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Take a feather and a brick, and drop them at the same time; the brick will reach the ground faster. These days we know that the cause is air resistance: there is proportionally more friction resisting the fall of the feather, so the brick falls more quickly. But back in ancient Greece, Aristotle proposed that it is simply in the nature of heavier objects to fall faster.

Two thousand years later, Galileo was having none of it. In his final book, Two New Sciences, he proposed a thought experiment: consider two rocks of different weights, which (if Aristotle was right) should fall at different speeds. Now imagine tying them loosely together with a thin piece of string.

The string is much lighter than the rocks, and presumably would have a negligible effect on their motion. By Aristotle’s reckoning, at some point the string becomes taut as the lighter rock trails the heavier, slowing it. But at that point the combined system of the two rocks has a larger mass than either individually, and Aristotle says they should now fall faster. Our intuition is being pulled in two different directions, which led Galileo to suggest that, air resistance aside, the natural tendency of objects is to fall at one rate, regardless of their mass.

Thought experiments have long played an important role in the progress of science. One of their foremost practitioners was Albert Einstein, who thought his way to crucial insights about the nature of space and time. One of Einstein’s most famous thought experiments investigated, as had Galileo, the nature of gravity.

Mass in motion

Imagine you are in a sealed room and want to calculate the gravitational field inside. You might drop some objects and see how fast they fall. But aha, said Einstein, maybe you are in an elevator, or an accelerating rocket ship, which would throw off your measurements. Is there any way to distinguish between the force of gravity and the effects of acceleration? Eventually he concluded that there is no way to tell the difference, and therefore that gravity is better thought of as a feature of space-time itself – namely, its curvature – rather than as a force of nature.

Ultimately our knowledge of the world comes from real experiments that collect real data, not from thought experiments that don’t require us to leave the comfort of our armchairs. But thought experiments allow us to consider regimes of physical reality that we can’t access directly, because the real experiments would just be too hard.

When thought experiments work, they do so because a correct theory of the universe must do more than simply fit the data: it also has to make sense. That’s a slippery criterion, of course.

That cat

In a famous thought experiment, Erwin Schrödinger pointed out that a decaying quantum particle could give rise to a cat that was both alive and dead at the same time. Despite being one of the founders of quantum mechanics, Schrödinger was reluctant to accept its most surprising implications: the lesson he took from his cat was that quantum theory must be incomplete. Ever since, people have debated whether we should really accept the possibility of cats that are simultaneously dead and alive. (We should, but that’s a different article.)

Thought experiments continue to keep theoretical physicists up at night, and gravity and quantum mechanics remain favourite subjects.

These days physicists are bedevilled by black holes, which according to Stephen Hawking will eventually evaporate away by emitting quantum radiation. That’s fine, but what if we threw a book into a black hole, and then waited for the black hole to evaporate completely? What would happen to the information in the book? Would it be somehow encoded in the outgoing Hawking radiation, or lost forever?

We don’t know. Black holes certainly exist (as was recently verified with the discovery of gravitational waves by the LIGO observatory), but we don’t have access to the very small ones that would give off a measurable amount of radiation. So the only experiments we can do are of the thought variety. Let’s hope they keep pointing us in the right direction.