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After the accident which sends Carter to the alternate universe, the episode was very heavy on the physics of alternate phases and alternate universe. I say this as an astronomer! Carter has seen alternate universes before, so I don't know why she had to chatter about it so much.
I will admit that I do enjoy seeing an "alternate" way that things could have happened. The idea that Atlantis had never been discovered, the stargate's existence had been revealed, and the Ori had attacked Earth once already are certainly huge differences between the universes. I do think that the reaction of the population to the stargate (lots of unrest) was probably pretty accurate.
In this universe, General Hammond is still in charge of the SGC, and Landry has become president. Colonel Mitchell left the service after his crash in Antarctica, and Major Lorne (or is he a colonel in the alternate universe?) is in charge of SG-1. Daniel Jackson has been captured by the Ori, Teal'c returned to the Jaffa some time ago, and Vala is in prison. The accident that brought the "real" Carter to the alternate universe was also determined to have killed the Carter of that universe. Strangely, however, no one seems too upset by that. I wondered when Carter was fishing for people she knew why she didn't ask for General O'Neill...they could have at least made up an excuse why she couldn't talk to him - heck, the writers could have said he was dead.
Carter finishes the phase-shifter/forcefield weapon that she had been working on in the "real" universe, just in time to save the Earth from another Ori attack. Since the stargate and the Ori are public knowledge, Carter's actions make her famous. President Landry, who has in the past had to institute martial law to keep the country under control, uses her as a moral booster for his administration. In fact, he considers her too valuable to want to let her try to return to her universe. This part of the episode is a neat turn-around to part of last season's episode "Ripple Effect": in that episode, a Dr. Frasier from an alternate universe pleaded with General Landry to be allowed to return to her universe because of urgent events happening there. Now Carter is in that situation, and Landry still isn't willing to cooperate.
A side note about the celebration party that Carter goes to: as an Air Force major (her rank in the alternate universe), shouldn't she be in uniform? Especially since she saved the Earth in a military capacity? Having her be in a revealing dress and high heels seems a little cheap, and it's hard to take her seriously, even for me.
Carter is determined to return to the "real" universe, since her weapon will be crucial there as well. She contacts her ex-husband in the alternate universe, Rodney McKay. Frankly, casting so many SG: Atlantis people on this episode is kind of annoying, and having her be married to McKay just seems to be going for some snickers. But, it is true that McKay is one of the few people with the knowledge and ability to help her figure out how to get back to her universe.
During these efforts, Carter is becoming more and more aware of the restrictive policies of President Landry's leadership. She sees a Goa'uld weapon (one of the sticks that causes pain and makes the victims eyes and mouth light up) used on a protestor. She is followed by Landry's subordinates. She learns that the election for the president have been postponed due to "civil unrest". In a crucial scene, she goes to visit Colonel Mitchell. She finds him with non-functional legs in a wheelchair in a dingy apartment with an ample supply of booze and cigarettes. He tells her that after the dogfight in Antarctica, he was a public hero and was getting first-class treatment for his injuries. But when he began to speak out against Landry's non-democratic practices, Mitchell was shunned and his medical treatment was stopped. It was certainly a shocking scene to see the vibrant Mitchell appear so defeated.
Carter decides to play along with the President and do the public appearances he wants. In her first interview on a news show, she begins to speak out against the President's policies. I did like that she did so in a very smart way: she played the President up as being willing to change his ways because he was smart and his intentions were good. Nevertheless, the President's lackeys cut off the news show. (As a side note, I did like that the reporter on the show was Julia Donovan, a reporter we've seen on SG-1 in the past, such as on "Prometheus" in season 6.) When Carter leaves the news station, she is forcibly abducted by the President's lackeys. I was happy to see that she took out several of her attackers before they subdued her - she has learned from her past abductions, after all. I was shocked that the President was willing to take such actions in public.
Finally, Carter is told that since she won't cooperate, she's allowed to try to return to her universe. McKay has been coerced to replace her brains at the SGC. He apparently helps her return, since before we can blink, she's back home in the "real" universe.
Frankly, letting Carter go so easily doesn't seem believable. After all, the alternate universe no longer has "their own" Carter, and even with McKay, certainly two brains are better than one. Apparently total coercion is beyond the will of even the alternate Landry.
When Carter returns to the "real" universe, she discovered that her friends didn't even know that she had left the universe. They thought she was simply out of phase. Because of that, they apparently spent a good deal of time initially in the room, talking to her to keep her company. That's a hilarious revelation. Of course, no one will reveal what they actually said to her. This seems fair, since Carter doesn't want to talk about what the alternate-universe SGC was like.
So what are the implications of this episode, since the events didn't happen in the "real" universe? Well, in the alternate universe, Carter was appalled that Earth no longer had ties with the Jaffa, Tok'ra, or other allies. The alternate universe characters countered with the idea that since they could protect themselves (via Carter's weapon), what did they need allies for? They had become completely isolationist and short-sighted and predicted that the "real" Earth would become that way as well if the weapon worked for them. Consequently, will Carter continue working on the weapon with the same zeal? Will she try to take any safeguards to keep Earth's alliances going?
In addition, she saw how easily the US could slip into a more totalitarian regime under the excuse of the Ori threat. Will she be able to take any steps to help prevent that in our universe? In the alternate universe, she seemed uncharacteritically forthright in her opposition to the President and General Hammond. Could she do this in our universe?