# 13.5 billion year age versus 93 billion due to spatial expansion?

• diagopod
In summary, Nick says that the age of the universe is 13.5 billion years, but that due to the expansion of space the actual age is closer to 93 billion years. He says that C is a speed limit and that most galaxies are receding faster than c.

#### diagopod

I was watching a video on the scale of the observable universe. At the end, it shows the famous WMAP imagery and at the bottom it reads that the age of the observable universe is about 13.5 billion years old, but that due to the expansion of space the actual age is closer to 93 billion years. I hadn't heard this before and can't quite follow that logic. Could anyone help clarify that point?

If the "observeable" universe is 93 billion light years in diameter whereas the *actual* age of the universe is 13.5, how then can we observe those parts that must have obviously moved - if "moved" is even the right word - away at velocities greater than C?

Nick's answer covers it, but maybe I can fill in some extra detail.
A common way for astronomers to talk about the distance now to some matter that we are seeing amounts to imagining that you can freeze the expansion process right now and then time a light signal going from here to there (with everything frozen in place).
That's called the proper distance and it is the type of measure used with the Hubble law: the standard way to describe expansion.

It is in that sense that we say that the distance now to the farthest matter we can see is about 46 billion lightyears. We are currently receiving light which that matter emitted some 13.7 billion years ago, not long after the start of expansion. The matter was much closer then.

Notice the difference between measuring time and measuring distance. years is a measure of time, lightyears is a measure of distance (which because of expansion doesn't need to correspond to travel time in any simple way.)

The 46 billion lightyear radius of the portion of the universe we currently can observe can be thought of as the combined effect of what distance the light could have traveled on its own, without expansion, plus the added effect of expansion. By itself, in a static universe, the light could have only traveled 13.7, but in fact the oldest light comes from source material which is now around 46 from us.

Max Faust said:
If the "observeable" universe is 93 billion light years in diameter whereas the *actual* age of the universe is 13.5, how then can we observe those parts that must have obviously moved - if "moved" is even the right word - away at velocities greater than C?

When you hear the word "recession rate" it is not strictly about the ordinary motion idea of traveling from point A to point B in a static geometry. To understand the Hubble law you really need to include the cosmic microwave background CMB in your picture, or what was earlier known as the Hubble flow before the CMB was observed.

So you are right to be cautious and say "if moved is even the right word". It's good to be aware that the word can be applied to different processes basically because largescale geometry is not static.

Most of the galaxies which we are now looking at with telescopes have redshift greater than 1.4 and any such galaxy is receding faster than c. So that raises a very interesting question. Most of the galaxies we can see in the sky are receding faster than c, so how do we see them? How could the light have gotten here?

I think this is at the heart of your question. It's a good question to be asking. We've answered it many times here at PF cosmo forum, and sometimes just by referring to the 2005 Scientific American article by Lineweaver Davis, that explains it with a very simple picture. Nicksauce already gave a link to something in the Lineweaver SciAm---it's a great article. I keep the link to the main article in my sig for quick reference.
You could have a look at it, see if you then understand how light can have gotten here from a galaxy that is now receding > c, and then if you aren't fully satisfied come back with a further question.

Please see if you can find the Lineweaver link in my sig, Faust. Ask if there's any problem.

Thanks for the responses everyone, makes a lot more sense now.

marcus said:

F...ing damn right there is a problem!

I have come to believe that C is a constant. A speed limit. NOTHING can move faster than C. The explanations I have heard are all about a conversion principle between energy and mass, the "treacle" of the Higgs field, and all that jazz. Which I have struggled to comprehend and make sense of. But this may be limited to mass and physicality but not structure and "spatial distance" in an expanding "nothingness". I can imagine how "space" can expand faster than C (if "faster" is even an operative concept here). I have heard about "dark flow" and the almost incomprehensible ideas that the "new" cosmologists are sporting... but I still fail to see how we can observe (and determine) that there are objects in this universe that accellerate away from us at > C velocity. It just doesn't make any sense. Which of course may be just because I don't understand what's going on (which is indeed very likely)... so... are we talking about a "ripple in space" kind of thing that has nothing to do with "mass" as we know it? And if so, how did they find out?

I also don't understand how we can pass c. Can someone explain this to us?

You cannot surpass c locally. Globally, that is a different matter. Relativity does not forbid superluminal global expansion.

but I still fail to see how we can observe (and determine) that there are objects in this universe that accellerate away from us at > C velocity.
That's very easy: we can't.
We can observe objects that are said to be moving away with >c. But we can't determine that their speed is greater than c by any - more or less - direct measurement.
This "speed" is defined in a certain coordinate system. Without going into details, GR - contrary to SR - allows for arbitrary coordinate systems, and in arbitrary systems you can have arbitrary velocities. Such coordinate velocities don't have the strict physical meaning that speed in SR has. They can mean something different, with more or less similarity to the speed concept of SR.
For example, the cosmological "recession velocity" in a flat spacetime (an empty or almost empty universe) is not the speed of receding "test particles", but their rapidity. So you can have "velocities" >c even in flat spacetime, just by a redefenition of coordinates.

Cosmologists use such strange coordinates because, in curved spacetimes, rigid SR coordinates simply don't work. There is also no well defined concept of relative velocity for objects that are far apart.
So one uses coordinates that do work, along with these coordinate velocities. That's ok, but much too often these concepts get confused with the standard SR ones. For some reason many cosmologists seem reluctant to address this point.

marcus said:
When you hear the word "recession rate" it is not strictly about the ordinary motion idea of traveling from point A to point B in a static geometry. To understand the Hubble law you really need to include the cosmic microwave background CMB in your picture, or what was earlier known as the Hubble flow before the CMB was observed.

So you are right to be cautious and say "if moved is even the right word". It's good to be aware that the word can be applied to different processes basically because largescale geometry is not static.

Most of the galaxies which we are now looking at with telescopes have redshift greater than 1.4 and any such galaxy is receding faster than c. So that raises a very interesting question. Most of the galaxies we can see in the sky are receding faster than c, so how do we see them? How could the light have gotten here?

I think this is at the heart of your question. It's a good question to be asking. We've answered it many times here at PF cosmo forum, and sometimes just by referring to the 2005 Scientific American article by Lineweaver Davis, that explains it with a very simple picture. Nicksauce already gave a link to something in the Lineweaver SciAm---it's a great article. I keep the link to the main article in my sig for quick reference.
You could have a look at it, see if you then understand how light can have gotten here from a galaxy that is now receding > c, and then if you aren't fully satisfied come back with a further question.
...

It's generally most efficient if anyone with a question about Hubble law recession rates takes a look at the Lineweaver Scientific American article first and THEN asks questions.

diagopod said:
Thanks for the responses everyone, makes a lot more sense now.

Sounds like diagopod may have read Lineweaver SciAm. I keep the link in my signature because it has been referred to many times over the years at Cosmo forum. E.g. see Nicksauce's reference earlier in this thread.

Max Faust said:
F...ing damn right there is a problem!

biltoft said:
I also don't understand how we can pass c. Can someone explain this to us?

Here's the link to that SciAm article. A good introduction.

It is a princeton.edu link because they use it at Princeton as supplemental reading in their introductory Astro course. The author, Charlie Lineweaver, was one of the leaders in the mapping of the cosmic microwave background (COBE mission). He is a world class authority and moreover is good at explaining things nontechnically at a wide audience level.

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diagopod said:
I was watching a video on the scale of the observable universe. At the end, it shows the famous WMAP imagery and at the bottom it reads that the age of the observable universe is about 13.5 billion years old, but that due to the expansion of space the actual age is closer to 93 billion years. I hadn't heard this before and can't quite follow that logic. Could anyone help clarify that point?
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Hi Diagopod. Here is a little bit of information about the age of the Universe from CERN:"CERN, the European Organization for Nuclear Research, is one of the world’s largest and most respected centres for scientific research. Its business is fundamental physics, finding out what the Universe is made of and how it works. At CERN, the world’s largest and most complex scientific instruments are used to study the basic constituents of matter — the fundamental particles. By studying what happens when these particles collide, physicists learn about the laws of Nature."
Clues to the early Universe
The Universe has changed a great deal in the 13.7 billion years since the Big Bang, but the basic building blocks of everything from microbes to galaxies were signed, sealed and delivered in the first few millionths of a second. This is when the fundamental quarks became locked up within the protons and neutrons that form atomic nuclei. And there they remain, stuck together by gluons, the carrier particles of the strong force. This force is so strong that experiments have not been able to prise individual quarks or gluons out of protons, neutrons or other composite particles.