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How to teach Special Relativity to high school students

I am tutoring a couple of students in high school physics and have for the first time come across the problem of how to teach high school students the basic concepts of relativity. I explained the MM experiment and they found that comparatively easy, but upon getting to time dilation they started to get confused. As most people I assume do upon first coming across it, just as I did a few years back.

But I was wondering what are some tips on the best way to teach this? Stay conceptual, or introduce some paradoxes then explain how they are overcome, or go into equations?

I have only covered MM and then time dilation (using the concept of a light clock) both of which served as a basic intro to the frame of reference concept. I was then going to cover simultaneity then length contraction finishing up with mass changes. Is that the best order?

The students are expected to know, and apply, the Lorentz factor for length contraction/time dilation/mass change. However no Minkowski space, or velocity addition.

Any help would be greatly appreciated.
 

CompuChip

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I have some experience explaining SR to high school students. It is a good idea to start with the MM experiment and use that to explain why the constancy of the speed of light in vacuum is taken as an axiom. For the other axiom (physical measurements yield the same in every frame) appealing to intuition will suffice. Then I sketch a situation (a train with Bob inside moving at a constant velocity past a station where Alice is sitting, yadda-yadda) and I guide them through some calculations: Alice throws a ball horizontally from one end of the train to the other. Show that for Alice, t = L / u (where t is the flight time, L the length of the train and u the velocity of the ball) and for Bob, t = (L + v t)/(u + v) with v the velocity of the train -- prove that solving the latter for t also gives t = L / u. Then do the same for a light beam (u = c) using that in the denominator of the second expression you get c because of our axiom. This will already give the student some intuition about the origin of the "discrepancy" in the measured time.

Then with simple algebra you can set up the mirror-clock experiment (two opposite mirrors, a light beam between them) and let them solve t'(t). This gives you the opportunity to introduce the gamma factor (I let them rewrite it in terms of beta = v / c, then sketch it for 0 < v < c and examine the limits in a loose way, e.g. plugging in very large / small numbers and checking what happens). By doing something similar with a light pulse moving up and down the length of a ruler, you can similarly derive length contraction.
Finally I close with an example about the life time of atmospherically created muons, which we detect on earth although they should have decayed long before that.

In my experience this is very well understandable for the students as long as
* you keep hammering on the relativity of observers (they cannot be accelerating; whenever they think they have found a preferential reference frame, make it clear that this is because they are used to having their school building, the station or the night sky as "fixed" orientation points and their argument fails in empty space, for example)
* you guide them through the calculations (i.e. make "show that ... leads to this quadratic equation, and use the quadrature formula to solve it"-type questions).
* keep the physics in mind. If they have derived that the time gets multiplied by gamma, ask questions like: "is it longer or shorter than what you would expect? seeing that the light has to catch up with the front of the train which is moving away from it, is this logical? I see someone else's watch run slow, but by our axiom the converse would also be true - isn't this a paradox?"

I hope this helps a bit. I have some stuff on paper, but it is in Dutch so it probably won't help you.
 
I hope this helps a bit. I have some stuff on paper, but it is in Dutch so it probably won't help you.
Thanks for all of this. I'll run through this exactly over the next couple of weeks. I'll let you know how it all goes.

Cheers mate,
Matthew.
 

robphy

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The students are expected to know, and apply, the Lorentz factor for length contraction/time dilation/mass change. However no Minkowski space, or velocity addition.

Any help would be greatly appreciated.

Are you saying that they don't need to know Minkowski space...
but it would be okay if they did?

Or that what you seek should not make reference to Minkowski space?
 
Are you saying that they don't need to know Minkowski space...
but it would be okay if they did?

Or that what you seek should not make reference to Minkowski space?
Well the curriculum does not require it, at all. I think introducing Minkowski S/T diagrams would be more confusion when essentially all the students need to know is there are differences in the order of events in difference frames. However quantifying that, even diagrammatically is not needed. And while the diagrams help, they only would serve to help after explaining simultaneity in much more depth.

This is a very basic introductory course. It doesn't really allow for the students to get any real appreciation for what is occuring, just that there is time dilation/length contraction/changes in simultaneity.

I went through parts of CompuChip's suggestions and they seem to understand. I augmented it with clips from The Mechanical Universe; for its easier to see moving objects than have my hand waving.
 

George Jones

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I know this is a little late in the day, but

http://www.fitzhenry.ca/detail.aspx?ID=8461

is a very short book that is meant to be a resource for high school teachers (and others).
Thanks George! I have to cover relativity in an outreach session to high-school teachers in two weeks. It will be great to be able to have a resource to share.. and this book is a great price! Hopefully it arrives at my place in time to look over it before I do the session.
 

robphy

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I augmented it with clips from The Mechanical Universe; for its easier to see moving objects than have my hand waving.
The Mechanical Universe (http://www.learner.org/resources/series42.html episode 42? or 43?) drew animated spacetime diagrams.
In particular, they drew one for a transverse light clock.

A few years back, I drew my own animated spacetime diagrams...
and found that the longitudinal light clock [as a follow up to the transverse light clock] was more revealing.

Together, the two transverse and longitudinal light clocks are like a Michelson-Morley apparatus.
If you go further and use a circular array of lightclocks, you get [in my biased opinion] a nice visualization of proper time [e.g, my avatar]... with no equations required by the audience.

http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/ [Broken]
[URL [Broken]
physics.syr.edu/courses/modules/LIGHTCONE/LightClock/#circularlightclocks[/url] (the key animation)

I think this can be presented to a non-mathematical audience.
 
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