# Electron Question: Is Electron a Superposition of Sizes?

• Canute
In summary, the conversation discusses the concept of size and spatial extension in relation to electrons in quantum mechanics. It is explained that electrons do not have a specific size, but rather a probability of occupying a certain volume of space. When unobserved, an electron can be described as a probability wave extending over space, but when observed, it is a point particle at a specific location. The concept of measurement and the interpretation of quantum mechanics are also briefly touched upon.
Canute

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?

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.

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.

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.

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?

seratend said:
...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"?

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Canute said:
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.

Canute said:
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.

## 1. What is a superposition of sizes in relation to an electron?

A superposition of sizes refers to the concept that an electron does not have a specific, well-defined size like a physical object. Instead, it exists as a probability distribution, meaning that it can be described as having a range of possible sizes simultaneously.

## 2. How is the size of an electron measured if it is in a superposition?

The size of an electron cannot be measured directly, as it is not a physical object with a specific size. Instead, scientists use mathematical models and experiments to determine the probability distribution of its size. This is often done through techniques such as electron scattering or spectroscopy.

## 3. Does the superposition of sizes affect the behavior of an electron?

Yes, the superposition of sizes plays a crucial role in the behavior of an electron. In quantum mechanics, the probability distribution of an electron's size influences its position and momentum, which in turn affect its behavior and interactions with other particles.

## 4. How does the superposition of sizes relate to the uncertainty principle?

The superposition of sizes is closely related to the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle with absolute certainty. This is because the probability distribution of an electron's size is directly linked to its momentum, meaning that the more precisely we know its size, the less we know about its momentum and vice versa.

## 5. Are there any real-world applications of understanding the superposition of sizes in electrons?

Yes, understanding the superposition of sizes in electrons is crucial for many modern technologies, including transistors, lasers, and solar cells. It also plays a role in fields such as quantum computing and cryptography, where the behavior of electrons in superposition is harnessed for practical uses.

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