0
$\begingroup$

What's the probability that I will tunnel through a solid wall?

By "tunnel" I mean, the probability of finding me on the other side of the wall.

Assumptions

  • Wall thickness = $d$
  • Clearly state any other assumptions required for your solution: e.g. assumptions about the environment, geometry of set-up, etc.
$\endgroup$

closed as too broad by Floris, John Rennie, CuriousOne, David Z Jun 21 '15 at 8:14

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ You are already on the other side of the wall - at a distance of about 40,000 km. This question is too broad and ill-defined - and smells of a homework question. ("clearly state any other assumptions...") $\endgroup$ – Floris Jun 20 '15 at 23:22
  • 1
    $\begingroup$ @Floris The question is meant to stimulate one's imagination by galvanizing them to put-forward interesting solutions, which will depend on the assumptions made. $\endgroup$ – Mustapha Mond Jun 20 '15 at 23:36
  • 1
    $\begingroup$ I'm sorry - I don't feel galvanized. I will step aside and let others do their thing. $\endgroup$ – Floris Jun 20 '15 at 23:51
  • 1
    $\begingroup$ I could tell you if I assumed that you were a giant clump of non-interacting n=1 hydrogen atoms that numbers enough to make up the mass of a human body. If I really wanted to be fancy, instead of assuming n=1 for all atoms, I could make each one draw n from a Boltzmann distribution at room temperature. But I haven't even the faintest clue if that's anywhere near resembling a reasonable approximation for the actual joint wave function of all the particles of your body. $\endgroup$ – Bridgeburners Jun 20 '15 at 23:53
  • $\begingroup$ @Bridgeburners I think that's a good place to start $\endgroup$ – Mustapha Mond Jun 21 '15 at 3:03
2
$\begingroup$

The probability of just one of your atoms getting through the wall is very low, multiply that probability (which is way lower than 1) by the probabilty that all of your atoms go through, you get a number so small that the universe would almost certainly have ended long before you got through the wall.

A 70 Kg human body has approximately 7 X $10^{27}$ atoms, each of which has to get through the wall.

Environmental conditions would have no real effect, unless it was very hot and easier for your atoms to split up and tunnel, but you would be dead from the heat before that happened.

$\endgroup$
  • 1
    $\begingroup$ If $p$ is the probability of one atom getting through, the probability of all atoms is $\approx p^N$ where $N$ is the total number of atoms. This assumes incoherent co-tunneling. $\endgroup$ – DanielSank Jun 21 '15 at 2:01

Not the answer you're looking for? Browse other questions tagged or ask your own question.