Probability and quantum possibilities

[NanaToru]

So this might be a too simplistic question on many accounts.

My pchem professor said to us that in QM, anything that can happen will. And it's a matter of probability, right?

I guess I'm just curious what the scales are for something like, say, walking through a wall (the go-to example for a lot of popular science books on QM)? Like, 1 in a billion or what?

 

[Drakkith]

My pchem professor said to us that in QM, anything that can happen will. And it's a matter of probability, right?

Not quite. It says that anything that can happen, well, can happen. (It is not guaranteed to happen) Yes it is a matter of probability. But don't take this to mean that all of reality and life is probability. Even if it is you don't live your life in fear that every particle in your body is going to quantum tunnel in random directions at the same time.

I guess I'm just curious what the scales are for something like, say, walking through a wall (the go-to example for a lot of popular science books on QM)? Like, 1 in a billion or what?

1 in a billion ^10²³. Actually I don't know the right number, and I doubt anyone actually does, but I guarantee it to be so large it is effectively incomprehensible.

 

[DrChinese]

The likelihood of that happening is so low that the universe is far too young for that to be an outcome.

At least, most likely. You never know, maybe something like that has happened.

 

[soothsayer]

1 in a billion ^10²³. Actually I don't know the right number, and I doubt anyone actually does, but I guarantee it to be so large it is effectively incomprehensible.

That number probably does the odds some justice. I remember calculating the probability of jumping and tunneling all the way to Jupiter, and it was like $e^{10^{10^6}}$ or something. I don't even remember now.

It should be noted that anything that can happen will happen with enough time. Even the probability above says that if the universe lasts long enough, a tunneling event of that magnitude should likely happen.

 

[Drakkith]

That number probably does the odds some justice. I remember calculating the probability of jumping and tunneling all the way to Jupiter, and it was like $e^{10^{10^6}}$ or something. I don't even remember now.

It should be noted that anything that can happen will happen with enough time. Even the probability above says that if the universe lasts long enough, a tunneling event of that magnitude should likely happen.

My god that's an enormous number.

 

[soothsayer]

It may have been smaller, I can't remember now XD It was definitely e^10 to a really big power, but it may have been closer to 100 than one million. At that point though, what's the difference, really? It's not going to happen, lol.