Time measurement

Time is one of the basic physical quantities. It has been influencing human life since ancient times, and people have been aware of the passage of time since they began to consciously notice their surroundings. Time differs from other basic physical quantities by the fact that it flows in only one direction. From the point of view of fundamental physical theories, such as the general theory of relativity, time has yet another, much more general significance – the reflection of the invariability of space-time against the shift in time, which is manifested by a key natural science law, a generalized law of Energy conservation. If we look at time with the eyes of quantum mechanics, we observe different time than that of classical physics. The time is quantized in tiny grains with a size of 10–35 s, as described by the prominent German physicist Max Planck at the turn of the 19th and 20th century. What is even more remarkable, is that time has its unstoppable beginning, the moment in which time arose together with the whole universe. We call this moment the Big Bang. Whether the time also has its end, it is again linked to the existence of the entire universe. If the universe has its end, it will end with a huge collapse called Big Crunch and time will end with it.

Perception of time

As stated above , time belongs to the physical quantities whose existence man began to realise first. The first perception of the passage of time relates to the perception of regular alternation of day and night. However, the cause of this phenomenon, that is, the rotation of the Earth around its axis (the gradual illumination of various places on the Earth by sunlight) was revealed much, much later. The second time interval that people began to realise was the gradual alternation of the phases of the Moon. Even here the perception of the phases of the Moon was very much preceded by an understanding of the reasons for their creation.

Units of time

Very simply, we can conclude that the first units of time that man begins to register are the day and the month. The existence of these units allows to construct long-term time intervals, the most typical being the year. What the length of the year is and how it relates to the length of the day and month that is the question addressed by the calendar or calendars. We focus on the issue of calendars in one of the following chapters, where we discuss the nature of the calendars, their historical development and the way how the creation of calendars was influenced by gradually improving knowledge of the Universe and the processes in it, including the suggestions, how to implement these into curricular and extracurricular activities for children aged 7–10 years. If a calendar is a means of recording longer time intervals, it is evident that in the process of human civilization development, people are beginning to be interested in determining time intervals shorter than one day with an increasing need for accuracy. In both fields of time intervals measurements, the basic standard is the nature, most often in the form of astronomical processes which determine the measurement of time and confirm (or disprove) the correctness of the measurement methods. As the knowledge of astronomical processes progresses, the accuracy of the verification of time measurement methods improves.

Measuring the time

When measuring time and transforming it into teaching methods, it is important to distinguish two basic types of measurements. One is the measurement of „What the time is“, where we are accustomed to using all sorts of clocks or watches, in the past the most commonly used were different types of sundials. The second is the measurement of the length of the time interval, i.e., measuring „How long the phenomenon lasted“. We can also use clocks or watches, record the beginning and end of the phenomenon and determine the duration of the phenomenon from the difference of these values, but very often in these cases special timekeeping devices are used, such as the stopwatch, earlier for example, the hourglass, water, candle or other clocks. To transform the process of measuring time, it is very useful to remind historical time gauges, as mentioned in the previous paragraph, but it is necessary to know the system limitations of individual gauges or methods of measuring time.

Year and month

From an astronomical point of view, the basic standard is one year, which is given by the revolution of the Earth around the Sun. Astronomers distinguish several definitions of the year associated with different reference systems. Out of these, the most important are tropical year (used most often in everyday life and linked to the calendar), Sidereal year and anomalistic year.

A tropical year year is defined as the time between two successive passages of the Sun through the vernal point (the vernal point is the intersection of the ecliptic, that is, the imaginary trajectory of the Sun in the celestial sphere, when it crosses the celestial equator, in which the Sun is located at the beginning of spring). It equals 365.242 192 129 days (365 d 5 h 48 min 45 s). It is a period when the seasons change in the temperate zones.

A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. It equals 365.256 363 051 days (365 d 6 h 9 min 9 s).

The anomalistic year is the time between two passages of Earth through perihelion (the point where the Earth is closest to the Sun). It equals 365.259 635 864 days (365 d 6 h 13 min 53 s).

Similarly, a month can be also defined differently. For calendar purposes, a synodic month is used, describing changes to the shape of the lunar disc from the observer‘s perspective from the Earth. Its length is 29.530, 588 853 days. The sidereal month is the period of revolution related to distant stars with a length of 27.321 661 547 days. The tropical month is related to the vernal point and equals 27.321 582 241 days, the anomalistic month is the period between two passages of Earth through perigee with a length of 27.554 549 878 days and the draconic month is related to the output node of the lunar orbit (this is the intersection of the trajectory of the centre of the lunar disc in celestial sphere with a celestial equator, in which the moon disc gets north (that is, „above“) from the celestial equator, and its length is 27.212 220 817 days.

In terms of measuring time as a topic for school or extracurricular education, shorter time units are more important. The basic unit of time is the second, which is defined as the duration of 9 192 631 770 periods of radiation, which corresponds to the transition between two layers of the very fine structure of the basic state of the atom 133Cs. Other units are units derived from the Sexagesimalsystem: Minute (1 min = 60 s), hour (1 h = 60 min = 3 600 s) and day (1 d = 24 h).


As mentioned above , the basic gauge of time in the sense of „what the time is“ are the sundials. Although there are more types of sundials, most often sundials show time in the way that the shadow thrown by the rod hits the dial with the sundial scale. The rod is referred to by its position relative to the dial as a gnomon (the rod is perpendicular to the plane of the dial) or as a style (the rod has a shift parallel to the Earth‘s rotary axis). The time measured by the sundial is derived from the movement of the solar disc through the sky. We refer to this time as a true solar time, and it is a time that is close to the one we have on clocks or watches however it is still different. There are three main causes of the differences:

  • In civil life, we use mean solar time, that is, a time that, unlike true solar time, runs evenly. The uneven flow of true solar time is because the tilt of the Earth’s axis towards the ecliptic (the plane of revolution of the Earth around the Sun) is 66.5 °, and the Earth‘s orbit around the Sun is an ellipse, not a circle. This makes true solar days different in length: the shortest true solar day is at the turn of June and July, when the Earth crosses the farthest point of its trajectory, the aphelion. On the contrary, the longest true solar day is at the turn of December and January, when the Earth passes the nearest point of its trajectory, the perihelion. Mean solar time is „averaged“ solar time, whose all days are the same length. The difference between true and mean solar time is changing over the course of the year, with the biggest differences in mid-February and early November, by approximately 15 minutes.

  • In civil life, we use zonetime, which is in the case of the Czech and Slovak republics and in the case of the Federal Republic of Germany mean solar time equivalent to the 15th meridian of eastern longitude In places that are west of this meridian, the value of true solar time is less, by 4 minutes to each degree of longitude. Similarly, in places east of the 15th meridian true solar time is greater (again by 4 minutes for each degree of longitude).

  • In civil life, we use summer time (Daylight saving time) which is an hour ahead of the Central European Time, from the end of March to the end of October.

We have to take these differences into account when constructing the sundial. On the other hand, the awareness of these fundamental differences between true and mean solar time makes it possible to explain these natural phenomena and their consequences in more detail. The simplest way is to „compensate“ the third stated difference (Daylight saving time): The scale can be supplemented with one more graduated scale with daylight saving time values. The second difference between mean and true solar time (latitude) is a constant shift of the scale. However, it is possible to compensate for the first difference, the gradual change of the differences between true and mean solar time caused by the tilt of the Earth’s axis and the elliptic trajectory of the Earth. In that case, the time indicator on the sundial’s scale will not be the line segment, but of the analemma curves. Such sundials can actually be seen in some places, but their construction is much more demanding and unsuitable for school purposes.

Some sundials may contain a spherical end, called a nodus at the end of the rod. Usually, such sundials have, in addition to the scale, other curves on the watch face that show the length of the shade on various important days of the year, for example, on the days of Equinox and Solstice (on the day of the Solstice the shadow of the node falls exactly on the solstice curve etc.). Then the sundials, in addition to the time telling, may be roughly showing, „which month of the year it is“. It can be acknowledged that this term is quite inaccurate and ambiguous for most months (only a pair of the respective months of the year may be determined from the length of the shade).

Measurement of the duration

Instruments to measure the duration of „how long the phenomenon lasted“ are also very appropriate for the school demonstration. It is possible to use both original measuring instruments, but pupils themselves make devices that are even more suitable. The most suitable for such production are hourglass and water clocks (of course, candle clocks are easily feasible, but in the conditions of pupils under 10 years of age, especially in larger groups there is a high risk of damage or injury.


For hourglass, it is important to use the most regular particles of sand. The best in this sense is river sand exposed to the long-term action of water, where the individual particles are abraded and acquire a regular, almost spherical shape by the action of water erosion and interaction with other particles. Before use, it is advisable to sieve still the sand through the strainer to eliminate the presence of larger grains of sand. Despite all the thoroughness of the preparation of the hourglass, it is necessary to expect that the time of trickling of sand from one part to another, and back, will not be the same. This is a typical feature of any physical phenomenon or process and is manifested by the fact that in different measurements we obtain different results. The demonstration of this phenomenon is a secondary but no less significant result of the work.

Water clocks

For water clocks made from a PET bottle with a hole in the lower part, it is possible to measure the time of liquid discharge from the bottle after opening the lid. Additionally, the bottle can be graduated, for example by means of a felt-tip pen, which allows to measure even smaller lengths of time intervals. It turns out that the scale is not even because the rate of discharge of the liquid decreases with decreasing water level in the vessel. The discharge also affects the size of the upper opening of the bottle, so it is possible to show a change in the time of water discharge from the bottle, for example, after partial loosening of the cap, or when closing the bottle with a lid of a suitably large hole. When working with water clocks, it is necessary to count with an increased disorder and the need of greater intensity of the teacher’s attention.