I made a number of interesting discoveries recently, about just how widely most pianists misunderstand the nature of gravity and relaxation. Try standing and holding your arms out as if to play, then abruptly relaxing. Can you feel the path of elbow and notice that activities that had been keeping it in place- before it slumps inwards? Then go to a piano and do the same, sliding off the keys. I realised that virtually anyone demonstrates this exercise, keeps their palm remaining face down as they slide off. I think that shows a major lack of awareness of tensions in the shoulder. If you pay attention to what happens in the truest of relaxation, there should be a notable feeling of the forearm turning outwards (so the fifth angles downwards) as you slide back and of the elbow collapsing inwards against the torso. All kinds of movements occur within 3 dimensions. If you start with the hand in different regions of the keyboard, there are many different paths that result from relaxation.
While a lot of people encourage the feeling of how the hand might fall straight through the keys, I think that awareness of what gravity does elsewhere tends to be very poor (to a large extent probably even BECAUSE the pianist is trying to angle everything so the hand drops straight down- where complete release largely pulls it backwards from the keys). When you spend some time perceiving what the true relaxation of the whole arm and shoulder entails, it's far easier to put the balancing muscular activities in efficiently. When you have a sense of exactly what you are matching muscular actions to (so balance only just occurs at all), there is far less effort than when you just thinking about keeping things still in a certain position. Typically, pianists are so focussed on positions that there is minimal awareness how wastefully we maintain it. The elbow is probably the most severe case of all.