Did universe expand faster than speed of light?

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In Brian Greene's book, Fabric of the Cosmos, he mentions that not enough time has passed for light from some parts of the universe to reach us. (I'm paraphrasing, but I think this is pretty much what he said, and I've heard similar statements from others). How is this possible if the universe started from a singularity, and expanded at the speed of light? My understanding of the nature of space is that any location can be considered the center of the universe, so no point should be beyond the distance that light will have traveled.
 

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  • #2
PeterDonis
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In Brian Greene's book, Fabric of the Cosmos
Just as a caution, this is a pop science book, and pop science books, even when written by scientists, are not good sources if you want to learn the actual science. The particular statement you refer to appears to be ok (see below), but in general pop science books can easily give rise to misconceptions, and Greene's books are particularly prone to this.

not enough time has passed for light from some parts of the universe to reach us.
This is correct; there has only been a finite time for light to travel, so light has reached us from only a finite portion of the universe.

How is this possible if the universe started from a singularity, and expanded at the speed of light?
Neither of these things are true. The universe did not start from a singularity; the singularity is an artifact of a particular idealized mathematical model and is not something that is believed to have actually happened. The "speed of expansion" of the universe is not really well-defined; there are ways to assign a "speed" to the expansion, but any such "speed" will not be the same everywhere, and will certainly not have the value of the speed of light everywhere (or even at the same distance at different times).

My understanding of the nature of space is that any location can be considered the center of the universe
This is not correct. The correct statement is that there is no spatial "center" of the universe.

I suggest reading Ned Wright's cosmology tutorial and FAQ:

http://www.astro.ucla.edu/~wright/cosmolog.htm

It gives a good overview of the standard Big Bang model and addresses the issues discussed here.
 
  • #3
Buzz Bloom
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Hi Sean:

I think what may be confusing you is your assumption
How is this possible if the universe started from a singularity
There are quite a few PH threads that have discussed the concept that the universe did NOT start from a singularity. Any singularity is considered to be not a part of the universe's past, present, or future. Here is one example:

You can find others by searching the PF with the keywords:
cosmology universe singularity

The bottom line is that the best fit model for our universe has always been infinite in size. As we look backward in time, the mass-energy density of the universe increases everywhere and "approaches" infinity as time "approaches" zero. What this means is that time=0 is not included in our cosmology.

Hope this helps.

Regards,
Buzz
 
  • #5
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In Brian Greene's book, Fabric of the Cosmos, he mentions that not enough time has passed for light from some parts of the universe to reach us. (I'm paraphrasing, but I think this is pretty much what he said, and I've heard similar statements from others). How is this possible if the universe started from a singularity, and expanded at the speed of light? My understanding of the nature of space is that any location can be considered the center of the universe, so no point should be beyond the distance that light will have traveled.
Don't imagine the first state of the universe as a point. Imagine everything in the entire universe condensed down into a point. Okay, got it? Now imagine an infinite number of those points all next to each other. Now go, see how our universe grows to its current size, but there is way way waaaaaaay more out there. The universe did not start from a point, it started dense, but not a point.

Also, about the faster than light thing, you aren't thinking of the universe as a whole. Think about a rubber band with two marks on it, now stretch the rubber band. If you double the length of the rubber band from one foot to two in 1 second, the endpoints moved away from each other by one foot in a second, but two points that start only an inch apart, have only separated at a speed of 1 inch / sec. Now scale up to the size of the universe, as the whole thing expands, the further two objects get away from each other, the faster they separate, the ends of the visible universe are moving away from each other far faster than light. There was also a brief moment in the very early universe when the entire universe expanded so rapidly that points right next to each other moved away faster than that.

Nothing can travel THROUGH space faster than light, but space itself can expand with no upper limit on speed.
 
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  • #7
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I appreciate all the replies. Let me see if I am interpreting these answers correctly. I think most of you are saying that if the universe had started from a singularity, then it would be true that no two points could be further apart than the distance light could have traveled. But this is not the case. The universe has existed forever, and there have always been points that were too distant from each other for light to have ever traveled between them. Do I have this right?

So if there was no time zero, then the universe is infinite in a time dimension (at least going back). Wouldn't this mean it is also infinite in spatial dimensions? In other words, if an infinite amount of time has already passed, and light still can't connect two very distant points in the universe, that seems to be the very definition of an infinite spatial dimension.

Thanks for all the replies. I am very interested in the subject and happy to read lengthy wikipedia pages and other links if you want to post them, but I'm hoping someone has a clear way of putting this simply first.
 
  • #8
PeterDonis
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I think most of you are saying that if the universe had started from a singularity, then it would be true that no two points could be further apart than the distance light could have traveled.
No, we're not saying that. The idealized mathematical models in which there is a singularity still have only a finite time for light to travel, so it's still true that there can be regions which have not had enough time for light to travel between them.

The universe has existed forever
No, we're not saying that either. The universe has only existed for a finite time, at least in our best current models.

Please take the time to read the cosmology FAQ and tutorial that I linked to. It will give you a much better background for this kind of discussion.
 
  • #9
PeterDonis
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Don't imagine the first state of the universe as a point. Imagine everything in the entire universe condensed down into a point.
That's not a good description of "the first state of the universe" in the actual models used by cosmologists. In the actual models, we don't know what the "first state" of the universe was, so we don't model it. We only model things back to the inflationary era. The exact model of inflation is still under investigation, but in at least some proposed models (the "eternal inflation" ones), our universe is not all that there is; it started a finite time ago (at least according to "time" in our universe) when a small piece of whatever-it-is-that-is-eternally-inflating underwent a transition and stopped inflating and created a hot, dense, rapidly expanding state that we call the Big Bang. (Note that this state was not a "singularity"; it had high, but not infinite, density, and the matter and radiation that occupies our current observable universe was contained in a very small volume, but not a point.)
 
  • #10
Buzz Bloom
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our universe is not all that there is
Hi Peter:

I suggest that this would be a bit clearer if you inserted the word "observable" before "universe". If you disagree, I would much appreciate an explanation.

Regards,
Buzz
 
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PeterDonis
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I suggest that this would be a bit clearer if you inserted the word "observable" before "universe". If you disagree, I would much appreciate an explanation.
In context (remember I was referring to a particular class of inflationary cosmology models), the statement is true without "observable" inserted. In those models, our universe is just one "bubble" in an eternally inflating "multiverse". (There are similar speculations in string theory.)
 
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  • #12
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Also, about the faster than light thing, you aren't thinking of the universe as a whole. Think about a rubber band with two marks on it, now stretch the rubber band. If you double the length of the rubber band from one foot to two in 1 second, the endpoints moved away from each other by one foot in a second, but two points that start only an inch apart, have only separated at a speed of 1 inch / sec. Now scale up to the size of the universe, as the whole thing expands, the further two objects get away from each other, the faster they separate, the ends of the visible universe are moving away from each other far faster than light. There was also a brief moment in the very early universe when the entire universe expanded so rapidly that points right next to each other moved away faster than that.

Nothing can travel THROUGH space faster than light, but space itself can expand with no upper limit on speed.

Just like a Alcubierre Drive.

Ok, but I hear that an Alcubierre Drive, if it could be made, would travel back in time, because even if it´s the space-time around the ship which is moving, it would still go fast than the Speed of Causality (aka Light Speed).

If going faster than C even if through space-time geometry modifications (Warp Drive, Wormholes, etc) lead to causality violations (to the past), would that mean that matter, travelling WITH the space-time at the moments after the Big Bang orders of magnitude faster than C, would be travelling to the past? What about galaxies on the edges of the universe (which still distance from each other faster than C)?
 
  • #13
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Just like a Alcubierre Drive.

Ok, but I hear that an Alcubierre Drive, if it could be made, would travel back in time, because even if it´s the space-time around the ship which is moving, it would still go fast than the Speed of Causality (aka Light Speed).

If going faster than C even if through space-time geometry modifications (Warp Drive, Wormholes, etc) lead to causality violations (to the past), would that mean that matter, travelling WITH the space-time at the moments after the Big Bang orders of magnitude faster than C, would be travelling to the past? What about galaxies on the edges of the universe (which still distance from each other faster than C)?
No, it just means that the two objects are not causally connected, so discussing one in reference to the other is nonsensical. They might as well be in different universes.
 
  • #14
PeterDonis
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Just like a Alcubierre Drive.
Not really. An Alcubierre Drive requires exotic matter; that's what produces the causality violations.

Ordinary expansion of the universe, even at "faster than light" speeds (there are limitations to this interpretation, which is why I put "faster than light" in quotes) does not require exotic matter, and can take place without any causality violations.
 
  • #15
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I have a question: Are the equations that I learn in school about relativity hold up under these weird circumstance? In every equation that I know of (time dilation, lorenz contraction...) there is a gamma, which would go into imaginary numbers if v > c.

If I try to calculate the length of an object moving away from me at 2c, I would come up with a solution to the Lorentz transformation of exactly i. This makes any discussion of them in relation to each other non-sensical, or are there math tricks to get some sort of meaningful answer? I always considered objects moving apart at that speed to essentially be in different universes from each other's perspective.
 
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Not really. An Alcubierre Drive requires exotic matter; that's what produces the causality violations.

Ordinary expansion of the universe, even at "faster than light" speeds (there are limitations to this interpretation, which is why I put "faster than light" in quotes) does not require exotic matter, and can take place without any causality violations.
can you be more specific why exotic matter produces causality violation? Let's not talk about what we would need to create a warp drive, but simply about the mathematical models for the geometry to be created.

why would the geometry of spacetime of a warp drive create causality violation, but not the expansion of the universe?
 
  • #17
PeterDonis
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can you be more specific why exotic matter produces causality violation?
It's actually not just any exotic matter, but the specific kind that is required for an Alcubierre Drive. The key is that the exotic matter is localized; it basically forms the walls of the "bubble" that the warp drive ship is inside, and which moves faster than light relative to objects in the rest of the spacetime. This can lead to causality violations for the same reasons that FTL travel in general can.

why would the geometry of spacetime of a warp drive create causality violation, but not the expansion of the universe?
Because the expansion of the universe does not involve any kind of localized exotic matter, or any kind of localized "FTL" travel the way an Alcubierre drive does.
 
  • #18
PeterDonis
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If I try to calculate the length of an object moving away from me at 2c, I would come up with a solution to the Lorentz transformation of exactly i.
This is irrelevant to the case of the expanding universe, because there are no global Lorentz transformations in curved spacetime, and the "relative speed" between you and a galaxy far enough away that its recession speed is 2c is not a "relative speed" in the sense that term is used in a Lorentz transformation.

(Strictly speaking, there is no such thing as a Lorentz transformation for ##v > c## anyway. The Lorentz transformation is singular at ##v = c##, so trying to do it for ##v > c## would mean moving "through" a singularity, which isn't mathematically well-defined.)
 
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  • #19
PeterDonis
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it just means that the two objects are not causally connected
This is not correct. Objects far enough away that their current recession velocity from us is greater than c are not necessarily causally disconnected from us. Wikipedia actually has a fairly good discussion of the different types of horizons:

https://en.wikipedia.org/wiki/List_of_cosmological_horizons

The "particle horizon" is the maximum distance an object can be "now" that could have sent us light signals within the age of the universe. The "Hubble horizon" is the distance at which an object's recession velocity from us "now" is c. The latter distance, as noted in the article, is currently 4.2 Gigaparsecs; while the particle horizon distance is currently 14.4 Gigaparsecs, as noted here:

https://en.wikipedia.org/wiki/Particle_horizon
 
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