Teaching Einsteinian Physics in Schools

An Essential Guide for Teachers in Training and Practice

Magdalena Kersting, David Blair

• Publisher: Routledge
• Year: 2021
• ISBN:
  9781000374131
• Edition: 1
• Topic: Education
• Subtopic: Education General

In our world today, scientists and technologists speak one language of reality. Everyone else, whether they be prime ministers, lawyers, or primary school teachers speak an outdated Newtonian language of reality.

While Newton saw time and space as rigid and absolute, Einstein showed that time is relative – it depends on height and velocity – and that space can stretch and distort. The modern Einsteinian perspective represents a significant paradigm shift compared with the Newtonian paradigm that underpins most of the school education today. Research has shown that young learners quickly access and accept Einsteinian concepts and the modern language of reality. Students enjoy learning about curved space, photons, gravitational waves, and time dilation; often, they ask for more!

A consistent education within the Einsteinian paradigm requires rethinking of science education across the entire school curriculum, and this is now attracting attention around the world. This book brings together a coherent set of chapters written by leading experts in the field of Einsteinian physics education. The book begins by exploring the fundamental concepts of space, time, light, and gravity and how teachers can introduce these topics at an early age. A radical change in the curriculum requires new learning instruments and innovative instructional approaches. Throughout the book, the authors emphasise and discuss evidence-based approaches to Einsteinian concepts, including computer- based tools, geometrical methods, models and analogies, and simplified mathematical treatments.

Teaching Einsteinian Physics in Schools is designed as a resource for teacher education students, primary and secondary science teachers, and for anyone interested in a scientifically accurate description of physical reality at a level appropriate for school education.

Section 1

Motivations and needs to teach Einsteinian physics

1Intuition in Einsteinian physics

Bernard Schutz, FRS

What?

This chapter sets the stage for the rest of the book by exploring the role of intuition as a tool to deepen the understanding of Einsteinian physics. Drawing on examples from the history of general relativity, Bernard Schutz argues that the development of physical intuition is a crucial goal in physics education in parallel with any mathematical development of a physics subject.

For Whom?

This chapter is intended for readers who wish to learn how expert physicists think conceptually about their subjects to understand them, and also, for those who wish to see how we can introduce Einsteinian physics to students by developing their intuition as well as teaching them mathematics.

Introduction

If you say the word “Einstein” to an average person, the first thing likely to come to their mind is an image of Einstein's iconic wild hair. The next thought will probably be that his science, however important, is far beyond the understanding of the average person. Both of these things place Einstein outside everyday society, a curious phenomenon to be wondered at. The teaching of physics at schools has until recently reinforced this view, mostly leaving Einsteinian physics to specialist university courses. The mathematical framework for this physics is challenging, and that has seemed a good reason to teach it only to those advanced university students who have mastered enough mathematics.

But it can't be left to the boffins any more. Everyone has heard of black holes; even small children want to know what they are. Recently, gravitational waves have also entered our vocabulary: their first detection in 2015 caused a media sensation, coming as they did from two black holes merging together! Other terms in common use that could come straight out of a general relativity textbook include the big bang, wormholes, and even the warp drive. And then, there is the quantum side of Einsteinian physics. Our lives would come to a halt without the Internet, computers, mobile phones, microwave ovens, and other devices that only work because of quantum principles. I would guess that well more than half of the world's economic activity today is enabled by physics that was only developed in the last 100 years and which is still thought to be too difficult to teach at the school level.

Does this leave us in a tough spot? Is the world to be divided between “users” who have no idea what is inside the box and “experts” whose work is too arcane to explain to the rest of the world? That would be dangerous for society. If we don't want that, can we open up the world of physics concepts to the people who don't have the mathematics to deal with the equations in which the physics is framed?

I believe that we can do it, and that we can, at the same time, improve the way we teach Einsteinian physics even at the advanced level. The way to do it starts with realising that even the experts think conceptually about their subjects in order to understand them; they don't go around just solving complex equations any time they want to answer a question. They use what we call physical intuition: a basic understanding of how things work and fit together that requires little or no mathematics. We should be introducing Einsteinian physics to students by developing their intuition as well as teaching them the mathematics.

Without intuition, science just would not work. Scientists today are specialists, and communication between different specialties requires a shared physical intuition. For example, if an astronomer wants to understand how a black hole might affect a star that is near it because he might want to observe the star in his telescope, he does not need to be able to solve Einstein's equations himself. Rather, he can approach a specialist in general relativity for insight, and she will explain to him how the gas gets pulled off the star by the black hole's gravity, how it will then get hot and therefore bright as it gets near the hole, and finally how it will vanish from view after being swallowed by the hole. None of their conversations will use arcane mathematics. Instead, they will rely on shared intuitive concepts about fluids, heat, and gravity. And these are concepts that are taught in school.

What is not always taught, either at school or at university, is an appreciation of the important role played by intuition in science. Some physicists I know don't display much intuition; they work mostly with the mathematics of their specialty, and they consequently don't have much interaction with other specialties. However, other physicists have been famous for their intuition. One example was Richard Feynman, who won the Nobel Prize for helping develop the theory of quantum electrodynamics. He was a member of the scientific panel that investigated the deadly 1986 Challenger disaster, when a space-shuttle launch failed because its booster rockets exploded. Feynman famously demonstrated on television that the fault lay with the decision to launch in cold weather; he dipped a piece of rubber used in the booster assembly into ice water, and then simply snapped it in half. End of discussion. There are plenty of other stories showing how Feynman was able to cut through confusions in apparently complex physics problems with a simple physical argument that even a high-school student could understand.

It is important to be clear about what intuition is. I would distinguish between the kind of intuitive thinking Feynman demonstrated and “popular science” presentations, although there is an obvious overlap. Popularising science is important, but such talks often aim at entertaining the audience. Here, we aim at teaching young scientists to use intuition in order to do science more effectively.

I believe that intuition plays a key role in scientific thinking, even though in casual discourse, it is often used as a synonym for sloppy thinking. Intuition is not the opponent of logic; rather, it complements logic. A brain governed entirely by logic would be a brain in paralysis, unable to generate an original thought. We educators need to guide students toward a fruitful interplay between the creativity and model-building of the intuitive process and the analytical and critical facilities of logic.

I will, therefore, focus in this chapter on developing physical intuition as part of learning physics, and then using intuition as a tool for deepening understanding, one that works in parallel with any mathematical development of a physics subject. The teacher can then grab hold of those intuitive concepts in students' minds to link up with other parts of physics, even parts where the mathematics is more complex. This should be done at school (and it often is) and university (often not). Doing this is important because, as I will argue later, intuition is central to how our brains work and how we make sense of the real world. We are not computers, and teaching us physics is not like programming a computer. So, my aim in this chapter is to explore how we can use the way intuition works in physics and in the physicist's brain to improve the learning of science.

Intuition in General Relativity: Examples

First, I will try to make the notion of intuition more concrete by giving three examples from the most mathematically complex work by Einstein: general relativity. The first example is from the history of the subject. The equations were more or less complete by late 1915 (the cosmological constant came later), the fundamental solution for what we now call a black hole was discovered by Schwarzschild in 1916. Einstein discussed gravitational waves already in 1916 and arrived at what we now call the “quadrupole formula” showing how systems emit gravitational waves in 1918. In the 1920s, the theory was applied to cosmology, ready for Hubble's discovery of the expansion of the universe in 1929. So, one might have expected rapid progress following on from these major achievements, placing general relativity on a firm physical basis. But instead, we find that even in the 1950s, physicists could not agree on whether Schwarzschild's solution described real objects, nor on whether gravitational waves were physically real or just an artefact of the complicated mathematics. Einstein himself changed his mind on these questions several times.

In my view (Schutz 2012), the root problem was that, in the period 1930–1950, people who worked on relativity approached it mainly mathematically. Naturally, we don't come into the world equipped with a relativity intuition: we have to gain it through “experiences” in the subject. Scientists commonly do this when entering unfamiliar territory, using an intuitive tool called heuristics, in which complex systems are approximated by a few simple characteristics that might be found by studying particularly simple examples. The mathematics of relativity gets quite complex for realistic problems, and occasionally people (including Einstein) wrote papers with fundamental errors that simply clouded the subject. But in the early period, few of the mathematicians working on relativity tried to work on heuristics; instead, they trusted only what they could get mathematically from the full Einstein equations.

In the 1950s real progress in relativity began because some brilliant physicists who were already skilled in heuristic thinking began working in the field. A famous example is Feynman himself, who at a key conference in 1957 (DeWitt & Rickles 2017) gave a simple physical argument showing that gravitational waves had to be real and had to carry energy (up until then hotly questioned). Feynman also pointedly remarked at this meeting that progress in physics did not always come from doing the mathematics better, but could come instead by working on simple situations or approximations, and then by doing experiments. What he was saying that relativists needed better physical intuition.

Physicists spent the next several decades developing this intuition: working on simple examples, using approximations to bridge between the simple examples, asking physical questions about what could be measured by experiment and observation, and doing experiments and observations. The 1957 conference kicked off discussions aimed at intuition-building among a growing number of scientists working in this field. The more scientists joined in, the more important it was to develop a language, a body of heuristics, an intuition that could be shared, that would help them communicate with one another.

By around 1990, there was a well-developed corpus of heuristics about black holes, gravitational waves, gravitational collapse, and cosmology, the study of which led relativists to a deeper intuitive grasp of the theory. In parallel, astronomers had been opening up a fascinating universe, beginning to gather evidence for black holes, gravitational waves, and the Big Bang. This input of data nicely validated the heuristic concepts that the theorists were developing. At this point, 75 years after its auspicious beginning, general relativity was at last ready to become a working part of astrophysics. Mathematics alone had not been enough to get there.

My second example follows one part of the above story. It is how physicists finally came to terms with black holes. We now understand that the Schwarzschild solution represents a black hole, deep inside of which is a “singularity”, a place where gravitational forces become infinitely large, but that surrounding the singularity is a surface we call the horizon, which is a one-way membrane: things from outside can cross to inside, but not the other way around. We are troubled by the singularity because the laws of physics, as we currently understand them, don't tell us what happens when an infalling body reaches it, nor what happens next. But this is something we can live with because it is not even in principle observable: no information can get out to us through the horizon. Crucially, therefore, it does not disturb our ability to use physics to describe things outside the black hole. Notice that the description I have just given is intuitive: without mathematics, you can still make sense of it because I have linked it with your understanding of causality in...