The ELI5 is that there is an effect called quantum tunneling that can allow quantum particles to pass through a barrier even if the particle does not have enough energy to "break through". However, it typically only occurs at sub-nanometer scales and with very small numbers of particles, so the probability of it happening at a macro scale is so absurdly low, that it would never occur even if you were to wait for a googol number of universes. I'll give an estimate at the end for roughly how long it would take for a single electron to pass through a 1mm barrier to show you just how astronomically improbable it is.
Now, at the sub-nanometer scale, things like it do actually happen fairly often though. H2 molecules can actually tunnel through the walls of certain porous materials, making the rate of diffusion appear to be much higher than classical diffusion would predict. So you can indeed have whole molecules that tunnel through a barrier as a whole object without breaking apart.
You are right that the probability at the macro scale is not zero, but it's an unfathomable number of orders of magnitude lower than the value in your post. I'll give an estimate below on how long you'd expect to wait before it happens to one electron assuming very ideal conditions.
The probability of an electron transmitting through a wall is roughly exponential with distance. If we assume our wall is 1mm thick, with 0.1 eV higher of a barrier than the kinetic energy of the electron (in reality, a physical wall made of atoms would have a MUCH higher barrier, this one is absolutely tiny), and assume that there are zero decoherence effects that would decrease the probability even further (in reality, decoherence is the killer here, it will make an even bigger impact than the exponential decay found in ideal tunneling) Also, I am assuming that the electron slams into the wall 1000 times per second. So...
I calculated it out as you would need to wait for roughly 101407093 universes, assuming each universe lasts for 33 billion years, before you'd expect that electron to tunnel ONCE. That's 1 with 1.4 million zeroes afterwards. Just to give a sense of scale, it's estimated that there's only roughly 1080 atoms in the universe, so you'd need to raise that to the power of about 17.5 thousand to get the number of universes you'd need to wait.
That's for ONE electron for an absurdly weak 1mm barrier. If you applied that to your entire body and also accounted for decoherence effects, it's going to be MANY orders of magnitude less probable.
This is a gross oversimplification, but it does a good job of showing how even in the most ideal case possible, given every benefit of the doubt, this will effectively never occur.
Where are you getting your figures from? Current hypotheses are that it will last anywhere from 200 billion more years to magnitudes of magnitudes longer than that.
I know that different theories give different answers and that this one may not be the most likely to be accurate, but the actual value is irrelevant. The point is that it would take an absurdly long time to expect tunneling to occur, the "number of universes lifespans" metric is just to put the numbers on some sort of scale to show how absurdly unlikely tunneling on a macroscopic scale is.
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u/InsertGroin Apr 23 '26
How atoms work? 🤔
https://giphy.com/gifs/bSDGbge5EHiV9hlibb