First, a brand new movie, Decay (2012), was released by the LHC students 12 seconds ago. If you have 75 minutes for a truly independent (I warned you!) underground bound state of comedy, unexplained quenches, VW New Beetles, unfaithful girlfriends, extra shifts ordered by CERN's Russian Director General (who may be less innocent than you think), LHC waking up spontaneously, radiation alerts, zombies running through the LHC tunnels (horror starts at 24:50 or so and then 26:50) and outside (1:02:00, 1:09:00), and Higgs bosons and Higgs bioentanglement, watch the video above. See also their website, Wikipedia, their Twitter, and HD downloads. To say the least, it's a great opportunity to look into the interiors of the LHC and how the "real people" use it. And let me admit, I was totally terrified when I was watching the film: you don't want to be an experimenter! ;-)
Now, to mention one of them in a less terrifying context, Aidan Randle-Conde of the U.S. LHC blogs is recording some kind of a particle physics advent calendar. For the December 5th, he talks about pentaquarks, and so on. December 7th was all about the spin:
Advent Calendar 2012 December 7thHe thinks the electron is not spinning in any way. Moreover, he thinks that the very term "spin" is just some blunder caused by historical misunderstandings and it perhaps depends on the outdated old Bohr model of the atom.
I disagree with these (widespread) musings and I view them as contributors to the general misunderstanding of quantum mechanics.
This is the comment I originally wrote over there:
It’s an interesting monologue but sorry, Aidan, I completely disagree with your statements that nothing is spinning and/or the word “spin” is caused by some historical inaccuracies or accident.His reply suggests he didn't try to think about my points too much:
Spin is a perfectly valid description of the physical concept that doesn’t depend on the old Bohr atom in any way – although people started to observe things related to the spin before the modern quantum mechanics was really established in its current form.
But the electron *is* spinning. It’s rotating. The previous two sentences are mathematically equivalent to the fact that the angular momentum connected with the spin is nonzero. The angular momentum is what measures whether something is spinning. If it’s nonzero, it’s spinning.
A valid comment would be that the spin can’t be described or visualized by classical physics. But no other observable at the microscopic scale – and therefore controlled by quantum mechanics – can be properly described by classical physics, either. It doesn’t prevent us from using observables that become the usual classical observables in the classical limit. The angular momentum is one of them and despite the fact that the spin is tiny and quantized, it is a term in the angular momentum.
The quantization applies not only to the spin but to any other form of the angular momentum, too. It’s a true fact about Nature. For large objects, the spacing between allowed angular momenta (\(\hbar\) or \(\hbar/2\)) is so small relatively to the total angular momentum that the total angular momentum becomes approximately or effectively continuous. But strictly speaking, it’s still quantized, even for the Earth. The spin of a spin-1/2 particle is just the smallest positive contribution to the angular momentum one may have.
When one thinks about Nature correctly in terms of quantum mechanics, it’s clear that the character of various concepts we know from classical physics will be altered, the predictions and behavior will be different. But they’re still the same quantity and the [quantum] spin *is* the [classical] spin subjected to the quantum formalism to treat observables.
It’s true exactly in the same sense as energy is energy and momentum is momentum. In quantum mechanics, momentum may be quantized in the compact space. The energy is quantized for bound states. It also violates the classical intuition of energy as some “continuous substance” that may be “gradually added”, and other things. One may also construct superpositions of different energy eigenstates, just like for the spin. But it’s still energy. It’s the quantity that is conserved because of the time translational symmetry, much like the angular momentum is the quantity that is conserved due to the rotational symmetry, and when these quantities become large and other conditions guarantee that the classical limit is appropriate, these quantities take on their almost exact and usual classical meaning!
So I think it’s misleading to pretend that the spin is something “entirely different” than the spin of the Earth etc. It’s the same thing, it’s just smaller, and what needs to be changed is the thinking about all of physics – all observables. The transition from classical physics (and/or classical rotating objects and other things) to quantum physics (and the spin of a particle) isn’t about adding a new observable analogous to other classical observables but different. Instead, it’s about keeping the same observables and changing the overall logic and “heart” of physics, how we think about statements, measurements, and predictions. It’s about the replacing of the classical framework, realism, and determinism by the probabilistic, positivist postulates of quantum mechanics based on the linear operators on the complex Hilbert space. But the observables are “the same”, just properly treated.
Hi Lubos, thanks for the comment! I don’t think you’ll be surprised to find that I disagree with your statements about whether the electron is spinning or not. It can’t be spinning in the classical sense since it is a point-like object...Well, the electron is not spinning in the classical sense. I would agree with that. But nothing in the microscopic world is behaving in the classical sense – more precisely in the classical way. Particles aren't moving in the classical way, they don't decay in the classical way, they don't oscillate in the classical way, they don't transfer energy in the classical way, they don't carry information in the classical sense. Pick any activity or any verb you want and I may say that the microscopic objects aren't doing it in the classical way or classical sense.
They're doing everything in the quantum way because the world is quantum, stupid.
But that's something else than saying that particles aren't moving, decaying, spinning, or doing other things. They definitely are. When we say just "moving" or "spinning", we should never assume that it means "moving in the classical sense" or "spinning in the classical sense" – which is the huge mistake that Aidan is explicitly and proudly doing – because this huge mistake means that we fool ourselves into thinking that the "classical sense" is the "normal sense" or "default sense" or the "sense we should always assume". But it's not.
Now, Aidan says that the electron is not spinning because it's pointlike. Even if we adopt the usual definitions that were developed in the classical framework, this statement by Aidan is wrong at both levels. First, it's not true that the electron is strictly point-like. Before the Planck scale, all particles have to have an internal structure because quantum gravity doesn't allow distances shorter than the Planck length to be resolved. The internal architecture of particles therefore can't be "strictly and sharply point-like". In all perturbative string vacua, the electrons are vibrating strings (occupying space comparable to the string length, a few orders of magnitude longer than the Planck length) and indeed, the spin may be understood as coming from some internal degrees of freedom that are localized at an extended object.
In fact, the stringy picture of the spin tells us exactly where the reasoning that pointlike or tiny objects can't carry a nonzero or rather large angular momentum breaks down. The string is locally a very heavy object – the tension or the linear mass density of the fundamental string in string theory is huge – and the motion of this string just a string length away from the center of mass has a big, Planck's-constant-sized impact on the angular momentum. On the other hand, the overall rest mass of the resulting particle may be small or even zero because of various cancellations, including the fact that the sum of integers is equal to \(-1/12\) which is the primary identity guaranteeing that some stringy vibration modes remain exactly massless (and others' masses only arise from some much smaller corrections).
My broader point is that Aidan's attempt to treat the proton's spin as something qualitatively different from the electron's spin is totally misguided as well. It's absolutely the same property or process, when it comes to the right mathematical description as well as its measurable consequences. The spin carried by the proton is totally the same thing and has the same magnitude as the spin carried by the electron!
The only difference is that we already realize that the proton is a composite, extended particle which is why the angular momentum may be visualized as the motion of the components around the axis, at a nonzero distance from it. The electron is not composite in the Standard Model and most likely, it will always be elementary in any quantum field theory correctly and usefully approximating the phenomena around us. But at the end, it's also an extended object – a string or whatever quantum gravity tells you (quantum gravity doesn't allow you to make things that are strictly point-like) – so it's qualitatively analogous to the proton. And the naive argument that an angular momentum that would be this large would require a very light particle such as the electron to rotate superluminally simply has loopholes because the lightness of the particle may arise – and in string theory (and perhaps many other descriptions) explicitly does arise – from cancellations of large contributions to the mass.
The second level of Aidan's proposition is conceptually misguided, too. He says that a particle isn't allowed to be pointlike for it to be spinning. But that's also false. Check your definition of the rotation or the spin in your closest encyclopedia. The "spin" is the rotation around an axis that goes through the center of mass while the rotation around an external axis is "orbital motion" composed of "revolutions".
It's easy to check that even if the electron were point-like, which it's strictly speaking not in the most complete theory, its type of rotation would agree with the definition of "spin" in the encyclopedia. All the points on the electron remain at a fixed distance from the axis that goes through the center of mass of the electron, so the kind of rotation we see is clearly the spin. If the electron were strictly point-like, we couldn't determine the angular frequency from pure geometry. In particular, it's not true that the angular frequency is apparently zero. The angular frequency is the ratio of the "travelled distance over radius" so for a point-like particle, it is the 0/0 indeterminate form and may be anything.
Fortunately, we don't need to be finding out the angular frequency because the "amount of spin" is measured as the "amount of angular momentum" and we know that relatively to any axis, the electron's spin is \(\pm\hbar/2\). It's nonzero. In fact, the electron's spinning can't be stopped at all.
Again, what I find so deeply misguided about Aidan's (widespread) approach is that he wants to make himself think that instead of the Earth's spin, he is supposed to learn just another type of motion or properties of objects but all these processes will still occur "in the classical sense" because it's his default sense he will attribute to any verb or any idea. He believes that everything that looks unusual about the spin must be due the spin's not being the internal angular momentum. But that's totally wrong because classical physics is wrong both for the spin as well as for everything else in physics, especially physics of the microscopic world. One must adopt quantum reasoning and when he does, he will realize that what we call the spin is nothing else than than the usual concept of the "spin" or "internal rotation" as quantified by the angular momentum that we have always known. The reason why many facts about the spin are surprising is not that it's something else than the internal angular momentum; the actual reason is that while it is the internal angular momentum, the whole reasoning about physics must be replaced by the postulates of quantum mechanics that have an impact on everything, especially in the microscopic world.
The spin manifests as a form of angular momentum because it is the angular momentum required to balance the books, but that’s not same as saying that it’s spinning.It is the same thing. And electron is spinning is surely a possible – although not the most widespread – way to discuss the existence of electron's spin in Physical Review and elsewhere. When we want to determine whether a particle is doing something or not, we have to find some observable whose value informs us about the answer. The right universal observable by which we measure whether things are rotating around their axis or not – whether they're spinning – is called the angular momentum. Because the value of the angular momentum of the electron is nonzero, it's spinning. Period, end of the story.
In an analogous way there are no magnetic sources, even though it’s useful to speak of them (ie North and South poles). Magnetism is just a relativistic effect that’s required to balance the books and maintain invariance, but it can’t be treated in the same way that electrostatics is treated.Well, this example has nothing to do with the discussion about the spin but independently of the spin discussion, it is wrong, too. First of all, the magnetic monopoles probably exist although their masses are near the GUT scale. Second, in accessible experiments, we probably won't find one and the total magnetic (monopole) charge is what determines whether an object is magnetically charged. Indeed, we will find out that \(q_m=0\) for the electron or any other object we know, so it means that they're not magnetically (monopole-like) charged. However, the analogous quantity for the spinning is the angular momentum \(\vec J\) and \(J_z\neq 0\) for an electron (similarly for any axis) so the electron is spinning.
Incidentally, when the GUT-scale magnetic monopole charges are correctly added to the theory, magnetic phenomena may be treated exactly by the same mathematical tools as electric phenomena, in a strike contrast with Aidan's opinions. This fact is guaranteed by the electromagnetic duality of Maxwell's equations – a rigorous way to exchange the electric and magnetic field (a symmetry transformation) that we know in many important field theories as the S-duality. Even when we assume that there are no magnetic monopoles, which we often do for analyses of all low-energy physics situations we know of, the electromagnetic duality is a very potent weapon to solve many questions.
The comparison between spin and energy/momentum is not a fair one to make. They remain continuous in quantum mechanics (although in some circumstances they are, of course, quantized) and there is no “extra” momentum or energy that must be expressed in the same way as spin.The claim that energy is continuous in quantum mechanics is a remarkably stupid statement to be made. The fact that energy – namely the energy carried by the electromagnetic waves (separated to \(E=\hbar\omega\) quanta, photons) in 1900 or 1905 and, later, in the 1910s and 1920s, the energy of the electron in the Hydrogen atom and other atoms – has a discrete spectrum was the original reason why people invented the name "quantum theory" and later "quantum mechanics" in the first place. The momentum on compact spaces is discrete, too. In other situations, energy may have a continuous or mixed spectrum but even when it does, the classical tools to analyze its behavior are as wrong as they are in the context of the discrete spectrum! It's not true that the discreteness of the spectrum is the only deviation from classical physics that quantum mechanics introduces. Far from it.
The situation and transformation of the concept of spin is absolutely equivalent to the situation and transformation of the concepts of energy and momentum. After all, in some situations – e.g. electron in the magnetic field – the energy is the same thing as the spin, up to an overall coefficient. With the arrival of quantum mechanics, absolutely the same thing has happened to all these observables. They had to be reinterpreted and reanalyzed in a completely new framework for physics. All of them became Hermitian operators on a Hilbert space. All of them reduce to the old classical concepts whenever the classical limit is applicable (usually for macroscopic, decohering objects). All of them have totally new properties in any microscopic situation.
It's just totally wrong and stupid to suggest that the spin is any different from other observables in this respect.
The axioms of quantum mechanics make it very clear that energy and momentum are to be treated in the same way as they are classically (although subject to the uncertainty principle), that is they are continuous and the result of the spatial and temporal translational invariance.Huh!? Quantum mechanics says that the energy and momentum are to be treated in the same way as they are classically? Sorry, Aidan, but this is too much stupidity to be tolerated for an experimental particle physicist. Nothing is kept about the properties of momentum and especially energy, especially its allowed values, the ways how the values are calculated and predicted, and everything else that makes sense to be discussed. Nothing from classical physics is left intact. The concept of energy becomes the Hamiltonian and it is the operator that dictates all of time evolution. If it were treated in the "same way" as in classical physics, we would treat time evolution in the classical way. The whole physics would be classical.
But the correct physics isn't classical. It's quantum and it's an entirely different thing. All observables – isospin, spin, orbital angular momentum, energy, momentum, number of particles, you name it – are Hermitian operators and predicted probabilistically. Most of them have a discrete (or mixed) spectrum in most situations. The reason for the discreteness is always the same, it's the basic postulates of quantum mechanics, it's the discreteness of the solutions to an eigenvalue equation.
The most general definition of the angular momentum has a totally analogous origin to that of momentum or energy. Via Noether's theorem, energy and momentum are conserved because of Nature's symmetry under the temporal and spatial translational symmetry. Totally analogously, the angular momentum is conserved due to Nature's rotational symmetry. The philosophy behind all these concepts is exactly the same, and so is the character of the transformation that these observables underwent during the quantum revolution.
It's really incredibly idiotic to suggest that energy is what it was and only the spin is new.
All quantum mechanics does is add the requirement that momentum is proportional to the gradient of the wavefunction, and quantum effects follow from there.In the very same way, quantum mechanics "only adds" that the angular momentum \(J_z\) is the derivative of the wave function with respect to the polar or axial coordinate \(\phi\), a gradient of a sort, and quantum effects (including the quantized values) follow from there. But in both situations, it's wrong to say that "everything in quantum mechanics" follows from these mathematical ideas. The "gradient thing" is an extremely ill-advised starting point to be treated as as a postulate of quantum mechanics. It's just some technicality – a particular form of a particular operator in a particular basis. It's just not a way to learn quantum mechanics and it's clear that Aidan has never understood quantum mechanics.
If you want your electron to physically spin then you need to find a way to show that a single point has enough structure to do so. Imagine you’re sitting next to the electron- how would you see if it’s spinning if you only have access to a single point in space?There are millions of ways to measure the angular momentum of the electron. Send it to a magnetic field. If it is spinning, the running electric currents inside the electron – using a classical explanation that Aidan needs – give the particle a nonzero magnetic moment, too. This magnetic moment will drive the electron in one direction or another, depending on the value of the spin, in the magnetic field. The spinning electron is a little magnet, indeed. Every charged spinning particle – and every spinning particle with charged components – is a little magnet.
I may also shoot the electron to other particles and try to induce reactions that only occur if the electron is spinning up or if the electron is spinning down (or in another way).
Also, if you give me one trillion of electrons or other particles with the same spin, I may just shoot them to a thin foil so that they are absorbed. The foil will start to macroscopically spin and its totally classical spin may be divided by one trillion to determine the spin of each electron. The spin is the spin. It is the internal rotation and every experiment able to check whether it's there will say Yes.
(Ask the same question of the proton and things get easier. Just watch the valence quarks move around each other!)This is bullshit. It's not possible to measure the spin of the proton by measuring the velocity of quarks – a simple reason is that the velocity of a single quark doesn't commute with the overall spin and, even more seriously, the position and velocity of a quark inside the proton can't be measured accurately enough at the same moment due to the uncertainty principle. At most, one may get some correlation between the velocities and the spin, but not a sharp, reliable answer. The measurement of the proton's spin is actually done by the same methods as the measurement of the electron's spin because it's exactly the same thing! The only reason why Aidan and others think that it's totally different is that they don't understand quantum mechanics at all.
Incidentally, if you adopt some "nonreliable" measurement of the spin from the constituents' positions and velocities (which must be approximate), I must say that exactly the same thing applies to the measurement of the electron's spin from positions and velocities of pieces of the underlying string. It's undoable in practice today but the same comment applies to the "measure positions and velocities of quarks" to find the total spin, too.
Hello again! I should also point out that certain atomic transitions are forbidden precisely because of spin being an act of balancing the books, and not an actual spinning of the electron. If the electron was actually spinning it should be possible to change its spin by radiating a photon, flipping its spin and jumping down to a lower energy orbital.An electron at rest can't emit a photon because of the energy conservation law. In the initial electron's rest frame, the total energy is \(E=m_0c^2\) while the total final energy in this frame is the higher kinetic energy of a moving electron (already too much) plus another positive energy of the photon (even higher, even worse). This reason has nothing whatsoever to do with Aidan's bizarre claim that the spin isn't a spin.
(If this would violate some symmetry then it can exchange a virtual photon with the nucleus and everything is happy again.) Since an electron cannot do that, then it cannot just change the direction of its spin spontaneously, implying it is not spinning in the first place.What a breathtaking amount of ignorance. Of course that when the energy conservation obstacle is circumvented by considering a more complicated process, the electron will become able to emit a photon and change its spin accordingly to guarantee the angular momentum conservation law. Ever heard of Bremsstrahlung? Even ordinary radiation of the atoms also becomes sensitive to the spin – because it is the angular momentum, after all – above some accuracy (and in the real world).
The process of an electron spontaneously falling to a lower energy level surely happens – that's why 2s may fall to 1s and emit the corresponding photon – but most of such emissions preserve the electrons' spins for a simple reason: the leading non-relativistic Hamiltonian commutes with the spin.
But this ain't the case for the exact Hamiltonian. The leading relativistic corrections include the spin-orbit interaction and be sure that this term in the Hamiltonian is responsible for processes that Aidan considers impossible or blasphemous. The only ultimate, exact conservation law of this kind is the total angular momentum conservation law. If it isn't violated, the process is allowed.
(The orbital angular momentum can change by \(0\) or \(\pm 1\) as well but I don't want to discuss all the selection rules here. The only fact I need and stress is that \(\Delta S = 0\) isn't a valid selection law.)
The electron's spin is a spin and in most situations, quantum mechanics allows more processes to occur than classical physics. Be sure that we observe tons of atomic radiation emissions in which an electron's spin is changed. Aidan's understanding of all these things is upside down. It's wrong at every level. Unfortunately, he's very far from being the only one.
And that's the memo.
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