What do we really want when we ask God in prayer for something? Say we ask God to heal someone or to protect someone from harm or to give someone wisdom etc., what are we expecting him to do? Well, let's assume that the world progresses along according to its natural mechanisms (things fall when we drop them, etc.) which we seek to describe using physics or science in general. In these requests we want God in some way to change the state of the world from what it would otherwise be, given this natural unfolding of physics. That is, we want God to intervene in this world and perturb its physics.
The key point is that there is a significant difference between getting God to do something and getting a person to do something. A person is a physical being and when he or she acts no laws of physics are broken; his/her actions are all within the system and perfectly describable by physics. But God is not material and hence outside of the natural physical interactions. If he does something that changes the state of the world from what it would naturally be, he must by definition be breaking the "laws of physics," i.e. temporarily changing the natural mechanisms that govern physical interactions.
One reply to this is to claim that God governs the universe and all physical interactions, and hence he can do as he wishes without breaking anything. Well given this claim, the question then is whether God has himself set up mechanisms or rules (which I was calling natural mechanisms or physical laws) that determine the outcome of physical interactions, or if he decides every time two atoms get close how they will interact. The incredible success of physics at describing nature strongly points to there being a consistent set of interaction mechanisms. So whether these are God governed or not, God must break them in order to answer someone's prayer.
Another reply: due to quantum mechanics, given the state of the world at any time, there are many possible outcomes. Prayer asks for God to select a particular outcome of the possible ones. In this way surely it wouldn't be breaking physical laws, but it would still be influencing the world. However, the problem with this is that while there may be many possible outcomes, their likelihood is governed by a probability determined by the wave function. This statistical probability is part of the physics of the system. If this probability is changed by fixing the outcome, then the physics is also changed.
So this is a serious thing: do we really want the laws of physics to be broken or changed by God so that our desires can be satisfied? Is it possible for me to think scientifically, and at the same time believe in prayer causing physical changes in the world? There are surely many scientists that hold onto both, but if they do it is in separate spheres: the lab vs. personal life. Making this separation is a contradiction that many people are happy to live with. Not only that, this power to break the laws of physics within the reach of everyone is very attractive -- a kind of David vs. Goliath power. But if the world is filled with these outside perturbations, then the goals of physics are a lost cause. If anything does not fit the theory, it is probably God perturbing the world, and there is no point developing a more encompassing theory to describe it. This is opposite to the natural mechanism assumption that has lead to the success of physics. Which is one to choose? Clinging to two contradictory world views is surely dishonest, and a truth seeker would not do that.
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