After a bit of thinking about the precursors to believing in relativity, I
have some thoughts. (I always have some thoughts!)
Try to first find out if the person believes in Galilean relativity. What
would they say happens if you throw a ball upward in a uniformly moving
vehicle? If they say anything other than it goes up and straight down, the
battle is already lost. So you first have to show them movies of these
types of things to convince them of Galilean relativity.
Then another step would be to go to the classic Einsteinian thought
experiment of the simultaneous lightning strikes at either end of a train
car. They are simultaneous from the ground observers' point of view who is
standing near the middle of the car on the ground. But the conductor inside
the center of the moving car sees the flash first on the front of the car.
But he knows that light always travels at the same speed, so he concludes
they were not simultaneous.
The second barrier is that the person may not visualize the second scenario
with the conductor, so you might have to use a motion map to show this
situation. The third barrier is the idea that the speed of light is
constant no matter who measures it. There you would have to appeal to
various experimental results.
Finally you can go to the light clock to show the apparent "time dilation".
But at that point the central idea is to accept that an observer on the
"moving" light clock will observe your light clock as going slower. This
requires an initial acceptance of Galilean relativity. Now you have bridged
to Einsteinian special relativity.
Now a person adept in math including vectors might be able to understand the
arguments based on the vector interpretation. But they will not believe
that it applies to "real" life. This is a common occurrence when students
have mastered math, but still can't grasp the physics models. The math was
merely number and symbol games, which they found to be fun, but didn't apply
to real life. To the psychologist the math will likely be mumbo jumbo.
Another thing that is needed is time. Once you have mastered one concept
and built a particular mental model it takes about 2 weeks to integrate it.
Laws found that scores on the FCI/FMCE continue to rise for 2 weeks after an
effective method of teaching. So you can not just immediately jump to the
next part of the argument. This is one reason why the compressed time frame
of summer school may not work as well as the more leisurely semester
approach. Very quick individuals may not need as much time, but one must be
careful there.
This sequence is designed to start with things the person understands, and
move towards things that are alien. But you must do so in steps where the
person can see how one idea is similar to or relates to the next idea. In
the Clement/Camp lessons they start with an anchor situation, and bridge to
closely analogous situations, until finally they arrive at the target
situation which illustrates the concept. This particular pedagogy is
extremely powerful, and should be used by all teachers when appropriate.
For example many students do not believe in the normal force F_N because
they believe that forces are only exerted by animate objects. A simple 20
min anchor and bridging analogy works far better than an hour of lecture.
But the analogy has to be discussed by the students at every step and they
have to buy into each step, which lectures do not do. I highly recommend
everyone who teaches should read John J. Clement's papers in JRST and get a
copy of "Preconceptions in Mechanics" by Clement&Camp. You might learn
something! His work even predates a lot of the other PER work, and did not
rely on the FCI.