How to conclude that some correlation does imply causation I'm trying to prove that all physical THEORIES are just experiments and tests that conduce to assumptions about correlations between causes and results. BUT how physicists conclude that a relationship is a CAUSATION and not only CORRELATION ?
When can something related to something else be classified as a cause and not only as an accompanying phenomenon ?
Positive examples : mass and gravitation , electric charge and electric field , night and sun
Negative examples : rain and rainbow , wings and flying ..
(they are related but are not a reason or result for each other)
 A: Experimentation is the key.  You find things correlated in data.  You hypothesize a law that quantifies the correlation.  Then, you take the two variables, in a controlled environment, and you vary one of them.  If the dependent variable changes in the predicted way, then you've shown that your independent variable(s) have a causal relationship with the dependent variable.  
The key point is that you don't really know until you've done the experiment.  There is more sophisticated stuff you can do, but this is really the essence of this.  For instance, Newton's law of gravitation was not really shown to be a truly causal theory until Cavendish did his experiments with the lead balls.
A: This probably belongs more in philosophy but usually if things are strongly correlated but one isn't the cause of the other, they are both caused by a third thing. So for example, global temperature is strongly correlated with the number of pirates, both which are probably "caused by" an increasing industrializing human population. One can rule out pirates as a cause of global warming by manipulating the number of pirates independently. On the other hand, if we directly manipulate that variable, it's a strong indicator that a third, independent thing isn't at work.
From a physics point of view, I'm not sure rain and rainbows are a good example. Rain can be both a cause of rainbows and correlated with it. In other words, something can have multiple causes.
A: Let me take an example. The human population increases every year by a huge number, on average. Similarly, galaxies and clusters millions of light years away from us move away by millions and billions of kilometers every year. There is an increase in both quantities. (Population and Distance.) Does this imply that the increase in human population cause galaxies to move away from us at a farther rate? No chance. This implies that correlation does not necessarily imply causation. (people could even have a complete physical model about human population and spacial expansion but that still wouldn't imply that humans cause galaxies to move away.)
