Electrodynamics of moving bodies - §2: On the relativity of... (again)

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Discussion Overview

The discussion revolves around Einstein's 1905 paper "Electrodynamics of Moving Bodies," specifically focusing on the relativity of simultaneity and the synchronization of clocks in different inertial frames. Participants explore the implications of Einstein's thought experiments and the interpretation of light propagation in moving systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants interpret Einstein's description as indicating that observers in a moving rod cannot determine their motion relative to other systems, allowing them to apply synchronization criteria as if they were at rest.
  • Others argue that Einstein's exposition is unclear, possibly due to translation issues, and emphasize the need for modern interpretations to clarify the concepts.
  • One participant suggests that the synchronization of clocks in the moving frame is complicated by the fact that light takes different times to reach the ends of the rod, leading to a misunderstanding of simultaneity.
  • Another participant highlights that the clocks are synchronized in the stationary system, which affects how they appear to run in the moving frame, challenging the idea of simultaneity.
  • Some participants propose that the light source must be offset in the stationary frame for events to be simultaneous, complicating the synchronization process in the moving frame.

Areas of Agreement / Disagreement

Participants express differing interpretations of Einstein's arguments and the implications for clock synchronization. There is no consensus on the clarity of Einstein's exposition or the best approach to understanding the relativity of simultaneity.

Contextual Notes

Participants note that Einstein's original paper lacks diagrams and clarity, which may lead to misunderstandings. The discussion reflects the complexity of the concepts involved and the evolution of teaching methods over the past century.

Who May Find This Useful

This discussion may be of interest to those studying the foundations of special relativity, particularly in understanding the historical context and interpretations of Einstein's work.

  • #31
What is the "Galilean metrics"?

In the standard formulation of Newtonian mechanics, there's time as an oriented 1D "real line" with the standard topology and space, which is a 3D Euclidean affine manifold. There's not (pseudo-)metrical meaning that would justify to introduce spacetime vectors as is very natural in special relativity leading to Minkowski space, where four-vectors have a very convenient meaning.
 
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  • #32
vanhees71 said:
What is the "Galilean metrics"?
Galilean spacetime is a special case of a Newton-Cartan spacetime
( https://en.wikipedia.org/wiki/Newton–Cartan_theory )
which has
In Newton–Cartan theory, one starts with a smooth four-dimensional manifold M and defines two (degenerate) metrics.
A temporal metric t_{ab} with signature (1,0,0,0) used to assign temporal lengths to vectors on M
and a spatial metric h^{ab} with signature (0,0,0,1) [ used to assign spatial lengths to vectors on M].
 
  • #33
This doesn't look very natural though.
 
  • #34
vanhees71 said:
This doesn't look very natural though.

Your opinion has been noted.
It's an established approach in relativity research,
introduced by Élie Cartan[1][2] and Kurt Friedrichs[3] and later developed by Dautcourt,[4] Dixon,[5] Dombrowski and Horneffer, Ehlers, Havas,[6] Künzle,[7] Lottermoser, Trautman,[8] and others.
The point is...
can we formulate it to explain things and to make predictions that can be tested by experiment?
 
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  • #35
PeroK said:
We have a wagon of length L, as measured in a frame in which it is traveling with speed v to the right.
Is L the rest length of the wagon?
 
  • #36
David Lewis said:
Is L the rest length of the wagon?
No.
 

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