Donna,
Nobody will disagree with Mr. Einstein, yet the increase is fairly miniscule and cannot overcome the adverse effects of too light weight for stability over long range. Momentum is a key factor when other forces are at work on an object, in this case gravity, drag and a horizontal force of wind. What Einstein's realitivity concedes is that a projectile pushed at increasing velocities will compress by certain amounts which, in turn, decreases ballistic coeffiency. The practical implication of this is proven that nearly all 1,000 yard tournaments and military snipers use bullets that are a bit long and have extremely high ballistic coefficients. Yes, these are typically pushed at high speeds, but not to the effect of noticeable compression. Sure we could shoot short bullets that are extremely dense, but the aerodynamic shape of the bullet is more adversely affected by drag that something of a longer, sleeker design. Granted this is taking it to the extreme, but a flying dense disk isn't as effective or efficient as a flying, dense spear.
Another problem, as I see it, is bullets are designed and manufactured and operate at a range of velocities, pushed too fast and they will either destabilize or come apart, pushed too slow and they will destabilize and not expand. Granted the stabilization issue can be compensated somewhat by the rate of twist for a given bullet shape, length, density and speed, but I don't think Barnes or anyone else will guarantee bullet performance in the 8mm or any other big game caliber over 4,000 fps in living tissue and bone.
I, for one, have made the mistake of pushing bullets well beyond their design parameters. Many years ago I purchased a 270 Wby Mag. Thinking that if a 270 Win was good for long range shooting of deer size game, well the 270 Wby would be so much more the better, right? It was to varying degrees as long as the animal was far enough away to allow the bullet to perform within it's designed velocities. What ended up happening was, in the real world, my hot 130 grain handloads were pushed fast enough that when I encountered game (deer and caribou) much closer than I anticipated, the bullet came apart with explosive affects. Yeah the animals died and they died on the spot. That might have been fine for a lot of hunters, but I do enjoy eating the meat that I shoot and a shoulder shot caribou, or even if I hit ribs, lost of lot of the meat I intended to utilize. Also range testing different loads to find something that would stand up to bone at close range, I found that 140 grain bullets, even though they started out a bit slower than the 130's, had a much better shape, sectional density (and because of these two - a much higher BC) actually had a flatter trajectory. I know all things drop due to gravity at the same rate over a specified amount of time, but the 140's actually covered 300 yards and more over a shorter amount of time than the lighter 130's did.
I don't mean this in any way, except to state for long range shooting, what we are looking for is the best fit of BC, speed, and stability. We can't make a bullet with less than ideal shape and weight measure up to bullet with better fit of ideal shape and weight, no matter how fast we push it. For the 8mm, a bullet of 200-220 grains of proper shape and construction pushed at 8mm Rem Mag speeds is a much better choice of bullet than a 180 grain bullet pushed at 4,000 fps. 180 grain 8mm bullets just don't have the sectional density or construction to perform reliably at 4,000 fps. As long as we stay within the design parameters of the bullets, barrels and pressures of the cartridges, we should have an excellent hunting rig. Get too fast or too much pressure and things don't perform well.
The last comment is what increase in weight constitutes an increase? Dealing in absolute terms, any weight added, but in the manufacturing world (where bullets are made and sold) even if using the concept of six sigma quality control, we are only looking at +- 3sd of weight, those variances being far above any "weight" gained by Einstein's theory of relativity. To operate in the world, a bullet from any manufacturer labeled 180 grains will never weigh exactly 180.000000000000 grains. Significantly, using 3 sd above or below the mean for any given batch, will be within manufacturing specs, of say, 180.001 grains (or whatever industry standards there are). So, to me, there is no weight gain in the practical world or manufacturing world that really can be considered or even should be, it never really becomes a factor.
Whew, enough engineering for one day.
Donna, by the way, you have a very nice website. Lots of good information there. Kudos to you, that must of taken a lot of work to put up there. I, for one, would like to thank you for doing so.