Some Definitions
![[url=https://pixabay.com/en/oldtown-bern-switzerland-historical-733435/]"Bern Clock Tower"[/url] by successcoach is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]
The clock tower in Bern, Switzerland that Einstein walked past daily on his way to work at the patent office as he pondered the nature of space and time.](https://www.geogebra.org/resource/Nd6JzrTc/TPil5HJqV732QkWL/material-Nd6JzrTc.png)
Observers and Events
Since trains - albeit not as modern as the one in the photo - were the only form of rapid transit in Einstein's day, it is common to derive the expressions of relativity using trains as representative of a moving reference frame as measured by an observer on the platform.
We will take the same view. But first we must establish two definitions - that of an event, and the word observe (and observer). In the context of relativity, an event is nothing like a concert. An event like a concert lasts for hours and is spread out all over a stadium or theater. In relativity an event must take place at one location (a point) and at one time. It is more like a fire cracker going off. Pop! Over there it went off, and lasted for only an instant. Think about an event occurring at a coordinate x,y,z,t.
When the word observer is used in ordinary language, we think of someone looking at something and maybe taking note of what happened. This is not what is meant by an observer in relativity. Rather, an observer is more like an omnipresent being in the sense that the news of an event takes zero time to propagate to the observer. It would make a mess of all of our discussions if we had to worry about how long it might take light to bring information to the observer from some event that takes place. Instead, we leave that complicating factor out entirely be imagining that the observer is always present at the location of the event in question. Later discussions will revolve around what other observers in other frames would measure if they are, for instance, distant from an event or moving with respect to an event, or perhaps both.
The Proper Frame
The proper reference frame is one in which the event being observed is stationary with respect to the observer. There are only two frames meaningful in relativity - the proper frame, and all others which move at some speed with respect to the proper frame. Keep in mind that the event is never the travel of a beam of light. The second postulate tells us that in all frames the light will be seen to move at c. Rather, if we are talking light beams, it is the source or the detector of the light that must be at rest in the proper frame.
EXAMPLE: A uranium atom is speeding around inside a particle accelerator. Does the scientist in the lab frame measure the proper lifetime of the particle?
ANSWER: No. The proper lifetime of the particle is only measured if the particle is at rest.
EXAMPLE: A spacecraft is heading toward a distant star and an on-board astronaut measures the distance to reach that star. An earth-based observer makes the same measurement. Who measures the proper distance?
ANSWER: The earth-based observer does. Both earth and the star are at rest in this frame, while both are in motion to the astronaut.
EXAMPLE: Consider again a spacecraft leaving earth and heading toward a distant star system which we will assume is roughly stationary with respect to earth. An earth-based observer measures the duration of the trip, and an astronaut on-board the ship does as well. Who measures the proper trip duration?
ANSWER: The astronaut does. In this case it is tricky since to the earth-based observer the spacecraft is moving and to the astronaut the earth and star are moving. So what helps us decide? An easy way to decide in such cases is to ask how many stationary clocks are required in each frame to take the measurement? There need be only a single clock on-board the spacecraft to measure both the departure and arrival time. In the earth frame there would have to be one clock on earth and another stationary clock on the star that would await the arrival of the spacecraft. One clock would not suffice since it would otherwise be moving and not therefore measuring time in the earth frame.
Gedanken Experiments
When doing derivations of effects in special relativity, it is common to use trains as the moving reference frames. While we think of these derivations which use pictures of trains as mathematical exercises today, in the early days they were called gedanken experiments, which is German for thought experiments. Those terms are worth knowing as a student of physics. The "experiments" were done as thought experiments rather than real, physical experiments because it's hard to find a train (or any other vehicle) that can move a fair fraction of the speed of light.
QUESTION: Is having the thought "I wonder if this stuff is real" a gedanken experiment?
ANSWER: No. Having any thought is not a thought experiment. One has to have a precise and quantifiable question in mind and a means of finding that answer. You will see two of these in the following sections.