Stop me if you've heard this before

My latest story for Chemistry World is strictly for chemistry nerds. But this one for Physics World – extended version below – has hopefully a little more general interest in its all-round boggleworthiness. Charles Bennett’s comments seem to imply that the key question is whether it is possible to find a way of experimentally distinguishing between this remarkable interpretation and the more prosaic one he suggests.

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What you do today could affect what happened yesterday. This is the bizarre conclusion of a thought experiment in quantum physics described in a preprint by Yakir Aharonov of Tel-Aviv University in Israel and his colleagues.

It sounds impossible, indeed as though it is violating one of science’s most cherished principles: causality. But the researchers say that the rules of the quantum world conspire to decorously preserve causality by ‘hiding’ the influence of future choices until those choices have actually been made.

At the centre of the idea is the quantum phenomenon of nonlocality, in which two or more particles exist in inter-related (‘entangled’) states that remain undetermined until a measurement is made on one of them – whereupon the state of the other particle is instantly fixed too, no matter how far away it is. Albert Einstein first pointed out this instantaneous ‘action at a distance’ in 1935, when he argued that it meant quantum theory must be incomplete. But modern experiments have confirmed that this instantaneous action is real, and it now holds the key to practical quantum technologies such as quantum computing and cryptography.

Aharonov and his coworkers describe an experiment much like that proposed by Einstein, but on a large group of entangled particles rather than just two. They argue that under certain conditions, the experimenter’s choice of a measurement of the states of the particles can be demonstrated to affect the states they were in at an earlier time, when a very loose measurement was made. In effect, the earlier ‘weak’ measurements anticipate the choice made in the later ‘strong’ measurement.

The work builds on a way of thinking about entanglement proposed by Aharanov three decades ago. This entails looking at the correlations between particles in the four dimensions of spacetime rather than the three of space. “In three dimensions it looks like some miraculous influence between two distant particles”, says Aharonov’s coworker Avshalom Elitzur. “In spacetime as a whole, it is a continuous interaction extending between past and future events.” Quantum systems are generally described by a ‘state vector’: a set of quantum states propagating forward in time. But Aharanov’s view considers also a second state vector propagating from future to past – which is why it is called the ‘two state vector formalism’ (TSVF).

Aharonov and coworkers have now discovered a remarkable implication of the TSVF. It bears on the question posed by Einstein once the early quantum theorists began to appreciate how measurement not just reveals but may determine the state of quantum systems. If observation has this effect of fixing how the world is, said Einstein, then can we be so sure that the Moon is there when no one is looking?

“The ordinary physicist replies, ‘Go away, this is a philosophy not physics’”, says Elitzur. It is equivalent to asking what is the state of a particle between two measurements. “Of course you're not going to measure the particle, because then you will have the particle's state upon measurement rather than between measurements.” But Aharanov’s perspective shows that it is possible to get at the intermediate information – by making sufficiently ‘weak’ measurements on a whole bunch of entangled particles prepared in the same way, and then averaging the statistics. Elitzur explains that this amounts to saying “Give me sufficiently many particles during of this time interval and I'll tell you precisely what you want to know.”

The weak measurements tell you something about the probabilities of different states (spin value up or down, say) – albeit with a lot of error – without actually collapsing them into definite states, as a strong measurement does. The weak measurement does perturb the system, but not enough to fix an outcome for sure. “A weak measurement both changes the measured state and informs you about the resulting localized state”, says Elitzur. “But it does both jobs very loosely. Moreover, the change it inflicts on the system must be weaker than the information it gives you.”

As a result, Elitzur explains, “every single weak measurement in itself tells you nearly nothing. The measurements provide reliable outcomes only after you sum them all up. Then the errors cancel out and you can extract some information about the ensemble as a whole.”

In the researchers’ thought experiment, the conclusions of these weak measurements will agree with those of later strong measurements, in which the experimenter chooses freely which spin orientation to measure – even though, after the weak measurements, the particles’ states are still undetermined.

What this means within the TSVF, says Elitzur, is that “a particle between two measurements possesses the two states indicated by both of them, past and future!” This even seems to evade Heisenberg’s uncertainty principle, which forbids simultaneous precise knowledge of a particles position and momentum. “If you measured position first and momentum later, then the particle possesses both precise values, never mind Heisenberg”, says Elitzur. Heisenberg himself felt that his uncertainty principle undermined causality – he’d have been shocked to find this kind of backward causality actually seeming to undermine his own law.

But causality does emerge intact, after a fashion. For the catch is that the weak measurements in themselves appear to leave many options for what the particles states are. Only by adding subsequent information from the strong measurements can one reveal what the weak measurements were ‘really’ saying. This means that the weak measurements by themselves can’t show you what the later strong measurements will reveal. The information is there, but encrypted and only exposed in retrospect. So causality is preserved, even if it is not exactly causality as we normally know it.

Why there is this censorship is not clear, except from an almost metaphysical perspective. “Nature is known to be fussy about never appearing inconsistent”, says Elitzur. “So she's not going to appreciate overt backwards causality – people killing their grandfathers and so on.”

He says that some specialists in quantum optics have expressed interest in conducting the experiment, which he thinks should be no more difficult than previous studies of entanglement.

Charles Bennett of IBM’s research laboratories in Yorktown Heights, New York, a specialist on quantum information theory, is not convinced. For a start, he sees the TSVF as only one way of looking at the results. “People in quantum foundations are often so wedded to their own interpretation or formalism that they say it is the only reasonable one, when in fact quantum mechanics admits multiple interpretations, which except for a few outliers are entirely equivalent to one another. The differences are aesthetic and philosophical, not scientific.”

Bennett believes that the findings can be interpreted without any apparent ‘backwards causation’, so that the authors are erecting a straw man. “To make their straw man seem stronger, they use language that in my opinion obscures the crucial difference between communication and correlation. They say that the initial weak measurement outcomes anticipate the experimenter's future choice but that doing so causes no violation of causality because the anticipation is encrypted.” But he thinks this is a bit like an experiment in quantum cryptography in which the sender sends the receiver the decryption key before sending (or even deciding on) the message, and then claims that the key is somehow an ‘anticipation’ of the message. With this in mind, it is not clear whether even an experiment will resolve the issue, since it would come down to a matter of how to interpret the results.

Aharonov and colleagues suspect that their findings might even have implications for free will. “Our group remains somewhat divided on these philosophical questions”, says Elitzur. “I keep teasing Yakir that he will go down in history as the person who has abolished free choice. He on the other hand is confident that TSVF secures free will a place within physical formalism. His conclusion is somewhat Talmudic: Everything you're going to do is already known to God, but you still have the choice. On the other hand Yakir's God sharply differs from Einstein's in that she loves to play dice from morning to night.”