Is Time a Mobius Dimension in Relativity Theory?

  • Context: Graduate 
  • Thread starter Thread starter Neo
  • Start date Start date
  • Tags Tags
    Dimension Time
Click For Summary

Discussion Overview

The discussion explores the concept of time as a "Mobius dimension" within the framework of relativity theory, examining its potential non-linear topology and directional properties. Participants engage with theoretical implications, mathematical interpretations, and the relationship between time and space.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that time could be conceptualized as a "Mobius dimension," drawing parallels between the properties of a Mobius strip and the characteristics of time in relativity.
  • Others question the relevance of Mobius coordinates to real-world applications and suggest that while the idea is intriguing, it may lack practical significance.
  • A participant argues that time in Minkowski space is linear and does not resemble a Mobius strip, emphasizing that the Mobius strip is a compact manifold, unlike the infinite nature of time.
  • There is a discussion about the nature of time during the Big Bang and whether it could have expanded differently in relation to space, suggesting a continuum between the two.
  • Some participants clarify misunderstandings regarding the relationship between speed, time dilation, and reference frames in relativity, asserting that time behaves differently depending on the observer's frame of reference.
  • Concerns are raised about the use of terms like "non-linear topology" and "one-way linear," with a participant suggesting that these phrases lack meaning in a mathematical context.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the concept of time as a Mobius dimension, with no consensus reached on its validity or relevance. Disagreements arise over the interpretation of time in relativity and its mathematical representation.

Contextual Notes

Limitations include the ambiguity of terms used in the discussion, the dependence on definitions of topology and manifolds, and unresolved mathematical interpretations of time's properties in relation to the Mobius strip.

Neo
Messages
71
Reaction score
0
Is it possible for time to be a "Mobius dimension," with its non-linear topology and simultaneous one-way linear direction, as described by relativity theory?
 
Physics news on Phys.org
What do you mean by Mobius dimension? Is it a reference to Mobius coordinates?
 
I imagine some mathematician has probably solved the field equatiosn for a metric using Mobius coordinates. AFAIR I don't think it was interesting though, as it doesn't seem to have relevance to the real world.

I thought about that a bit as an undergrad, kinda in the 'wouldn't this be cool'.
 
selfAdjoint said:
What do you mean by Mobius dimension? Is it a reference to Mobius coordinates?

Well imagine a "Mobius dimension" based on the concept of a Mobius strip. What are the properties of the strip? Namely:

1. Non-linear topology
2. One-way linear direction due to only one "side"

Now time based on relativity:
1. Non-linear topology due to time-space curvature
2. One-way linear direction due to entropy

Is it possible that time is a "Mobius dimension"?
 
Haelfix said:
I imagine some mathematician has probably solved the field equatiosn for a metric using Mobius coordinates. AFAIR I don't think it was interesting though, as it doesn't seem to have relevance to the real world.

What is AFAIR? As far as I remember? (Sorry, I'm new here) Theoretically, it corresponds to reality fairly accurately. The shape of time based on relativity is undeniably quite similar to that of a Mobius strip. Do you disagree?
 
Neo said:
What is AFAIR? As far as I remember? (Sorry, I'm new here) Theoretically, it corresponds to reality fairly accurately. The shape of time based on relativity is undeniably quite similar to that of a Mobius strip. Do you disagree?

The R in AFAIR could be remember or recall.

Time in relativity does not resemble a mobius strip at all. The mobius strip is a compact manifold - basically that means it's finite so every infinite point set on it converges. But time in Minkowski space in linear, and contains nonconverging point sets. As for the twist, the relationship of time to space in relativity is different than a mobius twist.
 
Time grows linearly right now. Did it always grow linearly? What about during the Big Bang? Could it be possible that time expanded faster (the opposite of time dilation) at the time of explosive spatial growth if time is intricately connected to space in an inseparable continuum?

Take Einstein’s (Temporal) Relativity Theory:
The faster something is moving, the "slower" time is moving for it. So if space is expanding explosively, is time growing because it is in a continuum with space or is it dilated because space is moving so quickly?
 
Neo said:
Take Einstein’s (Temporal) Relativity Theory:
The faster something is moving, the "slower" time is moving for it.

This isn't so. Something is moving faster only with respect to something else. Possibly by moving faster with respect to one thing, it's moving slower with respect to something else. And every massive object experiences its own rest frame, in which it isn't moving at all. And the time of this object, as physically experienced in these three frames is different in each one. In the rest frame time is not dilated at all.

It is these facts, and not mobius twists, that you should strive to learn about relativity.
 
Also, please try to learn some mathematics while you're at it. The phrases "non-linear topology" and "one-way linear" are meaningless. The Mobius strip is a compact, non-orientable manifold. That's really all that one can say about it.

Off to Theory Development this one goes...

- Warren
 

Similar threads

High School Is imaginary time a fourth dimension?
  • · Replies 13 ·
Replies
13
Views
2K
High School What Is the Fourth Dimension and How Does It Work?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Does string theory falsify the theory of special relativity?
  • · Replies 19 ·
Replies
19
Views
3K
High School On the four dimensions of special relativity
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Which theory of time is the most evidence-based?
  • · Replies 32 ·
2
Replies
32
Views
4K
High School Is Einstein's Space-Time Theory Overfitted or Simply a Visualization Tool?
  • · Replies 29 ·
Replies
29
Views
3K
Undergrad How can the Universe know when you change directions?
  • · Replies 42 ·
2
Replies
42
Views
4K
Undergrad Spacetime expansion - time dimension expansion
  • · Replies 48 ·
2
Replies
48
Views
4K
Undergrad Could spacetime be non-orientable?
  • · Replies 49 ·
2
Replies
49
Views
5K
High School Is time a unique dimension or a constant across all dimensions?
  • · Replies 14 ·
Replies
14
Views
15K