Science fiction has long embraced the idea of travelling backward in time, but the advent of Einstein’s general theory of relativity transformed these ideas from fantasies into potential – albeit contested – realities. In particular, solutions to the equations of general relativity known as closed time-like curves (CTCs) seem to allow a system’s trajectory to return to a previous point in time. Although the existence of CTCs has never been proven, their admissibility within general relativity has inspired many physicists to study their implications, which include increases in information processing speeds as well as retrograde time travel.

Inspired by the 2014 film Interstellar, in which a father sends messages to his daughter in the past, Kaiyuan Ji and Mark Wilde of Cornell University, together with Seth Lloyd at the Massachusetts Institute of Technology, have now investigated the potential advantages of a retrograde messaging channel based on a CTC. As well as deriving an exact expression for the information capacity of such a channel, they showed that this capacity exceeds that of regular channels that do not involve backward time travel.

Post-selected CTC models

To model their CTC, the researchers used an approach that Lloyd and his then-collaborators developed 15 years ago. This approach exploits the mathematical equivalence between a CTC and the combined operations of quantum teleportation and post selection, so it is often referred to as a post-selected CTC model. Previous analyses established that this model disallows time-travel paradoxes such as going back in time to kill your grandfather, while still preserving correlations between the system that travels backward in time and the environment.

The latter feature is important, Ji notes, because quantum CTC models without it have a distinct drawback: “If you travel through that closed time-like curve, you end up in the past, but basically you lost all the memory of what has happened before you do time travel,” he explains.

A further advantage of the team’s chosen model is that it does not prohibit causal loops in which correspondents in the past and future influence each other. To return to the Interstellar scenario, Ji explains that while the daughter is influenced by her father’s message, she also influences her father, because he witnessed how she decoded the message and therefore used that information to optimize his encoding protocols.

The existence of causal loops in the model allowed Ji and his colleagues to formulate an expression for the channel’s bit capacity. It also pointed towards the best way of maximizing that capacity. The optimal strategy, Ji explains, would involve the father using his memory from the past when encoding his message to the past, which makes sending messages to the past more efficient (and capable of a higher bit capacity) than sending messages to the future. “The causal loop is essential to the design of the optimal communication protocol in this retro causal communication setting,” he tells Physics World. “It is not possible in standard communication from the past to the future.”

Capacity for messages

The CTC can also be used to form a quantum channel capable of transmitting either regular classical data or quantum data back in time. Using their expression for the channel’s bit capacity, the researchers were able to show that its classical bit capacity is twice that of its quantum counterpart.

Nicole Yunger Halpern, a theoretical physicist at the University of Maryland who has studied some implications of CTCs for metrology but was not involved in the current work, describes the research as “creative and technically impressive”. She points out that while calculating a communication channel’s capacity is a common challenge in the field of information theory, obtaining straightforward answers can be difficult. “The authors combined this workaday task with a highly unusual (retrocausal) setting and, moreover, obtained a simple solution,” Halpern says.

Not everyone is sold on the mathematical format of post-selected CTC models, though. Scott Aaronson, a computer scientist at the University of Texas at Austin, US, who has previously studied the speed advantages of information processing using CTCs, believes that studies with this approach “attempt to model time travel but don’t fully succeed at it”. However, with respect to the question of channel capacity, Aaronson concedes it may be “interesting to prove things”.

While the current model considered the effects of distortion (“noise”) on messages in the channel, Ji suggests it might be interesting to broaden this to include noise in the memory of the process – like the father in Interstellar having a hazy recall of his daughter’s decoding protocol. Ji also notes that the post-selection CTC model has some mathematical equivalence with black hole final state projections, and he says it might be interesting to explore these connections, too.

The research is described in Physical Review Letters.

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In today’s technologies, mechanical mechanisms generally provide the brawn while electronics supplies the brains. This is partly because it is challenging to write information into mechanical memories without resetting each bit individually. However, that could change as researchers led by Pedro Reis at École Polytechnique Fédérale de Lausanne in Switzerland and Martin van Hecke at AMOLF in the Netherlands have now found a practical means of writing mechanical bits. Their technique, which they describe in Science Advances, uses structures that resemble children’s slap bracelets placed on a rotating turntable. While they acknowledge it is unlikely to replace electronic memories, they argue that it could have specialist applications and might produce insights that translate into electronic innovations.

“The framework we propose could be very useful, for example, in the domain of physical intelligence, where you provide hardware with capabilities that don’t require essentially a brain or an electronic control system to do individual tasks,” Reis says.

Mechanics for memory

Reis and van Hecke’s interest in mechanical memory stems from their research on metamaterials, which are materials that are defined not just by their composition, but also by the structures within them. Mechanical systems offer a tangible means of getting to grips with the complex behaviour of these metamaterials. “Often, all sorts of things that we do rely on nonlinear responses,” van Hecke notes, adding that such responses are much easier to study in mechanical systems than in optical devices.

A metamaterial made up of an array of switchable mechanical elements could function as a form of mechanical memory. However, to be practical, it needs to be possible to flip the states of individual mechanical bits using global controls, as opposed to addressing them individually. Otherwise, writing data will be very fiddly.

A solution emerged from Reis’ interest in rotating platforms, which he describes as “a very versatile way of loading mechanical systems”. While the pair had been friends for more than two decades, they had been working independently until, during a visit, the penny dropped and they realized that placing the metamaterial array on a rotating platform could provide the control they needed.

Because the angular velocity of the platform sends its momentum outwards, each mechanical object experiences a force in the radial direction, known as the centrifugal force. If this angular velocity is not constant, the object will experience an additional force in the orthogonal azimuthal direction, known as the Euler force. “So you have a complex force and bi-directional field that is highly tuneable,” says Reis. “And this tuneability is what we realized is very powerful.”

A rotating array

To construct their array, the researchers used clamped beams with two stable mechanical states – a little like a slap bracelet can be coiled up or flat, except these beams could either curve to the right or to the left. To individually address different beams, they ensured that each beam was unique in its width, the angle it was clamped at, and so on, all of which affect how much force is needed for a beam to ping into the opposite state. By tuning the parameters of each clamped beam and the angular acceleration of the rotating platform, they could engineer the applied force to switch (or not switch) specific beams, thereby writing data into the array purely by rotating the platform.

Doing this accurately requires a level of precision in acceleration control that surpasses what standard lab motors can achieve. However, the researchers say they were able to team up with a local company that had designed high-spec rotating platforms for its high throughput silicon chip production process. By programming platforms with five tailored clamped beams and the right rotation functions, they showed they could write the letters of the alphabet in ASCII script.

“This is a significant advance because it points toward future smart devices and robots that can be reprogrammed remotely without complex wiring or electronics, using only carefully designed motion‑based signals driven by a sole dynamic driving strategy,” explains Damiano Pasini of McGill University, Canada, who studies systems for mechanical computing but was not involved with this work directly.

Reis says he is excited about the scalability of the approach and its potential in high throughput experiments. Meanwhile, van Hecke is looking into how the idea might transfer to other systems, such as applying engineered force functions to crumpling sheets of complex glasses. “It just opens up possibilities for both studies, really fundamental studies of complex systems, but also real applications where you use this dynamic idea,” he tells Physics World.

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