rede96 said:
Doesn’t that just mean the energy of that system doesn’t change?
Yes.
rede96 said:
I thought all systems must have zero point energy as if the didn’t it would violate the uncertainty principle?
Sort of. The idea of "zero point energy" originally came from the fact that, if you solve the most basic QM harmonic oscillator, there is a term in the Hamiltonian that is present even when the oscillator is not oscillating at all (i.e., where classically we would say that it had exactly zero energy). But that term in the oscillator Hamiltonian does not "vary"; it isn't uncertain at all. It's a definite value. So all it really means is that the vacuum--the state with zero oscillations--is also an eigenstate of the Hamiltonian. It doesn't mean there is any "uncertainty" that drives the vacuum to have "zero point energy". (This also means that the common idea of "vacuum fluctuations" is, at best, somewhat misleading. I believe there is a series of PF Insights articles on this.)
More generally, any physically reasonable Hamiltonian must have a ground state, i.e., an eigenstate of lowest energy. Often, if you just solve the equations and don't make any adjustments, the energy of this eigenstate won't be zero, just as for the harmonic oscillator. But, as I said before, absolute values of energy in QM have no physical meaning; only energy differences do. So you can always just subtract the ground state energy from the Hamiltonian to get a Hamiltonian whose lowest energy state has exactly zero energy. That's what is normally done.
A better reason for thinking of real systems as having "zero point energy" is that, for any real system, it's impossible to get it exactly into the vacuum state--because that state would be a state with nothing at all present, and if nothing at all is present, how can you have any equipment that prepares anything in any particular state? So what actually happens when you try to get some particular system into its vacuum state is that it is in a state which is "close" to the vacuum, but also has nonzero amplitude to be in some non-vacuum state--i.e., its state is not an exact eigenstate of the Hamiltonian. That means that, when you measure the system's energy, it will not always be the same, and some people interpret this in terms like "vacuum fluctuations". (IIRC, the Insights series I referred to above talks about this.)
rede96 said:
Just to be clear ‘no change’ to me means no change in anything. Momentum, position, energy etc.
That's not possible, because, for example, momentum and position can't both have definite values in any state. An energy eigenstate will generally be a momentum eigenstate, but certainly not a position eigenstate. So it is impossible to have any quantum state that does not "change" by your definition. Which means your definition is unhelpful, since it doesn't pick out any particular states at all.
rede96 said:
going up or down is change
Change in two different directions (up vs. down), yes. Not "just one direction of change", which is what you were claiming.