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But No Simpler

23 December 2014

Quantum theory is one of those things that isn’t portrayed very accurately in the popular press. It’s used to justify everything from Matrix Energetics to homeopathy, it’s described as mysterious physics that no one understands, and even used to claim that the universe is a hologram. Even when claims are more mundane, the resulting press release hypes the story beyond recognition. For example, recently there’s been a flurry of news articles claiming that “Quantum physics just got simpler!” as if new research has finally solved a big mystery of physics. Not so, when you look at the actual research.1 The work looks at a connection between particle-wave duality, and something known as entropic uncertainty.

While quantum physics isn’t mysterious, it does have some properties we would consider strange. One of these is the fact that quantum objects have some properties similar to particles and some similar to waves. This particle-wave duality, as it is often known, shows up in the results of certain experiments, such as the photoelectric effect and the dual slit experiment. Often in popular science this is presented as objects “sometimes” being a particle and “sometimes” a wave, and it chooses which to be depending on the experiment you perform. In reality, quantum objects are simply quantum objects, and you can perform experiments that demonstrate their particle or wave behaviors.

Another aspect of quantum theory is known as Heisenberg’s uncertainty principle. This is often presented as the fact that you can’t measure both where an object is (position) and where it is going (momentum) with perfect accuracy. It’s a bit of a misrepresentation, because the uncertainty principle isn’t just a consequence of crude measuring devices, it is a fundamental aspect of quantum objects. We can’t measure an exact simultaneous momentum and position for an electron, for example, because electrons don’t have a simultaneous position and momentum. This “fuzziness” factor leads to important physical phenomena, such as quantum tunneling, which is central to solar fusion. There are other “fuzzy” quantity pairs as well, such as energy and time, which leads to thing like virtual particles and Hawking radiation.

According to the popular articles, new research has shown that particle-wave duality and the Heisenberg uncertainty principle are the same thing. But anyone who’s taken a college-level quantum mechanics course has likely seen a derivation showing that the former leads to the latter, and vice versa. So this is nothing new. What is new is how it relates to entropy. While we usually talk about quantum theory in terms of particles and waves, it can also be viewed in terms of information. In this way, Heisenberg’s uncertainty isn’t just a limit on what can be measured, its a limit on the amount of information a quantum system can contain. This is useful for a range of fields, such as quantum cryptography and quantum computing. One of the other thing we know is that the amount of information a system contains can be related to the entropy of that system. So the uncertainty principle can be generalized as a kind of entropic uncertainty.

It’s been debated whether entropic uncertainty and particle-wave duality were one and the same, just as particle-wave duality and the uncertainty principle are. An an earlier paper argued that the two weren’t equivalent,2 but now this new paper shows that in fact they are. This is useful for folks who study quantum information, but it isn’t a fundamental breakthrough that revolutionizes our understanding of quantum theory. It’s good work, and should be presented as such.

Unfortunately most popular articles don’t look beyond the hype.


  1. Coles, Patrick J., Jedrzej Kaniewski, and Stephanie Wehner. “Equivalence of wave–particle duality to entropic uncertainty.” Nature communications 5.1 (2014): 1-8. ↩︎

  2. Yang, Chen, et al. “Losses-based test of wave-particle duality with Mach-Zehnder interferometers.” arXiv preprint arXiv:1402.0370 (2014). ↩︎