> The question is: can I create a situation which can not lead to stability?
From the perspective of the universe there is no "create" or "destroy" because time is not experienced, it is just one dimension of its existence. The concept of "create" only exists from the perspective of a 3 dimensional being experiencing the time dimension. We believe we can choose the future because we believe it hasn't happened yet, but that's an illusion of perspective. In a sense, this means that there is no free will, but that's a different argument.
So to answer the question: no, because the fundamental nature physics drops the probability that you would choose such an action to 0, the same way electrons have 0 probability of choosing paths that lead to the gap regions in the double slit experiment.
> And if so, what happens? Will it simply not work? Or will every situation lead to the possibility of stability?
From your perspective, every situation will lead to stability in the end, because the universe where it didn't has a probability of 0.
> Say, I travel back in time at the moment the universe "ends", and from that point onward in the past I destroy all time machines with a certain technology. Then, no one can fix what I did, and no stable loop could exist.
> I mean, my guess is that such a situation simply can not exist, therefore I can not experience it - I can not live in this universe where this is possible. So, I can only live in the universe where my technology somehow fails exactly when someone travels back in time to correct my loop.
Pretty much yes. Though universes in which the situation you describe is impossible to achieve regardless (either because time travel does not exist or because there's nothing you could do to prevent it from being invented again) are significantly more likely.
From the perspective of the universe there is no "create" or "destroy" because time is not experienced, it is just one dimension of its existence. The concept of "create" only exists from the perspective of a 3 dimensional being experiencing the time dimension. We believe we can choose the future because we believe it hasn't happened yet, but that's an illusion of perspective. In a sense, this means that there is no free will, but that's a different argument.
So to answer the question: no, because the fundamental nature physics drops the probability that you would choose such an action to 0, the same way electrons have 0 probability of choosing paths that lead to the gap regions in the double slit experiment.
> And if so, what happens? Will it simply not work? Or will every situation lead to the possibility of stability?
From your perspective, every situation will lead to stability in the end, because the universe where it didn't has a probability of 0.
> Say, I travel back in time at the moment the universe "ends", and from that point onward in the past I destroy all time machines with a certain technology. Then, no one can fix what I did, and no stable loop could exist.
> I mean, my guess is that such a situation simply can not exist, therefore I can not experience it - I can not live in this universe where this is possible. So, I can only live in the universe where my technology somehow fails exactly when someone travels back in time to correct my loop.
Pretty much yes. Though universes in which the situation you describe is impossible to achieve regardless (either because time travel does not exist or because there's nothing you could do to prevent it from being invented again) are significantly more likely.