Vacuum Energy - Pair Production Confusion

[benk99nenm312]

So, let's get this straight . Black hole evaporation is, by the layman's version, supposedly due to a negative mass particle entering the black hole, while it's counterpart leaves, as radiation. These particles are formed near the black hole by vacuum fluctuations (i.e. pair production). I'm not entirely certain, but when a pair is formed in vacuum fluctuations, I've always assumed they both had positive mass (since antimatter and matter both have positive mass when real). So I have a contradiction here. Is it something to do with the fact that they are virtual particles? But even so, what allows a virtual particle to have negative mass? What's going on here?

 

[humanino]

I'm not entirely certain, but when a pair is formed in vacuum fluctuations, I've always assumed they both had positive mass

Virtual particles can have pretty much any mass, positive, negative, imaginary if you want. The above description of BH evaporation entails the concept of local vs global energy in general relativity, which is yet another complication to the problem. Take it that way : the zero of energy is not the same on the horizon and at infinity. Among the two particles of the pair created, although both of them locally carry positive energy, one of them will have less energy than the other, and at infinity it looks like they carry nothing on average. So at infinity, it looks like the one carrying less energy, which is more likely to fall, actually carried negative energy.

Sorry, I know this is quite sketchy, but it's a long topic.

 

[benk99nenm312]

Among the two particles of the pair created, although both of them locally carry positive energy, one of them will have less energy than the other, and at infinity it looks like they carry nothing on average. So at infinity, it looks like the one carrying less energy, which is more likely to fall, actually carried negative energy.

I'm not sure I follow you here. Why would one particle have less energy than the other?

- yeah, this is a sketchy topic

 

[benk99nenm312]

Also, I think a problem is: what exactly do the virtual particles created by the vacuum fluctuations anhilate into? By that I mean, what comes out.. a virtual photon.. nothing..?

 

[humanino]

I'm not sure I follow you here. Why would one particle have less energy than the other?

Usually we are given a background and a field on top of it. Then you Fourier transform your field and the proper modes with negative frequency are re-interpreted as anti-particle with positive energy. So the sketchy argument is that what is locally zero near the horizon allowing one to define antiparticle there does not trivially transport to infinity, because of a non-negligible contribution from the gravitational field itself. From infinity it looks like two particles (not able to tell antiparticles from particles) with positive energy, but one has less energy and is therefore more likely to fall. Eventually what comes out of the BH seems like a thermal radiation of both particles and antiparticles, measured at infinity.

I wish someone more competent could help.

 

[benk99nenm312]

You're doing fine , but i agree... where is everyone?

 

[Chronos]

Virtual particles are an artifact of the uncertainty priciple. They don't last long enough to be of any real consequence. In most quantum gravity theories they are, however, of great importance.

 

[humanino]

They don't last long enough to be of any real consequence.

This is a rather strange statement honestly speaking. Turn off first order corrections and pretty much all measurements in the realm of high energy physics are changed, I'm referring now to so-called radiative corrections. Historically, we obtained evidence for the correctness of renormalization thanks to them for instance. It is beyond my understanding that anyone would consider them "an artifact" without "any real consequence".

 

[benk99nenm312]

This is a rather strange statement honestly speaking. Turn off first order corrections and pretty much all measurements in the realm of high energy physics are changed, I'm referring now to so-called radiative corrections. Historically, we obtained evidence for the correctness of renormalization thanks to them for instance. It is beyond my understanding that anyone would consider them "an artifact" without "any real consequence".

Many physicists deny the existence of their own mathematical conclusions. However, without them, we wouldn't have an accurate explanation for electromagnetism. But, I don't want to talk about that. I was wondering if anyone had an answer to my question in post number 3, or 4 as seen numerically on the page.

 

[Sourabh N]

I think it has something to do with Einstein's that equation E = mc^2. Energy in some(?) form is converted to mass when that pair is produced. Someone please support that! or correct me

 

[malawi_glenn]

Virtual particles are an artifact of the uncertainty priciple. They don't last long enough to be of any real consequence. In most quantum gravity theories they are, however, of great importance.

no they are a mathematical artifact by perturbation formulation of a calculation in QFT.

 

[Chronos]

Another failed attempt at humor. Pair production is only relevant under unusual circumstances - like near the event horizon of a black hole. It also manifests itself as the casimir effect. It is undoubtedly real and well confirmed by experimental evidence. Virtualy particles ordinarily self annihilate, crashing one into the other. Near an event horizon, the 'positive' energy particle can escape, leaving the other particle holding the bag, so to speak. The event horizon thus effectively 'bleeds' energy over time [Hawking radiation]. An even weirder effect occurs in the case of Unruh radiation, but is equally well founded based on the same premises.

 

[malawi_glenn]

But then one can say that ee scattering is also proving the existence of virtual particles, of course Casimir Effect etc CAN BE EXPRESSED in terms of virtual particles, they can be formulated with different concepts, e.g. the Casimir effect can be formulated just using a zero-point energy. etc. Virtual particles are just a tool.

 

[benk99nenm312]

Virtualy particles ordinarily self annihilate, crashing one into the other.

So, are you saying that nothing comes out of the annihilation?

I know virtual particles are a tool, but I'm trying to understand whether empty space, consisting of a few virtual particle pairs, produces any energy.

 

[malawi_glenn]

So, are you saying that nothing comes out of the annihilation?

I know virtual particles are a tool, but I'm trying to understand whether empty space, consisting of a few virtual particle pairs, produces any energy.

produces as in increasing the total energy? No

 

[benk99nenm312]

produces as in increasing the total energy? No

Interesting. So it's like a negative and positive mass virtual particle pair will completely annhilate, with nothing left over. Is that correct?

 

[malawi_glenn]

Energy is mass so net energy is the same all the time

 

[benk99nenm312]

Energy is mass so net energy is the same all the time

Well, I think I understand where you're coming from... this is a confusing subject for me. So, let's just say this. I have one virtual particle pair created in the vacuum. They annhilate. Would there be something that comes out of the annhilation, to balance the total energy of the virtual pair, or would they completely annhilate, leaving nothing to come out? (When I say come out, I mean like a photon, or a virtual photon).

Sorry, my knowledge on this subject is not great.

 

[malawi_glenn]

Interesting. So it's like a negative and positive mass virtual particle pair will completely annhilate, with nothing left over. Is that correct?

they would produce energy, the amount of energy they got when they became "created" by the vacuum.

E = {pair created}: E_0 + E_virtual-pair ={pair annihilated}: E

 

[benk99nenm312]

they would produce energy, the amount of energy they got when they became "created" by the vacuum.

E = {pair created}: E_0 + E_virtual-pair ={pair annihilated}: E

Oh, I see. So, in what form is that energy?

Is this dark energy?

 

[malawi_glenn]

Oh, I see. So, in what form is that energy?

Is this dark energy?

No, or really I don't know in what "piece" the vacuum energy belongs to xD

 

[benk99nenm312]

No, or really I don't know in what "piece" the vacuum energy belongs to xD

Haha. Does anyone? Or is it not known yet?

 

[malawi_glenn]

Haha. Does anyone? Or is it not known yet?

Everything I know is that at least some cosmologists have tried to interpret the cosmological constant as the vacuum energy -> i.e. dark energy.

 

[Sourabh N]

From wiki :
In physics, the word (annihilation) is used to denote the process that occurs when a subatomic particle collides with its respective antiparticle. Since energy and momentum must be conserved, the particles are not actually made into nothing, but rather into new particles. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed.
http://en.wikipedia.org/wiki/Annihilation"

 

[malawi_glenn]

From wiki :
In physics, the word (annihilation) is used to denote the process that occurs when a subatomic particle collides with its respective antiparticle. Since energy and momentum must be conserved, the particles are not actually made into nothing, but rather into new particles. Antiparticles have exactly opposite additive quantum numbers from particles, so the sums of all quantum numbers of the original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed.
http://en.wikipedia.org/wiki/Annihilation"

which seems different from what is said above.

we were discussing virtual particles, not real particles

 

[Sourabh N]

oh my bad there sorry.

http://www.physics.ucdavis.edu/Text/Carlip.html#Hawkrad", by Steve Carlip, says the total energy is always zero, it was zero throughout the process.

Am I missing out again?

 

[malawi_glenn]

oh my bad there sorry.

http://www.physics.ucdavis.edu/Text/Carlip.html#Hawkrad", by Steve Carlip, says the total energy is always zero, it was zero throughout the process.

Am I missing out again?

I just called it "E", the exact numerical value is not of interest to me here

 

[benk99nenm312]

oh my bad there sorry.

http://www.physics.ucdavis.edu/Text/Carlip.html#Hawkrad", by Steve Carlip, says the total energy is always zero, it was zero throughout the process.

Am I missing out again?

This actually helped me a bit. Thanks.

 

[benk99nenm312]

Wait, hang on. For clarification purposes, I ask this question: is the value of the energy non-zero?

 

[malawi_glenn]

Wait, hang on. For clarification purposes, I ask this question: is the value of the energy non-zero?

The vacuum energy in QFT is infinite, and in QFT with supersymmetry not-infinity.

What the author of that "article" has done is that he has shifted the energy axis so that vacuum energy is 0, hence we have renormalized the vacuum energy. In QFT with supersymmetry, we do not need to renormalize it.

 

[humanino]

...

Well this may be confusing. The definition of the vacuum to start with is the state with the lowest possible energy, and only energy differences matter : at this point with do not need perturbative methods. I think it is worth emphasizing before embarking into perturbative calculations of the energy of the fluctuations.

 

[malawi_glenn]

Well this may be confusing. The definition of the vacuum to start with is the state with the lowest possible energy, and only energy differences matter : at this point with do not need perturbative methods. I think it is worth emphasizing before embarking into perturbative calculations of the energy of the fluctuations.

I actually wrote something similar yesterday.. I thought it was in this particular thread.. that is why I wrote about perturbation calculations in my latest posts.. doh, I must get my memory back :D