Complications un-needed

Un-necessary complication, and even cognitive-dissonance, on the information-superhighway may be spread inadvertently by folks who were taught relativity using Einstein's pre-1915 language, which helped inspire special-relativity but is largely useless in accelerated frames and curved spacetimes. Instances of this might include:

1. Discussion of a "relativistic mass" that changes with speed. This amounts to thinking of the relativistic-momentum 3-vector equation p = mγv as a product of  "relativistic mass" m' = γm times coordinate-velocity v = dx/dt, rather than as a product of frame-invariant rest-mass m times synchrony-free proper-velocity w = γv = dx/dτ.  Both result in a momentum equation of the form mass times velocity, but only the proper-velocity segmentation (yielding the spatial components of a 4-vector) holds up in (3+1)D and in curved spacetimes. The most obvious contradiction for "relativistic mass" arises with 2 or more spatial dimensions, when one finds m' to be dependent on direction!

2. Use of symmetrically-equivalent (e.g. primed and unprimed) frames of yardsticks and synchronized clocks, when only one extended map-frame is involved so that proper-time τ, proper-velocity γv and proper-acceleration α are adequate to understand in detail what's going on with the moving clock. In any case symmetrical equivalence (and the tangent free-float-frame simultaneity of Lorentz transforms) only works provided neither frame changes its speed or direction. A classic example is the problem of π+ mesons with a (proper-time) half-life of τo = 2.6×10-8 seconds created 100km up, that make it to ground even though lightspeed might only take them 3×108m/s×τo ≈ 7.8 meters before elapsed map-time might predict their decay. It is easiest to find the proper-speed (map-distance per unit traveler-time) needed to make it to ground, by just dividing Δx/Δτ = 100km/τo ≈ 12,829 c i.e. lightyears/traveler-year. This ridiculously-high proper-speed is apparently easy to reach if you are created by impact in the upper-atmosphere of an incoming cosmic-ray i.e. a super-relativistic atomic-nucleus.

3. What else?

These changes are slowly working their way into texts at all levels, but not uniformly and over periods of decades rather than years.