*Notes to a video lecture on http://www.unizor.com*

__Time__

*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

(1/1000

^{th}of a second), microseconds (1/1000000

^{th}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*.

CONCLUSION

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)***and**

*y(t)***of real argument (time)**

*z(t)***. The only thing we need is a system of Cartesian coordinates and a moment of time we choose as the beginning of motion.**

*t*
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