Misconceptions about Virtual Particles - Comments

[A. Neumaier]

Concerning the misconceptions in the interpretation of vacuum polarization in QED via virtual particles, see the discussion here.

 

[Buzz Bloom]

No. In a quantum field theory of gravity and matter, all massive physical particles also carry a gravitational field; everything is completely analogous. A static gravitational field behaves quantum mechanically in the same way, except that it can also produce two photons, because photons are their own antiparticles. Or two neutrinos, etc.. There is no energy barrier for photon production since photons are massless, but to achieve a noticeable effect, the field has to be extremely strong.

Hi @A. Neumaier:

I think I am gradually understanding more about the Hawking Radiation phenomenon, but I still have some confusion.

I get that the energy in the gravitational field outside the event horizon is able to create pairs of particles, but I have come to understand that the concept of this field is entirely represented by its space-time distortion represented by the Swartzchild metric. Is this correct? If so, does this mean that when a particle pair is created, and the particles do not annihilate each other, the corresponding loss of energy in the field is manifested by a corresponding change in the distortion of space-time? If this is so, then presumably after a brief time, the distortion becomes represented by a Swartzchild metric with a slightly smaller value for

R_s=2GM/c²,​

since a part of M corresponding to the energy in the field has been reduced by the creation of the particle pair.

If all of this is correct, then what is the mechanism that reduces the greater part of M represented by the mass inside the event horizon? In the absence of such a mechanism, then the net result of the Hawking radiation would seem to be the eventual elimination of the gravitational field outside the event horizon, while the mass inside the event horizon remains there forming a black hole that has no observable gravitational field.

Regards,
Buzz

 

[A. Neumaier]

does this mean that when a particle pair is created, and the particles do not annihilate each other, the corresponding loss of energy in the field is manifested by a corresponding change in the distortion of space-time?

No. The loss of energy is encoded in the distortion of the metric of the 3-dimensional space when moving the time of slicing spacetime into 3D spaces at fixed times. Note that in a space-time view, the latter corresponds to dynamics!

 

[Buzz Bloom]

No. The loss of energy is encoded in the distortion of the metric of the 3-dimensional space when moving the time of slicing spacetime into 3D spaces at fixed times. Note that in a space-time view, the latter corresponds to dynamics!

Hi @A. Neumaier:

I apologize for being sloppy with my use of language. I meant that the Swartzchild metric components for both dr² and dt² are distorted relative to flat space by the respective factors

(1 - R_s/r)-1 and c² (1 - R_s/r) .​

Is it correct to say that the creation of the particle pair (which survives rather than self annihilating) reduces the energy in the field, will ultimately manifest itself by changing the R_s factor in these metric components, and that this means that the energy in the entire field outside the EH has been reduced by the energy of the created particle pair?

My confusion is whether this change in the field metric has any effect on the amount of mass inside the EH? If it does, then what is the mechanism that makes this happen?

Regards,
Buzz

 

[A. Neumaier]

the energy in the entire field outside the EH has been reduced by the energy of the created particle pair?

Of course, if the mass of a black hole is reduced, the gravitational field everywhere also weakens.

But note that the Schwarzschild metric only describes a classical black hole in isolation, whereas the Hawking effect describes a quantum black hole interacting with QED. The quantum black hole can be described by a Schwarzschild metric with a variable mass only in some approximation

 

[Buzz Bloom]

Of course, if the mass of a black hole is reduced

Hi @A. Neumaier:

You say "Of course," and I understand that Hawking also said that the mass inside the EH is lessened. What I am asking is:

What is the mechanism that causes the event of particle pair creation outside the EH, to reduce the mass inside the EH?​

I have not seen anywhere any explanation about HOW this happens. It seems to me to be a very strange kind of non-locality phenomenon. The only thing that crosses the EH is one of the created pair particles going from the outside to the inside. How can this reduce the mass inside?

Regards,
Buzz

 

[A. Neumaier]

he only thing that crosses the EH is one of the created pair particles going from the outside to the inside. How can this reduce the mass inside?

The pair is initially created (spontaneously, according to Born's rule of quantum mechanics) near the horizon from the field of the black hole, which subtracts energy corresponding to two masses from the black hole. One of the particles returns into the black hole, while the other leaves. The balance is one lost particle mass. Maybe this link helps.

 

[Buzz Bloom]

The pair is initially created (spontaneously, according to Born's rule of quantum mechanics) near the horizon from the field of the black hole, which subtracts energy corresponding to two masses from the black hole.

Hi @A. Neumaier:

I much appreciate your patience with my difficulty in trying to understand this phenomenon.

I understand that what you have described to be an accurate physical summary of the Hawking Radiation phenomenon. I have read the discussion at the link you gave. I also read the cited John Baez description. I am still not getting any concept of the physical mechanism that causes a subtraction of energy corresponding to two masses from inside the EH when the particle pair is created outside the EH. Do these two events, one inside and one outside the EH, occur simultaneously? Or, does the outside event happen before the inside event? In the latter case, what takes place during the interval between the two events?

Do you think it might be useful for me to start a new tread specifically on this question which might attract some additional PF participants into the discussion?

Regards,
Buzz

 

[A. Neumaier]

the physical mechanism that causes a subtraction of energy corresponding to two masses from inside the EH when the particle pair is created outside the EH. Do these two events, one inside and one outside the EH, occur simultaneously?

Note that the black hole is the whole nonlocal object including the field - not just the mass concentration in its center. Even classically, the Schwarzschild metric defining a class of isolated black holes is an extended object, not just the singularity, and also not just ending at the event horizon. (An observer crossing the event horizon doesn't notice anything special!)

The physical mechanism is quantum gravity interacting with the electromagnetic field. Study the formulas and you have the formalsim. One cannot dissect this into several spatially or temporally events as you'd like to have it. Hawking radiation of a single particle is a single event, not two events. This event does not happen instantly but takes time. Enough time for the field to redistribute itself without any violations of causality or local conservation laws. Like in a scattering event where particles decay one cannot speak of particles during the decay, only asymptotically - before and after the event. During the event one only has a very complex quantum field description where the particle picture is inappropriate. Intuitively - but this is only an analogy - you might think of the energy of the field concentrating more and more (taking away energy from the surrounding that flows towards the point of activity) until it is concentrated enough to ''become'' a particle pair.

In fact, the Hawking radiation process for photons is not even a sequence of single pair creation events but a continuous process producing a coherent state of photons with an indefinite number of photons in it. It is only for the purposes of analysis that one treats it as a single event. At the end one has to average over all soft photon states to get an infrared-finite result. The photon picture for Hawking radiation is the same simplification applied when analyzing laser light in terms of photons rather than in terms of coherent states, which gives the more correct description.

Do you think it might be useful for me to start a new tread specifically on this question which might attract some additional PF participants into the discussion?

You could try the forum Special and General Relativity, where specialists on general relativity might answer. (If you do so, please place here a link to the new discussion.) But your questions are of a kind nobody can answer to your satisfaction since they are based on the assumption that quantum field processes can be dissected into elementary pieces. If you are trying to do this you only end up in subjectively animating virtual reality. Thus you are likely to generate only more confusion. If you'd study the matter yourself (by going to the formal literature on the subject) you'd find that as you get more insight you'll gradually change your view of which kind of questions one can reasonably expect to answer.

 

[Buzz Bloom]

If you'd study the matter yourself (by going to the formal literature on the subject) you'd find that as you get more insight you'll gradually change your view of which kind of questions one can reasonably expect to answer.

Hi @A. Neumaier:

I understand that my confusion is due to my lack of understanding of quantum gravity concepts. I now understand the concept that a single QG event takes place over a period of time during which the related math has no intermediate interpretation. I am now guessing that the concept I am missing relates to some process involving an interpretation of some mathematical model in which a single event involves (1) changes at a distance from the center mass of the BH (particle creation outside the EH) and also (2) changes (the total vanishing of a matter particle and its mass) some distance away close to the center of the BH. Where in the formal literature can I find an explanation of this concept, or why this concept is incorrect with respect to QG.

Regards,
Buzz

 

[A. Neumaier]

a single event involves (1) changes at a distance from the center mass of the BH (particle creation outside the EH) and also (2) changes (the total vanishing of a matter particle and its mass) some distance away close to the center of the BH

These are not classical events! Like everywhere in quantum field theory, one can interpret only the end result of complicated calculations. One cannot say more about the process than the analogy of flow mentioned in my previous post.

your questions are of a kind nobody can answer to your satisfaction

 

[Buzz Bloom]

Like everywhere in quantum field theory, one can interpret only the end result of complicated calculations.

Hi @A. Neumaier:

Would it be OK to say that one "end result" of the Hawking Radiation phenomenon is the following?
1. One particle of a pair created by the HR phenomenon near the outside of the EH, which does not self annihilate, will have escaped from the vicinity of the BH.
2. The other particle of the pair will have crossed to the inside of the EH.
3. One or more particles which are constituents (quarks and/or gluons?) of the BH mass near the center of the BH will have disappeared without having had its/their mass converted to corresponding energy.

Regards,
Buzz

 

[A. Neumaier]

Would it be OK to say that one "end result" of the Hawking Radiation phenomenon is the following?
1. One particle of a pair created by the HR phenomenon near the outside of the EH, which does not self annihilate, will have escaped from the vicinity of the BH.
2. The other particle of the pair will have crossed to the inside of the EH.
3. One or more particles which are constituents (quarks and/or gluons?) of the BH mass near the center of the BH will have disappeared without having had its/their mass converted to corresponding energy.

A particle cannot self annihilate. Apart from that 1 and 2 are ok. But not 3. At the center of the black hole are no particles, only (semiclassically) a singularity corresponding to the gravitational field of a point mass. This mass is a parameter that will have decreased. What one has instead in full quantum gravity is unknown.

 

[Buzz Bloom]

A particle cannot self annihilate.

Hi @A. Neumaier:

Again I apologize for careless language. I meant that the pair did not self annihilate.

1 and 2 are ok

Well, I am feeling that I am finally making some progress. 2 out of 3 ain't so bad. ;-)

At the center of the black hole are no particles, only (semiclassically) a singularity corresponding to the gravitational field of a point mass.

Is the above description based on QG, or might it also be a correct description based on a combination of particle physics together with GR, or perhaps based on just GR alone?

Regards,
Buzz

 

[A. Neumaier]

the pair did not self annihilate.

It never will. The two particles created will have opposite momentum, hence fly in opposite directions and are very unlikely to meet again.

Is the above description based on QG, or might it also be a correct description based on a combination of particle physics together with GR, or perhaps based on just GR alone?

The singularity corresponds to the classical GR description. Particles will fly into the singularity in a very short (external) time and disappear. The quantum version is unknown until we have a proper theory of quantum gravity plus matter.

You cannot expect to get in a few sentences answers to questions where experts struggle for years to get understanding.

 

[Buzz Bloom]

I want to thank everyone who has helped me in this thread to better understand the Hawking Radiation phenomenon,
especially @A. Neumaier who showed great patience in answering what must been many dumb questions.

I have started a new thread in the Special and General Relativity forum to continue asking more questions about this phenomenon unrelated to virtual particles. The thread is:

Qs re Hawking Radiation – Part I​

Regards,
Buzz

 

[A. Neumaier]

The thread is:
Qs re Hawking Radiation – Part I

Thus here.

 

[Buzz Bloom]

Thus here.

Hi @A. Neumaier:

How do you create a link like that?

Regards,
Buzz

 

[A. Neumaier]

How do you create a link like that?

I copy the target link from the ''bookmark'' position at the bottom of each post into the clipboard, then mark the text for the link using the chain symbol in the edit toolbar, paste the text from the clipboard into the free space for the link address, and remove the trailing text ''/bookmark/''.

 

[Buzz Bloom]

the ''bookmark'' position at the bottom of each post

Hi @A. Neumaier:

I do not see (or recognize) any bookmark position at the bottom of any post. I see "edit", "delete", "report", "quote", and "reply".

ADDED
Ah ha! I found it! I right click on "quote" and save the link.
Thanks.

Regards,
Buzz

 

[ftr]

If virtual particles are just a calculation tool, then what(entity) is responsible for the force transfer?

 

[mfb]

The fields.

 

[ftr]

The fields.

So there are no particles as "force carriers", correct?

 

[mfb]

Depends on your interpretation of "force carriers".

 

[ftr]

Depends on your interpretation of "force carriers".

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

It seems in one place it can be said that the field is a mathematical description of the particle and does not exist if an ACTUAL particle is not there. Then again it seems that the field can exist EVEN if a particle does not show up, as in Higgs for example. It seems physics is done which way is convenient at the time.

Then my confusion, is it the field of the force carriers or the field of the particles that interact?

 

[jtbell]

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

It seems in one place it can be said that the field is a mathematical description of the particle and does not exist if an ACTUAL particle is not there.

Where exactly did you find what I put in bold face?

 

[A. Neumaier]

It seems physics is done which way is convenient at the time.

Talk about physics is indeed done in whatever way it seems convenient.

But the physics is not in the talk but in the formulas. The formulas are the same even when different people talk about them in different (more sloppy or more careful) ways. On the formal level you always have the fields, and sometimes you can interpret them as particles (with the same names as the fields) . But since particles are easier to visualize, one often prefers to use the particle language, knowing that it is not fully appropriate. This is deemed acceptable by many since anyway no talk can fully express the complexities studied in quantum mechanics.

Thus strictly speaking the gauge fields are the force carriers since manifestations of the fields cause the forces between particles (that are themselves field excitations). It is convenient to say that the gauge bosons mediate the forces. Here ''gauge bosons'' may still refer either to the gauge fields or the associated particles.

If one combines this with the virtual particle analogy, one can say without too much error that virtual gauge boson mediate the force (and hence serve as force carriers). The big mistake is made only when one takes the virtual particles as real objects moving in time rather than as graphical abbreviations of the formulas that allow one to calculate the forces.

 

[mfb]

It seems in one place it can be said that the field is a mathematical description of the particle and does not exist if an ACTUAL particle is not there.

That is certainly wrong.

Then again it seems that the field can exist EVEN if a particle does not show up, as in Higgs for example.

That is right.

It seems physics is done which way is convenient at the time.

Physics is not about "reality", it is about making good predictions, if different models can make the same good predictions then they are equally fine. In particular, the predictions are from quantum field theory, and QFT does not care about our words "particles" and "fields".

 

[ftr]

Where exactly did you find what I put in bold face?

That is certainly wrong.

How I understand QFT is that it is a generalization of QM wave function which itself has an unwieldy and controversial existence. Certain computations FROM the wavefunction can be interpreted as a physical outcome. And yet in QFT some of those are also become controversial like position. EVEN then the single particle state is only an approximation, DR A. Neumaier will tell you that. The uninterpretable "virtual particles" also point to the mathematical nature of fields.

I am not saying that it is wrong using them I just think there should be something that has a better picture.

 

[ftr]

More specificallyhttps://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf

quote page 3
"Physics education is affected directly, and scientific literacy indirectly, by what textbooks say about wave-particle duality and related topics. To find out what textbooks say, I perused the 36 textbooks in my university's library having the words "quantum mechanics" in their title and published after 1989. 30 implied a universe made of particles that sometimes act like fields, 6 implied the fundamental constituents behaved sometimes like particles and sometimes like fields, and none viewed the universe as made of fields that sometimes appear to be particles. Yet the leading quantum field theorists argue explicitly for the latter view (Refs. 10-18). Something's amiss here."

 

[A. Neumaier]

It seems in one place it can be said that the field is a mathematical description of the particle and does not exist if an ACTUAL particle is not there. Then again it seems that the field can exist EVEN if a particle does not show up, as in Higgs for example.

The first sentence is nonsense. The field always exists (in the sense that one can in principle measure the field expectations anywhere). In the special case where the field primarily consists of one or more elementary excitations of the vacuum state it can be described approximately in terms of particles. For interacting fields, the particle interpretation is strictly valid (without approximation) only in an asymptotic sense - for times $t\to\pm\infty$.

Nevertheless, the particle terminology is frequently used in a pictorial way since it looks simpler and more intuitive than the field picture. The price to be paid for it is that the picture becomes highly misleading when taken literally.

 

[vanhees71]

How I understand QFT is that it is a generalization of QM wave function which itself has an unwieldy and controversial existence. Certain computations FROM the wavefunction can be interpreted as a physical outcome. And yet in QFT some of those are also become controversial like position. EVEN then the single particle state is only an approximation, DR A. Neumaier will tell you that. The uninterpretable "virtual particles" also point to the mathematical nature of fields.

I am not saying that it is wrong using them I just think there should be something that has a better picture.

If you refrain from too much speculation, aka "interpretation", the QM wave function (appropriate for a part of non-relativistic physics, where the particle numbers are strictly conserved) has a very clear meaning, providing the probabilities for the outcome of measurements via Born's Rule. From a physics point of view there's not more but also no less to it than that, and there's nothing controversial about it since this "minimal interpretation" is very well confirmed by all the very accurate experimental tests of QM we have available these days.

The same holds for relativistic QFT. Among physicists there's not much controversial about it. The perturbative evaluation of renormalized perturbation theory together with some resummation techniques and the use of renormalization-group methods as well as ab-initio calculations of the interacting theory on the lattice (for QCD) is also among the theories with the best confirmation by experiment ever (for some observables up to 12-16 significant digits!).

If you take out philosophical quibbles and stick to the physics part of QT (both non-relativistic and relativistic), it's a great success story without much controversies!

Of course there are open physical questions. Among them is a consistent description of gravity, applicable to observable effects (maybe even to find observables for quantum behavior related with gravity at all!), a perhaps related way to understand the observed values of the constants entering the standard model of elementary particle physics and standard cosmology, particularly the observed value for the cosmological constant/"dark energy" in the universe, a clear confirmation of the existence of "dark matter" and identification of corresponding "new particles" if they exist. So there's a lot to do in physics besides the philosophical muttering, too often discussed in this subforum, and I'm very sure that these open questions won't be solved by philosophical speculations but by the usual solid work of experimental and theoretical physicists, i.e., by model building based on solid observational input, as it has been in the last ~400 years of modern science since Galileo and Newton!

 

[ftr]

The first sentence is nonsense. The field always exists (in the sense that one can in principle measure the field expectations anywhere).

How do you do that.

Do each electron has its own field, or all the electrons in the universe share one field.

How can a specific point in space-time carry all the values of the fields of all known particles since these are suppose to be real and intrinsic and not effective like temperature or pressure.

 

[vanhees71]

There's one electron field (Dirac field) in the standard model of elementary particle physics. Why should there be more than one? There's a well-defined kind of quantum field for any particle species in the standard model (leptons, quarks, gauge bosons, and Higgs bosons).

Also, what's the problem to have several fields defined in space-time? In my room the air has a temperature, a velocity field, a density, a pressure field. This makes a lot of fields, which all can be measured at any point in space and at any time. Then there's also light in my room, i.e., an electromagnetic wave field, which I can measure at any point in space and time, if I wish. That's all. There's nothing mysterious in this.

Of course, quantum fields and observables expressed in terms of them are at a higher level of abstraction than these classical fields.

Perhaps I don't understand your questions right...

 

[ftr]

There's one electron field (Dirac field) in the standard model of elementary particle physics. Why should there be more than one? Perhaps I don't understand your question right...

Does this one electron field has a value at a specific space time representing all the electrons in the universe or has multiple values for each electron.