More of a philosophical question. I’ve read the broad description at the physics-for-laymen PhysLink site.

I also cannot figure out the math variables for the running start (the joules, right?), the density of the tree, its atomic makeup, and other factors whose existence I have no idea.

I still would like the calculations for my odds of the tree-me thing.
It just occurred to me that it really is a succession (static states?) of tree-me and tree-me quasi-states. But I’m just blowing smoke out of my xxx here.

But as far as the specifics of the header, I suspect that yet again it is a problem of natural language of concepts in the everyday vs. that expressed clearly only in QM.

Not unless it looks like this. Our best interpretation of quantum tunneling is that, no, you are never ‘inside’ the tree - assuming by “in the tree” you mean a forbidden state. Quantum mechanics in the first place means there is no smoothness to the state of some objects. Tunneling is the way in which an indeterminate state based on probability yields results that might be ‘across’ a barrier. Something tunnels when that slim chance puts it on the other side of the barrier, and this is something that does indeed happen at the [sub]atomic level.

I was thinking you meant the tree as an analog to understanding the ‘barrier’ in QT. But now I think you were talking about an actual tree, and whether you can be on the other side of it (like the de Broglie wavelength when you walk through a doorway … look that one up only if you want more confusion). That’s more complicated, and more than I can try and fake an estimate about.

By forbidden I’m talking about the fact that under certain conditions, there are energy states that particles cannot be in. Actually it’s not entirely relevant; I just though that’s what you meant the tree to be.

‘No smoothness’ means like what you said - you’re either in state X or state Y, but not in between. That’s what ‘quantum’ means to imply. There is no ‘halfway between X and Y’. This is whether you are tunneling or not.

It’s ultimately a philosophical question, but most physicists would say that you do not “pass through” it. You have a probability of hitting the tree and getting injured, and a really tiny probability of appearing on the other side, without ever having been “in between.” Now I can’t give you an estimate for the probability of quantum tunneling through a tree, but rest assured it is negligibly small. Much less than 0.00000…hundreds-of-zeros…1%, I mean really, ridiculously small. Don’t try it

Well, the quantum state, i.e. the wave function, certainly is smooth – in fact, its smooth continuity is part of how you derive the tunneling probability. It’s exponentially dampened, i.e. its magnitude falls off exponentially in the forbidden zone (i.e. the zone where the quantum particle does not have enough energy to classically traverse it), and the magnitude it falls off to over the range of the barrier is essentially a measure for how likely it’ll get out on the other side. See this picture: both the sides to the left and to the right of the barrier are classically allowed states, while the inside of the barrier is forbidden; a classical particle would be totally reflected, while a quantum wave function is nonzero within and beyond the barrier.

Whether or not this means that the quantum particle is ever ‘within’ the barrier, though, is indeed philosophical – typically, quantum object are considered to only have definite properties in the context of some measurement, and the attempt of assigning definite properties absent such a context leads to inconsistencies (for most kinds of such properties one can consider); so since you only ever measure whether or not the particle’s gotten through, talking about it being inside the barrier is a bit dicey, because talking about its being anywhere is a bit dicey.

I think that one of the most interesting yet seldom discussed aspects of QM is the lack of transition states that it implies.

A photon is created and then moves with the speed of light. It does not go through the intervening speeds. It is there, poof. Quantum tunneling does the same. An electron that tunnels is on the other side. Poof. I’m sure there are other examples.

The quantum world is so fundamentally different from the macro world that we don’t have language to talk about most of it, but the lack of transition is something counter to everyday experience but graspable.

This is typically discussed under the heading of ‘quantum jumps’, which was coined in referral to the discontinuous state changes of electrons between different atomic orbitals. In a broader context, the term is used to refer to instantaneous transitions between different quantum states, such as the famous ‘wave-function collapse’.

However, despite this appearance, the basic quantum mechanical evolution obeying Schrödinger’s equation is absolutely smooth and continuous; it’s only when something special happens, that doesn’t fit within the framework of Schrödinger evolution, that the apparent discontinuities arise. Typically, the ‘something special’ is a measurement of one sort or another, and according to the received view on quantum mechanics, here indeed something discontinuous happens.

More modern approaches typically seek to reconcile these two processes that govern quantum systems. One promising program is that of decoherence, in which there is only Schrödinger evolution, but interaction with some large enough system – such as an observer, or more generally the environment – quickly leads to a loss of coherence, and hence, the disappearance of typical quantum effects like interference, giving the impression of a wave function collapse. So despite appearances, it’s not really clear if there is any actual discontinuity in quantum mechanics.

Even quantum tunneling can’t break the speed of light limit, though (despite some claims to the contrary a couple of years back), so it doesn’t really happen instantaneously. And why would it be any more natural to expect a photon to be created at rest? You probably wouldn’t expect, say, an electron to have to ramp up its mass to the desired value – its mass has the right value instantaneously.

Yes and no… A virtual electron, which only lives for a short time, can be “off its mass shell”, and the shorter it lives, the further off-shell it can be, on average.

And in a tunneling situation, before the waveform is collapsed, it does have a nonzero amplitude within the barrier, which could be interpreted in some sense as being “partly within the barrier”.