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

In summary, on a Minkowski-spacetime diagram, you should be drawing Minkowski-perpendiculars... not Euclidean-perpendiculars.
  • #1
jainabhs
31
0
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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  • #2
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.
 
  • #3
  • #4
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.
 
  • #5
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.
 

1. What is a spacetime diagram?

A spacetime diagram is a visual representation of space and time, where time is represented on the vertical axis and space is represented on the horizontal axis. It is used to illustrate the relationships between events and the flow of time.

2. What is an event E on a spacetime diagram?

An event E is a specific point on a spacetime diagram that represents a specific location in space and a specific moment in time. It can be thought of as a single occurrence or happening at a particular place and time.

3. What do the coordinates K and K' represent on a spacetime diagram?

The coordinates K and K' represent different frames of reference on a spacetime diagram. K is the reference frame of an observer who is stationary in space, while K' is the reference frame of an observer who is moving at a constant velocity relative to K.

4. How are events and coordinates related on a spacetime diagram?

Events are represented by points on a spacetime diagram, and the coordinates of those points are determined by the specific location and time of the event. The coordinates of the event may differ depending on the frame of reference used to measure them.

5. How can spacetime diagrams help us understand special relativity?

Spacetime diagrams are a useful tool for understanding special relativity because they allow us to visualize how space and time are interconnected and how they are affected by the speed of an observer. By looking at how events and coordinates change between different frames of reference, we can gain a better understanding of the principles of special relativity.

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