On Tuesday, February 13, 2018 at 7:45:59 PM UTC-6, Pierz wrote:
> 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?
The Hamiltonian is the generator of time development. A quantum wave
function ψ(t) is pushed to the time t' > t by the operator exp(-iH(t' -
t)) so that ψ(t') = exp(-iH(t' - t))ψ(t).
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