The Science of Time: This is taken from appendix 5 of my new book, How to Time Travel, which will be available on Amazon in early September 2013.

Approaching a scientific definition of time

How is coordinate time related to proper time? Einstein’s special theory of relativity relates coordinate time and proper time by the following convention. For an observer with a clock in an inertial frame of reference, the coordinate time at the event is equal to proper time at the event when measured by a clock that is stationary relative to the observer and at the same location as the event. This convention assumes synchronization of the clock at the event with the observer’s clock. Unfortunately, there have been numerous methods suggested for accurately synchronizing clocks and defining synchronization. For our purposes in defining coordinate time and proper time, it is only important to assume the hands of both clocks move in unison, independent of the method of synchronization.
Most of the scientific community agrees that the most accurate definition of time requires integration with the three normal spatial dimensions (i.e., height, width, and length). Therefore, the scientific community talks in terms of spacetime, especially in the context of relativity, where the event or observer may be moving near the speed of light relative to each another.

Let us consider an example. A clock moving close to the speed of light will appear to run slower to an observer at rest (one frame of reference) relative to the moving clock (another frame of reference). In simple terms, time is not an absolute, but is dependent on the relative motion of the event and observer. It may sound like science fiction that a clock moving at high velocity runs slower, but it is a widely verified science fact. Even the clock on a jet plane flying over an airport will run slightly slower than the clock at rest in the airport terminal. Einstein predicted this time dilation effect in his special theory of relativity, and he derived an equation to calculate the time difference.

Other physical factors affect time. For example, another scientific fact is that a clock in a strong gravitational field will run slower than a clock in a weak gravitational field. Einstein predicted this time dilation effect in his general theory of relativity.
Lastly, the time dilation effects of high velocity and strong gravitational fields are additive. That means a clock moving near the speed of light will move slower if it enters a strong gravitational field.
I termed this section “Approaching a scientific definition of time” for a reason. There is no consensus on the scientific definition of time. However, we can help ourselves conceptualize time by summarizing the salient points discussed above:

• In our everyday existence, time appears to be an absolute. Time is the same for everyone. When an event occurs, we believe it to occur simultaneously regardless of its relative position or velocity to us, or our relative position or velocity to the event. This is our everyday reality. We typically do not worry about accurately synchronizing our watches, since a minute one way or the other does not matter for most real-life applications. The simple fact is that treating time as an absolute works in most real-life applications. However, it is an illusion and breaks down as the relative velocity of any constituent approaches the speed of light, or when the distances from the event become extremely large and different for the observers. On this last point, regarding relative distances, consider the following example. An observer close to an event will record its occurrence a thousand years sooner than an observer a thousand light-years from the event. The reason for this is that it takes the light a thousand years to reach the furthest observer. This means that the stars we view at night may no longer exist. The light has traveled thousands to millions of light-years to reach our eyes. The stars may have died long ago, but we will not know it for thousands to millions of years.
• In the world of relativity, where frames of reference can move near the speed of light or gravitational fields can play a factor, time becomes relative. Here are four examples.

1. A clock moving near the speed of light will appear to run slower to an observer at rest, relative to the clock.

2. A clock in a strong gravitational field will appear to run slower to an observer a distance (as little as one meter) farther away from the gravitational field.

3. A clock will run even slower when moving near the speed of light when it enters a strong gravitational field (i.e., the affects are additive).

4. An event will appear to occur first to the observer closest to the event. The farther away an observer is from an event, the longer it will take the light to travel to the observer, and for the observer to become aware of the event.

Notice that all our attempts to define time fail. Instead, we describe how time behaves during an interval, a change in time. We are unable to point to an entity and say “that is time.” The reason for this is that time is not a single entity, but scientifically an interval. We cannot slice time down to a shadow-like sliver, a dimensionless interval. In fact, scientifically speaking, the smallest interval of time that science can theoretically define, based on the fundamental invariant aspects of the universe, is Planck time.

Planck time is the smallest interval of time that science is able to define. The theoretical formulation of Planck time comes from dimensional analysis, which studies units of measurement, physical constants, and the relationship between units of measurement and physical constants. In simpler terms, one Planck interval is approximately equal to 10^-44 seconds (i.e., 1 divided by 1 with 44 zeros after it). As far as the science community is concerned, there is a consensus that we would not be able to measure anything smaller than a Planck interval. In fact, the smallest interval science is able to measure as of this writing is trillions of times larger than a Planck interval. It is also widely believed that we would not be able to measure a change smaller than a Planck interval. From this standpoint, we can assert that time is only reducible to an interval, not a dimensionless sliver, and that interval is the Planck interval. Therefore, our scientific definition of time forces us to acknowledge that time is only definable as an interval, the Planck interval.