Watching the Quantum Pot

Watching the quantum pot

How do particles of matter, including atoms, behave? We
have learned from quantum physics that in some sense they do not really exist, as
particles, when nobody is looking at them — when no experiment is
making a measurement of their position or other properties. Quantum
entities exist as a so-called superposition of states unless something from
outside causes the probabilistic wave function to collapse. But
what happens if we keep watching the particle, all the time? In
this modern version of the kind of paradox made famous by the Greek
philosopher Zeno of Elea, who lived in the fifth century BC, a
watched atom can never change its quantum state, as long as it is
being watched. Even if you prepare the atom in some unstable,
excited high energy state, if you keep watching it the atom will stay in that state forever, trembling on the brink, but only able to jump down to a more stable
lower energy state when nobody is looking. The idea, which is a
natural corollary to the idea that an unwatched quantum entity does
not exist as a “particle”, had been around since the late 1970s. A
watched quantum pot, theory says, never boils. And experiments first made
at the beginning of the 1990s bear this out.
Zeno demonstrated that everyday ideas about the nature of time and
motion must be wrong, by presenting a series of paradoxes which
“prove” the impossible. In one example, an arrow is fired after a
running deer. Because the arrow cannot be in two places at once,
said Zeno, at every moment of time it must be at some definite place
in the air between the archer and the deer. But if the arrow is at
a single definite place, it is not moving. And if the arrow is not
moving, it will never reach the deer.
When we are dealing with arrows and deer, there is no doubt
that Zeno’s conclusion is wrong. Of course, Zeno knew that. The
question he highlighted with the aid of this “paradox” was, why is
it wrong? The puzzle can be resolved by using the mathematical
techniques of calculus, which describe not only the position of the
arrow at any moment, but also the way in which the position is
changing at that instant. At another level, quantum ideas tell us
that it is impossible to know the precise position and precise
velocity of the arrow at any moment (indeed, they tell us that there
is no such thing as a precise moment, since time itself is subject
to uncertainty), blurring the edges of the argument and allowing the
arrow to continue its flight. But the equivalent of Zeno’s argument‹`‹
about the arrow really does apply to a “pot” of a few thousand ions
of beryllium.
An ion is simply an atom from which one or more electrons has
been stripped off. This leaves the ion with an overall positive
electric charge, which makes it possible to get hold of the ions
with electric fields and keep them in one place in a kind of
electric trap — the pot. Researchers at the US National Institute
of Standards and Technology, in Boulder, Colorado, found a way to
make the pot of beryllium ions boil, and to watch it while it was
boiling — which stopped the boiling.
At the start of the experiment, the ions were all in the same
quantum energy state, which the team called Level 1. By applying a
burst of radio waves with a particular frequency to the ions for
exactly 256 milliseconds, they could make all of the ions move up to
a higher energy state, called Level 2. This was the equivalent of
the pot boiling. But how and when do the ions actually make the
transition from one quantum state to the other? Remember that they
only ever decide which state they are in when the state is measured
— when somebody takes a look at the ions.
Quantum theory tells us that the transition is not an all or
nothing affair. The particular time interval in this experiment,
256 milliseconds, was chosen because for this particular system that
is the characteristic time after which there is an almost exact 100
per cent probability that an individual ion will have made the
transition to Level 2. Other quantum systems have different
characteristic times (the half-life of radioactive atoms is a
related concept, but the analogy with radioactive half-life is not exact, because
in this case the transition is being “pumped” from outside by the
radio waves, which is why îallï the ions make the transition in just
256 milliseconds, but the overall pattern of behaviour is the same).
In this case, after 128 millisecond (the “half-life” of the
transition‚ there is an equal probability that an individual ion
has made the transition and that it is still in Level 1. It is in a
superposition of states. The probability gradually changes over the
256 milliseconds, from 100 per cent Level 1 to 100 per cent Level 2,
and at any in between times the ion is in an appropriate
superposition of states, with the appropriate mixture of
probabilities. But when it is observed, a quantum system must
always be in one definite state or another; we can never “see” a
mixture of states.
If we could look at the ions halfway through the 256
milliseconds, theory says that they would be forced to choose
between the two possible states, just as Schrödinger’s cat has to
“decide” whether it is dead or alive when we look into its box.
With equal probabilities, half the ions would go one way and half
the other. Unlike the cat in the box experiment, however, this
theoretical prediction has actually been tested by experiment.
The NIST team developed a neat technique for looking at the
ions while they were making up their minds about which state to be
in. The team did this by shooting a very brief flicker of laser
light into the quantum pot. The energy of the laser beam was
matched to the energy of the ions in the pot, in such a way that it
would leave ions in Level 2 unaffected, but would bounce ions in
Level 1 up to a higher energy state, Level 3, from which they
immediately (in much less than a millisecond) bounced back to Level
1. As they bounced back, these excited ions emitted characteristic
photons, which could be detected and counted. The number of photons
told the researchers how many ions were in Level 1 when the laser
pulse hit them.
Sure enough, if the ions were “looked at” by the laser pulse
after 128 milliseconds, just half of them were found in Level 1.
But if the experimenters “peeked” four times during the 256
milliseconds, at equal intervals, at the end of the experiment two
thirds of the ions were still in Level 1. And if they peeked 64
times (once every 4 milliseconds), almost all of the ions were still
in Level 1. Even though the radio waves had been doing their best
to warm the ions up, the watched quantum pot had refused to boil.
The reason is that after only 4 milliseconds the probability
that an individual ion will have made the transition to Level 2 is
only about 0.01 per cent. The probability wave associated with the
ion has already spread out, but it is still mostly concentrated
around the state corresponding to Level 1. So, naturally, the laser
peeking at the ions finds that 99.99 per cent are still in Level 1.
But it has done more than that. The act of looking at the ion has
forced it to choose a quantum state, so it is now once again purely
in Level 1. The quantum probability wave starts to spread out
again, but after another 4 milliseconds another peek forces it to
collapse back into the state corresponding to Level 1. The wave
never gets a chance to spread far before another peek forces it back
into Level 1, and at the end of the experiment the ions have had no
opportunity to make the change to Level 2 without being observed.
In this experiment, there is still a tiny probability that an
ion can make the transition in the 4 millisecond gap when it is not
being observed, but only one ion in ten thousand will do so; the
very close agreement between the results of the NIST experiment and
the predictions of quantum theory show, however, that if it were
possible to monitor the ions all the time then none of them would
ever change. If, as quantum theory suggests, the world only exists
because it is being observed, then it is also true that the world
only changes because it is not being observed all the time.
This casts an intriguing sidelight on the old philosophical
question of whether or not a tree is really there when nobody is
looking at it. One of the traditional arguments in favour of the
continuing reality of the tree was that even when no human observer
was looking at it, God was keeping watch; but on the latest
evidence, in order for the tree to grow and change even God must
blink, and rather rapidly!
So we can “see” ions frozen into a fixed quantum state by
watching them all the time.

Adapted from my book Schrödinger’s Kittens; for an update see my Kindle single The Time Illusion.

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My latest for the Literary Review

The Last Man Who Knew Everything: The Life and Times of Enrico Fermi, Father of the Nuclear Age

By David N Schwartz

(Basic Books 453pp £26.99)

 

In spite of its title, this is not another book about Thomas Young, the subject of Andrew Robinson’s The Last Man Who Knew Everything (2006). If anyone deserves that description, it is indeed Young, a linguist, classical scholar, translator of the Rosetta Stone, medical doctor and pioneering scientist at a time when scientists were very much generalists. The subject of David Schwartz’s book, Enrico Fermi (1901–54), might more accurately be described as the last man who knew nearly everything about physics, but that wouldn’t make such a catchy title.

Fermi’s name tends to crop up these days in connection with the Fermi paradox, his suggestion that if intelligent life exists elsewhere in the universe we ought to have been visited by now. This argument is more forceful than ever nowadays, in the light of the recent discovery of more planets than you can shake a stick at, but it gets disappointingly little attention from Schwartz. To historians, Fermi is better known as a pioneering nuclear physicist, responsible for the construction of the first controllable nuclear reactor (called an ‘atomic pile’ at the time) and for his contribution to the Manhattan Project. All this gets disappointingly too much attention from Schwartz, who goes into tedious detail. His background is in political science, and it shows.

One reason for this is spelled out in the author’s preface. There are no personal diaries to draw on and few personal letters in the archives. ‘One searches in vain for anything intimate,’ Schwartz says. So the biographer has to fall back on discussing the physics. Unfortunately, although his father was a Nobel Prize-winning physicist, Schwartz is in his own words ‘not a physicist’.

The worst of several infelicities occurs when Schwartz is describing Fermi’s most important contribution to theoretical nuclear physics: the suggestion that there is a force of nature, now known as the weak interaction, that is involved in the process of radioactive decay. He tells us that it gets its name ‘because it takes effect only when particles come into extremely close range of each other’. This is nonsense. Its weakness has nothing to do with its range. Indeed, another short-range force, known as the strong interaction, is the strongest of all the forces of nature, and the weakest force, gravity, has the longest range.

Fermi was also one of the discoverers – or inventors – of Fermi-Dirac statistics, which describe the behaviour of such particles as electrons, protons and neutrons (collectively known as fermions). Unusually for his time, he was a first-class experimenter as well as a first-class theorist. This was probably a factor in his early death. In the 1930s, Fermi briefly headed a world-leading group of nuclear physicists in Rome, before political events led it to break up. In one series of experiments, target materials had to be bombarded with neutrons to make them radioactive, then carried down a corridor for their radioactivity to be measured by apparatus kept in an area separate from the neutron source. Running down this corridor clutching the samples to his body, Fermi was repeatedly exposed to radiation. In 1954, at the age of fifty-three, he died of a heart attack, his body ravaged by cancer.

By 1938, Fermi, whose wife was Jewish, knew that it was time to leave Italy and move to America. Before departing, however, he received a unique enquiry. He was asked whether he would be able to accept the Nobel Prize in Physics if it were offered to him. Schwartz is on much surer ground in explaining the intriguing background to this approach, the only example of a recipient being approached in advance by the Nobel Committee. The Swedish Academy was concerned that, were Fermi to be awarded the prize, Mussolini might follow the lead of Hitler, who had been angry when Carl von Ossietzky received the Nobel Peace Prize in 1936 for revealing German rearmament the previous year and forbade any German from accepting an award from the Nobel Committee. There was also the question of how Italian currency restrictions might affect the prize money. Nevertheless, Fermi accepted the accolade. Following the ceremony in Stockholm, the Fermis went on to America with their prize money, equivalent to more than $500,000 today, which certainly eased the transition. And there he was roped into developing nuclear weapons technology, in spite of being, after December 1941, an enemy alien.

It was in the context of his work on the first atomic pile that Fermi famously remarked to a colleague that he could ‘calculate almost anything to an accuracy of ten per cent in less than a day, but to improve the accuracy by a factor of three might take him six months’. He applied a similar approach in his private life, where he enjoyed doing odd jobs and was happy as long as the end products worked, however they appeared. ‘Never make something more accurate than absolutely necessary,’ he once told his daughter.

This tiny glimpse into his mind exacerbates the frustration caused by the lack of more insights of this kind. Schwartz has probably done as good a job as possible with the available material about one of the most important scientists of the 20th century. But it is a pity he did not have the draft read by a physicist, who might have picked up the howlers. A special place in hell should, though, be reserved for the publicist, who tells us that the book ‘lays bare the colourful life and personality’ of Fermi. The author is at pains to point out that this is not the case, so clearly the publicist has not read even the preface. The Last Man Who Knew Everything is well worth reading, but not if you are looking for colour and personality.