The Crime That The Time Patrol Cannot Prevent

A lone time criminal sends a doomsday devise programmed to detonate on arrival to a time before the earliest Time Patrol or other extratemporal presence on Earth. This would generate a timeline in which:

Earth exploded before any Terrestrial life had developed;
before the explosion, no time traveler had arrived from the prevented future;
even if a time traveler had arrived, s/he would not have been able to do anything to prevent the explosion.

Why would anyone commit such a crime? Some people do mad things.

It is possible that this crime has been committed. The bomb leaves timeline 1 to arrive and explode in timeline 2. In timeline 2, no one knows that a crime has been committed. In timeline 1, only the perpetrator knows.

There is a moment, t1, at which the criminal presses the button that sends the bomb backwards along the familiar temporal dimension and, we must add, forward along a second temporal dimension. In my opinion, from the point of view of its inhabitants, timeline 1 exists until t1 and continues to exist after t1.

Before t1, the criminal exists and is conscious of his existence. However, if he accepts the Time Patrol view of time travel paradoxes, then, before t1, he thinks, "After t1, it will be true to say that I have never existed; it will then be true to say that I did not exist even at this present moment when I am thinking this."  A patently self-contradictory thought.

However, there is no contradiction in saying that:

the criminal exists at t1 in timeline 1 but does not exist at t1 in timeline 2, in fact has never existed in timeline 2;
timeline 2 succeeds timeline 1 along a second temporal dimension;
if there is any observer for whom the second temporal dimension is his single temporal dimension, then, from that observer's perspective, it is true to say that timeline 1 has ceased to exist but not that it has never existed.

Thus, in timeline 1, the Time Patrol remains unaware that a time criminal has generated timeline 2. I specified that the explosion occurred before the earliest Time Patrol presence on Earth. However, suppose that, because of a quantum change in space-time-energy, one Time Patrolman did travel to a time before the explosion. That Patrolman might then travel forward into timeline 2. But everyone else would remain unaware of timeline 2.