Absolute Time

According to Newton, absolute time is the real and true time. You might think of it as the time kept by God's stopwatch, though anyone but fundamentalists should use this only as a metaphor. Like the British Royal Family, absolute time flows smoothly without relation to anything external and is not liable to any change.

Relative, apparent, and common time is, or was, measured by a sundial. But the solar day, the time it takes the sun to return to zenith, varies by about 20 minutes per year. Tapping the sundial will not correct this, and moving it every time the sun misbehaves pales very quickly. Ptolemy tried to avoid relative time using a sidereal day — the time it takes a star to return to zenith — he assumed this to be constant, because the (supposed) outermost celestial sphere has (supposedly) a constant, absolute motion. But once the outer rotating celestial sphere had been recycled into Newton's infinite space + rotating earth, astronomers had to think again.

Newton said, "it may be that there is no such thing as an equable motion whereby time may be accurately measured"[1]. Newton's laws of motion and Newton's universal law of gravitation indicate that any moving object that can be used as a clock can be knocked out of kilter by anything from a drunk tripping over it to a cosmic ray damaging its innards. We may never get to look at God's stopwatch. 

Newton believed that accelerating an object to any velocity, even close to the speed of light, would have no effect on absolute time. But deductions from *Einstein's special theory of relativity showed that that time measured by someone in a rocket ship would be slower than that measured by someone on earth. This led physicists to believe that there is no absolute time. Just as there is no scientific reason to believe in God, there is no scientific reason to believe in his stopwatch.

Newton also said, "The duration or perseverance of the existence of things remains the same, whether the motions are swift or slow." But in his time he had neither the means or inclination to test this idea experimentally. We now know that, for instance, unstable elementary particles will remain in existence longer if they are travelling swiftly relative to an observer than if they are motionless relative to the observer. Again, this follows from Einstein's Special Theory of Relativity.

Reference: [1] Scholium to the definitions in Philosophiae Naturalis Principia Mathematica, Bk. 1 (1689) (reading this is optional).