On another message board, I have proposed a definition of causality. No one there has been able to give me significant feedback on it. I think that it is appropriate to the QM thread because the parts that are applicable to general physics are pretty much beyond dispute; it is the parts that apply (or don't) to QM that strike me as potentially controversial. Please let me know what you think, and what corrections you might suggest.
First, I must define five characteristics that causal interactions obey, then I must define "causally connected" as opposed to "cause-to-effect." I believe that by defining these last two separately, it will clarify the meaning of causality for both the classical and quantum realms, and result in illustrative differences between the two. It might then be easier to discuss my questions on the DCQE from another thread. And I should point out that I have merely posed the first of several interesting questions about this experiment; I see this issue of causality as central to questions both about the DCQE and about EPR, and the ones about EPR appear to be a hot topic right now.
First, the characteristics, and these are intended to be exhaustive:
- Correlation: the cause always makes the effect more probable. In macroscopic non-statistical experiments, if the cause is present, then the effect is rendered 100% probable. In microscopic experiments, however, because of the probabilistic nature of quantum mechanics, we can only say that the presence of the cause makes the effect more probable than its absence; this might mean that the probability is zero without the cause and greater than zero with it, which is the most effective and convincing case, or simply that it is lower without and higher with. This microscopic interpretation also makes sense for any statistical results; i.e. thermodynamics, or drug studies in a population of humans, or the effects of increased growth of acacia trees on the cheetah population.
- Negative correlation of alternatives: there is no other potential cause. In physics, this is accomplished by either eliminating all other variables, or showing that their variations do not correlate to the effect. This is true for both macroscopic and microscopic experiments. For statistical populations in realms other than physics, this can become extremely complex; this is often a source of controversy. Because of the statistical nature of thermodynamics, there remain a few controversies even in physics over this.
- Repeatability: the cause always causes the effect. For macroscopic experiments, this must be true; for microscopic experiments, and statistically determined effects, it is merely the requirement that the probability change always occurs when the cause is present.
- Sequentiality: the cause precedes the effect. This is true for all macroscopic experiments, physics or not, but not necessarily true in microscopic physics experiments. The cause in quantum mechanics can be in the future. Review the delayed choice quantum eraser and EPR experiments for possible examples of violations of this criterion.
- Locality: the cause is present in the immediate environment of the effect. This is true for all experiments except microscopic physics experiments. In microscopic physics experiments, the cause can be spacelike separated from the effect. Review the EPR experiment for a possible example of a violation of this criterion.
Now, "causally connected" can mean that both events are effects of a common cause, or that one is the cause and the other the effect. This relationship can be established by any two of the first three criteria above.
"Cause-to-effect," on the other hand, is much more difficult; it requires at least four of the five criteria be met.
All five criteria must be met for any macroscopic experiment, but microscopic quantum experiments can violate one of the last two without violating quantum causality.
The border region is of great interest; at what point do objects become complex enough that they can no longer violate one of the last two criteria?