Any quantum physicists in here? Little help, por favor.

[MrCoffee]

So I'm reading a book about quantum physics, and the author says "The 'probability' of quantum mechanics is the probability of observing an observed system in a given state at a given time if it was prepared in a given initial state."

With those conditions, why isn't the probability always 1? I'm having a hard time figuring out the variable here.

[billyskank]

1. Because the "given state" is not the only possible state that may be observed.

From the given initial state, you might find the system later in one of any number of possible alternative states, and the book is referring to the likelihood of it being any one of those possibilities.

[billyskank]

7. Imagine a single electron orbiting a hydrogen nucleus.

Say in the initial state, you knew the electron's exact position. This would mean that (because of the uncertainty principle) you do not know its momentum. This means that you cannot say where it will be later.

So you have its wave function, which expresses mathematically the probability of the electron being in any state at a later time. 'State' in this case refers to position, so the variables of the wave function are spatial and temporal coordinates. If you have no idea at all about the electron's momentum, then the wave function will describe a sphere: meaning that at an arbitrary time after the initial measurement, you would expect the electron to be somewhere in that spherical shell, although all positions within it are equally likely.

This is my slightly-better-than-lay-person's view, which is probably very simplistic (and maybe even flat out wrong). Full disclosure: I have a batchelor's degree in physics: you take a risk in accepting anything I say. My knowledge is very general and quite shallow.

[SOteric]

11. Whoa.

Way to go, billy. Physics are hot.

[billyskank]

18. ...

:blush:

;)

[MrCoffee]

12. Yeah, but the electron is still somewhere in the shell, right?

I'm not so concerned with the result of the measurement, just the idea that the probability is something less than 1 even though we have a given initial state and a given time lapse...I'm still fuzzy on how we...oh....wait a second...


Heisenberg is why we have probabilities? Because we are limited in what we can know in the initial state?

[HiFructosePronSyrup]

15. "Heisenberg is why we have probabilities?"

Well, he is the guy who developed the uncertainty principle.

"Because we are limited in what we can know in the initial state?"

It's more fundamental than that, if we had a superpower microscope (think Maxwell's demon) that could see an electron's position, it's momentum would be intrinsically undefined. Think of it like dividing by zero.

[billyskank]

16. Exactly so.

The electron is not totally free - that's the importance of the wavefunction. The wavefunction tells you, the electron must be somewhere within this shell. Moreover, the wavefunction also tells you the likelihood of it being at any particular point in that shell.

That's why physicists stopped thinking long ago about electrons orbiting nuclei like planets - now they think of electrons as more like clouds. The wavefunction tells you the shape of the cloud.

[MrCoffee]

8. Ok...and there are only a finite number of possible alternative states, right?

[billyskank]

9. There may or may not be.

Depends on what 'state' actually refers to. It is a general term to mean whatever it is you are measuring.

[HiFructosePronSyrup]

14. No.

Technically there are an infinite number of states.

Although many are so improbably you can simplify a problem by assuming only a few states.

Somebody upthread asked "so the electron stays in its shell?"

No. An electron is usually in its shell. But there's a small probability it's in the shell of the next door atom, or in Disneyland, or on Uranus. This is how we end up with quantum tunnelling.

[billyskank]

17. Don't complicate things

;)

[Connonym]

2. I'm not a quantum physicist but I did watch the movie "What the Bleep do We Know"

http://www.imdb.com/title/tt0399877/ and I didn't understand jack shit

[Dogtown]

3. You need to ask

Shrodinger's cat...

[WannaJumpMyScooter]

4. what billyskank said, and

the act of observing MAY change the given state... obfuscation courtesy of Heisenberg

[Dr. Strange]

5. Locking.

This thread is now locked with a probability of 43%. However, 57% of responses will still get through. EarlG will deal with them as necessary.

[WannaJumpMyScooter]

6. or not

[Tuesday Afternoon]

10. 42

and thanks for all the fish.

[pokerfan]

13. Look no further than radioactive decay

A Carbon-14 atom. At some point it will transform into a Nitrogen -14 atom and emit some radiation.

It is impossible to predict when a given atom will decay but given a large number of atoms we know that half of them will transform in 5730 years.

Have you gotten to quantum entanglement yet? That will really blow your mind.