Quantum Evolution, Johnjoe McFadden. Chapter 8

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Quantum Evolution - Chapter 8 - Measurement and reality

‘… Zeno was born in the Greek colony of Elea in Southern Italy in the fifth century BC. He travelled widely for many years and then returned to his birthplace only to be tortured to death after being implicated in a plot to assassinate the city’s tyrant Nearchus. He appears to have been a resilient character: he is said to have bitten off his tongue and spat it at the tyrant during torture. However, it is for his activities during happier days that he is chiefly remembered; particularly a series of paradoxes set in the form of short fables. The most famous concerns a race between Achilles (fleetest of foot of all mortals) and a tortoise. Being far slower than Achilles the tortoise is given a head start of say ten metres. But once the race is off Achilles easily reaches the tortoise’s starting position with a few lengthy bounds. But by now the tortoise has moved on. Achilles leaps after the tortoise but on reaching its last position the tortoise has again advanced by some tiny amount. Achilles again advances but each time Achilles moves to close the gap, the gap is widened. Achilles appears to be unable to ever reach the tortoise (or even to move at all) because to do so he must advance through an infinity of ever decreasing distances.

Zeno knew of course that motion was possible and Achilles would catch up with the tortoise. His paradoxes were to illustrate that something must be wrong about our simplistic notion of time and motion. It took two millennia of mathematical head scratching to solve Zeno’s paradox by demonstrating that an infinite sum can add up to a finite number. However, the paradox lives on in the quantum Zeno effect and the inverse quantum Zeno effect, which describe how a quantum system can be manipulated by measurement.

We have in fact already met an aspect of the inverse Quantum Zeno effect in our experiment with the three Polaroid lenses. You may remember that when two lenses are placed perpendicular to one another (e.g. at twelve-o-clock and three-o-clock) then there is zero probability for photon transmission. However, inserting an extra lens at one-o-clock (sandwiched between the first two) increases the probability for transmission from zero to 6%. What has happened is that the one-o-clock lens has projected the state vector onto its eigenstates. Only some of the original photons will go through the one-o-clock lens but all those that emerge will be polarised at one-o-clock. A significant fraction of these one-o-clock photons can then pass through the three-o-clock lens; whereas the original twelve-o-clock photons were unable to.

Oblique quantum measurement (measurement that is slightly shifted from the previous state) is thereby able to rotate the angle of polarisation of photons. This process can be continued with more lenses. A fourth lens inserted at two-o-clock, will cause a further rotation of polarisation. The two–o-clock lens will project the state vector of the photons emerging from the one-o-clock lens onto its eigenstates. Only those photons that collapse into the two-o-clock eigenstate will be transmitted, but all those that do will all be polarised at two-o-clock. These two-o-clock photons will pass even more readily through the final three-o-clock lens so that the probability for transmission through all four lenses will be increased to 29%. Addition of additional lenses will allow even more light through. A series of fifteen Polaroid lenses orientated at one minute, two minutes, three minutes, four minutes and so on up to 15 minutes, would increase the probability of transmission to greater than 90%. In fact an infinitely dense series of lenses will increase the probability of transmission to 100%.

This is an example of the inverse quantum-Zeno effect whereby a dense series of measurements of a quantum system along a particular path will force the dynamics of the system to evolve along that path. The polarising lenses can achieve this effect by performing a dense series of measurements along a rotating path of polarisation angle. But the inverse quantum Zeno effect is a general phenomenon that can direct any aspect of the dynamics of a quantum system. Consider an atom sitting at some arbitrary position we will call A. Position is of course a quantum property that may be represented by a wave function or state vector, say y[{atom at A}]. But like polarisation angle, the position state vector can be represented as a superposition of orthogonal (perpendicular) state vectors that add up to the original state, such as: y[{atom a bit to the left of A, at B} (+/-) {atom a bit to the right of A, at C}]. An equally valid description would be: y[{atom a bit north of A, at X} (+/-) {atom a bit south of A, at Y}]. In quantum mechanics, each of these representations describes precisely the same state.

We now place a measuring device, say a powerful electron microscope, over the position B. Since the microscope might detect the atom at B (it lies within the atom’s position uncertainty), this constitutes a quantum measurement that will project the atom’s state vector onto the eigenstates of the microscope. Any atom that the microscope detects must be at B, and so it will have quantum jumped from A to B. We can repeat this process by placing another microscope at some position D, a bit to the left of B. This measurement will project the atom at B onto its eigenstates. Any atom that is detected, will have quantum jumped to D.

A ® B ® C ® D ® E ® F ® G ® H, or indeed along any path we choose (Figure 8.3). So long as the measurements are sufficiently dense, the inverse quantum Zeno effect will capture the atom and drag it along that measured path.

An important point to note about the inverse quantum Zeno effect is that although each measurement along the path may generate a classical signal (as it must to constitute a quantum measurement), the product of the measurement – the measured particle/state – must continue to exist at the quantum level. Only in this way can the next measurement along the line decompose the measured state into a new superposition. If instead, the state that emerges from the measurement is converted to a classical state - perhaps by some kind of amplification process - then the inverse Zeno effect is powerless to modify it. The inverse Zeno effect only works on quantum systems. Classical systems cannot be decomposed into a superposition of states. An irreversible amplification of the quantum system to the classical level represents the end of the line for the inverse quantum Zeno effect (as shown in Figure 8.4).

To get some kind of conceptual feel for what is going on in the inverse Zeno effect, consider again the thought ‘note’ which, as I discussed above, can in a sense be decomposed into component states: musical note + banknote + written note. Now imagine yourself sitting on a psychiatrist’s couch and hearing ‘note’ and being asked to report the next thought that entered your mind. You might say, ‘five-pound’ or ‘writing pad’ or ‘piano’. You would be very unlikely (would have a very low probability) of saying the word ‘prison’. Now imagine the psychiatrist holding up successive images - a piano, a piano key, a door key, a securely locked door - and then asking you to say the next thing that came into your mind. You still might not say ‘prison’, but the probability would now be much higher than it was before. In a sense, the chain of associations have laid down a series of measurements in your mind that have taken the thought ‘note’ to a place where it is much closer to ‘prison’. This chain of mental associations has some similarity to how the inverse Zeno effect drags the state vector along a chosen path. Your eventual utterance irreversibly amplifies the thought and becomes the end of the line for the chain of associations; just as an irreversible amplification to the classical level represents the end of the line for the inverse Zeno effect.

The inverse Zeno effect is described as inverse because its reverse, the quantum Zeno effect (which was described first, by Misra and Sudarshan of the University of Texas in 1977) describes how continuous measurement can freeze the dynamics of a quantum system. We can see how this works by imagining an atom spontaneously moving along a path A ® B ® C ® D. We now fix our microscope securely over A, and perform a dense (in time) series of measurements of the atom at A. However, now each time the amplitude of the state vector drifts off towards B, then quantum measurement at A, captures the particle and drags it back to A. Continuous measurement at A will prevent the particle moving along the path A ® B ® C ® D. The quantum Zeno effect will freeze the dynamics of the system.

It is much easier to perform a dense series of measurements from the same position, than following a particle along a path; so the quantum Zeno effect has been more intensively studied than its inverse. David Wineland and colleagues at the National Institute of Standards and Technology in Boulder, Colorado, succeeded in using the quantum Zeno effect to freeze the motion of electrons in a pot of beryllium ions. They first used a laser to force the electrons to move from one atomic shell to another but showed that continuous observation of the electrons would prevent that transition. The quantum Zeno-effect arrests motion by continuous observation; or as the science writer John Gribbin describes it, ‘a watched quantum kettle never boils’.

Both the quantum Zeno effect and the inverse Zeno effect are really aspects of the same phenomenon: the ability of quantum measurement to interact with, and shape the dynamics of a system. The special relationship between quantum objects and quantum measuring devices draws out classical reality from the quantum world. If you will allow me one last analogy, the process may be compared with the kind of Improvisation Theatre pioneered by the American artist Viola Spolin in the 1930’s. Spolin’s revolutionary approach to the theatre was to throw away the script. Instead the actors would respond to the reactions and prompting of the audience by improvising the ensuing action. At the start of each performance the improvised play can be said to be indeterminate in the same way that the word ‘note’ is indeterminate. The play has certain potentialities dependent on the set of characters present, but no defined plot. With no audience present, we could imagine a quantum play in which all possible plots were acted out as a quantum superposition. However, in a real performance, the interaction between the actors and their audience draws out the course of action, the plot for that night’s performance. Just as the audience of an improvised play draws out from the infinity of possible plots, a single reality for each live performance, so measurement of a quantum system draws out from the quantum superposition of all possible states, a single reality for the physical world. As Niels Bohr said, ‘one must never forget that in the drama of existence we are ourselves both actors and spectators’.

But who then or what are the actors and spectators inside a living cell of an animal? Is it the cell, the animal, or we that observe the animal? Can living cells draw out their own reality or do they need an audience? To answer these questions we next need to explore the nature of physical reality and discover why the world is real.’