A thought experiment is an experiment which is carried out in the realm of the imagination, rather than in a laboratory. Thought experiments are designed to test ideas, theories, and hypotheses which cannot physically be tested, at least with current scientific equipment. In addition to being used in some branches of the theoretical sciences, thought experiments also crop up in fields like philosophy, where people often explore complex topics which cannot be empirically tested or observed.
The most famous thought experiment is probably that of Schrödinger's cat, which is used to illustrate a concept known as quantum indeterminacy. In this thought experiment, one is asked to imagine a cat in a box with a vial of poison and a single radioactive atom which has a 50% chance of decaying and triggering the vial, causing the cat to die. In this thought experiment, before the box is opened, the cat is considered to be both alive and dead, because one has no way of knowing what's inside the box.
While Schrödinger's cat is kind of a gruesome example of a thought experiment, it poses an interesting conundrum. Using the current laws of physics as they are understood, something cannot be alive and dead at the same time. However, in this thought experiment, the possibility of such a state is clearly illustrated, thereby opening the door to an entirely new consideration of physics.
Thought experiments have been widely conducted since the 1800s, although researchers and philosophers in prior centuries laid the groundwork. A thought experiment can be used to challenge an accepted idea, to explore the outcome of a given hypothesis, to think about physics or other branches of the sciences in a new way, or to test the limits of a theoretical hypothesis. Many noted researchers have used thought experiments in their work, and thought experiments have led to very famous breakthroughs in the sciences, like Einstein's Theory of Relativity.
When someone performs a thought experiment, the boundaries of the mind and imagination are tested to their limits. It is often necessary to suspend disbelief, or to make intuitive leaps, two things which are normally not encouraged in the sciences. The ability to think outside the box by performing a thought experiment can be critical for people in the theoretical sciences, as it promotes unusual ways of thinking which can be used to power radical and sometimes extremely intriguing ideas.