Deep in the heart of physics there’s a lucky guess. It was an incredibly good guess, one that remains solid in the face of time and experiment, and is now a fundamental principle in quantum mechanics.
It’s called the Born rule, and while it’s used for predictions, nobody truly understands how it works. But a bold new attempt to rewrite it could be the break we’ve been looking for to finally understand it in full.
University College London physicists Lluís Masanes and Thomas Galley have teamed up with Markus Müller from the Austrian Academy of Sciences to find a new way to describe this basic law of physics.
They’re not the first to look for deeper truths to this most mind-boggling of quantum principles. And, let’s be honest, they won’t be the last. But if there is a solution to be found, it’ll probably require a unique approach like theirs.
First, to understand what’s so special about the Born rule, we need to back up a little.
It’s become a cliché to say quantum mechanics is weird. What with cats that are at once alive and dead and particles teleporting information across space and time, we’re used to seeing the basement of physics as a magic show.
Big names like Schrödinger, Heisenberg, and Einstein tend to get the glory, but it’s the German physicist and mathematician Max Born who truly deserves the credit for the monumental headache that quantum mechanics delivers.
To understand his contribution, we only need to look at the hot mess physicists found themselves in the early 1920s. The structure of the atom had recently been revealed to consist of a dense, positively charged nucleus surrounded by smaller negatively charged particles.
Why the whole system didn’t collapse was the Big Question being kicked around, until the French physicist Louis de Broglie came up with an audacious suggestion – just as light waves had a particle nature, those negative electrons could remain aloft if they were also wave-like.
The duality of light was already hard enough to swallow. But describing solid-seeming matter as if it was a wave on the ocean was just plain nuts. Still, experiments showed it was a good match.
Then, in 1926, Born came up with a simple suggestion – drawing insight from the mathematics of his colleagues, he showed how these waves reflected probability and came up with a rule that married observations with measures of chance. This rule allows physicists to predict the position of particles in experiments, using the probabilities reflected by the amplitudes of these wave functions.
But the Born rule wasn’t based on some basic set of axioms, or deeper truths of nature. In a lecture he gave on receiving a Nobel Prize in Physics for his work in 1954, Born explained the ‘aha!’ moment emerged from Einstein’s work.
“He had tried to make the duality of particles – light quanta or photons – and waves comprehensible by interpreting the square of the optical wave amplitudes as probability density for the occurrence of photons,” said Born.
It was an inspired guess, and an accurate one at that. But there were no basic axioms, no fundamental laws drawing Born to his conclusion. It was purely predictive, saying nothing about deeper principles that turn a multitude of maybes into a single actuality.
Einstein hated the implications, famously claiming God does not play dice, and felt quantum mechanics was an incomplete theory waiting for new pieces to make the picture clear.
Nearly a century on, those pieces are as elusive as ever. And the Born rule still sits at the heart of it, silently predicting without revealing the secret to its choice.
What’s needed is a reformulation of the famous law that retains its power of prediction while hinting at further truths. So Masanes, Galley, and Muller reworked the rule’s formulation based on a handful of seemingly trivial assumptions.
Firstly, they pointed out that quantum states are described according to measures of magnitude and direction.
Secondly, they showed how these states can be described according to what’s known as unitarity. This jargon refers to the information that connects a process’s start and end points. (To use a crude analogy, we might not know how we got home from the bar, but the method that got us there also describes the route back.)
Next, they assumed however we choose to group the parts of a complex quantum system, it shouldn’t make a difference to the measurement of the final state. Dividing a rainbow into seven colours is a choice we make subject to context; nature isn’t always concerned with convenient divisions.
Lastly, they affirmed that the measurement of a quantum state is unique. After all is said and done, a myriad of possibilities ends in a solid answer.
From these simple starting points, the trio logically built back up to the Born rule. Their work is available for anybody to read through on the pre-peer review website arxiv.org, but is already sparking discussion.
It’s not a solution in itself, mind you, as it falls short of explaining why a wave of possibility collapses into the reality we observe.
Instead, it shows how fundamental assumptions can give rise to the same law, providing a new perspective on how to approach the problem.
For now, God still rolls those dice fair and square. Maybe this is how we’ll catch him cheating.