On the lack of time travelling tourists

Okay, so one of the standard arguments against time travel goes something like this. Let's say at some point in the future time travel is invented. It doesn't matter when. Unless the civilisation that produced the inventor is suddenly wiped out immediately after the invention, people from that civilisation would start travelling in time.

Every single future person from that point on who travels into the past to witness a certain historical event, such as the crucifixion of Jesus, was at that historical event. However, billions of time travelling tourists didn't attend all the big significant historical events.

You'd think someone would've noticed if they had.

The only reason, the argument goes, they aren't there is because at no point in the future does anyone invent time travel.

Now, the problem with this argument is that it assumes that time is one fixed block-like whole. That isn't, however, necessarily the way the world is. Consider instead that time is fluid, made up of multiple, dynamic, interacting timelines. The way that modern physics tends to see it.

In this model, a time machine is an alternate world creator. Every trip into the past splits off a separate timeline. Therefore, even if a civilisation builds time machine factories producing billions of time machines over thousands of years, each such time machine is at the centre of a conglomeration – or nest – of timelines it's created.

Or to put it another way, from the perspective of one particular world (such as ours) out of the infinity of alternates there can only ever be one time machine in operation, not billions.

Logically, it should be mine.