Understanding Spacetime Diagrams: Event E & Coordinates in K & K

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Discussion Overview

The discussion revolves around understanding spacetime diagrams, specifically focusing on the representation of an event E as observed from two reference frames, K and K'. Participants explore the geometric relationships and coordinate transformations involved in these diagrams, including the implications of Minkowski geometry versus Euclidean geometry.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about how to determine the time coordinate of an event in a spacetime diagram, questioning why a perpendicular is drawn to the CT axis.
  • Another participant emphasizes the importance of using Minkowski-perpendiculars instead of Euclidean-perpendiculars in spacetime diagrams, noting that Minkowski-perpendiculars relate to hyperbolae.
  • A participant mentions that the diagram in question is sourced from a specific website and recalls a comment about misinformation regarding relativity on the internet.
  • Another participant suggests constructing a standard Minkowski diagram with a 45-degree diagonal for light paths to clarify the relationships between the axes and the coordinates.
  • There is a reference to different definitions and representations of spacetime diagrams in literature, indicating that various sources may present conflicting information.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to spacetime diagrams, with some advocating for the use of Minkowski geometry while others highlight potential issues with specific diagrams. The discussion remains unresolved regarding the best practices for constructing and interpreting these diagrams.

Contextual Notes

Participants note potential limitations in the diagram's representation and the varying definitions found in literature, which may lead to confusion. There is an acknowledgment of the need for clarity in the geometric relationships depicted in spacetime diagrams.

jainabhs
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Hi
I have some very basic doubts on spacetime diagrams.
Please refer the figure attached.
Here in this spacetime figure an event E is shown as observed from K and K'.
K' moves with v with respect to K.
The axis CT is tilted angle alpha following vt, so that any event that occurs at x' = 0 in K' would occur at x = vt in K.
For frame K, to find space coordinate of the event, draw a perpendicular to x-axis.

But to find time coordinate draw a perpendicular to CT. why??
I don't get this and moreover the length of perpendicular gives x'??
Please explain

Abhishek Jain
 

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On a Minkowski-spacetime diagram, you should be drawing Minkowski-perpendiculars... not Euclidean-perpendiculars. Minkowski-perpendiculars to radii are tangents to hyperbolae, just as Euclidean-perpendiculars to radii are tangents to circles.
 
space-time diagrams

morrobay said:
Hello
I had some problems with that exact diagram, its from:
www.colvir.net/prof/richard.beauchamp/rel-an/rela.htm
I recall pervect stating there is a lot of misinformation on relativity on the internet.
I only mention that different space-time diagrams we find in the literature define i the same way the space-time diagrams of the involved events. As I learned from a teacher of mine: There is no advantage without disadvantage. See please for instance a book by Shadowitz devoted to the subject.
 
jainabhs said:
...I have some very basic doubts on spacetime diagrams.
Please refer the figure attached. ...

I agree that the problem seems to be with this particular diagram. Can you construct a Minkowski diagram in the usual way, with a 45-degree diagonal representing a light path? Then a moving reference frame is drawn with x' and ct' axes at equal angles from the diagonal and on opposite sides of it. Just as lines of constant t are parallel to x, lines of constant t' are parallel to x' (and not perpendicular to each other). Likewise, constant x' lines are parallel to t'.

I know this is elementary, but it's worth going through the exercise to see if it clears up your doubts.
 

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