Richard Feynman - The Character of Physical Law - Part4 Symmetry in Physical Law (full version)
Why Physics Stack Exchange recommends it
Physics Stack Exchange answerers point people to it for Feynman's intuitive account of Noether's theorem (around 45:25) and for his explanation of how parity violation lets you tell left from right.
Recommended by 4 people across 6 different months, 2012 to 2021.
What it is
Part 4 of Richard Feynman's 1964 Messenger Lectures at Cornell, titled 'Symmetry in Physical Law'. He discusses symmetries of physical laws such as translation, rotation, time and parity, the link to conservation laws, and the failure of left-right symmetry in beta decay. This is a full-length upload of the lecture.
What people said
Recommends Qmechanic · 2012-01 · Physics Stack Exchange · on “What's the interpretation of Feynman's picture proof of Noether's Theorem?”
I) Off-shell vs. on-shell action. What may cause some confusion is that Noether's theorem [LINK] in its original formulation only refers to the off-shell action functional $$ I[q;t_i,t_f]~:=~ \int_{t_i}^{t_f}\! {\rm d}t \ L(q(t),\dot{q}(t),t), \tag{1}$$ while Feynman's proof [1] $^1$ mostly is referring to the Dirichlet on-shell action function $$ S(q_f,t_f;q_i,t_i)~:=~I[q_{\rm cl};t_i,t_f], \tag{2}$$ where $q_{\rm cl}:[t_i,t_f] \to \mathbb{R}$ is the extremal/classical path, which satisfies the equation of motion [LINK] (e.o.m.) $$\frac{\delta I}{\delta q} ~:=~\frac{\partial L}{\partial q} - \frac{\mathrm d}{\mathrm dt} \frac{\partial L}{\partial \dot{q}}~\approx~ 0,\tag{3}$$ with the Diric
Recommends Qmechanic · 2012-01 · Physics Stack Exchange · on “What's the interpretation of Feynman's picture proof of Noether's Theorem?”
For those of you who don't have the book, let me mention that Feynman makes a similar argument approximately 50 minutes into this [this video] Youtube video. Noether's theorem is covered in 45:25-51:27 [this video] .
Recommends Qmechanic · 2012-05 · Physics Stack Exchange · on “The Planck constant $\hbar$, the angular momentum, and the action”
The dimensions of the Planck constant $\hbar$, the action $S$, and the angular momentum, are constrained by the following important facts: A conjugate pair [LINK] of two observables is quantum mechanically related to the Planck constant $\hbar$ via a Heisenberg uncertainty relation [LINK] . A conjugate pair of two variables is classically related to the action $S$ via Noether's Theorem [LINK] , cf. e.g. this [LINK] Phys.SE post. Listen e.g. to Richard Feynman approximately 50 minutes into this [this video] YouTube video. The conjugate variable [LINK] to an angular momentum is an angle (angular position), which is usually treated as dimensionless.
Recommends user10851 · 2014-01 · Physics Stack Exchange · on “Defining left and right independent of a human body?”
Indeed most examples of unambiguously labeling chiral states fall back on having another pre-labeled chiral object on hand. For a long time it seemed as though "left" and "right" were entirely interchangeable labels. This symmetry is known as parity . However it turns out there is a way to distinguish left from right in a fundamental way; parity is not respected in certain circumstances. A very good talk on this topic [this video] was given by Richard Feynman. (See also the corresponding text [LINK] .) Summarizing what he says, consider the beta decay of a neutron: $$ n \to p + e^- + \bar{\nu}. $$ Experimentally it was observed that the electron always comes out with left-helical spin. That is, i
Recommends shai horowitz · 2018-02 · Physics Stack Exchange · on “Why does angular momentum point up for a counterclockwise rotation? Why not down?”
Could you use this information to inform someone not aware of any of our conventions (left right, up down, positive charge negative..) which way is right vs left? I think this will help really show the asymmetries. a good lecture on the topic [this video]
Recommends Qmechanic · 2019-09 · Physics Stack Exchange · on “Fermat's Principle: no first-order change in time?”
By no first-order changes Feynman means that the first-order functional derivative vanishes, or equivalently, the path is stationary. By the way, no first-order changes is a common talking point of Feynman. Listen e.g. to 46:48-48:48 [this video] in the talk The Character of Physical Law, part 4, where he makes similar remarks about the principle of least action [LINK] .
Recommends Andrew · 2021-02 · Physics Stack Exchange · on “Intuitive explanation for why time-translation symmetry implies conservation of energy?”
Feynman has a good discussion of Noether's theorem in his lecture series for a popular audience, "The Character of Physical Law." You can watch it on youtube, starting at 45:25: [this video] This is the closest I have ever seen to an intuitive explanation.
Cites Mark Eichenlaub · 2013-01 · Physics Stack Exchange · on “Translation Invariance without Momentum Conservation?”
Momentum conservation doesn't automatically follow from translation invariance. That only happens because of special features of physical laws, so if you want to prove that translation invariance implies conservation of momentum, you'll need to use some principles of physics to do it. Make up new laws that break those principles and you can indeed have translation invariance without momentum conservation. The principle you need is called "least action". You need to be able to write the physical law in a way so that it's minimizing something, like, for example, light taking the fastest path between points (and minimizing travel time). This is a simple example of what to minimize; others are m