Something that has always confused me

[gravenewworld]

As we know electron and light have dual natures, they can be thought of as waves and as particles. The thing I never understood is why can you talk about say something like the angular momentum of an electron. In order for an electron to have momentum it needs to have mass. Yes, I know that the mass of an electron is found to be roughly 9.1x10^-31 kg, but when the electron appears as a wave what happens to its mass? Waves don't have mass, so what happens to its angular momentum? Is this why angular momentum comes in only discrete certain values? I want to know why you can describe certain things about electrons and light that depend on mass when electrons and light are not always particles.

 

[ZapperZ]

As we know electron and light have dual natures, they can be thought of as waves and as particles. The thing I never understood is why can you talk about say something like the angular momentum of an electron. In order for an electron to have momentum it needs to have mass. Yes, I know that the mass of an electron is found to be roughly 9.1x10^-31 kg, but when the electron appears as a wave what happens to its mass? Waves don't have mass, so what happens to its angular momentum? Is this why angular momentum comes in only discrete certain values? I want to know why you can describe certain things about electrons and light that depend on mass when electrons and light are not always particles.

There are MANY things in QM in which the "names" or labels attached to certain things have different meaning than what you are familiar with. "Spin" is one clear example. The "angular momentum" that you are referring to is the angular momentum you obtain when you solve for the atomic orbitals in an atom. However, for anyone who has ever done that, one would see that this is not your standard classical "angular momentum". What it is is the solution to the angular part of the wavefunction - meaning in spherical coordinates, it contains the polar and azimuthal angle components, not the radial. Because of this, the "eigenvalue" that one obtains in the solution is called the "angular momentum" quantum number. So the name is assigned due to historical and "familiarity" reasons.

You also need to be aware that the "wave" in QM is a "probability wave" (if we follow standard textbook QM). It is not a real wave in real space. It is a wave in "configuration" space. It describe various systems with all the possible outcomes as it evolves through space and time. When you make a measurement on an electron, for example, you do NOT end up measuring the mass of a "wave".

The moral of the story is that you need to figure out what exactly is the meaning of certain words and properties as they are used in QM, and not to take the classical or literal meaning of these words. Unfortunately, to be able to understand the QM definitions, one needs to study it carefully and understands the mathematics. It is my opinion that only the mathematical forms would give the most unambiguous definition of any physical property or description.

Zz.

 

[Nenad]

there is a lot of confusion around this subject. I read that the spin number can be interpreted as a way of observing the particle. A particle with a spin of 1/2, will have two symmetircal sides, so when you revolve it 180 degrees, you will be back at the beginning and see the same this over again that you saw for the firs 1/2 of the revolution. A particle with spin 1 will be like looking at a beachball, you revolve it 360 degrees and you are back at the beginning. Here is were the tricky part comes in, a particle with spin number 2 would be like revolving a beachball twice, 720 degrees, and seing different features the whole time. Its like having a ball and rotating it twice to get back to the begginig of rotation. It sounds confusing but that is qm.

 

[ZapperZ]

there is a lot of confusion around this subject. I read that the spin number can be interpreted as a way of observing the particle. A particle with a spin of 1/2, will have two symmetircal sides, so when you revolve it 180 degrees, you will be back at the beginning and see the same this over again that you saw for the firs 1/2 of the revolution. A particle with spin 1 will be like looking at a beachball, you revolve it 360 degrees and you are back at the beginning. Here is were the tricky part comes in, a particle with spin number 2 would be like revolving a beachball twice, 720 degrees, and seing different features the whole time. Its like having a ball and rotating it twice to get back to the begginig of rotation. It sounds confusing but that is qm.

Actually, you have it slightly wrong. With a 1/2 spin, a rotation over 4pi (2 complete rotations) will get you the same symmetry as before. So single-valuedness is not preserved in such cases (at least over 1 complete rotation).

Zz.

 

[Nenad]

ya, thanx, I am not good with the numbers. My mistake.

 

[gravenewworld]

You also need to be aware that the "wave" in QM is a "probability wave" (if we follow standard textbook QM). It is not a real wave in real space. It is a wave in "configuration" space. It describe various systems with all the possible outcomes as it evolves through space and time. When you make a measurement on an electron, for example, you do NOT end up measuring the mass of a "wave".

I still do not understand. Why can't electrons or photons be waves in real space? Didn't de Broglie show that electrons and photons are waves or have wave like properties even though they have mass? I stilll don't understand how particles like photons and electrons can have mass and be waves at the same time.

 

[selfAdjoint]

Particles do have wave nature, but that wave nature (see Compton Wave length )is different from the "wave function" (or amplitude function or quantum state) which describes them and which is a solution of e.g. the Schroedinger equation.

 

[alpha_wolf]

I stilll don't understand how particles like photons and electrons can have mass and be waves at the same time.

What you have to understand, is that the wave description, and the particle decription, are just models. The actual entity is neither that OR the other - it is something entirely different, something we cannot truly visualize, but it can be described as a wave, or a particle, to explain the experimental results and perform calculations. It can also be described as a wave function, as a string, or loop, or even brane, and probably as a bunch of other stuff we haven't thought of yet. These are all just models. They don't tell us what the entity is, only what it behaves like.

 

[gravenewworld]

wait i think it just hit me over the head. Waves carry or are energy right? E=hnu. Then according to einstein e=mc^2 so waves and mass have to be related right?

 

[whydoyouwanttoknow]

Aren't the waves just the probability of the particle being found in that space because you can't know a particles location and energy at the same time?