Per Hannibals original question:
'SO. I posed the question, what happens to the finely trued receiver when you hang an 8 lb or more heavy/varmit floated barrel off one end of the action? The answer was, proper bedding will prevent action deflection. So. I asked, just how far from the recoil lug toward the muzzle end does the bedding need to extend to compensate for the barrel weight and prevent deflection?'
Short answers are
a) The muzzle of a heavy barrel does droop and stresses are transferred into the receiver which deforms the receiver, however minutely. The amount of deformation is in proportion to applied stress, and that proportion is dependent on the receiver material.
b) The bedding would have to extend completely to the muzzle to totally eliminate bending stress.
In reality, this is not significant in any reasonably designed and manufactured action, barrel, and stock assembly. What does matter to accuracy is uniformity from shot to shot. Uniformity is easier to achieve when all components are co-axial, perpendicular, etc. and have uniform section thickness so that stresses are evenly distributed. The success of this approach is evident in many free floated heavy barrels that repeatedly shoot tiny groups.
The bottom line is that if the barrel weight deforms the receiver the same way every time, the barrel will deflect the same way in response to pressures and stresses of the cartridge firing and the bullet will exit the barrel uniformly. This applies to lighter weight barrels as well as heavy barrels, so applying the build techniques will pay off if the shooter has the knowledge and skills to shoot to the build's potential.
Some of the best visuals for understanding the several factors involved in this can be found at
http://varmintal.com. See the barrel harmonics and tuner pages. There is a mention of muzzle sag a bit less than halfway down the page on barrel tuner analysis.
Another noteworthy finding came from the Houston Warehouse experiments. The late Felix Robbins mentioned the finding from Houston that there was an optimum barrel length for ultimate accuracy. I suspect it is related to the speed of sound in steel, the speed of the pressure pulse through the high pressure gas in the barrel, vibrations of the barrel, and the barrel harmonics per Varmint Al's discussion.
BeeMan