Simultaneity in Special Relativity and lorentz transformation

Click For Summary

Discussion Overview

The discussion revolves around deriving the equation for simultaneity using Lorentz transformations in the context of special relativity. Participants explore the relationship between simultaneity in different inertial frames and the implications of time dilation, while referencing educational resources and diagrams.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks help in deriving the equation for simultaneity from Lorentz transformations and mentions a lack of resources that connect mathematical derivations to these transformations.
  • Another participant describes that two spatially-separated events that are simultaneous in one frame will not be simultaneous in another frame after a Lorentz transformation, indicating a fundamental aspect of the relativity of simultaneity.
  • A reference to an arXiv paper is made, which presents a space-time diagram illustrating that simultaneity is not absolute and varies between reference frames.
  • Further elaboration on simultaneity is provided, explaining that events are simultaneous in one frame if they share the same time coordinate, and this condition changes when transforming to another frame.
  • A mathematical expression for the line of simultaneity in the transformed frame is derived, showing that it can be expressed in terms of the coordinates from the original frame.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding and approaches to the topic, with no consensus reached on a definitive method for deriving the equation for simultaneity. Multiple viewpoints and references are presented without resolution.

Contextual Notes

Some participants reference specific educational materials and diagrams, indicating that there may be limitations in the available resources for understanding the derivation of simultaneity in Lorentz transformations.

kevin86
Messages
20
Reaction score
0
How do I derive the equation for Simultaneityfrom one of the lorentz transformation.

If you can help me with that, please help with time dilation as well.

The textbook focused mainly on the mathematically derivation without using the lorentz transformations, and I cannot find any answers online.
 
Physics news on Phys.org
Take two spatially-separated events A and B that are simultaneous in one frame: So, x_A=/=x_B and t_A=t_B. After a Lorentz Transformation, you'll find that in another frame t'_A=/=t'_B.
 
simultaneity

kevin86 said:
How do I derive the equation for Simultaneityfrom one of the lorentz transformation.

If you can help me with that, please help with time dilation as well.

The textbook focused mainly on the mathematically derivation without using the lorentz transformations, and I cannot find any answers online.
Please have a critical look at

arXiv.org > physics > physics/0511062
Physics, abstract
physics/0511062

Illustrating the relativity of simultaneity

Subj-class: Physics Education

We present a relativistic space-time diagram that displays in true magnitudes the readings (date times) of two inertial reference frames clocks. One reference frame is the rest frame for one clock. This diagram shows that two events simultaneous in one reference frames are not compulsory simultaneous in the other frame. This approach has a bi-dimensional character.

Full-text: PDF only
 
kevin86 said:
How do I derive the equation for Simultaneityfrom one of the lorentz transformation.

If you can help me with that, please help with time dilation as well.

The textbook focused mainly on the mathematically derivation without using the lorentz transformations, and I cannot find any answers online.

Try the wikipedia article on the relativity of simultaneity

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

Basically, events are simultaneous if they have the same t coordinate.

Suppose we have two frames: S1, with coordinates x and t, and S2, with coordinates x' and t'.

Then two events are simultaneous in frame S1 if they have the same t coordinate, i.e. t(event1) = t(event2).

Two events are simultaneous in frame S2 if they have the same t' coordinate, i.e. t'(event1) = t'(event2).


The two sets above are not the same.

Because the Lorentz transform gives t' and x' in terms of t and x, one can determine the equation of a 'line of simultaneity' in S2 in terms of x and t.

Let us find the set of events simultaneous with the origin. Then we have

t' = gamma * (t - v*x/c^2) = 0

This means that the equation of t'=0 is t = vx/c^2 , which defines the equation of the "line of simultaneity" of events in S2 in terms of the coordinates (t,x) of S1.

If you work out a more general example, you'll find that all lines of simultaneity have the same slope on the space-time diagram, which by the example above is slope = dx/dt = c^2 / v.
 

Similar threads

  • · Replies 33 ·
2
Replies
33
Views
3K
Replies
8
Views
2K
  • · Replies 54 ·
2
Replies
54
Views
4K
  • · Replies 17 ·
Replies
17
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 101 ·
4
Replies
101
Views
7K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 116 ·
4
Replies
116
Views
10K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K