Many claims are made about the power of prayer. From The Gospel of Matthew:
18:19 Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven.
18:20 For where two or three are gathered together in my name, there am I in the midst of them.
This invites the question of what is meant by 'ask,' 'in my name,' and 'gathered together.'
There have been statistical studies attempting to measure whether hospitalized patients recover better if they are being prayed for by a volunteer group. The results are generally inconclusive.
There has certainly been no shortage of effort by humans to affect reality by prayer but this has not spared humanity from repeated catastrophes.
To understand the subject deeper, we have to understand prayer as something other than pleading, expecting or commanding. We also must understand it as conscious activity in the sense of objective consciousness.
From In Search of the Miraculous:
'Well, give me an example of something that the Lord cannot do," said the examining bishop. "It won't take long to do that, your Eminence," answered the seminarist. "Everyone knows that even the Lord himself cannot beat the ace of trumps with the ordinary deuce." […]Turgenev wrote somewhere that all ordinary prayers can be reduced to one: "Lord, make it so that twice two be not four." This is the same thing as the ace of trumps of the seminarist. […]
"Cannot prayer help a man to live like a Christian?" asked someone. "It depends upon whose prayer," said G. "The prayer of subjective man, that is, of man number one, number two, and number three, can give only subjective results, namely, self-consolation, self-suggestion, self-hypnosis. It cannot give objective results." "But cannot prayer in general give objective results?" asked one of those present. "I have already said, it depends upon whose prayer," G. replied. "One must learn to pray, just as one must learn everything else. Whoever knows how to pray and is able to concentrate in the proper way, his prayer can give results. But it must be understood that there are different prayers and that their results are different. This is known even from ordinary divine service. But when we speak of prayer or of the results of prayer we always imply only one kind of prayer--petition, or we think that petition can be united with all other kinds of prayers. This of course is not true. Most prayers have nothing in common with petitions. I speak of ancient prayers; many of them are much older than Christianity. These prayers are, so to speak, recapitulations; by repeating them aloud or to himself a man endeavors to experience what is in them, their whole content, with his mind and his feeling. And a man can always make new prayers for himself. For example a man says--'I want to be serious.' But the whole point is in how he says it. If he repeats it even ten thousand times a day and is thinking of how soon he will finish and what will there be for dinner and the like, then it is not prayer but simply self-deceit. But it can become a prayer if a man recites the prayer in this way: He says 'I' and tries at the same time to think of everything he knows about 'I.' It does not exist, there is no single 'I,' there is a multitude of petty, clamorous, quarrelsome 'I's. But he wants to be one 'I'--the master; he recalls the carriage, the horse, the driver, and the master. 'I' is master. 'Want'--he thinks of the meaning of 'I want.' Is he able to want? With him 'it wants' or 'it does not want' all the time. But to this 'it wants' and 'it does not want' he strives to oppose his own 'I want' which is connected with the aims of work on himself, that is, to introduce the third force into the customary combination of the two forces, 'it wants' and 'it does not want.' 'To be'-- the man thinks of what to be, what 'being,' means. The being of a mechanical man with whom everything happens. The being of a man who can do. It is possible 'to be' in different ways. He wants 'to be' not merely in the sense of existence but in the sense of greatness of power. The words 'to be' acquire weight, a new meaning for him. 'Serious' --the man thinks what it means to be serious. How he answers himself is very important. If he understands what this means, if he defines correctly for himself what it means to be serious, and feels that he truly desires it, then his prayer can give a result in the sense that strength can be added to him, that he will more often notice when he is not serious, that he will overcome himself more easily, make himself be serious.' [End quote]
From the passage of Matthew 18:20, we also have a reference to combining for praying. But again, if two cannot understand each other, then how can they say the same prayer? Thus this joining would have the power referred to in 18:20 only within the esoteric circle or close to it. This would also entail having the understanding of not praying that twice two cease to be four.
Another aspect of this question touches on man's internal division. The conscious part prays for world peace and the unconscious affirms that same peace is lacking. The one with more power to affect reality seems to be the subconscious. Also the question of anticipation ties into the question. Intent is one thing, imposing dictates on the universe by fixed expectation seems to block realization. The Cassiopaea material discusses this in more detail.
Another category of possible consciousness-reality interaction has to do with objectivity. A wide divergence between consciousness and reality makes for a system with more entropy than one in which these are aligned. Subjectivity contributes to a winding down of the universe through entropy, so to speak and therefore usually collapses on itself. Some negative entities are however capable of such consistency and intensity of subjectivity that they progress quite far beyond the human level before this deceit catches up with them.
Another problem that can easily arise with prayer is intent to violate another's free will or interfere in another's lesson plan. This was blatantly ignored for example in the experiments on efficacy of prayer mentioned at the beginning. Such energy interactions, if effective, may simply build karma. Deciding what is best for another is an act of pride. Offering or sharing knowledge is different but this is hardly ever the mode of such intercessory prayer.
The Philokalia, a compilation of Eastern Orthodox tradition from the earliest church to the fall of Constantinople, has a section titled 'On Prayer' by Evagrios the Solitary. Following are extracts from this:
3. Prayer is communion of the intellect with God. What state, then, does the intellect need so that it can reach out to its lord without deflection and commune with Him without intermediary?
11. Try to make your intellect deaf and dumb during prayer, you will then be able to pray.
19. If you endure something painful out of love for wisdom, you will find the fruit of this during prayer.
23. If you patiently accept what comes, you will always pray with joy.
27. If you arm yourself against anger, then you will never succumb to any kind of desire. Desire provides fuel for anger, and anger disturbs spiritual vision, disrupting the state of prayer.
31. Do not pray for the fullfilment of your wishes, for they may not be in accordance with the will of God. (...)
35. Undistracted prayer is the highest intellection of the intellect.
36. Prayer is the ascent of the intellect to God.
38. Pray first for the purification of passions; secondly, for the deliverance from ignorance and forgetfulness; and thirdly for deliverance from all temptation, trial and dereliction.
45. When you pray, keep close watch on your memory, so that it does not distract you with recollections of your past. But make yourself aware that you are standing before God. For by the nature intellect is apt to be carried away by memories during prayer.
46. While you are praying, the memory brings before you fantasies either of past things, or of recent concerns, or of the face of someone who has irritated you.
49. Having prayed as you should expect the demon to attack you; so stand on guard, ready to protect the fruits of your prayer. For this from the start has been your appointed task: to cultivate and protect (cf. Gen. 2:15). Therefore, having cultivated, do not leave your fruits unprotected; otherwise you will gain nothing from your prayer.
52. We practice the virtues in order to achieve contemplation of the inner essences (logoi) of created things, and from this we pass to contemplation of the Logos who gives them their being; and he manifests Himself when we are in a state of prayer.
53. The state of prayer is one of dispassion, which by virtue of the most intense love (footnote includes interpretation of `intense longing') transports to the noetic realm the intellect the intellect that longs for wisdom.
54. He who wishes to pray truly must not only control his incensive power and desire, but must also free himself from every impassioned thought.
57. When the intellect no longer dallies with dispassionate thoughts about various things, it has not necessarily reached the realm of prayer; for it may still be contemplating the inner essences of these things. And though such thought is dispassionate, yet since it is of created things, it impresses their forms upon the intellect and keeps it away from God.
64. While all else produces thoughts, ideas, speculations in the intellect through changes in the body, the Lord does the opposite: by entering the intellect, He fills it with whatever knowledge he wishes; and through the intellect He calms the uncontrolled impulses in the body.
67. When you are praying, do not shape within yourself any image of the Deity, and do not let your intellect be stamped with the impress of any form; but approach the Immaterial in an immaterial manner, and then you will understand.
72. A man who is tied cannot run. Nor can the intellect that is a slave to passion perceive the realm of spiritual prayer. For it is dragged about by impassioned thoughts and cannot stay still.
73. When the intellect attains prayer that is pure and free from passion, the demons attack no longer with sinister thoughts but with thoughts of what is good. For they suggest to it an illusion of God's glory in the form pleasing to the senses, so as to make it think that it has realized the final aim of prayer. A man who possesses spiritual knowledge has said that this illusion results from the passion of self-esteem and from the demon's touch on a certain area of the brain.
74. I think that the demon, by touching this area, changes the light surrounding the intellect as he likes. In this way he uses the passion of self-esteem to stir up in the intellect a thought which fatuously attributes form and location to divine and principle knowledge. Not being disturbed by impure and carnal passions, but supposing itself to be in a state of purity, the intellect imagines that there is no longer the adverse energy within it. It then mistakes for a divine manifestation the appearance produced in it by the demon, who cunningly manipulates the brain and converts the light surrounding the intellect into a form, as we have described.
75. When the angel of God comes to us, with his presence alone he puts an end to all adverse energy within the intellect and makes its light energize without illusion.
81. Know that the holy angels encourage us to pray and stand beside us, rejoicing and praying for us (cf. Tobit. 12:12). Therefore, if we are negligent and admit thoughts from the enemy, we greatly provoke the angels. For while they struggle hard on our behalf we do not take the trouble to pray to God ourselves, but we despise their services to us and, abandoning their Lord and God, we consort with unclean demons.
84. Prayer is the energy which accords with the dignity of the intellect; it is the intellect's true and highest activity.
127. If you want to pray as a monk, shun all lies and take no oath. Otherwise you vainly pretend to be what you are not.
133. If you are praying to overcome some thought, and it subsides easily, examine carefully how this came about; otherwise you may be deluded into attributing the cause to yourself.
139. At night the cunning demons try to disturb the spiritual teacher by direct attack; in the daytime, they attack him through other people, besieging him with slander, distraction and danger.
153. If when praying no other joy can attract you, then truly you have found prayer.
From all the above we would distill that joining and intent and objectivity coupled with a multifaceted understanding and pondering of each concept in the prayer, all applied to the now might be a way to pray in the service to others mode. There are issues of the quality of attention and quality of knowledge which language is incapable of exactly representing, thus our description is perforce not complete and may seem contradictory in places.