Beginner to QM with some questions

[JasonWuzHear]

1. Is there any reason to interpret the wave function as probabilities of specific states rather than an actual interference of those states? Or are there some types of measurements that are better thought of as probabilities? For example, thinking of the particle as a point-like object with the probability to be in a location x versus the particle 'smeared' out with the strength/weight associated at x. Is there a real difference between those two?

2. At the moment, my concept of particles now are discrete-matter-wave-interference things. I don't really understand why all particles are the same, or how it's possible for things to be discrete other than 'they just are'. Is there a good reason that explains why all electrons must have the same rest mass or charge? I know asking 'why' is pretty dangerous, but I mean it in the most lenient way.

3. In my course, there's only been a couple examples of wavefunctions, and all of them still have some probabilities at distances much larger than uncertainty of x, albeit very very small probabilities. Does this mean the particle is technically everywhere at once? If a particle's wavefunction can interfere with another particle's wavefunction, can they interfere at very large distances instantly? Is physics only kind of local?

Thanks for reading and possibly helping out. I'd ask my professor after next class, but I'm feeling impatient and can't stop thinking about this stuff.

 

[The_Duck]

1. Is there any reason to interpret the wave function as probabilities of specific states rather than an actual interference of those states? Or are there some types of measurements that are better thought of as probabilities? For example, thinking of the particle as a point-like object with the probability to be in a location x versus the particle 'smeared' out with the strength/weight associated at x. Is there a real difference between those two?

The point of a physical theory is to make predictions about the results of experiments. The predictions QM makes are of the form, "if you do this experiment, you will get result A with probability P, result B with probability Q, etc."

2. At the moment, my concept of particles now are discrete-matter-wave-interference things. I don't really understand why all particles are the same, or how it's possible for things to be discrete other than 'they just are'. Is there a good reason that explains why all electrons must have the same rest mass or charge? I know asking 'why' is pretty dangerous, but I mean it in the most lenient way.

Quantum field theory, a more advanced topic, gives an explanation for why all electrons have the same properties: it turns out that they are all "excitations" of the same underlying "electron field."

3. In my course, there's only been a couple examples of wavefunctions, and all of them still have some probabilities at distances much larger than uncertainty of x, albeit very very small probabilities. Does this mean the particle is technically everywhere at once?

At any rate, it means that there is a small but nonzero probability to find the particle at very large distances if you look for it.

Notice I'm not saying anything about what "is," only about what will happen when you do an experiment to locate the electron. QM can only tell you about the results of experiments.

If a particle's wavefunction can interfere with another particle's wavefunction, can they interfere at very large distances instantly? Is physics only kind of local?

Think about two very long ocean waves interfering with each other. This does not violate locality. Neither does a similar situation in QM.

 

[bhobba]

1. Is there any reason to interpret the wave function as probabilities of specific states rather than an actual interference of those states?

No reason. We have interpretations that make assumptions like that eg Bohmian Mechanics. The issue is deciding between them experimentally.

Or are there some types of measurements that are better thought of as probabilities? For example, thinking of the particle as a point-like object with the probability to be in a location x versus the particle 'smeared' out with the strength/weight associated at x. Is there a real difference between those two?

QM is a theory about observations that appear here in an assumed classical world. According to the theory all you can predict are probabilities. But interpretations exist that have varying degrees of ordinary reality associated with the theory eg Nelsons Stochastics:
http://philsci-archive.pitt.edu/8853/1/Nelson-revised.pdf

At the moment, my concept of particles now are discrete-matter-wave-interference things. I don't really understand why all particles are the same, or how it's possible for things to be discrete other than 'they just are'. Is there a good reason that explains why all electrons must have the same rest mass or charge? I know asking 'why' is pretty dangerous, but I mean it in the most lenient way.

Well actually we know that one - its because particles are excitations in the underlying quantum field for that particle ie for electrons we have an electron field, photons the quantised EM field etc.

In my course, there's only been a couple examples of wavefunctions, and all of them still have some probabilities at distances much larger than uncertainty of x, albeit very very small probabilities. Does this mean the particle is technically everywhere at once? If a particle's wavefunction can interfere with another particle's wavefunction, can they interfere at very large distances instantly? Is physics only kind of local?

This can be a bit confusing to start with because textbooks, especially beginner ones, don't state what's going on outright. They usually follow a semi historical approach but once they reach the point where we have the full quantum theory don't then say, clearly, what that theory says. I will correct that now to avoid confusion and misconceptions. As said above QM is a theory about observations - when not observed the theory is silent. That's all there is to it. Particles are not smeared out when not observed or any picture you can think of - the theory simply doesn't concern itself about such issues so forget about it - its not part of the theory. Interpretations speculate on it - but the theory says nothing.

To break this down check out the following:
http://www.scottaaronson.com/democritus/lec9.html

Locality in QM is a difficult thing - check out Bells theorem:
http://www.drchinese.com/Bells_Theorem.htm

Many of the questions you are asking require Quantum Field Theory to answer. Its normally an advanced subject but recently books have started to appear understandable with a first course in QM like you are doing:
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

Basically you need to have quantised the Harmonic oscillator and know a bit of relativity.

Thanks
Bill