Quantum Evolution, Johnjoe McFadden. Chapter 7

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Quantum Evolution - Chapter 7 - What is quantum mechanics?

‘… Consider again a beam of light but now one that is shone through a screen with a one centimetre wide slit. We know that if we choose to measure momentum for a photon passing through the slit then its position becomes uncertain and, according to the standard interpretation of quantum mechanics, unreal. But we will, for the present, deny this viewpoint and with clenched fists assert the right of our photon to occupy a real position within the slit, irrespective of whether or not we choose to measure it. If a single photon does occupies a real and unique position then it must pass through one discrete area of the slit but not others. To prove the reality of position for our photon - our realist position assertion - we will replace the screen that had a single wide slit with a another screen pierced by two adjacent narrow slits. We will therefore force our photon to choose a particular path through the screen, either through the left slit or the right slit.

We first perform the experiment with the left slit covered up. This is essentially the same set-up as the single-slit experiment and we see a diffuse (diffracted) image, illuminated upon the wall (labelled [RIGHT]). Similarly, with the right slit covered up we will see a similar diffuse strip of light (labelled [LEFT]). With both holes we might expect to see the product of the two single diffraction patterns, [RIGHT] + [LEFT]. This is the pattern we would expect if we were firing conventional particles (such as bullets) through the slits. But when we shine light through the screen we do not see the expected composite pattern but instead we see a series of light and dark bands on the wall (Figure 4). This image is certainly not a simple addition of two independent beams of light, since areas on the wall that were bright with either single slit open are now dark and other areas that were dark are now bright. This pattern of light and dark bands is known as an interference pattern.

Imagine yourself standing against the wall at the position marked BRIGHT-DARK in the Figure. From this position, in one of the dark strips of the interference pattern, no light reaches you from either slit so it looks as if neither slit is open. Yet you can confirm that the slits are indeed open by taking a step to the right or to the left (into a bright band) when you see that the both slits are indeed bright from your new viewpoint. Now (whilst standing within the dark band), you ask a colleague to close the left slit. Immediately you see a bright strip of light shining out of the right slit. Yet all that has happened is that the left slit has been covered! How can preventing light passing through the left hole, cause light to emerge from the right hole?

The reason is that, at the position you are standing, light can reach you from the right slit, but only if the left slit is closed. With the left slit open, the light emerging from that slit interferes with light coming from the right slit. So you can see that the interference pattern is a funny kind of addition of the pattern of light that you see when either slit is open. At some positions on the screen the light from both sources adds up to generate a bright band; whereas at other positions the light from each source cancels each other out to generate a dark band. To indicate the anomalous nature of the pattern of light and dark strips we will designate it as [RIGHT (+/-) LEFT]. The (+/-) term and italics denotes the fact that the interference pattern is a kind of complicated addition of the image with both slits open (+) and the image obtained with neither slit open (-).

This experiment is in fact more-or-less the same as a classic experiment performed by Thomas Young at the turn of the nineteenth century. It was one of the crucial experiments that ‘proved’ the wave theory of light. Light, so the theory goes, is emitted as a series of spherical wavefronts. When the waves pass through the screen of the two slit experiment, the emerging light from a single slit becomes the source of its own series of spherical wavefronts. The pair of wave-fronts emerging from the pair of slits converge and interfere with one another before they reach the screen. The light bands correspond to regions where the two waves arrive in phase (peaks and troughs marching together) and reinforce one another. The dark bands are areas where the waves arrive out of phase (peaks meets troughs) and cancel one another out.

Interference is a feature of waves. Waves are spread out across space, allowing them to pass through two places at once - the two slits in our screen – but then to be recombined to generate the interference pattern. Interference is not a feature of classical particles. Classical particles are localised in space and cannot travel through two separated points. It was Young’s discovery of light interference effects that clinched the wave theory of light for nineteenth century physicists.

But then how can we square interference effects with the evidence for particles of light, photons. How do we account for phenomena like black body radiation, the photoelectric effect and even the silver dots that make up a photographic image? The simplest interpretation would be to conclude that the wave-like behaviour of light is a manifestation of the dynamics of millions of photons of light. In this case single photons would have real positions in space and their individual dynamics would betray no trace of the wavy interference patterns. To prove our realist position assertion for photons, all we need to do is to repeat the two slit experiment, a photon at a time.

To test this idea, we must again reduce the intensity of light such that only single photons are emitted, one at a time, from our source and are individually detected at the photographic plate. If we do this with only the right slit open then the collection of dots fall within the same area [RIGHT] that was illuminated by the strong beam of light was diffracted as it passed through the right slit. We will call this distribution of photon landings a scatter pattern, as it is exactly the distribution we would expect for particles (such as bullets) that were scattered as they passed through the narrow aperture. Similarly, with the left slit open, the photons land within the illuminated area [LEFT] that represents the scatter pattern for particles going through the left slit. With both slits open we might expect that individual photons must now pass through either the left or the right slit. For any photon that chooses to pass through the right slit, it should make no difference whether the left slit is open or closed. We would expect it to fall within the same [RIGHT] area as it did when the left slit was closed and this was the only route open to it. Similarly, for any photons that chose to travel through the left slit, we would expect them to land within ([LEFT]). The pattern of dots would then form the ([RIGHT]+ [LEFT]) image that is a simple product of the scatter patterns for each single slit experiment.

We fire one photon at the screen with both slits open and, as expected, the photon’s arrival is recorded as a discrete silver dot on the photographic plate. We fire another and get a second dot. We keep on firing individual photons until we have lots of dots on the screen. Did each photon pass through only a single slit in the screen? As the pattern of dots recording each photon landing accumulate on the photographic plate, the image obtained forms exactly the same interference pattern of light and dark bands [RIGHT (+/-) LEFT] that we saw with the strong beam of light. No scatter patterns. Single particles show interference effects!

Our aim was to demonstrate that position was a real property of photons (though it may not be simultaneously measurable with momentum). If we were right, then light particles, taking a single defined trajectory through space, should have travelled by a single route through only one of slits. Yet, contrary to our naïve expectation, single photons appeared to pass through both slits to generate an interference pattern.

Photons must, like a wave, pass through both slits at once. The conclusion is inescapable. Contrary to our realist position assertion individual photons do not always have a real position in space. Quantum mechanics wins.

Richard Feynman, the Nobel prize-winning physicist and architect of the enormously successful theory of quantum electrodynamics (QED) considered that “the experiment with two holes …has in it the heart of quantum mechanics. In reality, it contains the only mystery. … In telling you how it works we will have told you about the basic peculiarities of quantum mechanics.” The experiment with two holes reveals the wave-particle duality of both matter and radiation.’