# Has anyone calculated the amount of energy required to expand space/time?

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#### Airthumbs

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##### Has anyone calculated the amount of energy required to expand space/time?
« on: 23/03/2012 03:32:43 »
And where is that energy coming from? It can't have all come from the big bang as the expansion is accelerating!
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#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #1 on: 28/03/2012 13:46:10 »
AT this one is a lot trickier than one first think

First of all, if I want to define a energy I need a 'same reference frame' to do it from. Let's take something 'moving. You know already that all 'relative motion' is observer dependent, right?

If it is, then the 'energy' you will define to that motion also will be observer dependent. Relativity teaches us that to agree on something we first must define from where and how we will 'measure'. And if you look behind that statement you will realize that all definitions based on common, but different, approaches then will be as correct. And that's also where  E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws makes its appearance, as well as the ideas Lorentz expressed in his Lorentz transformations. That even if the universe somehow becomes all 'relative' we can still find ways to relate those views conceptually.

And this is why I doubt all formalism of QM not taking this into consideration, at least if it wants to believe in 'whole SpaceTime' not solely locally defined. Although, if you do define it locally you can make it work, at least as I think of it now.
« Last Edit: 28/03/2012 13:50:03 by yor_on »
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#### JP

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #2 on: 28/03/2012 17:25:55 »
The short answer is yes, they have.  We know that if space itself contains energy, the universe will expand at an accelerating rate (from the equations of General relativity).  We also know by observing the accelerating expansion what value we need to plug in for this energy content of space to match our observations.

What we don't know is where it comes from.  We haven't found a cause for this energy of space or measured it on a smaller scale.  Our evidence is the accelerating expansion of the universe.

#### Airthumbs

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #3 on: 01/04/2012 22:11:18 »
Thanks for the answers, Yor_on can you not use light as a frame of reference as the speed is constant?

And JP, if we know the energy exists, then for example, could we say how much of this unknown source energy is contained within a one meter cubed, volume of space?

And if no one has any idea where this energy comes from, yet that it is there, then how to we find a way of extracting it?
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#### JP

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #4 on: 01/04/2012 22:41:20 »
I've never seen it done, but you should be able to say how much is in 1 m3 of space.

There are a couple of problems with "extracting" it.  First, there isn't much of it in space.  Within our galaxy, for example, mass and energy from other sources are way more important than dark energy, and that's true even in "empty space, " such as between various star systems.  The reason dark energy is important, however is that there is so much empty space between galaxies that it really adds up.  The universe is so big that even this tiny amount of energy adds up to something big.  So because there's so little of it in any region of space, we wouldn't be able to do much with it compared to, for example, absorbing light from other stars to power something.

The second problem is that to use energy to do work you have to let the energy flow from high energy regions to low energy regions, and this flow powers whatever engine you're running.  To do useful work with dark energy, you'd have to have a regions with higher dark energy and those with lower dark energy, and as far as I know, dark energy is basically uniform everywhere.  Since we can pump it from a high region to a low region, we can't extract it to run any machines.

#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #5 on: 02/04/2012 04:11:27 »
It's possible to define a cubic meter locally, as long as you use your clock and your ruler. And you're correct in that if we assume radiation to define the best clock, measuring a arrow, that cubic meter should be the same for all measuring it locally. That's also a good argument for why conversation laws can work the same, as I think of it.

But then you have only defined it locally.

Trying to define it from a conceptually 'whole indivisible' SpaceTime, not including Lorentz transformations? Then it becomes tricky or rather impossible. Using Lorentz transformations though, should take you back to what I name 'locality' as it always use the 'constant' of radiation as its guide.

So that's the only way I can think of measuring, locally.

But philosophically it's a quagmire, if the only measurements you can make is local, then what I see and what you see is two different things. Assuming that 'distance' exist as a true measure 'universally' and not only locally defined, as well as assuming that the arrow of time being 'universally same' and not only 'locally same'.

And without 'distance' and 'the arrow' being the same?
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#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #6 on: 02/04/2012 04:34:05 »
It's tricky though.

Assuming that all relative motion being the same that is. Assume that A is moving relative Earth having double the speed of B, both in the same direction relative (towards) Earth and themselves. Then assume both to be uniformly moving. that will mean that A will have a higher Lorentz contraction than B.

Now the question becomes, even though their arrow of time can be said to be 'locally' the same, if superimposing. Can we also say that the distance measured, to Earth for example, are the same?

The answer I find is that a meter can only be a meter locally.
Never conceptually.

Or maybe you would like to turn that around and say that a meter can only be a meter conceptually
But it is still locality that rules, and using that you don't compare, you just use your local ruler and clock.
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#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #7 on: 02/04/2012 04:48:12 »
Most of the confusion I get comes when I try to work in the framework of one indivisible SpaceTime, shared by us all. It's not possible to define anything from that as I find it. But using 'locality' I can define a lot of things to my own pleasure. My SpaceTime has some principles that we all share, constants being the important ones. But what I see and what I measure is mine, and what you see and what you measure is yours. It's constants that allow us to define it as us being in a same SpaceTime, nothing else.
=

Expanding a little on 'distance'.

When I say that all meters are the same locally I'm specifically thinking of space and the question of 'zero point energy' here. I expect that to be true that no matter your relative 'speed/velocity' we will find that cubic meter to have the same amount of 'energy' if we now could measure it. And you might be able to test that assumption, assuming that a Casimir effect truly is an effect from that 'hidden 'space' energy' instead of coming from the property's of matter.

But if I'm correct there, then we need to question some other things. Mostly it is how to define things though, not a question if 'distance' really exist. We know it exist locally, we use it daily as well as the arrow. But to see 'SpaceTime'.
« Last Edit: 02/04/2012 04:59:44 by yor_on »
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#### Æthelwulf

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #8 on: 02/04/2012 05:52:32 »
And where is that energy coming from? It can't have all come from the big bang as the expansion is accelerating!

Yes, we have calculated it, and often it is called a vacuum energy (or some might even refer to it as the cosmological constant which is the overall energy density of the entire universe).

Consider a uniform energy density

$$\nabla \phi + \Lambda = 0$$

where

$$\nabla \phi = \Lambda$$

here $$\Lambda$$ is the energy density of the vacuum. Differentiating $$\phi$$ with $$x^2+y^2+z^2$$ the solution itself for a three dimensional vacuum we have

$$\phi = \frac{\Lambda}{6}[x^2 + y^2 + z^2]$$

Continued expansion then is how the energy density is in a particular direction, so for the Cartesian Coordinate $$x$$-direction the force required for expansion is

$$\frac{\partial \phi}{\partial x} = \frac{\Lambda}{6}2x$$

That's just the same as the expression $$\frac{\Lambda x}{3}$$ and there you have it, viola!

You can find continued reading, for instance, if you use google and look for calculations for the energy density descreprency of 122 orders of magnitude.

#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #9 on: 02/04/2012 06:37:19 »
Yeah, but the energy defined is just like with photons. You expand space you get a red shifted photon, that photon will now, according to your measurement, have less energy. So according to you it loses energy by an expansion. And if we assume that one cubic meter 'space' always contain the same energy, then a expansion must state that with more 'space' there will be more 'energy'.

So?

But if I'm correct about my assumption of that 'cubic meter' space always giving us a same 'energy' reading, no matter our apparent velocity relative something else, and there the Casimir effect offer a good test for it, possibly? Then I wonder?

It all goes back to how to define a 'distance' for me.

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#### Æthelwulf

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #10 on: 02/04/2012 06:39:24 »
Yeah, but the energy defined is just like with photons. You expand space you get a red shifted photon, that photon will now, according to your measurement, have less energy. So according to you it loses energy by an expansion. And if we assume that one cubic meter 'space' always contain the same energy, then a expansion must state that with more 'space' there will be more 'energy'.

Basically, yes. As the universe expands, more energy is released into the vacuum. If you like, the energy has always been there, it is just becoming more diluted.

#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #11 on: 02/04/2012 07:22:52 »
Are you thinking of 'gravity' as a 'negative energy' Wulf?

To me gravity is a geometry firstly, not a 'energy' although we use descriptions as 'potential energy' of matter relative a gravitational potential. I'm not sure what you mean by diluted?
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#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #12 on: 02/04/2012 07:39:25 »
In some weird way it makes some sense though

Photons really lose 'energy' in a expansion, differing it from a gravitational redshift in where we assume them to be intrinsically the same, no matter your measurement. And that goes for measuring a photon being in relative motion too, where you can find a blue/red shift depending on your direction relative the photon. But in a expansion all observers, no matter their relative motion, should agree on it losing 'energy', all as I understands it. And that is indeed weird as it is assumed to be 'time less'? To see that one one need to differ between something 'intrinsic', belonging to itself, and something created by its relation to the detectors relative motion/gravitational potential.

So where do a photon find 'time' to become intrinsically weaker?
==

By 'making sense' I was thinking of the 'space intrinsic energy' becoming greater relative/following the measured distance in a expansion, at the same time as our 'propagating' radiation gets weaker. Seems as a balance somewhere, well, possibly?

« Last Edit: 02/04/2012 11:23:06 by yor_on »
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#### Æthelwulf

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #13 on: 02/04/2012 07:40:17 »
Are you thinking of 'gravity' as a 'negative energy' Wulf?

No, not at all. Gravity is strictly positive in our corner of the universe. There maybe antigravitational substances like exotic matter. In fact if my memory serves me correctly, I believe there is in fact a very very small amount of negative energy when the zero point energy interacts on small scales.

#### Æthelwulf

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #14 on: 02/04/2012 07:42:50 »
I'm not sure what you mean by diluted?

If you have a compact bit of sand, and place it into water, the sand will dilute and spread apart in it's new medium. Matter and energy is the same, given enough amount of time, it will dilute over spacetime.

#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #15 on: 02/04/2012 07:58:04 »
Okay In GR energy isn't conserved as I understand it, as well as in a expansion, but it might have to do with what definitions one use. As we all would like to join QM and GR it could become a matter of defining how they relate.

But that is me.

Also, you seem to assume the same as me?

That there should be a defined value for 'energy' relative SpaceTime. But then it also becomes a question of what one mean by a SpaceTime. It's rather unfortunate that so many differ between QM and Relativity, as if they were two different things. They can't be, they are in the same universe.
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#### Æthelwulf

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #16 on: 02/04/2012 08:31:40 »
I actually don't believe energy is a conserved quantity for our universe. I brought this up somewhere else, perhaps in the time is an illusion thread, that if we live in a timeless universe, we can not translate energy in time, meaning we cannot conserve it. I offered this as an explanation of accelerated expansion.

#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #17 on: 02/04/2012 10:03:17 »
I don't know, maybe it isn't? But then there can't be a 'closed universe' either as it seems to me, or maybe it can? I don't think so myself, and I would start to wonder over all conservation laws if so.
==

what I'm talking about as 'closed' here is the geometry, sort of

If we have a universe that leaks it's not 'closed', and in such a universe all conservation laws that works must then become special circumstances of a open geometry, as I think of it.

And 'energy' seems the simplest definition of all that exist.
« Last Edit: 02/04/2012 10:29:23 by yor_on »
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#### yor_on

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #18 on: 06/04/2012 23:10:54 »
But I've been wondering about that. It's possible to think of it in form of 'densities'. Assume that we have densities that are measurable,and then others that we can only infer. Those inside what we can define as SpaceTime then becomes something floating in a ocean of unmeasurable densities that creates what we see as 'constants'. But that's also a totally philosophical suggestion as I can't see how to prove such an assumption
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#### Airthumbs

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #19 on: 08/04/2012 18:40:30 »
I thought matter as we know it consists of only something like 5% or even less of the known Universe.  If Anti-hydrogen and hydrogen have the same mass and there is a lot more Dark matter out there then matter, how can it be that universally, matter generates more energy?
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#### richardgarrick

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##### Re: Has anyone calculated the amount of energy required to expand space/time?
« Reply #20 on: 02/05/2012 15:40:07 »
Either the energy comes from inside this universe or it comes from outside of this universe.  If the energy is from inside the universe I think the most likely source is from the various effects we describe as entropy.

I think it is more interesting to think of the energy coming from outside of our universe.  I believe our universe is a black hole in a much larger universe.  If we could look at our universe from the outside we could relate changes to the diameter of the black hole to the amount of mass failing into the event horizon.  Assuming the event horizon has a size relationship to the universe it could contain.

If we are looking inside our universe than we would have to a local space-time distortions related to measurable amounts of entropy.  We would also have to consider that not all units of space have the same energy requirements.