Your teacher is right. Indeed, the spin of an electron doesn't come from a rotation of the electron around itself. But there is a law of the logic that says that one doesn't define a concept by saying what it is NOT, but by saying what YES it is.

The spin concept comes from the fact that the electron is a QUANTUM object, and has a WAVE-FUNCTION. These tiny particles are uncommon objects they have both properties of a particle (like a piece of chalk) and of a wave, as the (sound-waves).

Now, if you want to describe if your house is well arranged or is in disorder, would you care about a system of coordinates that describes the position of your house? I mean, would you care if the X axis of such a system of coordinates points to New York, or points to Cyprus?

Well, without getting into mathematical formulas, it was discovered that the wave-function of the electron DOES care about the orientation of a system of coordinates. Assume that we choose the origin of the system of coordinates there where is the electron. So, the electron has x = y = z = 0. For the beginning, let the X axis point to New York. If we rotate now the system of coordinates s.t. the axis X point to Cyprus, the coordinates x, y, z, won't change, but the wave-function describing the electron changes.

A fundamental property of the electron is that at a rotation of the system of coordinates, around whichever direction in the space, by an angle π, the wave-function CHANGES SIGN with respect to the wave-function before the rotation. Because of this property the electron is called also, FERMION.

To the contrary, for other particles e.g. the Hydrogen atom, or the alpha-particle, the wave-function doesn't change sign at a rotation by an angle π. Such a particle is called BOSON.

Good luck !

Dear Muhammad

What you’re asking is a deep question to which, as far I’m aware, there is still no simple answer.

One of the best sources I’ve found for building an intuitive undergraduate (or even beginning-graduate level) understanding of quantum mechanical spin is contained in a high-level popularisation: Bruce A. Schumm’s excellent “Deep Down Things - The Breathtaking Beauty of Particle Physics.” (ISBN 0-8018-7971-X (2004).) He’s a professor of physics, not just a populariser, so he knows very well what he writes about – on p. 177 he writes “The question of the origin of quantum-mechanical spin and the nature of spin-space is a conundrum that physicists have yet to solve."

This is a topic with which I’ve struggled for many years, and find it helpful to start from the following simple perspective and take the path outlined below, which I hope will eliminate some of the confusion that soon develops if you plough ahead too rapidly in the usual (mathematically dense) textbooks. Those more expert than me doubtless will correct/expand on this:

- Observationally, quantum-mechanical particles such as electrons, protons and even neutrons, can behave in magnetic fields as if they are spinning electrical charges – and, classically therefore, have an intrinsic magnetic moment.

- The “amount of spin” however, is fixed for each type of quantum particle, and is quantified (i.e. measured) in terms of a spin quantum number (e.g. s = ½ for an electron) which in turn relates to the number of different orientations a spinning quantum particle possessing a magnetic dipole moment (which includes the electrically neutral neutron, but differs for the photon*) can take in a magnetic field (= 2s+1 directions, so for an electron 2s+1 = 2 directions for an electron).

- This is evidenced most convincingly by the Stern-Gerlach experiment in which a beam of randomly-oriented electrons is split into just two streams by an inhomogeneous magnetic field (rather than fanning out in a continuous range of directions). For particles with different spin quantum numbers, the number of streams will also be 2s+1 where s can take any positive half-integer number (I think 5/2 or 7/2 are about the largest I’ve seen in print)

- The axis of a spinning quantum particle does not usually align precisely with the direction of the field, but rather rotates around the field direction - so we're thinking of two types of rotation:

Hopefully this at least partly answers your initial question:

- So we can say that the observed properties of spin are best accounted for by treating it as an intrinsic angular momentum (spin on its own axis, rather than orbital spin). Nevertheless, QM spin had to be accounted for artificially ("phenomenologically", by W. Pauli) until it was found from theoretical considerations.

- For a good introduction to the basic issues of QM spin you can also look it up in Wikipedia, via the link below. This may be as far as you wish to go without delving into the deeper maths.

- If you do want to go further: QM spin emerged naturally from the Dirac Equation, a one-electron equation combining quantum mechanics with special relativity that is first-order in space and time (as distinct from Schrodinger’s first relativistic equation that eventually became the Klein-Gordon equation describing spinless particles). 

- The description resulting from the Dirac equation is in terms of a 4 complex-component wave-function – a mathematical object known as a spinor (lots of literature on this, especially on the web), which itself has some very peculiar topological properties – dealt with in some detail in Bruce Schumm’s book referred to above, but in a very accessible way. At this level you need to start looking at it from the viewpoint of symmetry, using the powerful but rather abstract techniques of group theory.

Clarification in response to the following private message: "Dear Paul, I saw your answer to that question. Of course, it is a correct answer, but the fellow who asked, wanted to feel what, phenomenologically is this spin. So, to send him to mathematics is of little help. He will probably learn later about Dirac equation and so. But, he has the difficulty that we all have, when we begin learning quantum physics; we all try to translate in our minds the quantum phenomena to something classical. He asked about interpretation. Kind regards …"

Rather than try to answer the OP ‘s deep question with a short and necessarily inadequate message, my reply was intended to offer a pathway towards seeking an understanding of spin (derived, incidentally, from my own struggles with the concept). The recommended book is very approachable, being comparatively short on maths and much longer on textual and diagrammatic explanations, but without oversimplifying – precisely the type of explanation that I expect the OP needs in order to build some sort of mental representation encompassing QM spin (I think you would agree that that is what the OP seeks). We know QM spin isn’t like classical spin, yet it behaves like angular momentum. Correct me if I’m wrong, but I believe the experimental evidence of QM spin depends ultimately on the magnetic moment, and experiments such as the SG. Beyond that, any further understanding, I suggest, has to come together with the theories that enable us to account for e.g. atomic spectra, and so at some point the OP will have to start dealing with the maths if he wants to get beyond hand-waving arguments and potentially misleading analogies. If anyone else can provide a way, as you say, “to feel what, phenomenologically this spin is” then I’d be delighted to learn of it.

Hope this helps - Paul

* for e.g. uncharged photons – see 2nd link below for some discussion

PS I'm grateful for the abovementioned private message, which induced me to try to extend, and hopefully improve, the reply for the benefit of the OP

http://en.wikipedia.org/wiki/Spin_(physics)

https://www.physicsforums.com/threads/sterngerlach-experiment-with-photons.390481/

In a Stern-Gerlach experiment an electron passes through a  an non-homogeneous magnetic field. The experiment shows that the electron doesn't continue its trajectory, but is deflected either in the direction of the magnetic field, or in the opposite direction. So, the electron has a MAGNETIC DIPOLE. Though, this dipole doesn't come from the fact that inside the electron some charges orbits around some axis. Whatever axis one would take in space, the electron has a magnetic dipole along it. Experimentally, in the Stern-Gerlach experiment, in whatever direction is oriented the magnetic field, the electron is deflected either in that direction, or opposite. There is no axis in the space on which the magnetic momentum of the electron is zero.

By analogy with the classical physics where the magnetic momentum is related with a rotation movement that endows the object with an angular momentum, the electron can be attributed also an angular momentum. But trials to attribute a rotation movement, failed.

Good luck,

Sofia

A CORRECTION !!!!!

THE WAVE-FUNCTION OF THE ELECTRON CHANGES SIGN AT A ROTATION OF THE FRAMES OF COORDINATES BY 2π, NOT BY π.

For more details I recommend in the "Quantum Mechanics" of Landau and Lifschitz, the section "Spinors".

Many thanks to Paul G. Ellis for calling my attention on my error.

Many Scientists now believe that electron is a "particle" since electron is a charge particle and it accelerates so it radiates. The waves coming from electron is just because of its charge. One will suddenly think that than "why neutron radiates?" since neutrons are compose from quarks and quarks have charge. so, the net effect of that three quarks may responsible of radiations from neutron.

The above things i mentioned is for you sofia.

Paul and sofia i need more explanations. Both of your answers are helping but still there is a ambiguity. Whenever we start Q.M we always take analogies from Classical Mechanics. for example Bohr take analogy from planetary motion for the motion of hydrogen like atoms and this really explain the hydrogen like atom. but when we deeply see the motion of subatomic particles than there is no physical interpretation. That is my basic question. How can we physically interpret the motion of electron?

I need complete picture of physical interpretation of motion of electron? 

Muhammad

My best answers to your reply (including the version in your message asking for “ "True" "Physical exist" three dimensional motion of electron”) are:

1) Our description of the electron, and of the results of experiments, is encoded in mathematical expressions – classically in Maxwell’s equations, and more recently, quantum mechanically, in quantum field theory. That is all there is.

2) The interpretation of the mathematical description is only the attempt, in the network of electrical signals in our brains, to construct our own personal models (interior representations) of the physical events and of their descriptions. These internal representations are intended to be isomorphic to the physics and/or the maths, though in fact, they are only partially successful, and then mainly for classical physics. Some of these models, especially diagrammatic models, can be communicated to (and to varying degrees understood by), other people. Others of our internal representations may be less communicable.

3) The wave function of an electron extends to the boundaries of the universe, and can be represented as a complex-valued number-field in space-time. To a first approximation its motion is described by the time-dependent Schrodinger equation. A better description is given by quantum electrodynamics. This is the nearest answer I can give you to your question regarding the true, physically existing, three-dimensional motion of the electron. If you want to look a bit deeper into it, I recommend Professor Brian Cox’s recent book “The Quantum Universe: Everything that can happen does happen.” ISBN-13: 978-0241952702 (2012). It is another popularisation, using high-school-level mathematics to try to give some (communicable) mental pictures of what’s described by the maths.

4) Basically, your question is asking about “piercing the veil” over our insight into quantum effects in a way that no-one has yet managed to do to the depth that you seem to be asking. Personally, I believe that as the human race’s experience of quantum effects increases we may – over time – develop better and more useful mental representations of some aspects of the quantum level of existence. The motion of electrons is described by spinors (the complex-valued number-field mentioned above) but as one of the world’s experts on this topic, Sir Michael Atiyah, has said:

• “No-one fully understands spinors. Their algebra is formally understood but their geometrical significance is mysterious. In some sense they describe the square root of geometry and, just as understanding of the concept of "the square root of minus one" took centuries, the same might be true of spinors.”

(And so, I would add, therefore no-one fully understands the motion of the electron, as described by spinors).

5) Having myself been through a search similar to the one you're now going through (and, if I'm honest, admitting that I'm still on it too) the best advice I can offer is to keep your questions in mind while reading around the subject, including the mathematical as well as the less mathematical texts, and discussing the questions with others who are also interested, so you can refine your questions in the light of what you learn.

Hoping this helps.

Paul

As the physicists penetrated the proton and neutron, proving that there are even more elementary "bricks" from which the universe is constructed, maybe one day the electron will be penetrated too. The existence of a magnetic momentum testifies some dynamics, some motion. But which one? It was proved that a model of the electron rotating around itself isn't good.

But MAYBE if we will succeed to penetrate the electron, we will become wiser.

Well, for the moment we have to accept that the electron magnetic momentum IS and by analogy with classical physics we introduce the concept (maybe misleading) of spin.