Box is still, not in free fall; and let's say that tunneling happens in an infinitesimal time. Only the object is affected by the force. I just took gravity as an example, any force is good to create a potential well.

So wouldn't object always tunnel to lower energy state?

Is that right or wrong? If it's right, how doesn't it directly violate conservation of momentum?
As far as I know, it applies universally and at quantum scales too.

5. If one particle tunnels 1 nm against gravity from time to time or if 100 atoms tunnel 10 cm agaisnt gravity once every 10^100 years it has no observable effect on the conservation of energy as a whole and would be balanced out by the opposite happening just as often. It would be just as bad to tunnel in the direction of gravity because then energy is lost. It is unknown how particles interact via gravitation so I doubt if anyone knows for sure how gravity affects the statistical properties.

In quantum mechanics, energy is defined as proportional to the time derivative of the wave function. Lack of commutation of the time derivative operator with the time operator itself mathematically results in an uncertainty principle for time and energy: the longer the period of time, the more precisely energy can be defined (energy and time become a conjugate Fourier pair). However, quantum theory in general, and the uncertainty principle specifically, do not violate energy conservation.

I just hope I haven't confused everyone to death with this, or you just find this so archetypally boring that you avoid it? I mean everyone else, bjorn probably had enough.

In a really strong field it would then be extremely distorted and all sorts of observable effects would appear that no one have observed. Also as you probably suspected, devices that used tunneling does not appear to be greatly affected by how they are pointed relative to ground.

So it seems quite clear that a weak gravity field does not affect the tunelling significantly so we must ask ourselves at what level is energy conserved.

You would always spend billions of times more energy than it is possible to exctract. Only in a special case can you extract energy but it happens so rarely that it compares well to a compressed air drill running on air molecules that by random chance move in the same direction through it.

If it is possible to "borrow" energy from the vacuum energy it might completely break "our" conservation of energy and yet still conserve it as a whole. Since the mechanisms and topology of the universe is unknown in the details it is all just speculation.

thought, sum of all interactions particle can interact by must create favorable energy state for it to tunell.

Not the first time I hear phrase 'vacuum energy' - and yet I know nothing about it except that it's poorly described and that it makes excellent buzz word for overunityers and conspiracy theorists.

The problem is that the interaction of gravity is not known in detail so it is very difficult to reason how it behaves in a gravity gradient. Since there are gradients in all directions everywhere in the universe it can't tunnel in any direction without changing it's potentional energy relative to some galaxy at the other end of the universe.

My claim is that even if we can't deduce a way to account for the change in energy it will not break any laws since the laws are statistical in nature and does not apply for single random events.

No one knows the nature of it. It arises from the fact that vacuum is far from empty and that theoretical work and measurements indicated that it contains energy.

The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alter the vacuum expectation value of the energy of the second quantized electromagnetic field. Since the value of this energy depends on the shapes and positions of the conductors and dielectrics, the Casimir effect manifests itself as a force between such objects.