Time and Relative Dimensions in Space

‘Time Crystals’ may sound like the exotic invention of a ‘70s science-fiction writer, but for over a year now they have been verging dangerously close to the realms of science fact. The idea was first proposed in February last year when the Nobel Prize-winning physicist Frank Wilczek published the theoretical derivation that originally led him to these strange, seemingly impossible structures. Unsurprisingly, there is a mother lode of crazy new science surrounding them which has the potential to change the way we view time and the role it plays within Einstein’s space-time continuum.

An Example of a Crystalline Structure

Einstein’s theories of relativity have forever sewn together space and time, revealing them as two parts of an inseparable 4-dimensional reality. The notion of time as a dimension is where the idea of time crystals came from. In 2010, Wilczek began to think about the classification of crystals. He stated that “it’s natural to think about space and time together, so if you think about crystals in space, it’s very natural also to think about the classification of crystalline behaviour in time.” A crystal is a spatially repeating assembly of atoms; the balance of the forces within the crystal creates the characteristic three-dimensional lattice structure. This means that atoms within the crystal must occupy areas of balance, where the resultant force is zero, called ‘lattice points’. As a result, the atoms have a discrete set of places in space in which to exist. This is said to break the spatial symmetry of nature, which states that all places in space are fundamentally equivalent.

Wilczek’s ‘time crystals’ exhibit the same characteristic repetition as spatial crystals, but unlike their spatial counterparts, their repeating pattern exists in time, like the minute hand rounding a clock. This enables a special form of perpetual motion, an idea whose absolute impossibility has become an axiomatic truth of thermodynamics. The reason this can happen is because, like spatial crystals breaking spatial symmetry, time crystals ‘break’ the symmetry of time, and idea which states that:

• The reversal of time yields the same results. For example, a ball being thrown up and falling back down, when watched in reverse, is still a ball being thrown up and falling down.
• Physical systems retain their features over time. For example the ball mentioned above has gravitational potential energy mgh, and if we were to repeat the whole process tomorrow, it would still have potential energy mgh.

Many situations exhibit breaks in temporal symmetry, and the universe as a whole is asymmetric upon time reversal. Since the second law of thermodynamics states that entropy must always increase over time, watching events in reverse would show a decrease in entropy, and therefore break temporal symmetry. Even in the above example of the ball, some energy is lost and entropy increases. This is where the definition of temporal symmetry is less than helpful, time crystals are said to break the symmetry of time because they are temporally symmetric. Reversal of time does yield the same result, and they therefore break the symmetry of time by not following the asymmetry exhibited by observable reality. Atoms within the time crystal do this by forming a repeating lattice structure in time, which means they return to their original arrangement after a discrete period of time has passed. Consequently, atoms within the time crystal can move through space freely so long as they return to their original structure once their fixed period is over. The atoms within time crystals must therefore continue moving eternally without expending energy, so long as their motion remains cyclic over time.

The History of the Universe

To fully appreciate this, a scale of time is needed. Long after our sun has burned out and the next few generations of stars have come and gone, the laws of thermodynamics predict an entropic end to the universe, one in which disorder has taken over and all matter has reached a constant temperature. This has become known as the heat death of the universe. After this, matter will decay into energy and spread uniformly throughout all space. Even after this end, time crystals will still have their structure. As long as time itself still endures, time crystals will exist in exactly the same way they have existed since their creation, in truly perpetual motion.

As you would expect, this idea was not very well received, and certainly appears to be a major break in the accepted laws of physics. But the paper has survived expert peer reviews, which suggests that the theoretical existence of these bizarre structures makes sense. The next stage, as with any hypothesis, is to test the theory against reality, and the only way to do this is to forge a bridge between science fiction and science fact. The only way to test this theory is to create a time crystal.