Quantum Evolution, Johnjoe McFadden. Chapter 9

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Quantum Evolution - Chapter 9 - What does it all mean?

‘…Consider a single photon in a closed box. If we have no knowledge about the polarisation state of this photon then it may subsequently be found with any angle of polarisation, è,ë,ì or é or any angle in between. In quantum mechanics we describe the state of this photon with a wave function made up of a superposition of all these possible states: y {è} (+/-) { ë} (+/-) { ì} (+/-) { é}]. Our classical minds might ask, “but which state is the photon actually in”? However, if we are only considering the photon in isolation then these states are all the same, even classically. If there is no external reference direction then è, ë, ì and éare indistinguishable – they are the same state. It is only when we place the photon in an environment with reference points on which one can map out particular directions, does the state è become distinguishable from ë. It is only after this mapping takes place that it makes any kind of sense to talk about a photon having a direction of polarisation at all.

Similarly, the concept of position only makes sense when a particle is mapped to a space. In empty space without external reference points, positions loses its meaning. The same considerations apply to concepts like energy, momentum or time - they can only be defined with reference to externally mapped reference points and/or an external clock. So in order to define a particular state it is necessary to have some kind of environment and only by reference to this environment do classical concepts like a single defined direction of polarisation, or a single energy state of a single position, become real. This is one aspect of any measuring device; it allows the quantum system to be mapped to an external environment and thereby legitimises classical concepts such as position or momentum. In the absence of an external environment, the quantum wave function becomes the only legitimate description of any system.

However, who is doing the mapping to make a particle’s position real? We could imagine a particle such as an atom in an empty infinite space where it has no definable position. It can be said to exist as a superposition of all possible positions within that space. An external object is placed alongside the atom. Now the atom’s position can be mapped with reference to the object. Will it remain as a superposition of all possible positions? If the external object is a scientist equipped with an electron microscope then she can measure the atom’s position and thereby force it to adopt a real position. What if the external object is a cat, or a microbe, or a rock? Can these objects measure the atom’s position? What if the cat is blind? We can see that this is bringing us back to the lair of Schrodinger’s cat. However, this way of looking at the problem does reveal an essential feature of quantum measurement: there must be some exchange of matter or energy between the quantum system and its environment/measuring device. If a rock is merely placed alongside the atom, how could the rock and atom know of each other’s existence? For the rock to know the atom there must be some sort of exchange of matter or energy between them. For the rock to measure the position of the atom, some of the possible positions of the atom must make a difference to the rock. Perhaps in one particular position the atom will release a photon on a trajectory that will impact with on the rock, which happens to be poised on a ledge, so that the tiny quantity of momentum delivered by the photon is sufficient to topple the rock over the ledge. The key point is that for a quantum measurement to take place there must surely be some kind of record of the quantum system (the atom) held in the environment (the rock). There must be some leakage of information about the system, into its environment.

But what if the object placed alongside our atom is another fundamental particle such as an electron. As we have discussed above, the new particle can become entangled with all of the possible positions of the original particle as an EPR-pair. No measurement can take place. A rock may be capable of measuring a particle’s position but a lone electron would not. What about two or three electrons, or a million, billion or a trillion electron inside a trillion atoms? Clearly we will eventually be reaching the kind of number of atoms within the average person or cat (somewhere in the region of 10^³⁰ atoms). Between an atom, rock, cat and person there must be some point of transition where quantum entanglement gives way to classically separated states. Where is this point?

To answer this question we will return (one last time!) to the two slit experiment. When light was shone through the slit screen we saw an interference pattern. However, it is actually quite tricky to obtain the interference pattern. In our experiment we used a laser as a light source because it releases monochromatic light (light of a single frequency or colour) in phase. The critical feature of monochromatic laser light is that the waves all have the same wavelength and are emitted in the same phase: the peaks and troughs of the waves all march along in step. Only this kind of coherent light will generate the sharp strips of light and dark bands that characterise the interference pattern. If instead polychromatic light is used, which is made up of a mixture of light of different wavelengths, then the waves quickly fall out of step, they become incoherent. When the waves arrive at the screen the peaks, the peaks and troughs are all mixed up and arrive at different times. The more-or-less random addition and subtraction of the incoherent peaks and troughs leads to cancellation of all the quantum superposition {RIGHT (+/-) LEFT} terms. Only the simple [RIGHT] + [LEFT] scatter pattern remains with no interference bands.

Another way to disturb the coherence of light is to jiggle the photons around a bit. The argument will be clearer if at this stage we switch to firing electrons through the slit to generate an electron interference pattern. As with photons, the interference effects indicate that each electron is somehow able to travel through both slits as a quantum superposition. The electron lives in the quantum world. We next fire photons at the electrons to jiggle them about. Some electrons will gain momentum from the impacts; others will lose momentum. The net result is a loss of coherence for the electron beam (decoherence), and destruction of the interference pattern. But isn’t this precisely how we detect electrons? The kind of detector we use to catch electrons in their flight, fires photons at the electrons and measures their deflection. But we have so far accepted the loss of interference as evidence of quantum measurement: collapse of the wave function. Yet it turns out that - at least in this situation - we do not need the collapse hypothesis to account for the phenomenon. Applying standard quantum mechanics principles to both the electrons and photons demonstrates that decoherence alone leads irrevocably to the loss of interference. With the loss of interference effects we have also lost the evidence for electrons going through both slits. For all practical purposes, the electrons now live in the classical world. It is as if a quantum measurement has taken place, but without the intervention of any Copenhagen-style observer. The environment (the photons) has effectively measured the quantum system.

It is important to note that the evidence for electron interference has not entirely vanished from the world. But where has it gone? It has in fact been carried off by the photons. If all of the photons that impacted the electrons were trapped and analysed then the evidence for interference would still be discernible. But it is virtually impossible to catch all of these photons and analyse them. The evidence for the electrons passing through both slits may still exist within the world, but for all practical purposes (or FAPP, as John Bell succinctly puts it), a quantum measurement has taken place and the quantum world is lost to the experimenter.

Wojciech Zurek working at the California Institute of Technology has proposed that the reason why the entire world appears classical to us is because of decoherence. Just as an electron beam may be bombarded with photons so any open system is continually bombarded with photons, electrons, atoms and other particles. The quantum system will inevitably become entangled with the fate of billions of particles in its environment and this entanglement will cause decoherence. Interference effects will be erased so that the world will appear classical. The environment will measure the quantum system.

In decoherence models, the environment need not be limited to the external environment but can include the internal environment of the quantum system – its degrees of freedom. Metal rods held at temperatures close to absolute zero, known as Weber bars, are used to detect gravity waves. The rigidity of Weber bars, combined with freezing temperatures, induces the atoms to vibrate in unison – coherently. In this state, the Weber bar can display quantum interference effects. However, if a bar is heated then the thermal motion of its atoms and molecules, jiggling and bumping about, randomises the phase of the atomic vibrations so that they no longer vibrate coherently: decoherence. Interference effects are no longer detectable. If the bar were made of more flexible material then the random motion of atoms and molecules within the bar, even at low temperatures, would similarly lead to decoherence. Decoherence is the same as with the electron beam but now it is the internal environment of the quantum system – rather than its interactions with an external environment - that is doing the jiggling. As with the electron beam, the interference effects have not vanished from the world. If any particle within the bar were examined then it would continue to attest to its ability to exist as a quantum superposition. It is only when we examine the entire bar that the interference effects cancel each other out. For all practical purposes, the interference effects have vanished and the bar behaves classically. However, once again it should be borne in mind that it is only the evidence for quantumness – the interference effects – that have vanished from the world. Individual particles still exist, as quantum superpositions; we just don’t see them. The quantum weirdness is hidden, but it is still there.

The key to decoherence is the involvement of an interaction between the quantum system and a complex environment. After the measurement, the environment must hold some kind of indelible record of the quantum event. The record could be carried off into space on the backs of photons; or it could be dissipated amongst a billion particles within the quantum system itself. But for decoherence to cause quantum measurement there must be some leakage of information into the environment.

Decoherence provides an explanation for why we never see the evidence for quantum superposition in big objects. An object as big as Schrödinger’s famous cat would rapidly fall prey to decoherence. Its atoms and molecules have billions of degrees of freedom that would interact with each other and with the external environment. The quantum superposition of both live and dead cat would be swiftly abolished by decoherence. Decoherence also explains why the thermodynamic processes we examined in Chapter 6 never display quantum effects. Steam engines and chemical engines that are driven by incoherent motion have billions of degree of freedom. The bumping and jiggling about of their atoms and molecules destroys interference affects and so causes decoherence. Most natural phenomena like the weather or the motions of the planets are also driven by incoherent motion and similarly fall prey to decoherence. Even self-organising structures such as convection flow, anticyclones or the Belousov-Zhabotinsky chemical reactions are, at the molecular level, driven by incoherent motion. Quantum effects are washed away by decoherence.

So does decoherence solve the measurement problem? Not entirely. For one thing, it does not strictly lead to the same result as quantum measurement, à la Copenhagen. If you remember, we earlier abbreviated quantum measurement in the two slit experiment to: y[{photon at RIGHT} (+/-) {photon at LEFT}] + Qmeasurement ® y[photon at RIGHT detected by right detector] or y[photon at LEFT not detected by right detector]. This correctly describes the situation that before a measurement the system was in a quantum superposition but after measurement, wave-function collapse forced the system to choose a single state. Decoherence generates an almost identical situation: y[{photon at RIGHT} (+/-) {photon at LEFT}] + Decoherence ® y[photon at RIGHT detected by right detector] and y[photon at LEFT not detected by right detector]. Just as with the wave-function collapse equation, the quantum mechanical, (+/-) term that gave rise to the interference effects has disappeared after decoherence.

The departure of the (+/-) interference term allows us to ignore the influence of quantum superposition, just as if a quantum measurement had taken place. The only difference between this and the standard wave function collapse is that decoherence leaves us with the two possible outcomes linked by and, rather than or. When a large number of electrons are fired through the screen in the two slit experiment, then we obtain what is termed a statistical mixture of states with some of the electron predicted to travel through the left slit and some of the electrons predicted to travel through the right slit. By allowing the environment to measure the quantum state, we have a perfect agreement between theory and experiment, but now entirely within the framework of the Schrödinger equation, without having to resort to any arbitrary wave-function collapse hypothesis.

The problem comes when we try to use decoherence to predict what happens to a single electron. The decoherence-reduced measurement equation gives us precisely the same answer as for an ensemble of electrons: y[photon at R detected by R detector] and y[photon at L not detected by R detector]. The interference terms are gone, which is fine. It is the remaining and, that is the problem. How can a single electron go through both the left and the right slit? This brings us back to the same thorny old problem of quantum superposition. If we try to measure the electron then we will find it inhabits only a single state. But the decoherence equation describes a measurement that includes both states. What has happened to the state that has been discarded?

Many physicists take the stance that quantum mechanics is solely about statistics; it has nothing to say about the fate of individual particles. Since these physicists often also claim that quantum mechanics encapsulates everything that can be said about the world, they often go on to claim that questions about individual particles are therefore meaningless. However, this is becoming increasingly untenable as experiments are beginning to probe the realm of single particles. Researchers in the advancing field of nanotechnology have already developed techniques for manipulating individual atoms to construct ultra-microcircuit boards. And of course (as we discovered in earlier chapters) living cells learned to manipulate single particles billions of years ago. The cells of those physicists, who deny the reality of events involving single particles are living proof of the absurdity of that claim.

Physicists who do worry about the problem, or have to deal with it, tend to look to the many-worlds interpretation for deliverance. When a single electron passes through two slits then the universe splits. If no attempt is made to discover the electron’s route then the two universes somehow inhabit the same space and the two particles interfere with one other. However, if you attempt to detect the electron path, then your measurement causes decoherence, the universes separate, and the electrons go their own way in separate universes. The universes no longer interact, eliminating interference. You can discover which universe you happen to inhabit by observing whether your electron went through the left or right slit.

It is generally assumed that the universe splitting coincides with decoherence, but this does not necessarily follow from the decoherence equations. Remember that decoherence destroys the evidence for quantum superpositions, the interference effects, not necessarily the superpositions itself. Superposition may persist beyond decoherence, but leave no trace (for all practical purposes). Finally, it should be remembered that decoherence is not exclusive to the many worlds interpretation. One could just as easily invoke a Copenhagen-style wave function collapse to eliminate the excess states that are left by decoherence.

Although the phenomenon of decoherence is certainly real and is one of the reasons why the world appears normal to us, it cannot be the only reason. Yet it does however give us a tool that we can use to find the border between the quantum and classical world. The next question we must address is: at what level within living cells does that border lie?’