The losties who escaped the island in the helicopter broke free into a parallel universe. The island is a plug between the universes, the waves the losties saw when they looked back was not the island disappearing but rather sinking. In the same way a button when pressed will be compressed, the island extends out of the water into one universe but remains below in the alternate universe. The island can only exist as its mirror opposite in the alternate universe of the button. In the same way as it acts as an amusing universe on/universe we know off indicator, it also explains why those we move the island cannot return. It is not possible to return to your own universe, just another one of many multiple universes.
The 'exotic matter' the button pressing by Desmond controlled was the alternate universe, the same energy which allowed apparations of Kate's horse and Locke's and Desmond's visions. When released by not pressing the button, the sky changed colour and Desmond saw multiple outcomes, which co-insides with seeing the outcome of what happens in multiple universes.
Mrs Hawking's assertion that it is not possible to change an outcome appears to be wrong, if there are multiple universes, multiple outcomes are possible because they exist as eventualities in multiple universes. If the losties are moving between universes, as Desmond may have been whilst mind jumping, anything is possible.
Mrs Hawking appears to believe the course of events as she understands them must be controlled or the alternative universe will apply and destroy their universe. This would imply a parallel universe which was created by the losties actions and there being the possibility of only one universe existing.