Nonlocal correlations that define quantum entanglement could be reconciled with Einstein’s theory of relativity if space–time had two temporal dimensions. That is the implication of new theoretical work that extends nonlocal hidden variable theories of quantum entanglement and proposes a potential experimental test.
Marco Pettini, a theoretical physicist at Aix Marseille University in France, says the idea arose from conversations with the mathematical physicist Roger Penrose – who shared the 2020 Nobel Prize for Physics for showing that the general theory of relativity predicted black holes. “He told me that, from his point of view, quantum entanglement is the greatest mystery that we have in physics,” says Pettini. The puzzle is encapsulated by Bell’s inequality, which was derived in the mid-1960s by the Northern Irish physicist John Bell.
Bell’s breakthrough was inspired by the 1935 Einstein–Podolsky–Rosen paradox, a thought experiment in which entangled particles in quantum superpositions (using the language of modern quantum mechanics) travel to spatially separated observers Alice and Bob. They make measurements of the same observable property of their particles. As they are superposition states, the outcome of neither measurement is certain before it is made. However, as soon as Alice measures the state, the superposition collapses and Bob’s measurement is now fixed.
Quantum scepticism
A sceptic of quantum indeterminacy could hypothetically suggest that the entangled particles carried hidden variables all along, so that when Alice made her measurement, she simply found out the state that Bob would measure rather than actually altering it. If the observers are separated by a distance so great that information about the hidden variable’s state would have to travel faster than light between them, then hidden variable theory violates relativity. Bell derived an inequality showing the maximum degree of correlation between the measurements possible if each particle carried such a “local” hidden variable, and showed it was indeed violated by quantum mechanics.
A more sophisticated alternative investigated by the theoretical physicists David Bohm and his student Jeffrey Bub, as well as by Bell himself, is a nonlocal hidden variable. This postulates that the particle – including the hidden variable – is indeed in a superposition and defined by an evolving wavefunction. When Alice makes her measurement, this superposition collapses. Bob’s value then correlates with Alice’s. For decades, researchers believed the wavefunction collapse could travel faster than light without allowing superliminal exchange of information – therefore without violating the special theory of relativity. However, in 2012 researchers showed that any finite-speed collapse propagation would enable superluminal information transmission.
“I met Roger Penrose several times, and while talking with him I asked ‘Well, why couldn’t we exploit an extra time dimension?’,” recalls Pettini. Particles could have five-dimensional wavefunctions (three spatial, two temporal), and the collapse could propagate through the extra time dimension – allowing it to appear instantaneous. Pettini says that the problem Penrose foresaw was that this would enable time travel, and the consequent possibility that one could travel back through the “extra time” to kill one’s ancestors or otherwise violate causality. However, Pettini says he “recently found in the literature a paper which has inspired some relatively standard modifications of the metric of an enlarged space–time in which massive particles are confined with respect to the extra time dimension…Since we are made of massive particles, we don’t see it.”
Toy model
Pettini believes it might be possible to test this idea experimentally. In a new paper, he proposes a hypothetical experiment (which he describes as a toy model), in which two sources emit pairs of entangled, polarized photons simultaneously. The photons from one source are collected by recipients Alice and Bob, while the photons from the other source are collected by Eve and Tom using identical detectors. Alice and Eve compare the polarizations of the photons they detect. Alice’s photon must, by fundamental quantum mechanics, be entangled with Bob’s photon, and Eve’s with Tom’s, but otherwise simple quantum mechanics gives no reason to expect any entanglement in the system.
Pettini proposes, however, that Alice and Eve should be placed much closer together, and closer to the photon sources, than to the other observers. In this case, he suggests, the communication of entanglement through the extra time dimension when the wavefunction of Alice’s particle collapses, transmitting this to Bob, or when Eve’s particle is transmitted to Tom would also transmit information between the much closer identical particles received by the other woman. This could affect the interference between Alice’s and Eve’s photons and cause a violation of Bell’s inequality. “[Alice and Eve] would influence each other as if they were entangled,” says Pettini. “This would be the smoking gun.”
Bub, now a distinguished professor emeritus at the University of Maryland, College Park, is not holding his breath. “I’m intrigued by [Pettini] exploiting my old hidden variable paper with Bohm to develop his two-time model of entanglement, but to be frank I can’t see this going anywhere,” he says. “I don’t feel the pull to provide a causal explanation of entanglement, and I don’t any more think of the ‘collapse’ of the wave function as a dynamical process.” He says the central premise of Pettini’s – that adding an extra time dimension could allow the transmission of entanglement between otherwise unrelated photons, is “a big leap”. “Personally, I wouldn’t put any money on it,” he says.
The research is described in Physical Review Research.
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