Question: When I consider my own existence with respect to time I can imagine three possibilities: 

(1) **Time extends infinitely into the past.** In this case, how can the present, with me in it, exist, since there would be an infinite period of time that existed before the present. That seems illogical. 

(2) **Time had a starting point from which everything in our universe evolved to the present (t=1).** That possibility would require something (God) to start the clock ticking (t=0). But in this case we're back to square 1 with the problem of an infinite past. So the only possibility that makes sense to me is a third possibility 

(3) **Where time is some sort of abstraction in human consciousness that we need in order to relate cause and effect.**

Answer: 
A popular saying is: "Time doesn't exist, only clocks exist."

Time, like all units of measurement, are abstractions.

In physics, the purest way of comparison is the direct one: How long is this thing compared to that thing. It yields a fraction of some sort, which most importantly is *invariant*.

This fraction has no units, is directly bound to the original question and never varies, no matter our frame of reference or unit of measurement.

The thing is, if we can't measure one of the things before tomorrow, and we can't measure the other thing after today. That is when we introduce units of measurements, because units of measurement *co-vary*.

When we change our frame of reference, say by pretending everything is twice as big (effectively cutting all our reference units in half), all off our measurements go up by a factor of two.

Therefore, comparing the measurements to one another still yields an invariant fraction!

Time is measured in seconds, which is defined as some high number of periods in microwave radiation emitted by Cesium atoms cooled to some low temperature under some special conditions, in an atomic clock.

But atomic clocks are subject to time dilation courtesy special and general relativity.

If you put an atomic clock on a spacecraft (which has been done, by the way) and send it into orbit, the lower gravity will make the space clock disagree with an identically calibrated twin left on earth.

So when we say "it takes N seconds" we really mean "if I put an atomic clock next to this thing, the dial on the atomic clock would show the number N when this process has reached the end state."

Humans feel time passing because of some physical processes in our brains behave like (very inaccurate, compared to atomic ones) clocks.

**But what does time then abstract?** Entropy.

The universe is continually descending into informational chaos, usually in the form of heat. Entropy starts in the laws of quantum mechanics where a certain ubiquitous interaction causes loss of information; this can be proven to be an instance of Liouville's Theorem.

Some cosmologists and epistemological mathematicians currently believe that the final formulation of quantum mechanics will not include "time" as a parameter anywhere, and that time will be a derivable quantity.
You've presented a false dichotomy: just because something is a "mental construct" doesn't mean that it can't also be a real property of the physical universe.

Take length as an example. "Length," as such, doesn't exist physically. It's not something you can see or touch. Nevertheless, it is a real quality of physical objects--it exists "out there" and not just in our heads. In this respect, length is like any other *measure*--it's an abstraction in the sense that it does not exist in and of itself, but it nevertheless describes real qualities of physical objects.

Time is no different. The more you understand of physics, the less sense it makes to think of time "extending" in any direction. Time isn't a medium, it's a *measure*, and what it measures is **change.** As for what change itself is, well...that's still an [unanswered question!](http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics)