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: 
You've hit upon one of the lines of thinking by Kant.

In his thinking both options (1) & (2) are true; to Kant this suggests this is an actual contradiction, an *antinomy* in his language, and which is irresolvable; by us; one can say we are at the limit of thought, of the human capacity to reason - hence *a critique of pure reason*; establishing thus limits.

Contradictions & antinomies in the main current of European philosophy are severely frowned upon; there is an assumption, perhaps since the Enlightenment that reason can solve all, that the world in its entirety is an ordered and intelligible whole. The *mysterium tremendum* has only be looked at in the proper fashion, in right spirit of sustained enquiry for it to reveal itself as less tremendous and less mysterious.

We can suppose that the ontological tissue of the world, the fabric of reality is intelligible but we can also suppose by being finite creatures that we must then be epistemlogically finite; and between these two thoughts, which are separate thoughts and also the same thought is an antinomy; an antinomy that is nonetheless no less an antinomy for being dynamic.

Kant declared himself a new Copernicus; who recentred Philosophy in a new orbit; he swapped the role of subject and object; time and space lose there object-ive character and become subject-ive; they are the forms of intuitions that the mind has such that it can experience at all; they are the conditions for experience; but by being the substrate of subjective experience they also retain their objective character; this appears as an antinomy, but it is a resolvable one.

The phenomenal realm is both the objective and the subjective realm as normatively understood. Kant by outlawing noumena, by rendering it unspeakable and unsayable is outlawing the numinous. From Spinozas emanationist ontology he retains the mode of extension and of thought; the other modes, the infinity of them - the attributes of God and God himself are placed permanantly behind a veil.

In Ghazalis Occasionalism; not only is God required to create the world; he is required to create it from moment to moment; or rather to sustain it; to propel it along through the dynamic of natural law - his law (we may also call it the law of Vishnu); thus also the law of cause and effect. 

Kant, in a Promethean move takes this out of the hands of God and into the mind of Man; but that part of the mind that is inaccessible to us; not Freuds unconcious; nor something lower; but something that is immanent to mind. Can one put time out of mind? One can certainly write the words...

What was once a triad: Man - God - Object; is now a dyad: Man - Object; Kant banished God as once God banished man; then after the exile - execution: the Nietzschian gesture.
3 is correct. Time is a abstraction, a filing system used to arrange events and memories into a logical system of cause and effect.

Per relativity, space and time are not discrete entities, but a single construct called spacetime. Saying something is X km long is equal to saying it is Y seconds long. All units of time are based on and can be reduced to measures of distance.

Time is a mental construct used to make sense of movement. Movement produces the sensation and experience of time, not the other way around.