Age vs. Size of universe.

[Archosaur]

Hi all,

This is my first endeavor into the astronomy forum.

I have a question, regarding three things I think I know about the universe.

1. the universe started as a singularity.
2. it has expanded to 78 billion light-years across.
3. it did that in only 13.7 billion years.

How did it do that without things moving faster than the speed of light, relative to other things?

I'm sure someone has answered this Q before, but I couldn't find anything. Feel free to direct me to another thread instead of answering this Q again.

[DaveC426913]

Special Relativity prohibits objects moving through space faster than c. It does not prohibit space expanding faster than c.

[Archosaur]

So, relative to space, the galaxies aren't moving faster than c, but are they moving faster than c relative to us?

[DaveC426913]

So, relative to space, the galaxies aren't moving faster than c, but are they moving faster than c relative to us?
Yes. Locally, they are not moving faster than c. In fact, locally, they can be considered at rest, depending on what you use as a reference point (such as their local cluster).

Galaxies distant from us are receding - due to the expansion of space - faster than c.

[Archosaur]

So, since light moves through space at a constant velocity c, regardless of the velocities of the source or the observer, then once a galaxy is receding faster than c, relative to us, it should "disappear", right?

If that's the case then "curtain" around us, outside of which no emitted electro magnetic radiation will ever reach us, right?

[DaveC426913]

So, since light moves through space at a constant velocity c, regardless of the velocities of the source or the observer, then once a galaxy is receding faster than c, relative to us, it should "disappear", right?

If that's the case then "curtain" around us, outside of which no emitted electro magnetic radiation will ever reach us, right?
Right.

It is called "the observable uiniverse" and it forms the boundary of what science will address.

You are remarkably clever. I hope you are making good use of it.

[Chronos]

This is where time dilation comes into play. We routinely observe galaxies that were receding faster than c when photons now reaching us were emitted. They just take longer to reach us. As space stretches, it also stretches the wavelength of light passing through it, resulting in redshift - aka known as time dilation.

[Wallace]

Note that the notion of 'space expanding' is inherently co-ordinate dependant, that is to say, it is not a physical process or physical law, but a notion that has relevance for a particular (and very usefull) co-ordinate system. Nothing anyone has said here is incorrect, but the statements are correct only from a certain point of view (albeit a very usefull point of view). Just be cautious about thinking too literally about the expansion of space being a physical or causative process.

A consuquence of the important property of general covariance that GR obeys is that you cannot uniquely describe what 'space' does, you can only unambigously talk about space-time, and even then the theory forbids the specification of any unique set of co-ordinates.

[DaveC426913]

Note that the notion of 'space expanding' is inherently co-ordinate dependant, that is to say, it is not a physical process or physical law, but a notion that has relevance for a particular (and very usefull) co-ordinate system. Nothing anyone has said here is incorrect, but the statements are correct only from a certain point of view (albeit a very usefull point of view). Just be cautious about thinking too literally about the expansion of space being a physical or causative process.

A consuquence of the important property of general covariance that GR obeys is that you cannot uniquely describe what 'space' does, you can only unambigously talk about space-time, and even then the theory forbids the specification of any unique set of co-ordinates.

Cool. So what might an alternate valid way of viewing the expanding universe be?

[Wallace]

Well, for instance, if you transform the usual FRW metric into a form that is a conformally related to the Minkowski metric then you have a model in which everything (say all galaxies) are moving away from wherever your chosen origin is, and all redshifts can be thought of as being purely doppler shifts due to the relative velocities. There is no 'expanding space' in such a model, yet it describes the exact same underlying physical system as the FRW metric. Remember that velocity is the change in distance divided by the change in time. Since neither distances or times are unique in GR (they depend on how you've defined your co-ordinates) the 'velocity' of a distant galaxy actually has no unambigous meaning. That's why you can choose a co-ordinate system in which the co-ordinates themselves encode all the physics that gives you the redshift. Incidentaly this is also why no one need get their knickers in a knot about galaxies recceeding faster than light. It it purely to do with how velocities are defined in the FRW system. In the conformal metric, there are no super-luminal velocities. Just by chaning co-ordinates we have apparently turned super-luminal motion into sub-luminal motion! The lesson is that co-ordinate velocities shouldn't be compared with c in that way. There never was super-luminal motion that needed to be explained away by an ill defined notion such as 'space can expand at faster than c'.

I don't suggest that such a metric is more usefull than the FRW one we use, far from it! I just point out that there is no physical basis for expanding space that appears when you use the FRW system. That's not to say it is an unhelpful concept, but just one that needs to be treated with caution. The idea that galaxies are at rest in an expanding background has a lot of utility, you just have to always keep in mind that this is just one particularly useful co-ordinate description, rather than being physically true in an unambigous way. By all means continue think about the expanding universe in this way, and explaining it to others in this way, just remember though that you are explaining something that is at best a metaphor.

[DaveC426913]

Well, for instance, if you transform the usual FRW metric into a form that is a conformally related to the Minkowski metric then you have a model in which everything (say all galaxies) are moving away from wherever your chosen origin is, and all redshifts can be thought of as being purely doppler shifts due to the relative velocities. There is no 'expanding space' in such a model, yet it describes the exact same underlying physical system as the FRW metric. Remember that velocity is the change in distance divided by the change in time. Since neither distances or times are unique in GR (they depend on how you've defined your co-ordinates) the 'velocity' of a distant galaxy actually has no unambigous meaning. That's why you can choose a co-ordinate system in which the co-ordinates themselves encode all the physics that gives you the redshift. Incidentaly this is also why no one need get their knickers in a knot about galaxies recceeding faster than light. It it purely to do with how velocities are defined in the FRW system. In the conformal metric, there are no super-luminal velocities. Just by chaning co-ordinates we have apparently turned super-luminal motion into sub-luminal motion! The lesson is that co-ordinate velocities shouldn't be compared with c in that way. There never was super-luminal motion that needed to be explained away by an ill defined notion such as 'space can expand at faster than c'.

I don't suggest that such a metric is more usefull than the FRW one we use, far from it! I just point out that there is no physical basis for expanding space that appears when you use the FRW system. That's not to say it is an unhelpful concept, but just one that needs to be treated with caution. The idea that galaxies are at rest in an expanding background has a lot of utility, you just have to always keep in mind that this is just one particularly useful co-ordinate description, rather than being physically true in an unambigous way. By all means continue think about the expanding universe in this way, and explaining it to others in this way, just remember though that you are explaining something that is at best a metaphor.

Sooooo...

Rather than space expanding, it could be time contracting?

[Wallace]

Rather than space expanding, it could be time contracting?

Potaytos and Potartos....the point is that it doesn't matter and there is no difference either way! Neither 'space' or 'time' have unique meanings beyond our local reference frame, so there is no unique way to talk about those concepts, they depend on entirely arbitrary choices in how you construct your co-ordinate system. As I say, the co-moving co-ordinates that the FRW metric is usually written in are far and away the most useful and easiest to work with, just don't get carried away with things and imbue properties of that co-ordinate system with physical reality.

So when you say 'Rather than space expanding, it could be time contracting?', you first have to understand what the 'it' you speak of is referring to? If by 'it' you mean 'the cause of cosmological redshift' then neither answer is wrong or right, it depends on the co-ordinates you use. There is no mystery, paradox or problem with this, it's just a consuqence of general co-variance.

[Archosaur]

You are remarkably clever. I hope you are making good use of it.

Thanks, Dave. This really did make my day. I'm hoping to become a physics teacher. Anything on our scale comes pretty easily to me, but I'm fairly new to quantum mechanics and astrophysics.

Anyway, I had a couple more questions about relativity. I hope they don't make you revoke your comment :)

1. Shouldn't we be able to look back at earlier stages of the universe, but see them very very red-shifted? Maybe as radio waves, by this point? What is the lowest frequency wave we can detect without interference? How long ago would that represent? We'd obviously do any detection from outside our atmosphere.

2. I understand how we detect the expansion of the universe, but how do we quantify it?

3. As galaxies are separated, aren't their gravitational potential energies increasing? If so, that energy would have to come from somewhere, so wouldn't that put a cap on how big the universe can get? Wouldn't a forever-expanding universe be impossible?

[mgb_phys]

1. Shouldn't we be able to look back at earlier stages of the universe, but see them very very red-shifted? Maybe as radio waves, by this point? What is the lowest frequency wave we can detect without interference? How long ago would that represent? We'd obviously do any detection from outside our atmosphere.
Yes we do, it's the reason for infrared astronomy. The UV lines from hot early star formation are shifted into the Near IR for distant galaxies.
The limit for looking back is the point where matter/photons decoupled (essentially the universe became large and cool enough that matter ha a chance of staying around and not being immediately annihilated). This is the microwave background an has been redshifted from it's initial extremely high energy to microwaves at 2.7Kelvin

2. I understand how we detect the expansion of the universe, but how do we quantify it?
Hubble's law, rescission speed is proportional to distance. So for every every MParsec a galaxy is away from us it's speed is around 72km/s faster

3. As galaxies are separated, aren't their gravitational potential energies increasing? If so, that energy would have to come from somewhere, so wouldn't that put a cap on how big the universe can get? Wouldn't a forever-expanding universe be impossible?
There was a lot of energy at the start of the universe, E=mc^2 where m is the mass of everything in the universe! It used to be thought that the energy of the universe was zero, so if you took the negative potential energy of the expanding galaxies it balances ll the mass. It now looks like that isn't true.

[Chronos]

The observational limit on the universe is, and will always be, the CMB - about 2.7 degrees kelvin. You can convert this to a radio frequency of around 0.3 cm according to current measurements. The temperature at the time of emission is estimated at about 3000 kelvin. Note that if you divide the estimated emission temperature by the current measured temperature you get about 1100 - which is the redshift of the CMB.