FTL Expansion of Space: Rapidity & Infinity

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Discussion Overview

The discussion centers on the concept of faster-than-light (FTL) expansion of space, particularly in relation to rapidity and the implications of such expansion within the framework of special relativity and cosmology. Participants explore the nature of recession speeds, the definitions of speed, distance, and time, and how these relate to the expansion of the universe at large scales.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the expansion of space can be considered to have "more" than infinite rapidity, raising questions about how this concept works.
  • Others argue that recession speeds in cosmology are analogous to rapidity rather than traditional speed, suggesting a different interpretation of FTL expansion.
  • A participant questions how faster-than-light expansion avoids the concept of transfinite rapidity, indicating a need for clarification on this point.
  • It is mentioned that light has infinite rapidity, leading to the assertion that there is no faster-than-light expansion in this context.
  • Some participants express the belief that space expansion is indeed faster than light at the largest scales, referencing external sources to support this view.
  • Another point raised is that the definitions of speed in special relativity do not easily apply to cosmological contexts, where curvature of spacetime complicates the definitions of distance and time.
  • A participant explains that expansion is better represented by a scaling factor rather than a speed, illustrating this with an example of increasing distances over time.
  • There is a discussion about the relative motion of distant points in space, suggesting that without relative motion, there is no rapidity or velocity between them.
  • One participant cautions that the common phrasing about FTL expansion can be misleading, as it implies that light can also move faster than light under certain definitions, which complicates the understanding of invariant speeds.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the nature of FTL expansion and rapidity, with no consensus reached on the implications of these concepts within the frameworks of special relativity and cosmology.

Contextual Notes

The discussion highlights limitations in the definitions of speed, distance, and time when transitioning from special relativity to cosmological models, as well as the unresolved nature of how these definitions affect the understanding of rapidity and FTL expansion.

AlexDB9
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If the expansion of space in the macrolevel is faster than the speed of light then it should have "more" than infinite rapidity. How does that work out?

Thanks.
 
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Actually, the recession speeds in cosmology are, in special relativity, analogous to rapidity rather than speed.
 
I understand that, but how faster than light avoids transfinite, or "more" than infinite, rapidity?
 
As light has infinite rapidity, in this view, there is no faster than light expansion.
 
But I thought it is proven, or at least largely believed, that space expansion is faster than light at the greatest scales. Quote from Wikipedia: "Two reference frames that are globally separated can be moving apart faster than light without violating special relativity". So rapidity ceases to be valid here?
 
Since speed = distance/time, the definition of "speed" depends on the definitions of "distance" and "time". The definitions used in special relativity do not generalize easily to the curved spacetimes of cosmology. The definitions used in cosmology are, however, easily applied in special relativity. When this done, speed turns out to rapidity!
 
Expansion is best represented by a scaling factor and not a speed. It acts as a multiplicative factor on distances. If two "comoving" points are separated by a distance of 2 light years at time t, and the distance becomes 2.1 light years at time (t+1year), then the same rate of expansion will take a distance of 200 light years to 210 light years. That's an increase of 10 light years in 1 year, or "faster than the speed of light". But any rate of expansion will have a "faster than light" increase in distance if you start with a large enough distance between points. Of course, the speed of light limit only applies to the relative speed of two objects at the same point in space, not two distant points.
 
As far as I understand it, for two distant points in space, like two far off galaxies, unless there is motion between the two relative to the expansion of space, then there is no relative rapidity or velocity between the two. I.e, you wouldn't have a Lorentz boost between their frames.
 
AlexDB9 said:
I thought it is proven, or at least largely believed, that space expansion is faster than light at the greatest scales.

While this phrasing is common, it's misleading. The easiest way to see how it's misleading is to observe that, by this definition of "faster than light", light itself can move faster than light! That is, if we take a galaxy that is further from us than our current Hubble radius, so that it is moving away from us "faster than light", and look at light emitted by this galaxy in the direction away from us, the galaxy will not "outrun" the light; the light will "outrun" the galaxy, i.e., it will move away from us faster than the galaxy itself does. So nothing actually moves faster than light in any invariant sense; no object outruns a light beam in its local vicinity.
 

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