The Time Machine

In the year 1899, Dr. Alexander Hartdegen (Guy Pearce) is a young inventor teaching at Columbia University in New York City. Unlike his conservative friend David Philby (Mark Addy), Alexander would rather do pure research than work in the world of business. After a mugger kills his fiancÃ©e, Emma, he devotes himself to build a time machine that will allow him to travel back in time and save her. When he completes the machine four years later, he travels back to 1899 and prevents her murder, only to see her killed by a horseless carriage.
Alexander soon comes to realize that any attempt to save Emma will invariably result in her murder through other circumstances. Distraught, Alexander travels forward in time to 2030 to discover if, by then, science has been able to solve his question of how to change the past, thus determining whether Emma's life can be saved. At the New York Public Library, a holographic librarian called Vox 114 insists that time travel is impossible, so Alexander continues into the future until 2037, when the accidental destruction of the Moon by space colonists renders the Earth virtually uninhabitable. When he restarts the time machine to avoid falling debris, he is knocked unconscious and travels to the year 802,701, at which point he regains consciousness and stops the machine.
By now, the human race has reverted to a primitive lifestyle. Some survivors, called "Eloi", live on the sides of cliffs of what was once Manhattan. Alexander is nursed back to health by a woman named Mara, one of the few Eloi who speak English. One night, Alexander and Mara's young brother, Kalen, dream of a frightening, jagged-toothed face. The next day, the Eloi are attacked and Mara is dragged underground by ape-like monsters. The creatures are called "Morlocks" and they hunt the Eloi for food. In order to rescue her, Kalen leads Alexander to Vox 114, which is still functioning after 800,000 years.
After learning from Vox how to find the Morlocks, Alexander enters their underground lair through an opening that resembles the face in his nightmare. He is almost immediately captured and thrown into an area where Mara sits in a cage. There he meets an intelligent, humanoid Morlock, who explains that Morlocks are the evolutionary descendants of the humans who went underground after the Moon broke apart, while the Eloi are evolved from those who remained on the surface. The humanoid Morlocks are a caste of telepaths who rule the other Morlocks.
The Morlock explains that Alexander cannot alter Emma's fate because her death is what drove him to build the time machine in the first place: saving her would create a temporal paradox. He then reveals that the Morlocks have brought the time machine underground, and tells Alexander to get into it and return home. Alexander gets into the machine but also pulls the Morlock in with him, carrying them into the future as they fight. The Morlock dies by rapidly aging when Alexander pushes him outside of the machine's temporal bubble. Alexander then stops millions of years in the future in the year 635,427,810, revealing a harsh, rust-colored sky over a wasteland of Morlock caves.
Finally accepting that he cannot save Emma, Alexander travels back to rescue Mara. After freeing her, he starts the time machine and jams its gears, creating a violent distortion in time. Though pursued by the Morlocks, Alexander and Mara escape to the surface as the time distortion explodes, killing the Morlocks and destroying their caves along with the time machine. Alexander begins a new life with Mara and the Eloi in 802,701.
While Alexander shows Mara and Kalen a clearing that was once the location of his laboratory, back in 1899, in the same spot, Philby and Alexander's housekeeper, Mrs. Watchit, are in the laboratory and sadly discuss his absence. Philby tells Mrs. Watchit he is glad that Alexander has gone to a place where he can find peace, then tells her that he would like to hire her as a housekeeper, which she accepts until Alexander returns. Mrs. Watchit bids Alexander farewell and Philby leaves, looking toward the laboratory affectionately, then throws his bowler hat away in tribute to Alexander's distaste for conformity.

Question: Who's fate can Alexander not alter?
Answer: Emma's