Inflation & Time: Exploring the FTL Expansion of the Early Universe

[SW VandeCarr]

The FTL expansion of the early universe is explained by the "stretching" of spacetime itself so that a meter stick would be uniformly "stretched".

Two questions:

1. Is the stretching of the meter stick only in the direction of the expansion? Is it sensible to talk about the direction of expansion? Perhaps the meter stick just gets larger in 3 spatial dimensions?

2. Does time also "stretch"? If it does, than lightspeed could be preserved. If so, inflation is may not really be FTL.

 

[mathman]

The FTL expansion of the early universe is explained by the "stretching" of spacetime itself so that a meter stick would be uniformly "stretched".

Space is stretched. Meter stick is not.

 

[Chalnoth]

The FTL expansion of the early universe is explained by the "stretching" of spacetime itself so that a meter stick would be uniformly "stretched".

Faster-than-light expansion is a misnomer. The units of expansion are 1/time. This is not the units of speed, and so it cannot be compared to any speed. It was, however, a rapidly-accelerated expansion.

1. Is the stretching of the meter stick only in the direction of the expansion? Is it sensible to talk about the direction of expansion? Perhaps the meter stick just gets larger in 3 spatial dimensions?

Mathman's answer is good here.

2. Does time also "stretch"? If it does, than lightspeed could be preserved. If so, inflation is may not really be FTL.

Well, there is some ambiguity as to precisely what the time dimension is (depends upon your choice of coordinates). However, with the coordinates that we usually use, which are quite possibly the most intuitive coordinates, there is no expansion of the time dimension.

 

[SW VandeCarr]

Thanks mathman and Chalnoth. However, if measuring rods and time don't expand, how is it that inflation doesn't violate SR? By violating SR, the universe would be younger at the end of expansion than at the beginning, no?

 

[mathman]

SR limit of light speed applies to stuff, not space itself.

 

[SW VandeCarr]

SR limit of light speed applies to stuff, not space itself.

OK. I guess it has to be that way. But this seems to go against the grain of any TOE. Given this dual structure of "stuff" and "space between stuff" any TOE would have to reject a truly unified field, no?

 

[Chalnoth]

Thanks mathman and Chalnoth. However, if measuring rods and time don't expand, how is it that inflation doesn't violate SR? By violating SR, the universe would be younger at the end of expansion than at the beginning, no?

As I said, expansion has units of 1/time. Speed has units of distance/time. So it is simply inaccurate to describe any expansion as super-luminal.

Furthermore, special relativity simply isn't accurate in curved space-time. The major difference is that in curved space-time, you can only compare speeds of objects at a single point: it is impossible to compare the speeds of objects far away from one another. Thus the speed of light limitation in special relativity gets promoted to a slightly different rule in general relativity: it is impossible to outrun a ray of light.

What this means is that if you do the incorrect thing and start subtracting speeds of objects far enough away in an expanding universe, you'll get differences in speed that are greater than the speed of light. This isn't a problem, though, because neither object is outpacing light rays near it. Also note that it doesn't even matter how fast the expansion is: with a fast expansion rate, you won't have to go very far before you start getting nonsensical results from naively subtracting speeds. With a slower expansion, it still happens, but you have to go further.

 

[SW VandeCarr]

As I said, expansion has units of 1/time. Speed has units of distance/time. So it is simply inaccurate to describe any expansion as super-luminal.

Furthermore, special relativity simply isn't accurate in curved space-time. The major difference is that in curved space-time, you can only compare speeds of objects at a single point: it is impossible to compare the speeds of objects far away from one another. Thus the speed of light limitation in special relativity gets promoted to a slightly different rule in general relativity: it is impossible to outrun a ray of light.

What this means is that if you do the incorrect thing and start subtracting speeds of objects far enough away in an expanding universe, you'll get differences in speed that are greater than the speed of light. This isn't a problem, though, because neither object is outpacing light rays near it. Also note that it doesn't even matter how fast the expansion is: with a fast expansion rate, you won't have to go very far before you start getting nonsensical results from naively subtracting speeds. With a slower expansion, it still happens, but you have to go further.

Fascinating! I never considered that measuring the apparent velocity of an object is relative to the distance from observer to object. And this is characteristic of measuring velocity in curved space but not flat space? It makes sense, especially when curvature is pronounced as it would have been during inflation. I would also seem that this not a characteristic of the present universe since it seems very nearly flat.

What do you say to mathman's statement that material objects such as meter sticks don't expand? Even if you accept that only empty space expands, but not "stuff", atoms are mostly empty space, so you would expect atoms to expand even if there were no change in mass.

 

[Chalnoth]

Fascinating! I never considered that measuring the velocity of an object is relative to the distance from observer to object. And this is characteristic of measuring velocity in curved space but not flat space? It makes sense, especially when curvature is pronounced as it would have been during inflation. I would also seem that this not a characteristic of the present universe since it seems very nearly flat.

It is. It's just that the length scales are different. Special relativity holds locally in any small region. The magnitude of the curvature determines just how small. In the present universe, special relativity holds pretty well to quite long distances (millions, perhaps billions of light years), as long as you're not talking about what's going on near very dense objects. During inflation, that distance would have been much smaller than the size of a proton.

What do you say to mathman's statement that material objects such as meter sticks don't expand? Even if you accept that only empty space expands, but not "stuff", atoms are mostly empty space, so you would expect atoms to expand even if there is was no change in mass.

One way to understand this is that the expansion itself is driven by the forces between matter (specifically gravity). A meter stick won't expand partially because the effect of gravity on a meter stick is small compared to the electromagnetic force. Similarly, a galaxy won't expand because the gravitational effect of all the other matter in the universe (the stuff that drives expansion) is small compared to the local gravity.

 

[SW VandeCarr]

One way to understand this is that the expansion itself is driven by the forces between matter (specifically gravity). A meter stick won't expand partially because the effect of gravity on a meter stick is small compared to the electromagnetic force. Similarly, a galaxy won't expand because the gravitational effect of all the other matter in the universe (the stuff that drives expansion) is small compared to the local gravity.

Now I'm a little confused. Isn't the gravitational force only an attractive force? How does gravity drive expansion? I guess anti-gravity would, which I believe is postulated by some to be a characteristic of dark energy. Dark matter, on the other hand, doesn't seem to interact with ordinary matter, so it should not be a factor in holding galaxies together.

 

[Chalnoth]

Now I'm a little confused. Isn't the gravitational force only an attractive force? How does gravity drive expansion? I guess anti-gravity would, which I believe is postulated by some to be a characteristic of dark energy. Dark matter, on the other hand, doesn't seem to interact with ordinary matter, so it should not be a factor in holding galaxies together.

Gravity is only an attractive force for normal matter. It becomes repulsive if the relationship between energy density and pressure is negative for a particular form of matter. A number of hypothetical forms of energy/matter conform to this property, such as certain scalar fields and the cosmological constant.

And dark matter does interact with normal matter. It's just that the only significant interaction is through gravity. This is why we know it's there. We do hope it also interacts very weakly through other means so that we have a chance of detecting it directly and determining what its makeup is.

 

[v2kkim]

It is generally accepted that the universe expands much faster than the speed of light in very far away stars from here, which is consistent with uniform expansion rate everywhere. One thing to make me somewhat sad is that we can not get any info from these very far stars, because their red shift is so huge that virtually those stars are not visible to us, so those remote stars are out of our reach in principle. But still we like to wonder the universe is finite or not ...

 

[Chalnoth]

It is generally accepted that the universe expands much faster than the speed of light in very far away stars from here, which is consistent with uniform expansion rate everywhere.

I really dislike this language, as it is highly misleading. Expansion just isn't something that can be compared to speed: it's got the wrong units. And furthermore there is no one way to compare velocities of things far away in General Relativity. So while one can multiply the expansion rate H by a distance d and get a number greater than the speed of light, this isn't really something that provides any real information as to what the system is doing at any given time.

To illustrate this, I'll go over a couple of questions:
1. Does it mean that light from this object can never reach us? No, because the expansion rate changes with time. Specifically, it tends to decrease, such that if H*d is very close to the speed of light now, that light still may reach us in the far future just because H will be lower then.
2. Does it mean that the object is moving faster than the speed of light? No, because light traveling at the far-away object will always be measured by observers at that object to be moving at the speed of light.

So yeah, I think that stating that things far away actually have a recession velocity greater than the speed of light is quite misleading.

 

[v2kkim]

Sorry for confusing language, but the universe is complicated but interesting.
I agree with you that the relativity holds true, and in general the speed of objects can not exceed 'c', but it is only in general. When it comes to space expansion it can exceed the speed of light, but I do not want to challenge the famous relativity.
My focus is on receding stars and how fast etc here: First we can define distance to remote stars, like 1 billion light yrs, and we can calculate the distance after 1 sec based on space expansion theory, in this sense we can think of expansion velocity, and it can be faster than 'c'.
However people figured out that in space expansion the relativity does not apply, for example, the red shift from remote stars are, in general, caused by space expansion and it does not include relativistic effect, like time dilation, speed of light etc. In short the red shifts from local motion of an object and from space expansion, are calculated differently. In this way we can avoid any disrespect of relativity.
So, if there is a remote star rotating fast a massive black hole, then we need to use 2 different formula for its red shift, one from space expansion and the other from local motion including relativistic effect.
Regarding space expansion speed, anyway, maybe I need more research to get a suitable expression.

 

[Chalnoth]

Sorry for confusing language, but the universe is complicated but interesting.
I agree with you that the relativity holds true, and in general the speed of objects can not exceed 'c', but it is only in general. When it comes to space expansion it can exceed the speed of light, but I do not want to challenge the famous relativity.
My focus is on receding stars and how fast etc here: First we can define distance to remote stars, like 1 billion light yrs, and we can calculate the distance after 1 sec based on space expansion theory, in this sense we can think of expansion velocity, and it can be faster than 'c'.
However people figured out that in space expansion the relativity does not apply, for example, the red shift from remote stars are, in general, caused by space expansion and it does not include relativistic effect, like time dilation, speed of light etc. In short the red shifts from local motion of an object and from space expansion, are calculated differently. In this way we can avoid any disrespect of relativity.
So, if there is a remote star rotating fast a massive black hole, then we need to use 2 different formula for its red shift, one from space expansion and the other from local motion including relativistic effect.
Regarding space expansion speed, anyway, maybe I need more research to get a suitable expression.

What you're talking about here is the recession velocity, not expansion. And it's worth mentioning that we can't ever measure a recession velocity greater than c. We can only infer it from the expansion of the part of the universe we can observe.