# Hubble's Law: Exploring Beyond the Speed of Light

• Thrice
In summary: So I wouldn't be interested unless your wiki had security features and limited write access.I'm not sure about security features but we do have limited write access - on a per-page basis. If you want to edit something, ask on the talk page, and it's more or less OK, we'll let you. I'm not sure if that's good enough for what you want.My general idea for the wiki is to only have articles on physics, math, and their history. OK, so more like a textbook than a wiki. And a forum for discussing the articles. And a place to store data such as interesting problems, journals, people, etc.In summary, the conversation discusses the concept of recession velocities of galaxies and
Thrice
Since the galaxies are receeding with velocity propotional to distance, I'm curious what happens at or beyond the point where the velocities approach the speed of light & how that's possible. One source I looked at said the galaxies are invisible. Another source said the spacetime is what's stretching & there's no speed of light limit to that. Yet another source said the concept is incoherent because you can't compare vectors at different points in spacetime (in different tangent spaces).

I don't know much about differential geometry yet, but I do know you physicists need to get your junk together. What is going on? Some math please.

Try Ned Wright's cosmology FAQ, http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL

tutorial http://www.astro.ucla.edu/~wright/cosmo_01.htm

and Lineweaver & Davis "Expanding confusion" paper.

http://arxiv.org/abs/astro-ph/0310808

The short answer is that it is not possible to compare vectors in a coordinate independent manner at different points in space-time. However, there is a coordinate dependent defintion of distance that most cosmologists use, comoving distance. The rate of change of this distance with respect to cosmological time defines a sort of velocity. This is what goes into Hubble's law.

So there is a way of defining the velocity, but one should be aware that this defintion is a) coordinate dependent and b) not compatible with special relativity.

What's particularly enlightening is that the "comvoing distance" does NOT reduce to the familiar notion of distance in SR in the limit of an expanding universe with a very low mass density.

So cosmologists do have something in mind when they talk about recession velocities and the "distances" of distant objects, but it's based on a particular coordinate system that's convenient and common, and it's also not SR-friendly.

Thanks, pervect. I'll work through that.

Incidentally I don't know if this is the right place to ask this, but would you guys be interested in starting a relativity wiki? Something along a more pedagogical approach, almost textbook-like. I can probably figure out how to do it in a few days.

Ed Harrison in his book "Cosmology, the Science of the universe" takes the point of view that expansion is not limited by c as would be the case in SR - the Nebula are being wafted outwardly by expansion - it is space itself that is stretching rather than galaxies moving wrt to space - so in this sense there is no limit to the velocity since we are not dealing with relationships between relatively moving inertial frames. I think this is consistent with what pervect said

I wouldn't be terribly surprised if you have some more specific questions after doing some reading.

As far as the wiki goes - you are talking about a wiki in the generic sense, not Wikipedia, right? I rather doubt I'll find the time, I havaen't even been keeping up with what I really want to do for the Wikipedia wiki.

Hmm GR locally reduces to SR, right? So roughly would it be accurate to say the reason is because the metric in GR can't always be split into a "space" and "time" with definite meaning?

That other post on the front page reminded me that I hadn't posted a reply here. Incidentally, I think http://en.wikipedia.org/wiki/Distance_measures_(cosmology)" page is quite useful for illustrating the different distance measurements.

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GR reduces to SR locally. This means that if you have two bodies that are at the same point in space-time, or very close to each other, that you can determine their velocities using the techniques of SR.

Velocities are mathematically represented by vectors. If the two bodies are distant, you have to define a mechanism for transporting a vector at one point of the manifold to another. As I remarked in another recent post, the tangent spaces are different at distant points of the manifold, this is what causes the difficulty.

So an extended discussion is needed to define exactly how a velocity "here" is transported to a velocity "there" in GR. This involves issues like chosing to use parallel transport vs Fermi-Walker transport vs other possibilities, and what curve connecting the two points to use to perform the tranpsort.

Relativity wiki?

Thrice said:
Thanks, pervect. I'll work through that.

Incidentally I don't know if this is the right place to ask this, but would you guys be interested in starting a relativity wiki? Something along a more pedagogical approach, almost textbook-like. I can probably figure out how to do it in a few days.

Some other disaffected former Wikipedians and myself discussed something like that, but our concern was with rectifying the absence of effective quality control at Wikipedia by controlling write access to qualified editors, allowing signed essays, and introducing other innovations. So, I wouldn't be interested unless your wiki had security features and limited write access.

Your wiki should probably use MediaWiki since this seems to currently feature the most convenient implementation of latex-like pseudocode for mathematical markup.

Chris Hillman said:
Some other disaffected former Wikipedians and myself discussed something like that, but our concern was with rectifying the absence of effective quality control at Wikipedia by controlling write access to qualified editors, allowing signed essays, and introducing other innovations. So, I wouldn't be interested unless your wiki had security features and limited write access.

Your wiki should probably use MediaWiki since this seems to currently feature the most convenient implementation of latex-like pseudocode for mathematical markup.
Well I've started the wiki since I made this post. I have a thread on it https://www.physicsforums.com/showthread.php?p=1207342", see what you think.

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Chris Hillman said:
Some other disaffected former Wikipedians and myself discussed something like that, but our concern was with rectifying the absence of effective quality control at Wikipedia by controlling write access to qualified editors
I've ran a wiki before & I've become convinced that's really not worth it. It simply kills your wiki unless you already have a very large audience. And quality control is quite easy to do with something this size. Of course i'd be willing to implement it if most everyone disagrees.

Chris Hillman said:
allowing signed essays, and introducing other innovations.
The first is already (sort of) up & any suggestions on the second are appreciated.

## What is Hubble's Law and how does it relate to the speed of light?

Hubble's Law states that the farther away a galaxy is from us, the faster it is moving away from us. This is because the universe is expanding. It relates to the speed of light because the speed of light is the fastest possible speed in the universe, and galaxies are moving away from us at speeds that are faster than the speed of light.

## How was Hubble's Law discovered and by whom?

Hubble's Law was discovered by astronomer Edwin Hubble in the 1920s. He observed that galaxies appeared to be moving away from us at a rate that was proportional to their distance from us. He later developed a mathematical formula to describe this relationship.

## What is the significance of Hubble's Law in our understanding of the universe?

Hubble's Law is significant because it provides evidence for the expanding universe theory, which states that the universe is not static but is instead constantly expanding. This has led to the development of the Big Bang Theory, which is the most widely accepted explanation for the origins of the universe.

## Can Hubble's Law be used to measure distances in the universe?

Yes, Hubble's Law can be used to measure distances in the universe. By measuring the redshift of light emitted from distant galaxies, astronomers can calculate the distance of those galaxies from us using Hubble's Law. This has allowed us to create a more accurate and detailed map of the universe.

## Is there any evidence to suggest that Hubble's Law may not hold true in all cases?

Yes, there is evidence to suggest that Hubble's Law may not hold true in all cases. For example, the expansion of the universe appears to be accelerating, which is not predicted by Hubble's Law. This has led to the development of theories such as dark energy to explain this discrepancy.

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