Understanding Orbital Shapes: The Probability of Electron Location

[Dale]

Even if we don't make measurement, there will be electron in the atom, I hope this is obvious. This means, there is a probability of finding electron anywhere, at least very close to the nucleus, even if don't make measurement.

Finding electron = measurement. If you don't measure then P(measurement)=0 and therefore P(finding electron)=0. This is true even classically.

QM goes beyond that. In QM the electron does not even have a definite position until its position is measured. The only time that you can assert that a QM mechanical system has a definite property without measuring it is if the system is in an eigenstate of the corresponding operator. The ground state is not an eigenstate of position.

 

[Meson080]

Ok, let's assume that we have a girl moving randomly over a certain area, with a elastic rope tied to her hand, assume that the other end of the rope is tied to the nail. The nail is fixed at the center of the area over which she moves randomly. Compare this situation with our electron, where electron is the girl, and the flexible rope refers to the force which holds electrons in the atom.

Now, assume that we are all standing in our countries closing our eyes, trying to catch her and give her freedom, everytime waving our hands, would the girl reach us? If she reaches, will the rope gets cutted off?

For catching the electron, let's say we have the field trapper, which exerts electric field on the electron to steal it.

Sorry, if I am asking the same question again and again, I think this will allow me to understand better. What would you say, do we get her or not?

 

[Nugatory]

Compare this situation with our electron, where electron is the girl, and the flexible rope refers to the force which holds electrons in the atom.

The two situations are not comparable. The girl and the flexible rope consist of something on the order of 10²⁵ particles, all of which are constantly interacting with one another. Because they are always interacting you will never find any significant number of them, let alone all them, in an energy eigenstate where energy is certain but position is not. That's exactly opposite from how it is for a few electrons around an atomic nucleus.

You could try googling for "quantum decoherence"; this is the process by which systems composed of many particles collectively behave according to our classical intuition even though each one of the individual particles is behaving according to the Rules of Quantum Mechanics. Or, if you find the math a bit heavy going, you could try the pretty decent non-technical explanation in a book called "Where does the weirdness go?". It's available through Amazon: https://www.amazon.com/dp/0465067867/?tag=pfamazon01-20

 

[Dale]

I agree. The girl scenario is completely irrelevant to the electron scenario. Electrons don't behave like girls and the electric field doesn't behave like an elastic rope. You cannot learn anything about one by considering the behavior of the other.

 

[Meson080]

I agree. The girl scenario is completely irrelevant to the electron scenario. Electrons don't behave like girls and the electric field doesn't behave like an elastic rope. You cannot learn anything about one by considering the behavior of the other.

In layman terms, can you explain the difference between the two scenarios?

 

[Nugatory]

In layman terms, can you explain the difference between the two scenarios?

In layman's terms, the girl consists of about 10²⁵ interacting particles whereas the electron in the potential of a hydrogen nucleus is a single particle.

 

[voko]

I would put it differently. An electron is quantum mechanics, a girl is classical mechanics. It is not possible to interpret quantum mechanics via classical mechanics, that simply does not work.

 

[Meson080]

Ok, let's leave the girl . We don't want her, atleast for you all.

Consider the same situation, where we all are standing in our own countries, closing our eyes, with the "electron trappers" in our hands, to to trap the electron (assume that they use electric field to trap electron as said before). Will the electron of the atom from an alien world's alien, ever come and gets trapped into the trapper? If it reaches the trapper, does the electron losses the influence of the atom? If we don't trap it, will it return to its parent?

 

[voko]

If an electron gets trapped, it further evolution depends primarily on the "trapper". If no electron is trapped, then we have no information at all (unless our experiment is more complex and we have other detection devices).

 

[Dale]

In layman terms, can you explain the difference between the two scenarios?

I think that Nugatory's answers did that pretty well. The only other thing I would mention is that in classical mechanics the state space is not a vector space while in quantum mechanics it is. This is the root of most of the quantum weirdness.

 

[Dale]

Will the electron of the atom from an alien world's alien, ever come and gets trapped into the trapper?

Probably not in our lifetime.

If it reaches the trapper, does the electron losses the influence of the atom? If we don't trap it, will it return to its parent?

Once you have measured it to be in any position the wavefunction will collapse to the corresponding eigenstate of the position. This was mentioned by Nugatory in post 18. Such an eigenstate is no longer the ground state, so the electron is no longer bound to the nucleus, however, such a state is also not a stationary state, and the wavefunction will evolve over time. How it evolves probably depends more on the design of the box than on the parent nucleus.

 

[Meson080]

Probably not in our lifetime.

Once you have measured it to be in any position the wavefunction will collapse to the corresponding eigenstate of the position. This was mentioned by Nugatory in post 18. Such an eigenstate is no longer the ground state, so the electron is no longer bound to the nucleus, however, such a state is also not a stationary state, and the wavefunction will evolve over time. How it evolves probably depends more on the design of the box than on the parent nucleus.

See (you are also expected to be blind in this experiment ) I don't know whether the electron comes near me or not, I am closing eyes (I am blind!) , with trapper in my hand, waving it every time. Suppose it reaches and I will not catch it, assume that I will not be knowing whether it came near me or not, will it return to its parent?

I asked this question in my last post itself, I felt this question was not answered.

 

[phinds]

See (you are also expected to be blind in this experiment ) I don't know whether the electron comes near me or not, I am closing eyes (I am blind!) , with trapper in my hand, waving it every time. Suppose it reaches and I will not catch it, assume that I will not be knowing whether it came near me or not, will it return to its parent?

I asked this question in my last post itself, I felt this question was not answered.

Yes, it HAS been answered. If you don't catch it you have NO information and cannot "assume" that it was anywhere near you.

 

[Nugatory]

See (you are also expected to be blind in this experiment ) I don't know whether the electron comes near me or not, I am closing eyes (I am blind!) , with trapper in my hand, waving it every time. Suppose it reaches and I will not catch it, assume that I will not be knowing whether it came near me or not, will it return to its parent?

In quantum mechanics, as "observation" is any irreversible interaction with the environment. It is irrelevant whether the environment includes a conscious observer looking to see whether there was an interaction.

Does the electron interact with the trapper or does it not? If it does, the electron has been detected in the location defined by the trapper, whether someone looks or not. If it does not, then there is no detection and the electron still has no position.

 

[Dale]

Suppose it reaches and I will not catch it, assume that I will not be knowing whether it came near me or not, will it return to its parent?

I asked this question in my last post itself, I felt this question was not answered.

What exactly do you feel was unanswered? I specifically stated that it is not bound to the nucleus.

Whether or not you are blind or choose not to look at the answer is not relevant, as others have mentioned. What matters is whether or not the experimental apparatus interacts with the electron in such a way as to measure the position.

 

[Meson080]

Does the electron interact with the trapper or does it not? If it does, the electron has been detected in the location defined by the trapper, whether someone looks or not. If it does not, then there is no detection and the electron still has no position.

Yes, electron interacts with the trapper.

To measure the position of the electron you have to interact with it, and that interaction supplies any necessary energy. The total energy of the system (nucleus, electron, and measuring device) is conserved.

Does the trapper's interaction supplies energy for the electron to come far from the nucleus?

 

[Nugatory]

Does the trapper's interaction supplies energy for the electron to come far from the nucleus?

That was answered back in #13 of this thread - yes.

There is one quantum system consisting of an electron, the trapper device, and the nucleus. The total energy of that system is conserved as it goes from the state "electron is bound to nucleus" to "trapper has trapped electron".

 

[Meson080]

That was answered back in #13 of this thread - yes.

There is one quantum system consisting of an electron, the trapper device, and the nucleus. The total energy of that system is conserved as it goes from the state "electron is bound to nucleus" to "trapper has trapped electron".

Do you think the trapper gives the electron an energy, to run from the nucleus for a long, long distance?

 

[Dale]

Do you think the trapper gives the electron an energy, to run from the nucleus for a long, long distance?

The electron doesn't run a long long distance in this scenario. It was unlocalized prior to the measurement, and it was localized after the measurement. It didn't run a long distance because it wasn't localized before the measurement. It was localized in a surprising location, but that does not imply that it went through some definite classical path to get there.

 

[Nugatory]

Do you think the trapper gives the electron an energy, to run from the nucleus for a long, long distance?

No, because when you say "run from" the nucleus , you're implying that the electron is moving from near the nucleus to into the trapper (what else could "run from" mean?) and that only makes sense if it's moving, and it can only move if it has a position that can change, and we've already said about 83 bazillion times that it doesn't have a position. (You might want to google for "quantum tunneling" for an example of why we cannot say that the electron "moves" from near the nucleus to near the trapper).

What I can say is that the total energy of the system is the same (assuming that we didn't have to provide power to the trapping device) before and after the electron is trapped. It doesn't work to think of the "energy of the electron", the "energy of the nucleus", and "the energy of the trapper" as three separate pools that energy moves between - the total energy of the system comes from the interactions between the nucleus, the electron, and the trapper.

(BTW, the standard term for what you're calling a "trapper" is "detector")

 

[Meson080]

Ok big guns, give the conclusion for the main question, I will read QM. Thank you for all your cooperation.