Disappearances

I have finished reading the 454-page Volume II of SM Stirling's Nantucket Trilogy and have begun to read the 630-page Volume III. (See image.) The single sentence that I will discuss in this post is equally relevant to Poul Anderson's Time Patrol series:

"...an entire history - three millennia of people, being born and living, fighting and bearing children and dying - had...vanished...when the Event happened."
-SM Stirling, On The Oceans Of Eternity (New York, 2000), Chapter One, p. 8.

If I vanish or disappear to you, then you cease to perceive me either because I have ceased to exist or for some other reason. At time t2, time t1 has vanished or disappeared to us. Is this because t1 has ceased to exist or for some other reason? What would it mean to say that t1 does not exist? Does this mean just that, at t2, t1 is not the present moment because t2 is? If someone was alive at t1 but is no longer alive at t2, then it follows that he does not exist at t2 but it does not cease to be true that he was alive at t1.

Stirling has written a series describing later events in the "vanished" timeline, thus confirming that that timeline has not ceased to exist. However, in this post, I merely address the logical implications of the vanishment of a timeline. If the timeline did exist but is no longer perceived by the Nantucketers, then it seems to be in the same ontological category as the t1 that is no longer perceived by those who have lived from t1 into t2. t1 and the vanished timeline are past. t1 is in the past of the current timeline. Since the vanished timeline is an entire timeline, it exists not in the past of the current timeline but in the past of a second temporal dimension at right angles to the first. The current timeline exists in the present of the second temporal dimension.