How can you best define the concept of time? How can we say that time started after the Big Bang? How did this arbitrary concept first come about?
Time is a very slippery concept.
Are you wanting a concept based on the "conventional"?
Or are you willing to consider radical ideas?
See below references
See this: http://www.exactlywhatistime.com/
Check this out:
Time can get very philosophical !!
Time is the fourth dimension of four dimensional spacetime.
Time used to be thought of as an independent variable. It was considered that time passed at the same rate for all observers. It went linearly from past to future. This is the Newton model. Velocity is distance divided by time. So, time as a concept is the interval between two events.
This model was proved incorrect. Relativity describes the universe as four dimensional spacetime. Time is the fourth dimension. Every object has event which are points in spacetime. The distance between event is both spacial distance and the time interval between events.
Different observers each experience time passing at the same rate. Observers also observe time passing more slowly for others who are travelling at high speed or in a strong gravity field.
As time is a dimension of spacetime, it makes no sense of saying "before" the big bang. Spacetime came into existence at the big bang. So, time came into existence at the big bang.
Time is a variable. Time is part of the space time universe
Time is affected by gravity. In a gravitational field time is slowed down. This creates what is called mass lensing. Light doesn't slow down it experiences time differently in gravity. This is what causes the appearance of the bending of light in an eclipse. ( The predicted bending of light due to gravity confirmed in an eclipse verified the theory of Relativity.)
Time is affected velocity at the speed of light time ceases to exist. For a photon traveling at the speed of light time does not exist. (As the Hebrew poet stated a thousand years is the same as a day, and a day the same as thousand years.) Light year are a good measure of distance but not a valid measure of time.
As time is part of the space time continuum time did not and could not exist without the space time continuum. So when the space time continuum came into existence time came into existence. Time is not arbitrary it is an essential part of the existence of the universe. Without time the universe can not exist. Without the universe time can not exist.