Physics

Physics So Far

[latexpage]

Some Background

  • Classical physics and the universe as we know it was based on…
    • Newtonian mechanics
    • Maxwell’s equations of electricity and magnetism
  • Statistical mechanics was a well-developed descipline used for describing systems with a large degree of freedom
  • Einstein introduced special relativity which was compatible with Mathwell’s equations but changed our understanding of space-time and modified our concept of mechanics
  • Planck hypothesized that electromagnetic energy was always emitted in quanta
    • E = h\nu = \hbar \omega
    • Solved the blackbody radiation problem
  • Much later, deBroglie derived the wavelength for particles: \lambda = h/\rho
  • These discoveries lead to the development of quantum mechanics in which all particles are understood to have both wave and particle “behavior”
    • Research Question: do organisms follow wave-particle duality? If so, the “soul”-unit (probably involving DNA and blood flow) would correspond to wave-like behavior and the (physical) body-unit would correspond to particle-like behavior

Summary of Disciplines

  • Classical Mechanics
    • Objects far larger than 1 \mathrm{\AA}
    • Objects traveling far slower than 3 \cdot 10^8 \mathrm{m/s}
  • Quantum Mechanics
    • Objects \approx 1 \mathrm{\AA}
    • Objects traveling far slower than 3 \cdot 10^8 \mathrm{m/s}
  • Reletivistic Mechanics (RM)
    • Objects far larger than 1 \mathrm{\AA}
    • Objects traveling \approx 3 \cdot 10^8 \mathrm{m/s}
  • Quantum Field Theory
    • Objects \approx 1 \mathrm{\AA}
    • Objects traveling \approx 3 \cdot 10^8 \mathrm{m/s}

Note:

1 \mathrm{\AA} = 10^{-10}  \mathrm{m}  and  the speed of light \approx 2.997 \cdot 10^8 \mathrm{m/s}


The Standard Model – Elementary Particles

Note: a lot of this material is new for me, so if you see anything I have typed of wrong, please feel free to correct me! Once again, I took these notes a few months ago and I cannot remember which website I got the info from, but once I find it I’ll post a link!

Standard Model
Figure 1

Fermions = half-integer spin; obey Fermi-Dirac Statistics

Quarks and antiquarks

  • Properites
    • Participate in strong interactions
    • At any given time an individual quark is “assigned” a particular “color charge”: red, green, or blue
      • Generally, one hadron particle (e.g., a proton) contains three quarks, each of which discretely obtains one of the three “color charges”
      • Within a hadron, any of the three quarks may transition to another color charge
        • A second quark (the one “assigned” the color the first quark transitioned into) will subsequently transition into the original color of the first quark
          • This maintains our “color equilibrium” condition that all three quarks in a given hadron obtain a discrete color charge
            • Note: I know there is more to it than this, and I’ll try to make a blog post dedicated to qarks in the near future. Until then, here is a link to the wikipedia page for quarks.
  • Generations
    1. Up (u), Down (d)
    2. Chrarm (c), Strange (s)
    3. Top (t), Bottom (b)

Leptons and antileptons

  • Properties:
    • No color charge
    • Electroweak charge
  • Generations
    • Electron (\mathrm{e}^-), electron neutrino (\mathrm{\upsilon}_e)
    • Muon (\mathrm{\mu}^-), muon neutrino (\mathrm{\upsilon}_{\mu})
    • Tau (\mathrm{\tau}^-), tau neutrino (\mathrm{\upsilon}_{\tau})

Bosons = integer spin; obey Bose-Einstien statistics

Gauge bosons

  • The spin of a gauge boson cannot equal zero
  • Force carrier particles
  • Four kinds (i.e., four fundamental interactions in nature)
    1. Photon (\mathrm{\gamma}) ⇒ electromagentic interactions
    2. W and Z bosons (\mathrm{W}^+ , \mathrm{W}^-  , \mathrm{ Z}) ⇒ weak interactions
    3. 8 types of gluons (\mathrm{g}) ⇒  strong interactions
    4. Graviton (\mathrm{G}) ⇒ gravity (hypothetical, not proven to exist)

Scalar bosons

  • Spin = 0
  • One kind: Higgs boson

Notes:

  • The antielctron (\mathrm{e}^+) is traditionally called a positron
  • The known force carrier bosons all have a spin of 1, thus they are called vector bosons 
  • The hypothetical graviton has a spin of 2 and is a tensor boson 

The Theory of Everything so Far

If you watch the first video link I posted under my recommended videos at the bottom of the page, you’ll notice one of the two equations the speaker presents in his presentation is the one displayed below. I’m not going to pretend I understand it, but I thought it might be fun for referencing once and a while.

David-Tong-Theory-of-Everything-so-far-equation


Notes I took from General Chemistry (Linus Pauling) book (Chapter 25):

In 1928, Paul Dirac predicted the existence of two types of matter (antimatter and “regular” matter) on the basis of relativistic quantum mechanics

  • Aside: Dirac was the first person to come up with a theory of quantum mechanics compatible with the theory of relativity

When an a particle and its antiparticle collide, they annilate each other and their masses are 100% converted into high-energy light waves or lighter particles with high speeds

  • $E=mc^2$ gives the energy released when a particle and antiparticle annihilate each other to form radiant energy
  • Antiparticles have a charge opposite of their “regular” particle counterpart

Discoveries

1886: E. Goldstein observed a proton

1897: J.J. Thompson discovered the electron

1906: J.J. Thompson classified the proton as an independent particle in 1906

1932: the positron is discovered after observations of interactions between matter and cosmic rays

  • Note: positrons are identical to electrons, except they have a positive charge (rather than a negative charge)
  • Many fundamental particles have been discovered during the study of cosmic rays

1995: Segre et al. discover the antiproton


References

  • I originally took half of these notes in July of 2017, but did not record the sources I used. Once I determine the sources for this information I will post them up (in the time being, most everything is honeslty pretty easy to verify)
  • Pauling, L. (2014). General chemistry. New York: Dover Publications.

Recommended Videos:

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