The Klein-Gordon and Dirac Equations · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Why relativity forces spin and antiparticles

Science · Quantum & Modern Physics · ages 23-24
Name ______________________   Date ____________

  1. Which pair names the two Klein-Gordon problems?

    • Bottomless negative energies and negative probabilities
    • Too many solutions and too few variables
    • Faster-than-light speeds and imaginary masses

  2. What relation does the Klein-Gordon equation quantize?

    • Half the mass times velocity squared
    • The relativistic energy momentum relation
    • The force equals mass times acceleration rule

  3. First order in time forces the coefficients to be matrices rather than plain numbers.

    Circle one:   True   False

  4. The Stern-Gerlach beam split into two bands. What did that support?

    • Electrons carrying no spin at all
    • Two spin states of the electron
    • Four components of every atom

  5. What do the four Dirac components stand for?

    • Four different particles with unrelated masses
    • Two particles and their two decay modes
    • Particle spin up and down plus antiparticle spin up and down

  6. Why can Klein-Gordon not serve as a one-particle equation?

    • Its probabilities can turn negative
    • It uses too many components
    • It forbids all negative energies

  7. A Dirac spinor lists particle spin up, particle spin down, antiparticle spin up and antiparticle spin down. Type how many components it has.

    Answer: ______________

  8. A student claims Dirac added the positron by hand after 1932. What is the truth?

    • The positron was assumed from the start
    • Antimatter was borrowed from another theory
    • The negative roots predicted it before it was found
LightMySky · lightmysky.comW1-mt_njCW9OEevW-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Why relativity forces spin and antiparticles W1-mt_njCW9OEevW-s1

  1. Bottomless negative energies and negative probabilities · No bottom under the energies and probabilities that turn negative.
  2. The relativistic energy momentum relation · It quantizes E squared equals p squared c squared plus m squared c to the fourth.
  3. True · Numbers cannot anticommute, so matrices must do the job.
  4. Two spin states of the electron · Two bands match spin up and spin down.
  5. Particle spin up and down plus antiparticle spin up and down · Two spin states times particle and antiparticle make four.
  6. Its probabilities can turn negative · A probability must stay nonnegative, and here it does not.
  7. 4 · Two spin states times two kinds gives 4 components.
  8. The negative roots predicted it before it was found · The equation gave negative roots first, and the positron matched them.
Worksheet · LightMySky