the sun colliding with the cometary dust particles. “Yes,” interjects Nefertiti, “and I remember that a Japanese spacecraft called IKAROS was powered on its journey to Venus by harnessing the pressure of photons from the sun”. “Well,” continues Uncle Albert, “there’s a case of wave-particle duality if ever there was one. And we would expect, would we not, that a photon’s momentum would be linked to its energy? And we know that the energy depends, in turn, on the wavelength. So, if we could, somehow, find a theoretical framework that would enable us to derive the wavelength – momentum relationship, we would have an equation that embodies wave-particle duality. Now, I wonder who might have developed such a theory?
