Electron Question: Is Electron a Superposition of Sizes?

[Canute]

A basic question about electrons.

As I understand it electrons do not have a size as such, but rather have a certain finite probability of occupying a particular volume of space. Does this entail that an electron has a finite probability of being a point particle and also a finite possibility of being infinitely extended (or non-local)? If so, is it correct to say that an unobserved electron is a superposition of all its possible size-states, up to and including these two extreme states?

 

[inha]

What exactly is a size-state? There is no concept of size defined in QM as far as I know. And I don't get why there would be a connection between a particle's size and the volume of space it is in at some probability.

 

[Canute]

It was said in another thread that an electron does not have a particular size but rather has a finite probability of occupying a certain volume of space. Is this not correct? The poster seemed to know what he or she was talking about. Presumably an electron is spatially extended so must have a size in some sense or other.

 

[seratend]

In classical QM, electron is "a point". The meaning of "a point" in this sentence means that the probability to get (measurement) an electron at 2 separate spatial locations is null.

Now depending on the state of the electron, you have a certain probability to detect it at several positions in space (spatial extension of the wave function). However you cannot detect it "at the same time" at 2 different places ("point particle").

Do not confuse the spatial extension of the electron wave function with the detection of the electron at a given spatial position.

Seratend.

 

[Canute]

Thanks. That makes sense. Would it be correct to say that once observed an electron is a point particle and that when unobserved its wave function gives it some probability of being observed anywhere (everywhere) with some finite probability? In other words, is an electron non-local until observed?

 

[lightarrow]

...Now depending on the state of the electron, you have a certain probability to detect it at several positions in space (spatial extension of the wave function). However you cannot detect it "at the same time" at 2 different places ("point particle").

But this is not because, in that case, two detections in different places at the same time would be interpreted as "two electrons arrived"?

 

[nrqed]

Thanks. That makes sense. Would it be correct to say that once observed an electron is a point particle and that when unobserved its wave function gives it some probability of being observed anywhere (everywhere) with some finite probability? In other words, is an electron non-local until observed?

Yes, this is the way most physicists think. Once it is observed, it is a point particle at a definite location. When it is not observed, it is "described" by a probability wave extending over space.

Of course, if you think about it for a second this is highly unsatisfactory. What defines a "measurement", exactly? If a measurement is made over here, how does the rest of the wavefunction "knows" that it must vanish except at the point where the particle was detected? And on and on. At this point, one is getting into "ontological" issues (what does all this really *mean*?). But, at a first pass through QM, it is better to view things the way you described it and to get familiar with the equations and the formalism and with the calculations. On se second pass, one may start to think about deeper issues about the interpretation of it all.

 

[jtbell]

Would it be correct to say that once observed an electron is a point particle and that when unobserved its wave function gives it some probability of being observed anywhere (everywhere) with some finite probability?

Yes to both of the above statements.

In other words, is an electron non-local until observed?

This gets into the realm of interpretations of quantum mechanics, and some people argue vigorously about this point. Strictly speaking, we don't know what an electron is "really like" between observations, and we don't know any way to find out by experiment.