Does space-time have an energy itself?

[Quarlep]

Is space time has a energy itself ?

Thanks

 

[julcab12]

.. Depends on how loosely you want to define energy and some non trivial solutions. In GR -- property of the Enistien's vacuum solution to field equation is that spacetime 'might' have gravitons If you buy into the idea that gravity is mediated by it. You can imagine a bunch of gravitons as the quanta of space-time itself, these gravitons could exist independently of any source. The particular configuration of just space-time itself could contain information. IN QM, space time is made of quantum fields.

 

[wabbit]

You can interpret the cosmological constant as an energy density of spacetime, which is fine though only one way to see it.

 

[Quarlep]

You can interpret the cosmological constant as an energy density of spacetime, which is fine though only one way to see it.

If space-time has energy density it means it has a energy isn't it ?

 

[wabbit]

Yes you can integrate this density over a volume and this gives an energy.

However (at least if it is a cosmological constant) there is no way to convert this energy into any other form - not kinetic energy, not heat, nothing. It's only effect is the expansion of space.

 

[marcus]

If space-time has energy density it means it has a energy isn't it ?

Hi Q,
So far the observations are consistent with the cosmological constant interpretation. IOW not necessarily anything we would recognize as energy (in the usual senses) but better thought of as an intrinsic tendency for distances to expand at a small permanent rate (not affected by matter and radiation).

The present rate of expansion is somewhat higher and is observed to be gradually declining as if it is going to level off at this small residual rate. That's all we know--what we observe. We don't observe any energy, we see a longterm trend in geometry. I'll give you some numbers to make this more definite.

 

[wabbit]

Thanks, sounds like a much better way to put it than my "yes in a sense but..." contorsions

 

[marcus]

I thought you gave a good answer. Some people like to think of this small intrinsic curvature as arising from an imagined unknown form of "dark energy". Some people don't. In Einstein's treatment, a tendency for distances to expand is a spacetime curvature (spacetime is curved and therefore we have no right to expect largescale cosmic distances to remain the same.) He allowed for a constant curvature Lambda (on the left side of the GR equation) not associated with any energy density (energy densities are on the right.)

It seems fair to want to satisfy and make room for both types of people. Those who like to think of Lambda as a small intrinsic spacetime curvature (a residual tendency for distances to expand at 1/173 of one percent per million years).
And those who like to posit imaginary form of "energy" to explain this constant curvature and want to move Einstein's curvature term over to the righthand side of the equation, algebraically transformed into a type energy density which we don't see.

I wouldn't call that kind of polite fairness "contortions". I would describe allowing for both preferences as a kind of tactful agility

 

[marcus]

Q,
I'm a slow typer. I promised I'd get you some numbers but it might take a few minutes. The present rate of distance growth is 1/144 % per million years and the longterm residual rate it is tending towards is 1/173%. That is what you get from Einstein's Lambda constant. But I'd like to show a curve that plots the history of that growth rate say from year 1 million up to the present, and on into the future some so you can see it leveling out.
...it took me a while...
what I had in mind was something like this (I have to explain the time scale. it is in units of 17.3 billion years, so x=1 is 17.3 By and the present, about year 13.8 billion is around x = 0.8
using that time scale makes the formula simpler. I'll get a conversion table for the time scale later, for now just remember that the present is 0.8.

This shows the history of the growth rate. It is leveling out at about 6% per billion years. You can see it leveling out at around 0.06, which is 6%
More precisely 1/17.3 = 0.0578, but .06 is close enough so let's call it 6% per By growth.
The current rate is close to 0.07, about 7% per billion years.
If you look closely at the graph where x = 0.8 you'll see it says 0.07.

 

[Quarlep]

The present rate of distance growth is 1/144 % per million years and the longterm residual rate it is tending towards is 1/173%. That is what you get from Einstein's Lambda constant. But I'd like to show a curve that plots the history of that growth rate say from year 1 million up to the present, and on into the future some so you can see it leveling out.

Thank you very much. I am 18 years old so let me be repeat this knowladge.As I understood that space-time itself have a energy density which is cosmological constant but you said that's not quite true cause that lambda is a curvature of universe. Its smthing like constant and you showed me a graph but I dindt understand the main idea cause my english ls bad can you explain me simpler.

Thanks

 

[Quarlep]

Your first graph shows us how lambda change with time and second is how universe geometry changes with lambda or smthing else ? I am sorry but what's the y and x axis

 

[marcus]

The second graph was too much too fast, I'll delete it and we can discuss it later after we look at the first graph. Let's talk about the first one.
I wish I knew what your main language is, I might be able to explain one or two basic concepts better.

Do you know what a growth rate is? It is a number per unit time. Like "4% per year".
That means 0.04 per year.
Something grows by 1/25 of its size per year.

Do you know the trigonometry functions? Like sin(x) and tan(x)? Do you know the hyperbolic trig functions
like sinh(x) and tanh(x)?

It turns out that our universe's distance growth rate is not constant but declines along a kind of nice sloping curve.

Lambda is a constant that helps to define that curve.

But first, tell me if you have had any school work with trig functions (like tangent(x) and cotangent(x), or tan(x) and cot(x), for short). And if you have met their relatives tanh(x) and coth(x).

If you haven't then I need to think of a different way of explaining that first curve. It is y=coth(x) and it turns out the universe's growth rate has declined following that curve.

 

[Quarlep]

Whats the y-axis on this graph you are trying to tell me change in time and change in smthing but I didnt understand the other y-axis excuse me but what's means present rate of distance growth 1/144% per million years and what's the grow rate why there's % (these question can be simple or stupid but I don't have enough english and cosmolgy knowladge to learn understand it)

Thanks for help

 

[marcus]

The x-axis is ordinary time divided by 17.3 billion years.
That makes a convenient small number.
For example, the present time is usually said to be around 13.8 billion years.
If you divide that by 17.3 billion years you get 0.8.

So suppose you print the graph out on a piece of paper. You can put a dot on the x-axis at 0.8. That is the present day.

The y-axis is fractional growth per billion years.
So you can read from the graph that the present rate of distance growth is 0.07 per billion years. that is 7% per billion years.
That is the present growth rate that astronomers measure
and their observations show that it is heading down towards 6%. Or just slightly less than 6%

 

[Quarlep]

I didnt see your answer and I asked again sorry for that. my main language is turkish. I know trigonometry but I don't know tanh and coth

 

[Quarlep]

Do you know what a growth rate is? It is a number per unit time. Like "4% per year".
That means 0.04 per year.
Something grows by 1/25 of its size per year.

If I have 100 $ than I l ll have (in %4 growth per year) I ll have 104$ than 104+104/25 so 108.16 isn't it

 

[marcus]

No problem. You can ask twice. It doesn't hurt to answer twice.

Whats the y-axis on this graph you are trying to tell me change in time and change in smthing but I didnt understand the other y-axis excuse me but what's means present rate of distance growth 1/144% per million years and what's the grow rate why there's % (these question can be simple or stupid but I don't have enough english and cosmolgy knowladge to learn understand it)

Thanks for help

Well 1/144 = 0.007

So imagine that in a million years the distance grows by .007% of itself.

0.007% is the same as 0.00007. In a million years the distance grows by 0.00007 of itself.

In cosmology, distances grow very slowly

Now the growth rate does not always stay the same! It declines according to that curve I plotted.

But if it did stay the same for a billion years, the distance would grow by 0.07 of itself. (I took away three zeros because we stepped up from million years to billion years, so larger fraction.)

Does this make sense to you? The current expansion rate is 0.07 per billion years (but that is just the rate per unit time.)

 

[marcus]

If I have 100 $ than I l ll have (in %4 growth per year) I ll have 104$ than 104+104/25 so 108.16 isn't it

Yes that is right.

 

[Quarlep]

So now our universe diameter is r and we are multiplying it 1/144 per billion years(that grow rate is diameter of universe isn't it) after billion year we will multiply it 1/173 per billion year than we will multply it some number which your graphs show

 

[marcus]

So now our universe diameter is r and we are multiplying it 1/144 per billion years(that grow rate is diameter of universe isn't it) after billion year we will multiply it 1/173 per billion year than we will multply it some number which your graphs show

I think you are getting the idea.
But you left out the decimal point. It is not "1/144 per billion years". the present growth rate is 1/14.4 per billion years. that is roughly 0.07

The longterm rate (determined by the cosmological constant Lambda) is not "1/173 per billion years", it is 1/17.3 per billion years.
Very roughly that is 0.06

So you can see that the curve is 0.07 at present and tending towards 0.06

I should make you a table for converting time (in usual scale of billions of years) to time on the x-axis scale.
To convert you have to divide by 17.3.
Imagine that we have a new unit of time called the UNIVERSE DAY, it is 17.3 billion years long. Or we will name it after you and call it a QDAY.
Now the present age of the universe is 0.8 Qdays.
Can you get used to thinking of time measured in Qdays? That is what the x-axis of that plot measures.

 

[Quarlep]

I should make you a table for converting time (in usual scale of billions of years) to time on the x-axis scale.
To convert you have to divide by 17.3.
Imagine that we have a new unit of time called the UNIVERSE DAY, it is 17.3 billion years long. Or we will name it after you and call it a QDAY.
Now the present age of the universe is 0.8 Qdays.
Can you get used to thinking of time measured in Qdays? That is what the x-axis of that plot measures.

I understand your idea.I can get used to think time measured in Qdays I guess. 1 Qday is 17.3 billion years. 1/Qday is expansion rate that's why graph is look like 1/x graph. This graph is y=1/Qday isn't it

 

[marcus]

Now maybe we are ready to look at the expansion history. It is the history of any large cosmic distance. Growth is proportional to size, so every history looks the same. The unit of distance is arbitrary, you can choose what you want it to be. Suppose you choose it to be a billion light years. Then this graph plots the size of a distance between two galaxies which was one billion light years at time x=0.6.
That is 0.6 Qdays, which corresponds roughly to about year 10 billion.

I think you are getting the idea, Q. This distance was 0.3 billion LY back at time 0.1 Qday.
then it grew and grew. By 0.6 Qday it was already 1 billion LY.
Then it continued growing and by the present day of 0.8 Qday it is already 1.3 billion LY.

 

[phinds]

Thanks, sounds like a much better way to put it than my "yes in a sense but..." contorsions

Yeah, Marcus has a habit of doing that

 

[Quarlep]

Now we have a galaxie which distance is 1 billion light year away.than x-axis shows us the change in 1/Qday and y is distance from galaxy.

So If I get it when x=0.23 than distance from galaxy is 0.5 light years. and that day universe is 0.23xQday=4 billion years after universe created

 

[marcus]

Now we have a galaxie which distance is 1 billion light year away...

So If I get it when x=0.23 than distance from galaxy is 0.5 light [billion] years. and that day universe is 0.23xQday=4 billion years after universe created

Good.

We are talking about a galaxy which is 1 billion LY from here at time 0.6 Qday. And we are looking at what distance it is at other times.
You point out that at 0.23 Qday it is just HALF as far---it is only 0.5 billion LY.
and truly on that day the age of the universe is 4 billion years. Your number is correct.

 

[Quarlep]

Hi Q,
So far the observations are consistent with the cosmological constant interpretation. IOW not necessarily anything we would recognize as energy (in the usual senses) but better thought of as an intrinsic tendency for distances to expand at a small permanent rate (not affected by matter and radiation).

The present rate of expansion is somewhat higher and is observed to be gradually declining as if it is going to level off at this small residual rate. That's all we know--what we observe. We don't observe any energy, we see a longterm trend in geometry. I'll give you some numbers to make this more definite.

So there's no energy in space-time this lambda is a geometric thing which we discussed.Theres no energy density too. Its a wrong idea.

All these things are true isn't it. I learned many things today about lamda and universe expansion thank you very much.

 

[PeterDonis]

So there's no energy in space-time this lambda is a geometric thing which we discussed.Theres no energy density too. Its a wrong idea.

As marcus said in an earlier post, according to our best current knowledge, it is possible to view $\Lambda$ as either a "geometric thing" or as an "energy density"; it just depends on which side of the Einstein Field Equation you put the term on. Moving a term from one side of the equation to the other doesn't affect any physics.

The real physical question is whether this $\Lambda$ can change. If it can't, if it's the same constant everywhere and at all times (which, according to our best current data, it is, but our data is still fairly limited), then even if you view it as an "energy density", it can't exchange energy with anything else. As long as that's true, viewing it as a "geometric thing" works just as well.

However, if we ever find evidence that $\Lambda$ can change--that it can be different at different points of spacetime--then viewing it as a "geometric thing" will no longer work; we will have no choice but to view it as an energy density, because that energy density can be exchanged with other kinds of energy density. But this "lambda energy density" will still have all the counterintuitive properties that make people hesitant to view it as an energy density: it will still produce negative pressure and it will still violate various energy conditions that other kinds of energy density obey. So if your reason for wanting to view it as a "geometric thing" instead is those counterintuitive properties, you should be aware that it is still possible (though most physicists think it unlikely) that we will find evidence someday that $\Lambda$ can vary.

 

[marcus]

Q,
Wait. Don't go away yet. What you said is one point of view, and I tend to agree: Lambda is a constant feature of spacetime geometry, which is how Einstein originally put it in the equation in 1917, and how you see it if you go to Wikipedia and look up "General Relativity".

But we have to leave room for people who seriously believe that Lambda arises from some unknown form of energy. They like to convert it to an energy density and move it over to the righthand side of the equation with the other densities (of matter and radiation).
We do not KNOW that this is wrong. Maybe some new kind of energy will be discovered!

We can be skeptical about this, but we have to leave room for both preferences, or both viewpoints.

I urge you to keep on asking questions, when you have time to reflect on these things

 

[marcus]

Hi Peter, our posts crossed, I saw yours only after I posted. I think that's a good statement and sums up the important thing. So far Lambda seems to be constant and with no evidence that it can vary or exchange energy with various stuff on the righthand side of the equation. So the simplest version seems good at least for now. But we don't know the future and it might turn out to vary.

I think Q probably went off line. His last post was a bit past 2PM pacific which I think must be after midnight where he lives.

I must say I enjoyed the questions.

It's possible Q will be back here tomorrow, so I'll post something...or maybe not. Maybe wait until he gets back.

 

[Quarlep]

Lamda can be both sides of the equation.In left side its a constant and there's no meaning to talk about energy density.In right hand side lambda will no longer a constant so that time lambda will be a energy density.But we don't have any evidence to prove lambda is a constant or not(In a long term).

 

[Quarlep]

Your second graph shows us the observable universe include lambda isn't it ? And ls 1/Qday a Hubble constant or that's lamda

 

[Quarlep]

If there's any equations can you give me about this graps

Thanks

 

[marcus]

Your second graph shows us the observable universe include lambda isn't it ? And ls 1/Qday a Hubble constant or that's lamda

Yes the second graph includes the effect of Lambda, that is why it changes from convex to concave around x=.45
as long as matter is dense enough it dominates and slows expansion
but then after a lot of expansion the matter is thinned out
and the natural tendency to expand wins, and expansion accelerates.

by "convex" I mean rounded like a dome, by "concave" I mean hollowed like a cup or bowl. there is a point where the curve changes, around .45
it is hard to find precisely, but it happens.

Your other question is interesting. 1/Qday in a certain sense is BOTH things. It is not the OFFICIAL Lambda but it is a useful practical form of Lambda.
To get the official Lambda, as Einstein put it in his GR equation you must square 1/Qday and multiply by 3.

1/Qday is the practical form of the cosmological constant that is useful here---it is the longterm eventual Hubble constant---you can write it H_∞
It is a growth rate of about 0.06 per billion years. Or 6% per billion years. We always have this in mind, it is the eventual rate towards which our present H is tending.

But in 1917 when Einstein was writing his equation he was not thinking about our standard model expanding cosmology with its Friedmann equation (that all came later). And the most convenient thing for him to write down in the context of his equation for GR was not H_∞.

It was, in fact, 3H_∞².

That is a number per square time. Or if you want you can divide by c² and have a number per square distance----a number per unit area.

I tend to think of that as just fiddling around with the algebra---algebraic manipulation. For me these are just different versions of the same cosmological constant. I actually prefer thinking of it as H_∞

 

[marcus]

Quarlep, this might sound like it is unrelated to the discussion but I'm interested to know. Did you learn some differential calculus already?

For example, did you learn that the slope of the sin(x) is equal to the cos(x)? You sound like someone who has learned some calculus as well as trig.

For doing calculus, it is best to measure angle in radians, not in degrees.
I will denote the derivative or slope of a curve by the ' so the slope of f(x) can be written simply as f'(x)
and then
sin'(x) = cos(x)
and
cos'(x) = - sin(x)
Is all that familiar to you?

BTW I couldn't reply to your posts earlier because I went outdoors to watch the eclipse around 5 AM pacific time on Saturday morning and missed a lot of sleep. So yesterday I got sleepy early in the evening and couldn't keep my eyes open. Otherwise I would have replied earlier.

The moon was, of course, red. Because it was being illuminated by the circle of sunsets and sunrises that were happening at that moment all around the earth. It was being lit by the red light of all those sun-sets-and-rises. But that doesn't have anything to do with the topic.

 

[Quarlep]

Quarlep, this might sound like it is unrelated to the discussion but I'm interested to know. Did you learn some differential calculus already?

For example, did you learn that the slope of the sin(x) is equal to the cos(x)? You sound like someone who has learned some calculus as well as trig.

For doing calculus, it is best to measure angle in radians, not in degrees.
I will denote the derivative or slope of a curve by the ' so the slope of f(x) can be written simply as f'(x)
and then
sin'(x) = cos(x)
and
cos'(x) = - sin(x)
Is all that familiar to you?

Yeah I know simple calculus.I know find a function derivative (every type of them arccosx,sinx,lnx,e^x ...