UPDATE:
We all instinctively feel that the the nusach reflects some kind of relationship between the two kinds of illness, but it's hard to nail down exactly what that relationship is.
Avrohom (no last name) brought in the Ramban about Ani Hashem rof'echa, and I rejected the comparison, because the Ramban is just saying that if you are a tzadik gamur, Hashem will do nissim and keep you healthy. Abbie Jakubovic referred to the Rambam, who in several places deals with Choli HaNefesh as an illness that needs refuah no less than physical illness. I initially did not believe that the Rambam was relevant.
But then Michael (no last name) sent us to the Maharsha in Shabbos 67a, and the Maharsha is exactly what we were looking for. The Maharsha also brings Abbie's Rambam, and develops it beyond what I saw in the Rambam's words. I also am starting to wonder if Avrohom's Ramban is indeed relating spirituality and physical ailments, beyond a general l'maalah miderech hateva.
Yasher kochachem. Very satisfying to have a Maharsha that is clear and exactly on point! (I'm still not sure whether the Maharsha is only bringing the Rambam as a starting point, or he held that the Rambam had the Maharsha's approach in mind as well, but that does not really matter.)
The Maharsha, verbatim, has been added toward the end of this post.
-We just received two excellent remarks from Refoel NJ (no last name) which have also been added at the end of the post, after the Maharsha.
All in all, the explanations are so good that I'm beginning to wonder why the standard nusach of Refa'einu in Shmoneh Esrei does not use this expression.
1. From my father-in-law shlitah, Harav Reuven Feinstein:
Basically, he said that refuah is refuah, and just like in Havdala we mention all kinds of havdala, and in Birkas HaMazon we thank Hashem for everything besides the food we ate, so, too, when we ask the Ribono shel Olam for one kind of refuah, we should ask for a bracha for all kinds of refuah.
In more detail- In Megilla 17 it brings Yeshaya 6:10
2. I said that in Nedarim 40a it brings from Tehillim 41
3. My son, Harav Mordechai Eisenberg, said that when we are mispallel for a choleh, we ask for him as one among all the cholei yisrael. There are, unfortunately, both cholei hanefesh and cholei haguf in that group, and when we are mispallel for refuah for cholim, they are all the same, they all need the same rachmei Hashem for a refuah shleimah. So we use a nusach that is appropriate for all of the cholim. This is similar to #1, from his grandfather.
4. My nephew, Harav Geilan Grant, directs our attention to the Magen Avraham. The Magen Avraham in 6:4, and see the Machatzis Hashekel there, brings from the Kisvei haAri zal that every food comprises gashmiyus and ruchniyus, the combination being vital to the sustenance of the human being, who similarly embodies both elements. If so, we can say that every physical affliction involves a similar infirmity in the corresponding spiritual aspect, and we ask for a refuah sheleima that cures both.
This is not limited to the Gemora in Shabbos 55 that suffering is proof of of עוון, because even יסורים של אהבה, I think, would qualify as refuah hanefesh. Otherwise, it would be inappropriate impute sin to your friend. Also, I don't think it's appropriate to approach the Ribono shel Olam to say that your friend is a sinner but please forgive him.
As with anything from the Arizal, I am ignorant of all beyond the literal meaning of what I see brought down.
5. Several friends, including R' Duddy Maler and Rav Yitzchak Resnick.
There is no wall between the physical and the mental/spiritual. When a man suffers physically, his "nefesh" suffers as well, and that can involve spiritual and emotional affliction. Sometimes, the secondary problem lingers long after the primary problem has ended. Additionally, spiritual and emotional intervention can be enormously therapeutic- music, visits of a sympathetic friend, even something as trivial as petting an animal. A refuas hanefesh can be the key to refuas haguf.
Please see below for updates.
6. THE MAHARSHA. (Yasher koach to Michael (no last name))
Abaya in Shabbos on 67a prescribes a cure for a certain fever that involves doing things and saying some pesukim, pesukim whose connotation can mean a diminishment of heat. The Maharsha says the following:
7. RNJ's answer.
First, RNJ criticized our use of the Maharsha, because it doesn't make sense for Reuven to be mispallel that Shimon's middos should improve. I responded, based on a different Maharsha by the story of Reb Meir in Brachos on 10a, that tefillos for the improvement of another person are not impossible. One can hope that he finds better friends, or experiences something that will inspire him.
Second, RNJ suggested the following.
The yesod here is that everything that happens to a person is for the good. Thus, if Hashem brings illness upon a person, this too is for his benefit. Since the illness does not bring him any physical benefit, it must be that there is a spiritual benefit i.e. the physical illness itself brings about a spiritual elevation, or "refuah" for the person's soul. (You can understand this in a number of ways, such as in terms of suffering that atones for sins, or in terms of developing positive middos like humility, etc, or in terms of the person suddenly feeling his vulnerability and needing to strengthen and deepen his connection to Hashem, etc etc) In recognition of this belief, when we daven to Hashem to heal the person's illness, we don't want to make it sound as if we are accusing Hashem of doing bad to the person by making him ill. Therefore, we incorporate into our tefillos the acknowledgement of the above-mentioned "refuas hanefesh", but we ask Hashem to change His plan so that the "refuas hanefesh" can be combined also with a refuas haguf as well. Thus the phrase "refuas hanefesh u'refuas haguf".I like his teretz, and I would only change his sentence " In recognition of this belief, when we daven to Hashem to heal the person's illness, we don't want to make it sound as if we are accusing Hashem of doing bad to the person by making him ill." I would modify that by including the idea of the tefilla we say on Yom Kippur ומה שחטאתי מרק ברחמיך הרבים אבל לא על ידי יסורים וחליים רעים. Yes, suffering heals the soul by being memareik sins. We recognize that the illness was sent with a purpose, to improve the sufferer's ruchniyus. We are asking that the improvement, the necessary refu'as hanefesh, should be achieved without excessive suffering- that it should be with rachamim, not through יסורים וחליים רעים.
Update 2020.
I've read several articles since writing this. What I've read reinforces the idea that the nefesh is central in healing. One was an article on Reiki in The Atlantic. Obviously Reiki is not a scientific method and is associated with foreign spiritual beliefs. But among the practitioners are individuals with estimable educations and careers in scientific medicine. The point they made was that the placebo affect is not evidence that the illness was never physical but instead points to the ability of the body to heal itself.
The ailments that Reiki seems to treat most effectively are those that orthodox medicine struggles to manage: pain, anxiety, chronic disease, and the fear or discomfort of facing not only the suffering of illness but also the suffering of treatment. “What conventional medicine is excellent at is acute care. We can fix broken bones, we can unclog arteries, we can help somebody survive a significant trauma, and there are medicines for all sorts of symptoms,” Yufang Lin, an integrative-medicine specialist at Cleveland Clinic, told me. But medicine, she said, is less successful at recognizing the way that emotion, trauma, and subjective experience can drive physical health—and the way that they can affect recovery from acute medical care.
Lifesaving surgery is miraculous but requires drugging the body, cutting it open, altering it, stitching it back together, and then asking it to heal. Chemotherapy causes the body to fall to pieces; it can damage the brain, wreck internal organs, and destroy nerve endings, sometimes permanently. Medicine is necessary, but it can also be brutal. Lin, like several of the physicians I spoke with, emphasized that healing is something that happens within the body, enabled rather than imposed by medicine. When we are traumatized, survival is the priority and our healing mechanisms are on lockdown, Miles observed. “We have to pull out of that stress state and get into a parasympathetic-dominant state before the body is able to self-heal and actively partner with conventional medicine.”
Along the same lines is something called Resignation Syndrome, or traumatic withdrawal syndrome, in which refugee children lose the will to live and slip into essentially a catatonic state. This is rare and tends to concentrate in geographic locations, indicating an element of intent or hysteria. But a more common phenomenon is "Psychogenic Death," a loss of the will to live that leads to physical deterioration and death. It is also called "Give-Up-Itis." This was the subject of research by Dr. John Leach in 2018.
Another example, from Dr. Simon Galperin, a Neurologist:
Human beings have more control over our physiological functioning that is generally believed. Our thoughts and attitudes have a strong effect on the health of our bodies. For example, it is well known that a strong sense of purpose has a powerful positive effect on physical health. The psychologist Viktor Frankl was convinced - based on his experiences in concentration camps during the Second World War - that a strong sense of purpose could keep people alive, and that the loss of purpose could lead to illness and death. Frankl believed that a “loss of hope” could lead to a person "giving up" and allowing themselves to die. So a person’s intention and will can certainly help to determine their survival or death. Frankl was convinced that a “loss of hope” could lead to depression and possibly even to death. There are many cases of people who are seriously ill, in the process of dying, who keep themselves alive in order to experience specific events - such as the marriage of a daughter, a final Christmas or a birthday. Once the event has passed, the person “allows’ themselves to die.
The point is that a person can lose the desire to live and this will make his death more likely, while another's will to live might extend his life.
Late last year, in a small, windowless microscope room, she pulled out slides from a thin black box, one by one. On them were slices of hearts, no bigger than pumpkin seeds, from mice that had experienced heart attacks. Under a microscope, some of the samples were clearly marred by scars left in the aftermath of the infarction. Others showed mere speckles of damage visible among streaks of healthy, red-stained cells.
The difference in the hearts’ appearance originated in the brain, Haykin explains. The healthier-looking samples came from mice that had received stimulation of a brain area involved in positive emotion and motivation. Those marked with scars were from unstimulated mice.
“In the beginning we were sure that it was too good to be true,” Haykin says. It was only after repeating the experiment several times, she adds, that she was able to accept that the effect she was seeing was real.