freyar
Extradimensional Explorer
The fact that inertial frames have a special name means they are distinguished! But the second part of your sentence is the content of the assumption. That's not something additional --- it's exactly what the postulate is saying.That is, it pulls a notion that an initial frame of reference is a distinguished frame, and that physical properties such as the rate of passage of time (as measured by common physical processes, say, decay rates) will be measured as the same thing for different observers in the same initial frame, and similarly, that distances can be reliably measured (say, as a count of wavelengths of light as emitted, again, by common physical processes), and will yield a consistent result by different observers, and that these measurements will be stable over time.
Then, the notion of an idealized clock must be presented as physically meaningful, even if no actual ideal clock can be made. And, it turns out that certain physical processes can be used to make very accurate clocks. As well, one must demonstrate that if a number of idealized clocks may be created, they will be shown to record the passage of time uniformly, so that any irregularities must be shared by the clocks and by the observer.
I think you're getting a bit confused or hung up on something. An idealized clock is one without irregularities. It is a perfect clock. This is really not special to relativity but is in fact how physics is done. We think of perfect systems, stripped of worries about experimental noise, etc, etc. Theoretical physics is like what the world is in our imagination; experimental physics is about making measurements as close to that idealized imagination as possible.
Just transport them infinitely slowly. We're just doing this in our minds, so we can take an infinite amount of time to set things up.It must also be shown that an idealized clock can be transported to various locations and remain accurate. (Knowing the results of the experiment, we will know that the clocks will show slightly different times after they are transported, but, they will still show the same rate of passage.)