Is the universe 13.7 Billion years old? There seems to be a contradiction

[Andrew Mason]

So, I take it that on cosmological distance scales the unit of distance as measured by an observer on earth, the light year, is NOT the distance that light takes one year to travel as measured by an observer on earth. So what is it and how is it measured?

AM

 

[marcus]

So, I take it that on cosmological distance scales the unit of distance as measured by an observer on earth, the light year, is NOT the distance that light takes one year to travel as measured by an observer on earth. So what is it and how is it measured?

AM

That's right, a lightyear is the distance light would travel in a non-expanding universe in one year. In our galaxy (and local group of galaxies) the effect of expansion is essentially non-existent. There is an alternative unit of distance called "parsec" defined using parallax angle and a parsec is 3.26 lightyears. You could define a lightyear as 1/3.26 parsecs.

In cosmology typically what we measure is redshift. Distances and times are determined from redshift using a model.

One kind of distance measure is instantaneous "freeze-frame" distance which is what you would measure (say by how long light would take) if you could stop the expansion process right now.

A time measure that has a complicated relation to distance is the "lookback time" or "light travel time" that it is also possible to calculate from the redshift, using the model.

I'd say anyone interested in cosmology would be well-advised to learn to think in terms of the redshift. And get used to using the available calculators that convert redshifts to distances, and also give travel times.

If you google "cosmo calculator" and put in a redshift like z = 0.5 it will tell you the instantaneous distance now (labeled comoving in the readout) and also what the instantaneous distance WAS back when the light was emitted and started out on its way to us. That is labeled "angular size distance" in the readout.

These will be given both in parsecs and in lightyears (which are 1/3.26 of a parsec). The calculator will also give the light travel time in years. Not terribly useful as a measure of distance but nevertheless nice to know.

 

[twofish-quant]

Here is a useful paper:

http://arxiv.org/PS_cache/astro-ph/pdf/9905/9905116v4.pdf

The problem is here is defining what we mean by a "distance". What exactly is a distance, anyway. What do I mean when I say that television set is four meters away? Well, I do an experiment, and the answer comes back four meters. The interesting thing is that I can do different experiments and the answer comes back "four meters".

The complication with cosmology, is that if you do different experiments that come back with the same answer when you measure "short" distances, you end up coming back with different numbers. So when you are talking about something being "far" away, you have do define what you mean by distance and there are ten of so different definitions for "distance". The paper that I referenced lists then and tells you how to convert between different types of "distance."

 

[bcrowell]

So, I take it that on cosmological distance scales the unit of distance as measured by an observer on earth, the light year, is NOT the distance that light takes one year to travel as measured by an observer on earth. So what is it and how is it measured?

General relativity doesn't provide any uniquely defined way of measuring distances, nor does it associate a particular distance-measuring procedure with a particular observer's state of motion, as do Galilean relativity and special relativity.

 

[Tanelorn]

Ben, does this mean that there is a point where we no longer use distance, and that distance no longer has meaning? If so under what circumstances does this happen and what is the real world physical source for this?

 

[bcrowell]

Ben, does this mean that there is a point where we no longer use distance, and that distance no longer has meaning?

You can define measures of distance, but they're not uniquely defined. Someone else can define a different one, and it can be equally valid. In cosmology, the most convenient measure of distance is usually proper distance, which is defined as what you would get with a chain of rulers, extending along a spacelike geodesic, each of them at rest relative to the Hubble flow.

If so under what circumstances does this happen and what is the real world physical source for this?

Under the circumstances described in #30.

 

[marcus]

... In cosmology, the most convenient measure of distance is usually proper distance, which is defined as what you would get with a chain of rulers, extending along a spacelike geodesic, each of them at rest relative to the Hubble flow...

I agree. Nice concise description of what is commonly called "proper distance". I often call it instantaneous or "freeze-frame" distance because it is what you would get if you could freeze the expansion proces (the Hubble flow) at a particular moment in time.

And then, having frozen it, so that distances would not be changing while you measured, use any familiar means like rulers or radar.

To amplify something Ben said, one reason it is so convenient is that it is the distance which is used in formulating basic features of the standard model, like the Hubble law v=Hd. This is a statement about proper distances and their instantaneous rate of increase.

 

[marcus]

Here is a useful paper:

http://arxiv.org/PS_cache/astro-ph/pdf/9905/9905116v4.pdf
...

That paper by David Hogg is a total classic! Somebody should have it tattooed in their signature. It gets referred to here regularly over the years. In fact you are pointing out the importance of operational definitions in science. A term like "distance" has no meaning in the abstract. It only means something if you have some procedure in mind for measuring the distance. We do not know or predict Nature. We only know and predict events observations measurements...

Tanelorn asks "does the idea of distance become useless?" and the answer is no it remain useful. Very useful! We just have to be more aware of the processes used to evaluate it---its operational meanings.

Google "wright calculator" and find the distances corresponding to some redshift and think about the fact that the "angular size distance" which it gives is actually the same as the proper or instantaneous distance at the moment that the light was emitted and started on its way to us. Think about what angular size distance means, how you would determine it (how far away a meterstick looks, by what angle it subtends) and why it is the same as the proper distance back then. I still find the equivalence intriguing

 

[Tanelorn]

Marcus, Ben, So proper distance is the real distance between the objects, the one we measure in everyday situations with a ruler. The speed of the objects and the expansion of space are all frozen for the measurement and we have an extremely long ruler that can be instantaneously moved into position between the objects?

 

[yheyman]

13.7 billion years is the distance to the Hubble sphere... the age of the Universe need to be recomputed.

If the recession speed exceeds the speed of light, the photon would never reach the observer, this is why there exists a horizon of the visible Universe (the Hubble sphere), beyond which light would never reach us. Historically the age of the Universe was computed from the loockback time between a redshift zero and infinity, which yields 1/Ho. Note that this measure gives the lookback time to the Hubble sphere because the redshift must converge towards infinity at the horizon of the visible Universe. Here is a reference showing the calculations with a De Sitter Universe (http://www.jrank.org/space/pages/2440/look-back-time.html). Another reference where the age of the Universe is computed with the look-back time between a redshift of zero and infinity: http://www.mpifr-bonn.mpg.de/staff/hvoss/DiplWeb/DiplWebap1.html . See A.36 et A.37.

Using another approach we can show that an apparently steady Hubble coefficient in the light travel distance framework is equivalent to a time-varying Hubble coefficient in the Euclidean framework of order two (i.e. Universe expanding at a steady acceleration pace). This approach gives an age of the Universe of about 20-25 billion years. This figure is compatible with the age of the Universe obtained from the datation of old stars. According to Chaboyer (1995) who analysed metal-rich and metal-poor globular clusters, the absolute age of the oldest globular clusters are found to lie in the range 11-21 Gyr. Bolte et al. (1995) estimated the age of the M92 globular cluster to be 15.8 Gyr. Th/Eu dating yields stellar ages of up to 18.9 Gyr (Truran et al., 2001). A paper describing this appoach is available online: http://fr.calameo.com/books/00014533338c183febd92

 

[mitrasoumya]

How is the universe exactly 13.7 billion years old, in absence of absolute time?
Distribution of mass across the universe is not even. Therefore, passage of time should vary according to gravity. Which means at places time will pass at a higher pace or a lower pace than in respect of other places. Then, how is the entire Universe exactly 13.7 billion years old?

 

[Chronos]

The source of cmb photons was a mere ~46 million light years distant [in comoving coordinates] when the photons we now detect were emitted 13.7 billion years ago. Hellfire has a very useful cosmo calculator for this sort of thing. Cosmology is a fickle mistress.

 

[Mark M]

How is the universe exactly 13.7 billion years old, in absence of absolute time?
Distribution of mass across the universe is not even. Therefore, passage of time should vary according to gravity. Which means at places time will pass at a higher pace or a lower pace than in respect of other places. Then, how is the entire Universe exactly 13.7 billion years old?

Cosmological time is the time measured by an observer at rest with respect to the CMB.

 

[Lino]

... SR is flat non-expanding geometry, so it is mainly good where gravity is not too strong (so curvature can be neglected) and where the expansion of distance is so small or slow that it can be neglected...

... As an example where SR *is* a good approximation, the Andromeda galaxy lies at a distance of d=2.5 million light years, so d^2H^2 is on the order of 10^-7. ...

Marcus / Ben, I understand the basics of what your are saying, re the impact of curvature, but I would have thought that the impact was greater (and therefore more significant) at shorter distances! What I mean is: over shorter distances (Milkyway to Andromeda) objects are gravitationally bound (implying greater curvature), while over larger distances, like those mentioned in earlier posts, expansion rules (implying that the average curvature would be closer to (an average of) zero). I appreciate that I am fundementally miss-stating something - could you give me a pointer as to where I am going wrong please?


Regards,


Noel.