There was a very interesting discussion here a few years ago on this subject, with interesting points on both sides, most of which I don't remember.
In my view, and I am not a physicist, for a given string, no matter how far from the nut and bridge the ends of the string are secured, in order for that string to vibrate at a given pitch, the tension of the string between the nut and bridge will be the same.
As an illustration, say that on your headstock, the tuning machine sits on a groove that runs the length of the headstock and that the tuner is currently near the nut. The string is tuned to E. Now push the tuner (you'll need some kind of pneumatic device to actually move it) down the groove away from the nut and toward the end of the headstock. You are increasing the tension and the pitch is increasing; it's no longer tuned to E. (It's the same effect you get with a whammy bar on your bridge; by pulling on the bar you increase the distance from the nut, increase the tension, and increase the pitch.) You will have to reduce that newly increased tension by turning the tuning knob to get the tension between the nut and bridge back to where it was so that the pitch is returned to E.
Changing the length of the string beyond the nut or bridge can have effects. For instance, notice how the string on most instruments is just laying on the nut. When you strike the string, some of the energy passes beyond the nut into the portion of the string that's off the finger board. The longer that portion of the string is, the more energy is absorbed beyond the nut. This can be compensated for by increasing the angle of the headstock. This is why you see string trees on the strings that have the longest distance to the tuner on some in-line headstocks.
As Olie and Adriaan alluded to, having the strings pass through the body will allow you to use 35 scale strings on a 34 scale bass. This would have a similar effect as tuning down to D or D# with the same strings on a 35 scale bass.
And having the strings pass through the body may help transfer energy to the body woods to some degree.
In Olie's case, in order to get the string to vibrate at a given pitch, he's had to actually reduce the tension. I'm guessing he can probably do string bends and finger vibrato easier on that bass than if he took the same string and put it on a 35 scale bass. This is why Stevie Ray Vaughn tuned down; he could use big fat strings and manipulate them much easier than if he was tuned up to E.
Take a 35 scale bass, tune the string to E. Now put a capo on the 1st fret; you've shortened the scale length. The new shorter scale length is tuned to F; to get the string tuned to E in the new shorter scale length, you will have to reduce the tension by turning the tuning key down.
Again, I'm not a physicist; this is just what seems to make sense to me. And some other members made some interesting points in the previous thread that I can no longer remember. So take it with a few grains of salt; my ideas here may be inaccurate.
