I do not believe you are using the term “cause” in the same sense that the apologists are. There are typically referring to something like the “prime mover”, which be another physical object that will pick up and carry or knock the alpha particle to a distance where it will no longer be held by the nuclear force. They also typically deny that abstract laws and equations such as the Schrodinger equation have causative factors.
Models are all we have. If there is a reality that lies beyond these, it is also beyond our powers of perception. All we can do is form working models of reality and see how well they predict what we will observe.
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If by “prime mover” you mean something like Aristotelian’s prime mover, what you described has nothing to do with what Aristotelians refer to. Motion in Aristotelian metaphysics is not exactly the same concept as our modern, post-Newtonian change-in-position sort of motion, but refers to change that a substance undergoes - a much broader category of phenomena.
I’m not sure what you’re referring to here. A Christian could simply say that God upholds the order of the natural world such that the laws of quantum mechanics (including Schroedinger’s equation) holds true, allowing radioactive decay and quantum tunneling to happen.
I also don’t see anything obviously philosophically incoherent with saying that God causes a particular instance of alpha decay to happen, or that God causes a particle to be spin-up instead of spin-down. After all, God transcends space and time - He is the ultimate non-local hidden variable! (Not that I endorse this particular interpretation, but just speculation.)
I actually agree with you on this point.
By the way, @Eddie & @Faizal_Ali - I think the discussion would be more engaging and interesting if we refrained focusing on personal accusations and trying to pin down “gotcha” moments. This is a fascinating topic by itself. 
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In addition to what @dga471 said, let me add that while the bits about the rules of physics or the Schrodinger equation being “causes” were not what apologists you encountered mean when they say “cause”, I believe that these parts:
apply to the types of “causes” that you are talking about. The first, that the shape of the wavefunction is caused by the potential barrier is analogous to the classical statement: the shape of water is caused by its container having that particular shape. The second, that an observation causes collapse of the wavefunction (thus allowing for an alpha particle to be found outside of the nucleus) is the case of an event (the observation) causing something to happen (the wavefunction collapse) - I find that to be what people usually mean when they say “causation”.
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I never said anything about quantum tunneling one way or the other, so there’s no egg on my face. What I challenged was your repeated assertion (stated in various phrasing) that modern physics has proved that there are events that occur without any cause, or that are self-caused. As far as I can see, all the physicists who have spoken here so far have cautioned against such stark conclusions. They seem to have a more nuanced view of what modern physics has shown than you do. Which is not surprising, since, being in that field, they would be more aware of nuances.
Also, you argued above than an event can be caused merely because there is some probability that the event will happen. You haven’t defended that claim. “The bridge collapsed because there was a .015% chance that it would collapse” would not count as an explanation in most scientific circles that I’m aware of.
Also, I can confirm Daniel Ang’s correction regarding the use of the term “prime mover” in Aristotelian thought.
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I am not saying there is anything incoherent about this claim. I am saying that it cannot be rationally claimed that a being like a god is required for this to happen.
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Fair enough. However, that is the sense in which apologists are using the term, it seems to me, when they say the universe must be “caused” to begin to exist by a personal being with will. That is the specific claim I am arguing against here, which I admit I have not made sufficiently explicit. The term “cause” is one that allows for a large degree of ambiguity and equivocation.
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The two physicists who have commented here have confirmed it, though of course in far less simplistic terms than I used.
Aristotle’s God is not “a personal being with will,” so dragging in Aristotelian terminology such as “prime mover” to characterize modern Christian discussions of “cause” in cosmology is not helpful. It just muddies the waters. You can make whatever point you are trying to make without using the term “prime mover.”
I missed the spots where they said that the mere fact that an event has a probability of happening is the actual cause of the event’s happening.
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OK, and I don’t know for sure which arguments by Christian apologists are you referring to. But it is quite common to appeal from the existence of the laws of nature to the need for someone or something to create and uphold those laws, otherwise there would be no reason why those laws exist. See, for example, what we’re discussing here: What are Laws of Nature?
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Here is a specific example of the type of argument I am alluding to:
Ghazali argued that this Uncaused First Cause must also be a personal being. It’s the only way to explain how an eternal cause can produce an effect with a beginning like the universe.
Here’s the problem: If a cause is sufficient to produce its effect, then if the cause is there, the effect must be there, too. For example, the cause of water’s freezing is the temperature’s being below 0 degrees Celsius. If the temperature has been below 0 degrees from eternity, then any water around would be frozen from eternity. It would be impossible for the water to begin to freeze just a finite time ago. Now the cause of the universe is permanently there, since it is timeless. So why isn’t the universe permanently there as well? Why did the universe come into being only 14 billion years ago? Why isn’t it as permanent as its cause?
Ghazali maintained that the answer to this problem is that the First Cause must be a personal being endowed with freedom of the will. His creating the universe is a free act which is independent of any prior determining conditions. So his act of creating can be something spontaneous and new. Freedom of the will enables one to get an effect with a beginning from a permanent, timeless cause. Thus, we are brought not merely to a transcendent cause of the universe but to its Personal Creator.
I believe the example of alpha decay “caused” by quantum tunneling shows this reasoning to be unsound. The “cause” exists for an indefinite period of time before the emission of the alpha particle occur. This contrary to the example Craig gives of water freezing when the temperature reaches the freezing point.
That is essentially what PdotQ refers to here:
Not quite; in a quantum tunneling problem we still need an observation that then causes the wavefunction to collapse. Because this wavefunction is non-zero outside of the nucleus, once it collapses there is a probability for the observer to measure the position of the particle to be outside of the nucleus.
Edit: @Faizal_Ali, perhaps you are referring to spontaneous emission instead of the alpha-decay tunneling problem?
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But what “causes” the particle to be in one particular place at the time the observation is made? That is simply a matter of probability, and there is no hidden variable that moved it to that particular location, correct?
Only on some interpretations of QM. This is not true on the Many-worlds interpretation, nor in pilot-wave theory, for example.
I think you are at least partially correct here in that radioactive decay shows a possible example of an event with an indeterministic, impersonal cause. So Craig’s inference that the cause of the universe must be personal isn’t sound, without some further premises and support.
In the Copenhagen interpretation, the particle never moved at all. The wavefunction collapses because of the observation. The place it collapse to is probabilistic, but probabilistic does not mean uncaused.
Looking back at your posts, I feel that your position might be more supported by spontaneous emission than quantum tunneling of alpha particles. Have you taken the chance to look at it yet?
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Probability is effectively a prediction rather than a cause, is it not?
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All good questions. I don’t have an answer to the question why there should be decay at a particular moment and not at another particular moment, and I’m not sure any physicist does. However, note that I was responding to the claim that the nucleus decays at a particular moment for no other reason than that there was a finite and small probability that it would decay at the moment. I don’t believe that this is the explanation physicists give for nuclear decay at a particular moment. I think that Faizal Ali is misrepresenting what physicists say on this. “It happened at 1:22:35.346579 p.m. on January 4, 2019, because there was a small probability that it would happen then” is not something I’ve ever heard any physicist say. Even those most fully committed to the “Copenhagen” view of quantum mechanics wouldn’t phrase things in that way. At least, I’ve never heard one do so.
It is one thing to say that the timing of the decay is arbitrary, and therefore it might just as well have been at one time as at any other time, but quite another thing to say that it happened at that one specific time precisely because there was a probability that it would happen then. If one says that it happened at that specific time because there was a finite probability that it would happen then, then one has to explain why it didn’t happen exactly one second earlier or later, when both those times had exactly the same finite probability of being the time. This shows that the “causal” phrasing is bogus – bad metaphysics and bad epistemology.
“Probability” as such doesn’t “cause” any particular event. It gives us a mathematical map of the possibilities and their likelihoods. It leaves the instantiation of one equally probable outcome (as opposed other equally likely outcomes) unexplained. “Probability” isn’t an entity, a force, a substance of some sort that makes particular things happen. It isn’t parallel to “gravity” or “friction” or “strength of magnetic field” or other such things. Faizal Ali’s discussion is seriously misleading.
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You are incorrect:
Radioactivity is one very frequently given example of exponential decay. The law describes the statistical behaviour of a large number of nuclei, rather than one individual nucleus. In the following formalism, the number of nuclei or the nuclei population N , is of course a discrete variable (a natural number)—but for any physical sample N is so large that it can be treated as a continuous variable. Differential calculus is used to model the behaviour of nuclear decay.
The mathematics of radioactive decay depend on a key assumption that a nucleus of a radionuclide has no “memory” or way of translating its history into its present behavior. A nucleus does not “age” with the passage of time. Thus, the probability of its breaking down does not increase with time, but stays constant no matter how long the nucleus has existed. This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates. However, whatever the probability is, it does not change. This is in marked contrast to complex objects which do show aging, such as automobiles and humans. These systems do have a chance of breakdown per unit of time, that increases from the moment they begin their existence.