Fields and Their Particles: With Math

Getting a rough understanding the basics of particle physics — our current understanding of the most elementary aspects of the universe — isn’t that hard.  If you’ve had a class on physics at the advanced pre-university or beginning university level, it’s even easier.  If math terrifies you, try the non-math version of this presentation [sorry, that version won't be ready for a while yet.]  But if you can handle algebra, sines and cosines, and (perhaps not even necessary) the simplest aspects of calculus, then you can learn how fields work and how particles arise.  There’s one leap of faith you’ll need, which involves learning a tiny bit about what quantum mechanics does.  I won’t explain it in math, I’ll just tell you the answers.  But once you accept that one point, everything else will follow.

Here are the articles

1,2. The ball attached to a spring:

3,4,5. Waves (classical formula and equations of motion, and quantum waves)

6,7. Fields and their particles

8. How fields and particles interact with each other

Once you’ve read these, don’t miss How the Higgs Field Works

14 responses to “Fields and Their Particles: With Math

  1. Pingback: A Brief Tour of Resonance | Of Particular Significance

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  3. If people could just realize that [tex]\epsilon_0[/tex] and [tex]\mu_0[/tex] are the essential properties of the space. Just like the lengths are the properties of the space. That is all. But it turned out to be the hardest thing to realize.

    Length, time, [tex]\epsilon_0[/tex] and [tex]\mu_0[/tex], is everything we need to start with, concerning space. To accept them as axioms, for which Maxwell already discovered the fundamental relation:
    The change of a photon position in time is equal to the reciprocal value of the [tex]\displaystyle \sqrt{ \epsilon_0 \cdot \mu_0}[/tex]

    [tex]\epsilon_0[/tex] and [tex]\mu_0[/tex] are something that was discovered, measured, long time ago. They are electromagnetic properties. Of the space.
    Photon also has electromagnetic properties.
    [i]Electromagnetic[/i] is that what [i]attaches[/i] energy and space, what enables the propagation of a photon, what enables photon’s existence in the way it exists – as a linearly propagating EM-energy-oscillation, which has the wavelength (spatial property), and the period of oscillation (time property). The time in which a photon makes one full EM-oscillation is [tex]\displaystyle \Delta t = \Delta s \cdot \sqrt{\epsilon_0 \cdot \mu_0}[/tex].

    Any photon will propagate with the velocity [tex]\displaystyle \frac{1}{\sqrt{ \epsilon_0 \cdot \mu_0}}[/tex], regardless of its energy.
    A photon’s energy is [tex]\Delta E = h \cdot \nu \Rightarrow \Delta E \cdot \Delta t = h[/tex].

    The equation [tex]\Delta E \cdot \Delta t = h[/tex] is the law that each photon has to obey.

    In the above text are given all that is necessary to derive all of the most important equations in physics, using simple infinitesimal calculus, because all of the essential properties of space and of a photon can and do change continually.

    A photons mass, non-inertial mass, is [tex]\Delta m = \Delta E \cdot \epsilon_0 \cdot \mu_0[\tex], that is, it is the measure of coupling, the convolution of photons elementary energy and epsilon-mu-space.

    http://www.thenakedscientists.com/forum/index.php?topic=46034.0

    Best regards,
    Zordim

  4. There is nothing silly about it. The last sound science was the explanation of photoelectric effect. After that, the whole century of silliness passed. Enough with that. Stop embarrassing yourself.

    • thank you for your comment. I’d like to see you build a transistor or a laser or a GPS system with your theory of the world. And meanwhile, what business is it of yours if I embarrass myself? Go run your own website.

  5. The transistor was made with clever experimenting, based upon accidental discovery, and only after it was made and tested, it was also modeled mathematically, using the “in”, “fancy” theory of that time, the QM. That model is as good as Ptolemy-helicoids which described the movement of the heaven-bodies – it describes, but explains nothing. Does not enable any theoretical analysis on which one could rely in order to make modifications/improvements. The same was with the laser. And, concerning the GPS systems, the equations that I have derived, simply, accurately and comprehensibly, from their fundamental, elementary level physical origin, are the equations upon which the future GPS systems will be made, and the engineers will know completely and exactly why and what are they doing when they make them. The kids in high-school will soon, easily, and with understanding, derive the Newton’s principles, relativity equations, Newton’s gravitation law, … .
    And, as an electrotechnics engineer (electronics with telecommunications as the main course of study) and Computer Systems expert, I’ve significantly contributed in making the state-of-the-art thermo-optical DWDM TC devices (nxn SVTs, EDFA GTC, several versions of AWGs, several versions of ROADMs), through which, me and you exchange these messages today. I spent 4 years, 10-12h per day in the test&measurement lab, measuring, testing, evaluating, programming the lasers, power monitors, spectrum analysers, polarizers, robotic-measurement-stages, performing measurements, creating and automating the evaluation procedures,… And I can tell you, not even the q of quantum mechanics was used to develop them. Only experiments, and good old classical physics. Because, practically, QM is of no use. It is only for showing off, when presenting results in journals and on conferences.
    I won’t bother you any more, but, please, stop embarrassing yourself. It is not what a clever man should do.

    • Its not true that QM was used to explain the workings of the transistor only after it was made. There was this PBS documentary in the early 2000s which described, for example, how Bardeen worked out the effect of surface electron states on the resistance at the interfaces between the semiconductors. Besides, even to understand the propagation of electrons in simple metals, as well as the inertness of certain elements and insulators, one needs QM. In fact for a lot of macroscopic properties and phenomenon (magnetism, rigidity of solids, chemical reactivity of elements, etc) one needs to invoke some QM principles even at the qualitative level!

  6. We agree on one thing: one of us is embarrassing himself.

  7. Pingback: Sábado, reseña: “El bosón de Higgs” de Alberto Casas y Teresa Rodrigo « Francis (th)E mule Science's News

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