7. Symmetry and Conservation Laws
In the end you can summarize symmetry in Physics with a list of symmetries
and the corresponding conserved quantities. But what does this list mean
? For a mathematician it is straightforward:each physical phenomenon is
described by a mathematical equation;you apply to this equation a transformation
and you see that the equation remains the same. Just a piece of machinery.
In fact you can try to find new transformations that leave the equations unchanged:this was what did Lorentz discovering its transformation for the Maxwell equations
which describe electromagnetic phenomena. But it was necessary the genius of Einstein to understand what was behind this mathematical machinery:
so the relativity theory was born.
Nevertheless there are some conservation laws which are easy to understand applying some common sense reasoning.
It goes like this: when we have a phenomenon, to measure it, we need an observer. Now if I move,for example, in space my apparatus it is possible that this will change the result of my experiment.But,wait a moment, a move of the apparatus
is the same than a move of the observer and you don't expect the result to
depend on the fact that the observer is here or there. So,we can say, that (most) experiments are independent from the place where they occur:the conservation of momentum. Similar argument can be applied to time:you don't really think that it matters if I do my experiment Monday o Friday? So indipendence from time implies
conservation of energy. The same for the orientation in space and conservation
of angular momentum.
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