Probablity of Walking through a Wall

[Paul is Cool]

Apparently, if all your particles are primed for tunnelling through a wall then you can walk through it, but the probability of all your particles tunnelling simultaneously is so low that you would have to attempt it more times than the age of the universe in years. Could someone please explain this to me. Thank-you very much.

 

[Fredrik]

It's hard to answer when we don't know if you know anything about quantum physics already. For example, do you know what a wavefunction is? Would calculations make any sense to you?

For now, let me just assure you that although the probability is non-zero, it is much, much, much less than you (or I) can even imagine. The probabilities we're talking about are typically less than 1/10^(10^30).

As a comparison, the age of the universe, in seconds, is less than 10^19 seconds.

 

[humanino]

Welcome Paul_is_Cool

if you wait long enough, diamonds will appear in your pocket. Maybe you should find an occupation for the meantime

Maybe you know that QM is only about probability. Physicists gave up predicting A or B, they can just predict prob(A) or prob(B). Of course, this does not change the old classical physics, where prob(classical event) = 0.9999999999999... and this = 1 for all purpose.

 

[DaveC426913]

"...if all your particles are primed for tunnelling through a wall then you can walk through it..."

This description is a bit romantic. It's more like "there is a chance (not in your control) that at any given moment, you would suddenly find yourself on the other side of a wall."



It's not really a meaningful thought experiment, it's "reducto ad absurdum". If you even crack the door on the possibilities of quantum mechanics, it is knocked out of your hands and flung wide.

But really, it's more of an obsolete concept. Your level of sophistication is already beyond this. This thought experiment is a way that people of the early 20th century, steeped in classical physics, grappled the non-sensical nature of the new quantum universe. In classical physics particles were particles. They moved classically from here to there. They had a size, a mass and a speed. And that was that.

Quantum mechanics came along and waggled its hand and said - "Weellllllll, no. Particles are not particles. Their size, mass speed and even their location is - well... open to debate."

Classical physics said "But if what you say is true, then all bets are off. We can't count on setting a particle down, walking away, and coming back to find it there. You're saying we might find it, say, inside this closed glass beaker. You're saying nothing in our universe can be trusted! You demand that we start rebuilding it from scratch - and that even at our most careful, we can never truly "know" anything."

And Quantum mechanics said: "Yeah, that's pretty much what I'm sayin'..."





Tunnelling - a layperson's explanation - disclaimer on accuracy:

Electrons do not "orbit" the nucleus of an atom. They appear in a cloud of probability. At any given moment, if you measure it, the electron will be in some location, and the cloud defines the likelihood of where. There is an rapidly diminishing chance that the electron will suddenly appear a few or many atomic diameters off to the left. In this sense, it is possible for an electron to "tunnel" beyond its usual orbital, and find itself outside the atom altogether (could use some technical tweaking here, my description is inadequate).

Because one particle can do it, they *could* all do it (and larger particles, such as atoms can do it too).

In terms of odds though, to say they're stacked against you is an understatement. The phenomenon scales up extremely poorly.

1] The distances involved are on the order of atomic distances. Electrons just *don't* jump one micrometer, let alone one metre. Imagine rolling a dice that has millions of sides. You roll a 1, you get a large leap on the order of nanometres. Imagine a die that has bajillions of sides. You roll a 1, you get a leap of millimetres.
2] Now, count the number of atoms in your body. Roll that many dice. Keep rolling until you get a "yahtzee" - a one on *all* of them. All your atoms jumped at the same time.
3] Of course, there's no reason for them to jump in the same direction, so you may have to roll all those 1's on all those dice bajillions of times before they all happen to jump in the right direction.
Take all those one-in-a- bajillions - there's about four of them. Multiply them together.


Now ask yourself - in your lifetime, has even the tiniest fraction of a part of any person on Earth leapt more than an inch from its current location? Because all that would have to happen countless times before a larger coincidence happened.

Dave

 

[Paul is Cool]

Thank you so much for that explanation; it was very enlightening. The truth is I'm actually doing this as part of a maths poster in order to show probability in an interesting way (a poster that says ' what's the chances of me appearing on the other side of a wall?' in bold lettering attracts people to read it).

 

[vanesch]

Apparently, if all your particles are primed for tunnelling through a wall then you can walk through it, but the probability of all your particles tunnelling simultaneously is so low that you would have to attempt it more times than the age of the universe in years. Could someone please explain this to me. Thank-you very much.

You know what really hurts ? When HALF of your particles tunnel through the wall. That probability is billions and billions of times higher than that ALL of them tunnel through...

cheers,
Patrick.

 

[danitaber]

The truth is I'm actually doing this as part of a maths poster in order to show probability in an interesting way (a poster that says ' what's the chances of me appearing on the other side of a wall?' in bold lettering attracts people to read it).

Paul, just make sure you say "what *are* the chances", and not "what is the chances", or "What is the chance?" singular. That whole subject-verb agreement thing can put a big dent in the impact of said poster.
At college, we had a pi-day. I was going to set up e-day the next year, (Feb 17), starting at 2:22 am (that's 1:82 base 60), but, well, I got sidetracked.

You may even want to put Vanesch's blurb about half of the atoms tunnelling, great visual.