Transformations in higher dimensions

Click For Summary

Discussion Overview

The discussion revolves around the concept of transformations between different dimensions, particularly focusing on whether there are equations analogous to Lorentz Transformations that can facilitate such transformations. Participants explore the implications of higher dimensions on time and events, questioning how observers in different dimensions might perceive time and events occurring in the fourth dimension.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant inquires about alternative equations to Lorentz Transformations for transforming vectors between dimensions.
  • Another participant asserts that vectors cannot be transformed between dimensions as the dimension of a vector space is a fixed attribute, suggesting that mappings can be defined instead.
  • A question is posed regarding whether time remains constant when considering events in higher dimensions, particularly in relation to observers moving at different velocities.
  • Several participants express confusion about the concept of an observer in a higher dimension and seek clarification or examples to understand the implications of such a scenario.
  • One participant proposes a hypothetical situation involving a being in the fifth dimension observing events in the fourth dimension, questioning the perception of time in that context.
  • Another participant challenges the terminology used, arguing that we experience all four dimensions rather than just the fourth dimension.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and agreement on the concepts discussed. There is no consensus on the nature of transformations between dimensions or the implications of higher dimensions on the perception of time and events.

Contextual Notes

Participants exhibit uncertainty regarding the definitions and properties of dimensions, as well as the terminology used in the discussion. Some assumptions about dimensionality and experience remain unresolved.

Rahma Al-Farsy
Messages
12
Reaction score
0
Is there an alternative set of equations similar to Lorentz Transformations that transforms vectors from one dimension to a higher or lower dimension?
 
Physics news on Phys.org
It is unclear what you mean, please be more specific. If not, you leave everyone to guess your intention.
 
You can't "transform" vectors from one dimension to another (by which I assume you mean, for example, transforming a vector in 4-dimensional space to a vector in 3-dimensional space). The dimension of a vector space is a fixed attribute of the vector space.

You can define mappings between vectors in one space and vectors in another space. But such a mapping would not be similar to a Lorentz transformation.
 
Okay, thank you Peter. What if you have an event that occurred over a certain period time in the 4th dimension, will the time still stay the same in higher dimensions? Or if an observer in a higher dimension were to have a frame of reference moving at a velocity, v, relative to the event's frame of reference would normal lorentz transformations still apply?
 
Rahma Al-Farsy said:
What if you have an event that occurred over a certain period time in the 4th dimension, will the time still stay the same in higher dimensions?

I don't understand what you mean by this. Can you give a concrete example?
 
Would an observer in a higher dimension experience time the same as a an observer in the 4th dimension? I am new to this topic so I am not sure what sought of example I would be able to give :/
 
I don't understand what you mean by "an observer in a higher dimension". Perhaps you could explain how you came up with this idea, or give a reference to a book or article where you got it?
 
I just came up with the idea so cannot give any references. But what I am trying to say is: we experience everything in the 4th dimension right? What if theoretically a being lived in the 5th dimension, and an event occurred in the fourth dimension. Would it seem faster or slower to him compared to us? Or would it just be the same?
 
Rahma Al-Farsy said:
I just came up with the idea so cannot give any references. But what I am trying to say is: we experience everything in the 4th dimension right? What if theoretically a being lived in the 5th dimension, and an event occurred in the fourth dimension. Would it seem faster or slower to him compared to us? Or would it just be the same?
The problem is that you are using words in ways that don't make sense. No, we don't "experience everything in the 4th dimension", we experience things in all four dimensions. As for what a "being living in the 5th dimension", by which I assume you mean a being living in 5 dimensions, before we can say anything about that, you need to say what you mean by this "5th dimension". What properties does it have? Are you really clear on what a "dimension" is?
 
  • #10
Okay, I understand my question was confused. Thank you anyways
 

Similar threads

Undergrad How Is Intrinsic Curvature Measured in Higher Dimensions Like 4D Spacetime?
  • · Replies 19 ·
Replies
19
Views
2K
Undergrad Lorentz transformations: 1+1 spacetime only
  • · Replies 93 ·
4
Replies
93
Views
8K
High School Newton's Constant in Higher Dim. Spacetimes, Velocity of Light=1
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Lorentz transformation on mode functions
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Time and Lorentz transformations
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Time as a Dimension: Exploring Galilean and Lorentz Transformation
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Lorentz Transformation in One-Dimensional Space
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Derivation of SR's time-dilatation in 1d?
  • · Replies 60 ·
3
Replies
60
Views
5K
High School What Is the Fourth Dimension and How Does It Work?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Coord Transform in de Sitter Space: Phys Significance &Linearity?
  • · Replies 5 ·
Replies
5
Views
2K