TYPES OF ENTANGLEMENT (आरादुपकारक & संनिपत्योपकारक) – 2. – Shri Basudeba Mishra
Everything in the universe can be divided into two groups based on whether they are directly perceptible through their distinguishing position, velocity and form (macro – भावप्रत्ययः) or whether their position, velocity and form is indeterminate – hence, indirectly inferred (micro – उपायप्रत्ययः). The indirectly inferred are divided further into two groups: quantum particles (देवाः) and beyond quantum (प्रकृतिलयाः). For example, we can’t isolate quarks (परिमाण्डल्य) or know how they come into being. The quantum particles (देवाः) can have symmetric wave functions (bosons) or anti symmetric (actually non-symmetric) wave functions (fermions). There is no conclusive theoretical basis for the present classification of which particles are Bosons and which particles are Fermions.
Spin is a universal phenomenon of rotation of a particle around its own axis. Fermions are said to have spin values that are integer multiples of 1/2, while bosons are said to have spin values that are integer multiples of 1. Spin behaves a lot like angular momentum. Angular momentum, like velocity, is a vector quantity that can take on only certain values. There is nothing surprising about it. Spin (आवर्त्तनम्) refers to the direction of rotation irrespective of the frame of reference (आवपनम् – सर्वतः आधारभूमी). But angular momentum (भ्रमणम्) relates to the orientation of an object with reference to an origin in any frame of reference (आयतनम् – एकतः आधारभूमी).
Angular momentum can be thought of as an arrow of some length that can point in different directions, but the scientists can’t ever have complete information about the direction. If we measure the projection of the arrow along the z axis, we know the total angular momentum, but it is said that this destroys any information about its projection along other axes. Obviously, the other axes get turned. There is nothing like a fixed angle in rotation.
Everything about angular momentum is also true for spin. In fact the mathematical description of the way spin behaves is so similar to the mathematics of angular momentum that spin and angular momentum can apparently be added together. However, the magnitude of the spin quantum number is an intrinsic attribute of a particle.
Literally spin means a swift whirling motion – revolving quickly and repeatedly around one’s own axis to regain the original appearance. Take a pack of cards. Put the queen of hearts on the table and slowly rotate it. After you rotate 180 degrees, it looks as it was originally. That is half-integer spin. Now take the ace of hearts and rotate. Only after full 360 degree rotation, it would regain its earlier shape. That is integer spin.
Or take an ellipse or an egg and rotate it on its center for 180 degrees. Its appearance is invariant. That is half-integer spin. Now rotate a non-uniform body like a piece of ginger on its center. Only after rotating it for 360 degree, will it appear invariant. That is integer spin. Sometimes it may take more rotation, if it is not symmetric in the third dimension. But what if you rotate a circle on its center? You rotate for any angle – its appearance will be invariant. What about photon? It is the tip of electromagnetic radiation. The concept of mass can be applied to discreet particles. Otherwise we have to deny the concept of weight (mg), a discreet value.
A photon is not discreet. When two planes (electric and magnetic fields) move perpendicular to each other, they intersect in a straight line. When they move in a direction perpendicular to both, it will be the locus of the straight line – a mobile point. That is photon. This is how it carries electromagnetic radiation. How can we rotate a point moving in a straight line? The W bosons are vector bosons and decays very fast. How can you determine its spin? The Higg’s boson is a scalar boson with zero spin. All photons are said to have spin 0. For them “projection” does not make much sense unless we remember that the total projection of spin of all particles as zero. But then any number remain unchanged when zero is added to it. And zero added to zero is zero.
Spin is actually a combination of two attributes, one of which is intrinsic while the other can be gained or lost. Although scientists do not have a deep understanding of what spin is, they have a Mathematical description of how it behaves – in particular, of how the total spin of a system of particles depends on the spins of the constituents. This allows them to compare spin’s behavior to the behavior of other things.
It is said that all electrons have total spin ½, with two possible projection values. The projection can be changed, but the total spin of ½ is fixed for all time. It is part of the definition of an electron. But WHAT is an electron? The proton is radioactive and like the Sun, continuously radiates out or pulsates in two opposite directions like pulsars. This radiation is stopped by the negative charge surrounding it in both directions. The point where these radiations are stopped are called electrons. For this reason, the exact position of an electron can’t be predicted.
In Quantum Field Theory (QFT), a “state” is a configuration describing all the particles in a system (for example an atom). It is said that two identical fermions (like electrons) with identical energies can be swapped, by introducing a negative sign to the state (making it a positron). But if we swap two bosons, there is no change of sign. Adding the plus and the minus signs in the fermion case results in zero, but for bosons, they do add up. This means any state containing two identical fermions of the same energy has zero probability of occurring. Whereas a state with two identical bosons of the same energy has an enhanced probability of occurring.
Consider an example: In beta minus decay, a neutron decays into a proton, an electron, and an antineutrino. Where the electron released goes to? Though a neutron decaying into a proton and an electron can form a hydrogen atom, it is very rare. In beta plus decay, a proton decays into a neutron, a positron, and a neutrino. Where the positron released goes to? Nowhere. They are captured by some other proton or neutron. Beta decay (वहिर्याम) is an interaction starting from the nucleus and ending at shells and orbitals. It is like our changing clothes. We change one cloth and wear another. Someone wears the cloth left by us. Since both electron and positron have identical energies, they are swapped with sign reversed.
Particles with half-integer spin are the matter particles – fermions and the particles with integer spin are those associated with forces – bosons. This description has some interesting fall outs. It is common practice to represent the total angular momentum of a nucleus by the symbol l and call it “nuclear spin”. For electrons in atoms, a distinction is made between electron spin and electron orbital angular momentum. Then both are combined to give the total angular momentum. But the nuclei often act as if they are a single entity with intrinsic angular momentum l. Associated with each nuclear spin is a nuclear magnetic moment, which produces magnetic interactions with the environment.
A characteristic of the collection of protons and neutrons, which are fermions, is that a nucleus of odd mass number A will have a half-integer spin and a nucleus of even mass number A will have integer spin. All nuclei with even atomic number Z and even N have nuclear spin l = 1. For example, iron with an atomic number 26 has six isotopes with atomic mass varying from 50.2315 to 55.8154 GeV/c^2 (A = 54, 55, 56, 57, 58, 60). Of these A = 54, 56, 58 and 60 have spin 0. The isotope with A = 55 has spin = 3/2, while those with A = 57 has spin =½. This suggests that the angular momenta of nucleons tend to form pairs.
The nuclear data for cobalt shows dramatically different nuclear spins. The nuclides with even neutron number shows half integer spins associated with odd protons. For example, for Z = 27, A=57 and 59, the spin = 7/2. Those with odd neutron number show large integer spins associated with the two nucleons which are unpaired. For example, for A=56 the spin = 4 and for A=60 the spin = 5. This shows that the classification of particles with half-integer spin as matter particles – fermions and those with integer spin as forces – bosons is not applicable to the nucleus. This also shows the difference in the mechanism of structure formation between atoms and subatomic particles.
The intrinsic angular momentum of a rigid body or particle or atomic nucleus or a subatomic particle, as distinguished from any angular momentum resulting from its motion, is called its spin angular momentum. The actual angular momentum is a quantum number multiplied by Dirac’s constant. So the classification of particles based on their spin is unscientific.
The quantum mechanical rules for particles that have integer spin are very different from the rules for particles with half-integer spin. All the half-integer particles (e.g., electron, proton, and neutron) are distinguishable from each other: if they are in the same system, they must differ in at least one quantum number. This is not so for the integer-spin particles (e.g., photon, meson, gluon). These can be indistinguishable and have the same quantum numbers including position – though the term position for them has a different connotation.
(to be continued).