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  • Richard Feynman called it

  • the jewel of physics

  • Of all of our mathematical descriptions of the universe,

  • this one has produced the most stunningly precise results

  • I'm talking about quantum electrodynamics - the first true quantum field theory

  • Quantum mechanics is perhaps

  • the most unintuitive theory ever devised

  • And yet it's also the most successful in terms of sheer predictive power

  • Simply by following the math of quantum mechanics, incredible discoveries have been made.

  • It's wild success tells us that the mathematical description provided by quantum mechanics

  • reflects deep truths about reality

  • and by far the most successful,

  • most predictive formulation of quantum mechanics

  • is Quantum Field Theory

  • It's the best description we have of the fundamental workings of reality.

  • And the first part of quantum field theory that

  • was derived, Quantum Electrodynamics

  • is the most precise, most accurate of all.

  • Quantum field theory,

  • QFT

  • describes all elementary particles as vibrational nodes

  • in fundamental fields that exist at all points

  • in space and time through the universe

  • quantum electrodynamics - QED

  • provides this description for one such field:

  • the electromagnetic field.

  • the pillars of QED are the description of

  • the behavior of the EM field,

  • and the description of the behavior of the electron

  • by the Dirac equation.

  • We covered the Dirac equation last time,

  • and you really should watch that episode first if you haven't already.

  • Now, before we start thinking about

  • vibrating quantum fields,

  • or even fields at all, let's talk about vibrations.

  • knows that a stretched string vibrates

  • with a certain frequency, when plucked.

  • It also vibrates with an amplitude that depends on

  • how hard you pluck it. A larger amplitude

  • and/or a larger frequency means the

  • vibration carries more energy. At any point in time,

  • every point on a vibrating string, is displaced by

  • some distance from its relaxed (or equilibrium) position.

  • and that displacement changes over time,

  • as the string oscillates back and forth.

  • Guitar strings are 1-dimensional,

  • but we can expand the analogy to any number of dimensions.

  • In 2D, we have a membrane. Like a drum skin.

  • Everywhere on the surface of a vibrating drum skin,

  • there is a displacement from the flat equilibrium state

  • in the up-down direction.

  • The 3D analogy is harder to imagine.

  • Every point in space, has some displacement

  • in some imaginary extra direction.

  • Analogous to, but not the same as a 4th dimension.

  • For example, in a 3D room full of air,

  • sound waves are oscillations in air density.

  • That air density has an equilibrium value,

  • which is just the average density,

  • but in every point in the room,

  • a soundwave can cause air density to oscillate:

  • to higher and lower values.

  • We describe air density as a field,

  • because it has some value everywhere in the space of the room;

  • and that's all a field is,

  • some property that has some value throughout the space.

  • Ok,

  • let's go----quantum.

  • And let's go back to the string.

  • If this were a

  • quantum mechanical guitar string,

  • there's need to be a minimum amplitude

  • for the vibration that depended on its frequency.

  • No vibrations with amplitude smaller than that minimum could exist.

  • And every larger vibration

  • would have to be a whole number,

  • an integer multiple of the smallest amplitude.

  • This is exactly how light behaves.

  • tells you that you can only have one fermion, so electron, quark,

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量子場論的第一堂課(The First Quantum Field Theory | Space Time)

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    qxecrfg297 發佈於 2021 年 06 月 12 日
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