Every time we learn a new theory which is supposed to explain some physical phenomena we try to understand what is behind its axioms, why certain definitions were introduced and what is the physical meaning of the derived theorems. Let’s think about what it really means to understand and what we want to achieve from our study. Maybe it is fair enough just to be convinced about the significance of the theory without any deeper understanding.
Investigating a problem usually goes for searching for the logical reasoning between facts we find to be a cause of observed effects and using for this physical theories as a framework. To give an example, if we consider the planet movement we expect to take into account the gravitational interaction. Then we are able to foresee their future position but do we really get the underlying physics? The answer is yes; if we only wanted to describe another planetary system, we would succeed in doing so again. However, we cannot be satisfied, at this point we still do not know the interaction mechanism and cannot justify the formula for gravitational force.
With no doubt we should always examine the reasons for which the theory introduces its concepts. It is the best way to get to know all restrictions of the theory and to take a critical look at all made assumptions. On the other hand we will always face the wall of ideas and axioms, which not necessarily have to be intuitive. The definition of kinetic energy was introduced by classical mechanics and became a part of the everyday language but still it is a purely theoretical notion. So it looks like we are condemned to play the game with known rules, we may even enjoy the game but will never find the explanation of all principles. We have to accept that there is a limit which we will never cross.
Quite often we just accept the validity of formulas and expressions proposed by other researchers. Maybe the reason of this attitude comes from the academic pressure. Having just a taste of the new theory we might be in the position to quickly identify some problems that could be solved within it. Things are fine as long as we remember to take the next step – going into the details of the theory. However, we can also say that using the elaborated model without considering all technical details does not have to indicate we are lazy. We may just want to get the new results based on what has been done by our predecessors.
It is very subjective when we can say, “OK, I’ve understood.” Maybe it is when we are ready to explain certain problems to others or we are just convinced about our knowledge and thanks to it we can predict the results of experiment. Most likely we will never succeed in our attempts to understand the whole nature. Thus the statement “Still I don’t understand” takes the advantage as it drives our scientific progress.