Posted on 07/18/2015 3:40:12 PM PDT by BenLurkin
Because perturbation theory doesn’t work, it is very hard to predict the consequences of the strong force. One thing we do know is that the binding energy of the strong force which holds the quarks together inside them is responsible for almost all of the mass of protons and neutrons, and hence almost all of the mass of you. Calculations on supercomputers (such as the DiRAC facility in the UK) use “lattice” methods to make calculations when perturbation theory doesn’t work. These involve approximating the space-time continuum by a lattice of discrete points and events; they are now able to make some pretty firm predictions, although calculating the details of pentaquarks remains in the future - the experiment is ahead here.
All the hadrons known until recently consist of either three quarks, or one quark and one antiquark. The reasons for this are nicely explained in a series of articles by Ben Still here (using Lego!). Particles made of two quarks and two antiquarks (known as tetraquarks) have been seen by the Belle experiment and by LHCb in the last few years, but this one - four quarks and one antiquark - is a new kind of beast.
We would like to know is whether pentaquarks are made up of all four quarks and the antiquark clumped together, or whether they consist of a quark-antiquark pair more loosely bound to the other three quarks, as shown in the illustration below.
(Excerpt) Read more at theguardian.com ...
...hold on! I think I may have screwed up on my calculations. I’ll try it again in a few.
The word "pentaquark" means "five quarks". They are hypothetical particles made out of five quarks-or-antiquarks.
The Greek prefix is being used to remember the times when Greece was an advanced country, some 2,000 years ago.
http://motls.blogspot.com/2015/07/pentaquark-discovery-claimed-by-lhcb.html
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Ouch!
Because perturbation theory doesn’t work...
Why would anyone refer to a nonsense idea? “Theories” that don’t work are nothing but blather, no matter how many eggheads talk about them. We’re just talking about guesses based on guesses based on assumptions at this level anyhow.
Duz the fith quark affect your spelllllink? ;-)
Yet we are surrounded in our everyday lives by incredible technology that is based on such "nonsensical theories".
DS9 - The name of the 5th floor lounge in Quark’s bar. but no dabo girls are there.
Er, we aren’t.
I was referring to the theories of nuclear physics and quantum mechanics.
Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional “perturbing” Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as “corrections” to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. ...”
1 Applications of perturbation theory
2 Time-independent perturbation theory
2.1 First order corrections
2.2 Second-order and higher corrections
2.3 Effects of degeneracy
2.4 Generalization to multi-parameter case
2.4.1 Hamiltonian and force operator
2.4.2 Perturbation theory as power series expansion
2.4.3 Hellman–Feynman theorems
2.4.4 Correction of energy and state
2.4.5 Effective Hamiltonian
3 Time-dependent perturbation theory
3.1 Method of variation of constants
3.2 Method of Dyson series
4 Strong perturbation theory
5 Examples
5.1 Example of first order perturbation theory – ground state energy of the quartic oscillator
5.2 Example of first and second order perturbation theory – quantum pendulum
6 See also
7 References
https://en.wikipedia.org/wiki/Perturbation_theory_%28quantum_mechanics%29
Perturbation theory is an important tool for describing real quantum systems, as it turns out to be very difficult to find exact solutions to the Schrödinger equation for Hamiltonians of even moderate complexity. The Hamiltonians to which we know exact solutions, such as the hydrogen atom, the quantum harmonic oscillator and the particle in a box, are too idealized to adequately describe most systems. Using perturbation theory, we can use the known solutions of these simple Hamiltonians to generate solutions for a range of more complicated systems.
For example, by adding a perturbative electric potential to the quantum mechanical model of the hydrogen atom, we can calculate the tiny shifts in the spectral lines of hydrogen caused by the presence of an electric field (the Stark effect). This is only approximate because the sum of a Coulomb potential with a linear potential is unstable (has no true bound states) although the tunneling time (decay rate) is very long. This instability shows up as a broadening of the energy spectrum lines, which perturbation theory fails to reproduce entirely.
The expressions produced by perturbation theory are not exact, but they can lead to accurate results as long as the expansion parameter, say α, is very small. Typically, the results are expressed in terms of finite power series in α that seem to converge to the exact values when summed to higher order. After a certain order n ~ 1/α however, the results become increasingly worse since the series are usually divergent (being asymptotic series). There exist ways to convert them into convergent series, which can be evaluated for large-expansion parameters, most efficiently by Variational method.
In the theory of quantum electrodynamics (QED), in which the electron–photon interaction is treated perturbatively, the calculation of the electron's magnetic moment has been found to agree with experiment to eleven decimal places.[1] In QED and other quantum field theories, special calculation techniques known as Feynman diagrams are used to systematically sum the power series terms.
Under some circumstances, perturbation theory is an invalid approach to take. This happens when the system we wish to describe cannot be described by a small perturbation imposed on some simple system. In quantum chromodynamics, for instance, the interaction of quarks with the gluon field cannot be treated perturbatively at low energies because the coupling constant (the expansion parameter) becomes too large. Perturbation theory also fails to describe states that are not generated adiabatically from the "free model", including bound states and various collective phenomena such as solitons.
Imagine, for example, that we have a system of free (i.e. non-interacting) particles, to which an attractive interaction is introduced. Depending on the form of the interaction, this may create an entirely new set of eigenstates corresponding to groups of particles bound to one another. An example of this phenomenon may be found in conventional superconductivity, in which the phonon-mediated attraction between conduction electrons leads to the formation of correlated electron pairs known as Cooper pairs. When faced with such systems, one usually turns to other approximation schemes, such as the variational method and the WKB approximation. This is because there is no analogue of a bound particle in the unperturbed model and the energy of a soliton typically goes as the inverse of the expansion parameter.
However, if we "integrate" over the solitonic phenomena, the nonperturbative corrections in this case will be tiny; of the order of exp(−1/g) or exp(−1/g2) in the perturbation parameter g. Perturbation theory can only detect solutions "close" to the unperturbed solution, even if there are other solutions for which the perturbative expansion is not valid.
The problem of non-perturbative systems has been somewhat alleviated by the advent of modern computers. It has become practical to obtain numerical non-perturbative solutions for certain problems, using methods such as density functional theory. These advances have been of particular benefit to the field of quantum chemistry. Computers have also been used to carry out perturbation theory calculations to extraordinarily high levels of precision, which has proven important in particle physics for generating theoretical results that can be compared with experiment.
If it moves like a subatomic particle, makes sounds like a subatomic particle and quarks like a subatomic particle, then I say it’s a subatomic particle.
I don’t know. It sounds like witchcraft to me.
God derived the function we discovered as mathematics. Mathematics gave us physics, and thus the keys to the universe. Witchcraft and the like are pure hokum.
Thanks BenLurkin.
ETL: "Yet we are surrounded in our everyday lives by incredible technology that is based on such 'nonsensical theories'. "
Pretty much any wild-*ss*d idea can be called a scientific "hypothesis".
If or when it gets strongly confirmed, then we promote it up to the rank of "theory".
But if, as sometimes happens, further evidence & new ideas strongly falsify a theory, then it's no longer called a "theory", it looses its stripes and gets busted back down to the rank of "hypothesis".
Indeed, after a certain point we don't even call it that, it's just a dumb-*ss*d idea, with a dishonorable discharge from legitimate science.
For an easy example, think "flat earth".
So, all that incredible technology surrounding us is based on confirmed theories, not just hypotheses, much less dumb-*ss*d ideas.
I was referring more specifically to the theory of Quantum Mechanics, where there remains lots of room for interpretation and speculation, yet it still works in terms of building most electronic gadgets today.
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