1 - Time, gravity, and quantum mechanics

Summary

The role that time plays in Einstein's theory of gravity and in quantum mechanics is described, and the difficulties that these conflicting roles present for a quantum theory of gravity are discussed.

Gravity and time

The relation of any fundamental theory to time is crucial as was evident from the earliest days of physics. If we go back to Newton's Principia, in which he established a general theoretical structure for the field of physics, we find an odd series of sentences in the first few pages. He tells us that it is unnecessary to define time as it is obvious to all, but then proceeds to do just that. And his definition is, certainly to modern eyes, rather strange. To quote

I do not define time, space, place, and motion as being well known to all. Only I observe, that the common people conceive these quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

I. Absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

Reading this definition today, it is hard to see what the fuss is about. Time for us common folk is exactly Newton's true time.