Expanding Universe question

[mistermack]

I just wondered, as the Universe expands, is it gaining energy in some way?

If the Milky Way moves one kilometer further away from the Andromeda Galaxy, (ignoring it's existing motion), doesn't that mean that a stupendous amount of potential energy has been added to the system? Because of the distance apart being part of the energy equation?

Is there a known source for this, or have I got it wrong in the first place?

[imatfaal]

First small point.  Milky way is gravitationally bound to Andromeda; they are in (complex) orbit with each other and various minor satellite galaxies

Expansion.  Two things flying apart in normal space.  No change in energy - conversion of kinetic to potential.  (if you are talking about an outside influence moving two galaxies apart - then yes huge energy required)

Accelerated Expansion.  Now this is where it gets difficult.  When the space through which particles are moving is changing then energy is not conserved.  You could also think that all the conservation laws are parallels to translation laws - Noether.  Energy conservation is the same a time reversibility - but the change in space is one directional so we do not see this as an time reversible / energy conservational process

 

[J.C.MacSwell]

8 hours ago, imatfaal said:

 

Expansion.  Two things flying apart in normal space.  No change in energy - conversion of kinetic to potential.  (if you are talking about an outside influence moving two galaxies apart - then yes huge energy required)

 

This part to me describes what happens without expansion effects, like say two bodies moving with respect to each other inside our solar system.

 

So what if they are far apart enough for an expansion effect, but not enough to lose contact? It would seem like a gain in energy as mistermack alludes to, even without accelerated expansion.

[Eise]

15 hours ago, mistermack said:

I just wondered, as the Universe expands, is it gaining energy in some way?

For some 20 years the answer would have been definitely 'no'. It was assumed that the expansion slowed down due to gravity. So this would have been the usual process of turning kinetic energy into potential energy in a gravitation field. The only question was if the kinetic energy was enough to let the universe expand forever, or that it would once contract again.

But then it was discovered that the expansion is accelerating. This needs a source of energy, and as there is no explanation yet what it is, it is called 'dark energy'. This is still one of the greatest riddles in cosmology.

15 hours ago, mistermack said:

If the Milky Way moves one kilometer further away from the Andromeda Galaxy, (ignoring it's existing motion), doesn't that mean that a stupendous amount of potential energy has been added to the system? Because of the distance apart being part of the energy equation?

You can't ignore its existing motion: the kinetic energy would be the source of the potential energy. The sum of kinetic and potential energy stays the same. But the gravitational attraction between Andromeda and the Galaxy is stronger than the expansion of the universe (at the moment!). In fact, we are moving to each other, and we will eventually collide.

15 hours ago, mistermack said:

Is there a known source for this, or have I got it wrong in the first place?

Well, once set in motion, there is no energy source needed for an object to move away from a gravitational centre. Just throw a ball in the air, and as soon as it has left your hand it moves on without any energy source. You gave it the initial kinetic energy, and if the energy would suffice the ball would leave the earth forever. So if we take instead of Andromeda a galaxy that is billions of light years away, its movement away could be explained by the the initial big bang. However, this movement should slow down due to gravity, and as said above, it doesn't.

[mistermack]

So the current thinking is that the dark energy is already here, hidden, in a mysterious form, and is gradually being converted to the increasing amounts of potential and kinetic energy ? 

Or could it be that there is a constant trickle of dark energy from an unknown source in so-far unknown dimensions?

[Eise]

2 hours ago, mistermack said:

So the current thinking is that the dark energy is already here, hidden, in a mysterious form, and is gradually being converted to the increasing amounts of potential and kinetic energy ? 

Or could it be that there is a constant trickle of dark energy from an unknown source in so-far unknown dimensions?

I'll better refer to Wikipedia before I say something wrong...

But my understanding is that the cosmologists suppose that dark energy is constant per volume. But as the universe expands, there is more and more dark energy, so the expansion rate of the universe increases. But there are people here that may know it much better.

Edited July 26, 2017 by Eise

[Mordred]

That last descriptive is accurate 

[Vmedvil]

Well, I am not going to explain this twice in the same forum read this thread, it explains it http://www.scienceforums.net/topic/110290-so-called-dark-energy-and-gravity/  No, the Universe is not gaining Energy. 

[Strange]

7 minutes ago, Vmedvil said:

Well, I am not going to explain this twice in the same forum read this thread, it explains it http://www.scienceforums.net/topic/110290-so-called-dark-energy-and-gravity/  No, the Universe is not gaining Energy. 

The equation you post appears to contradict that statement. The rate of expansion is increasing, which implies an increasing lambda.

Also, where did that equation come from? It looks like, but is different from, the standard Friedmann equation.

[Vmedvil]

1 hour ago, Strange said:

The equation you post appears to contradict that statement. The rate of expansion is increasing, which implies an increasing lambda.

Also, where did that equation come from? It looks like, but is different from, the standard Friedmann equation.

Well, the membrane of the universe has no mass, thus there should not be any energy increase if you look at SR, E= γMC^2 , if you find the membrane of the universe to have mass then you should take that up with Einstein not me.

M= 0 , E = 0

Doesn't matter the velocity of increase, if you want to put it into those terms.

If you doubt then solve the Tensor field yourself.

Edited October 2, 2017 by Vmedvil
More detailed Einstein Field.

[MigL]

Just as volume of space increases with expansion, and, as Eise notes, vacuum/dark energy increases with the volume, we also have gravitational separation increasing.
This leads to a NEGATIVE ( because of convention and abhorrence of infinities ) increasing gravitational potential.

And no, I'm not bright enough to figure out if the negative gravitational potential is equal to the positive dark energy

[Mordred]

7 hours ago, Vmedvil said:

Well, the membrane of the universe has no mass, thus there should not be any energy increase if you look at SR, E= γMC^2 , if you find the membrane of the universe to have mass then you should take that up with Einstein not me.

M= 0 , E = 0

Doesn't matter the velocity of increase, if you want to put it into those terms.

If you doubt then solve the Tensor field yourself.

There is no membrane to the universe, there is however apparent horizons based on observer limits under GR in terms of the killing vectors under specified metrics of the FRW.. Such as Hubble horizon, particle horizon and Cosmological event horizon.

 The question on whether or not the conservation of energy/momemtum laws apply on the cosmological scale, however I can quarantee the Einstein field equations does not address that issue. As we don't know what causes Lambda we cannot know if it applies under the conservation laws or not.

How can we ? As far as radiation and matter, then yes you are correct. Under an adiabatic and isentropic expansion conservation of energy does apply. Adiabatic meaning no net inflow or outflow of energy.

 However this does not mean a closed system.....

The conservation laws only apply in closed systems...

The EFE works equally well for open systems, so why would you think it means the universe is conserved?

Edited October 2, 2017 by Mordred

[Vmedvil]

6 hours ago, Mordred said:

There is no membrane to the universe, there is however apparent horizons based on observer limits under GR in terms of the killing vectors under specified metrics of the FRW.. Such as Hubble horizon, particle horizon and Cosmological event horizon.

 The question on whether or not the conservation of energy/momemtum laws apply on the cosmological scale, however I can quarantee the Einstein field equations does not address that issue. As we don't know what causes Lambda we cannot know if it applies under the conservation laws or not.

How can we ? As far as radiation and matter, then yes you are correct. Under an adiabatic and isentropic expansion conservation of energy does apply. Adiabatic meaning no net inflow or outflow of energy.

 However this does not mean a closed system.....

The conservation laws only apply in closed systems...

The EFE works equally well for open systems, so why would you think it means the universe is conserved?

Yes, I didn't know the proper term for it, but yes, the point where particles would violate moving faster than the speed of light, if they were moving at the speed of light from the time of the Big Bang that is fine. Cosmological Event Horizon, The reason I think it is a closed system is something very simple, we have never found stable wormholes or "White Holes" which we would expect in a "Open System Universe", Under what method does new Matter/Energy/Dark Energy, gain entry into the Universe?  Now we have found Black-hole's but we also see black-hole's lose mass as hawking radiation happens then evaporate after long period of time, There is no known method of energy entering or leaving, without evidence to show that is does indeed exit/enter the universe, we can assume it does not. That being said near the Cosmological Event Horizon, there could be a sort of "Universe Hawking Radiation" if it functions like a Black-Hole. We can safety say that something does not happen if there is no evidence to show it is happening until that evidence appears. Remember, that extraordinary claims require extraordinary evidence, as Thunderf00t says.

Edited October 3, 2017 by Vmedvil

[Strange]

1 hour ago, Vmedvil said:

We can safety say that something does not happen if there is no evidence to show it is happening until that evidence appears.

Accelerating expansion may be evidence that energy increases as space expands.

[Vmedvil]

1 hour ago, Strange said:

Accelerating expansion may be evidence that energy increases as space expands.

Yes, but that could also be proof that matter density is changing or radius is balancing out curvature or even changing curvature as unlikely as that would seem and not a increase in Dark Energy levels via the Cosmological constant or increase in Energy-mass. hints f(p,t,R,k), my actual bet is that increase in radius is balancing out the curvature to be the reason for acceleration in expansion. As I said, resolve or play around with the Einstein Field if you think I am wrong.

On 7/25/2017 at 1:52 PM, imatfaal said:

First small point.  Milky way is gravitationally bound to Andromeda; they are in (complex) orbit with each other and various minor satellite galaxies

Expansion.  Two things flying apart in normal space.  No change in energy - conversion of kinetic to potential.  (if you are talking about an outside influence moving two galaxies apart - then yes huge energy required)

Accelerated Expansion.  Now this is where it gets difficult.  When the space through which particles are moving is changing then energy is not conserved.  You could also think that all the conservation laws are parallels to translation laws - Noether.  Energy conservation is the same a time reversibility - but the change in space is one directional so we do not see this as an time reversible / energy conservational process

 

 

The problem with "When the space through which particles are moving is changing then energy is not conserved." is in the Energy-momentum tensor 

Then in Maxwell's equations

do you see how, ∇ * B = 0 and ∇ * E = p/  ε₀ 

Momentum is still conserved and that breaks the electromagnetic field if it is not.

Edited October 3, 2017 by Vmedvil
Conclusion added.

[Mordred]

You might try posting the correct tensor. The energy/monentum tensor is [latex]T^{\mu\nu}[/latex]

Not [latex]T^{\alpha\beta}[/latex]

The conservation element to the stress tensor is the continuity equation [latex]\partial_\nu T^{\mu\nu}=0[/latex]

You posted the electromagnetic stress tensor which is not the same as the stress tensor under the EFE. Different tensor elements 

Edited October 3, 2017 by Mordred

[Vmedvil]

2 hours ago, Mordred said:

You might try posting the correct tensor. The energy/monentum tensor is Tμν

Not Tαβ

The conservation element to the stress tensor is the continuity equation ∂νTμν=0

You posted the electromagnetic stress tensor which is not the same as the stress tensor under the EFE. Different tensor elements 

Lol, those pictures have it labeled Incorrect that is still the Energy Momentum Tensor, I didn't look close enough, but it is still right, let me correct that, but the Electromagnetic Tensor is F_uv. Ya, WTF? , they forgot the C⁴ too and why is it negative, ya that original EFE equation is wrong.

Correction, The correctly labeled EFE and  Energy Momentum Tensor. ya, I don't know why they used T_ab instead of T_uv , In any case, it doesn't really matter doesn't effect the outcome.

Correct Einstein Field Equation

 

Correct Energy Momentum Tensor

 

Electromagnetic Field Tensor

 

Edited October 3, 2017 by Vmedvil
Added Labels, WTF, Another Website had the EM Tensor Wrong, It amazes me when Wikipedia is the best source. This was on University Websites, I blame Grad students!

[Vmedvil]

23 hours ago, Vmedvil said:

My reaction to those images of incorrect Tensor Matrices, Field Equations, and labels being on university websites, Good looking out Mordred, I blame Grad Students! That Einstein Field Equation being COMPLETELY WRONG DO NOT USE.

Edited October 3, 2017 by Vmedvil

[Strange]

Another reason why you should ALWAYS provide references for the sources you uses.

[Mordred]

Anyways errors aside from that site you used.

You may want to read the following.

"Most writers on General Relativity fail to acknowledge that Eq. (1) is not so much a conservation law, as a law for energy transfer."

Equation 1 is the standard form you usually see the stress tensor applied to.

https://arxiv.org/abs/1010.5557

Which bring us back to my original point that the EFE equation you posted doesn't provide a detail on the conservation law as equation 1 only applies for strictly freefall. (article includes this detail)

[Mordred]

14 hours ago, Vmedvil said:

My reaction to those images of incorrect Tensor Matrices, Field Equations, and labels being on university websites, Good looking out Mordred, I blame Grad Students! That Einstein Field Equation being COMPLETELY WRONG DO NOT USE.

 

Anytime you see [latex] T^{\alpha\beta}[/latex] think specifically under the Newton approximation.

The above superscript denotes a particular class of solutions comparable to Newtons gravity. 

Lets detail this further.

Start with a" perfect fluid" which has two conditions. No heat induction and no viscosity...

So [latex]T^{\alpha\beta}[/latex] is the flux of the [latex]\alpha[/latex]th component across a constant surface [latex]x^\beta[/latex]

[latex]T^{00}=[/latex] flux of O'th component energy across time surface N^0= energy density. For null pc^2. (time-time component)

[latex]T^{0i}=T^{i0}=0[/latex] energy flux of constant x^i (heat induction statement}

[latex] T^{ij}[/latex] flux of i momentum across j surface= stress.... in this case i does not equal j

so

[latex]T^{\alpha\beta}=\rho_0+\frac{p_0}{c^2}U^\alpha U^\beta-p_0\eta^{\alpha\beta}[/latex]

So check your references, see if they are describing

a) perfect fluid

b) pressureless dust

c) Newton approximation including vacuum solutions.

Conservation of energy momentum of the above (as per many textbooks,see previous post and article)

[latex]T^{\alpha\beta}=\frac{\partial T^{\alpha\beta}}{\partial x^\beta}=0[/latex]

note we use partial derivitaves in the above where [latex]T^{\mu\nu}[/latex] uses covarient derivitaves...

Reference to above equations etc 

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px436/notes/lecture6.pdf&ved=0ahUKEwjOyKGD-dXWAhVfImMKHQd9CNcQFgggMAE&usg=AOvVaw352GUmErn2XX3x4cVR1l98

 

I was looking to see if there is a specific named identity to the tensor above. Some papers call it the dust stress tensor, others the matter stress tensor. I find the above treatment more specific to the nature of the above tensor.

 So decided to post, it is good info to be aware of

(the above is from the reference but is also described in numerous GR textbooks. )

Unfortunately dummy indices are arbitrary choices, so they can be interchanged. Really just breaks down to conventions. So unfortunately there is no golden rule but alpha beta is too easy to confuse with Eulers change of basis forms. 

Edited October 4, 2017 by Mordred

[Vmedvil]

3 hours ago, Mordred said:

 

Anytime you see Tαβ think specifically under the Newton approximation.

The above superscript denotes a particular class of solutions comparable to Newtons gravity. 

Lets detail this further.

Start with a" perfect fluid" which has two conditions. No heat induction and no viscosity...

So Tαβ is the flux of the α th component across a constant surface xβ

T00= flux of O'th component energy across time surface N^0= energy density. For null pc^2. (time-time component)

T0i=Ti0=0 energy flux of constant x^i (heat induction statement}

Tij flux of i momentum across j surface= stress.... in this case i does not equal j

so

Tαβ=ρ0+p0c2UαUβ−p0ηαβ

So check your references, see if they are describing

a) perfect fluid

b) pressureless dust

c) Newton approximation including vacuum solutions.

Conservation of energy momentum of the above (as per many textbooks,see previous post and article)

Tαβ=∂Tαβ∂xβ=0

note we use partial derivitaves in the above where Tμν uses covarient derivitaves...

Reference to above equations etc 

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px436/notes/lecture6.pdf&ved=0ahUKEwjOyKGD-dXWAhVfImMKHQd9CNcQFgggMAE&usg=AOvVaw352GUmErn2XX3x4cVR1l98

 

I was looking to see if there is a specific named identity to the tensor above. Some papers call it the dust stress tensor, others the matter stress tensor. I find the above treatment more specific to the nature of the above tensor.

 So decided to post, it is good info to be aware of

(the above is from the reference but is also described in numerous GR textbooks. )

Unfortunately dummy indices are arbitrary choices, so they can be interchanged. Really just breaks down to conventions. So unfortunately there is no golden rule but alpha beta is too easy to confuse with Eulers change of basis forms. 

Oh, so the negative form of the relativity T_ab = the fluid pressure movement of Energy then? Why does the metric for GR have a negative and missing 1/ C⁴ I know that it has many F(x²) in it does that make this a quadratic root of it? So, is this the reverse tensor of the normal metric being physical manifested as the curve of Time-Space?

Edited October 4, 2017 by Vmedvil

[Mordred]

In essence. The covariant and contravariant scripts denote objects that would be identical if one flips the axis involved 180 degrees.

So in the case of positive pressure you have a vector with a magnitude and direction. You flip the direction of the vector but the scalar quantity remains unchanged. It is the same object just under a 180 degree rotation.

[Vmedvil]

19 hours ago, Mordred said:

In essence. The covariant and contravariant scripts denote objects that would be identical if one flips the axis involved 180 degrees.

So in the case of positive pressure you have a vector with a magnitude and direction. You flip the direction of the vector but the scalar quantity remains unchanged. It is the same object just under a 180 degree rotation.

So, that 1/C⁴  missing from the negative EFE equation is indeed an error and not part of the reverse Vector, but the negative is not an error.

Edited October 5, 2017 by Vmedvil

[Mordred]

edit forget last post forgot to reread your context.

The aspect to recall is we are using a coordinate basis. So certain relations are treated as rotations under symmetry. This can alter how quadratic expressions are handled, in particular under a "Coordinate Basis" this is an important distiction to constantly be aware of.

So for example a quadradic parabola will be in essence divided by the quadratic geometry treatment under your covariant and contravariant rotations.

So the two real or imaginary values that arise from quadradic expressions ie the plus/minus is treated under coordinate rotation symmetry relations.

Edited October 5, 2017 by Mordred