Time Dilation

Present scenario and experiments

Recently, researchers at the National Institute of Standards and Technology (NIST), Maryland, USA, used an optical clock which exploits the electronic transitions of an aluminium atom to record time intervals. It’s electrons switch states over a quadrillion times each second. This boosts the accuracy of the clock up to forty times than those of conventional caesium atomic clocks.

There was a clear difference in the readings of two optical clocks stationed at a vertical separation of fifty centimetres, at the same instants of time. Moreover, the effect was also demonstrated at speeds as minuscule as four meters per second.

Atomic clocks are essentially based on the natural transitions of electrons among different energy levels in an atom. The length of a unit time interval (that is, 1 second) is determined by the total number of complete oscillations (jump to the higher level and back to the original level) carried out by an electron. Such a measure is much more stable than a mechanical pendulum whose to and fro motion can be easily manipulated by the most feeble environmental or internal disturbances.

The experiments clearly demonstrated one of the basic postulates of Einstein’s theory. Firstly, there is a marked difference in the speed of time for an object placed farther away from the gravitational field as compared to another placed closer to it. Since, the latter object is subjected to a stronger gravitational pull, it also suffers greater time dilation, and hence, a clock attached to it runs slower. This is what has led to the popular phrase, “Time runs faster at your face than at your feet”, or, that our head is older than our feet.

Einstein’s Special Theory of Relativity

The famous Theory of Special Relativity, propounded by Albert Einstein, found its way to the scientific journal in 1905. Among many intriguing theoretical results, the theory also introduced concepts like time dilation, length contraction, and mass changes. The concept of time dilation states that time runs slower for an object as its speed increases.

Intuitive justification

The curious behaviour of time as explained by the special theory can be understood by a simple, crude analogy. The physical nature of the spacetime fabric is the foundation of Einstein’s Theory of General Relativity (that followed the Special Theory of Relativity). Space and time being inseparably intertwined with each other makes the phenomenon of time dilation quite intuitive.

Imagine a two-dimensional graphical representation with ‘North’ as the ‘Y’-axis, and ‘East’ along the ‘X’-axis. A car advancing through the space confined within the co-ordinate system can either move unidirectionally (that is, along either one of the two axes) or inclined at any non-zero angle (to the two axes). Clearly, the movement of the car in the latter fashion divides its motion between the two directions. A little more inclination towards North (‘Y’-axis) would give it more speed along the same direction, whereas, it would simultaneously lose an equivalent amount of speed along East (‘X’- axis). Employing the same analogy, if the ‘Y’ and ‘X’ axes are replaced by ‘time’ and ‘space’ respectively, the phenomenon of time dilation stands out as intuitive as Newton’s laws of mechanics. Considering ourselves in place of the car, travelling through space at a faster speed reduces the rate at which we perceive time to flow past us, and vice-versa. This crude analogy dovetails with Einstein’s theory of Special Relativity, headlong.

Although the comparison proffers no justification for the universal speed limit being that of light neither sheds any light on the fastest rate at which time can flow, it clearly explains why time is relative. Conclusively, time eventually stops (that is, the speed of time becomes zero), when one begins to move (only) along the space axis (which occurs when the speed of light is adopted).

The most natural offshoot of the aforementioned theory is that whenever we gain speed through our daily physical activities, we involuntarily force time to slow down (in our own frame of reference). This phenomenon is known as time dilation. Everyday changes in time are not appreciable enough to be detected, but are very much a part of reality. Understandably enough, the theory rocked the nineteenth century physicists off their chairs, given its flavour of scientific rebellion in an era when the absoluteness of time and space was a sacred school of thought.

Thus, in case of a non-zero velocity, one would always suffer a loss in the speed of time. This is exactly what happens when two points of the same object occupy different points of space with different effective, external forces. Since our feet are closer to the earth’s gravitational field, they endure greater time dilation as compared to our face which is stationed way above the surface.

Applications

Experiments with atomic clocks find useful applications in the field of navigation. For example, commercial airliners, which narrow down on the geographical co-ordinates of the aircraft, depend on the GPS (Global Positioning Services) satellites orbiting the earth at an altitude of around twenty thousand kilometres.

Since the satellites are in continuous motion, the time signal as sent by them is corrected for relativistic deviations, in order to achieve the acceptable accuracy of twenty to thirty nanoseconds. GPS satellites are installed with clocks having an accuracy of nearly few billionths of a second, and suffer a relativistic time dilation of about 4 microseconds a day. When combined with the effects of gravity, the number climbs up to about 7 microseconds (or, 7,000 nanoseconds). This difference is so tangible that a GPS unit without a relativistic correction showing the next gas station within the radius of half a mile, would be offset by nearly 5 miles the very next day.

On a more general scale, these experimental results may also contribute to testing of fundamental physics theories, like the character of space-time.

Time dilation has further added fuel to the active research in time-travel, and wormholes. Whether or not we are able to witness a time machine in the near future is uncertain. However, the special and general theories of relativity are one of the most beautiful examples of how mathematical and theoretical research can unveil the unseen character of our reality. That is, how space and time conspire together to make our world different from what we believe it to be!