# I Relation between quantum fluctuations and vacuum energy?

#### Frank Castle

Conventional Feynman diagrams represent time-ordered expectation values, not Wightman correlation functions. (The latter need the CTP formalism.)
Sorry, I meant it to be a time-ordered correlator, but just got lazy when I was typing and didn't include the time-ordering symbol.

If you really want to understand quantum physics, concentrate on the formulas, and view the talk about it only as a very loose and fallible guide.
I try to do that, but then I feel like I'm following the math blindly without having any physical intuition and this in itself feels uncomfortable to me.

Don't worry about it. It happens in physics all the time. You start out with stuff of dubious validity that gets corrected later, either explicitly or you are supposed to cotton onto it yourself. But what you have done is developed intuition which actually is more important. The only issue is not realizing whats going on and even then it generally causes issues only when discussing foundational issues rather than actually solving problems. Guess what most discuss here .
Thank you for being patient with me, I really appreciate it!

I think a big part of my problem is, when I first was taught QFT I didn't give these notions much thought as I was already completely bogged down with trying to get a grip with all the formalism, and it wasn't really expounded upon by my lecturer. Now that I've had a little more experience with QFT I'm questioning all these aspects a lot more, and I am in a constant state of worry and confusion that I don't really understand at all what is going on

#### bhobba

Mentor
Now that I've had a little more experience with QFT I'm questioning all these aspects a lot more, and I am in a constant state of worry and confusion that I don't really understand at all what is going on
Then you have reached the second later phase I talked about

Thanks
Bill

#### A. Neumaier

Science Advisor
I meant it to be a time-ordered correlator, but just got lazy when I was typing and didn't include the time-ordering symbol.
is this your way to excuse yourself for having talked nonsense? You repeatedly wrote what you later claimed you didn't mean - this makes it very difficult to communicate. It is much better to check if what you wrote is what you meant before sending things off.

As for the talk accompanying the formulas, they don't mean much, and if one can't make sense of them it is often because they don't make sense - except by very superficial analogy. The only thing to make sense of is the formulas, and how they relate to (possibly) experimentally accessible information. So you have to look for the latter in the words.

#### Frank Castle

is this your way to excuse yourself for having talked nonsense?
No, definitely not. I put down what I'm thinking at the time and I'm fully aware that sometimes (hopefully not always) it can be nonsense, but it's just me trying to make sense of things. Often I think a bit more about it afterwards and take into account what you and others have written in response and then try and formulate my updated thoughts. I apologise that I'm sometimes incoherent, I will try to improve my posts in future.

Then you have reached the second later phase I talked about
I guess at least it's reassuring that I'm not the only one that has struggled/is struggling with these things.

#### aries0179

Sorry, I meant it to be a time-ordered correlator, but just got lazy when I was typing and didn't include the time-ordering symbol.

I try to do that, but then I feel like I'm following the math blindly without having any physical intuition and this in itself feels uncomfortable to me.

Thank you for being patient with me, I really appreciate it!

I think a big part of my problem is, when I first was taught QFT I didn't give these notions much thought as I was already completely bogged down with trying to get a grip with all the formalism, and it wasn't really expounded upon by my lecturer. Now that I've had a little more experience with QFT I'm questioning all these aspects a lot more, and I am in a constant state of worry and confusion that I don't really understand at all what is going on
look, its kinda a major undertaking to even be in a quantum class, and i know cause i went through 12 years of study and working towards my own answers that i wasnt satisfied with in a text or class. the problems begin when all the calculations and measures take over your ability to process the scenario and be confident in your own knowledge and experiences. the qualified academics in any form of quantum sciences generally do not have the true qualifications to lead upcoming brains in the extremities of for example quantum mechanics and quantum theory, those happen to be the interests that i pursued based on the entire quantum spectrum of sub choices to focus my own personal talents and intellect towards those portions of a greater entity then i think its possible for any one person to have even a good grasp upon...... its too much information and alot of the various scientists are teaching or saying the same things, they just rather have the exclusive rights on the ideas and formulas but they dont. so do not get down from the lack of understanding that someone else may have, and i will say this with high certainty, the knowledge that i have achieved has been mainly from my own ideas and knowledge based on exploring the accepted science and being able to use my brain to get beyond what is accepted by the masses. one more thing it does make a difference who you listen and learn from and the only way to get the best and most respected minds to use as a guide is to do some background on a few people like Michio Kaku, or university ofberkeley professor alex filippenko. from my own experience it was so liberating and thoughtful for me when ive gone to a weekend of lectures to be able to get first hand guidance and help from the people that i respect and look at as mentors, sorry i kinda am lengthy with my answers i guess that may come with the territory, but i wanted to give you several aspects of helpful ideas to think over and go with your comfort level.

#### Frank Castle

look, its kinda a major undertaking to even be in a quantum class, and i know cause i went through 12 years of study and working towards my own answers that i wasnt satisfied with in a text or class. the problems begin when all the calculations and measures take over your ability to process the scenario and be confident in your own knowledge and experiences. the qualified academics in any form of quantum sciences generally do not have the true qualifications to lead upcoming brains in the extremities of for example quantum mechanics and quantum theory, those happen to be the interests that i pursued based on the entire quantum spectrum of sub choices to focus my own personal talents and intellect towards those portions of a greater entity then i think its possible for any one person to have even a good grasp upon...... its too much information and alot of the various scientists are teaching or saying the same things, they just rather have the exclusive rights on the ideas and formulas but they dont. so do not get down from the lack of understanding that someone else may have, and i will say this with high certainty, the knowledge that i have achieved has been mainly from my own ideas and knowledge based on exploring the accepted science and being able to use my brain to get beyond what is accepted by the masses. one more thing it does make a difference who you listen and learn from and the only way to get the best and most respected minds to use as a guide is to do some background on a few people like Michio Kaku, or university ofberkeley professor alex filippenko. from my own experience it was so liberating and thoughtful for me when ive gone to a weekend of lectures to be able to get first hand guidance and help from the people that i respect and look at as mentors, sorry i kinda am lengthy with my answers i guess that may come with the territory, but i wanted to give you several aspects of helpful ideas to think over and go with your comfort level.
Thanks, I appreciate your comments.

Are there any good notes by Michio Kaku, or Alex Filppenko (or others) on the subject that you would recommend reading?

#### Frank Castle

Then you have reached the second later phase I talked about

Thanks
Bill
In a set of notes I've read in the last couple of days the author refers to quantum fluctuations of a quantum field in terms of the variance of its Fourier modes $\delta\phi( t, \mathbf{k}) =\sqrt{\langle\phi^{2}\rangle}$ about its expectation value $\langle\phi\rangle =0$. I'm not saying I place any trust in this description, but I was just wondering what your thoughts are on it?

#### aries0179

from the looks of it it seems incomplete or maybe to not fully cover the full amount of required information to get a correct field variance, i only say that because this may be a calculation based on a set of info that in those settings the calculation always reads as such. but i have to say i cant find any real issue with the values in relation to the sum, i know that may not help but i would need to do a little digging to verify for sure. for instance i need to know where the equation came from who ran the numbers and how they came to the solution and base that on the values accounted for. make sense?

#### Frank Castle

from the looks of it it seems incomplete or maybe to not fully cover the full amount of required information to get a correct field variance, i only say that because this may be a calculation based on a set of info that in those settings the calculation always reads as such. but i have to say i cant find any real issue with the values in relation to the sum, i know that may not help but i would need to do a little digging to verify for sure. for instance i need to know where the equation came from who ran the numbers and how they came to the solution and base that on the values accounted for. make sense?
I think their reasoning is that although the expectation value (average) of the field will be zero, the variance in general won't be and this quantifies how the value of the field fluctuates around the expectation value (but I'm aware this may be nonsense).

#### A. Neumaier

Science Advisor
lthough the expectation value (average) of the field will be zero, the variance in general won't be
The variance is infinite hence meaningless, as it also is for olassical stochastic processes. The fluctuations are descibed by the correlations (covariance functions) or their Fourier transform, which give an equivalent description.

#### bhobba

Mentor
In a set of notes I've read in the last couple of days the author refers to quantum fluctuations of a quantum field in terms of the variance of its Fourier modes $\delta\phi( t, \mathbf{k}) =\sqrt{\langle\phi^{2}\rangle}$ about its expectation value $\langle\phi\rangle =0$. I'm not saying I place any trust in this description, but I was just wondering what your thoughts are on it?
How can an operator vary? Obviously they are in some way referring to the variance of an observation of some sort.

Thanks
Bill

#### A. Neumaier

Science Advisor
How can an operator vary?
In general, an operator is the noncommutative version of a random variable. (Probability theory is equivalent to the theory of operators acting by multiplication on a function space. The multiplication operators all commute.)

#### Brage

I think it is not quite right to say that vacuum fluctuations are not physically real (which is what it seems to me you are saying), as a lot of effects are very precisely described by them. Take for instance Hawking radiation and the lambda shift (which was not predicted by the Dirac equation). I believe I saw you (A. Neumaier) comment earlier on how (and I paraphrase) "Hawking radiation is produced from the gravitational field" (or so I gathered), and therefore not due to virtual particles. Correct me if I am wrong on this recollection, but such a statement wouldn't be well founded as we have yet to formulate a consistent theory of quantum gravity that is validated by experiment.

#### bhobba

Mentor
the lambda shift
Have you heard of Lattice Gauge Theory:
https://en.wikipedia.org/wiki/Lattice_gauge_theory

That predicts the Lamb shift and has no vacuum fluctuations or virtual particles. Nor is it the explanation for Hawking radiation as has been discussed many times on this forum.

All such are is intuitive cruxes for the math to aid intuition. That is not to belittle their importance - developing intuition is vital They get repeated in populist press and we get people who, for reasons that perplex me, wont accept what those that have studied the theory in detail tell them - namely they are fictions.

This isn't the only area it happens - it occurs all the time in advanced areas. I mentioned previously about the 'hole' issue in how transistors work. You will find electronics textbook after textbook that promulgates the same load of rubbish. But one must start somewhere. Feynman commented on it. He would prefer to tell the truth, the whole truth, and nothing but the truth, from the start. But being the great educator he was and having thought hard about it realised it would be very unwise doing that. So as you proceed from beginner to advanced you need to unlearn things. Its nothing to really worry about except when those at the beginner level do not believe what those at the more advanced level tell them. That is unbelievably frustrating as I know only too well.

Its one of the many myths of QM:
http://arxiv.org/abs/quant-ph/0609163

I have posted the above many times. It should really be the end of the matter but it isnt - people have so many ingrained ideas that are hard to shift.

Thanks
Bill

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#### A. Neumaier

Science Advisor
"Hawking radiation is produced from the gravitational field" (or so I gathered), and therefore not due to virtual particles. Correct me if I am wrong on this recollection, but such a statement wouldn't be well founded as we have yet to formulate a consistent theory of quantum gravity that is validated by experiment.
If you insist on waiting for a consistent quantum theory of gravity one cannot discuss Hawking radiation at all - any statement about it would be ill-founded according to this overly stringent criterion!

The whole concept of Hawking radiation depends (at present) on semiclassical reasoning. And in semiclassical reasoning, Hawking radiation is produced from the gravitational field.

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#### bhobba

Mentor
Correct me if I am wrong on this recollection, but such a statement wouldn't be well founded as we have yet to formulate a consistent theory of quantum gravity that is validated by experiment.
Validated by experiment probably has some validity (although I would like an experimental type to comment) but its a, admittedly very common, misconception we don't have a quantum theory of gravity.

We indeed have one, and it elegantly explains Hawking radiation:
http://blogs.umass.edu/grqft/effective-field-theory/

What we don't have is one valid to beyond about the Plank scale - but gravity is not alone in that - the standard model is not trusted in that region either.

As I am wont to say it doesn't make developing a full quantum theory of gravity any easier, but is an interesting take that keeps what really is going on in perspective. Its not quite the mess some sources make it out to be.

Thanks
Bill

#### vanhees71

Science Advisor
Gold Member
If you insist on waiting for a consistent quantum theory of gravity one cannot discuss Hawking radiation at all - any statement about it would be ill-founded according to this overly stringent criterion!

The whole concept of Hawking radiation depends (at present) on semiclassical reasoning. And in semiclassical reasoning, Hawking radiation is produced from the gravitational field.
Well, what's even more interesting is, whether there is any empirical evidence for Hawking radiation. I'm not aware of any...

#### A. Neumaier

Science Advisor
Well, what's even more interesting is, whether there is any empirical evidence for Hawking radiation. I'm not aware of any...
We can be lucky, it would require a very big black hole close to us...

#### vanhees71

Science Advisor
Gold Member
Well, whether this is a lucky situation, is another question ;-)).

#### George Jones

Staff Emeritus
Science Advisor
Gold Member
We can be lucky, it would require a very big black hole close to us...
Big???

#### vanhees71

Science Advisor
Gold Member
Yeah, real big, because otherwise we have no chance to detect Hawking radiation. However, if we come too close (which I guess we should to detect the radiation), maybe we have no time to write the paper publishing the discovery ;-)). Anyway, I guess Hawking radiation is a safe place to make theoretical predictions, because it's very unlikely to be disproven empirically ;-).

#### George Jones

Staff Emeritus
Science Advisor
Gold Member
Yeah, real big, because otherwise we have no chance to detect Hawking radiation
But the Hawking temperature of a black hole is inversely proportion to mass, and power radiated goes as T^4. The temperature of a solar mass black hole is far, far lower than the 2.7 K CMB temperature, so something much, much less massive is needed in order to be detectable.

#### A. Neumaier

Science Advisor
But the Hawking temperature of a black hole is inversely proportion to mass, and power radiated goes as T^4. The temperature of a solar mass black hole is far, far lower than the 2.7 K CMB temperature, so something much, much less massive is needed in order to be detectable.
Far away from a black hole of typical astrophysical size, Hawking radiation is indeed completely swamped by the microwave background radiation, while small black holes that have a higher Hawking temperature are not radiating enough to be detectable from far away. Since the intensity of Hawking radiation decays with distance like $r^{-2}$ it is not detectable unless one is reasonably close to the black hole and a lot of radiation is produced, which in turn requires a high gravitational field and hence a big black hole.

But one can study in the lab Hawking radiation in so-called analogue black holes, optical analogues where nonlinear optics simulates a quantum metric; see Hawking radiation from ultrashort laser pulse filaments:
the same physics that underlie black hole evaporation in the form of Hawking radiation may be found and studied in other, more accessible systems. Our measurements highlight spontaneous emission of Hawking radiation from an analogue event horizon generated by an “evaporating” refractive index perturbation and suggest a path towards the experimental study of phenomena traditionally relegated to the areas of quantum gravity and astrophysics.
There are also acoustical analogue black holes; see, e.g., http://arxiv.org/abs/1410.0238.

#### vanhees71

Science Advisor
Gold Member
Well that are analogues but not the true thing. In this sense you could say that we have discovered all kinds of "exotic" particles like anyons, magnetic monopoles, Majorana and Weyl fermions,... However all these are, of course, no elementary particles but quasiparticles in condensed matter physics :-).

#### Demystifier

Science Advisor
2018 Award
We can be lucky, it would require a very big black hole close to us...
Well, Hawking radiation is much easier to detect for a small black hole.

EDIT: Now I have seen that George Jones already said that.

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