The direction of cause and effect was brought into question for quantum objects more than a decade ago, but new calculations may offer a way to restore it.
First comes cause, then comes effect – or does it? This order of events has previously been upended in the quantum realm, with the possibility of both A-causes-B and B-causes-A happening simultaneously. But a new mathematical analysis suggests this quantum quirk may be hemmed in by the very structure of space-time.
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For more than a decade, physicists have been grappling with the idea of indefinite causal order –instances where it is impossible to tell whether cause came before effect or vice versa, because the two scenarios are in a quantum superposition where both and neither are true at the same time. Strikingly, a 2017 experiment showed that a particle of light can pass through two gates such that it is impossible to tell which it went through first. This further established indefinite causal order as an unavoidable oddity of quantum theory.
“Causality is central to how we explain how things work. We observe things around us and want to ask, ‘Why does that happen?’,” says V. Vilasini at the Grenoble Alpes University in France.
To investigate causality further, she and Renato Renner at ETH Zürich in Switzerland were informed by two foundational theories. The first is quantum information theory, in which cause and effect are connected by the flow of information. The second is Albert Einstein’s theory of special relativity, which suggests all causal influence must be slower than the speed of light.
This second constraint describes the space-time we live in and bakes into its structure a clear notion of before and after. Experiments that feature indefinite causality happen in that same space-time, yet seem to contradict this structure, says Christina Giarmatzi at Macquarie University in Australia.
Vilasini and Renner derived two theorems that aim to reconcile this contradiction. The first states that for causality to be muddled, information about an object in question must become delocalised – smeared out in space-time instead of contained in one place, such as a detector. Say two people, Alice and Bob, are exchanging a particle of light to which conventional causality may not apply. For the particle to arrive before she sends it, Alice would have to “become soup”, says Pablo Arrighi at Paris-Saclay University. Remarkably, Alice becoming soup isn’t forbidden by quantum mechanics.
But the second theorem is more prohibitive. In it, the team found that if you are able to look at a process closely enough, you will see causality eventually emerge among its finer details. We can think of A-causes-B in a more fine-grained way: A is actually a series of events called A1, A2 and A3, while B is similarly split up. We may see A-causes-B and also B-causes-A, but, upon closer inspection, it could be that A1 causes B1, B2 causes A2 and A3 causes B3. Renner says that all experiments to date that have reported indefinite causal order could be reinterpreted as causal by a similar zooming-in.
Časlav Brukner at the University of Vienna in Austria says that while it may be possible for researchers to obtain more information through this type of fine-grained approach, this information may not be relevant for light particles or other quantum objects.
Brukner doesn’t question the findings, just their implications. “If the mathematics of a theorem is correct, then it must be correct. But what it means, and when it’s relevant, this is where we can disagree,” he says.
Arrighi says that staking a definite position on the plausibility of indefinite casual order in any particular experiment may come down to how a researcher interprets quantum theory itself. For Giarmatzi, the issue may only be resolved with more experiments.
However, Arrighi says that the two theorems invite examinations of how relativity and quantum theory can combine. Specifically, the work doesn’t explore what could happen if space-time itself were quantum. This opens the tantalising possibility that within a fully fledged theory of quantum gravity – which physicists have been seeking for decades – causality could once again be in peril.
Journal reference
Physical Review Letters DOI: 10.1103/PhysRevLett.133.080201
Journal reference
Physical Review A DOI: 10.1103/PhysRevA.110.022227