What is the 'charge' and 'mass' of an electron means before measurement?

Question

What I have learnt: We can't talk about an electron's position,momentum,angular momentum,energy...anything 'before the measurement'. An electron simply doesn't have these physical parameters before measurement. The measurement/"interaction with a classical object" creates these dynamical variables. Electrons have no trajectory. We can't say it goes through one slit or another. If we demand so we will not be able to explain the collective interference pattern,in this way of thinking this phenomenon will appear to break the casuality. It is also wrong to imagine it spreads out like a classical wave and goes through both the slits, interfere with itself and somehow becomes localized when measured,this way of thinking is absurd because it can't explan the disappearence of interference pattern if an experiment is performed which is capable of determining whether one or another slit is actually taken. What we know about an electron is the wavefunction which is not a property of ensemble but associated with each and every electron. It is a complex function, a 'mathematical tool' we use to calculate the probability amplitudes of different events, using it we calculate the weightage of different possible values of a certain dynamical variable of an electron when a measurement i.e 'interaction with a classical object(a physical object which is governed, with sufficient accuracy, by classical mechanics) takes place. Wavefunction doesn't have a physical significance,it is just a'mathematical tool'(similarly path integral approach doesn't tell us electron takes all possible paths in the configuration space, it's also a mathematical tool which tells us about electron after the measurement). QM refuse to talk about an electron before the detection happens(even don't answer such questions as why it takes a particular value among so many possible values of a physical parameter when measured,QM states there is no machinary behind it), also, QM is a peculiar theory which contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation. But an electron should certainly have a measurement independent physical reality. Outside measurement We are basically representing it as an abstract mathematical object which has no physical significance but successfully predicts the possible outcomes of a measurement along with there relative weightage.But if an electron doesn't have a measurement independent physical reality then what's about its 'mass' and 'charge', are they also 'created' by the measurement?

My question is simple: What is the 'charge' of an electron (which, unlike other properties as position, momentum or energy takes only one unique value in each and every measurement possible) before the measurement? Is it also 'created' by the measurement process itself, in the same way that its momentum or position is?

N.B: I may be completely wrong, I am just a bigginer, trying to learn QM and having serious problem with it.

Answer 1

If you are having problems with quantum mechanics, you are on the right track. You are seeing that it is very different from anything classical. Some of these things would be impossible if physics was classical.

You can take the idea that an electron has no trajectory too far. In classical physics, we speak of an electron as a point particle that has a position. In principal you can measure it to as many digits as you like. This is not correct.

In quantum mechanics, the electron always has a state, a wave function, $\psi(\vec{x})$, even before you measure it. If you know the state, you can calculate everything it is possible to know about the position of the electron. Given a small volume $dv$, the probability of finding the electron there is $\psi(\vec{x})^*\psi(\vec{x})$.

So if $\psi(\vec{x})$ is concentrated in a small region and $0$ elsewhere, it is close to being point like. If $\psi(\vec{x})$ is spread out, the electron behaves differently. For example, it can go through two slits and interfere with itself.

From the Fourier Transform of $\psi(\vec{x})$ you can calculate everything you can know about the momentum of the electron. That tells you information about where the electron will be next. That is, you can calculate how the wave function evolves in time.

Like position, the momentum cannot be a definite value. But the Fourier Transform can be concentrated near a single frequency. That means the electron is close to having a definite momentum. Or it can be spread out over many frequencies, and the electron will behave differently from having a definite momentum.

The uncertainty principal comes from the Fourier Transform. A concentrated $\psi(\vec{x})$ has a Fourier Transform with many frequencies. You know a lot about where the electron is, and little about where it is going. A concentrated Fourier Transform comes from a spread out $\psi(\vec{x})$. You know a lot about which way the electron is headed, and little about where it is.

There is a middle ground where you have a fair idea of both. In this case, the electron has something like a trajectory. But you can only be so precise about it.