Newton's equations could be expressed algebraically. An equation describing a system in classical physics had only one solution. This resulted in the Victorian world view of a clockwork universe. The Creator may have started the universe working in the beginning, but once the system was set in motion, it followed through in accordance to unbreakable laws which predicted one and only one possible outcome. Newtonian systems were deterministic. If one described the initial set up, one could calculate the result.
The equations describing the behavior of subatomic particles are differential equations. Differential equations yield multiple answers. No matter how well one knows the initial system, one cannot know the end outcome. (In addition, it is impossible to precisely measure the initial conditions of a real world quantum system. The uncertainty principle assures that one not only can't know what is going to happen, but one can't even with full precision know what is happening as one takes a measurement.) The equations show multiple possible outcomes. The best one can do is determine the probability of observing each outcome. One can calculate the odds. Given a large number of particles, assuming that most of them are going to do the most likely things, if one closes one's eyes and keeps one's hands in one's pockets, one can almost pretend the world is causal.
Einstein did not approve of the lack of causality. His statement that God would not play dice with the universe expressed a desire to return to Newtonian certainty. Many scientists still would favor a return to Newton. Newton's universe was much more knowable. Thus far, however, no deterministic mathematics have been found that describes the behavior of subatomic particles. We are stuck with the differential equations, with their multiple answers.
What does this mean? There are at least three primary approaches to interpreting the multiple solutions to quantum equations.
The first is the Classic Copenhagen Convention, or CCC. The equations predict the probability of what one will observe. Making an observation collapses the equation. That is, once you know which solution has been observed, you can disregard all the others. They are no longer relevant. Until one makes the observation, the system is in an indeterminate state. One just doesn't know what happened. After the observation has been made, the end state is known. The "collapse" of the equation is quantum physics jargon saying since you know which answer to the equation was observed, you can pretty much ignore all the answers to the equation that were not observed.
The second approach is Neo Copenhagen. (NC) Under CCC, the collapse only occurs when an observer becomes aware of the result. Under NC, the collapse can occur when the particle interacts with other particles, makes its presence felt. For example, a photon striking photographic film or triggering an instrument effects the film or the instrument. Using Neo Copenhagen, a sentient observer is no longer required to cause a collapse, but all sentient observations still result in collapses. Anything that triggers a nerve ending by definition has effected other particles. Thus, once a particle has been recorded by a scientific instrument, the equation has collapsed, the device records where the particle was, and therefore it wasn't anywhere else. If no scientist has yet developed the film or examined the instrument, this doesn't matter. Once a particle influences other particles or objects in such a way to leave traces of its presence, the collapse has occurred.
The third option is Many Worlds. (MW) All solutions to the equation are assumed to be equally valid. There are many alternate realities implied by the equations. When we collapse the equation, we are choosing to ignore most of these alternate realities. This is generally the correct thing to do. Once we know which of the many alternate parallel universes we are in, we don't care about any of the other realities. Again, once the particle has either been directly observed or has left its mark in the equipment, we can disregard the possibility that the particle could have been observed elsewhere. The difference is purely in how the event is described. Instead of saying "we can collapse the equation now," one can assert which alternate reality we are in.
To a great degree, the differences between the three approaches is purely semantic. While one conjectural paper proposed that a sentient quantum level computer might be used to test the Many Worlds theory, I am dubious. For the most part, the three theories predict the exact same outcome. The theories are merely interpretive.
Many Worlds was developed as the universe seems to have existed before sentient beings evolved. Clearly, quantum systems collapsed before there were sentient beings to observe the collapse. The first human being did not suddenly alter the rules of physics. Neo Copenhagen was created to account for equations collapsing without sentients being involved. It allows quantum level interactions to occur when scientists are not watching without the Many World's "unnecessary hypothesis" of a large number of extra unobserved universes floating around in alternate dimensions.
If the arrow of time points clearly forward, if the past causes the present, there is no known experiment that could prove one of the three theories superior. It is more a matter of taste. Most scientists lean towards Neo Copenhagen. More than a few parapsychologists prefer Classic Copenhagen as a sentient mind plays a role in deciding how the random event happens. Most "observation theories" attempt to lever the role of the observer into the ability to participate, to manipulate the collapse. However, these CCC observation theories are not specific as to how the feedback mechanism works. The cannot say how the observer determines the nature of the collapse.
This paper proposes that the future can alter the probabilities of the present. The number of alternate futures alter the probabilities of how the collapse occurs. If the heads result of a coin flip results in more alternate futures than a tails, a heads result becomes more probable. Thus, with the future effecting the past, the Many Worlds can't be as lightly dismissed. One ends up comparing the heads futures with the tails futures to estimate the probabilities of the coin flip result.
If reverse time causality can be shown, then the three systems are no longer identical. It becomes possible to prove or disprove the existence of the alternate realities.