The discussion centers on the apparent contradiction of how matter can be observed 13.75 billion light years away within the same time frame since the Big Bang. It emphasizes that the universe's expansion is not uniform and that space itself is stretching, causing distant galaxies to recede faster than the speed of light. The concept of "lookback time" is introduced, clarifying that light from these galaxies was emitted when they were much closer than their current distance due to ongoing expansion. The conversation also touches on the complexities of defining speed and distance in the context of general relativity, where traditional definitions may not apply globally. Ultimately, the expansion of the universe and the nature of spacetime lead to nuanced understandings of distance and speed that challenge conventional perceptions.
#1
tesseract7d
2
0
I was reading about cosmology on Wikipedia (as I am won't to do) and have a question regarding the farthest galaxies we see. Supposedly the light coming from them is almost as old as the universe itself. This raises the question, how did matter get 13.75 billion light years away in 13.75 billion years? Is expansion going as fast or faster than light speed?
I was reading about cosmology on Wikipedia (as I am won't to do) and have a question regarding the farthest galaxies we see. Supposedly the light coming from them is almost as old as the universe itself. This raises the question, how did matter get 13.75 billion light years away in 13.75 billion years? Is expansion going as fast or faster than light speed?
We can't really see all the way to the beginning since the early universe was opaque, so not quite 13.7 billion. But that aside, you might take a look at Ned Wright's Cosmology Tutorial:
It's not as simple as saying it's expanding faster or slower than the speed of light. All of space is expanding, so the further away, the faster it recedes from us. Also, the speed of the expansion has not been constant over time. There was a period of very rapid expansion near the beginning.
One kind of "distance" is what you generally hear about: the lookback time. But when the object emitted the light you see, it was much closer than the lookback time. And it is now, in fact, much further than the lookback time. As the light propagated to us, the space itself has expanded, so the light had to go much further to get to us. And in that time, it has receded very significantly past the lookback time.
In fact, parts of the Universe have receded to far greater distances than a mere 13.7 light years in that time.
That's just a very brief explanation from a non-cosmologist. Hopefully I've gotten everything right (and if not, someone please correct me). But Ned's tutorial is a good source if you're interested in this stuff.
The universe is indeed expanding faster than light. Does that prevent us from seeing 'all' of it - No. The portions receeding at greater than 'c' are merely redshifted. This has been known for nearly a century.
#4
Amanheis
67
0
The matter didn't "go there", it always has been there. Right after the big bang, the universe and its contents were pretty homogeneous. Expansion of spacetime can not be thought of as an explosion of matter at a specific point.
Note that this doesn't address the deeper issues of your questions - but Grep already did that.
#5
tesseract7d
2
0
Thanks for the replies. I'm pretty new to cosmology, so you've all been a big help in getting me to understand it, especially Grep.
In special relativity (flat spacetime), there is a standard definition of (spatial) distance that can be applied both locally and globally. In other words, this definition of distance applies to nearby objects, and to objects that are far away. Speed is change in distance divided by elapsed time, so this standard definition of distance can be used to calculated speeds of objects that are near and far. Speeds of objects, near and far, calculated in this way always have the speed of light as their speed limit.
The situation in general relativity (curved spacetime) is far different. Because of spacetime curvature, the definition of (spatial) distance used in the flat spacetime of special relativity can only be applied locally, just as the Earth looks flat only locally. This leads to speeds of nearby objects that limited by the the speed of light, but it say nothing about the behaviour of objects that are far away.
Even though the special relativity definition of distance cannot be applied globally in curved spacetime, there is a standard cosmological definition of distance that is used in the Hubble relationships. Strangely, this cosmological definition of distance can be applied to the flat spacetime of special relativity (Milne universe), and when this is done, it produces a definition of distance (for special relativity) that is different than the standard definition of distance in special relativity!
A different definition of distance gives a different concept of speed, since speed is distance over time. This alternative definition of speed, even within the context of special relativity, produces speeds of material objects that are greater than the standard speed of light! In other words, this definition of speed produces, in both cosmology and in special relativity, speeds that are greater than the standard speed of light.
If v is standard speed in special relativity, and V is cosmological "speed" applied to special relativity, then some corresponding values (as fractions of the numerical value of the standard speed of light) are:
Code:
v V
0.200 0.203
0.400 0.424
0.600 0.693
0.800 1.10
0.990 2.65
Even though there can be different definitions of spatial distance, there is no ambiguity with respect to the prediction of experimental measurements. One just has to keep in mind what definition is being used.
I see that you often quote your post on the definition of speed, which is good. While I agree with everything you write, I'd like to add a little bit:
A different definition of distance gives a different concept of speed, since speed is distance over time. This alternative definition of speed, even within the context of special relativity, produces speeds of material objects that are greater than the standard speed of light! In other words, this definition of speed produces, in both cosmology and in special relativity, speeds that are greater than the standard speed of light.
Maybe you should mention that this definition of "speed" (arithmetic addition of small velocity increments) is well-known in SR as "http://en.wikipedia.org/wiki/Rapidity" ". So "recession speed" is actually a misnomer, as it wrongly implies that "superluminal speeds" are something special.
If it were called for what it is, it'd be clear that a rapidity > c has absolutely nothing to say about superluminal motion.
Further, it would be clear that plugging a rapidity in the doppler formula for speed doesn't work, so this could not be naively misused as a "proof" that cosmological redshift is fundamentally different from doppler shift, as Davis&Lineweaver did so successfully in 2005.
What's left is, as you said, that "speed" and "distance" are tricky concepts if there is spacetime curvature, and that gravity contributes to redshift, too. But, using standard definitions, "small" scale physics (up to some Gly) in cosmology is not fundamentally different from what we know. It is good old boring motion and gravitation.
You can really shock people with such truisms, btw, which is not a good sign.
