Time instant, time interval, units of time

clock inside an eye

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Instant in time

We use the symbol t for an instant in time (for example during the 4th

Our brain can rapidly process informations, we look at the clock and we translate this information to an instant in time.

We understant that time passes by every instant of a second, follows by another one and so on. There is a begging in creation itself . The universe has a intial moment , it’s birth .

Sundial in Sand

Sundial in Sand

Mr. Dionisis Mitropoulos a distinguished colleague , adds :

In our everyday language we use both the terms «a moment» and «a time instant» to declare a very small amount of time.

The last one (time instant) is described in Wikipedia as  «an infinitesimal moment in time, a moment whose passage is instantaneous …», implying actually an «infinitesimal time interval».

So, it is rather non – intuitive and hard for young students, to understand time instant in Physics, as just a «point on a timeline» which has no duration at all, in the same way as a geometrical point on an axis that has no dimensions.

Every day usage to the term moment , as little change in time has historical origin :


Byzantine Greek and Medieval Latin used terms as «points» and «moments» is several time periods as subdivisions of time .

One «point» has the time interval of  about 3 minutes (one hour is about 20 «points») and one «moment» has the time interval of about 1,5 minute (one hour is about 40 «moments»).

Αs sundials were used in day time and night time, the duration of one hour was … ranging. Each of the two corresponding to 1 / 12 of the length «East – West» and «West – East» .

We want to thank Mr. Dionisis Mitropoulos , for his useful comment (full of historical data and instructional value) .

Infinity Time


Δ(anything) means «change in» (anything) whatever quantity follows,

Δ(anything) = final (anything) – initial (anything) .

Δ is the greek letter delta, we use greek letters in physics honnoring the ascient Greeks.

An instant in time is different from the time taken or the time interval.
The symbol Δt is used for the time taken, for example students will start their lesson and they will hear the bell after one hour. In that case initial moment in time is t = 0 , and final moment in time is t = 1 hour.

Change in time :

Δt = tf – ti . 

Where tf is the final moment in time and ti is the initial moment in time.

We often set the initial moment in time as zero. A logical thing to do, as if we measure time with a chronometer. When we press the start button we set the initial time equals to zero, we later press the stop button and we mark the final time.

When we use chronometer Δt =  tf – ti = t – 0 = t, so in this particular case we may have Δt = t but generally an instant in time is not the same as the time interval.

time and clepsidra

Units of time

We measure time by seconds, 1 minute (min) = 60 seconds (sec) . The acient Babylonians created the 60 parts division which passed to anscient Greeks.

1 hour (h) = 60 minutes (min) , 1 day (d) = 24 hours (h) , 1 month = 30 days (d), 1 year = 12 months = 365 days (d).

We set 1 month equal to an average of 30 days and 1 year equals to an average of 365 days. Earth moves around the Sun in 365 plus ¼ days, and in our effor to analize and understand nature we make aproximations.


An example :

Μy daughter was born in 20th december of 2007 at noon (12 o’clock), it’s now 11th August of 2015 at noon also, let’s calculate her age in years, months, days, hours, minutes and seconds.

My little girl exists for 7 years, 7 months, 21 days.

In years:

21 days = (21 / 365) years =  0.057 years.

7 months = (7 / 12) years = 0.583 years.

So her age in years is:

7 + 0.057 + 0.583 = 7.640 years.

In months:

7 years = 7·12 months = 84 months.

21 days = (21 / 30) months = 0.7 months.

So her age in months is:

84 + 7 + 0.7 = 91.7 months.

In days:

7 years = 7·365 days = 2555 days.

7 months = 7·30 days = 210 days.

So her age in days is:

2555 + 210 + 21 = 2786 days.

In hours:

7 years = 7·365 days = 7·365·24 hours = 61320 hours.

7 months = 7·30 days = 7·30·24 hours = 5040 hours.

21 days = 21·24 hours = 504 hours.

So her age in hours is:

61320 + 5040 + 504 = 66864 hours.

In minutes:

We can follow the same process as before but we can also skip many steps:

66864 hours = 66864·60 minutes = 4011840 minutes.

In seconds:

We can follow the same process as before but we can also skip many steps:

4011840 minutes = 4011840·60 seconds = 240710400 seconds.

You can try to find your age in seconds.

a rusty clock

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