Just wondering about the following scenario.
It's probably easiest to explain in the context of this explanation of Lorentz contractions
The video outlines a common thought experiment in Einsteinian relativity, of two inertial, relatively moving observers, each with a light clock. It primarily shows things from the perspective of Albert, the observer on the platform. Moving relative to Albert is Henry; from Albert's perspective Henry's clock runs slower due to time dilation. Generally, the thought experiment is explained from the perspective of each observer, who label themselves as being "at rest" and ascribe the relative velocity to their counterpart; it is, of course, possible for each observer to labels themselves as "in motion" and their counterpart as "at rest" and measure their velocity relative to their counterpart, as opposed to themselves. In this case the contractions are reversed, presumably.
Albert & Evelyn
Let's say that Albert is joined by his cousin, Evelyn, on the platform; she is there when Henry passes, traveling at an inertial speed; Albert and Evelyn are at rest relative to each other. Now, let's say that Albert and Evelyn both decide to construct a mathematical reference frame to describe the scenario, and to find out the relative motion and relevant contractions.
Albert constructs his reference frame and labels himself as "at rest"; he measures Henry's relative velocity to be something like 0.8c. He concludes time, for Henry, is dilated, or that his clock is running slower than the clock shared by Albert and Evelyn.
Now, while Albert was busy at work, so too was Evelyn; but unlike Albert, Evenlyn constructed a reference frame which labelled Henry as "at rest"; Evelyn measured her and Albert's velocity, relative to Henry, as 0.8c. Evelyn concludes that the clock herself and Albert share is running slower than Henry's i.e. that time, for Albert and herself is dilated.
Both reference frames are equally valid, and supposedly represent the exact same scenario, but they seem to be contradictory. Who is right; for whom does time run slowly; or where have I gone wrong?
It is probably worth stating that, I don't think stating that reference frames have been mixed adequately addresses the question, because both reference frames are equally valid and both Albert and Evelyn are entitled to construct them how they wish; both should accurately represent the given scenario.