If the vacuum is a sea of energy

[ultrafind]

If the vacuum is a sea of energy, and let's assume that this vacuum has the same energy per cubic volume everywhere, and by Heisenberg UP, virtual particles can pop in and out of this vacuum, and if the particles popped out from a certain area and jumped into another area and vanished there, then wouldn't there be a loss of energy per cubic volume at the initial area and a surplus in the area where it vanished?

 

[lethe]

once the particles had vanished, the amount of energy would go back to what it was before they vanished.

 

[ultrafind]

My question may have been confusing.
Imagine the vacuum as a piece of cloth and this cloth is equivalent to the vacuum energy. Now, imagine that a virtual particle pops out from this vacuum equivalent to cutting out a small piece of rag from this cloth. Next, the virtual particle now returns to the vacuum but this time at another place not the same place again, equivalent to sticking back the rag at another place on the cloth but leaving a hole on the cloth. From this analogy, the hole is equivalent to a loss in energy in that part of vacuum at the vicinity of that hole in the cloth but a plus in energy at the vicinity of the cloth where the rag was sticked back again, yet the total amount of cloth, or the total amount of vacuum energy remains the same.

 

[damgo]

Virtual particles are in a sense only a tool used to describe the vacuum state. They don't pop "out" of the vacuum and fall back "in"; they are the vacuum state.

 

[lethe]

Originally posted by ultrafind
My question may have been confusing.
Imagine the vacuum as a piece of cloth and this cloth is equivalent to the vacuum energy. Now, imagine that a virtual particle pops out from this vacuum equivalent to cutting out a small piece of rag from this cloth. Next, the virtual particle now returns to the vacuum but this time at another place not the same place again, equivalent to sticking back the rag at another place on the cloth but leaving a hole on the cloth. From this analogy, the hole is equivalent to a loss in energy in that part of vacuum at the vicinity of that hole in the cloth but a plus in energy at the vicinity of the cloth where the rag was sticked back again, yet the total amount of cloth, or the total amount of vacuum energy remains the same.

virtual particles occur in pairs. one has positive energy, and one has negative energy (in a sense). once they have annihilated each other, the energy is the same everywhere as it was before they came into being.

 

[RuroumiKenshin]

What? Vacuum energy is negative, not positive, at least that's the way it is in quantum mechanics.

 

[Eh]

I think you're talking about the negative pressure of the cosmological constant. Particle pairs come with opposite charges.

 

[selfAdjoint]

Originally posted by MajinVegeta
What? Vacuum energy is negative, not positive, at least that's the way it is in quantum mechanics.

Are you thinking of the Dirac sea here? In the modern field theories the energy of the vacuum is taken as zero. That is, they know there is energy there, but all of observable physics happens "on the mass shell", that is, with positive energy relative to the vacuum, so calling the vacuum energy zero simplifies the math. It's like Celsius and Fahrenheit temperature; where you put the zero marker is just convention.

The idea that in spite of this there might exist vacuum states of greater or lesser energy is behind the idea of inflation in cosmology.

 

[damgo]

What? Vacuum energy is negative, not positive, at least that's the way it is in quantum mechanics.

I think you mean that the current cosmological evidence suggests that there is a positive cosmological constant, which would correspond to a negative zero-point or vacuum energy. If that's what's causing it.

In quantum field theory (not quantum mechanics, there is no concept of a vacuum state there) bosons contribute positive vacuum energy, and fermions negative vacuum energy. However, like selfadjoint said, the overall energy zero is arbitrary and so it's questionable how meaningful this is.

When you try and calculate out the total vacuum energy, you get a bunch of terms, both positive and negative, which are around 10^40 or 10^100 times as large as the observed one from cosmology, depending on your assumptions. This is considered a rather large problem, and a lot of people are looking for new physical principles or laws that would cause the miraculous cancellations necessary to get the observed value.

 

[RuroumiKenshin]

I was mainly thinking of the negative energy that deals with wormholes: http://www.physics.hku.hk/~tboyce/sf/topics/wormhole/wormhole.html

sorry for side tracking this discussion.

 

[wimms]

Flat surface of sand. Take one grain of sand from one place and put it to another. Excavate and create hill nearby a hole. When you traverse the two, you pass over curvature. You have created field.

If minute differences between adjacent grains are large enough to be detectable, you call it chunk of matter (hill). If difference is too small to be measurable, you call it curvature of space, field.

Thus I'd think energy density of vacuum is far from uniform everywhere, but dependent on field density there. Much like you can excavate and create a small hill both at sea level or on top of a mountain, locally you can only detect steepness of the local field, but hardly absolute density.

just opinion.

 

[marcus]

Originally posted by damgo
I think you mean that the current cosmological evidence suggests that there is a positive cosmological constant, which would correspond to a negative zero-point or vacuum energy. If that's what's causing it.

In quantum field theory (not quantum mechanics, there is no concept of a vacuum state there) bosons contribute positive vacuum energy, and fermions negative vacuum energy. However, like selfadjoint said, the overall energy zero is arbitrary and so it's questionable how meaningful this is.

When you try and calculate out the total vacuum energy, you get a bunch of terms, both positive and negative, which are around 10^40 or 10^100 times as large as the observed one from cosmology, depending on your assumptions. This is considered a rather large problem, and a lot of people are looking for new physical principles or laws that would cause the miraculous cancellations necessary to get the observed value.

The observed one from cosmology is about half a joule per cubic kilometer. (Please correct me if I'm mistaken.)
This is the dark energy density that the models need in order to supply the right amount of negative pressure to produce both the observed acceleration in expansion and the observed flatness.
So I do not see how the zero can be arbitrary.

Cosmologists must be working with a vacuum that has some concept of an absolute zero energy density. Because they can, in effect, observe a definite dark energy density.

Have I misunderstood something? Please explain. And indeed the huge unexplained vacuum energy in QFT is being called "The Biggest Embarrassment in Theoretical Physics"* essentially because it does not match the observed dark energy density but is off (like you say) by some factor like 10^100----anyway an immense factor depending on how it is calculated. But again that suggests that the people pointing out the mismatch are not working with an arbitrary zero. they have two energy densities both of which are calculated relative to absolute zero and the two don't happen to agree. Or?

*A good summary is in Making Sense of the New Cosmology by Michael Turner (U Chicago, Fermilab) a survey article online at

http://xxx.lanl.gov/PS_cache/astro-ph/pdf/0202/0202008.pdf

 

[damgo]

Well, in quantum field theory and pretty much everything except general relativity, the zero of energy is totally arbitrary -- only differences matter, so you can set E=0 at any point you like.

But direct calculation does give you a value -- in QFT, you can treat noninteracting fields as an infinite set of harmonic oscillators. Each mode has zero-point energy of w/2 (-w/2 for fermions), so if you allow arbitrarily high frequencies, you get an infinite total ZPE. If you cut things off at the Planck scale, you get the terms that are 10^100 too big. Adding SUSY cuts this down to ~10^40 times, IIRC.

 

[marcus]

Originally posted by damgo
Well, in quantum field theory and pretty much everything except general relativity, the zero of energy is totally arbitrary -- only differences matter, so you can set E=0 at any point you like.

I'm familiar with this practice, which makes good sense in most situations where only differences in energy between states matter. But here, at the mismatch between observed cosmic dark energy and QFT vacuum energy, it does seem that people are forced to tackle an absolute zero of energy. Or something very much like one.

But direct calculation does give you a value -- in QFT, you can treat noninteracting fields as an infinite set of harmonic oscillators. Each mode has zero-point energy of w/2 (-w/2 for fermions), so if you allow arbitrarily high frequencies, you get an infinite total ZPE. If you cut things off at the Planck scale, you get the terms that are 10^100 too big. Adding SUSY cuts this down to ~10^40 times, IIRC.

Does it strike you that there is a similarity between this problem and the blowups in the blackbody spectrum circa 1890s?
Planck was compelled by things like "ultraviolet catastrophe" IIRC---if I recall correctly---to come up with the h constant and the blackbody curve (1900) and quantum mechanics emerged from that with Einstein's (1905) use of hbar to solve another outstanding problem---photoelectric effect. Back then it was infinities or gross mismatches in the thermal spectrum and now it is the energy of the vacuum

As you indicated, this is a "very large problem". You wrote:

[When you try and calculate out the total vacuum energy, you get a bunch of terms, both positive and negative, which are around 10^40 or 10^100 times as large as the observed one from cosmology, depending on your assumptions. This is considered a rather large problem, and a lot of people are looking for new physical principles or laws that would cause the miraculous cancellations necessary to get the observed value.]

Yes, looking for new physical principles. Michael Turner calls this mismatch

"The Biggest Embarrassment in Theoretical Physics"

http://xxx.lanl.gov/PS_cache/astro-...202/0202008.pdf


The observed dark energy density from cosmology is about half a joule or three quarters of a joule per cubic kilometer, if memory serves. Do you happen to know it more accurately? Would be nice to be able to state it as well as it is currently known.

 

[damgo]

>>Does it strike you that there is a similarity between this problem and the blowups in the blackbody spectrum circa 1890s?

Yup. :) In QFT, such infinities that appear as a result of allowing arbitrarily high wavelengths are called "ultraviolent divergences" and those that appear as a result of allowing arbitrarily low wavelengths, "infrared divergences." This is a holdover from the old black-body problem, since of course the wavelengths cutoffs now are far higher and lower respectively than IR or UV light.

Ultraviolent divergences are usually taken as a sign of new small-distance-scale physics. However, the vacuum energy problem runs much deeper. The cosmological value you wanted is around 2e-10 erg/cm^3 -- corresponding to a mass cutoff of 0.001 eV, or distance scale of around 1mm, I believe. Obviously this is a big problem because we have tested our field theories well up into the GeV range now. So the problem isn't just new small-scale physics... there must be some mechanism causing everything to almost but not quite cancel, or else we just got really lucky. (anthropic argument)

Sean Carroll has a good intro paper covering all this and much more, at http://xxx.lanl.gov/pdf/astro-ph/0004075 .

 

[chroot]

ULTRAVIOLENT?!?

*can't... stop... laughing... can't... breathe... too... motherfelching... funny...*

- Warren

 

[marcus]

Originally posted by damgo
>>Does it strike you that there is a similarity between this problem and the blowups in the blackbody spectrum circa 1890s?

Yup. :) In QFT, such infinities that appear as a result of allowing arbitrarily high wavelengths are called "ultraviolent divergences" and those that appear as a result of allowing arbitrarily low wavelengths, "infrared divergences." This is a holdover from the old black-body problem, since of course the wavelengths cutoffs now are far higher and lower respectively than IR or UV light.

Ultraviolent divergences are usually taken as a sign of new small-distance-scale physics. However, the vacuum energy problem runs much deeper...

This is interesting. thanks.

Originally posted by damgo
...The cosmological value you wanted is around 2e-10 erg/cm^3 -- corresponding to a mass cutoff of 0.001 eV, or distance scale of around 1mm, I believe. Obviously this is a big problem because we have tested our field theories well up into the GeV range now. So the problem isn't just new small-scale physics... there must be some mechanism causing everything to almost but not quite cancel, or else we just got really lucky. (anthropic argument)

Sean Carroll has a good intro paper covering all this and much more, at http://xxx.lanl.gov/pdf/astro-ph/0004075 .

I was asking about dark energy density and you say around 2E-17 joules/cm^3 and go from there. The way I visualize that is 2E-2 joules per kilometer. It is the same density, but I can picture 0.02 joules in a cubic kilometer better, for some reason. (not pretending to be reasonable).

Now dark energy is generally accepted to be 0.7 of rho_crit, indeed MAP data is saying 0.73 (how they can be so sure!)
So you are saying, in effect that rho_crit is 0.028 joules per cubic kilometer.

rho_crit is equal to (3/8pi) F/A, where F is the Planck force
of 12E43 Newtons and A is the Hubble area (13.7 billion LY)^2
or in metric terms (1.3E26 meters)^2
I calculate F/A to be 7.1E-9 joule/cubic meter
and multiplying by 3/8pi gives me 8.5E-10 joule/cubic meter.
So I get that the critical energy density is 0.85 joule per cubic kilometer.

So we differ by a factor of 30 as to the critical density of the universe required for flatness.

I say (with this quick calculation) that it is about 0.85 joules per km^3 and that therefore 70% of it is about 0.6 joules per km^3
and that would be the dark energy.

You say that rho crit is about 0.028 joules per km^3 (or the CGS equivalent) and therefore 70% of it, the dark energy part, is
0.02 joules per km^3.

may have made some error here but will post anyway
and check later

Yeh, ultraviolent is funny and appropriate too.

 

[marcus]

That Sean Carroll paper you mentioned is from 2000.
There is something wrong there.
He has changed his figure for dark energy density to essentially what I gave. See for example
http://snap.lbl.gov/pubdocs/
where a January 2002 talk by Carrol:

http://snap.lbl.gov/pubdocs/Carroll-talk.pdf

is listed. In 2002 he says its about E-8 ergs per cm^3

It is hard to explain where Carroll's earlier figure
in the 2000 paper, which was off by a factor of 30,
could have come from! Maybe he was talking about something besides the observed dark energy density or there was
some other mixup. Anyway back in 2000 he said

2E-10 erg per cm^3

which is way different from what other people are saying.

For a representative up to date figure, corresponding to 6E-9 ergs per cm^3 see some March 2003 lecture notes from astronomy department of ohio state

http://www-astronomy.mps.ohio-state.edu/~ryden/ast162_10/notes41.html

In these notes the dark energy density is given as
6E-10 joules per cubic meter.

That is the same as the 0.6 joules per cubic km which I mentioned.

The calculation is straightforward assuming dark is 70% of critical density. The 70% is generally accepted now because of the Ia SN, and the critical density depends only on the Hubble parameter and that is now pretty well established. And flatness is too. So there is a consensus around this. [Whether or not they are right at least the cosmologists agree! :)]

Back in 1999 John Baez said order of magnitude E-9 joules per cubic meter for dark energy density---Usenet physics guru at UC Riverside.
http://math.ucr.edu/home/baez/vacuum.html
He was very tentative about it but what he said turns out to be the order of magnitude of 6E-10 joules per cubic meter, and same as what Carroll said in 2002.

Carrol was way out in left field in 2000 but by 2002 was saying essentially same thing as other people. At least that is how it
looks to me, let me know if I am missing something.

 

[damgo]

What's an order of magnitude or two between friends?

Like you noted, that paper is old -- a lot of the evidence for a big lamda, the supernovae and CMBR stuff, is rather new. Up until a few years ago, everyone was saying the cosm. constant was probably really close to zero... I assumed Carroll's number had come from after that stuff was out, but I guess I was wrong. Maybe he just screwed up, too, I dunno.

 

[marcus]

Indeed what is an order of magnitude between friends :)
I am very glad you are comfortable with this figure

it makes essentially no difference to what you pointed
out about QFT vacuum energy discrepancy

which Carroll is extremely clear about explaining
his article is excellent also in treatment of the metric and
the friedmann equations

the discrepancy is huge however you view it and this
is really exciting---similarity with the 1890s preQuantum
"ultraviolent" catastrophe. I hope to see the resolution of
it and that it spawns new physics. (you gave a reason
earlier why that new physics is expected to emerge at
planck scale)