In part I, we discussed the fundamental forces in physics and the dual nature of particles and fields. We also talked about how the elementary particles of the Standard Model are divided into fermions and bosons. In part II, we went over the essential characteristics of the elementary fermion family, and today we cover the elementary bosons. As before, we’re chopping these up into very short mini-lessons in order to combat the problem of people being too busy to read something like this if we’d crammed it all into one long lesson.
Unlike fermions, which have ½ integer spin quantum numbers, bosons always have either zero or integer spins; they do not obey Pauli’s aforementioned exclusion principle; and their statistical distribution throughout space is described by different mathematical functions than the fermions (Young and Freedman 1521). As we mentioned in our previous installment, bosons obey Bose-Einstein statistics, whereas fermions obey Fermi-Dirac statistics, but an actual mathematical explanation of what those distributions entail is beyond the scope of this lesson. In addition to the Higgs boson, which we’ll reserve for the next installment, all the particles which mediate the interactions of the four forces are also classified as bosons (Griffiths 55). The strong interaction is described by a theory called quantum chromodynamics, and is mediated by particles called Gluons (Griffiths 55). There are eight different Gluons (Carroll 296). The weak interaction is mediated by three particles: the neutrally charged Z boson, a positively charged W+ boson, and a negatively charged W- boson (Carroll 296). The electromagnetic force is mediated by the photon, and gravity is mediated by the graviton (Griffiths 56). Although the W and Z bosons have mass, photons, gravitons and gluons are massless (Griffiths 301).
Two additional things are worth noting here. The first is that, unlike gluons, photons and gravitons, the W and Z bosons have mass. This fact was one of the considerations which triggered the development of the Higgs field theory. The Higgs boson, which was discovered experimentally at the LHC at CERN in 2012, is the evidence for the existence of the Higgs field. We’ll cover the Higgs in more detail in the installment after next, but for now just understand that the Higgs field imbues certain particles with mass.
The second is that the graviton is merely hypothetical at this point. It hasn’t been confirmed experimentally. To add insult to injury, our leading theory of gravitation, Einstein’s General Theory of Relativity, has not been successfully re-formulated to conform to the framework of quantum mechanics. In fact, one of the most highly publicized goals of many theoretical physicists is to construct a theory that subsumes all of the successes of both GR and QM in a single framework: a theory of quantum gravity.
Check out my facebook page, The Credible Hulk. I also help run Stop the Anti-Science Movement. In part IV we’ll discuss Hadrons.
*This article was cross posted over at Reaper Nation in affiliation with Tombstone da Deadman and on behalf of Stop the Anti-Science Movement
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Julia · July 21, 2015 at 7:03 am
Harshpotatoes, thanks and also your etxnalapion of the essentially semantic reason for not calling degeneracy pressure fundamental is likely appropriate. However, the trouble remains that it is still insinuated in the framing of the issue that all forces between particles derive from the typical fundamental four: EM, grav, strong, weak. OK, call the exclusion force quantum mechanical , not mediated etc, but it is still ipso facto a force. See, I care about the proper use of language.And BTW if exclusion is a matter of principle (?), what determines the magnitude of the force/s derived from it?Also, food for strange thoughts: nuclei can have integer or half-integer spins (from the combination of effects despite each nucleon being a fermion.) This is basically the idea behind Einstein-Bose condensate (although put forth as the spin of atoms ) but then if so fundamental, why the need to cool the stuff so much? (I mean, to get them to intermingle per se more so than to achieve a single quantum state after all photons pack together without having to be in the same state but pardon any middle-brow confusion.) Messiness caused by the associated electrons?In any case, I don’t see much talk about distribution of fermionic v. bosonic nuclei in various stars at high density; pre-neutronium stage. Yet it seems it ought to affect the shrinkage and collapse of the star.
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Salih · July 20, 2015 at 7:17 pm
Neil,You can use density miearcts in something like 5 very much different ways. One of them is as you’ve described. But you can also take the pure states that are used in state vectors and convert them into pure density miearcts . These are exactly equivalent to the usual state vectors in terms of information content, except that state vectors have arbitrary complex phases that have no physical interpretation. (The physical uses of complex phase are shared with between density miearcts, otherwise they wouldn’t work.) So I wonder what physical significance there would have to be to a DM formulation, considering it is “a way of looking at things” more than an actual situation of thing. If you’re interested in the actual thing (or ontology), rather than mathematical ways of describing activity, then you’re probably interested in Bohmian mechanics. I’ve linked to a paper that discusses density miearcts with respect to Bohmian mechanics which was the first reference I saw on arXiv in 30 seconds, but there are a lot of more complete articles. It’s an active field.From the density matrix point of view, state vectors are a kluge that is done so that a quantum state can be converted from its natural bilinear condition, to an unnatural, but mathematically convenient linear one. The mathematical convenience is linear superposition , which is a principle that allows you to describe a large number of quantum states from taking linear combinations of other states, for example, the usual basis states in spin-1/2 of spin up and spin down.Linear superposition (as opposed to interference) does not translate into a literal experiment that can be performed in the lab. That would be like taking, for example, combining a spin up electron with a spin down electron and expecting to get an electron oriented with spin in the x direction. You will not get this as a result. Instead, you will get two electrons and to model them you will require a more complicated state vector, i.e. ++, +-, -+, as basis. Of course interference works fine in density matrix calculations just like with state vectors.The bilinearity of density miearcts can be thought of as describing a quantum state in terms of how it acts as an operator. The pure density miearcts are projection operators. This makes density miearcts, rather than state vectors, the natural way to define the Consistent Histories interpretation of quantum mechanics (which generalizes QM to quantum cosmology). Read the article on consistent histories at Wikipedia, or do a search for arXiv articles.So density miearcts have an interpretation of quantum mechanics that is devoted to their use and avoids the state vector formalism. At the very least this makes density miearcts the equal of state vectors but for those who prefer quantum mechanics that naturally fits into quantum cosmology, density miearcts are superior. And their sign does not change when you swap particles in them.Mathematically, this comes about because a density matrix is made from copies of the same state vector, a bra and a ket. When you swap two particles, you get a minus sign for the bra and a minus sign for the ket. Since (-1)(-1) = +1, the density matrix is unchanged.
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The Standard Model of Particle Physics: A Conceptual Introduction. By Credible Hulk (of StASM): Part II: Fermions - The Credible Hulk · May 12, 2015 at 10:56 pm
[…] next instalment will cover the elementary […]
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