# Does space-time have an energy itself?

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1. Apr 4, 2015

### Quarlep

Is space time has a energy itself ?

Thanks

2. Apr 4, 2015

### 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.

3. Apr 4, 2015

### wabbit

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

4. Apr 4, 2015

### Quarlep

If space-time has energy density it means it has a energy isnt it ?

5. Apr 4, 2015

### 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.

6. Apr 4, 2015

### marcus

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.

Last edited: Apr 4, 2015
7. Apr 4, 2015

### wabbit

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

8. Apr 4, 2015

### 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

Last edited: Apr 4, 2015
9. Apr 4, 2015

### 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.

Last edited: Apr 4, 2015
10. Apr 4, 2015

### Quarlep

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 thats 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

11. Apr 4, 2015

### 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 whats the y and x axis

12. Apr 4, 2015

### 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.

Last edited: Apr 4, 2015
13. Apr 4, 2015

### 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 whats means present rate of distance growth 1/144% per million years and whats the grow rate why theres % (these question can be simple or stupid but I dont have enough english and cosmolgy knowladge to learn understand it)

Thanks for help

14. Apr 4, 2015

### 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%

15. Apr 4, 2015

### Quarlep

I didnt see your answer and I asked again sorry for that. my main language is turkish. I know trigonometry but I dont know tanh and coth

16. Apr 4, 2015

### Quarlep

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 isnt it

17. Apr 4, 2015

### marcus

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

18. Apr 4, 2015

### marcus

Yes that is right.

19. Apr 4, 2015

### 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 isnt it) after billion year we will multiply it 1/173 per billion year than we will multply it some number which your graphs show

20. Apr 4, 2015

### marcus

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.

Last edited: Apr 4, 2015