The experiment with two holes
Faster than light
Solving the mysteries
Faster than light again
Uncertainty rules!
Molecules make waves
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Deepening the quantum mysteries

The "central mystery" of quantum physics just got more mysterious. Experimenters from the United States and Austria have got together to provide a new demonstration of how light going through a "double slit" experiment seems to know before it sets out in its journey exactly what kind of traps have been set for it along the way.

This is a variation on the Young's slit experiment, familiar from school laboratory demonstrations of the wave nature of light. When a beam of monochromatic light is shone through two narrow holes in a screen, the light spreading out from the two holes interferes, just like ripples interfering on the surface of a pond, to produce a characteristic pattern on a second screen.

The mystery is that light can also be described as a stream of particles, called photons. The light source in a Young's slit experiment can be turned down to the point where it consists of individual photons going through the experiment, one after the other. If the spots of light made by individual photons arriving at the second screen (actually a photoelectric detector) are added together, they still form an interference pattern, as if each photon goes through both holes and interferes with itself on the way through the experiment. It was Richard Feynman who described this as "the central mystery" of quantum theory, and then corrected himself, saying that in fact it is "the only mystery". If you understood this, you would understand quantum physics -- but as Feynman also said, "nobody understands quantum mechanics" (The Character of Physical Law, BBC Publications, 1965).

The new demonstration of how incomprehensible the quantum world is has been made by Raymond Chiao, of the University of California, Berkeley, Paul Kwiat, of the University of Innsbruck, and Aephraim Steinberg, of the US National Institute of Standards and Technology, in Maryland. Their results were presented at a meeting in Nathiagali, Pakistan.

In fact, the team has carried out several tests of the stranger predictions of quantum theory, but the most dramatic is what they call the "quantum eraser". In this variation on the Young's slit theme, the experiment is first set up in the usual way, and run to produce interference. Quantum theory says that the reason why interference can occur, even if light is a stream of photons, is that there is no way to find out, even in principle, which photon went through which slit. The "indeterminacy" allows fringes to appear.

But then Chiao and his colleagues ran the same experiment with polarising filters in front of each of the two slits. Any photon going one way would become "labelled" with left-handed circular polarization, while any photon going through the other slit is labelled with right-handed circular polarization. In this version of the experiment, it is possible in principle to tell which slit any particular photon arriving at the second screen went through. Sure enough, the interference pattern vanishes -- even though nobody ever actually looks to see which photon went through which slit.

Now comes the new trick -- the eraser. A third polarising filter is placed between the two slits and the second screen, to scramble up (or erase) the information about which photon went through which hole. Now, once again, it is impossible to tell which path any particular photon arriving at the second screen took through the experiment. And, sure enough, the interference pattern reappears!

The strange thing is that interference depends on "single photons" going through both slits "at once", but undetected. So how does a single photon arriving at the first screen know how it ought to behave in order to match the presence or absence of the erasing filter on the other side of the slits?

All of these experiments were carried out using beams of individual photons, and there is no way in which the results can be explained by using classical physics. They lay bare the mysteriousness of quantum mechanics in all its glory, and in particular demonstrate its "non local" nature -- the way in which a photon starting out on its journey behaves in a different way for each experimental setup, as if it knew in advance what kind of experiment it was about to go through.

Don't worry if you don't understand this. Richard Feynman didn't, and he warned "do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will go 'down the drain' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that."

More atoms that communicate faster than light

PHYSICISTS still struggling to come to terms with experiments which show instantaneous communication between quantum particles under special circumstances are now faced with another puzzle. Correcting a mistake made by Enrico Fermi more than sixty years ago, Gerhard Hegerfeldt, of the University of Gttingen, has shown that in theory any pair of atoms can communicate faster than light.

The now-familiar puzzle of what are called "non local" interactions develops from theoretical work by John Bell, of CERN, in the 1960s and experiments by Alain Aspect in Paris in the 1980s. Together, these show that a pair of photons ejected in opposite directions from an atom remain somehow entangled, as if they were one particle. Measuring the state of one of the photons instantaneously affects the state of the other one, wherever it may be. Now, it seems that even atoms which have never come into contact (from the perspective of classical Newtonian physics) are entangled in a similar way.

The calculation Fermi carried out in 1932, in the early days of quantum mechanics, concerned the response of one atom to radiation emitted by another atom of the same kind, some distance away. If the second atom is in an excited state, sooner or later it will emit radiation, falling back to its ground state. This radiation will have exactly the right frequency to excite the second atom (this is one of the principles underlying the way atoms are "pumped" into an excited state to make a laser).

Common sense tells us that the first atom cannot be excited until a finite time after the second atom decays -- until there has been time for radiation travelling at the speed of light to cross the gap. That is the result Fermi found. But it now turns out that he made a mistake in his calculation. Probably because the mistaken conclusion matched common sense, it took a long time for this to come to light. But Hegerfeldt's correct version of the calculation now makes it clear that there is a small chance that the first atom will be excited as soon as the second atom decays (Physical Review Letters, vol 72 p 596). As with all such quantum puzzles, this is only the beginning of the story; now, the experts have to explain what this mathematical result means. The best interpretation of the evidence so far seems to be that we should not think of any object, not even a single atom, as an "isolated system".

Because particles must also be considered as waves (one of the basic tenets of quantum mechanics), the individual particles in the atom are spread out, and there is a finite (though small) chance of finding them anywhere in the Universe. So the wave functions of the electrons in the first atom overlap with those of the electrons in the second atom. They are entangled, like the two photons produced in the Aspect experiment, and when an electron in one atom jumps down an energy level that can instantaneously make its counterpart in the other atom jump up by the same amount.

Solving the quantum mysteries

John Gribbin

For seventy years, physicists have worried about what quantum mechanics means. They can use quantum physics, to be sure; witness the successful designs of lasers and computer microchips, and the understanding of molecules that makes genetic engineering possible. But the equations that are a routine part of this kind of work contain one embarrassing feature. The say, according to the standard interpretation (the Copenhagen interpretation), that nothing is real unless you look at it, that an electron (say) exists only as a wave of probability, called a wave function, which collapses into reality when it is measured, and promptly dissolves into unreality when you stop looking at it. We are no further advanced philosophically, on this picture, than the image of the tree in the quad which disappears when nobody is looking at it.

In fact, few physicists worry about such things. Most of them prefer to ignore them, in the hope they will go away. But now there is another interpretation, which solves all of the quantum mysteries. The snag is, those physicists may not like this one, either, because it involves signals that travel backwards in time.

The archetypal example of the quantum mysteries is the "experiment with two holes", where the measured position of a single electron that passes through two holes in a screen can only be explained in terms of the wave function travelling through both holes at once and interfering with itself. But perhaps you've heard that one already, so here is a rather sideways look at the whole business of collapsing wave functions, a thought experiment which says that the lack of an observation can make the wave function of a system collapse. This wonderful example of the strangeness of the quantum world dates back to the early 1950s, and is known as "Renninger's negative- result experiment", after the German physicist Mauritius Renninger who first thought of it. It is one of the easiest examples of quantum strangeness to understand -- but not to explain.

Imagine that we have a source which will emit a single quantum particle in a random direction (ordinary radioactive nuclei do exactly this, so there is nothing special about the source). This source is in the middle of a large hollow sphere, and the inner surface of the sphere is lined with material that will give a flash at the point where the particle hits it. The accepted quantum description of what happens when the source emits a particle is that a quantum probability wave spreads out evenly in all directions around the source, since there is an equal probability for the particle being emitted in any direction. When the probability wave reaches the inner surface of the spherical shell, there is just one flash of light as the wave collapses to a single point. The particle is only "real" when it is being observed -- when it makes the flash of light -- not while it is travelling from the source to the sphere.

So far, simple enough. But now imagine that half way between the source and the sphere there is a hemispherical shield, which blocks off exactly half of the outer sphere from the field of view of the source. Like the outer sphere, this inner hemispherical shell is lined with scintillating material that will flash when it is struck by a particle from the source. Now what happens when the source emits a particle? We are not interested in exactly where on the outer or inner spheres the particle makes a flash of light, only in which of the two spheres it strikes. Either the particle strikes the inner sphere and makes it flash, or it strikes the outer sphere and makes it flash. There is an equal probability of either outcome of the experiment. Now, suppose that the source is once again triggered into emitting a particle. Once again, standard quantum theory describes this as an expanding spherical shell of probability, moving out evenly in all directions. We wait for a time longer than the time needed for it to reach the inner hemisphere, but too short for it to have reached the outer sphere, and see no flash on the inner sphere. So we know that the final state of the experiment will involve a flash on the outer sphere -- the particle must have been emitted in the wrong direction to strike the inner hemisphere. From a 50:50 probability of the flash occurring either on the hemisphere or on the outer sphere, the quantum wave function has collapsed into a 100 per cent certainty that the flash will occur on the outer sphere. But this has happened without the observer actually "observing" anything at all! It is purely a result of a change in the observer's knowledge about what is going on in the experiment. It requires an observer intelligent enough to infer what is happening, and what would have happened if the particle had been heading towards the inner hemisphere (so a cat, for example, clearly would not be intelligent enough to cause this particular collapse of a wave function). Under these circumstances, the absence of an observation can collapse the quantum wave function as effectively as an actual observation can. At least, so says the Copenhagen interpretation.

This central role for the observer -- not just any observer, but an intelligent observer -- lies at the heart of the standard Copenhagen interpretation of quantum mechanics.

But a giant leap in what might be called quantum philosophy has recently been taken by the American physicist John Cramer. He has taken a new look at the wave equations of quantum mechanics -- the famous Schrdinger equation, and the equations describing the probability waves, which travel, like photons, at the speed of light. What Cramer has pointed out is that the equations actually have two sets of solutions, one equivalent to a positive wave flowing into the future (a "retarded" wave), and the other describing a negative wave flowing into the past (an "advanced" wave). As all physicists learn at university (and most promptly forget) the full version of the wave equation has two sets of solutions -- one corresponding to the familiar simple Schrdinger equation, and the other to a kind of mirror image Schrdinger equation describing the flow of negative energy into the past.

The proper mathematical description of the wave function actually includes a mixture of both ordinary ("real") numbers and imaginary numbers -- those numbers involving i, the square root of minus one. Such a mixture is called a complex variable, for obvious reasons; it is written down as a real part plus (or minus) an imaginary part. The probability calculations needed to work out the chance of finding an electron (say) in a particular place at a particular time actually depend on calculating the square of the complex number corresponding to that particular state of the electron.

But calculating the square of a complex variable does not simply mean multiplying it by itself. Instead, you have to make another variable, a mirror image version called the complex conjugate, by changing the sign in front of the imaginary part -- if it was + it becomes -, and vice versa. The two complex numbers are then multiplied together to give the probability. For equations that describe how a system changes as time passes, this process of changing the sign of the imaginary part and finding the complex conjugate is equivalent to reversing the direction of time!

The basic probability equation, developed by Max Born back in 1926, itself contains an explicit reference to the nature of time, and to the possibility of two kinds of Schrdinger equations, one describing waves that move forward in time and the other representing waves that move backward in time.

The remarkable implication is that ever since 1926, every time a physicist has taken the complex conjugate of the simple Schrdinger equation and combined it with this equation to calculate a quantum probability, he or she has actually been taking account of the influence of waves that travel backwards in time, without knowing it. There is no problem at all with the mathematics of Cramer's interpretation of quantum mechanics, because the mathematics, right down to Schrdinger's equation, is exactly the same as in the standard Copenhagen interpretation. The difference is, literally, only in the interpretation -- Cramer accepts that the wave flowing backward in time is real, and should be taken seriously, not ignored. The way Cramer describes a typical quantum "transaction" is in terms of a particle "shaking hands" with another particle somewhere else in space and time. One of the difficulties with any such description in ordinary language is how to treat interactions that are going both ways in time simultaneously, and are therefore occurring instantaneously as far as clocks in the everyday world are concerned. Cramer does this by effectively standing outside of time, and using the semantic device of a description in terms of some kind of pseudotime. This is no more than a semantic device -- but it certainly helps to get the picture straight.

It works like this. When an electron vibrates, on this picture, it attempts to radiate by producing a field which is a time-symmetric mixture of a retarded wave propagating into the future and an advanced wave propagating into the past. As a first step in getting a picture of what happens, ignore the advanced wave and follow the story of the retarded wave. This heads off into the future until it encounters an electron which can absorb the energy being carried by the field. The process of absorption involves making the electron that is doing the absorbing vibrate, and this vibration produces a new retarded field which exactly cancels out the first retarded field. So in the future of the absorber, the net effect is that there is no retarded field. But the absorber also produces a negative energy advanced wave travelling backwards in time to the emitter, down the track of the original retarded wave. At the emitter, this advanced wave is absorbed, making the original electron recoil in such a way that it radiates a second advanced wave back into the past. This "new" advanced wave exactly cancels out the "original" advanced wave, so that there is no effective radiation going back in the past before the moment when the original emission occurred. All that is left is a double wave linking the emitter and the absorber, made up half of a retarded wave carrying positive energy into the future and half of an advanced wave carrying negative energy into the past (in the direction of negative time). Because two negatives make a positive, this advanced wave adds to the original retarded wave as if it too were a retarded wave travelling from the emitter to the absorber. In Cramer's words:

The emitter can be considered to produce an "offer" wave which travels to the absorber. The absorber then returns a "confirmation" wave to the emitter, and the transaction is completed with a "handshake" across spacetime.

But this is only the sequence of events from the point of view of pseudotime. In reality, the process is atemporal; it happens all at once. This is because, as Einstein explained with his special theory of relativity, signals that travel at the speed of light take no time at all to complete any journey -- in effect, for light signals every point in the Universe is next door to every other point in the Universe. Whether the signals are travelling backwards or forwards in time doesn't matter, since they take zero time (in their own frame of reference), and +0 is the same as -0 -- and all the quantum probability waves do travel at the speed of light.

The situation is more complicated in three dimensions, but the conclusions are exactly the same. This interpretation makes no predictions that are different from those of conventional quantum mechanics, but it provides a conceptual model which helps many people to think clearly about what is going on in the quantum world. It means that when an electron is faced with a choice of two holes to go through, the offer goes through both but the handshake only comes back through one, so it knows where to go; and in Renninger's experiment, the particle setting out from the radioactive nucleus has already made its handshake and knows which hemisphere it will end up on. There is no more mystery about the quantum mysteries at all -- provided you can live with waves that go backwards in time.

Photons faster than light

Nothing can travel faster than light -- unless it is a quantum particle "tunneling" through a barrier that, according to good old Newtonian physics, it should not be able to penetrate at all. Physicists have puzzled for decades over how long this mysterious tunneling process takes, but they need puzzle now longer, for it has been measured. And, sure enough, it takes place faster than light.

Quantum tunneling is of more than just esoteric interest. The phenomenon is related to quantum uncertainty, and to wave-particle duality. When two quantum particles, such as two protons, come close to one another, but do not actually touch, the uncertainty in their positions allows their quantum waves to overlap to some extent. As a result, they may "tunnel through" the gap between them, and interact. This is exactly what happens inside the Sun and stars -- protons which are kept at a distance from one another by the repulsion of their positive charge can still fuse together because of tunneling. And that nuclear fusion is what keeps the interior of the Sun hot, and makes its surface shine. Without tunneling, we would not be here.

Raymond Chaio, of the University of California, Berkeley, and his colleagues have actually been measuring a different, but related, kind of tunneling. They have devised an experiment in which two photons (particles of light) are produced simultaneously in a source, and travel on parallel paths. One photon goes straight to a detector; the other is confronted by a barrier which would reflect the light of the photons obeyed the laws of classical, "Newtonian" physics. But according to quantum theory there is a high probability that some of the photons arriving at the mirror will tunnel straight through, and go on their way to the detector.

Sure enough, that is what happens. The barrier is 1.1 micrometers thick, so anything travelling through it at the speed of light would take 3.6 femtoseconds (3.6 thousand million millionths of a second) on the journey. But the new experiment is so sophisticated that it can compare the arrival times of pairs of photons, one of which has gone past the barrier and one through it, and shows that the one which goes through the barrier arrives first. It tunnelled through the barrier faster than the speed of light, in less than 3.6 femtoseconds. As the researchers put it, "it is as though the particle 'skipped' the bulk of the barrier". But don't ask them, or anyone else, what it means -- in the words of Richard Feynman, "nobody understands quantum mechanics".

Uncertainty rules in the quantum world

IN SCENES reminiscent of the great debates between Niels Bohr and Albert Einstein in the 1930s, fundamental quantum physics has been tested in a series of new "thought experiments", and has passed those tests with flying colours.

The standard interpretation of quantum physics, known as the Copenhagen Interpretation, was established largely through the efforts of Bohr at the beginning of the 1930s. The strange features of the quantum world are founded on what Bohr dubbed complementarity -- the way an entity such as an electron can behave either as a wave or as a particle -- and on Werner Heisenberg's principle of uncertainty, which says that a quantum entity such as an electron does not possess both a position and a momentum simultaneously.

As Richard Feynman was fond of pointing out, the strangeness of the quantum world is encapsulated in "the experiment with two holes". If electrons (or photons, the "particles of light") are fired one at a time through a standard Young's double slit type of experiment and arrive at a detector screen on the other side, they leave the "gun" on one side of the experiment as particles, and arrive at the screen on the other side of the two slits as particles, each making a single spot on the screen. But somehow they pass through the two slits in between as waves, interfering with one another (even though they pass through one at a time!) so that the pattern built up on the screen by the accumulation of spots is an interference pattern.

This wave-particle duality is linked with the uncertainty principle. "Waviness" is a property associated with momentum -- a typical wave is spread out, so it has no definite location in space, but it does have a direction in which it is going. By contrast, a particle can have a precisely defined position. Heisenberg found that the quantum equations imply a strict tradeoff between the two complementary properties. If the position of a quantum entity is precisely defined (for example, when it hits a detector screen), its waviness is suppressed; but if it is allowed to give full expression to its wave nature, the particle aspect vanishes.

In practical terms, this means that we can never measure both momentum and position precisely, at the same time, for any particle. Einstein argued that this was simply a reflection of our clumsiness. Measuring the position of an electron, say, would involve bouncing light off it, and the very act of bouncing light off the electron would make it recoil, changing its momentum (and, indeed, its position). He thought that there were real little particles, like tiny billiard balls, involved in quantum interactions, and that the appearance of fuzziness and interference in experiments was a result of the deficiencies of the experiments.

Bohr argued that the fuzziness was an intrinsic feature of the quantum world, and that within the limits set by Heisenberg's uncertainty principle an electron itself does not "know" both where it is and where it is going. Over several years, beginning at the end of the 1920s, Einstein tried to dream up idealised thought experiments which could in principle measure both the position and the momentum of a particle such as an electron at the same time, thereby refuting Heisenberg. Each time, Bohr found a flaw in Einstein's argument, proving that the experiment could not work as Einstein had thought, even in principle. Bohr's success in this debate with Einstein was a major reason why the Copenhagen Interpretation became the established way of thinking about the quantum world. For sixty years, it seemed there was nothing to add to the debate. Then, in 1991 Marlan Scully, of the University of New Mexico, and colleagues claimed that they had found a way to carry out the kind of measurement Einstein had sought for in vain (Nature, vol 351 p 111). The essence of their argument (see Jim Baggott, "Beating the uncertainty principle", New Scientist, 15 February 1992) was that atoms could be sent through a double slit experiment in an excited state. Behind each slot there would be a detector known as a micromaser cavity, and the experiment would be timed so that each atom emitted a photon as it passed through the appropriate cavity. This would "switch on" one of the detectors, showing which slit the atom passed through, but would leave the atom free to carry on and make its mark on the final detector screen.

In such experiments without the cavities, atoms have been shown to behave like waves when passing through the two slits, creating an interference pattern. But if it is possible to detect which slit each atom passes through, without disturbing the flight of the atom, it would surely be impossible to produce interference. That requires something going through both slits at once. The presence of the cavities would make the interference pattern vanish, as if by magic, demonstrating the absurdity of the Copenhagen Interpretation. But now it seems that things are not that simple. Pippa Storey and colleagues at the University of Auckland have shown that even in this kind of idealised experiment that atoms are disturbed by the presence of the cavities, and in just the right way to "wash out" the interference pattern. They point out (Nature, vol 367 p 626) that although the ejection of a photon by the excited atom need not affect its forward momentum through the slit(s), there is always some uncertainty in the amount of sideways momentum imparted to the atom by the kick of the departing photon.

The situation is complicated by the prediction, in line with quantum uncertainty, that instead of a single photon being emitted cleanly from the atom, the atom can be involved in interactions with "virtual" photons, which emerge briefly from the vacuum (out of "nothing at all") before disappearing. But the conclusion is that provided the cavities are narrower than the separation between the two slits in the experiment (which they have to be if they are to tell us which slit each atom passes through), the interference pattern is destroyed. And the washing out of the interference pattern can even be understood by treating the atoms as waves. Interference can only occur if the waves passing through the two slits remain in phase, but "Because the atom's motion is primarily longitudinal," say the New Zealand team, "a transverse momentum kick will simply change its direction slightly . . . the displacement . . . is effectively the familiar phenomenon of refraction: a position-dependent change in the phase of a wave results in a change in the direction of propagation". The loss of interference from a double slit in the presence of cavity detectors is caused by momentum kicks, which are themselves of a size determined by the uncertainty principle. Einstein, no doubt, would have taken this as philosophically (if unbelievingly) as he took his other setbacks; but the ghosts of Bohr and Heisenberg must be smiling.

Molecules make quantum waves

THE WEIRDNESS of the quantum world has taken another step towards the everyday world as a result of experiments which show iodine molecules behaving as waves in interference experiments. This brings properties often regarded as unique to subatomic particles out into the open on much larger scales.

It is a fundamental feature of quantum mechanics that entities described by the quantum equations are not simply particles or waves, but exhibit a mixture of wave and particle properties. Light, for example, will behave as a wave in interference experiments, with two sets of waves interacting with one another to form a new pattern, just as ripples on a pond (or in your bath) interact with one another. On the other hand, in other experiments light will behave as a stream of tiny particles, called photons.

Wave-particle duality was first discovered to be a feature of light in the early part of this century (Albert Einstein's Nobel Prize was awarded for his proof that photons exist). In the 1920s, researchers found that electrons, traditionally regarded as particles, could behave as waves in experiments where an electron beam is diffracted from a crystal lattice -- indeed, in one of the nicest examples of wave- particle duality, the physicist J. J. Thomson {ED: NB always "J J", never referred to by name} received a Nobel Prize for discovering that the electron is a particle, while his son George received a Nobel Prize for proving that the electron is a wave.

Moving up the mass scale, first neutrons (each nearly 2,000 times the mass of an electron) and then beams of atoms and molecules were shown to diffract like waves when passed through small apertures. Over the past ten years or so, the wave-particle duality has been demonstrated ever more clearly. Not just diffraction (in which one beam, or wave, bends as it passes an obstruction) but interference (in which two beams or waves interact with one another) has been demonstrated both for electrons and atoms. Now, a team of researchers at the University of Paris-North, at Villetaneuse in France, has done the trick with molecules.

In the traditional version of the interference experiment with light, two beams of light are generated by passing light from a single source through two slits in a screen. Then, the two beams are allowed to interfere, producing a characteristic stripey pattern of light and shade. The new experiment is conceptually similar, but instead of passing through holes in a screen the iodine molecules (I2, which each have a mass about 254 times that of a neutron) interact with laser beams. The first interaction, with a pair of laser beams, puts each molecule into what is known as a "superposition of states", effectively two wave packets marching side by side. A second pair of laser beams recombines the wave packets to make "particles". At least, that is the theory. What happens in practice? After they have passed through the laser beams, the iodine molecules arrive at a detector. The distribution of the molecules arriving at the detector does not resemble the pattern you would expect if they were a stream of particles travelling through the experiment, but exactly matches the stripey pattern of peaks and troughs corresponding to interference by waves (Physics Letters A, vol 188 p 187). These are the heaviest "particles" which have ever demonstrated their wave "character" directly in experiments.

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