How can the future protect themselves by wiping out the past in Tenet?

Question

In Tenet, it is told that the future wants to wipe out the past because their rivers ran dry and oceans rose, because of global warming, etc...but if they wipe out the past completely including the Earth, the future will be wiped out as well, they won't exist.

So as the movie describes it as the Grandfather paradox, is that the reason? Will they, the future, still exist after wiping out the past?

Answer 1

It is explained at some point that the scientist that created the turnstiles in the future also discovered a way to invert the entropy of the entire world's flow (the Algorithm), not only a few objects and people.

As explained here,

The effect of the Algorithm being activated would be mass annihilation. Every particle in the world would simultaneously be reflected back in time and bump into its past self coming the other way. All of those particle pairs would cease to exist and there would be a release of energy on an unfathomable scale - though, in theory, this explosion would be directed backwards in time, leaving the world after the Algorithm was activated untouched.

Although obviously not realistic, the idea suggests that the future will still exist, and time would flow backwards so the future people will still be alive and well, and from their perspective time would flow normally, but towards the past.

Nolan himself said in an interview

This film is not a time-travel film. It deals with time and the different ways in which time can function. Not to get into a physics lesson, but inversion is this idea of material that has had its entropy inverted, so it’s running backwards through time, relative to us.

So it doesn't seem to be taking the Grandfather's paradox into the plot. He also said

I did have Kip Thorne read the script and he helped me out with some of the concepts, though we’re not going to make any case for this being scientifically accurate.

Answer 2

The case the movie seems to make (through Neil) is that it's unknowable what would actually happen, but that people in the future (the ones directing Andrei Sator, at least) believe that it would work out for them (or are willing to risk it).

NEIL
The classic thought experiment – if you went back in time and killed your own grandfather, how could you have been born to commit the act?

PROTAGONIST
What’s the answer?

NEIL
There is no answer, it’s a paradox. But in the future, those in power clearly believe that you can kick Grandpa down the stairs, gouge his eyes and slit his throat without consequence.

PROTAGONIST
Could they be right?

NEIL
It doesn’t matter. They believe it, so they’re willing to destroy us.

Source

If the future wipe out the past where their own ancestors live, then they can't exist, but if they don't exist then they didn't wipe out the past. There is no consistent explanation of how this could work (without invoking multiple timelines, or some sort of "meta-time" in which the regular timeline can undergo change; the characters have no evidence of any of that, and arguably couldn't observe any evidence even if it were real).

It's possible that the timeline can in fact undergo change (or fork multiverses), and so can change from one the one we know to one in which people from the future are living backwards into a completely different past. Perhaps in the future there is some scientific evidence of this, or perhaps they just take it on blind hubristic faith.

Or it's possible that the attempt to eradicate the past will eradicate both the past and the future.

Alternatively, it's possible that (as the protagonist wonders immediately after the quote above) the mere fact that the characters exist proves that the algorithm will never be activated.

The movie does not attempt to resolve this question. Rather it simply posits that the people in the future directing the war have resolved the question for themselves (whether in truth, in error, or in hubris, we do not know), and have determined to try to eradicate the past.

The protagonists believe that they need to fight against this effort, even though they aren't sure whether their enemy can actually achieve their goals; they aren't completely sure that the enemy can't win, either.

And thus we have the main conflict of the movie, even though the movie makes an argument that there is nothing to fight over.