# Virtual particles and quantum fluctuation

1. Sep 9, 2011

### No-where-man

the virtual particles that are created are the result of a quantum fluctuation ..but the energy of this fluctuation must be zero
so 1 particle has positive mass and the other has negative mass ...so that if they annihilate the mass is zero and they go back to not existing
but if the one with negative mass is sucked into the black hole ...it takes mass away from the black hole .
and the positive particle becomes real instead of virtual

basically, speaking, every time when negative particle enters the black hole, black hole loses energy because the negative-energy particle annihilates with the positive energy of the black hole, the black hole shrinks, but it doesn't radiate, while the positive particle that was outside the black hole all that time goes away from the black hole, and we see it as the hawking's radiation.

However, what are virtual particles?
I need your opinions on that matter!!!
I asked for a favor an astrophysicist and he told me the following:

Me: Virtual particle-antiparticle pair production is a mathematical technique for describing the state of a field. It does not describe real particles really appearing out of nothing.
Hawking himself wrote, in his seminal 1975 paper, "It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally."
Virtual particle-antiparticle pair production is a mathematical technique for describing the state of a field. It does not describe real particles really appearing out of nothing.
If there were real particle-antiparticle pairs really being created, then what mechanism could possibly force the negative energy particle to always fall into the black hole when the positive energy one can escape?

In what sense virtual particles are virtual and distinct from real ones? Honest question -I do not know.

Answer: Say that the number of particles in a box is x=20-18. Obviously, this means that there are 2 particles in the box But if you look back into your math, you'll see that there aren't only 2 particles present. There are 38: 20 positive particles and 18 negative particles, which combined to give you your 2 real particles. It would be really inconvenient to formulate the math without referencing the other 36 particles, but that doesn't mean that they have some sort of physical existence.

The math is usually just a teeny bit more complicated than integer subtraction, but that's the basic idea.

Me: This is something that always fascinates and puzzles me: If the math says something, on what grounds do we say "this is real" and "oh, this is just a math trick"? In the physics I've done, I've seen little of this, so perhaps that's why I am so puzzled.

Answer: That's a complicated question that I definitely have no idea how to answer in general. In this specific case, though, we call particles real if there is in principle some way to measure them, because that's generally what people mean when they talk about something being real.

Me: My understanding was that "they" have well measurable effects, however. Or am I wrong?
For example, after neutrino was predicted but before it was detected, was it considered "real", or not? I thought the former, because it was needed to preserve conservation laws, but again, perhaps I am misguided.
Mind you, I know how it comes across, but I am not subtly insisting that they have to be real. I am trying to understand how it works, where is the line.

Answer: They have measurable effects only in the sense that they're part of the math and the math predicts measurable things. If something is a real particle, it should be possible in principle to perform a measurement of its position, and you can't do that with virtual particles. This is somewhat tautological, but I'm only using it to explain why we make a distinction between virtual and real particles.

So, my question which math models should I take as the grain of salt???
Casimir's effect, virtual particles, something else???
We only have rock-solid proofs that black holes exist (they even detected dying pulses near the black holes, super-gigantic vortexes of infalling matter as well).
I'm getting confused here, really confused.

Also, just because gravity exists, it doesn't mean gravitons exist. Right?

Thanks to all.

2. Sep 9, 2011

### No-where-man

One useful way to look at these is to say that when a virtual particle- antiparticle pair is created in the vacuum, the total energy remains zero, but one of the particles has positive energy while the other has negative energy. (For clarity: either the particle or the antiparticle each/both can have negative energy).

However, what makes you think that positive-energy particle would not fall into the black hole, and the negative-energy anti-particle won't go away from the black hole?

3. Sep 9, 2011

### Ken G

I never understood that argument. If a virtual pair is separated by an event horizon and cannot annihilate, why can't we have observers on both sides of the event horizon to observe those particles? And since the laws of physics do not allow for real particles with negative mass, why are both observers not going to observe positive masses? And so how is mass going to be conserved in the whole story? Also, if we need a negative mass to fall into the black hole, how does an observer who is also falling in ever see a particle with negative mass? And if a particle with negative mass as reckoned from the outside has positive mass on the inside, then what about all the positive mass stuff falling in from the outside? Sorry to confuse you more, but something about that justification of Hawking radiation never seemed to really make sense.
I think the idea here is that the mass is constrained to be positive when it is observed on the outside, so that means the other one had to be negative mass, but the part I don't get is why can't there be an observer inside the event horizon to mess up that story?

4. Sep 9, 2011

### Polyrhythmic

It is a common misconception that antiparticles carry negative energy/mass. Antiparticles carry the opposite charge of their corresponding particles.

Virtual particles are a misleading interpretation of certain mathematical terms in a quantum field theoretical perturbation series expansion. When we talk about virtual particles, we mean internal lines in Feynman diagrams, which are used for mathematical convenience only. They carry no physical interpretation.

As I just explained, they are just a mathematical concept. For example, you can't describe them in terms of a physical state consisting of creation operators acting on the vacuum.

Well, if you study the theory and see what is going on, you actually realize that there is no reason to consider virtual particles as "real" in any way.

Well, the calculations they are part of lead to measurable quantities. But just because something is part of a mathematical formula, it isn't automatically a physical quantity.

This is not the same. Something like the neutrino could be detected in principle, even though for quite some time it was only a theoretical concept. This is different for virtual particles: they are purely mathematical, there is no reason to assume that they could be detected.

The best advice in such moments of doubt would be to actually put hands on the matter and check out the calculations. When I first heard about virtual particles, I also wasn't sure what to make of them. What people said confused me to some extent, but this changed when I actually started studying quantum field theory. If you see the calculations, you see the motivation behind the concept of a virtual particle. It is just a mathematical one.

This is the same story. Gravitons are hypotethical virtual particles corresponding to gravitational interaction. But since a working theory of quantum gravity has not been found so far, there is little we can say regarding the reality of gravitons.

5. Sep 10, 2011

### Chronos

The 'graviton' is obviously not a well behaved 'particle'. How would it otherwise exert influence beyond the event horizon of a black hole?

6. Sep 10, 2011

### No-where-man

Ok, I'm officially lost here: could you look at here. this guy is also an astrophycist, he say that one of the particles does have negative energy:

7. Sep 10, 2011

### Polyrhythmic

A few lines down into the text, he explains the issue:
"The final ingredient is a description of vacuum fluctuations. One useful way to look at these is to say that when a virtual particle- antiparticle pair is created in the vacuum, the total energy remains zero, but one of the particles has positive energy while the other has negative energy. (For clarity: either the particle or the antiparticle can have negative energy; there's no preference for one over the other.) Now, negative-energy particles are classically forbidden, but as long as the virtual pair annihilates in a time less than h/E, the uncertainty principle allows such fluctuations. "

The point is that virtual particles behave quite weird. I personally don't believe that this is really the mechanism for Hawking radiation (should it ever be detected), since it relies on a physical interpretation of virtual particles.

8. Sep 10, 2011

### No-where-man

Than what would be your approach?
Quantum tunneling, perhaps?
Could anti-particle truly escape from the black hole through quantum tunneling?

Also, how would you to layman (well, I'm not a pure layman, but I'm only an amateur) explain the process of Hawking's radiation?
Thanks for your time and patience.

9. Sep 10, 2011

### No-where-man

Well, I apologize for this raw explanation, this was taken from an other forum by a poster, who was trying to explain Hawking's radiation in layman's words, I guess he failed that, too.
Than what would be your approach?
Quantum tunneling, perhaps?
Could anti-particle or particle truly escape from the black hole through quantum tunneling?

Also, how would you to layman (well, I'm not a pure layman, but I'm only an amateur) explain the process of Hawking's radiation?
Thanks for your time and patience.

10. Sep 10, 2011

### Ken G

No need to apologize, your explanation is due to none other than Hawking himself. But I don't understand how he can motivate the idea that real particles always come out from the horizon, forcing negative-energy ones to go inward to conserve energy, when we can have observers on the inside of the event horizon also.
I would tend to agree with Polyrhythmic, not that I'm any expert on it, that the virtual particle concept can be over-interpreted and what we really need to do is look at how Hawking radiation emerges from the basic equations. There it is quite related to Unruh radiation, which is a topic around what you get when we merge what we know about light with what we know about proper acceleration, and then invoke the equivalence principle to use gravity to "cancel out" the acceleration and get Hawking radiation. Hawking likes to pretend that GR and particle physics have already been unified, but I'm not sure we can really know that it will work out that way when we finally succeed in doing that (if we ever succeed in doing that). But I think mostly what Hawking is doing is just give a more mechanistic interpretation to the mathematics, perhaps not to be taken too literally, I really don't know.
I don't see it as a tunneling phenomenon, because tunneling involves non-classical penetration of a potential barrier of some kind. We don't need any potential barriers in Hawking radiation, it is gravity that is separating the "virtual particles." But just how that occurs is not so clear (maybe you can think of it as tunneling through a Newtonian equivalent of the gravitational effect, there's probably someone who is explaining it that way). I've even heard people claim that it is the tidal effects of gravity that are responsible for "promoting" the virtual particle to real status, which must come at a penalty to the energy of the black hole. It's true that gravity is essentially defined by its tidal effects, but I'm not sure that explanation really gibes with Hawking's explanation, because you can monkey pretty arbitrarily with the strength of the tidal effects at the event horizon, just by considering black holes of vastly different mass. I don't buy that tidal effects are responsible when for supermassive black holes, the virtual particles would need to survive over huge distances before the tidal influences would match those of, say, a micro black hole.
That's pretty much what Hawking was trying to do, and given that the phenomenon carries his name, I would not endeavor to improve on his effort!

11. Sep 10, 2011

### No-where-man

Similar to your post I found here:
http://superstringtheory.com/blackh/blackh3a.html

As far as I remember, theUnruh effect is the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame; in layman's terms, a thermometer waved around in empty space will record a non-zero temperature. It is currently not clear whether the Unruh effect has actually been observed, since the claimed observations are under dispute. There is also some doubt about whether the Unruh effect implies the existence of Unruh radiation.
I don't know if Hawking is thinking that his hypothesis of Hawking radiation is wrong or not, but I guess he was trying to keep some laws of physics intact, like the law of entropy (if I remember correctly from his books).
The main assumption is that black hole should radiate to prevent the violation of the second law of thermodynamics, the law of entropy.
Quantum physics is always exciting, it's never boring.

12. Sep 10, 2011

### Ken G

I can't claim that was similar to my post-- that was a wonderfully clear exposition of Hawking and Unruh radiation at a basic level, glossing over exactly the technical details we want glossed over! It may gloss over one detail too many though-- it shows that acceleration turns a "white noise" radiation field into a blackbody radiation field, but it doesn't actually show that it will turn a vacuum into a blackbody radiation field that appears to come from the equivalent of the event horizon for constant acceleration. So it's just a beginning of a way to understand, but it is a nice beginning to be sure.
Yes, I think it is customary for people like Hawking to want to imagine this is all worked out, but skeptics say there could yet be more surprises.
I think that idea was actually that once he derived the existence of Hawking radiation, his student Bekenstein had the inspiration that this would have entropy consequences, which led to associating the area of the EH with its entropy. So the entropy issues resulted from the Hawking radiation, not the other way around, IIRC.

13. Sep 10, 2011

### Polyrhythmic

I honestly have no better explanation than the one that has already been discussed. Maybe a more experienced forum member can shed some light on this. I simply refuse the idea that something like a virtual particle carries any significance. I've seen and done thermodynamical calculations regarding black holes but I couldn't get the connection to virtual/real particle creation, maybe somebody could help us there.

14. Sep 11, 2011

### No-where-man

I just saw this response. You said that it has nothing to do with negative energy, than why Dr. Carlip mentions negative-energy particles are classically forbidden, but as long as the virtual pair annihilates in a time less than h/E, the uncertainty principle allows such fluctuations?
Now I read "Brief history of time" multiple times, but I still don't know what does it mean:
negative-energy particles are classically forbidden, but as long as the virtual pair annihilates in a time less than h/E, the uncertainty principle allows such fluctuations?
Does it mean negative-energy particles don't exist in a real universe or inside the real black hole once they fall or it simply means that virtual particles, once time passes h/e becomes real particles?

15. Sep 11, 2011

### No-where-man

Do you perhaps know which mathematical equations and models have come up with great discoveries and /or proven to be true?
The last time I read the great success with mathematical equations and models was discovery of neutrino, which has been proven to exist.
Unfortunately, we still don't have any proof whatsoever regarding the existence of gravitons.
Besides, neutrino was it something else?

16. Sep 11, 2011

### Polyrhythmic

The uncertainty principle is often used as an argument in in favour of the reality of virtual particles. I refuse to believe it though, in my opinion, it is quite unscientific to claim. Virtual particles are just mathematical constructs, and the uncertainty principle doesn't change that. That's why I'm not satisfied with the discussed explanation of Hawking radiation. If that explanation is enough for Carlip, that's alright, but it isn't enough for me.

17. Sep 11, 2011

### Polyrhythmic

Well, the first thing that comes to my mind would be the use of Riemannian geometry in general relativity. You use a huge apparatus of complicated math in order to formulate spacetime curvature and actually make predictions that can be verified to a high degree! But I'm not sure if that's what you're looking for. Maybe somebody more knowledgeable about physical history could provide more insight.

18. Nov 12, 2011

### Lost in Space

I've always understood (or been led to believe) that virtual particles aren't created in the vacuum but that the vacuum itself is created from virtual particles! These appear and disappear instantaneously thus supposedly not violating the law of conservation of energy but on previous occasions in discussing this with others they've said that this law is not relevant when talking about the whole system, i.e. the increased total volume of space with spatial expansion, as I've argued that the total energy of the vacuum must be increasing proportionately with the increase in volume even if the energy is negative. If not can this energy then only be described as virtual?
Would the duration of virtual particles be at Planck time or at an even smaller scale?
If virtual particles are just a mathematical construct does this then mean that this mathematical construct has no bearing on reality in that it makes things no clearer as to what they are? If the increased rate of the expansion of space is caused by negative energy overcoming gravity, where is this negative energy originating? The reason virtual particles appear and disappear is said to be because they annihilate each other very quickly. If virtual particles are 'borrowed' where are they borrowed from? The future? Some extradimensional space? And surely, if they annihilate each other why the imbalance between positive and negative energy?

19. Nov 13, 2011

### cbetanco

*sigh*
Ok, I will say it one last time, since I've said the same thing before in a couple other posts.

You can scatter off virtual b quarks in the proton during high energy physics experiments (like at the LHC), which can in turn produce b jets. These b jets will leave a unique signature in your detector. So from an experimentalist point of view, virtual particles do have have a physical existence, they are not just some mathematical tool. Also, all "real" particles are slightly off shell, and hence they are virtual as well. I would say that what is a mathematical tool and an idealization is the idea of a free particle, which by definition can't be detected. No particles are really free, and they all end their existence at the vertex of a Feynman diagram. I would argue all particles are virtual.

Also, I don't think people would spend so much time in studying PDFs if we didn't think sea quarks actually existed. We actually observe these sea quarks (like the virtual b quark) in the proton at high energies.... How can this only be a mathematical tool, when we actually measure their effects during high energy collisions? I think the majority view in the particle physics community is that virtual particles are indeed real, and make up part of what we call reality.

20. Nov 13, 2011

### Ken G

I don't have any personal expertise in virtual particles, but I've heard many people who do say they are nothing but pictorial descriptions of terms in an expansion of a solution that could, in principle, be obtained without any such expansion (or any such virtual particles). I've also heard people with expertise explain why they view virtual particles as a valid concept, or even take the stance you take, that they are the more general way to think about particles-- and non-virtual ones are the mathematical idealizations. So my conclusion is that the matter is largely one of opinion, much like interpretations of quantum mechanics, and different physicists may find value in either embracing or rejecting the concept. They are not a formal part of any physical theory that I know of, yet it is often unclear just what is the line between a "formal theory" and a "theory that gets used in the language and practice of physicists." Virtual particles do seem to have a prominent place in the latter.

My own feeling is that we should not get too bent out of shape about the issue, and instead should make statements like "here is how you can be a better physicist by rejecting the concept of virtual particles", or "here is how you can be a better physicist by embracing the concept", or even "here's how a non-physicist can gain better understanding by either rejecting or accepting the concept." Preferably, both types of comment can be made by the same person, though all too often it seems to require people on "different sides", as if there were sides, to make these points. But of course there are not sides-- there is just physics, and how to understand it, and that can include both embracing, and rejecting, virtual particles at our convenience. It seems like the "next theory" will either make it clearer what virtual particles are, or will reject them utterly, but until we get that more clarifying theory, the debate will rage. Better to just understand their advantages and disadvantages-- after all, they aren't actually real, whether they are less real, or more real, than "real" particles.