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Transformations and Symmetry
Introduction
Rigid Transformations
Congruence
Symmetry
Symmetry Groups and Wallpapers
Symmetry in Physics
Dilations
Similarity

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Transformations and SymmetrySymmetry in Physics

Leestijd: ~10 min

So far, all the symmetries we looked at were visual in some sense: visible shapes, images or patterns. In fact, symmetry can be a much wider concept: immunity to change.

For example, if you like apple juice just as much as you like orange juice, then your preference is “symmetric” under the transformation that swaps apples and oranges.

In 1915, the German mathematician Emmy Noether observed that something similar is true for the laws of nature.

For example, our experience tells us that the laws of Physics are the same everywhere in the universe. It doesn’t matter if you conduct an experiment in London, or in New York, or on Mars – the laws of Physics should always be the same. In a way, they have .

Similarly, it shouldn’t matter if we conduct an experiment while facing North, or South, or East or West: the laws of nature have .

And finally, it shouldn’t matter if we conduct an experiment today, or tomorrow, or in a year. The laws of nature are “time-symmetric”.

F =GMmr2 F =GMmr2

These “symmetries” might initially seem quite meaningless, but they can actually tell us a lot about our universe. Emmy Noether managed to prove that every symmetry corresponds to a certain physical quantity that is conserved.

For example, time-symmetry implies that Energy must be conserved in our universe: you can convert energy from one type to another (e.g. light to electricity), but you can never create or destroy energy. The total amount of energy in the universe will always stay constant.

CERN is the world’s largest particle accelerator. Scientists smash together fundamental particles at enormous speeds, to learn more about their properties. Can you see the person at the bottom, for size comparison?

The paths taken by particle fragments after a collision

It turns out that, just by knowing about symmetry, physicists can derive most laws of nature that govern our universe – without ever having to do an experiment or observation.

Symmetry can even predict the existence of fundamental particles. One example is the famous Higgs Boson: it was predicted in the 1960s by theoretical physicists, but not observed in the real world until 2012.

Archie