Symmetry as a Test of Physical Law

​In section 11-1 of the Feynman Lectures, symmetry is introduced not as a decorative or geometric idea, but as a deep principle about how physical laws behave. Feynman adopts Hermann Weyl’s operational definition: a system is symmetric if, after performing a certain operation on it, nothing observable changes. This definition is crucial because it shifts symmetry away from appearances and toward actions. What matters is not how something looks in isolation, but whether it behaves the same after a specific transformation.



The opening example of a left–right symmetrical vase is deliberately simple. Rotating the vase by 180 degrees around its vertical axis leaves it indistinguishable from its original state. The important point is not the vase itself, but the logic of the test: perform an operation, then check whether the outcome is identical. Feynman uses this everyday example to prepare the reader for a more abstract application of the same idea to physical laws, which are not objects we can see but rules governing motion and interaction.


He then extends the idea of symmetry to space by imagining a complicated machine with balls, forces, and interactions. The thought experiment asks whether the laws of physics are the same in different locations. If we build an identical machine somewhere else and start it under identical conditions, will it behave in exactly the same way? This is an example of translational symmetry: the idea that the laws of physics do not depend on where you are in space. The example is concrete because it replaces abstract language with a mechanical setup whose behavior we can easily imagine tracking step by step.


Feynman is careful to point out that this question cannot be answered naïvely. If the machine is rebuilt inside a wall, it will not behave the same way, but this does not mean the laws of physics have changed. Instead, it means that an additional influence—the wall—has been introduced. This highlights an important methodological lesson in physics: when symmetry appears to fail, the first assumption is not that the laws are wrong, but that the system has not been fully or correctly defined. The apparent violation of symmetry often reveals an overlooked force or interaction.


This leads to Feynman’s emphasis on “common sense” in applying physical ideas. Symmetry is not a purely mathematical statement divorced from reality. When physicists claim that an experiment should behave the same after being moved, they mean that everything relevant to the phenomenon must be moved as well. Gravity, electromagnetic influences, and mechanical constraints all matter. If an effect changes, physicists look for what was not carried along, rather than immediately abandoning the symmetry principle.


At the same time, Feynman explains why symmetry cannot mean moving literally everything in the universe. If we moved the planets, stars, and the entire cosmos along with the machine, the experiment would trivially be the same because nothing had meaningfully changed. The challenge, then, is to identify which influences are essential and which can be ignored. The success of physics lies in the fact that, in practice, this can usually be done: once all relevant forces are accounted for, experiments performed in different locations give the same results.


Overall, this passage uses simple physical examples to show how symmetry functions as a test of physical law. Symmetry is not assumed blindly; it is probed through careful thought experiments and experiments. When it holds, it tells us something profound about the uniformity of nature. When it appears not to hold, it pushes us to discover new forces or constraints. In this way, symmetry becomes both a guiding principle and a diagnostic tool in physics.

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