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Why can’t energy be created or destroyed?

Why can’t energy be created or destroyed?
Peter Barsby from South Yorkshire (Age 15-24)

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One Response

  1. Hello Peter! This is a great question. In a nutshell, there is a deep connection between symmetries and conservation laws. In particular, if the laws of nature are the same at different times (i.e. `isotropic in time’) then there is a quantity that is conserved. We call that quantity energy.

    At a mathematical level this connection between symmetries and conserved quantities is called Noether’s Theorem. Other consequences of Noether’s Theorem in Newtonian mechanics include:

    translation symmetry –> conservation of momentum
    rotation symmetry –> conservation of angular momentum

    A slightly more heuristic way of thinking about this is to say that the conservation of energy is a measurement of the same-ness of the laws of physics as time passes. Similarly, the conservation of momentum is a measurement of the same-ness of the laws of physics as you change your location.

    From the mathematical description of this theorem, one can then go on to show that these conserved quantities “energy” and “momentum” do, indeed, correspond to our notions of energy and momentum that we learn in school. At a deeper level, these symmetries *define* what we mean by energy and momentum.

    It is worth noting that these principles carry over to quantum theory as well. In fact, much of the progress in theoretical physics in the past 50 years has been based on this connection between symmetries and conservation laws!

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