I can't find some of the details you're referring to... like, the article I see doesn't mention Hilbert spaces? Is there a more complete version somewhere?
This stuff is really cool and NOT understood at all. But it's not completely new either, we were talking about it at Cherry Hill, Y2kelly's hubby and I were familiar with it and explained it to the skeptical group!
I think this research has been around, I'm gonna ball-park about 5 years.
Because they didn't mention the previous research, this must be in some way different... I'm gonna go on a hunt for some details...
Oh, I can describe, however, what quantum mechanical tunneling is, for anyone who's curious.
"Tunneling" can be explained very simply by saying that it's the ability of a particle to move THROUGH a "wall", when it shouldn't be able to. (In practical experiments, most commonly an electron is used because this explains many phenomena we see, such as radiation). The fact that tunneling is POSSIBLE is a complex question, that I'll answer after my little analogy.
It's not really a wall, in reality it's a "potential barrier" but the analogy of trying to put your physical hand through a wall is equivalent to trying to put a charged particle like an electron through a "potential barrier" that is "higher" than it is, in energy. Another good classical analogy is of a ball rolling up and down a half pipe, like that skateboarders skate on (like a 'U'-shaped road only longer). If the ball is dropped exactly at the top of the well, it will roll down it, rise up the other side, but it won't fly out because it can only go as high as it was dropped from, that's a little bit of common sense but also a consequence of conservation of energy/momentum. If the ball could tunnel like an electron can, it could jump THROUGH the barrier and come out outside of the half-pipe. That's essentially what a tunneling electron does.
Actually, this fact is part of what lead to the suspicion in the early 20th century that there was some new physics going on in the atom because Baquerel and others were observing radiation in the 1880's and 90's but when the mathematicians got their hands on the data and put it together with the Coloumb laws for electrostatics and basically said "how much radiation SHOULD we see come out of a nucleus?" they observed far MORE radiation coming out than the known laws of physics (at the time) predicted. The explanation for this was quantum mechanical tunneling, because if the particles in the nucleus (which are what become the radiation that we observe and measure the intensity of) have a certain energy and there is a certain energy level barrier keeping them in. So physicists said, "Ok with this much energy, then only ___ many particles will irradiate out of the nucleus and escape the nucleus' electrical potential well" but what they didn't know yet was that the particles inside didn't have to reach that level to be able to escape, they only had to reach "almost" that level, where they were able to possibly tunnel out. So a much higher number of particles escaped than the laws at the time would have predicted.
The question of exactly when and where a particle can do this is really an iconic symbol for the whole "probabilistic" nature of quantum mechanics that made (and still makes) so many people, philsophers AND physicists uncomfortable. It's of course almost universally accepted today (IMO the people who say QM's wrong are crackpots, because it has never failed to agree with experiment, not even on THIS crazy stuff. This crazy stuff violates Relativity, not QM.)
I can't give a complete qualitative explanation for exactly WHY this tunneling takes place. Part of it invokes the Uncertainty Principle because the value of the wave equation (the function defining the particle, which sounds weird) must be non-zero at the boundary, since the boundary is a definitive spatial location and zero is a definitive energy and momentum value. So if the wave function were zero at the boundary, the location and momentum would be simultaneously known, which violates the Uncertainty Principle, or more generally the Bell Inequalities (little discussed fact is that the Uncertainty Principle is just a specific application, a specific instance, of a more general rule, called the Bell Inequality, which holds for any two quantum variables that are not commutative - another long story). This statement "the wave function must be non-zero at the boundary" leads to the possibility that a particle can escape and "tunnel", in short.
But because when I took QM last year it was instructed to me in a mathematically rigorous presentation, the best way I can explain it most confidantly is in math terms, so if anyone wants THAT explanation, it would be this:
"Tunneling occurs because the probability distribution of the particle's wave function must be NONZERO outside of the barrier. Therefore, there exists a finite, non-zero probability that the particle's location can be outside of the barrier, and therefore tunnel. The probability distribution must be NONZERO in this region because there are requirements imposed upon the boundary conditions of any "well-posed" differential equations (such as that which governs the wave function) that are valid for the Hilbert space. These requirements are, among other things, that the wave equation's value at the barrier must equal the wave equation's value outside the barrier. This is also true of the first-order partial derivatives of the two wave functions, on each side of the barrier. The simplest function valid in the Hilbert space which fulfills this requirement is the exponential function (f=e^x), therefore the probability that the particle exists outside the barrier falls off exponentially as the particle's energy level relative to the barrier height goes down. In other words, the particle is more and more likely to tunnel through the barrier as its actual energy value approaches the height of the barrier, but less exponentially less likely as the particle's energy level relative to the barrier height gets lower.
A corollary to this which seals the deal for a non-zero probability distribution is the Uncertainty Principle, which prohibits the functions on each side of the barrier to being equal, but "equal to zero". As explained above, the UP prohibits the position and momentum of this particle from being known exactly, which fundamentally requires that its momentum at the barrier be NONZERO."As you can see, there is no overarching metaphysical truth to this concept that makes it intuitive and divine. It's just kind of arbitrarily mathematical, for how incredibly profound it is
But I must ask, does "microwave photons" weigh anything?
Wow. That's something, alright. Mind you, it's a long way from being able to jump a few particles to a whole ship, but Rome wasn't built in a day. Or a century. 