This is the trouble with "rules" and "scientifically studied techqniues" - it's all a little smoke and mirrors.
Some explanation and illustrations (albeit without the illustrations):
Firstly, why left to right? The obvious answer is that we read left to right and are used to analysing visual media in such a manner, from taking in a scene to reading subtitles. Of course, this is all well and good as long as your scene should be read from left to right. Perhaps the detail you want to be noticed first is to the right? The centre? Heading toward your character? Then this complicates matters.
In cinema history there have been various techniques used. For examples one direction of movement representing heading towards a location, and the other to represent leaving. As someone previously mentioned, the protagnist or good guy on the left, the antagonist or the bad guy on the right. The strong to the left, the weak to the right, and so on.
These are subtle psychological tricks which can work, but aren't always necessary.
Imagine one character (A) walking left to right, to then stop and the romantic interest (B) continues walking to A with a static shot. In this case, it would involve reversing the camera angle, to have them heading in the same direction on screen, which is confusing or frustrating for audiences - a basic continuity error. In this case, direction isn't important.
Another point is that the left to right works only when two conditions are met:
1. Only the subject needs to be followed.
2. It's intended for audiences who read left to right.
This is an old Hollywood standard for a reason: in English we read left to right. However, when I read Hebrew, it's right to left. Japanese (if I remember correctly) is read top to bottom. Cultural differences lead to different inclinations. Of course, this is somewhat semantic, as you're most likely thinking of a European language-derived audience.
Point 1, however, goes back to what I said before, what needs to be noticed in a scene.
Now, if the character is being chased by an enemy, then the old "rule" could apply, and as attention needs to be focussed on the fact that they are fleeing (i.e. it's negative), right to left would make sense.
However, there is something more to this "rule" which amounts to an actual rule:
Which ever directions you use, make sure to be consistent throughout. As Itype my 3 year old son is watching Lego Jurassic Park. Almost all the direction I've watched for the last 5 minutes while writing this is right to left, but when there is a scene cut, it's left to right, as it's portraying a change in location and characters, in time and space. So always be consistent in the directions you choose, unless there is a good reason to change them.
