Lecture 13: Spacetime (International Winter School on Gravity and Light 2015)

What people said

Recommends amilton moreira · 2019-04 · Physics Stack Exchange · on “Is magnetism caused by effect of relativity on interaction between moving charges?”

What we usually call electric field and magnetic field are components of geometric object called Faraday tensor. The object itself is independent of the observer but the components are. This is well explained in this lecture [this video]

Recommends Ben H · 2023-12 · Physics Stack Exchange · on “How is special relativity explained by general relativity?”

Frederic Schuller's lectures on GR reach this question in the middle of 13 - Spacetime [this video] . You can introduce a "light clock" (bouncing photons between mirrors) and see why the proper time of an accelerated observer is shorter than an inertial one, for travel between two events. GR generalizes special relativity by defining a light-cone at every point through the metric tensor $g$. While in special relativity, these cones are the same at every point, in a generic spacetime, they can smoothly change their orientation.

Recommends amilton moreira · 2025-12 · Physics Stack Exchange · on “Weird and short question on scalars and Lorentz transformations”

I depends how lorentz transformations are defined. On manifold lorentz transformation are defined on the tangent space, so the coordinates does not transform. See this [this video]

Recommends Tomás · 2026-03 · Physics Stack Exchange · on “Relation between the axioms of relativistic spacetime and the postulates of relativity”

I am watching the course on general relativity by the WE Heraeus international winter school on gravity and light given by prof. Frederic Schuller, concretely on Lecture 13 on relativistic spacetimes [this video] he provides the following definition of spacetime: A relativistic spacetime is described by a sextuple $ (M, \mathcal{O}_M, \mathcal{A^{\uparrow}}, \nabla, g, T)$ where $ (M, \mathcal{O}_M, \mathcal{A^{\uparrow}}, g) $ is a smooth oriented 4-dimensional Lorentzian manifold, $ \nabla $ is a torsion-free connection and $ T $ is a so called "time orientation", which is a smooth vector field that doesn't vanish nowhere and satisfies $ g(T,T) > 0 $ I understand this definition, the motivation

Cites wiktoria · 2019-09 · Physics Stack Exchange · on “The role of Lorentz tranformations”

My questions concern the role of Lorentz transformations in Special Relativity and General Relativity, as described in this fragment of a series of GR lectures [this video] (lecture 13 of the WE Heraeus International Winter School on Gravity and Light, 2015, by Frederic Schuller). In short, it says that: The role of Lorentz transformations is exactly the same in SR and GR. Namely, Lorentz transformations relate the frames of any two observers at the same point $p \in M$ and as such are the change of the basis of the tangent space at $p$ , $T_p M$ . Therefore, it is conceptually wrong to think of them as acting on the points of the spacetime manifold $M$ as transforming $x^\mu \to x'^\mu = \Lambda

Cites WillG · 2019-11 · Physics Stack Exchange · on “Does spacetime structure in GR break time symmetry?”

In Frederic Schuller's GR lectures [LINK] , he states [this video] as a postulate of GR that spacetime comes equipped with a time orientation that distinguishes the "past" direction from the "future" direction, vaguely speaking. More precisely, the metric specifies two light-cones at each point, and the time orientation selects (at each point) which light cone is the "future" direction. Two questions: Why is this structure necessary, if at all? How does this structure preserve CPT symmetry, if at all? It seems to me that we must pick between one of two problems: This structure is necessary for some intrinsic reason that affects physics, in which case, CPT symmetry does not hold , or This structur

Cites Clemens Bartholdy · 2023-04 · Physics Stack Exchange · on “How is the time defined with paths consistent with the idea that we assign time to frames?”

In 49:34 of this lecture [this video] by Frederic Schuller, it is explained that time is a derived quantity defined through this integral: $$\tau = \int_{\lambda_o}^{\lambda_1} \sqrt{ g(v_{\gamma}, v_{\gamma}) }$$ Where $g$ is the metric, the integral is done over a world line $\gamma$ . time is associated to world lines, but previously, I had learned that time is assigned to frame of reference in some special relativiy textbook. How do these two ideas relate?