Friday, April 13, 2018

Unizor - Physics4Teens - Mechanics - Kinematics - Time

Notes to a video lecture on


Time is an undefined concept. In this way it is similar to such concepts as geometric point. It is specifically physical concept, and Physics needs this concept to quantitatively characterize the physical processes.

As is the case with any mathematical undefined concepts, we study not the concept of time itself, but its properties that we postulate.

Though time-related postulates might not seem as mathematically
rigorous as Euclidean postulates in Geometry, we will try to describe
them with utmost accuracy.

First of all, time is one of the forms of existence of the world around us, and any change in the world are related to change of time.
There are no changes in the world not related to change of time and,
from the opposite side, there is no change in time without some changes
in the world.

Using this connection between change of time and some changes in the
world around us, we can choose one particular process that occurs in our
world with relative regularity as the main time-measuring device and
measure time by changes in this process. Obviously, this process should
be stable, repetitive, regular, predictable etc. to be used as a
time-measuring device.

So, what can be used as such a process?

In the previous lecture we have suggested that the rotation of the Earth
around its axis can be used as this process. We have divided the period
of one rotation into 24 hours, each hour - into 60 minutes, each minute
- into 60 seconds, and suggested a second as the main unit of time.

In addition, classical Physics (a subject of this course) assumes (postulates, makes it an axiom) the continuity of time,
which implies that we can divide any interval of time into however
small intervals and still obtain valid time intervals, reflecting
certain changes in the world. That's why we can talk about milliseconds
(1/1000th of a second), microseconds (1/1000000th of a second) etc.

That means that we can choose any arbitrary moment of time as the beginning of time
(zero point) and use a real number of seconds since or before this
moment to any other moment of time. So, time can be measured and any
moment of time can be characterized by a real number - the number of
second since or before the beginning of time to this moment. This real
number is positive for all moments of time that characterize the
processes happened after the beginning of time and it is negative for
those that precede the beginning.

But how to determine the period of one rotation of the Earth that we
suggested as a time-measuring device? Well, we can use a telescope fixed
at some place on Earth, look at the stars and watch how they change
their location in the telescope. Obviously, they will move, as our
planet rotates, and after one rotation the stars will be in the same
position on the sky and in the telescope.

Unfortunately, this might be a good measure for technology in Ancient
Egypt, but today's necessities need more precision. So, let us describe
the contemporary time-measuring process.

Atomic clock is considered nowadays a standard for precise time
measurement. The time interval of 1 second in the International System
of Units (SI) is derived from the oscillation between two states of an
atom of an element cesium. More exactly, 1 second is a time interval
during which 9,192,631,770 oscillations occur. This clock's precision is
1 second in about 30 million years - quite sufficient for all
foreseeable needs.

For all simpler practical reasons people use the clock as a time
measuring device, periodically synchronizing it with atomic clock
through different interfaces.

We have already discussed the first axiom of time - continuity.
There is another very important time-related axiom accepted by classical
Physics. It states that physical processes behave the same, regardless
of time when they occur. In other words, an experiment conducted today
will have exactly the same outcome as an identical experiment conducted
tomorrow. In this statement the word "identical" is very important, it
means that everything involved in the experiment today must be the same
as in the tomorrow's experiment. If this rule is observed, the only
difference between experiments is the time when they are conducted, and
that must not affect the results of an experiment.

Another form of this axiom is: time is uniform.


The continuity and uniformity are properties of an abstract concept of time
that we use as the characteristic of all processes occurred in our
world. Time intervals can be measured by different kinds of clocks, the
unit of measurement accepted in the International System of Units (SI)
is a second.

Using these properties of time to define the motion, we can
always describe a motion in our three-dimensional space as three real
functions (space coordinates) x(t), y(t) and z(t) of real argument (time) t. The only thing we need is a system of Cartesian coordinates and a moment of time we choose as the beginning of motion.

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