This aim could be judged too ambitious not only because of the young age of students but also because of the short time that is usually reserved by school curricula to the courses of physics in the schools.
To reach this aim it is useful to support the team work of the students for the realisation of hand made devices and systematic observations with critical discussions to make them aware of the motivation and the consequences of what is being studied.
The awareness of the historical dimension is of prime importance in this respect.
The frames and sample choosing for the description of phenomena are the foundation of any courses of physics.
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Rather than mere objects ,physics examines events in the sense of
what happens in space and time and we know that the evaluation of time
has always been a fundamental necessity for the social life of men. The fourth dimension of a space-time universe that leads, following Minkowsky Chronotopo (*), to present events that can be put in order only in space, and on the other side to different points of the space -time universe where it make sense to speak of "past" and "future" underlining possible cause-effect links, is a novelty only from a scientific point of view. |
The laws of physics always demand homogeneity of space and time ,that is to be the same at same conditions in any place and to remain immutable with the passing of time.
(*) Chrono = time - Topo = place but in italian it means "mouse".
"Quid est tempus ? Si nemo ex me quaerat, scio ; si quarenti explicare velim, nescio."
For Agostino , the time is a kind of becoming included between past and future :
"But theese two times, past and future, how are they ?
If the past is past and the future is not yet arrived ?
The present at least, if it always would be
present, never fluing on in past, could not be considered time but
eternity... "
When Agostino deals with the problem of the measure of an interval of time, he underlines that the time, enlarging, brings itself to divide into past and future so that the present can not have space.
"Where is indeed the time we can call long ?
Is it the future ? But we don't say "is long" but "will be long".
So ,when it will be long ?
..........but, my Lord, we have the perception of time intervals, we
compare one interval with anotherone, we say some of them are longer than
others, some shorter ....
but we do the meseaure while it's flowing on when we do it perceiving it.
On the contrary, the past that is not anymore and the future that is not
yet.......who can measure it ?"
......perhaps we can say the times are three:
Newton approachs the topic saying that there are two different things:
- a "......tempus absolutum, verum et matematicum in se et natura sua,sine
relatione ad externum quodvis....."
- and a practical measure of time interval .
It is not possible, at every level of school curricula in which physics is teached, from the first years of professional schools to classical liceums, to give even a vague idea of the problems of the chronotopic space in an even approximate eucledian structure or of the indetermination of quantistic nature.
It is on the other hand clear the need to introduce the concept of fundamental measures : and time is indoubtedly one of them, is sometimes explained in a slightly dogmatic way because of the problems implied in its teaching.
We believe that our suggestion on how to start its teaching in connection with the studying of astronomical phenomena may make it easier, more attractive and more stimulating.
To tackle the problem of the measure of time through its historical development implies the use of simple instruments that do not create any special difficulty in understanding their manner of working.
Moreover they present an immediate connection with natural phenomena, thus avoiding the need to use, for measuring operations , "black boxes" such as any modern watches from the most economic to the most sophisticated ones, would appear to our pupils.
We operated in a Professional Institute where the same teacher was teaching in parts of a course still organized in a way that now is changing : in this case we have physics from the second to the fifth (the last) year ; while in the course of new educational system the same teacher was teaching in the first and second year (in this case the students study physics only in the three first years.)
A different situation we have for teachers working in scientific liceum, where the courses of physics are for older students (16-17-18 years old) with rather a good knowledge of litterature , philosophy and history. In a classic liceum at least the students study physics only 2-3 hours a week and only the last two years.
We want underline that in Italy the political wind brings so many different proposals concerning the very wanted reform, that it is difficult to plan for different kind of schools the working programs.
Although the topic of measuring time, as we are proposing now, could seem to be hard to do because of the few hours of physics we have in our curricula, our experience brings us to say that, when we approach a big topic with enthusiasm in a modern way, the reaction of students is good, even if it is necessary for them a lot of work more .
It was necessary to choose different strategies and different levels of deeping not only for different ages but also for different curriculas.
For example measurements with gnomon (see later on) have been really done by youngest students while they have been only mentioned for the older students of liceum.
Vice versa we could'nt deal with the youngest pupils the historical and litterary citations which were so interesting and stimulating starting point for working groups of older students.
The preliminary discussion between teachers about which were the best
didactic paths to follow, brought us to the idea to alternate, anyway,
teorical considerations about the problem of measuring time with the
presentation of practical problems and relative discussions.
We could anyway recognize, between different strategies, some commun aims .
The measure of an interval of time, like any other measurement, needs a
sample and the decision to chooce a sample implies an arbitrary act.
It should be noticed that many natural phenomena give the observer the
impression of repeating themselves, within a certain approximation,
identically with the passing of time.
Saying that a phenomenon is periodic, for example that the seasons are recurring at equal intervals of time, that a star rises and sets always at the same time, that the rythmes of our pulse are regular , that the times for emplying a container repeat themselves every time the experiment is repeated......... implies a definition of what is intended by periodicity, a definiotion that in itself makes it necessary to measure an interval of time, that is an "a priori" decision to choose a phenomenon as a term of reference.
It is a problem that returns on itself ! In order to control if a phenomenon is periodic , we need to have a "watch" but a watch is based on the choice of a phenomenon as a pattern of periodicity.
If the pattern of periodicity is the time to empty a clessydra, the pulse beat at the awaking in the morning will be rather slower than the beat measured after having run the 100 metres in athletics. On the other hand, if we choose the pulse beat as the phenomenon that measures the time,we shall find ,after a quiet sleep, that the clessydra has accelerated, while it will have retarded after we have run the 100 metres : the clessydra is therefore a very bad watch !
Such simple examples make it clear that we must use our freedom of choice to discard such subjective patterns as pulse beat.
In other words it is only by means of a measure, that it becomes possible to find out if and how much an interval of time is longer, equal or shorter than anotherone, so it means, whether the phenomenon we have chosen can be assumed as a phenomenon periodic in time.
It must be quite clear that when we talk about arbitrarity in the choice of a sample we do not mean a purely casual choice without any bonds in point of opportunity or fitness for the interpretation of the phenomena; we only want to underline the methodological principle to which the researcher must stick.
Such awareness can be transmitted to the students in quite a lively way if they are made to consider the various historical steps by which this fundamental problem of measure has gone through, by means of the concepts of night and day, of the clessidra emptying, of the oscillation of the radiation emitted by an atom of Cesio.
The historical approach, even when simplfied in order to adapt it to a didactic method, has been proved as a very good channel to make the students understand the fundamental methodological implication in the choice of a sample.
The samples of the unity of time have varied in the course of the centuries not as a consequence of casual whims, or of changing fashions, or for national pride and not even linked purely to tecnological progress, but for the fundamental motivation of arriving at an instrument that could allowed a description of natural phenomena strictly connected to models of interpretation as simple ,as general and presumably as lasting as possible.
We have used these notions in order to make the students understand, by means of historical observations and references, the history of the time equation and the various choice as linked to local and biological factors.
On this point it is possible to conduct experiments in the classes (to evaluate the time without the help of a watch in conducting various activities , to compare it with the evaluation of people of different ages, to give special readings.....)
As for the calculations of dates we briefly refer to the Roman system that used three fixed days for the date of the month : the first (Calendae) the 5th or 7th (Nonae) and the 13th or 15th (Ides).
As for the hours the Romans used the first Italian scale we know in
historical time.
It is known as the scale of the "horae temporariae".
They distinguished the "dies naturalis" (from the dawn to the sunset ) from the "dies civilis o legitimus" inclusive of dies naturalis and the "nox".
They divided both, the day and the night ,in the four parts of three hours
each.
The four parts of the day were closed by hours "tertia", "sexta", "nona"
and "duodecima" which coincided with sunset ("solis occasus".)
At equinozi theese hours coincided with ours 9, 12, 15 and 18.
The lenght of day in Italy varies from a minimum of about 8 hours to a
maximum of about 16 hours, around the summer solstizio.
So in a period of solstizio the temporary hours may last 20 minutes less or more than ordinary hours.
In order to know the hour of a day ,it was built a sundial calibrated on
latitude of Rome, in 56 B.C. and an horizontal "meridiana" in Campo
Marzio.
In the proceding they built also clessidra and idraulic and mecanic clocks
which were scanning a time fluing in a uniform way in order to count ,for
example , the time to dedicate to each orator. So it means hours
"aequalia" or equinoziali.
The device you can see in the picture was built by students of second year of Istituto Professionale ( 16 years old ).
After the fall of Impero Romano d' Occidente it has been introduced in
Italy an important novelty imported from Jewish.
They began to count the start point of a day from the sunset .
The knowledge of the time of a day became a knowledge of all the people only beginning from IV cent., when, because of freedom in religion, after Costantino, the sound of bells used to remind time for prayers but also indicate all over the countryside the hours for men coming back from working .
So, temporary hours like those one in use in roman life but with the beginning point in the sunset, gave us during all medieval time news like this one:
"an earthquake in Pontremoli at two o'clock in the night....."
that means 45 past 8 p.m.
After temporary hours, we had what was called "ORE ITALIANE". It was an hour-counting system in use all over great part of Europe, from 1200 to 1800.
Their characteristic was to be all the same lenght but, as the starting point was the Ave Maria prayer in the evening, at the end of twilight, meaning about half an hour after sunset, we know that it means that different places with different distance from equator had different start point.
The device built by the students, that you can see in the picture, helps them to consider that it is an hour-counting system varying with seasons and with latitude, although they are hours of the same length.
| We have in Italy in used to say "portare il cappello sulle ventitrč" ;
it is "to wear the cap on the twentythree". The reason of this use becomes from italian hours and it is still in use. It dependes by the fact that one hour before the sun set (it is twentythree in this way of counting hours) you have to put your cap in a way so that sun rays do not hit your eyes. Students showed to appreciate this curiosity ! Referring to the same way to count hours we can find that Dante Alighieri says that the death of Beatrice happens "alla prima ora del nono giorno del mese" that means "at the first hour of the ninth day of the month" of June and it corresponds to 8 June, one hour after the sunset. |
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In order to put into practice the topic, after a discussion in the classroom, it were proposed exercises like the following two :
- What would you suggest to the workers ?
- Explain what's the difference between the two counting systems, expecially
concerning the money.
- Would your suggestion be the same if the work should be done to shovel the
snow during Christmas time ?
- Why ?
Answer :
The Northern part of Italy, Padana Valley, is exactely 45° latitude North, in a temperate climate zone of boreal hemisphere in which the mowing happens in June.
In Cirenaica ( Libia ), known as "granary of Rome", of course the mowing should be much before on Spring.
We can note on the hand made device, that from sun rise to midday (hora
sexta) there are six "horae temporariae", on the contrary the "aequales horae"
are eight, as you can see when you move the slider up to the line (21 june)
summer solstice.
So it's clear that the best for the workers is to be payed in the "aequales
horae" counting system.
Near Christmas day the "temporariae horae" remain six, while "aequales horae"
become three and half about.
The workers must do the opposite choice, it means to be payed in
"temporariae" hours.
We imagine a "temperatore" coming back to his job to reset the clock of a bell tower every seven days beginning from the middle day of 15 september.
What's the time at the moment of the 1rst regulation?
On which hour he must put the hands to indicate the midday, 8 weeks later ?
If we want te compare the time of this bell tower, still in midday, with the time of a clock that is on the 8th of november, in France where was in use the Gallicana hour system counting, that used to count the hours like us now, so it means from the middlenight, how many hours are the difference? Is this difference the. same all over the year ?Answer : On the 15th of september at rnidday the clock is pointed on 17 h 30 m. In fact from half an hour after the sun set (twilight) to middnight it lasts five hours and half, from middnight to midday that makes in total 17 hours and half.
In 8 (weeks) x 7 ( days) = 56 days the twilight has moved of 84 minutes ( 1 m 30 s x 56 = 84 m = 1 h and 24 minutes.).
It means that the distance between the twilight the next middav is now 1 hour and 24 m longer. 17h30 m + 1 h 24 m = 18h54 m.
The moderator must put the hands on six minutes before 19.
The 8th of November is exactly 8 weeks later (of l5th september ): so the shift of the clock is 6 hours and 54 minutes.
The shift referred to Gallicana hours counting system is now 6 hours and 54 rninutes. This difference obviously change along the year considering the different length of the night during the year.
During the discussions a very interesting problem arose about the theory of gravitational waves. At the moment we prefer not to tackle it , with students.
We limit asking which watches we must choose to sincronize each watch with another:
watches based on earth , solar cinematics, pendolum watches , it means watches based on gravitation forces, or atomic watches ? Isn't it a very interesting question ?
