How much energy do we need to make an expanding universe?

[Chalnoth]

No. In this case, the energy density is reasonably well-defined, but the volume is not. There is no one answer for, "What is the volume of our universe?"

 

[Quarlep]

But the best answer will be the observable universr

 

[Chalnoth]

Why?

 

[Quarlep]

Physics work with observable think.

 

[Chalnoth]

Sure, but there's more than one relevant length scale to choose from. We could pick the future horizon, or the comoving distance to the CMB, or the comoving distance to the past horizon. There are other potential choices as well, and no way to say which one is better.

 

[Quarlep]

Lets suppose I will going to write a theory.And I will going to use radius of the universe.I can't write "theres a infinite possibility"so I will write the observable one.In your logic "The only thing that I know is nothing" We can't be sure hundred per cent about anything

 

[marcus]

Hi Q,
what you say makes perfect sense to me. "Observable universe" has a conventional meaning in cosmology.
You just, to be clear, should include the adjective "observable".
Try to avoid just saying "radius of the universe" (although people do say that when they really mean the observable region).

If you say "radius of the observable universe" then I think most professional cosmologists would understand and would not quibble. It is not really ambiguous. One understands what you mean in this context is the so-called PROPER distance at this present moment in universe history.
I will tell you what the cosmologists mean by "proper" distance at some given moment.

But first I want to mention that "comoving" distance is just another word for the proper distance at THIS very moment...the proper distance NOW. It is very useful. You can give a label to every bit of matter we know about according to how far it is now and that label will not change. Even if at some time in the past that bit of matter was closer to us, it still has that "comoving" distance label. this is an extremely useful label. The proper distance that something is now.

 

[Quarlep]

Thanks

 

[PeterDonis]

If you say "radius of the observable universe" then I think most professional cosmologists would understand and would not quibble.

It's worth clarifying, though, that this is because "radius" also has a conventional meaning here, namely, the distance evaluated in a surface of constant comoving time. That does not mean this is the only physically relevant distance involved; as Chalnoth pointed out, there are others.

 

[Quarlep]

I ll be carefull using terms in cosmology

 

[marcus]

It's worth clarifying, though, that this is because "radius" also has a conventional meaning here, namely, the distance evaluated in a surface of constant comoving time. That does not mean this is the only physically relevant distance involved; as Chalnoth pointed out, there are others.

That's right, I was just getting to that
I want to make clear to Quarlep (unless you would like to) what is technically meant by proper distance at a given moment in cosmic time.
Q, this is very interesting. You may already know this. the universe has a criterion of STILLNESS. We can talk about the class of observers who are at rest with respect to the CMB. Because the CMB is a uniform soup of light which is the same temperature in all directions. But if you move in some direction the doppler effect of your motion will make it slightly warmer in that direction ahead of you and slightly colder behind you.
This can be measured and data can be corrected for the solar system and Earth's motion! We can correct our data so as to be from the standpoint of an observer which is at rest with respect to the uniform ancient gas and ancient light coming from it.

This is also the same as being at rest relative to the expansion process itself. If you are at CMB rest (ie. ancient light rest) then the expansion looks the same in all directions. Galaxies are not receding faster in one direction than in another. CMB rest really is UNIVERSE rest. It is a really beautiful fact that this is defined.

And this means we can define a preferred universe TIME which is the time measured by the class of observers all over the universe who are at rest.
They can in principle agree on time (after adjusting for some slight gravitational effects) so there is an unambiguous definition. (jargon=professional slang, these are sometimes called "comoving" observers.)

proper distance is what you would measure if you could pause the expansion process at some moment of history long enough to have time to measure it

 

[Quarlep]

Ok I understand it

 

[Chalnoth]

I find it very interesting that terms which we usually think of as being absolute here on Earth, such as relative velocity or energy, tend to lose their specificity when describing what happens in a curved space-time. It turns out to be quite difficult, and counter-intuitive, to come up with absolute measurements that are useful in General Relativity.

For example, the relative velocity between two different objects is well-defined in General Relativity if those two objects are passing the same point in space-time. If the two objects are far away from one another, we lose our ability to unambiguously state the relative velocity. This means, for example, if you were to ask me, "How fast is that galaxy moving away from us?" then the most honest answer would be, "Well, it depends. There are a few choices, and there's no way to say which is better." This is why the speed of light limitation in General Relativity only applies to objects passing one another: it cannot apply to far-away objects because that's not a well-defined quantity in General Relativity.

The same goes for energy, and for similar underlying reasons.

A related discussion, on the conservation of energy, can be found here:
http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

 

[Quarlep]

You are saying there's a few ways to calculate universe observable radius and these ways takes us different solutions.
Cause General relativity don't allow us to measure it

 

[marcus]

I ll be carefull using terms in cosmology

I know. I think you have been being careful, actually.
You are working in a language which is not your first language. And also there are these technical terms. Like "proper".

Measuring a distance at some given moment in time, by some conventional means like radar, or a long string, or laser beams etc. Measuring always takes time. But distances are changing. So you have to imagine PAUSING the expansion process long enough to measure. But then you have to have a preferred cosmic time---a "universe standard time"---so you can say I want to measure the distance NOW. That "NOW" has to have universal meaning throughout the region where you are measuring.

But usually you can just say "distance" and professionals will understand you mean proper distance ( at whatever the appropriate time is).
People of good will understand each other partly using context and rarely need to quibble.

So anyway, we were talking about the volume of the observable universe. Does anybody find that there is some ambiguity? Should we clarify or add some modifiers here?

In an earlier post I used the socalled "particle horizon" as the conventional meaning of the radius of the observable universe. It is the comoving distance (distance NOW) of the farthest matter we can in principle have gotten light or other signal from. A rough estimate is 46 billion LY. That is the current radius of the current observable region. The region grows as there is more time for light etc to come in from farther matter.

So I made a rough estimate of the volume of the (until now) observable portion of the universe assuming approximate flatness:
(4/3)πR³

 

[Chalnoth]

You are saying there's a few ways to calculate universe observable radius and these ways takes us different solutions.
Cause General relativity don't allow us to measure it

Sort of. Cosmologists usually mean a very specific way of writing down the distance when they say, "radius of the observable universe," but you shouldn't mistake that for an unambiguous, observed quantity.

Basically, when we start talking about things that are much, much bigger than the Earth, the definitions get weird and it becomes hard to be explicit. You can be explicit using math, but translating that to human language is difficult.

 

[Quarlep]

Volume of observable universe is increasing every time then you are telling me dark energy will be decrease.But thay cannot be true I guess (lamda doesn't change with volume)

 

[Quarlep]

Sort of. Cosmologists usually mean a very specific way of writing down the distance when they say, "radius of the observable universe," but you shouldn't mistake that for an unambiguous, observed quantity.

Basically, when we start talking about things that are much, much bigger than the Earth, the definitions get weird and it becomes hard to be explicit. You can be explicit using math, but translating that to human language is difficult.

I understand

 

[Chalnoth]

Volume of observable universe is increasing every time then you are telling me dark energy will be decrease.But thay cannot be true I guess (lamda doesn't change with volume)

The dark energy density stays roughly the same over time (if it's a cosmological constant, it stays exactly the same). So if the volume increases, that volume contains more energy from the dark energy.

 

[Quarlep]

So dark energy "energy" increase every time

 

[Chalnoth]

Essentially, yes. Energy is not conserved in General Relativity.