Rabbi Alfred Geiger Moses wrote:
“When I arrived at the home, I found the child in a critical state. Boldly varying the usual form [which required a ‘minyan’: 10 adult Jewish males], I took the infant in my arms, prayed with all my strength to G-d, and then at the mother’s advice declared the name changed from Rebeccah to Ruth. I left the house shortly after the incident, and later learned that the child began to improve at once.” 
(Rabbi Simchah Weintraub has written an excellent contemporary article on the “ceremony of name-changing for healing”:
Rabbi Moses performed this “name changing” ceremony for the critically ill child at the mother’s request, with the intention of comforting the mother, but not with any belief that it would heal the child.
Upon the positive outcome of this incident, Rabbi Moses based his subsequent life-long interest in spiritual healing. He coined the term “Jewish Science” after his era’s interest in a “scientific” approach to prayer and healing, which likewise gave rise to “Christian Science,” “Religious Science,” etc. His work became the basis of subsequent writing and healing-work by Rabbi Morris Lichtenstein, Mrs. Tehillah Lichtenstein, Rabbi Clifton Harby Levy, and others.
In retrospect, what was it that so impressed Rabbi Moses? He doesn’t seem to have subscribed to the more traditional explanation: When one is scheduled to die, G-d gives an angel a contract to pick up the soul of a person with that specified name. If the person changes his/her name, the angel’s contract is no longer “enforceable.”
Rather, in keeping with his era, Rabbi Moses seems to have inferred a more categorical principle: Any action that we do produces a corresponding response from the Divine. The similarity with Newton’s formulation isn’t accidental. Based on Newton’s expression of the laws underlying the workings of the physical world, the belief of the time was that “science” had promise to likewise explain all things, including prayer.
The overall category of “Action” includes “Thought.” Therefore, a change in our thought will produce a corresponding Divine response. Rabbi Moses’ understanding, then, seemed to be that the healing he’d witnessed had to do with a change in thought on his part and on the part of the child’s mother (note: not on the part of the child herself).
HaBaD Hasidic tradition reports a similar anecdote, in which the Tzemach Tzedek (the 3rd Lubavitcher Rebbe) told the father of a critically ill child, “טראכט גוט וועט זיין גוט; Tracht gut vett sein gut; Think ‘good’ and it’ll be good,”  after which the child had a full recovery.
Rabbi Morris Lichtenstein calls the same principle a Divine quality — “Responsiveness to Prayer”:
“All prayer rightfully offered meets with unfailing [Divine] response.” 
Elsewhere, he further explains “rightfully [or ‘rightly’] offered”:
“…there should never be formed any negative images; one should not declare in them his miseries or his want; one should never visualize the circumstances of his unhappiness, or the burdens which oppress him. He should see with his mental vision only the state in which he desires to be…” 
Such prayer is therefore typically called “Affirmative Prayer.”
Even when visualized, rather than affirmed in words, the same principle holds.
(for more on Affirmative Prayer, see also:
The basic Biblical model for Affirmative Prayer can be found in the opening verses of Bereishith/Genesis, in which G-d declares a thing and it’s done precisely as declared:
“G-d said, ‘Light: Be!’
and Light was.” 
The Tzemach Tzedek, Rabbi Moses, Rabbi Lichtenstein and others are telling us: This is within the scope of human spiritual growth, as well.
 Moses, Rabbi Alfred Geiger; Jewish Science — Divine Healing in Judaism; © 2011 Hudson Mohawk Press (reprint of 1916 edition); p. 27
 Lichtenstein, Rabbi Morris; Jewish Science and Health; © 1925; p. 21
 ibid., p. 51