Faster-than-light Updated 2024-12-15 +Created 1970-01-01
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In special relativity, it is impossible to travel faster than light.
One argument of why, is that if you could travel faster than light, then you could send a message to a point in Spacetime that is spacelike-separated from the present. But then since the target is spacelike separated, there exists a inertial frame of reference in which that event happens before the present, which would be hard to make sense of.
Even worse, it would be possible to travel back in time:
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Poincaré group Updated 2024-12-15 +Created 1970-01-01
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Full set of all possible special relativity symmetries:
In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.
There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:
  • space and time shifts, because their space origin and time origin (time they consider 0, i.e. when they started their timers) are not synchronized. This can be modelled with a 4-vector addition.
  • their space axes are rotated relative to one another. This can be modelled with a 4x4 matrix multiplication.
  • and they are moving relative to each other, which leads to the usual spacetime interactions of special relativity. Also modelled with a 4x4 matrix multiplication.
Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.
The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.
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Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) Updated 2024-12-15 +Created 1970-01-01
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Talk title shown on intro: "Today's Answers to Newton's Queries about Light".
6 hour lecture, where he tries to explain it to an audience that does not know any modern physics. This is a noble effort.
Part of The Douglas Robb Memorial Lectures lecture series.
Feynman apparently also made a book adaptation: QED: The Strange Theory of Light and Matter. That book is basically word by word the same as the presentation, including the diagrams.
According to www.feynman.com/science/qed-lectures-in-new-zealand/ the official upload is at www.vega.org.uk/video/subseries/8 and Vega does show up as a watermark on the video (though it is too pixilated to guess without knowing it), a project that has been discontinued and has has a non-permissive license. Newbs.
4 parts:
  • Part 1: is saying "photons exist"
  • Part 2: is amazing, and describes how photons move as a sum of all possible paths, not sure if it is relativistic at all though, and suggests that something is minimized in that calculation (the action)
  • Part 3: is where he hopelessly tries to explain the crucial part of how electrons join the picture in a similar manner to how photons do.
    He does make the link to light, saying that there is a function which gives the amplitude for a photon going from A to B, where A and B are spacetime events.
    And then he mentions that there is a similar function for an electron to go from A to B, but says that that function is too complicated, and gives no intuition unlike the photon one.
    He does not mention it, but P and E are the so called propagators.
    This is likely the path integral formulation of QED.
    On Quantum Mechanical View of Reality by Richard Feynman (1983) he mentions that is a Bessel function, without giving further detail.
    And also mentions that:
    (1)
    where m is basically a scale factor.
    such that both are very similar. And that something similar holds for many other particles.
    And then, when you draw a Feynman diagram, e.g. electron emits photon and both are detected at given positions, you sum over all the possibilities, each amplitude is given by:
    (2)
    summed over all possible Spacetime points.
    TODO: how do electron velocities affect where they are likely to end up? suggests the probability only depends on the spacetime points.
    Also, this clarifies why computations in QED are so insane: you have to sum over every possible point in space!!! TODO but then how do we calculate anything at all in practice?
  • Part 4: known problems with QED and thoughts on QCD. Boring.
This talk has the merit of being very experiment oriented on part 2, big kudos: how to teach and learn physics
Video 1.
Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) uploaded by Trev M (2015)
Source. Single upload version. Let's use this one for the timestamps I guess.
Video 2.
Richard Feynman Lecture on Quantum Electrodynamics 1/8
. Source.
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