A Dangerous Method

Sabina Spielrein arrives at the BurghÃ¶lzli, the pre-eminent psychiatric hospital in Zurich, with a typical case of hysteria and begins a new course of treatment with the young Swiss doctor, Carl Jung. He is using word association and dream interpretation as part of his approach to Freud's radical new science of psychoanalysis, and finds that Spielrein's condition was triggered by the humiliation and sexual arousal she felt as a child due to her short-tempered father's habit of spanking her naked. These conflicting feelings were compounded by her instinctive knowledge (imparted by an angel's voice that speaks in German) that she had done nothing to deserve such a punishment and in fact that she may have been a stand-in for her mother in her father's abuse (since her mother was unfaithful). Also, her affluent Russian Jewish family afforded her an exceptional education in preparation for university study, although not on the subject of sex, and she was a virgin.
Her intelligence and energy were immediately recognized and encouraged by Jung and Eugen Bleuler, the head of the hospital, and since she plans to study medicine they allow her to assist them in their experiments, including measuring the physical reactions of subjects during word association, to provide empirical data as a scientific basis for psychoanalysis and ameliorate the more sensational aspects of Freud's theories, which contend that all mental illness is rooted in childhood sexual experience, be it real or fantasy. She soon learns that much of this new science is founded on the doctors' observations of themselves, each other, and their families, not just their patients. The doctors correspond at length before they meet, and begin sharing their dreams and analysing each other, and Freud adopts Jung as his heir and agent.
Jung finds in Sabina a kindred spirit with a unique perspective as her self-awareness sharpens, and their attraction deepens in what was already well known at the time as transference. Jung's resistance to the idea of infidelity, and breaking the taboo of sex with a patient, is undercut by the wild and unrepentant confidences of another brilliant, philandering, unstable psychoanalyst who comes under his care, Otto Gross. He decries monogamy in general and suggests that resistance to transference is symptomatic of the repression of normal, healthy sexual impulses, exhorting Jung to indulge himself with abandon.
Jung finally begins their affair, which in the film includes rudimentary bondage and spanking Sabina at times. Things become even more tangled as he becomes her advisor to her dissertation; he publishes not only his studies of her as a patient but eventually her treatise as well. Her original ideas are rooted not only in her insights into her childhood trauma, but the intensity and conflicts in their relationship. Spielrein's thesis suggests that truly heroic, original creations can only emerge from the crucible of great conflict, such as the attraction of opposites and the breaking of taboos, and thus the instinct for creation is inextricably tied to a drive to destruction, and that these feelings and ideas are not restricted to sexual expression despite their roots in the biological drive to reproduce. This includes, finally, his refusal to give her a love child, which is the story behind the reference to Wagner's Der Ring des Nibelungen operas: they see themselves in the legend of Siegfried, the archetypal Teutonic hero born from a forbidden union. After his attempt to confine their relationship again to doctor and patient, she appeals to Freud for his professional help, and forces Jung to tell Freud the truth about their relationship, reminding him that she could have publicly damaged him but did not want to.
Jung and Freud journey to America. However, cracks appear in their friendship as they begin to disagree more frequently on matters of psychoanalysis. Jung and Spielrein meet to work on her dissertation in Switzerland, and begin their sexual relationship once more. However, after Jung refuses to leave his wife for her, Spielrein decides to go to Vienna. She meets Freud, and expresses that although she sides with him, she believes he and Jung need to reconcile for psychoanalysis to continue to develop.
Following Freud's collapse at an academic conference, Jung and Freud continue correspondence via letters, through which they decide to end their relationship, after increasing hostilities and accusations regarding the differences in their conceptualisation of psychoanalysis. Spielrein marries a Russian doctor and, while pregnant, visits Jung and his wife. They discuss psychoanalysis and Jung's new mistress. Jung confides that his love for Spielrein made him a better person.
The film's footnote reveals that Otto Gross starved to death in Berlin in 1919, that Freud died of cancer in London in 1939 after being driven out of Vienna by the Nazis, that Spielrein trained a number of analysts in the new Soviet Union, before she, along with her two daughters, was shot by Nazis in 1942, and that Jung emerged from a nervous breakdown to become the world's leading psychologist before dying peacefully in 1961.

Question: What is Freud's radical new science?
Answer: Psychoanalysis