You need to log-in or subscribe in order to use Student access.

Lunar time

Both NASA and ESA (the European Space Agency) are currently working on developing a coordinated lunar time zone. Normally, space researchers and technicians rely on UTC, or Coordinated Universal Time, to synchronise with different time zones around the globe, a system that also deals with issues of variation of the position of the Earth's poles, rotation rate and so on. It was set up in 1972 and is regulated by a global network of atomic clocks.

So why can't the Moon simply be included in that particular system? Well, the answer is gravitational time dilation, which causes terrestrial clocks to run 58.7 microseconds per day more slowly than clocks in the vicinity of our closest neighbour in space!

It's important not to confuse gravitational time dilation with a similar phenomenon predicted by Einstein's special theory of relativity. To explore this distinction further, without resorting to a rigorous mathematical discussion, let's put our trust in a couple of universally accepted conventions of modern physics.

First up is Einstein's assertion that the speed of light in a vacuum is constant in all inertial frames: frames of reference that are compliant with Newton's first law of motion. Put simply, they are not accelerating. The speed of light, or ‘c’ as it's usually notated, is the speed at which massless photons propagate through free space, which emerges from Maxwell's equations of electromagnetism. Most significantly it is the absolute speed limit within the fabric of space-time, as accelerating any body of mass to ‘c’ requires a force of infinite magnitude and is consequently impossible.

Probably the most startling consequence of this assertion is the inescapable fact that any clock at rest in a frame of reference that is in uniform motion, relative to an observer in a different inertial frame, will be observed to be running slow. Even if, let's say, a spacecraft is moving at a considerable speed, any light emanating from the craft in its direction of travel, will still be seen to be propagating at the speed of light - NOT the speed of light plus the speed of the craft! This necessitates the slowing of time in the rest frame of the spacecraft as observed by observers in other inertial frames. However, a passenger in the craft won't notice anything out of the ordinary; from their point of view, their clocks are running normally. This real effect has been proven experimentally on numerous occasions, and indeed, particle physicists in particular regularly observe the effect of time dilation extending the lives of unstable particles like muons, by virtue of them being accelerated to significant fractions of the speed of light.

As illustrated by the solution to the famous twins paradox, in which a star-hopping astronaut ages more slowly than their Earth-bound sibling, special relativity does not preclude the observation of time dilation in accelerating, or non-inertial frames. It's called a “special” theory simply because it is only concerned with global inertial frames. General relativity, on the other hand, accommodates all frames of reference, both global and local, which means that it can be invoked even in the presence of gravitational fields. One of the cornerstones of general relativity is the Principle of Equivalence, which roughly states that, in a suitably localised frame of reference, it is impossible to distinguish between the effects of being in a uniform gravitational field and the effects of uniform acceleration.

So returning to our hypothetical and now very small, windowless spacecraft, from the perspective of any passenger on board, it would be impossible to tell whether the craft was being accelerated by the propulsion system or if it was “parked” on the surface of a planet with a gravitational field of the same magnitude as the acceleration. Put simply, in either case, a carelessly dropped screwdriver or a knocked-over mug will be seen to fall to the floor. Furthermore, any external observer suitably distant from the spacecraft so as to be effectively beyond the influence of any gravitational field would observe the clocks on board the craft to be running slowly, regardless of whether it was at “rest” in a gravitational field or accelerating through “empty” space.

This gravitational time dilation, along with the closely associated phenomenon of gravitational redshift (where the wavelengths of any photons escaping a gravitational field are stretched), results from not only the spatial dimensions but also the temporal dimension of four-dimensional space-time being curved in the presence of a body of mass. This isn't science fiction, it is a real phenomenon that has been verified experimentally to a high degree of accuracy - and is indeed the reason why clocks on the high altitude GPS satellites that we all rely on for our phones and “sat navs” are set to run slightly slower than terrestrial clocks, which experience a stronger gravitational field strength.

Coordinated Lunar Time, or LTC, as it will probably be known, is set to be in place by the time the new Artemis rocket takes people back to the surface of the Moon - later this decade. In this era of high-precision navigational and positional technologies, a commensurate improvement in the synchronization of timings between the Moon and the Earth can't come too soon!

All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. Any unauthorised copying or posting of materials on other websites is an infringement of our copyright and could result in your account being blocked and legal action being taken against you.