Random or Intention
Now another question arises: How is it determined into which of all possible states the wave function will collapse? Is the wave function collapse random? Is it intentional? Is it determined by a third person or another unknown instance?
We are getting now into an area, which is speculation rather than science. Nevertheless we have logic as tool to investigate the different possibilities, even if there is currently no way to prove our conclusions experimentally.
When the wave function collapses, for example the decay of atoms of a radioactive isotope, it happens in a unpredictable way. This means we cannot say in advance, which atom will decay. All atoms have the same probability to decay, none of them is standing out or somehow preferred. If the atoms were not completely equal and interchangeable in this aspect and it was somehow predictable, which atom is the first to decay, we would immediately have our classic deterministic worldview back, which we just got rid of. So this is obviously not the case.
However an observer will see particular atom decay. So why is it this atom and not another one? Is the observer intentionally causing that this and not another one decays, as some people claim? So is the observer able to create reality intentionally? Or does it happen randomly without any causality? Or perhaps is it determined by somebody else, e.g. by a god or some higher instance?
According to the Copenhagen Interpretation it is the act of observation that causes the collapse of the wave function. So if it was a third party, another instance that determined into which state the wave function collapses, what would the observer be needed for? The wave function could collapse into this particular state without the act of observation. But we have seen in the above-mentioned experiments, that observation is needed, and without an observer, the wave function does not collapse. Therefore we can exclude the involvement of any third party like a god or any other higher instance.
So we are left with the question, whether the decision is randomly or influenced by the intention of the observer. But what is randomness? Is randomness a thinkable concept? How can a particular event take place, if all possible events are totally equal in all its aspects, and no possible event stands out in any way?
This is a philosophical question, and we would have to abandon causality, if we accept the concept of true randomness. And this is a tricky thing. Abandon causality means giving up the rules. We would even threaten the principles of logic. It is difficult to accept this idea and one would rather feel inclined to give up the Copenhagen Interpretation entirely in favor of the Many-Worlds Interpretation, which would be far more plausible, since it doesn't require the concept of randomness and acausality.
The assumption that the collapse of the wave function is intentionally caused by the observer is far more elegant and plausible. It would also provide an answer to several other philosophical problems like the free will and the question how our consciousness and the physical body relate to each other.
But there is another good reason to assume that the collapse of the wave function is caused intentionally by the observer. From the experiments above we have learned that causality does not work, as we believed. The concept of cause and effect is actually reversed. It is not the event that causes the effect of observation. It is the observation that causes the event. Without the observation, there is simply no event that could be observed. It is the observation that creates the event. Therefore observing is no passive process; it is an active process. The observation itself is the cause; the collapse of the wave function, i.e. the particular event that we observe, is only the effect.
If the observer was subjected to the randomness of the collapse of the wave function, he would not play an active role in this process and could not be the cause of anything. Therefore we have most likely to discard the concept of true randomness.
But supposed an observer can intentionally cause the collapse of the wave function, does this mean he can control the outcome of any event he observes?
The limitation of this control would naturally be the wave function of the environment and the collapses caused by other observers.
Furthermore we must not forget the concept of probability. Not all possible outcomes are equal. Some of them are preferred by the wave function. The world of quantum mechanics not only consists of possibilities, it consists of probabilities. Particular outcomes are preferred over others. Certain events are more likely to occur than others. It does not mean that a certain outcome is somehow predetermined, it may happen or it may not happen. It is just more likely to happen than others. In our example of the decay of an atom, it does not mean that an isotope with a half-life of one our will necessarily decay within two hours, it only means a certain probability for this event to occur. It is still possible that the atom does not decay after two hours or even after a whole day; this outcome just gets increasingly unlikely.
So if we assume that every outcome is caused by observation, unlikely outcomes are certainly harder to observe than more likely outcomes. May be it needs some more effort by the observer in order to observe an unlikely outcome.
If the observer can really intentionally influence a certain outcome, then it would require some stronger intention to observe a rather unlikely event. This raises the question, if we can strengthen our intention in order to make unlikely things happen. May be this strength is what some people call "faith", faith that is able to move mountains according to the bible, faith that manifests itself in the so called "placebo"-effect in medicine.
Since the whole universe is subject to probabilities, hardly anything would be impossible, it may just be very, very unlikely. And it may depend on our faith, if it can become real or not.