Penrose, however, thinks differently. “There has to be give on both sides,” he told me. “It’s not as though one wins over the other; it’s got to be an even-handed marriage.” And that union, said Penrose, means fixing what he thinks is wrong with quantum mechanics. “The trouble with quantum mechanics [is that] . . . it doesn’t really make sense,” he said.
He paused before continuing. “I shouldn’t appeal to authority here, you see,” he said. “You’ve got authorities on both sides.” Still, he pointed out that Einstein, Schrödinger, de Broglie, and even Dirac to an extent had all felt that something was not quite right with quantum mechanics. Schrödinger magnified his unease with his eponymous cat—a thought experiment that’s a clear affront to our classical sensibilities.
To illustrate the absurdity, Penrose has his own version of Schrödinger’s cat, a “more humane version,” he quipped. The cat is in one room and is confronted with two doors that lead to another room. The mechanism that opens one or the other door is quantum mechanical. Penrose imagines a photon going through a beam splitter—if it’s reflected it opens the left door; if it’s transmitted it opens the right door. This results in the system being in a superposition of “left door open, right door closed” and “right door open, left door closed.” If the cat goes through either door, it gets some food, but unlike the double-slit experiment, where the particle enters a superposition of going through both slits simultaneously, our classical sensibility says that the cat cannot go through both doors at once. But “quantum mechanically, you’d have to consider that both alternatives coexist in order to get the right answer,” said Penrose.
Treating the cat quantum mechanically leads to the wavefunction of the cat going through both doors in a kind of superposition of motions. According to the Copenhagen interpretation, some interaction with a classical system that can be considered an act of measurement, such as a CCTV camera recording the cat’s entry, would then collapse the wavefunction and show the cat going through one or the other door. As with most physicists who have trouble with quantum mechanics, Penrose finds the idea that measurement is necessary to collapse the wavefunction implausible.
One way out of this mess is if there is a clear divide between the quantum and the classical—and so the cat is always a classical object and cannot be treated quantum mechanically. Penrose has had a radical idea for decades that such a divide exists and it comes about because of the spontaneous collapse of the wavefunction without necessitating a measurement, explaining why an object as large as a superposed cat would remain in a superposition for only a small, small fraction of a second before collapsing into one classical state. In the case of Schrödinger’s cat, Penrose’s theory could cause a collapse of the total system, so the cat would be either dead or alive almost instantly.
The solution involves gravity and makes rough predictions about where we might find the classical-quantum boundary. “You have got to look not at the impact that quantum mechanics has on gravity, but the impact gravity has on quantum mechanics,” he said.
On that rather nippy English afternoon, sitting at a wooden table on a deck in his backyard, Penrose took off his glasses and placed them on the table. Glasses have mass, and according to general relativity, they will warp or curve spacetime in their vicinity. Gravity is the curvature of spacetime: the more massive the object, the greater the curvature (black holes really put a dent in spacetime, a pair of glasses, not so much). But if the glasses were in a superposition of being in two places—Penrose moved them back and forth for his show-and-tell—then the glasses at one location would warp spacetime one way, and another way at the second location. “Now, therefore, you have a superposition [of] two slightly different spacetimes,” he said. And that, said Penrose, is an unstable situation that destroys the superposition rapidly if the mass displacement is large.
Say you have an experiment in which you have put a little lump of material in a superposition of being in two different places, said Penrose. “I’d claim that the superposition will spontaneously become one or the other in a timescale which you can calculate, roughly.”
According to Penrose, a superposition of two spacetimes creates what he calls a “blister” in the four-dimensional volume of spacetime. When that blister grows to one Planck unit in four dimensions, where three of those are space dimensions (one Planck length equals about 10-35 meters) and one is the dimension of time (one Planck time is of the order of 10-43 seconds), the superposition will spontaneously collapse to one state or the other.
For his pair of glasses, such a blister in spacetime would form in far less than one Planck time. “It’d be instantaneous,” said Penrose. That is why we never see macroscopic objects in a superposition of states, whereas for subatomic particles, such a spacetime blister would take practically forever to resolve itself into one side or the other. “It could be about the age of the universe.”
Penrose has another way of thinking what happens when two spacetime configurations are in superposition. Take his glasses again. They have a property called gravitational self-energy, which is the energy required to hold the system together if there were no other forces, in a configuration resembling a pair of glasses. This is, of course, true of all matter, not just Penrose’s glasses. Now, if the glasses are in a superposition of being in two places, then there’s an uncertainty about the gravitational self-energy of the system. Penrose then resorts to one of Heisenberg’s uncertainty relations, to do with simultaneous measurements of energy and an interval of time: the more precisely you know the energy of a system, the less sure you are of the time interval, and vice versa. By applying this uncertainty relation to the uncertainty in the gravitational self-energy of the system in superposition, Penrose estimates the time interval for which the superposition can be stable before collapsing to one or the other state. Admitting to a bit of “hand-waving,” Penrose said, “I can’t say when it’ll happen and I can’t say which it’ll do, but I can give you an estimate.”
As convinced as Penrose is of his idea that gravity must play a role in the collapse of the wavefunction, the response from physicists and philosophers probing the foundations of quantum mechanics has been tepid. It’s probably because he’s proposing modifying quantum mechanics—particularly the way the wavefunction evolves according to the rules of the Schrödinger equation. The gravitationally induced collapse of the wavefunction messes up this rather beautiful picture. But then it does provide an explanation for why there exists a boundary between the quantum and the classical.
John Bell always found this boundary, unspecified but implicit in the Copenhagen interpretation, very troubling. After all, even a so-called classical measurement apparatus consists of atoms and molecules, each of which on its own is regarded as quantum mechanical, but an agglomeration of an unspecified number of atoms and molecules has to be at some point regarded as a classical object. Bell objected to what he called a “ shifty split” between the two worlds. Penrose’s work, while it messes with the elegant evolution of the wavefunction, gives a reason for why this split might exist in the first place.
Penrose is puzzled by people’s objections to modifying quantum mechanics. He points out that Newtonian mechanics lasted a lot longer than quantum mechanics has. “People were pretty convinced that that was a picture that was going to stick forever,” said Penrose. Yet it didn’t. And that too despite not suffering from any measurement paradox. “So I don’t see why people are so completely convinced by [quantum mechanics].”
Gravity-induced collapse of the wavefunction can be seen as one example of a more generalized solution to the measurement problem. In 1986, around the same time that Penrose and others, including most prominently the Hungarian physicist Lajos Diósi (who came to these ideas a touch earlier than Penrose), were formulating ideas about gravity’s role, three physicists, Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber, came up with another way of modifying quantum mechanics.
GRW, as the theory is called, changes the way the wave
functions of particles evolve. Rather than being completely governed by the Schrödinger equation, GRW adds a component to the dynamics of the wavefunction that causes it to collapse at random. But the collapse is not induced by gravity, à la Diósi-Penrose, or by a measurement, as in the Copenhagen interpretation. Rather, it is something spontaneous, and an elemental aspect of nature. It causes the wavefunction of a particle to go from being spread out to being relatively localized. Mathematically, the diffuse wavefunction, which says that the particle can be in many different locations at once, is multiplied by another function. Think of this function as something that is mostly zero at all physical locations but at one location rapidly rises to a certain peak. The net result of this multiplication is to collapse the wavefunction, leaving the particle roughly localized at one point in space and time.
To mimic the predictions of quantum mechanics, GRW has to ensure two things. One, that such spontaneous collapses are extremely rare for individual particles, so that they can remain in superposition of states for any measurable length of time. Two, that for a large collection of particles, say, those that make up a cat, the collapse of the wavefunction is near certain, so that the cat is always found in some macroscopically identifiable state and not in a superposition. In their earliest versions of the theory, GRW showed how to set up the theory so that it could take almost 100 million years for a single particle to collapse, whereas a macroscopic object with about 1020 particles would collapse almost instantly (a few tens of nanoseconds or less, but estimates vary).
As always with modifications to quantum mechanics, people found flaws with the GRW model, which others tried fixing with further tweaks. For example, the GRW model doesn’t deal well with a large collection of particles with identical properties (say a bunch of electrons, which cannot be distinguished from one another). Another version of spontaneous collapse fixes this problem. And of course, the parameters of the GRW model can themselves be fine-tuned in an ad hoc manner to suit the outcome of experiments—something that bothers naysayers. Nonetheless, the basic idea behind all these models is still the same: a spontaneous collapse of the wavefunction that has nothing whatsoever to do with measurement. “The collapse is something that is occurring all the time to every particle, at random, with a certain fixed probability per unit time,” said philosopher David Albert, who has a soft spot for the GRW theory. “There is no need to talk about measurements, or anything like that. There is no need to use any of these words.”
Even John Bell was suitably impressed when he first encountered the theory. “ Any embarrassing macroscopic ambiguity in the usual theory is only momentary in the GRW theory. The cat is not both dead and alive for more than a split second,” he wrote.
More important for Bell, collapse theories had the mathematics to back up claims of collapse. He said they “ have a certain kind of goodness . . . They are honest attempts to replace the woolly words by real mathematical equations—equations which you don’t have to talk away—equations which you simply calculate with and take the results seriously.”
Some experimentalists are doing exactly that. Whether it’s Penrose’s theory or GRW-like theories, they all make potentially testable predictions about where the boundary between the quantum and the classical might lie. And even though the predicted boundary seems out of reach of today’s experiments, it’s not stopping Markus Arndt, an experimentalist in Vienna, from looking for it. He’s doing that by sending larger and larger molecules (not just photons or electrons or atoms) through some complicated versions of the double slit and making them interfere. The day he can conclusively claim that molecules of a certain size don’t interfere because of their size—meaning they can’t remain in a coherent superposition of simultaneously taking two paths—he will have found nature’s dividing line. For now, he’s happy claiming that his team has worked with the biggest “Schrödinger’s cat” ever to confront two doors at once.
—
Schrödinger’s cat has become code for a macroscopic object that can remain in a superposition of multiple states. For Arndt, the molecules he works with are such objects. While they are certainly nowhere near as big as even the smallest possible cat, with the mass of 10,000 protons, they are the largest macroscopic objects that have thus far been seen in superposition going through a double slit. “I am claiming that we have the biggest Schrödinger cat,” Arndt told me, tongue in cheek. To count as Schrödinger’s cat, a quantum system should be “something that should be really macroscopic; it should be at least as warm as a cat and it should contain a biomolecule.” The objects that Arndt has put into superposition are certainly macroscopic, and they contain biomolecules. But unlike a cat that’s at room temperature, for experimental reasons, Arndt’s molecules are much hotter. “A real cat would be dead by then,” he quipped.
Arndt’s interest in such experiments began when he was a postdoc with Jean Dalibard at the École Normale Supérieure in Paris (Dalibard, as a student in the 1980s, had worked with Alain Aspect on tests of Bell’s inequality, but then did seminal work on his own, particularly on trapping atoms in place using lasers and magnetic fields). The Paris team demonstrated the validity of de Broglie’s ideas of matter-wave duality, using cesium atoms.
Arndt continued his postdoc phase with Anton Zeilinger, first in Innsbruck, Austria, and then moved with Zeilinger to the University of Vienna, and now runs his own labs on Boltzmanngasse. Among the many experiments Arndt’s group is doing, one with particular relevance to questions about the foundations of quantum mechanics has to do with molecular interferometry: doing advanced variants of the double-slit experiment with large molecules and nanoparticles. Zeilinger, in his early days, had been part of a team that demonstrated a double-slit experiment with single neutrons, the most massive particle to be tested in the 1970s. Soon physicists began showing that atoms could be placed in superposition of states and made to interfere. In 1991, Jürgen Mlynek and colleagues in Konstanz, Germany, sent helium atoms through two 1-micrometer-wide slits, about 8 micrometers apart, and saw the atoms interfere. (The history of atom interferometry is rich. Other prominent names include David Pritchard at MIT, who showed in 1983 that atoms could be diffracted at gratings, and Fujio Shimizu at the University of Tokyo, who reported in 1992 a double-slit experiment done with neon atoms.) Since then, it has become a race of sorts, with the attention shifting to molecules, to see who can bell the biggest Schrödinger’s cat.
The key issue with getting molecules to interfere is to ensure that they don’t hit any stray particles during the experiment. If a molecule interacts with a photon, or an electron, or an air molecule, the molecule being tested gets entangled with the environment. What starts off in a state of coherence undergoes decoherence. “In such a setting, I cannot detect [the which-way information], but the environment can,” said Arndt. In principle, the mere presence of which-way information in the environment is enough to make a mess of the superposition. The best way to avoid decoherence, then, is to carry out the entire experiment in a vacuum chamber.
In 1999, Zeilinger, Arndt, and their team were the first to do a multi-slit experiment with large molecules consisting of sixty carbon atoms each—a stable form of carbon that had been identified in 1985 and named buckminsterfullerene, or buckyball, because it has the segmented 3-D shape of the geodesic dome invented by Buckminster Fuller. A buckyball is about 1 nanometer in diameter, and when flying in a molecular beam at a speed of 200 meters/second, it has—according to de Broglie’s equation relating the wavelength of a particle to its momentum—a wavelength that’s about 350 times smaller than the size of the molecule. As objects get more massive, their de Broglie wavelengths get smaller and smaller, and it’s one of the reasons why we don’t observe the wave nature of such objects in ordinary encounters. However, according to quantum mechanics, their wave nature should be apparent when they go through a double slit, one molecule at a time. The researchers showed that the C60 molecules could indeed be put into a superposition of taking two paths at once
and made to interfere.
As with the experiment with single photons, Arndt is quick to stress that the interference being observed in these experiments is a quantum mechanical effect at the level of single molecules. A molecule can be described by a wavefunction for its center of mass. The amplitude of the wavefunction at different points in space lets us calculate the probability of finding the molecule at those locations. Each molecule that goes through the double slit has to have a wavefunction similar to the other molecules to ensure that the interference pattern that develops over time adds up; otherwise the pattern can get fuzzy or not form at all.
Getting photons or electrons or neutrons to have similar wavefunctions is relatively easy. Not so for molecules: you have to get them all moving in the same direction at the same velocity. A daunting task, since unlike atoms of gas, “molecules don’t like to fly,” said Arndt. They are more likely to stick to surfaces, to each other, do anything but go from the source to the double slit and beyond.
To get them to leave their sources, the molecules have to be heated or otherwise launched, but not in ways such that their internal thermal energy makes interference impossible. All of which, as the team has gone to bigger molecules, has meant resorting to some serious chemistry and designing custom molecules that have stable internal bonds between the atoms that make up each molecule, and yet the molecules are not drawn to each other; they are not “sticky.” The team’s best effort so far, in terms of molecules going through a multi-slit arrangement, is a whopper: it’s a bespoke molecule with 284 carbon atoms, 190 hydrogen atoms, 320 fluorine atoms, 4 of nitrogen, and 12 sulfur atoms. That’s 810 atoms in one molecule with a total atomic weight of 10,123. The molecule was synthesized by a team led by Marcel Mayor, of the University of Basel, in Switzerland. The high fluorine content acts like a Teflon shell—preventing the molecules from sticking to each other too readily.
Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality Page 16
