# Q: What is “spin” in particle physics? Why is it different from just ordinary rotation?

Physicist: “Spin” or sometimes “nuclear spin” or “intrinsic spin” is the quantum version of angular momentum.  Unlike regular angular momentum, spin has nothing to do with actual spinning.

Normally angular momentum takes the form of an object’s tendency to continue rotating at a particular rate.  Conservation of regular, in-a-straight-line momentum is often described as “an object in motion stays in motion, and an object at rest stays at rest”, conservation of angular momentum is often described as “an object that’s rotating stays rotating, and an object that’s not rotating keeps not rotating”.

Any sane person thinking about angular momentum is thinking about rotation.  However, at the atomic scale you start to find some strange, contradictory results, and intuition becomes about as useful as a pogo stick in a chess game.  Here’s the idea behind one of the impossibilities:

Anytime you take a current and run it in a loop or, equivalently, take an electrically charged object and spin it, you get a magnetic field.  This magnetic field takes the usual, bar-magnet-looking form, with a north pole and a south pole.  There’s a glut of detail on that over here.

A spinning charged object carries charge in circles, which is just another way of describing a current loop. Current loops create “dipole” magnetic fields.

If you know how the charge is distributed in an object, and you know fast that object is spinning, you can figure out how strong the magnetic field is.  But in general, more charge and more speed means more magnetism.  Happily, you can also back-solve: for a given size, magnetic field, and electric charge, you can figure out the minimum speed that something must be spinning.

It’s not too hard to find the magnetic field of electrons, as well as their size and electric charge. Btw, these experiments are among the prettiest experiments anywhere.  Suck on that biology!

Electrons do each have a magnetic field (called the “magnetic moment” for some damn-fool reason), as do protons and neutrons.  If enough of them “agree” and line up with each other you get a ferromagnetic material, or as most people call them: “regular magnets”.

Herein lies the problem.  For the charge and size of electrons in particular, their magnetic field is way too high.  They’d need to be spinning faster than the speed of light in order to produce the fields we see.  As fans of the physics are no doubt already aware: faster-than-light = no.  And yet, they definitely have the angular momentum necessary to create their fields.

It seems strange to abandon the idea of rotation when talking about angular momentum, but there it is.  Somehow particles have angular momentum, in almost every important sense, even acting like a gyroscope, but without doing all of the usual rotating.  Instead, a particle’s angular momentum is just another property that it has, like charge or mass.  Physicists use the word “spin” or “intrinsic spin” to distinguish the angular momentum that particles “just kinda have” from the regular angular momentum of physically rotating things.

Spin (for reasons that are horrible, but will be included anyway in the answer gravy below) can take on values like $\cdots, , -\hbar, -\frac{1}{2}\hbar, 0, \frac{1}{2}\hbar, \hbar, \frac{3}{2}\hbar, \cdots$ where $\hbar$ (“h bar“) is a physical constant.  This by the way, is a big part of where “quantum mechanics” gets its name.  A “quanta” is the smallest unit of something and, as it happens, there is a smallest unit of angular momentum ($\frac{1}{2}\hbar$)!

It may very well be that intrinsic spin is actually more fundamental than the form of rotation we’re used to.  The spin of a particle has a very real effect on what happens when it’s physically rotated around another, identical particle.  When you rotate two particles so that they change places you find that their quantum wave function is affected.  Without going into too much detail, for particles called fermions this leads to the “Pauli Exclusion principle” which is responsible for matter not being allowed to be in the same state (which includes place) at the same time.  For all other particles, which are known as “bosons”, it has no effect at all.

Answer gravy: Word of warning; this answer gravy is pretty thick.  A familiarity with vectors, and linear algebra would go a long way.

Not everything in the world commutes.  That is, AB≠BA.  In order to talk about how badly things don’t commute physicists (and other “scientists”) use commutators.  The commutator of A and B is written “[A,B] = AB-BA”.  When A and B don’t commute, then [A,B]≠0.

As it happens, the position measure in a particular direction, Rj, doesn’t commute with the momentum measure in the same direction, Pj (“j” can be the x, y, or z directions).  That is to say, it matters which you do first.  This is more popularly talked about in terms of the “uncertainty principle“.  On the other hand, momentum and position measurements in different directions commute no problem.

For example, $[R_x,P_x]=i\hbar$ and $[R_x,P_y]=0$.  This is more succinctly written as $[R_j,P_k]=i\hbar \delta_{jk}$, where $\delta_{jk}=\left\{\begin{array}{ll}1&when\,j=k\\0&when \,j\ne k\end{array}\right.$  This is the “position/momentum canonical commutation relation“.

In both classical and quantum physics the angular momentum is given by $\vec{R}\times\vec{P}$.  This essentially describes angular momentum as the momentum of something ($\vec{P}$) at the end of a lever arm ($\vec{R}$).  Classically $\vec{R}$ and $\vec{P}$ are the position and momentum of a thing.  Quantum mechanically they’re measurements applied to the quantum state of a thing.

For “convenience”, define the “angular momentum operator”, $\vec{L}$, as $\hbar\vec{L}=\vec{R}\times\vec{P}$ or equivalently $\hbar\vec{L}_\ell=\sum_{jk}\epsilon_{jk\ell}\vec{R}_j\vec{P}_k$, where $\epsilon_{jk\ell}$ is the “alternating symbol“.  This is just a more brute force way of writing the cross product.

Now check this out!  (the following uses identities from here and here)

$\begin{array}{ll}\hbar^2[L_j,L_k]\\=[\hbar L_j,\hbar L_k]\\=\left[\sum_{st}\epsilon_{stj}\vec{R}_s\vec{P}_t, \sum_{mn}\epsilon_{mnk}\vec{R}_m\vec{P}_n\right]\\=\sum_{stmn}\epsilon_{stj}\epsilon_{mnk}\left[\vec{R}_s\vec{P}_t,\vec{R}_m\vec{P}_n\right]\\=\sum_{stmn}\epsilon_{stj}\epsilon_{mnk}\left(\left[\vec{P}_t,\vec{R}_m\right]\vec{R}_s\vec{P}_n+\left[\vec{P}_t,\vec{P}_n\right]\vec{R}_s\vec{R}_m+\left[\vec{R}_s,\vec{R}_m\right]\vec{P}_t\vec{P}_n+\left[\vec{R}_s,\vec{P}_n\right]\vec{P}_t\vec{R}_m\right)\\=\sum_{stmn}\epsilon_{stj}\epsilon_{mnk}\left(-i\hbar\delta_{tm}\vec{R}_s\vec{P}_n+0+0+i\hbar\delta_{sn}\vec{P}_t\vec{R}_m\right)\\=i\hbar\sum_{stmn}\epsilon_{stj}\epsilon_{mnk}\left(\delta_{sn}\vec{P}_t\vec{R}_m-\delta_{tm}\vec{R}_s\vec{P}_n\right)\\=i\hbar\sum_{stmn}\epsilon_{stj}\epsilon_{mnk}\delta_{sn}\vec{R}_m\vec{P}_t-i\hbar\sum_{stmn}\epsilon_{stj}\epsilon_{mnk}\delta_{tm}\vec{R}_s\vec{P}_n\\=i\hbar\sum_{stm}\sum_n\epsilon_{stj}\epsilon_{mnk}\delta_{sn}\vec{R}_m\vec{P}_t-i\hbar\sum_{stn}\sum_m\epsilon_{stj}\epsilon_{mnk}\delta_{tm}\vec{R}_s\vec{P}_n\end{array}$ $\begin{array}{ll}=i\hbar\sum_{stm}\epsilon_{stj}\epsilon_{msk}\vec{R}_m\vec{P}_t-i\hbar\sum_{stn}\epsilon_{stj}\epsilon_{tnk}\vec{R}_s\vec{P}_n\\=i\hbar\sum_{tm}\left(\sum_s\epsilon_{stj}\epsilon_{msk}\right)\vec{R}_m\vec{P}_t-i\hbar\sum_{sn}\left(\sum_t\epsilon_{stj}\epsilon_{tnk}\right)\vec{R}_s\vec{P}_n\\=i\hbar\sum_{tm}\left(\delta_{tk}\delta_{jm}-\delta_{tm}\delta_{jk}\right)\vec{R}_m\vec{P}_t-i\hbar\sum_{sn}\left(\delta_{sk}\delta_{jn}-\delta_{sn}\delta_{jk}\right)\vec{R}_s\vec{P}_n\\=i\hbar\sum_{tm}\delta_{tk}\delta_{jm}\vec{R}_m\vec{P}_t-i\hbar\sum_{tm}\delta_{tm}\delta_{jk}\vec{R}_m\vec{P}_t-i\hbar\sum_{sn}\delta_{sk}\delta_{jn}\vec{R}_s\vec{P}_n+i\hbar\sum_{sn}\delta_{sn}\delta_{jk}\vec{R}_s\vec{P}_n\\=i\hbar\vec{R}_j\vec{P}_k-i\hbar\sum_{t}\delta_{jk}\vec{R}_t\vec{P}_t-i\hbar\vec{R}_k\vec{P}_j+i\hbar\sum_{s}\delta_{jk}\vec{R}_s\vec{P}_s\\=i\hbar\vec{R}_j\vec{P}_k-i\hbar\vec{R}_k\vec{P}_j\\=i\hbar^2\epsilon_{jk\ell}L_{\ell}\end{array}$

Therefore: $[L_j,L_k]=i\epsilon_{jk\ell}L_{\ell}$.

So what was the point of all that?  It creates a relationship between the angular momentum in any one direction, and the angular momenta in the other two.  Surprisingly, this allows you to create a “ladder operator” that steps the total angular momentum in a direction up or down, in quantized steps.  Here are the operators that raise and lower the angular momentum in the z direction:

$\begin{array}{ll}L_+ = L_x+iL_y\\L_- = L_x-iL_y\\\end{array}$

Notice that

$\begin{array}{ll}[L_z,L_+]\\=[L_z,L_x\pm iL_y]\\=[L_z,L_x]\pm i[L_z,L_y]\\=iL_y\pm i(-iL_x)\\=iL_y\pm L_x\\=\pm(L_x \pm iL_y)\\=\pm L_\pm\end{array}$

Here’s how we know they work.  Remember that Li is a measurement of the angular momentum in the “j” direction (any one of x, y, or z).  For the purpose of making the math slicker, the value of the angular momentum is the eigenvalue of the L operator.  If you’ve made it this far; this is where the linear algebra kicks in.

Define the “eigenstates” of Lz, $|m\rangle$, as those states such that $L_z|m\rangle=m|m\rangle$.  “m” is the amount of angular momentum (well… “$m\hbar$” is), and $|m\rangle$ is defined as the state that has that amount of angular momentum.  Now take a look at what (for example) $L_+$ does to $|m\rangle$:

$\begin{array}{ll}L_zL_+|m\rangle\\=\left(L_zL_+-L_+L_z+L_+L_z\right)|m\rangle\\=\left([L_z,L_+]+L_+L_z\right)|m\rangle\\=[L_z,L_+]|m\rangle+L_+L_z|m\rangle\\=L_+|m\rangle+L_+L_z|m\rangle\\=L_+|m\rangle+mL_+|m\rangle\\=(1+m)L_+|m\rangle\end{array}$

Holy crap!  $L_+|m\rangle$ is an eigenstate of $L_z$ with eigenvalue 1+m.  This is because, in fact, $L_+|m\rangle = |m+1\rangle$!

Assuming that there’s a maximum angular momentum in any particular direction, say “j”, then the states range from $|-j\rangle$ to $|j\rangle$ in integer steps (using the raising and lowering operators).  That’s just because the universe doesn’t care about the difference between the z and the negative z directions.  So, the difference between j and negative j is some integer: j-(-j) = 2j = “some integer”.  For ease of math the $\hbar$ were separated from the L’s in the definition.  The actual angular momentum is “$j\hbar$“.

By the way, notice that at no point has mass been mentioned!  This result applies to anything and everything.  Particles, groups of particles, your mom, whatevs!

So, the maximum or minimum angular momentum is always some multiple of half an integer.  When it’s an integer (0, 1, 2, …) you’ve got a boson, and when it’s not (1/2, 3/2, …) you’ve got a fermion.  Each of these types of particles have their own wildly different properties.  Most famously, fermions can’t be in the same state as other fermions (this leads to the “solidness” of ordinary matter), while bosons can (which is why light can pass through itself).

Notice that the entire ladder operator thing for any $L_j$ is dependent on the L operators for the other two directions.  In three or more dimensions you have access to at least two other directions, so the argument holds and particles in 3 or more dimensions are always fermions or bosons.

In two dimensions there aren’t enough other directions to create the ladder operators ($L_\pm$).  It turns out that without that restriction particles in two dimensions can assume any spin value (not just integer and half-integer).  These particles are called “anyons”, as in “any spin”.  While actual 2-d particles can’t be created in our jerkwad 3-d space, we can create tiny electromagnetic vortices in highly constrained, flat sheets of plasma that have all of the weird spin properties of anyons.  As much as that sounds like sci-fi, s’not.

It’s one of the several proposed quantum computer architectures that’s been shown to work (small scale).

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### 50 Responses to Q: What is “spin” in particle physics? Why is it different from just ordinary rotation?

1. Andrew says:

I laughed out loud at “pogo stick in a chess game.”

2. Sanjay says:

Great response!

3. Edd Writer says:

Damn gravy, it’s too thick for me to swallow… 🙁

4. Erfan says:

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5. Alyster says:

Hi, can you please explain what spinning faster than the speed of light means? Forgive my naiveté, but I don’t get how spinning can be measured in m/s. Thanks.

6. The Physicist says:

You’re completely right, rate of rotation is measured in “angle per time” instead of “distance per time”.
What the article is referring to is “tangential velocity”. For example, while the Earth turns at a rate of 360° per day (give or take), on the equator the tangential velocity is about 1,000 mph.

7. David says:

Wait, so if the angular momentum of say, electrons can only be deduced through their magnetic dipoles, then what is the difference between “spin” and “magnetic moment”?

Aren’t these each treated as separate, intrinsic qualities that that things have or am I (yet again) confused?

8. The Physicist says:

Spin is important for a number of reasons, with the magnetic moment being only one of them. The post talks about it a lot because it’s a good example of why spin can’t be classical (must be quantum mechanical).

9. Phyllis McLemore says:

According to Barbara Brennan, former NASA physicist, Consciousness vibrates faster than the speed of light. Instruments don’t pick it up because instruments cannot be built to detect any vibration not within this particular reality. In fact, parallel realities vibrate at faster and slower speeds (frequencies and amps) than the reality we think we are in right now. That is how we are not aware of them, except when angels and ghosts are seen. They are seen because they slow down.
Electrons are shown in pictures as making circles around the nucleus of an atom. If there is no spin of these electrons then why are the paths around the nucleus shown to be circular or oval? If there is no actual spin, then how is there energy? If spin has to be quantum mechanical that means it’s spin is so fast that it cannot be detected. It is just theory because the spin is faster than the speed of light.
Since all atoms have spinning electrons that are quantum speed that means that everything everywhere is quantum, not just at the macro size. I don’t understand how quanta are supposed to act differently that at the macro level. Isn’t the macro level full of spinning atoms? Aren’t atoms spinning as everything? Absolutely everything everywhere has to have a spin, a vibration or it does not exist.
Sorry I am not a physicist, but angels talked to me my whole childhood and since then. I have to figure out why they are not always seen. They must be vibrating faster than the speed of light or we would see them all the time. If spin was classical then that would mean we could see it, that it’s velocity is no faster than the speed of light?

10. Mark McCulloch says:

This is far and away the best explanation of quantum spin I have read. Well done in making a very un-intuitive subject accessible.

11. Swapnil says:

What does it mean by the spin of protons and neutrons? And why does it apparently cause magnetism to arise

12. eyelive4everNOW says:

If electrons do not spin, but rotate, then protons and neutrons must rotate.
Centrifugal force is why there is magnetism and gravity. Isn’t magnetism another kind of gravity? Seems the faster something rotates, the stronger the pull, the further the expansion. The earth spins and rotates. Somebody wrote me yesterday and said that gravity is just a theory. Then I looked up gravity and read that the effects of gravity are indistinguishable from the affects of acceleration. When a magnet pulls or repels another magnet isn’t that an acceleration?
Instruments have been built to measure gravity. A ship mounted gravimeter was developed by Lucien Lacoste and Arnold Romberg in 1936.
Acceleration is a very telling word. So since magnetism pulls or it repels energy, it too could be said “the effects of magnetism are indistinguishable from the affects of acceleration.” The faster the rotation, the harder the pull, the faster the acceleration.
Is pull the same as quantum entanglement? Is gravity and magnetism and quantum entanglement different words for the same force? or the same energy?
I’ve read that consciousness is vibrating all rotations and spins. So I like to study why there is rotation and spin at all. There is energy behind all movement and energy has to be directed. Or it would be like that quantum soup where quanta and photons just seem to go about willy nilly with no direction, but still pulsating and eternal and magical and mind bending.
But then, that willy nilly rotating suddenly turns, and then an idea, a creation is suddenly manufactured by these quanta/photons because they are in the building of the idea, they are there….and the idea turns them and then they picture what the idea is. It is holographic. The quanta/photons form a picture from the idea…..and then idea just seems to explode, to become a bigger picture.
I have read the picture is actually a series of waves which are measured as frequencies. Since waves are the core of everything, then magnetism and gravity and rotation and spin are all tied up together, affecting each other, ONE with each other all the time; always knowing what the other is doing.
No secrets there, just like between people. Thoughts are energy and they rotate and spin and accelerate, too. They flow through us and other people, changing the polarization of every quanta with magnetism, pull and acceleration.
It is an electromagnetic ocean of quanta, etc that we breathe and vibrate in.

13. As I understand string theory (and I do).

Take a 100,000 mile long “string” and make it conductive by plugging the ends together (a standing wave)
and you prove E=MC^2.

When the current flows EMF causes the loop to twist back on itself and compact
(a 5 ft. long loose coil of #32 copper wire and a 9v battery prove this).

The energized “string” spins and shrinks and a sub atomic “particle” is born.
(be careful it is spinning faster than the speed of light). Remember the string has a thickness of the plank length.

The internal spin of the “particle” creates mass/gravity (like gyroscopic spin creates mass/gravity).
The unit resonates and is stable vibrating at lower speeds which can be detected at about 10^-13m.

If you want to make other “particles” use different length strings. If you choose the wrong length it will
decay to a stable “particle” by shattering into radiation and/or by splitting into two or more stable “particles”.
All mater and energy will be conserved in the process because the radiation becomes part of the
UCBR (those tiny shreds from the past to short to make one of the original particles).
Put a “particle” in a collider and you can shatter it into sub-particles and radiation all of which may live
for a nano-second and poof they all disappear back into strings

Is that all it takes to make matter? (If the answer is yes, you got it right!).

The spin being discussed here is not spin but harmonic vibrations.
Regards, IGBY International

14. singing says:

What causes the energy to vibrate and resonant so that a string exists to form a particle?
Since we are a series of waves and strings why is the word “solid” used over and over just to confuse all of us? And it is a definite confusion. If we are solid, then we are left with no source, no purpose, no life after death. Then the world fights and murders and steals because the only purpose it sees is to gain more and more and more, whether it is oil, or land or love.
But we are not solid and we do have a source at least as intelligent as our DNA. We do come from somewhere for a reason before entering these bodies and we do go somewhere for a reason after leaving these bodies. DNA does not vibrate and resonate in such complex patterns with no reason and without a source.
Read the book “Hands of Light” written by the former NASA physicist Barbara Brennan. If I can, and I have, healed myself with vibrations instantaneously, then harmony was definitely present; the harmony of an intelligent source that vibrates my quarks and electrons and atoms, etc. Then, I am the source, perfectly oscillating with waves and strings and coils which are all in harmony.

15. Robert McLaughlin says:

Is it possible that the intrinsic ‘spin’ of elementary particles is a result of the vibrations of strings from string theory?

16. Hypatia says:

Is spin related to the difficulty of detecting a elementary particle? For example, the discovery of the Higg’s boson with a spin 0 has required an astounding amount of effort, and the graviton if it exists has a predicted spin 2.

17. Mariano Quiroga says:

Should we definitely rule out the possibility of superluminal rotation for particles? Nothing can outrun “c” traveling through space, but self rotating seems like a different situation. A seemingly impossible angular momentum might imply that, depending on the radius of the spinning object, its surface could be speeding at c, while the rest of the particle is not. Would this be relevant for particles that aren’t even considered 3 Dimensional? Could this make any sense among the weirdness of the quantum realm?

18. Alistair says:

I don’t have awareness of all current theory, or the necessary math to determine, whether it is possible for a universal bath of miniscule sub atomic particles to exist, that are omnipresent, and billionths or trillionths of times smaller than an atom. That they are like a gigantic McDonald’s ball bath, constantly spinning in unison, like rollers at the beer store. With different sized particles within it, reacting in different manners to the pressure, and spin, often by setting up patterns like clumping, orbiting, and such, because in these compositions, the ever present tiny balls, get themselves into an equilibrium again. Waves of “pressure” and “force” through these itty-bitty balls are the components of all “energy”. Everything in the universe becomes an explainable mechanical occurence at that point. no mystery forces. ???

19. Xerenarcy says:

@Mariano Quiroga
i’m with you on this. the speed of light applies to the propagation speeds of electromagnetic waves, it is not an absolute limit per se just that so much of physics involves EM it’s hard to find a situation when you’re not bound by it. this looks like one of those situations in principle but i’m not entirely sure.

furthermore, if spin is quantized then how does it change direction?

20. yoron says:

Would you agree to that spin isn’t anything similar to angular momentum? Or do you want it to be a equivalence? As for saying it is more important, is the idea that a macroscopic angular momentum could be a result from particles spin? As a ideal form of some type?

It really hurts my head this one, trying to connect spin to angular momentum, but it is information, isn’t it? And in that motto meaningful to the eye, and brain? We can see polarizations, that’s what sunglasses is for. On the other hand, if I get it right that is a macroscopic result from how matter is arranged. And yes, as always your explanation tries to give the gist of it.

but it still hurts my head.

21. Cass says:

It seems to me that when position and momentum are along the same axis, the result of RP-PR or PR-RP indicates movement through space in either the positive or negative direction along that axis, whereas when P,R commute, it indicates the particle is stationary in space.
Is that correct?
Thanks

22. M Abuzar bhatti says:

i think spin in atomic level is d same as in angular momentun in macro level,but we cant see the spin because d atomic particles moves with more than the speed of light and hence treat as a wave…and when these waves combine to form a macro particle,they slowed down their speed…….m i right?

23. Ziriax says:

I recently learned about Grassmann algebra and geometric algebra.

Using these algebra’s angular momentum is not defined using the cross product, but as a bivector, using the wedge product. The cross product is not invariant under reflection, while the wedge product is. Reflection plays an important part when it comes to rotations, since a rotation about an angle can be described as a double reflection. I wonder if the up/down electron spin is actually a side effect of using incorrect mathematical modelling, namely the usage of the cross product instead the wedge product?

24. Mason Stewart says:

Look, I definitely don’t have the required knowledge or experience to even comprehend most of the mathematical ‘lingo’, but in saying that, using the very limited knowledge I do have, to say that particles can’t have enough angular momentum to generate the magnetic fields being produced, due to them having to spin faster than the speed of light, and that they just ‘have it’, doesn’t seem to meet a philosophical standpoint as much as a scientific one. I mean, isn’t the hype around the Higgs boson and the Higgs field to finally help compete the standard model an finally know what creates mass? And, I mean, how can a particle just generate its own field out of no where? Another question would be when the particle isn’t observed and falls back into a superposition, does its magnetic field also cease to exist? And, once it has been observed and collapses into one of its probable states, this act of, for lack of a better word, ‘materialization’, does it itself occur any energy usage? Maybe this ‘materialization’ causes the particle to rotate. And as mentioned in an earlier comment, maybe our technology can’t recognize the particle rotating faster than the speed of light, much like how the faster one goes, the slower it ‘appears’ to be. To relate this, to identify black holes (please correct me if I’m most likely wrong), don’t we seek out the radiation emitted rather than the hole itself? Because we don’t have technology sufficient enough to actually ‘see’ in a black hole. Could the same principle be applied to this situation? And as for a philosophical standpoint (As science goes hand in hand), for the particle to just ‘create’, would be similar to that of a god, or something with infinite knowledge and resources to be able to do such a thing? I mean, are we saying electrons are the gods of the particle world? Haha I’m not too sure, please do correct me if I’m wrong, I’m only 16 with limited experience and knowledge in most things mathematical at the current moment, although I do have an interest in the quantum world :’).

25. Anton says:

Is it possible that fermions turn inside out instead of rotating, or perhaps rotate 4-dimensionally around the w-axis?

26. chris hedlund says:

How is it that elementary particles that have no charge can have spin? Doesn’t the particle need to have a magnetic moment to have a spin? How can it have a magnetic moment if it doesn’t have any charge?

27. chris hedlund says:

Fermat’s last theorem was difficult to prove because it involved proving a negative. How about proving this negative: there is no other non trivial function other than y=e^x that is its own derivative.

28. the basic tenet of quantum theory gives a hint at why the speed of light can be exceeded.this is achieved by using a sprinkle of magic called quantum tunneling.there is no other logical or illogical answer possible.i have in fact said nothing but there the matter must rest. Richard f says that anyone who claims to understand quantum physics has demonstrated the fact that they do not.well said Richard (rest in peace)

29. Clint says:

There is an equation that will give 1/2*hbar (electron spin) straight from the energy equation of pair production: Assuming no left over kinetic energy for now, E(of photon) = E(of electron) + E(of positron) ; then E(of photon) = h*f (frequency of photon); h*f = 2*pi*hbar*f; now 2*pi*f is angular frequency (Wphoton) so hbar = E(of electron)/Wphoton + E(of positron)/Wphoton and that impies 1/2*hbar = E(of electron)/Wphoton and 1/2*hbar = E(of positron)/Wphoton. So, the 1/2*hbar spin of the electron is related to the angular frequency of the photon the creates it. This implies to me that the electron is not a point source particle but more like the resonant cavity particle the Dr. Randell Mills describes. Further, the electron (or positron) should be allowed harmonic forms.

30. pete says:

all particles are made of groups of strings, strings are not all the same, in string world some combine to form particles of different energies levels and other properties. Vibrating strings form magnetic lines of force . like string can exist in the same place in space time. Strings with opposite spin or polarity can’t.
strings can form lines entanglement between particle Some think entangled particles are different ends of the same string .
gravity is simply a bunch of strings (boson) which recruits other strings because it has a the correct properties which allow this to happen. this effect follows the inverse square law

pete

31. Aieou says:

@eyelive4everNOW; You have a large post with many points, but I’d like to say one thing. First, a quote: “When a magnet pulls or repels another magnet isn’t that an acceleration? […] Acceleration is a very telling word. So since magnetism pulls or it repels energy, it too could be said “the effects of magnetism are indistinguishable from the affects of acceleration.” The faster the rotation, the harder the pull, the faster the acceleration.” When a magnet affects another, that is a force, not an acceleration. Imagine you’re sitting one of the magnets. The force (of the other magnet) is measurable as coming directly from the other magnet, but the acceleration is only measurable from your own magnet. So given *only* an accelerometer, you wouldn’t be able to tell if you were accelerating due to gravity, magnetism, the electric force, or whatever. The important thing about gravity is that you literally cannot distinguish it from acceleration even with other instruments, as far as we know. A “gravimeter” is only able to measure gravity because the characteristics of the vessel it’s mounted on are well known, i.e. the velocity, air resistance (from the exosphere), etc. so it’s just a very precise accelerometer.

32. Bill christie says:

I discovered that a classically rotating wave would explain relativity and more. Is it possible we have over compensated and made it too convoluted? If you pass a car on the highway, suddenly the helicities of the slower car electrons are flipped. So now chivalry is added to the mix to create another substate. If time and space are not connected and a function or structure of the electron is really the culprit (Dirac might have considered this), then the weirdness of quantum mechanics can be explained away. After all, who ever said it has to be weird. Maybe we have just not thought about the foundations enough. Why would it be bad to question. Even someone mentioned above that if QM is weird, then why couldn’t rotating waves at greater radii have tangential velocities greater than C? All I’m doing is following science.

33. Roger Beelen says:

When I googled “why do all things spin to the right” I ended up here. I am neither a mathematician or physicist, but having read all your speculations on the nature of electron spin, I see you are a bunch of multi-discipline thinkers and perhaps my observations can add a dimension and maybe someone could help me answer my question.
I am wondering why things grow and spin to the right from the south pole or point of growth. Here is a list of things I have observed: the earth, the moon around the earth and the other planets, vines growing up garden posts, whorls of seashells, DNA, pinecones and the right hand rule in electronics. I am thinking that this rule may apply to the very nature of creation at all levels. You may laugh.

34. Frank says:

On string theory, if one has a box of strings or wires say and one does many things using the content of this box and move the box around as well sloshing the contents around. It is apparent that strings and wire thread etc. in this box become entangled in each other and in them selves as well, in said box.

Thus strings and wires and thread always become knots.

This being true in the macro world as it might be in the minute subatomic world as well wouldn’t String Theory actually be more correctly and accurately be called
Knot Theory?
Not to be funny or to mean Not as a play on words.

35. Bill Christie says:

It is so simple and obvious. Rotating waves spin faster at greater radii and at some point go faster than the speed of light. Why say this is heretical? How dogmatic! Space and time only appear to be connected because it is the internal wave function of matter that makes it so. We are energy. We are transmitted through space, so thus no net fringe shift in the Michelson Morley experiment of 1887. We and the inferometer, the earth, etc. we’re all fringe shifting so to speak. All this time and we’ve being going down the wrong fork in the road. Albeit, great efforts of genius developed relativity and quantum mechanics plus particle physics and cosmology. All of that does not depend on the speed of light being constant. The speed of light is constant in a straight motion but goes faster at greater radii as it turns. That is the premise of the Rotating Wave. It resolves a lot of things that would otherwise look weird.

Beyond all that, there is probably more layers of underlying reality that go even much faster than zitterbewegung (zitter for short) which is a billion billion times a second. Why stop here?

36. Alistair Riddoch says:

I do not think that “spin” in the quantum world is different than “spin” as we understand the term. The problem is that we are not looking far enough down the scale. In a system where there is a medium comprised of spinning deformed spheres, that act in conjunction with one another, there would be actual spin. The “particles” we believe we “detect” are created within the spinning environment, and therefor are perceieved as “having the properties of spin, but not actually spinning”. The particles we believe we “detect” are more like a “hole” in a donut. Spin the donut, the hole spins. But holes are nothing and don’t “actually” spin. So where we have decided we are perceiving “particles” we are actually perceiving the partial surfaces of the group of spheres that create the hole, that we take to be a “particle”.

Consider the following shape, replicated endlessly, as a “creator of 3D spin array” which then in turn creates the collection of particles, waves, motion, existence, etc, that we live amongst:
https://www.flickr.com/photos/[email protected]/shares/P034Ln

It is more sensible to imagine that a physical-mechanical-kinetic substrate exists, than to believe in force fields, and miniscule particles that magically wing around it at the speed of light, held to it by a force capable of attaching to and staying attached to something moving that fast.

Occam’s razor would say, where a system/construct/theory is simpler, yet viable, it will more likely be the correct answer. So before we jump to the defense of “forces” and our beloved “wave particle duality”, we should consider the notion of a particle with wave-motions forced upon it, by it’s shape, it’s nature, it’s essence.

Which makes more sense, balls that come into and out of existence in nano-seconds (super symmetry), and particles that transform from physical substance to a wave, and back to a physical substance, OR a physical-mechanical-kinetic medium that creates “wave-particle duality”, “spin without spin”, etc. Leaving “the force” for the creators of intergalactic war stories. And bringing the physical back to physics.

Yes it is a paradigm shift in thought.

Perhaps out current system of time dilation, gluon fields, dark matter, dark energy, time dilation, wormholes, and wave particle duality is historically popular.

But come on! Common sense!!

Physics…..

37. Bill christie says:

Hi Allister,
Thanks for your comment. I listen to occams razor but don’t totally bank on it. Maybe we haven’t gone far enough down the strata as you say. I would like to learn about your theory in more detail. Sorry, i don’t get the doughnut hole, but think you are talking about substrata being composed of spinning particles as described in your graphic model. I took notice of the inverting topology.

I used common sense when realizing that a photon is bent around the sun on its journey to earth. Light as an electromagnetic wave (photon) has a defined location in 3d space and from that location has fluctuating EM transverse waves. When going in a straight forward motion, it travels at the speed of light C, because of the properties of aether (empty space). In contrast Einstein’s hypothesis, I state that the speed of light goes faster at greater radii of the classical rotating wave. Rotating waves of mass at the macro scale (eg the sun), interact and impart a bending of the photon, hence you get gravity. Since the sun itself and massive particles like fermions are rotating waves, then you get the equivalence principle. Now that is simple and fits our observations.

38. Terra says:

Hi,

Thanks for this it was very informative although I couldn’t follow all the maths. I find my self flip-flopping between belief and the strange suspicion that mathematics has become self serving in Physics. Electron spinning faster than light? A) there is something we have got wrong with nano scale magnetic fields lets investigate, B) Lets abstract the value so it doesn’t relate to any physical concept we can describe and balance that equation. If anyone asks we’ll just proclaim that the universe is strange lol (cynical I know).

“Pure” Mathematical physics need to be a separate subject, we need another seperate branch that concentrates on mechanics and causality (i.e. reality). Both useful, both interesting, but neither complete without the other. Einstein started this trend of mathematical explanations without mechanical ones, but I wonder if he thought it would become this dominant? His thoughts on entanglement were ironically firmly inclined in the mechanical direction, which I have always taken as an indication that even he viewed his own work mainly in abstract terms.

Still, excellent article, not your fault that I am paranoid 🙂

39. Bill Christie says:

Electrons (fermions) are wave functions that have “spin”. I for one think that “spin” is real and thus a planar wave front spinning or rotating around one axis must go faster at greater radii. I don’t take anything away from the math. Math teaches us to look in a certain way and thus leaves clues. Graphics illustrates the dynamics in another way, but is intimately connected with math. There are different ways to describe the dynamics such as matrices, vectors, and spinors. However, you must be aware of what you are dealing with.

I hope I am okay to do this, but you can see my Rotating Wave model (and the math)at:
http://fqxi.org/community/forum/topic/1928
and scroll down to Jan 11 2016 03:24 GMT attachment:
Rotating Wave of Electron WHF Christie Jan 03 2016z.pdf

40. James says:

quantum physics tells us matter and energy are quantize, but can the same be said about spacetime having an emergent nature I.e existing as discrete units or is spacetime continuous in nature?

41. Bill Christie says:

Spin in quantum mechanics is clearly a Rotating Wave. The photon is localized as it is transmitted through space. As it’s trajectory is bent by the sun’s gravity, the speed of the Wave goes faster at greater radii. If a photon is brought into full rotation, then an electron positron pair are created. If put into constant motion, then the electron Rotating Wave traces a helical path in accordance with Special Relativity. If accelerated by a gravitational field, then the Rotating Wave spirals. Reimannian surface curvature can be calculated on the path of the rotating wave and the 5th vector (rotor) of the Rotating Wave expands or contracts, explaining the Kaluza 5th Dimension. Simple mechanics in 3 D space. Space and Time are not connected. Relativity is only an effect of the wave mechanics.

You can see the graph and math under William H.F. Christie January 11, 2016 at:
http://fqxi.org/community/forum/topic/1928

42. What is Spin ? I think the answer is phase shift (= shift in coordinate).
1. I think the de Broglie waves of multiple particles in one quantum state are connected in series, and the each wave shift msλ at the connecting point. (ms:spin quantum number, λ:wave length)Let us consider a case in which two electrons are in one quantum state [n,l,ml,ms=+1/2].
The de Broglie wave of 1st electron shifts +λ/2 in coordinate. And the de Broglie wave of 2nd electron shifts +λ/2+λ/2 in coordinate. Accordingly the two waves destructively interfere.
[the Pauli exclusion principle]
2. Suppose that two electrons are moving in a single orbit, and suppose that the de Broglie wave of one electron shifts +λ/2 in coordinate and the de Broglie wave of another electron shifts -λ/2 in coordinate.
The two waves have the shift of exactly one wavelength, which leads to a constructive interference of the wave, making it possible for the two particles to move in the same orbit.
[the 4th quantum number]
3. The variable of wave function Φ{φez･(r ×p)} in φ direction has angular momentum r ×p.
Accordingly, the shift in coordinate msλ change the angular momentum as follows: ml(h/2π)→ ml(h/2π)+ms(h/2π).

I’m sorry that I’m not good at English.

43. Len loker says:

It looks like your equation for L+ implies [Lz,L+] should =[Lz,Lx+iLy] with no + or – sign.

44. Sharon Poole says:

Best understandable description of Electron Spin I have ever found. Thank you!