It's a fun film, if a bit unsatisfying because it presents viewers with a tantalizing scenario that it never fully explores: what if the Nimitz had stayed behind? What would be different about World War II? Robert Farley offers some speculation on the subject:
Integrating Nimitz into the fleet would have taken a while ("We're here from the future!") and it's not obvious what the most efficient way to use Nimitz would have been. One option would be to have Nimitz spearhead a task force to turn back and defeat the IJN invasions of the Dutch East Indies. With history driven intel, the obvious technological superiority of Nimitz, and the rest of the USN carrier fleet, the IJN would have been hard press to carry out operations with any degree of success. Nimitz would have been nearly invulnerable to Japanese air attack, assuming that A-7s and F-14s could be kept in the air for CAP. A successful attack would require waves of aircraft and suicidal tactics (press forward until Nimitz and her CAP ran out of missiles), and even then might not disable the carrier. A Japanese submarine could certainly give Nimitz a very bad day, but against sufficient escort and modern ASW, getting into firing position would be difficult.
An alternative use of Nimitz would involve trying to end the war right away by sustained air attacks on Tokyo. Nimitz would have carried a dozen or so A-6s, which in a sustained operation could have dropped a lot of bombs on Tokyo. The rest of the USN would either support Nimitz or concentrate on the DEI invasions. I'm no fan of strategic bombing, but on the heels of the sudden destruction of the IJN carrier fleet, the likely impending defeat of the IJN in SE Asia, and an essentially unstoppable bombing campaign over the capital, it wouldn't be terribly surprising to see the Japanese sue for peace. Of course, even the Nimitz couldn't stay on station indefinitely; eventually ordnance and jet fuel would run short, forcing Nimitz to retire (potentially for an extended period of time). [...]
The other big question (which Final Countdown does not touch upon) would be the availability of nuclear weapons onboard Nimitz. I simply don't know enough about nuclear weapons policy on USN carriers in the late 1970s and early 1980s, but it wouldn't be terribly surprising to find that Nimitz carried nukes. This would pose very interesting challenges; with sufficient weapons, Nimitz very likely could end both the Pacific and European wars before the end of 1942. Explaining the power of nuclear weapons to Roosevelt would be a challenge, as would convincing him not to use them, if Yelland and co. were even interested in going that direction.
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P.S. If you enjoy this type of speculative fiction, then you may be interested in some similar works:
Bombing Tokyo did nothing to bring the Japaneses any closer to suing for peace. Operation Meetinghouse (firebombing of Tokyo) destroyed 25% of the buildings in the city and killed an estimated 100,000, so a bunch of A-6s would have been pointless.
Since carriers carry lots of replacement parts and the specs for the ship dismantling it would have been a waste, same goes for the aircraft. Plus even then they carried a library of technical information, plus highly trained mechanics.
Its most effective use would have been if it would go solo (making even more difficult to find as it wouldn't have all those smoke stacks around) taking out everything that moved between Japan and any of the islands (assisted by the subs that did a great job at this too). This would have left the islands with far less supplied troops, in theory, making them easier to capture.
Of course I am not sure what kind of effect a dozen F-14s buzzing the Imperial Palace would have. Or capturing a few high ranking navy personal and giving them a tour, then dropping them off on main land Japan via a Sea King would have.
Robert Farley's speculation would only pan out if the Nimitz had arrived _after_ the attack on Pearl Harbour.
Destroying the IJN before it could attack would have removed the most pressing reason for the USA to declare war on Japan in 1941.
There may never have beed a declaration of war against Japan.
Arriving after the attack on Pearl would mean that (I imagine) after convincing the US navy who they were and what sort of capabilities that this one single aircraft carrier has, it would have been extremely hard to convince Roosevelt to not nuke Tokyo as soon as possible.