Train gedanken pitfall

The STE (Smarter Than Einstein) crowd often get into trouble when they
try to argue that observer M is "in the track frame" or M' is "in the
train frame."

Objects or events, if one speaks carefully, are not in any frame.
They just are "in" the world. What is "in" a frame are measurements or
coordinates. An exampe will perhaps be convincing:

Take a blank *** of paper. Draw a tiny star on it somewhere near
the middle but not exactly in the middle.

Now take your ruler and draw two perpendicular lines on the paper --
not in the middle -- all the way across. Give the pair of lines a
name, say S. Measure the perpendicular distance from the star to the
two lines, and call the results x and y. You can now say that the
coordinates of the star in S are x and y.

Next, draw another pair of perpendicular lines S' across the paper
anywhere at random, tilted if you like, and use the pair S' instead of
S in the same way to locate the star. You can say that the coordinates
of the star in S' are what you measured: x' and y'...

NOW THE BIG QUESTION:

Which set of axes, S or S', really contain the star?

This question is as silly as the question, which frame of reference is
M in?

The answer is that both M and M' observers can be located in time and
space using cordinates based on the track OR on the train. The walls
and roof of the train cars are not a theoretical obstacle to locating
the observers with respect to any frame of reference you can invent.

Don't say that objects are "in" a frame. Say that their coordinates
can be measured with respect to a frame. The other way is just begging
to confuse you. What is "in" a frame is a set of coordinates of an
object, not the object itself.

Uncle Ben
.

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