Is the energy of empty space concentrated differently in curved spacetime?

[Justin Hunt]

I have a question related to MOND and DM that I will post here rather than create a new thread. My thought stream begins with doesn't Energy create gravity as well as matter due to the E = MC^2 equation? Which leads to my question of whether or not empty space generates gravity due to the energy in empty space. I realize this would net to zero for uniformly distributed energy on flat spacetime, but I am interesting in the curved spacetime of galaxies. Is the energy of empty space more or less concentrated in these regions due to the spacetime curvature? and would this lead to a net increase or decrease of gravity?

 

[PeterDonis]

I have a question related to MOND and DM that I will post here rather than create a new thread.

It should have been a new thread--so now it is.

 

[PeterDonis]

doesn't Energy create gravity as well as matter due to the E = MC^2 equation?

Yes and no. Yes, energy creates gravity, but no, it's not "due to the E = MC^2 equation". It's due to the fact that the source of gravity in GR is the stress-energy tensor, which includes energy (including the energy equivalent of rest mass), momentum, pressure, and stress.

Which leads to my question of whether or not empty space generates gravity due to the energy in empty space.

There is no "energy in empty space" unless you mean the cosmological constant (aka "dark energy"). This can be considered a form of stress-energy and so contributes to the source of gravity as above, yes.

I realize this would net to zero for uniformly distributed energy on flat spacetime, but I am interesting in the curved spacetime of galaxies. Is the energy of empty space more or less concentrated in these regions due to the spacetime curvature?

No. Spacetime curvature in itself does not "store energy in empty space". Spacetime curvature is gravity--it's the thing that gets produced by the source--stress-energy--not the source.

 

[Justin Hunt]

@PeterDonis ty for the info. As far as energy in space I have heard that virtual particles are constantly being created and annihilating each other and that a cubic meter had about 10^-9 joles of energy. But, yes I was also thinking about Einstein’s constant and dark energy as well but wasn’t sure if those actually counted as energy or not for producing gravity

 

[PeterDonis]

As far as energy in space I have heard that virtual particles are constantly being created and annihilating each other and that a cubic meter had about 10^-9 joles of energy.

Can you give a specific reference? "I have heard" is not enough, particularly since you're quoting a definite number.

Also, you might want to read this Insights article about virtual particles:

https://www.physicsforums.com/insights/misconceptions-virtual-particles/

I was also thinking about Einstein’s constant and dark energy as well but wasn’t sure if those actually counted as energy or not for producing gravity

They do.

 

[Justin Hunt]

@PeterDonis i got the energy amount from Wikipedia on vacuum energy for empty space. But, Wikipedia isn’t necessarily very reliable which is why I ask here.

 

[PeterDonis]

i got the energy amount from Wikipedia on vacuum energy for empty space.

Please give a specific link.

 

[Justin Hunt]

https://en.wikipedia.org/wiki/Vacuum_energy

 

[PeterDonis]

https://en.wikipedia.org/wiki/Vacuum_energy

This number is, as the article says, based on the estimated value of the cosmological constant. It is not saying that this "energy of empty space" is something separate from the cosmological constant (aka dark energy). It is taking the common view (which is still not backed by a fully satisfactory theory, but it's the best we have right now) that the cosmological constant aka dark energy we observe (based on the acceleration of the universe's expansion) is due to the "vacuum energy" of empty space predicted by quantum field theory. As the article notes, however, there is a huge discrepancy between the value the theory appears to be telling us and the value we actually measure, which is called the "cosmological constant problem".

None of this affects the answers I've given already in this thread to your question about energy creating gravity.

 

[PeterDonis]

This article by John Baez gives a good overview of the "vacuum energy" question:

http://math.ucr.edu/home/baez/vacuum.html

 

[Imager]

This article by John Baez gives a good overview of the "vacuum energy" question:

http://math.ucr.edu/home/baez/vacuum.html

Awesome reference! I no longer need Christmas lights, there is big right over my head!

 

[TEFLing]

This article by John Baez gives a good overview of the "vacuum energy" question:

http://math.ucr.edu/home/baez/vacuum.html

I understand you could opt to keep the "Cosmological constant term" in the GR equation on the left hand side, and interpret it as part of the curvature tensor (instead of moving it over onto the RHS and interpreting it as a source of stress-energy).

If so, the Cosmological constant term would represent an "intrinsic curvature in the fabric of space-time", even in the absence of any matter or energy -- vaguely like a flatbed trailer bows upward in the middle, even with no load on it, the trailers are just manufactured with an "intrinsic upward bowing curvature".

The "fabric of space time doesn't lie flat" even in the absence of mass & energy, but has an "ingrained bowing warp" to it, would be a very crude way of representing the notion, which I understand is vague but informative -- you could interpret the term as curvature, instead of (exotic) stress-energy??

 

[PeterDonis]

you could interpret the term as curvature, instead of (exotic) stress-energy??

Not quite. You can interpret it as an intrinsic property of spacetime, instead of as a kind of stress-energy. But that doesn't make it curvature; curvature is still described by the Einstein tensor in the Einstein Field Equation. The presence of the cosmological constant just means that it is no longer possible to have a vanishing Einstein tensor (i.e., flat spacetime) if the stress-energy tensor vanishes (i.e., vacuum).