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?

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Time can get very philosophical !!

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 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.

Time can be best defined as a measurable dimension in which events occur in a sequence from the past through the present to the future. It is a fundamental aspect of the universe that allows us to quantify and understand the progression of events and changes. In physics, time is often considered the fourth dimension alongside the three spatial dimensions.

The concept of time starting after the Big Bang stems from our current understanding of cosmology. According to the Big Bang theory, the universe began as a hot, dense state approximately 13.8 billion years ago. Prior to this event, the universe is described as being in a singularity, a state in which the laws of physics as we understand them break down. Time as we know it emerged along with the expansion of the universe following the Big Bang. Therefore, when we refer to the beginning of time after the Big Bang, we are referring to the point at which our current understanding of time began to unfold.

The concept of time likely first arose as humans began to observe and record recurring phenomena such as the rising and setting of the sun, the phases of the moon, and the changing of the seasons. Early civilizations developed calendars and methods of measuring time to organize their societies, track agricultural cycles, and coordinate activities. Over time, as scientific understanding advanced, our concept of time evolved to include more precise measurements and deeper philosophical considerations, ultimately leading to its incorporation into various scientific theories, including those in physics and cosmology.