How is the Age of the Universe Calculated Despite Light Travel Distance?

[jtsw1959]

Does anyone know the estimated mass of the Universe? It's (E=Mc2) energy? Thanks.

 

[The riddler]

Sadly i don't think anyone knows the mass of the total universe, though i have heard that cosmologists are attempting to calculate the mass of the visable universe.

 

[jtsw1959]

Riddler: do you know who is trying to do that calculation? Thanks, JTSW

 

[The riddler]

jtsw1959, i have just found a webpage that shows an estimated mass, size, density and radius of the visable universe. I hope it answers your question.
http://www.cs.umass.edu/~immerman/stanford/universe.html

 

[marcus]

jtsw1959, i have just found a webpage that shows an estimated mass, size, density and radius of the visable universe. I hope it answers your question.
http://www.cs.umass.edu/~immerman/stanford/universe.html

Riddler the numbers there are way way off from modern estimates. It does not recognized 75% of the content of the U, and it mis-estimates the volume of the observable portion of the universe by more than a factor of 17.
It gives the radius as 18 billion LY instead of the usual modern figure of around 46.5 billion.

It references a 1986 textbook. (Any cosmo book before 2000 will likely do more harm than good, the field has changed so radically.)

Please be careful when you tap into the internet to check date and sources, references.

Anything after 2004 or 2005 has a chance of being OK.

What you have is pre-1998 info even though it says "last modified 2001"
The modification in 2001 was not a thorough update, evidently. Doesn't acknowledge the discovery of accelerated expansion in 1998, dark energy etc.

Wikipedia "Observable Universe" looks OK. It gives the current radius as 46.5 billion lightyears which agrees with what many of us use here at PF

 

[marcus]

Does anyone know the estimated mass of the Universe? It's (E=Mc2) energy? Thanks.

A common estimate of the energy density is 0.85 nanojoule per cubic meter.

That is with all the mass converted to it's energy equivalent (E=mc2). And includes everything, light CMB, ordinary matter, dark matter and dark energy.

If you just want matter then multiply the 0.85 by 0.27. I assume you want total energy in all forms so let's use 0.85.

That is the critical density needed if space is to be flat, and since it is observed to be very nearly flat the 0.85 figure must be very nearly correct.

=====================

You should be able to calculate the volume of the observable yourself.

In Highschool you learn volume = (4 pi/3)R^3
and the usual figure for the radius of the observable is 46.5 billion lightyears

So just type this into the Google window and press return (google has a built in calculator).

(4 pi/3)(46.5 billion light years)^3

Anybody can do that. It will calculate for you and give you a certain number of cubic meters.

then just multiply that by 0.85 nanojoule per cubic meter and you'll have it.

Or, do the whole thing in one step. Type this into google and press return:
(0.85 nanojoule per cubic meter)(4 pi/3)(46.5 billion light years)^3

It will calculate the energy in the observable universe and come back with a number like
3 x 10⁷¹ joules

==================
JTSM,
some advice. It is a good idea to be a little self-sufficient. Be able to calculate for yourself. Learn how to use the google calculator (it knows many units, masses, distances etc. It knows the G constant and the speed of light, so it makes it easy to be independent.)
Don't be totally dependent on asking people, who may be misinformed and may give you wrong info.

For example that figure of 0.85 nanojoule per cubic meter. It is easy to calculate. I can show you how. All you need to know is the Hubble rate of around 71 km/s per Megaparsec.

If you don't know the Hubble rate is around 71 then...well that is something anybody at Cosmo forum should know by heart.
==================

Also you began by asking about the mass or energy content of the entire universe. A lower bound on the volume of the whole universe was provided
last year in one of NASA's reports---the report of the 5th year of the WMAP mission data.

The volume could be infinite, we don't know yet. It depends on a curvature which we can measure. the measurements are getting more accurate. So far we just have this lower bound estimate, but I think we will know more before very long. The Planck mission will help narrow it down.

So if you ask and someone says that unfortunately we don't have a handle on the full size, well that is misinformation. We do have a partial handle and people are working on it and we are getting more.

If you want links to sources let me know. If you want the cubic lightyears figure, just say and I will show you how to calculate it for yourself.
Remember this is the whole thing, not the observable portion.

Enjoy. Try to use reliable, recent, professional sources too. But the main thing is enjoy

 

[Orion1]

Universe mass...

Does anyone know the estimated mass of the Universe? It's (E=Mc2) energy?

Affirmative.

the energy in the observable universe...3 x 10^71 joules

These are my equations for the Universe mass based upon the Lambda-CDM model parameters and the Hubble Space Telescope (HST) and WMAP observational parameters in Systeme International units.

$$H_0 = 2.3298 \cdot 10^{- 18} \; \text{s}^{- 1}$$ - Hubble parameter (WMAP)
$$\Omega_s = 0.005$$ - Lambda-CDM stellar Baryon density parameter
$$dN_s = 10^{22}$$ - Hubble Space Telescope observable stellar number
$$dV_s = 3.3871 \cdot 10^{78} \; \text{m}^3 \; \; \; (4 \cdot 10^{30} \; \text{ly}^3)$$ - Hubble Space Telescope observable stellar volume
$$M_{\odot} = 1.9891 \cdot 10^{30} \; \text{kg}$$ - solar mass

Observable Universe mass:
$$\boxed{M_u = \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3} = 1.048 \cdot 10^{55} \; \text{kg}$$

$$\boxed{M_u = 1.048 \cdot 10^{55} \; \text{kg}}$$

Universe mass-energy integration by substitution:
$$E_u = M_u c^2 = \left[ \frac{4 \pi M_{\odot}}{3 \Omega_s} \left( \frac{dN_s}{dV_s} \right) \left( \frac{c}{H_0} \right)^3 \right] c^2 = \frac{4 \pi c^5 M_{\odot}}{3 \Omega_s H_0^3} \left( \frac{dN_s}{dV_s} \right) = 9.419 \cdot 10^{71} \; \text{j}$$

Universe mass-energy equivalence:
$$\boxed{E_u = \frac{4 \pi c^5 M_{\odot}}{3 \Omega_s H_0^3} \left( \frac{dN_s}{dV_s} \right)}$$

$$\boxed{E_u = 9.419 \cdot 10^{71} \; \text{j}}$$


Reference:
http://en.wikipedia.org/wiki/Hubble%27s_law"
http://en.wikipedia.org/wiki/Lambda-CDM_model"
http://en.wikipedia.org/wiki/Universe"
http://en.wikipedia.org/wiki/Observable_universe"
http://en.wikipedia.org/wiki/Dark_matter"

 

[lazypast]

marcus, you stated the radius of the universe is 46.5bn LY. if we say the big bang happened in the centre (logically, i suppose) wouldn't the universe be 46.5bn year old?

oh wait wait, unless the expansion is faster than the speed of light?

if that's the case then what defines the edge and the rate at which is expands?

 

[marcus]

marcus, you stated the radius of the universe is 46.5bn LY. if we say the big bang happened in the centre (logically, i suppose) wouldn't the universe be 46.5bn year old?

oh wait wait, unless the expansion is faster than the speed of light?

if that's the case then what defines the edge and the rate at which is expands?

Like many newcomers you are suffering from this common misconception of the big bang as an explosion.

Please read the Sci Am article "Misconceptions about the Big Bang?". They have a special section devoted to that explosion misconception.
There's a good copy of the Sci Am article stored at the Princeton astronomy website and princeton.edu. They use it as course reading material.
Great article!

http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf

There is no special point in space where the expansion started.

(No unique spot you can point to and say "it started from there" and measure out from that point.)

There is no "edge". There is no "speed that the edge is traveling."

In the usual cosmo picture there is no empty space that stuff is going outwards into. There is just space with more or less evenly distributed matter--approximate uniform distribution. No "space outside of space".

The last thing big bang cosmology is like is an explosion with things flying out into empty space from some central location. Flush that image out of your brain and down the tubes if you can. It makes it too complicated. People work too hard. Correctly approached, cosmology should be simple and easy to understand.

The age since the start of expansion is 13.7 billion years and 46.5 billion lightyears is the current radius of the chunk of the universe that we are now looking at, because that is how far away from us stuff is today if its light took 13.7 billion years to reach us. The oldest light comes from stuff that today at this moment is 46.5 billion lightyears away from us, and the light is arriving today, and the light is 13.7 billion years old. That is how long it has been traveling. Naturally the distance has be more than just 13.7 billion lightyears because distances are expanding!

Try googling "wright balloon model" and watch Ned Wright's balloon animations. The second one "balloon2" is especially good if you can find it.
Try reading early parts of the "balloon model sticky thread". Remember that the analog is a pure 2D surface, no rubber, no 3D space inside, no 3D space outside, all existence concentrated on the 2D spherical surface.

 

[whybother]

It's a completely acausal question, honestly. Making exact statements about the mass/energy of the entire universe is impossible if you are seriously excepting causality. For an assumed very large universe, it's just not possible to have that kind of knowledge. Mass/energy density values are only meaningful in the region they were measured, not across the entire universe, and they are still dubious in those regions.

 

[marcus]

It's a completely acausal question, honestly. Making exact statements about the mass/energy of the entire universe is impossible if you are seriously excepting causality. For an assumed very large universe, it's just not possible to have that kind of knowledge. Mass/energy density values are only meaningful in the region they were measured, not across the entire universe, and they are still dubious in those regions.

You didn't get it, WB. We aren't talking about the "entire universe", we explicitly said we were talking about part that we can see today, the part were are currently getting light from.
To make the standard cosmo model work we need to be able to calculate stuff like densities and volumes. The standard model is called LCDM and what we are quoting is in terms of that model. The model fits the data very well! Of course it could be wrong and it might be improved later. But right now when you ask what is the mass of the observable region according to the standard LCDM, this is the answer you get.

Approx 3 x 10⁷¹ joules.

If you don't like the mainstream consensus model, then present your own model with your own figures. You might even be proven right sometime in future! But don't tell me I can't calculate stuff from LCDM. Because of "causality" no less!

 

[lazypast]

if it took 46.5bn years for the light to travel the radius, then surely the age of the universe would have to be 46.5 bn year old.

edit, after reading that pdf file marcus, I am still not convinced - or rather i can't get my head round it.

 

[marcus]

if it took 46.5bn years for the light to travel the radius, then surely the age of the universe would have to be 46.5 bn year old.
...

no. it took 13.7 billion years, not 46.

after light has traveled some distance (at its own steady speed) that distance expands. the distance it has put behind it increases by a certain percentage each year (like money in the bank compound interest)

so naturally the distance it now is away from the source material is much more than the distances it could have traveled on its own---unaided---in a non-expanding universe.

for heaven's sake google "wright balloon model" and watch the animation.
after 5 minutes of watching the animation this should be obvious to you.
the white dots are galaxies, which stay at the same place (same latitude longitude on balloon).
the colored wriggly things are photons, which always move at the same speed across the surface of the balloon---a speed like 1 millimeter per second, analogous to the steady speed of light.

after a few seconds all the photons are farther away from where they started than they could have gotten on their own---unaided by expansion.

It's a visual thing. Instead of saying you can't get your head around it, you should better just watch the simple computer animation---then ask questions if you have some.

I googled "wright balloon model" for you, to make it easy:
http://www.astro.ucla.edu/~wright/Balloon2.html

if it took 46.5bn years for the light to travel the radius, then surely the age of the universe would have to be 46.5 bn year old.
...

No, Lazy. The expansion is 13.7 billion years old. The light has been traveling 13.7 billion years. The distance away, that the light now is from the material that emitted it, is 46-some billion lightyears. If you save money at a steady rate, and put it in the savingsaccount getting some percent interest, then after a few years you HAVE to have more in the bank than you would have if you just keep it in your sock drawer, getting zero interest (the nonexpanding case).