How Can an Experiment Done Only in Your Head Teach Scientists Anything?

A Thought Experiment Follows an Idea Through in Your Imagination

A thought experiment is a scenario you work through in your mind instead of in a laboratory. You set up the situation, ask “if this idea were true, what would have to happen?”, and see where the reasoning leads. The Stanford Encyclopedia of Philosophy describes them as devices of the imagination used to investigate the nature of things [2].

The English name copies a German one, Gedankenexperiment. The physicist Ernst Mach is often credited with inventing the word, but the Stanford entry says that is not correct: a historian found it already in use in German in 1811 [2]. The habit of thinking this way is far older than any name for it.

Galileo’s Tied Stones Show That “Heavier Falls Faster” Contradicts Itself

For a very long time many people followed the Greek thinker Aristotle, who held that heavier things fall faster. In Two New Sciences (1638), Galileo writes the argument as a conversation. One speaker, Salviati, asks what happens if you tie a big stone and a small stone together [1][3].

Follow the idea as its believers would. The small stone is slower, so it should drag on the big one, and the pair should fall more slowly than the big stone alone. But tied together, the pair is a heavier object than the big stone, so it should fall faster. The pair cannot fall both more slowly and more quickly than the big stone alone. The Stanford entry tells the same story with a cannonball and a musket ball, and says the contradiction undermines the rule that heavier bodies fall faster, which leaves the conclusion that all bodies fall at the same speed [2].

Notice what the argument did. Galileo never dropped anything. He took his opponents’ own rule and showed it ruins itself.

Why a Thought Experiment Still Needs Nature to Have the Last Word

The tied-stone argument shows that one rule is inconsistent. It does not by itself describe everything that really happens. In ordinary air, a stone and a feather do not land together, because air resistance has a much larger effect on the feather’s fall. The usual modern statement is that, when air resistance can be ignored, falling objects speed up at the same rate whatever their weight, and that has been checked by observation and experiment, not only by argument.

The Stanford entry makes a related point about the most famous cat of all (more on it below): a thought experiment can expose a clash between a theory and what we expect of the world, but that is a different thing from measuring the world [2]. That is why good scientists treat these as tools for finding mistakes and asking better questions, and then go and look.

Einstein Imagined Falling and Chasing Light to Find New Questions

Einstein recalled two famous mental pictures. A 1920 recollection of his, quoted in a MathPages summary, calls the thought of an observer falling from the roof of a house the “happiest thought” of his life: for that person, at least nearby, gravity’s effects seem to vanish during the fall [4]. You know a small version of this feeling: in free fall you do not feel your own weight. Thinking about this helped lead Einstein toward general relativity (1915).

The other picture is older. Looking back late in life, Einstein said that at the age of sixteen (around 1895) he had stumbled on a paradox: what would a beam of light look like if you ran alongside it at light speed? He added that this paradox already held the “germ” of special relativity [5]. A careful note from the historian John Norton: Einstein did not study Maxwell’s theory of light until about two years later, so the thought may have started as a teenager’s hunch. Its real value, Norton argues, came later, when it helped Einstein see why certain older theories of light could not work [5].

Here the thought experiment did something different from Galileo’s. It did not simply refute a rule. It raised a question that years of mathematics and measurement then followed.

Schrödinger’s Cat Was Built to Make One Reading of Quantum Theory Look Strange

In 1935 the physicist Erwin Schrödinger described a cat shut in a steel chamber with a “diabolical device”: a tiny bit of radioactive material, a Geiger counter, and a hammer arranged so that a radioactive decay, perhaps within about an hour, would shatter a flask of poison [2]. If you apply one reading of quantum theory to the whole chamber, his description says, the living and the dead cat would be mixed together in the description of the system [2].

The point was not to propose hurting a cat or to claim real cats are both alive and dead. According to the Stanford entry, the scenario is best read as exposing a conflict between quantum theory, as Niels Bohr interpreted it, and our ordinary beliefs about cats, not as proving the theory self-contradictory [2]. It shows the same pattern as before: an imagined case that shows where an idea feels wrong, so that people will argue about it and test it.

Try It Yourself: Can You Argue Without Dropping Anything?

Here is one to try with a pencil and paper, the way Galileo’s story goes. I made up this activity; it is not part of Galileo’s original argument or the sources below.

1. Draw a heavy stone and a light stone joined by a string. Write down the rule “heavier falls faster.”
2. Next to the picture, write what the rule predicts for the light stone alone, the heavy stone alone, and the pair. Do two of your answers disagree?
3. Now make up your own “what if” question, such as “What if a ball were dropped inside a falling elevator?” Write what you expect, then ask: what could I look at to check?

If you want a real test afterwards, with an adult’s help, drop a flat sheet of paper and a book from a low height indoors, over a clear area, then try the paper crumpled into a ball. Does your first answer survive? Keep the drops low and nothing breakable below.

Sources

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