The Biggest Ideas in the Universe | 9. Fields
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it as a reference for field modes, plane waves and quantum field theory concepts, citing specific timestamps in their questions and comments.
Recommended by 1 people across 1 different months, 2020 to 2023.
What it is
Episode 9 of Sean Carroll's informal 'Biggest Ideas in the Universe' series, covering fields. It briefly treats classical fields, then focuses on quantum field theory and why a quantized field shows up as particles. Carroll presents it as a casual, unpolished lecture for a general audience, though he flags it as challenging.
What people said
Recommends TrentKent6 · 2023-12 · Physics Stack Exchange · on “For a classical scalar field, how can a mode have different energies if the energy is the mode's frequency of oscillation in time?”
For a classical real scalar field $\phi(\vec{x},t)$ of the type: $$\frac{\partial^2\phi}{\partial t^2}-\nabla^2\phi+m^2\phi=0$$ The modes $\phi(\vec{p},t)$ can be obtained by: $$\phi(\vec{x},t)=\int \frac{d^3p}{(2\pi)^3}e^{i\vec{p}\cdot \vec{x}}\phi(\vec{p},t)$$ Each mode satisfies the simple harmonic equation of motion: $$\frac{\partial^2\phi}{\partial t^2}=-(\vec{p}^2+m^2)\phi$$ Therefore each mode solves the equation of a harmonic oscillator vibrating in time at frequency: $$\omega_\vec{p}=\sqrt{\vec{p}^2+m^2}$$ Now, 2 statements: From the last equation it is evident that, for any given $\vec{p}$ , we have a unique $\omega_\vec{p}$ . This $\omega_\vec{p}$ is interpreted as the energy of t
Cites Jeff Bass · 2020-12 · Physics Stack Exchange · on “Reconciling QFT with chemistry?”
@kaylimekay Sure, it's in this video: [this video] at the 1:00:10 mark. He says "even in the vacuum, when you look you can get any answer" which seems to imply that this is not only the case in the vacuum.
Cites Victor Novak · 2021-06 · Physics Stack Exchange · on “Plane waves vs continuous sine waves”
I've started learning QFT from Sean Carroll's lectures, but I had to postpone it until I'll manage my notes)) Meanwhile, 1 question is bugging me: it's about 3D plane waves, which in QFT are analogous to field modes (continuous sine waves) - obtained when one calculates mode composition of some wave packet or another waveform in the Fourier series. So, here ( timecode [this video] ) he's saying that plane waves are characterized by "wave vector" $\vec{k}$ , which gives information about the wavelength of that 3D mode via $\lambda = \large\frac{2\pi}{\text{| }\vec{k}\text{ |}}$ , emphasizing that longer $\text{| }\vec{k}\text{ |}$ gives smaller $\lambda$ (as, of course, can be seen in formula). My