The
Senkaku/Diaoyu Islands lie in between Taiwan and Okinawa. As is the case with most modern territorial disputes, the islands are uninhabited barren rocks; the argument is not so much about the islands themselves, as it is about the control of marine resources (fish and petroleum) within the Exclusive Economic Zones surrounding the islands, should they be recognized as part of the sovereign territory of one country or the other.
A similar dispute has festered for decades in the South China Sea over the Spratly Islands, though in that case there are five/six territorial claimants rather than just the two/three (the uncertainty in numbers being caused by whether or not China and Taiwan ought to be considered two separate countries). So far, Red China has resisted going to war over either of these causes, though their recent buildup in naval power gives them much more capability to actually enforce their will in remote places if they choose to do so.
So much for the history lesson; your question was on possible futures, and specifically on whether the United States would be bound by treaty to come to Japan's aid if war actually broke out over these islands.
Japan's post-war pacifist Constitution in theory prevents them from forming a military force capable of launching an invasion of another country, or from actually declaring war - so if a war starts, it will have to be started by the Chinese. In practice, Japan does indeed have an army, navy, air force and other things a modern wealthy country needs for self-defence; they simply call them by different names and nominally place them all under civilian command to avoid violating their own Constitution. The Japanese
Navy Maritime Self-Defense Force, though legally just a part of the police force, is more than twice the size of the Australian navy. Military analysts both within Japan and outside generally believe it to be capable of doing what it's name implies: defending Japan from invasion. Facing a major full-scale invasion from a superpower (such as China or Russia), the JMSDF should at least slow the enemy down until the Americans come to the rescue.
And yes, there is a treaty between the United States and Japan in which America basically promises to defend the Japanese home islands against hostile invasion; US military bases are scattered across Japan to enable them to do this. But importantly, outlying islands are not included in the treaty. The southernmost of the Ryukyu Islands, for example, lie to the south of the Senkaku/Diaoyu Islands and, although they are internationally recognized as belonging to Japan and have a local population of over 100,000 people, America is not obliged to automatically respond to defend the Ryukyus if they are invaded by a hostile power (though of course Japan is free to ask for American assistance in such a circumstance; America is also free to act unilaterally to defend Japanese islands even without a formal Japanese request). Okinawa is one of the central Ryukyu Islands and has the largest US military presence of all the Japanese islands, so that island is probably safe; it's the islands south and west of Okinawa that are most vulnerable, as there is no formal US presence down there.
The Chinese, of course, are fully aware of the reduced legal obligations placed by the Americans on the outlying islands. If the Senkaku/Diaoyu Islands fall to China and America does nothing but whimper a lot, then I think the southern Ryukyus could well be next in their sights.
So, as I understand it, if China decides to actually use their sabres instead of just rattling them, but the war is limited to just the outlying islands, then America would be free to help Japan if asked - and would also be free to tell Japan that they're on their own in this regard.
