The Decline and Collapse of the Wavefunction Empire

Quantum mechanics is frustrating for everyone—theorists who don’t understand their own equations, experimentalists that have to jump around paradoxes to try and get a measurement, and students who just have no idea what’s happening. It also has the problem of being wrong. With space and time and everything made of particles, QM believers have to accept the enigma of wavefunction collapse (when the probability of states turns into a single state). Does it collapse when we poke at it? Are we somehow controlling the fate of the universe (even if the fate involves only a single photon)?

Experimentalists have had a notoriously hard time with understanding what the hell is going on, the main example being the famous double-slit experiment where electrons act as both particles and waves. In the wave form, electrons pass through both slits to create an interference pattern on the back wall. But when physicists tried to measure exactly which slit the electron passed through the electron turned back into a particle and the interference pattern was lost. It looked like measuring changed the nature of the electron—that we changed the nature of the electron. Crazy enough, buckyballs, which are large soccer-ball shaped collections of carbon atoms, also show wave-particle duality.

Now in a recent Nature paper, Berkeley scientists (of course) have mapped the slow demise of a wavefunction, in the solid state no less. They put a circuit in a superposition (a collection of energy states, i.e. acting as a wave), shoved it in a box, and shot microwaves at it. The energy states alter the microwaves in subtle ways as they pass through the circuit—something researchers can measure without collapsing their experiment. Over microseconds (horribly slow in quantum time), the researchers measured a “collection of snapshots” as the circuit’s wavefunction collapsed. They go on to suggest this measuring-at-a-distance can be used to manipulate wavefunctions, calling it ‘quantum steering.’

Nature wrote a nice article detailing the experiments in terms of quantum mechanics. But people blew up the comments complaining that the research should have been described in quantum field theory terms.  QFT gets rid of the pesky particles and replaces them with fields (like turning a molecule of water into an entire ocean… kind of), completely negating any paradox of wave-particle duality. One commenter, Timothy Eichfeld, had a good explanation of what was happening:

It is not so much as ‘measurement’ as it is the disruption of the very fragile energy states holding the system in place. The ‘wavefunction’ does not know if a human or a frog or stray muon has interfered with its energy system – it does not have a state of being ‘watched’ or not, the issue is that it is unstable and at the top of it’s energy state. It will be knocked back to it’s lowest state depending on what vibration was absorbed by the interaction of the interference pattern on it’s energy signature.

Also in the comments is everyone pitching the book they’ve written on the subject, because, of course, that’s what comment sections on a prestigious scientific website are for.

Simplify the Universe

Particle interactions calculated with a single term all done by hand?! That’s crazy. In case you have nothing to base calculating particle interactions in quantum field theory on, just imagine having thousands of puzzle pieces scattered everywhere to suddenly, without all the pesky pieces, having a single, unified picture. All it takes is some new thinking and a little geometry.

In this new model, physicists describe the universe by an amplituhedron, an infinite-dimensional geometric object. The volume of this object is equal to the scattering amplitude—the holy grail of particle physics—which physicists at the Large Hadron Collider use to describe particle interactions. In some amplituhedrons the amplitudes can be calculated directly. In others diagrams called “twistors” are needed.

What’s more, they’ve found the solution to everything. The volume of an infinite-sided “master amplituhedron” represents the amplitudes of all physical processes. The italics are supposed to impress you. Interactions between a finite number of processes, what us humans normally consider, are contained on various faces. Interesting to me, but probably not to anyone else, is that the master amplituhedron simplifies to a circle in 2D.


Amplituhedron representing an 8-gluon particle interaction, which normally needs ~500 pages of algebra.

The amplituhedron removes locality and unitarity. Particles that aren’t near either other in space or time can interact (what?) and the sum of the probabilities for all possible particle positions doesn’t have to be 1 (what?!). That works out for gravity though, which explodes—yes, explodes—in equations with locality and unitarity. Connecting gravity to particle physics is a big deal—no one’s been able to do it yet. Jacob Bourjaily, one of the researchers, described this method as “a starting point to ultimately describing a quantum theory of gravity.”

Nima Arkani-Hamed, the lead author (the main man, the head honcho), gave a talk about amplituhedrons at the SUSY 2013 conference, which is posted online. Warning: the talk is very technical, but interesting nonetheless (if only to watch a man in shorts and a shirt two sizes too large give a spitfire professional talk). Although, in the talk he says amplituhedrons can be “explained to a smart junior high school student,” which left me feeling like a stupid graduate student.