What are the effects of terrorism on world politics?
In general, terrorism makes world politics more complicated and difficult. This is because terrorism can cause very important problems even though terrorist groups are not clearly linked to states. The presence of non-state actors who can have a real impact on the world makes world politics more difficult.
We can see examples of this today. The best example is Al-Qaeda. Its 9/11 attacks damaged the United States without giving the US a clear enemy to attack. When Japan attacked Pearl Harbor in 1941, it was clear that the US was now at war with Japan. After 9/11 it was much less clear. The US ended up at war with Afghanistan and later with Iraq, but not with Saudi Arabia, the home country of the majority of the 9/11 attackers. The governments of Afghanistan, Iraq, and Saudi Arabia did not directly participate in the attacks, making it somewhat complicated and difficult to know how to respond to the attacks.
Terrorism also makes things difficult by making it possible to argue that the United States is at war against all Muslims. If one country had attacked the US, the US could retaliate against that country. Instead, the US is trying to retaliate against an entire phenomenon (militant Islam) that exists to some degree in many countries.
Thus, terrorism makes world politics more complicated. It allows non-state actors to affect the world, leaving states unsure as to how to respond to attacks.