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

[marcus]

Thanks. So roughly what would be the largest distance over which SR would be a useful approximation? any idea?

Ben Crowell might have a different idea but I'd say that what's a "useful" approximation depends a lot on how accurate you want to be and what kind of calculation you have in mind.

Just to pull a number out of the hat, I'm thinking of an application where 140 million light years is too far for comfort. That is the instantaneous distance that is increasing at 1 percent of the speed of light.

By instantaneous distance I mean what you would measure by ordinary means (radar ranging, yardsticks, tape measure) if you could stop the expansion process at this moment. That is the measure of distance that Hubble law tells us the instaneous rate of increase of.

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.
=====================
Oh! I see Ben already answered the question! I didn't need to post. But I will leave this up anyway because it illustrates a different way of responding to the question "what size distance can't you apply SR to usefully?"

 

[bcrowell]

Ben Crowell might have a different idea but I'd say that what's a "useful" approximation depends a lot on how accurate you want to be and what kind of calculation you have in mind.

I would definitely agree with this. I picked what the Riemann tensor measures (failure of parallelism) as my measure of how good or bad the approximation was, and that led to d^2H^2 as an order-of-magnitude estimate of the level of fractional error. But I'm sure it would be easy to come up with other examples, perhaps equally well motivated physically, where the fractional error would be on the order of (dH)^p, where p is 1 rather than 2, or something like that. OTOH, I think these things really do have to depend only on the quantity dH, since H is the only characteristic scale in the metric, and dH is the only unitless quantity you can construct from d and H.

BTW, the OP of this thread is a good example of how these error estimates work:

The universe is said to be 13.7 Billion years (check). [...Reasons based on SR...] So the universe must be at least 19.8 Billion years old now.

The OP tried using x=ct to determine the time required for a ray of light to travel a distance x. This is only valid in SR, and the error that results from applying it here is 44.5%, i.e., the fractional error is of order unity. This is exactly what we expect, since dH is of order unity.

 

[Jamders]

I think big bang was not a bang after all. for now may said. Observing our planet and Jupiter or Saturn, they are basically big masses with big gravitational forces, A solid center mass and an atmosphere where storms are visible that resemble galaxies. and if you'r in Florida can u see or feel a Typhon in Australia? Can u see it? All this math confusion seems similar to the ancient Greeks confusion thinking the planet was flat. This Universe is only a big storm that exist in the Elemental Gravity Mass Energy system wish is similar to his sons the palnets. even they hold flat formations when the distance reach some limits

 

[Jamders]

correct, inflation has nothing to do with it.

Thanks for the good answer.

I agree, the 13.2Gyr is sometimes referred to as "lookback time", and is not the current distance which would be ~32Glyr.

qraal is correct, the distance now would be much greater, more like ~32Glyr.



If you had Earth A and Earth B 100 million light years apart both traveling in parallel paths away from the galaxy at 0.9998c and sending light beams to each other, then your math would be correct that the galaxy would observe that it would take 4.99 billion years for the light to travel that 100 million light year distance between Earth A and Earth B. But that's not the situation we have with the Earth receding from the galaxy. The effect of relativistic time dilation is to affect the frequency (or wavelength) of the light observed, not the time it takes to reach the observer since it wouldn't take more than 200 million light years from either frame of reference for the light to arrive if it left when the separation was 100 million light years, if space wasn't expanding.

But cosmologists believe that space itself is expanding, which isn't accounted for in your equations at all. The redshift we observe is largely the result of the expansion of space governed by general relativity, and also partly the result of the Doppler effect of special relativity. For a proper treatment of the effects of general relativity regarding a galaxy moving away from the Earth, see this paper:
A comparison between the Doppler and cosmological redshifts, by Maria Luiza Bedran
http://www.df.uba.ar/users/sgil/physics_paper_doc/papers_phys/cosmo/doppler_redshift.pdf

That paper may also shed some light on the original question as suggested by the abstract:
"We compare the Doppler effect of special relativity with the cosmological redshift of general
relativity in order to clarify the difference between them. Some basic concepts of observational cosmology, such as the definitions of distance and cosmological parameters, are also presented."

the first stars should be at this present time at the edge or almost of the universe I m observing light that start traveling 13.5by ago. I was born 40 years ago right? but my location? what if that star is my neighbor which is let's said 5 million years apart?

 

[Arbitrageur]

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. Therefore SR is an excellent approximation over those distances.

Thanks to you and Marcus for the explanations and clarification with the example, because without it I would have also thought the distance to Andromeda might also be considered cosmological per your earlier reply. You gave me enough to research so I can figure out how to do the calculations (I hope) on what the errors are in the SR approximations.

Thanks very much for teaching me something regarding the limitations of SR approximations!

 

[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.