Spin was initially introduced to explain the polarizable behavior of electromagnetic photons, with respect to non-polarizable electrons, that led to de Broglie's hypothesis that electromagnetic photons had to involved two half-photons of spin 1/2, then being referred to as a boson, while the elementary electron was termed a fermion.

The spin however is related to the magnetic aspect of elementary particles. They can be either in relative parallel magnetic polar alignment, thus magnetically repelling each other or in anti-parallel magnetic polar alignment, thus magnetically attracting each other.

For non elementary particles, such as the proton, for example the 1/2 spin is the result of the correlation of three 1/2 spin sub components, two of them being in anti-parallel magnetic spin alignment, sort of cancelling each other, which leaves the third subcomponent accounting for the resulting 1/2 magnetic spin of the proton.

The same logic applies to the complex addition of the half spins of the elementary electromagnetic subcomponents of atoms:

https://file.scirp.org/pdf/JMP_2018042716061246.pdf

But André Michaud I think my question remains unanswered. Why the spin as half integral alters the statistical behavior so drastically.

Dear Viraj,

I couldn't answer this question in context, because in quantum mechanics, the spin is considered an intrinsic property of particles or systems of particles, while in more fundamental electromagnetism, it is a relative property, specifically referring to the relative mutual magnetic orientation of elementary electromagnetic particles.

If some means was found to reconcile the intrinsic perspective of QM with the relative perspective of electromagnetism, then maybe a coherent answer could come to light.

H3 has 3 half spin elementary subcomponents less than H4, (1 less neutron), so one elementary half spin subcomponent remains magnetically uncancelled (unneutralized).

Best Regards

André

Dear Vijay,

Probably a dialectical perspective of the quantum phenomena - the fundamental basis of the imaginary quantity (i) and the incorporation of complex- conjugate fields φ* along with the real field φ (non commutative algebra) by Dirac (for spin 1/2 particles) that lead to the recognition of the antiparticles and the existence of Majorana Particles (reported recently) would be helpful to answer your question. This is a new aspect of reality brought forth by the developments in quantum mechanics. Physics previously only dealt with integral spins of 0, 1 and 2 in its equations namely, the Klein–Gordon, Maxwell's (electromagnetism) and Einstein's (general relativity) equations, respectively; which readily accommodate real fields, as these equations are formulated using real numbers only and are represented by bosons.

In principle Majorana particles are those in which matter and antimatter exist together in the same unit as a dialectical contradiction of the “unity of the opposites” – a fundamental law of dialectics. A gamma-ray photon (that can produce electron-positron pair), proton, neutron etc. (which have quarks and anti-quarks combination) and particularly in meson and even more loosely bound entities like positronium etc., are in principle Majarona particles Please see the following article: Article Majorana Particle: A Dialectical Necessity and not a Quantum Oddity

Sorry, there is some error in the comment above and also in the reference that need to be corrected. The concept of spin 2 for gravity is wrongly attributed to Einstein's GR. It is in fact coming from the purported idea of gravitons (spin 2) in the quantum formulation of gravitation. Abdul

Abdul Malek - let me rephrase what bothers me. What is that the spin of particles makes them decide to take up antisymmetric or symmetric w.f.

Dear Viraj,

You wrote: "What is that the spin of particles makes them decide to take up antisymmetric or symmetric w.f."

In electromagnetism the answer to this question is very simple. It is because the antiparallel magnetic polar spin alignment is a "least action" state with respect to the only other possible state, which is the parallel magnetic polar spin alignment.

You can easily verify this at the macroscopic level. If you slowly push two magnets towards each other over the surface of a table, however respective relative positions you place them into, at some point they will suddenly snap into antiparallel polar alignment. If you are not careful and if the magnets are strong, you might even get hurt in the process.

The behavior is the same for the magnetic fields of elementary charged particles.

The proof being that orbitals can be filled only by electron pairs, and that macroscopic magnetic fields in ferromagnetic materials are known to involve only "unpaired" electrons that are forced by local stable electromagnetic equilibrium states to remain parallel to each other, their individual parallel fields adding to each other until the field becomes measurable at our macroscopic level.

http://ijerd.com/paper/vol6-issue12/B06120711.pdf

Best Regards

André

Vijay K Jindal

For quantum dynamics like dialectics, “motion” (of all kinds) is a fundamental attribute of any matter particle: “There can be no matter without motion and no motion without matter”. “Spin” is one particular type of motion like rotation, vibration etc. Why “spin” is integral or fractional (1/2, 1/3, 2/3 etc.) comes mainly from symmetry considerations as well as that of energetics.

Because spin is one of the invariants (the other is mass) that label a relativistic particle and, in 3+1 spacetime dimensions, spin can take only integer or half integer values. (It doesn't have anything to do with the motion of the particle.) That relativistic particles of integer spin give rise to multiparticle states that describe bosons, whereas those of half-integer spin give rise to multiparticle states that describe fermions, is a consequence of the assumptions of Lorentz invariance and of a Hilbert space with positive metric.

Cf. here: https://ejde.math.txstate.edu/conf-proc/04/w1/wightman.pdf

for the details. In less than 3+1 dimensions spin can take any real value, since the rotation group is abelian.

From the electromagnetic perspective, the rest mass of atomic nuclei is variable as a function of the distance between atoms, and the fact that only two half-integer spins are possible is due to the fact that only two relative magnetic polar orientations are possible.

“Because spin is one of the invariants (the other is mass) that label a relativistic particle and, in 3+1 spacetime dimensions, spin can take only integer or half integer values. (It doesn't have anything to do with the motion of the particle.)”

Einstein, (the idol of this commenter) will turn in his grave to hear a comment like this! Because for Einstein “matter” (mass) and “motion” were never primary nor important (these are illusions like Zeno and the early Greeks, perhaps?); but he imported these into his theories never-the-less, through the backdoor, probably with the help of “the Old One”!

Also for him and according to his SR, "mass" (matter and also time) is NOT invariant; “mass” increases with speed (m = mo ɤ) and may become infinite at the speed of light! I will let Einstein speak for himself, “Since the theory of general relativity (GR) implies the representation of physical reality by a continuous field, the concept of particles and material points cannot play a fundamental part and neither can the concept of motion. The particle can only appear as a limited region in space in which the field strength or energy density is particularly high”. Einstein, A. On the General Theory of Relativity, in David Levy (Ed.). The Scientific American Book of the Cosmos, N.Y., 2000, pp. 13.

Dear Abdul Malek ,

How much are you sure that SR/GTR is correct and nature follows this theory ?? Are you aware of the fact that origin of mass is due to pure quantum mechanical effect?? If really mass changes with velocity (we are not interested with only equation which suggest that mass should changes with velocity) , then Crystal structure and Bragg's diffraction condition will also changes with velocity... Are you aware of the consequence of length contraction and mass changes on the rule of quantum mechanics which nature follows absolutely?

Dear Gokaran,

You wrote: "If really mass changes with velocity (we are not interested with only equation which suggest that mass should changes with velocity) "

You simply need to study the Walter Kaufman experiments that first collected real physical data about the difference between increased transverse mass of relativistically moving electrons with respect to the known rest mass of the electron, and you will observe change in mass with velocity not stemming from suggestions from equations.

The data is on record. But nobody in academia has studied it.

His experiments could easily be reproduced to confirm the data.

This was also confirmed in the first cyclotrons. The minute electrons velocities entered the relativistic range, their increased mass systematically caused them to miss the target.

The higher their velocity, they farther their spiral trajectory strayed from the one that matched their rest mass.

Best Regards

André

Gokaran Shukla ,

You seem to have very little idea about my position on these issues. I think I am probably the most consistent and principled opponent (than anyone else) of Einstein's theories of relativity; because I am the only one (to my knowledge) in and outside RG who practice science from the conscious materialist dialectical perspective; which is in total contradiction with mathematical idealism.

If you are interested to know, please see my RG profile, references to published works and on going comments in various forums of RG, even a just posted one: https://www.researchgate.net/post/Why_are_there_lightspeed_particles_in_the_universe

Dear André Michaud ,

Can you please share that paper pdf file in which mass has increased with velocity?

You Wrote "This was also confirmed in the first cyclotrons. The minute electrons velocities entered the relativistic range, their increased mass systematically caused them to miss the target"

In cyclotron, Radius of circulation does depends on the velocity... R = m v/qB..... If one increases velocity then target will be missed and it has nothing to do with changes in mass ...

Thanks

Gokaran Shukla

Dear Gokaran,

You asked: " Can you please share that paper pdf file in which mass has increased with velocity?" with reference to cyclotron operation.

Unfortunately, this dates back to long before pdfs and even the Internet were conceived of. This dates back to the first half of the 20th century.

The first circular accelerator type that was conceived of was the more primitive cyclotron.

This type's main feature was that it accelerated charged electrons fed in at the center, that were then accelerated by a magnetic field on an outward spiraling trajectory until they hit a target located at the outermost edge of the accelerator.

It was effective only for non-relativistic velocities because its operation was dependent on the electron mass remaining constant. As soon as relativistic velocities were reached, the motion was observed as becoming desynchronized and the particles missed the target.

This is what prompted the development of a different type of circular accelerator to overcome this difficulty, in which electrons velocity and trajectory was not dependent on their mass. This new type was the Betatron and its main feature is that it is the only type of accelerator in existence that can continuously accelerate isolated electrons on a "perfectly circular" trajectory. This allowed easily accelerating particles to very near light speeds in spite of the increase in relativistic mass. The first betatron was the GE Betatron that John Blewett experimented with.

I heard that current cyclotrons designed for medical use compensate for this problem, possibly by synchronizing variations in the magnetic field intensity with velocity, but I didn't check.

But if you really are interested, no doubt could you investigate the historical archives and relocate the specs of the initial design with your easier access from inside academia. I don't remember where I got the info. It is somewhere in my pile of old refs. This was in the 1960's when I thought that this was general knowledge in academia. So I took no notes.

The Walter Kaufman papers though, are available in a couple of locations on the net, but only in German, I'm afraid.

Best Regards

André

Stam Nicolis I like the most qppropriate looking answer but difficult to comprehend physically - ... consequence of the assumptions of Lorentz invariance and of a Hilbert space with positive metric.". Despite the discussion that followed, I would be happy if you can elaborate it in simple physical model equivalent to perceive as a consequence of integer spin that a state can be multiply occupied.

Dear Vijay,

The Poincaré group is the Lorentz group SO(3,1) which has three rotation infinitessimal generators J and three K boosts plus the four translations associated to the energy-momentum There are only two Casimir invariants of such continous group. One of them is the inner product of 4-linear momentum which is associated to the rest mass and the other is the Pauli-Lubanski invariant "spin". Thus the spin is defined properly as a property of the general Poincaré group which summarize the main symmetries of all the interactions of Physics.

For asking your question we need to go further to the Lie group and enter in the Lie algebrae associated to it or to the representations taking vectorial functional spaces as Hilbert's or Fock's associated to states for a given Hamiltonian. What is interesting is that the fermionic representation made with fractional numbers is very different than the bosonic got with natural numbers and which can be even joined in supersymmetric algebra which contains both. These algebrae belong to the experience got with results (mainly with the atomic fulling of electrons) by the exclusion principle of Pauli for fermions or to have particle-antiparticle pairs. Meanwhile the bosonic is obtained for the opposite behaviour of having many bosons per state which is purely phenomenological and without any kind of theoretical explanation related with the integer or fractional number of their "spin". These are just mathematical representations (mainly using Clifford algebras) for the Poincaré group of Lie.

@Daniel your reply is too technical. If you could brief it in simple Physics why half spin endows particles to assemble in that special way compared to integral spins, it will be highly appreciated. Is there a classical analogue?

Dear Vijay,

Speaking with simple words, the fact that fermions are half-integer spin and bosons are integer spin is a form to classify phenomenogical quantum behaviours as periodic table shows. The interesting result is that these two classes of particles obey different quantum rules translated to representations of the Poincaré group. Thanks to that, those differences enable the existance of the matter as we know. And you are right to remark that for the difference of just ±1/2 in a quantity as the intrinsic angular momentum, or spin, has so dramatic consequences. Summarizing, we know phenomenologically the big difference between fermions and bosons and we can represent them in a quantum mechanical theory in a very satifactory form, but the real explanation of why all the particles fall in this classification is not known. This belongs to the same kind of facts as why two opposite electric charges attract while the ones of the same sign reppel or the mass only attract, etc..

Perhaps it is more than that equivalent of opposite charges. Here we are differentiating something like negative charges behave differently in very striking property like distribution as compared to positive charges. I have no issues if the 1/2 integral interact with integral spin but why this difference makes the particles themselves so different. It is perhaps more fundamental like nature has males and females, they have some drastically different properties in themselves.

Add to this, if you convert somehow 1/2 integral to integral by adding two 1/2 integrals, the behavior changes drastically again.

Dear Vijay,

Yes, I agree with you that this is a very important physical property and also that two fermions can by equivalent to a boson, But the spin is a very subtle quantum physical object (even its name is confussed): nothing is rotation there and in spite of it is an angular momentum. Even more, for given a full rotation it would take 720 degrees and no the 360 in usual rotation. Let me finish remember you that the addition of spins need to use the horrible Clebsch-Gordan coefficients and sometimes it is difficut to say the last behaviour (singlet, triplet, ...). Fortunately there are thumb rules as Hund's which allow to get good results without examining all the possibilities.

And @Daniel is there any classical analogue possible to appreciate if angular momentum or spin could dictate assembly of multiparticle state?

Dear Vijay,

I don't know if I have understood your question. As you know there are two components of the total angular momentum: the orbital and the spin. The spin only takes into account two associated states, up and down, while the orbital depends of the coordinates and it is possible see it as a classical object in some aspects. But in general I don't know the form to compare the spin addition or others with the classical angular momentum. Less in multiparticle states.

In magnetic nanparticles you assume a coherent state of spins for obtaining the magnetization (in fact the saturation magnetization) as the addition of their magnetic moments (associated to electronic spins).

Dear Daniel,

Just like He3 or He4 behave differently due to spins adding up to result in 1/2 integral as in former case of Fermions , so do molecues also behave differently from atoms?

Dear Vijay,

Your example is very simple to calculate. He3 is equivalent to the spin one electron which means that acts as a fermion (proton and the electron have opposite spins and therefore its composite spin is zero), meanwhile the He4 has a neutron more whose spin is opposed to the above remained electron. Thus He3 has spin 1/2 and it is a fermion and He4 has an whole spin zero being boson. Notice that we are playing with atoms having the same angular momentum, i.e. we only have s-electrons. In other higher atomic number the things would be much more complex.

Dear Daniel,

Thanks, yes that is ok. But if we form molecules and look for statistics of molecules instead of atoms, will they change behavior on suddenly changing conditions which facilitates formation of molecules from atoms? Say by altering temperature and pressure?

Further if zero or integral spin can assemble in the same state on effective model can one say that integral spin are interacting with each other that facilitates with same energies while 1/2 integral do the opposite. One might also extrapolate to conclude that half integral nuclear spin particles can not form molecules?

Dear Vijay,

If you want to create molecular states the main problem is that there are orbitals besides spins and they carry also dipoles, quadripoles ...which interact in addition to the statistics of the bosons or fermions.

Dear Daniel,

What is the chance that spin, dipoles and quadri-poles are all linked together?

Dear Gokaran,

In a fundamental particle as one electron the spin has a well associated magnetic dipole and nothing more, but if you go to a composite big particle as a molecule then you have more multipoles and their corresponding interactions.

As is well known there is not easy to find bosonic states for big molecules to allow bosonic condensed matter. The main problem is that besides the statistics there are more interactions which screen it. Let me to put just one example studied in this paper

http://www.nipne.ro/rjp/2013_58_9-10/1059_1063.pdf

The particle sets and their properties must be reconciled with their interaction with vacuum space. Just as EM polarizes local space to pass through it, the various particles modify local space in ways that represent other types of polarization. Space enforces limitations on the types of particles it will propagate, offering some explanation why fractional electrical charges are not stable as free particles in space. The Fermions and Bosons fit into the categories that the vacuum can accept. Notice the spins are in multiples and fractions of h. The implication is that vacuum space is probably quantized with spin angular momentum of h. Particles must spin in harmonics of vacuum space.

I think it may have something to do with the fact these particles live in a 3D space. They thus have exactly 3 components of angular momentum that satisfy the defining commutation relations, and using the raising and lowering operators we are led to integer and half-integer eigenvalues of the angular momentum. Had they been living in a lower (2D) or higher dimensional space (4D for example); different eigenvalues would have been possible.

In the 2nd edition of quantum mechanics textbook written by Cohen, there is a footnote on page 1387 which may provide you with a hint about your question. Basically, it says the different behaviors of bosons and fermions can be proved based on more general hypotheses. However, this is still another assumption and there is a possibility that bosons with half-integral spin might be found in the future.

Daniel Baldomir let me carry forward - does the molecule C60 behave as a single C atom behavior as far its fermion or boson identification goes? Further, if i relace one C atom by its 13 mass number isotope will the whole C60 change over in its characteristic?

Dear Vijay,

The classification between bosons and fermions is purely quantum and therefore, first of all, we have to make sure that there are quantum states for those molecules. When you place molecules of so many atoms, this causes bonding and anti-bonding states to appear in addition to the hybrids, which has a limit where the statistics no longer distinguish behaviors as clearly as the Pauli exclusion principle. Therefore, I would not dare to simply count the spins to see if they are fermions or bosons, I would reserve it for fundamental particles or small combinations of them in which they can be assigned a well-defined quantum state. Therefore I cannot safely help you in the molecule you propose to distinguish these very different statistical behaviors. Even in fluerenes where there are almost perfect symmetries within the molecule, it can be seen that carbon atoms hybridize as sp 2.3 and not as sp 2 as they would in planar graphene. That is to say, the states change when we increase the number of interactions between them, as is logical if we think that they are self-states of a Schrödinger equation in which there is a potential energy that plays a fundamental role.

Thanks, seems sound.