On Thursday, February 15, 2018 at 2:46:34 AM UTC+11, Lawrence Crowell wrote:
> 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).
Yes the good ole Schrödinger equation. The fact that the Hamiltonian is the
generator of time development *and* the operator for energy helped me to
understand that energy is change. But I'm trying to understand something
about the nature of the energy held in chemical bonds. A high energy
chemical bond must have a corresponding Hamiltonian that shows some kind of
evolution in the state of the electrons involved in the bond. The so-called
potential energy must be represented as some kind of state evolution of the
electrons - right?
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