Reality and space-time
I once read a long time ago that it is easier to teach relativity to small children than it is to teach adults, perhaps because children are more receptive to a world free of common sense than adults are. Relativity marks the beginning of this un-commonsensical world. I wrote a novella about a 20-year-old Alice who returned from Wonderland to teach her professor some physics that is uncaged from its Newtonian prison.
Welcome to Wonderland
The journey starts with the notion that up and down does not exist. We arbitrarily assign up and down to the universe. Hence, this is the reason why frames of reference are very important in physics. Even time is arbitrary, that is to say, none of it is absolute or real. This leads on nicely to this question: “What is reality?” (a good Theory of Knowledge vignette).
Enter space-time, for it is this fabric that our reality is played out on. But how do we meld the three dimensions of space with time? This is the opportune moment to take a break from the textbook and syllabus, and explore how space-time can be modelled, first graphically/diagrammatically and then, let it all loose.
In my experimental workshop with Year 13 physics students, I first read excerpts from An Evening In Wonderland – A Brief History of Maths, Physics & The Universe to the students, and then invited them to create their own space-time out of the jumble of art materials that I had brought along.
To my surprise, I discovered that the session opened a lot of conversations – and revision topics – as well as bold, new ideas. One student commented that the straw basket that I brought the art materials in was a good model for space-time: because our reality could be made of many baskets, each woven together by String Theory. Another student created a paper-chain and said that this represented a space-time that is being created all the time and is non-ending.
The three fundamental pieces
Once the fun part is over and students are sufficiently inspired, it is a good time to knuckle down to the three fundamental pieces:
- Inertial frames, lengths (proper length and length contraction)
- Galilean transformation and the concept that moving objects take the shortest path between two points in space-time (relate that back to the model)
- Gravitational mass and inertial mass (relate that back to the model)
Einstein’s principle of equivalence
I would start with the equations to link gravitational mass to inertial mass, discuss the differences (none experimentally, but huge conceptually) and relate that back to space-time. How does inertial mass and gravitational mass work in space-time, based on your experience of building your model of space-time? Which naturally leads to the big subtopic on gravitational attraction.
Moving on to Einstein’s principle of equivalence, we can unleash the creative mind again as we consider the various scenarios of Einstein’s relativity, namely speeding cars/train carriages, falling lifts and spaceship.
You could play gedanken and ask questions such as this one: You and a friend are stuck in a lift 100 floors up. Suddenly, the lift cables are cut. Do you jump to stay alive (OK, for a fraction of a second longer) or does it not make any difference?
Our beautiful cosmos
Armed with these three components, your class is now ready to enjoy the fun parts of general relativity, which are black holes (surface, core and Schwarzschild’s radius), gravitational lensing and the bending of star light rays by the sun.
For me, this is the part of the whole physics IB syllabus that brings the magic of physics to life: you look at the night sky with new eyes lit by the knowledge that the wonders beyond is all made sense of by the 100-year-old theory of a genius called Albert Einstein.
Play that note again
It may seem strange to leave the easy bit till the last, but bringing in special relativity at this late stage, but I do so intentionally because it is a wonderful opportunity to recap on this beautiful topic with a lot of new concepts, so students would probably benefit from covering the grounds again, albeit briefly.
If you are teaching IB physics, I hope my article inspires you to teach this option. You can find the resources in the TES Resources' Shop.
Jacqueline Koay teaches physics and chemistry as a subject specialist.