How we perceive and measure time.

Time – we experience its steady passing every day of our lives. It is a topic so central to physics and so intuitive to us, yet it leads to incredibly complex questions about the very nature of our 13.8 billion-year-old universe. For centuries, poets, artists, philosophers and scientists have been fascinated by it and its indefinite march which results in a progression of events occurring in irreversible succession. In this article, I will look at the various aspects of time which fascinate us, from its significance in physics and how we attempt to explain it, to the various ways in which we attempt to measure it.

Time is traditionally considered to be an ontologically basic property. What this means is that it is a primary concept, not made up of, or dependent upon any other property within a system. In classical physics, the concept of time is that of ‘absolute time’: a constantly-increasing value which progresses at a consistent pace everywhere throughout the universe. As we shall soon see, our current understanding of how time operates has advanced slightly owing to Einstein and his Theory of Relativity. Nonetheless, this basic understanding of time as a constantly moving sequence of events has been incredibly useful throughout much of the history of physics. The Equations of Motion, which describe the behaviour of a physical system in terms of its motion as a function of time, are a key example how time can be used to work out other variables. As early as the 16th century, mathematicians  were able to calculate to a high degree of accuracy the velocity or acceleration of falling objects based purely upon measurements of distance and time. Below is a basic equation of motion (constant acceleration) with time as a parameter.

However, when considering how moving observers or falling objects actually perceive the passing of time, it is necessary to consult Einstein’s Theory of Relativity. Until this theory came to be accepted, the vast majority of physicists believed that time passed at the same rate throughout the universe regardless of the observer/object experiencing its passing. Despite the fact that this belief is so intuitive, and that at the time there was scarcely evidence to prove it wrong, Einstein managed to do exactly this in early 20th century with the advent of his Theory of Special Relativity, by mathematically describing a phenomenon known as ‘time dilation’.

In order to understand time dilation, it is first necessary to know about what is meant by a ‘reference frame’. In special relativity, reference frames are used to specify the relationship between a moving observer and a phenomenon under observation. Time dilation states that if the observer and the observed are in two separate reference frames (moving relative to each other), then there will be a difference between the time which the observer perceives has elapsed, and the time which has actually elapsed within the observed reference frame. This relationship is given by the below formula:

(For the purposes of this article, I will not go into Gravitational Time Dilation, but it is worth noting that the effects of time dilation also occur when two reference frames are different distances from a gravitational mass.)

This can all seem very confusing, especially when one questions why boys who run from Queen’s Schools to Alington Schools don’t arrive in English looking younger than boys who have simply ambled across from Marten. However, the reason for this is that we are all on the same chunk of rock hurtling through space, and any relative velocities achieved between observers here on Earth are so negligible compared to the speed of light (given by c in the above formula) that the effects of time dilation are unnoticeable. To show this, I shall take the example of an observer on a passing bullet train watching a stationary man in a field for one second. In the formula, t represents the time which has elapsed according to the man in the field, and t0 represents the elapsed time perceived by the observer on the train. If we take the speed of the train to be 100m/s, we get:

Therefore, for the one second that passed for the man the in the field, 0.99999999999994 seconds passed for the observer on the train. This is a difference of 60 femtoseconds or 6 x 10-14 seconds, which I hope you would agree is negligible over the course of a lifetime.

Perhaps a more relevant example of the effects of time dilation is the ISS, which orbits the Earth at a speed of approximately 7,500m/s. As suggested by Einstein’s Theory of Relativity, time passes slower for everything on the ISS, and as a result, clocks on the ISS lag behind Earth clocks by 0.007 seconds for every six months of orbiting. There have also been various instances where physicists have experimentally tested the theory of time dilation, and in all cases, the results of the experiments served to further back up the theory. An example of an experiment that can be carried out is the comparison of muon lifetimes at differing speeds. (A muon is an elementary particle with the same charge as an electron.) In the laboratory, slow muons can be produced, and in the atmosphere, fast-moving muons (travelling at up to 98% the speed of light) are introduced by cosmic rays. By comparing the two, physicists have concluded that the lifetime of a cosmic ray produced muon is approximately five times longer than that of a laboratory muon, which is in agreement with our theory of time dilation.

It’s worth noting that the lifetime of a laboratory muon is approximately 2.2μs (2.2 x 10-6 seconds), so you may be wondering how we could possibly measure such tiny time increments. This leads on to the next focus of this article and another fascinating topic related to time: Horology, the measurement of time. We will never know who first decided to give structure to the measurement of time, but we do know that as early as 1,500 BC, the Ancient Egyptians were already using basic sundials and water clocks, which were typically used to time the duration of specific events.

The turn of the 13th century was a revolutionary time in the world of horology, as the first large pendulum clocks were invented. These devices had heavy weights attached by a chain, which had to be hand-wound around a cylinder. The mass of the weights and the extent to which the cylinder resisted turning had to be precise for the clocks to keep time accurately. As the cylinder turned, a circuit of cogs transferred this movement to the hour hand of the clock (the display of minutes or seconds did not emerge until the end of the 15th century). A mechanism called an ‘escapement’ could be attached by a coiled spring and its function was to keep the cylinder from unwinding. In later versions, the steady turning of the cylinder kept a pendulum of a specific length in harmonic motion, which accurately controlled the ticking of the second hand.

Most gear-controlled clocks today are very similar to pendulum clocks in terms of how their components fit together, though the vast majority are powered with the aid of quartz. This mineral has the property of being able to produce very precise and consistent vibrations when in contact with an alternating power source. This is known as ‘piezoelectricity’. Inside the clock, a current is sent to the quartz crystal. The crystal is cut in a specific way so as to vibrate at exactly 32,768Hz (215 times per second) when supplied with a specific current. In another circuit, these vibrations are used to generate regular electric pulses. These pulses can then be used to power an LCD display or to drive a tiny electric motor, turning gear wheels which spin the clock’s hands.

One of the most intriguing and advanced models of clock is the atomic clock. When exposed to certain frequencies of radiation, such as microwaves, electrons that orbit an atom’s nucleus will ‘jump’ back and forth between energy levels. In fact, the very definition of a second is based on the oscillations between energy states of a caesium-133 atom: 9,192,631,770 cycles per second to be precise. Like most clocks, atomic clocks make use of a quartz oscillator, but the reason why they are so accurate is that they also include an ingenious self-feedback loop to ensure the quartz oscillator is always at the correct frequency. Inside an atomic clock, caesium atoms are funnelled down a tube where they are exposed to microwaves. The frequency of these microwaves is determined by the frequency of the quartz oscillator. The percentage of atoms that change their energy state while passing through the resonator depends on how close the frequency of the microwaves is to the inherent oscillation frequency of caesium – the closer the frequency, the more atoms are affected. A magnetic detector in the clock measures how many atoms are in high energy states and if a low percentage of the atoms are in this state, the frequency of the microwaves (and thus of the quartz oscillator) must be slightly off. Using this information, a feedback mechanism in the clock adjusts the current, causing the frequency of the oscillator to be exactly 9,192,631,770Hz for as much of the time as possible. With modern atomic time standards and ultra-precise atomic clocks, time can now be measured to 10-15 seconds, which corresponds to a 1 second error approximately every 30 million years.

A prime example of everything I have described in this article is GPS technology. All GPS satellites carry atomic clocks onboard in order to make extremely accurate calculations for positions on Earth’s surface. In addition, these clocks have to factor in the effects of time dilation, something so unnoticeable and negligible here on Earth’s surface, but so critical to the working of this technology. Thus, GPS technologies (and so many other technologies for that matter) are not solely the work of the engineers who designed them; they also represent the work of centuries of clock-makers, inventors and theoretical physicists who sought to understand the concept of time.