Lorentz tranformations and time slices

  • Context: Graduate 
  • Thread starter Thread starter LegendLength
  • Start date Start date
  • Tags Tags
    Lorentz Time
Click For Summary

Discussion Overview

The discussion revolves around the application of Lorentz transformations in the context of a 'block' view of the universe, specifically how these transformations affect the representation of time slices in spacetime diagrams from different observers' perspectives. The scope includes theoretical considerations of spacetime geometry and the implications of relativistic effects such as time dilation and length contraction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether Lorentz transformations allow for a single 4D block representation of the universe or if separate representations are needed for each observer.
  • Another participant asserts that Lorentz transformations affect both time and spatial axes, suggesting that the entire space is distorted rather than just the time axis.
  • A participant seeks clarification on how time slices deform under Lorentz transformations, specifically whether they remain flat or can take on more complex shapes like parabolas.
  • One participant responds that the warping of time slices is not complex and is linear in nature.
  • Another participant notes that while the same space and metric are used, different observers have different basis vectors, implying a change in perspective rather than a change in the underlying structure.

Areas of Agreement / Disagreement

Participants express differing views on the nature of time slice transformations and whether they can be represented uniformly across observers. There is no consensus on whether the transformations lead to complex warping or if they remain linear.

Contextual Notes

The discussion does not resolve the implications of the Lorentz transformations on the representation of spacetime, leaving open questions about the complexity of time slice deformation and the nature of observer-dependent metrics.

LegendLength
Messages
21
Reaction score
1
I have a question about the way lorentz transformations work with respect to a 'block' view of the universe.

Take our universe as a 3d chart with 2 space dimensions and one time dimension (ignoring the other space dimension for simplicity). You chart it using some "god's eye view" reference frame, or just any single reference frame. So you end up with simultaneous events perpendicular to the time axis for any point in time. Each time slice is just a rectangle showing that moment in time (for the 'god-like' observer).

Now when you apply lorentz transformations for another observer, can you use that same chart? Is it true that the new observer just has a slightly angled time slice (due to the transformation) but still uses the same chart? So their time slices are stretched rectangles compared to the god-like observer?

Or do lorentz transformations change things so much that it would be impossible to represent the universe using a single 4d block (i.e. you'd need a different 4d block for each observer)?
 
Physics news on Phys.org
Lorentz transformations account for time dilation AND length contraction, so not only is the time axis different according to observers in different inertial reference frames, but the spatial axes also changes. Perhaps this video might be helpful for helping you visualize:



So I think It's more of the latter suggestion, it's not just the time axis that is stretched relative to an outside "god-like" observer, but in fact, the entire space that is distorted.
 
Last edited by a moderator:
Thanks that is a good video.

I guess my question is about the way a time slice deforms in the 'worst case'. For the 3d space-time example it would appear the time slices get transformed from a regular rectangle into a less regular rectangle. But would the rectangle have any curves in it or would it stay 'flat'?

For example could you always represent an observer's transformation as parabola or can it get more complex than that (for a 1d space, 1d time example)? When I look at the lorentz transformation formula (with a very untrained eye):

78195e8f63116bf11b2bbef574fbcc25.png


It seems simple enough that it wouldn't 'warp' the time slice in a very complex way. I just wonder what the limit of that warping is.
 
You're right, the warping is really not that complex. It's linear, in fact.
 
It is the same space and the same metric, just different basis vectors for different observers.
 

Similar threads

High School Reciprocal time dilation
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Can We Construct a Coordinate Chart Where Bell Observers Are At Rest?
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Block Universe Theory: Implications & Multiverse
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Derivation of SR's time-dilatation in 1d?
  • · Replies 60 ·
3
Replies
60
Views
6K
High School Calculating Time taken to reach speed with Time Dilation
  • · Replies 18 ·
Replies
18
Views
2K
Undergrad Does SR Length Contraction Halve Space Travel Time?
  • · Replies 17 ·
Replies
17
Views
2K
High School Clocks Vanishing into Thin Air - Gravitational Time Dilation
  • · Replies 27 ·
Replies
27
Views
3K
Undergrad Einstein Definition of Simultaneity for Langevin Observers
  • · Replies 11 ·
Replies
11
Views
3K
Undergrad Gravitational Field Transformations Under Boosted Velocity
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Does the past of an observer still actually exist in their "now"?
  • · Replies 58 ·
2
Replies
58
Views
6K