Stretching the imagination: How a rubber sheet challenges our knowledge of gravity

A popular analogy compares the geometry of curved spacetime to a rubber sheet. Yet, science educators have shown that this representation can get in the way of a more abstract understanding of Einstein’s theory of gravity. The findings hint to a deeper mechanism about how human cognition works.

No man can visualise four dimensions

The Earth circles around the Sun and we stay grounded on earth because of gravity. Yet, the nature of gravity eluded human understanding for centuries. By describing gravity as geometry, Albert Einstein offered a revolutionary explanation: He modelled the fabric of our universe as four-dimensional spacetime and gravity as manifestation of the curvature of spacetime.

Einstein was sure that no man could visualise four dimensional spacetime except mathematically. Image via licensed under Creative Commons CC0.

Still, there remains the challenge of visualising a theory whose geometry continues to confound. After all, humans are visual creatures and understand the world around them based on what they see. Even Einstein himself was sure that no man could visualise four dimensions except mathematically. He admitted that he thought in four dimensions only in abstract terms. In response to this imaginative challenge, Einstein introduced an analogy that would become ubiquitous in physics: He compared spacetime to a warped cloth floating in space. Nowadays, this cloth is usually replaced by a rubber sheet on which marbles circle around a central mass — a miniature model of the solar system held together by gravity.

While the picture of a rubber sheet has become the iconic symbol of general relativity used by physicists and laymen alike, the analogy has given rise to heated debates: Is the rubber sheet misleading despite its visual power and simplicity? Are physics students prone to form misconceptions because of an oversimplified depiction of gravity?

Embodied understanding of disembodied concepts

In a new study, science educators have presented a surprising answer to these questions: Our sensory experiences of gravity may actually contradict the concept of spacetime. The intuitive appeal of the rubber sheet analogy can run into conflict with a more abstract definition of gravity because of the way human cognition works.

The study probed physics students’ understanding of the rubber sheet analogy based on methods of embodied cognition: Embodied cognition extends the boundaries of the mind from being inside the brain to including the body’s physical interactions with the world. Humans conceptualise the abstract in terms of the physical. And curved spacetime is an abstract concept that one must grasp in terms of other areas of experience. Describing gravity according to Einstein requires metaphoric language.

Assuming that conceptual understanding of abstract concepts is grounded in embodied experiences suggests that figures of speech are more than just linguistic tools: Analogies are fundamental features of thought and mind. Language can serve as a window into the scientific conceptions of students — a window that science educators are eager to peek into. By analysing how physics students talk about gravity and spacetime, researchers try to understand how learners align their bodily sensations with mathematical models of gravity.

The good use of a bad analogy

An analogy works when it satisfies its purpose, namely conveying a feature of an abstract concept. For an analogy to be successful in communicating these features, the representation should not conflict with learners’ sensory experiences of the world. And it turns out that the rubber sheet analogy does exactly that.

To explain gravity as geometry, the rubber sheet analogy makes use of gravity to distort the geometry of the rubber sheet. Thus, the mechanism of the analogy depends on the very phenomenon it tries to explain — and on students’ everyday experiences of gravity: Through the rubber sheet, the notion of curved spacetime gets intimately linked to the embodied experience of being pulled down to the ground.

Our minds and bodies are prone to confuse cause and effect when conceptualising curved spacetime through the rubber sheet analogy.

The new findings suggest that the experiential knowledge of gravity often gets in the way of inferring the right analogical mappings — and thus, of understanding the concept of gravity successfully. Our minds and bodies are tuned to putting ourselves into the setting of the rubber sheet. In the study, physics students therefore often confused cause and effect: Instead of describing gravity as a manifestation of the curvature of spacetime, students turned this reasoning upside down and stated that gravity curved spacetime.

To explain gravity as geometry, the rubber sheet analogy makes use of gravity — the very phenomenon it tries to explain. Image via licensed under a Creative Commons Attribution-NonCommercial 2.5 License.

Studying the role of the rubber sheet analogy has the ultimate goal to improve instruction in general relativity. The new findings suggest how to put the ubiquitous rubber sheet analogy to good use — despite its inherent conceptual flaws. To counteract the lack of experience with relativistic phenomena, visualizations in form of digital simulations and animations can supplement traditional representations of spacetime. Moreover, teachers can supplement the analogy with other models of spacetime to prevent the one-sided presentation of curved spacetime as a deformed rubber sheet.

Educators need to be aware that embodiment can run into conflict with abstract disembodied concepts. Even when concepts are impossible to perceive directly, learners draw on bodily ways of knowing. To conceptualise gravity in the domain of relativity successfully, learners need to develop awareness of the tension between the physical force of gravity in the everyday sense and the curved spacetime explanation.

The Earth circles around the Sun and we stay grounded on earth because of gravity. Owing to modern science education, the nature of gravity does no longer need to elude our students in the 21st century.

Reference: Kersting, M., Steier, R. (2018) Understanding Curved Spacetime — The Role of the Rubber Sheet Analogy in General Relativity. Science and Education.