Quantum physics tells us that anything that commutes with the hamiltonian
is preserved (doesn't change), the hamiltonian being the measure of energy
in a system. This has led me to understand energy as a measure of change
over time in a physical system. That might be obvious, except I've never
heard anybody say it quite like that - with the result that many people
tend to reify energy as some kind of physical "thing". The fact that energy
and matter are interconvertible has led me to the summary that change
across space is matter, change across time is energy. The only problem in
this picture is potential energy, which you could simply call "deferred
change", but that does beg the question as to how it is deferred. I'm
trying to think about this in relation to chemical energy - the potential
energy held in chemical bonds. When I studied chemistry I was simply told
that certain bonds are more stable and have lower energy than other bonds
which are less stable and have higher energy. So energy is released when a
molecule reacts with another to form a more stable compound. The reason for
and nature of the stability wasn't explained. So I'm wondering, is the
"potential energy" in the chemical bond actually a kind of very localised
motion, with more motion occurring in high energy bonds than in lower
energy ones? In other words, the energy (motion/change) is temporarily
contained in the small area of the bond, thus hiding the energy it as it
were from the environment? If so, then this form of potential energy is not
really different in kind from other types of energy, it's just relatively
isolated. If this is valid, perhaps a similar analysis of other forms of
potential energy such as gravitational potential might be possible too? Can
a physicist/physical chemist perhaps shed light on whether my speculation
here regarding chemical energy is valid?
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