When I was in high school one of my favorite books was “Alice in Quantumland”, by Robert Gilmore.  In it, Alice is magically shrunk down to the size of an atom, and into a world where she can experience quantum mechanical effects as atoms do – she sees friendly electrons banging against brick walls again and again, until they mysteriously appear on the other side (tunneling).  She is able to hang out with the electrons, even though they’re all exactly the same and only two of them can ever sit together on the train.  I was totally engrossed in the book, in following Alice and playing in her quantum world.

While we can see many manifestations of the quantum world in our macroscopic one, in phenomena ranging from the spectra of atoms to superfluidity, we really can’t see quantum mechanics the way Alice got to.  We don’t grow fuzzier when we try to figure out too precisely how fast we’re moving, and we can’t travel multiple paths at once (until we’re observed somewhere).  But as far as we know quantum mechanics also occurs on the macroscale: it’s just that many of its effects are hard to measure or difficult to understand.  If this is not the case, then scientists will have some very interesting fundamental questions about the laws of physics, about where and when quantum mechanics ceases to apply.  However, for the moment it is plausible that we simply can not measure the effects of quantum mechanics on the macroscale because they are simply too small.  For example, every particle can also be thought of as a wave with a special wavelength, called the de Broglie wavelength.  For a tennis ball weighing 10 g moving at a velocity of 10 meters per second, this turns out to be 10^-34 m.  That’s a millionth of a billionth the diameter of a proton.  Which is pretty small.  So it’s no wonder we don’t tend to think of a moving tennis ball as having many wavelike properties, even though theoretically, it does.

After leaving the tennis court, imagine that you find a swing set. You can swing as high or low as you like (until you go too high and swing around the bar!). You can even stop swinging and wander away, and the swing will eventually come to a rest. Common sense, right? Not in  quantumland. When Alice gets on a swing, she can only make her swing go to certain heights, and she can’t ever stop it. Even if you got rid of the wind, and the effect of vibrations of trucks on the road and the effect of tiny earthquakes and so on, it is still impossible for that swing to stop moving completely, due to the Heisenberg Uncertainty Principle (the same principle that meant Alice got really fuzzy when she knew how fast she was going).  According to the principles of quantum mechanics, energy is not continuous but can only take on discrete values.  In the case of the swing, the minimum energy allowed is not in fact zero – this minimum energy is known as the zero point energy.  A system moving with its zero point energy is said to be in its ground state.  As far as we know, for a swing of normal dimensions the energy levels are so close together that what we see is an effective continuum of allowed swing heights, as any child could tell you, although possibly not in those words.  And you can stop the swing.

Scientists are now trying to observe macroscopic systems at this zero point energy.The first difficulty with this is that at normal temperatures any mechanical resonator will be excited far above its ground state by thermal (heat) noise.Thus if we want to enter quantumland, it will have to be very very cold. Recently, scientists at the laser wave gravitational interferometer (LIGO) have shown that it should theoretically be possible, with their current technology, to observe 8 kg masses in their ground state. LIGO is a huge experiment funded mostly by the National Science Foundation. Its goal is to detect gravitational waves, and thereby to open a new window for us into space using gravitational radiation instead of electromagnetic radiation (light, radio waves, x-rays etc.). By measuring tiny motions of test masses caused by passing gravitational waves, LIGO expects to directly detect this radiation. Gravitational radiation is given off by any accelerating mass, and should be detectable from enormous astronomical events such as supernovae.  The test masses are suspended, like pendulums (or even swings!) to isolate them from noise. This is relevant to our Alice because in order to measure the tiny oscillations (swings of the pendulums) that will be caused by the gravitational waves (around 10^-18 m, or the diameter of a proton), LIGO cools its test masses, which weigh 8 kg, to an effective temperature of 1.4 μK. This is within 200 quanta of the quantum limit, and in theory could be extended even further.

The detection of quantum effects is in itself an especially difficult problem, even theoretically.  Devising an experiment that can detect quantum mechanical behavior of relatively large objects without those effects being interfered with or even destroyed by the experiment itself is a huge challenge for scientists. Many scientists have been attempting to reach the ground state of micro- and nano- resonator systems.  The resonators range from tiny cantilevers, much like miniature diving boards vibrating after a diver jumps off, to tiny spheres that resonate a bit like a bell when struck.  Although the mechanical resonators the scientists are working on are not macroscopic, they are far from the atomic scale at which quantum effects are normally observed. Recently a nano-mechanical resonator a bit like a tiny guitar string was cooled to such a low temperature that the probability that it is in the quantum ground state, i.e. at its zero point energy, is 0.21 (21 %).

So far, although scientists have gotten close using a variety of methods, they haven’t quite made it yet.  But when they do, their observations and technological advances will open doors into an unexplored territory.  What else will we see when we visit quantumland? One of the most striking feature of quantum mechanics is the existence of superposition states, where an object appears to be in different situations, or places, at the same time. In order to see these states however, the object must be near its ground state, Already scientists are thinking up experiments to try to observe these superpositions in mechanical and living systems.  Will we, as conjectured, see resonators in two places at once (or like Schrodinger’s cat, both alive and dead)?  Scientists are following the white rabbit into quantumland, and who knows what they’ll find.

References

1. Putting Mechanics into Quantum Mechanics, K. Schwab, Physics Today, Volume 58, Issue 7, pp. 36-42 (2005)













2. Preparation and Detection of a Mechanical Resonator Near the Ground State of Motion,  Rocheleau et al., arXiv:0907.3313













3. Nanomechanical measurements of a superconducting qubit, M. Rourkes et al., Nature
   459, 960-964 (18 June 2009)













4. Entangled mechanical oscillators, J.D. Jost, Nature
   459, 683-685 (4 June 2009)













5. Towards Quantum Superposition of Living Organisms, O. Romero-Isart et al, arXiv:0909.1469v2













6. Alice in Quantumland: An allegory of Quantum Mechanics, Robert Gilmore, Springer (1995)