Does Hubble's Law violate special relativity?

[Sumo]

I was reading about Hubbles Law on wikipedia and came across this paragraph:

As the formula implies, in very distant objects, v can be larger than c. This is not a violation of special relativity, because the rules of special relativity only apply precisely within a small region: a special-relativistic description of two widely-separated galaxies would in general be incorrect. (Thus special relativity strictly says, not that no speed can be faster than light, but that nothing can move past another object at a speed faster than light).

My assumption is this is because we are not directly measuring the velocities, just the redshifts, SR was formed using rigid measuring devices and we have none in this case. But we could measure them could we not? We have methods of measuring distances that far, could we not find the change in distance over time?

I don't really understand what about SR makes it confined to "small regions", and what exactly defines a small region. If someone could explain that in as simple a way as possible please.

Thank you.

 

[pervect]

I was reading about Hubbles Law on wikipedia and came across this paragraph:

My assumption is this is because we are not directly measuring the velocities, just the redshifts, SR was formed using rigid measuring devices and we have none in this case. But we could measure them could we not? We have methods of measuring distances that far, could we not find the change in distance over time?

I don't really understand what about SR makes it confined to "small regions", and what exactly defines a small region. If someone could explain that in as simple a way as possible please.

Thank you.

The Wikipedia explanation as quoted is a bit murky - Ned Wright's explanation might be helpful:

http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL

Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light.

To paraphrase and simplify this a bit, there are many distance measures in cosmology, one of them is the comoving distance which is the sort of distance used in Hubble's law. The rate of change of this comoving distance with respect to time can be greater than 'c'.

This is not in conflict between SR because the comoving distance is not the same as the distance defined by SR. (There may also be differences in the measurement of time as well).

The comoving distance in cosmology is defined along a curve that has a constant cosmological time, t=now. This curve is not a straight line (more formally, it's not a geodesic). In SR, space-time is flat, and the curve along which distances are measured is always a straight line.

Hubble recession velocities greater than 'c' are not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and cosmological time is not the same time as the time in SR unless one is stationary with respect to the CMB.

The point here is that space-time for the universe as a whole is not flat, while SR deals only with flat space-time. (GR, which deals with curved space-time, is required to understand cosmology fully.)

The curvature effects of space-time however, are not important in a small region, much like the manner in which the spatial curvature of the Earth's surface can be ignored, *if* one considers a small enough region. For a large region, though, the curvature effects make a large difference to the geometry, and one cannot get sensible results without taking them into account.

 

[cos]

I once read that according to SR if we are looking at a galaxy that is moving away from us at .75c and another galaxy that is moving away from us in the opposite direction also at .75c we cannot add their velocities and conclude that they are moving away from each other at 1.5c however it seems that observers located in either of those galaxies would be allowed to reach this conclusion.

Bill

 

[Chris Hillman]

Generic warning about information on the web

I was reading about Hubbles Law on wikipedia

Unfortunately, Wikipedia articles are inherently unstable and unreliable since they can be edited by, you know, anyone at any time. Thus WP cannot be used as an information resource. I recommend using WP articles to gather possible search phrases to Google on at authoritative websites such as the website of Ned Wright already cited. Similar remarks hold, unfortunately, for some popular magazines such as New Scientist.

Be careful, Sumo, the number of crank websites dealing with cosmology greatly outnumbers the websites offering scientifically accurate information. A good rule of thumb is that websites officially associated with an astronomy or physics department at a good research university will be much better sources of information than websites put up by someone who may not have expert knowledge or may even seek to misleadingly promote fringe or cranky views as "accepted science" [sic].