# I 'Localization,' particle motion, and quantum fluctuations...

1. Dec 23, 2016

### asimov42

Hi all,

Some time ago I was reading about Anderson localization (posted a question about it was well) - this got me thinking about vacuum fluctuations. I think I have the wrong idea in my mind - so wanted to ask the great community here about it:

Quantum (vacuum) fluctuations must have an effect on particle motion? I'm wondering why we don't see effects similar to Anderson localization (although only for short periods), that is, the motion of a particle being temporarily restricted, or changes to particle trajectories, due to quantum fluctuations.

I realize that the above would imply all sorts of things, like transfer of momentum to the vacuum, which cannot occur. I'm just not sure I understand why.

2. Dec 23, 2016

### Staff: Mentor

They don't exist. They are an invention used by popularizations and beginner texts as a heuristic crux. This has been discussed many times here:

Now don't get me wrong - heuristics is VERY important - but as to being real and part of arguments like affecting particle motion - forget it. Its used in things like the heuristic explanation of why the charge of an electron increases as you get closer. Heuristically the virtual electrons and positrons arond the electron has a screening effect - in reality its due to renormalisatiom. But we all must walk before we cam run so there are a lot of 'wrong' ideas used at the start of QFT and vacuum fluctuations is one of them. Trouble is as people progress they sometimes forget its just a useful crux and you get them mentioned even in advanced professional papers. This leads to long threads here where people who have not been exposed to proper QFT argue about it - its quite maddening actually.

But take my word for it vacuum fluctuations are a load of rubbish. They appear as lines in Feynaman diagrams which is simply the pictorial representation of a Dyson series:
https://en.wikipedia.org/wiki/Dyson_series

They are not, repeat not, real.

Thanks
Bill

3. Dec 23, 2016

### asimov42

Thanks Bill - very interesting! I'd dispensed with the idea of 'virtual pairs popping in and out of existence', but had still understood that vacuum did fluctuate. Aren't there effects, like the Unruh effect (unproved, yes), that require the vacuum to have oscillations?

4. Dec 23, 2016

### Staff: Mentor

No quantum effects require vacuum fluctuations for its explanation. As I said some, even professional literature explains it that way. Another example is spontaneous emission - its insidious. Its supposed to be caused by quantum fluctuations of the vacuum - in fact its caused by since the electron is coupled to the quantum EM field its not in a stationary state - but the virtual particle explanation is still all over the place.

The Unruh effect is no exception and a number of threads have discussed it. It however is one of the worst cases of bad reasoning around - you will find many high powered physicists using it to supposedly prove virtual particles exist.

So I must wimp out here - because of that please start a new thread about explaining the Uhruh effect without virtual particles and the many high powered professionals that post here will give the right answer. But remember while virtual particles do not exist a quantum field for each particle type permeates all of space and motion through that may have effects:
http://math.univ-lille1.fr/~debievre/Talks/unruhrolla09A.pdf

But I will leave the details to those more knowledgeable.

Thanks
Bill

5. Dec 23, 2016

### asimov42

Ok, new thread coming up. But, given that there's a quantum field for each particle type, don't the fields oscillate randomly?

6. Dec 24, 2016

### asimov42

Wait, actually, now I'm a bit more confused - in Albert's article, he mentions "The starting point is the sound knowledge that there are technical notions of vacuum fluctuations (= nonzero vacuum expectation values)" ... so there are vacuum fluctuations?

7. Dec 24, 2016

### asimov42

Also, aren't there theories that the universe itself may have began as a quantum fluctuation?

The vacuum expectation value may vanish for fields except the Higgs, but this doesn't mean that there aren't transient fluctuations, does it? Peeking at the Wikipedia page for Quantum Fluctuations (https://en.wikipedia.org/wiki/Quantum_fluctuation) (not the best source, I realize), the probability density for the vacuum state is not always zero.

So what am I missing? Any comments? Thanks!

8. Dec 24, 2016

### vanhees71

Of course, there are quantum fluctuations in the mathematical sense that, e.g., the probability distribution of position of a particle has a finite width. At best it's sharply peaked around some value like a Gaussian distribution, but it has a finite width. Now one must remember the meaning of probabilities, which is a heatedly debated question, but for me as a theoretical physicist who tries to stay close to experiments, the only interpretation of probabilities making sense to me is the frequentist interpretation. This means you can measure a probality distribution by preparing very many quantum systems (here one particle) in the same way (i.e., in some pure or mixed quantum state) and then measure the observable one is interested in (here the position of the particle) and then making the "statistics" of the outcome of these measurements. The found distribution of these measured values should converge (in some weak sense) to the probability distribution predicted by QM. Each single experiment will give a different result (even when the measurement itself is perfectly accurate), and that's what I call "quantum fluctuation" in the strict sense.

Vacuum fluctuations are fictitious, because they cannot be measured. The vacuum in relativistic quantum field theory is just the Fock state with 0 quanta present. If you try to measure any property of this state you have to put equipment there, and then it's not a vacuum anymore. So you can only "probe the vacuum" by putting some matter there, and then you call "vacuum fluctuation" deviations from the leading-order result of perturbation theory. E.g., part of the Lambshift of the corresponding hydrogen lines is due to a "vacuum polarization of the electromagnetic field", in leading order a Feynman diagram with one loop. Formally the perturbation theory can be taken by the number of loops, which means a formal (asymptotic) series in powers of $\hbar$. The better notion for this is "radiative corrections" or simply "higher-order corrections" of perturbation theory than to call it vaguely "vacuum fluctuations". See also the long debate in the above mentioned thread:

9. Dec 24, 2016

### Staff: Mentor

No.

You must study QFT to understand whats going on.

Can you elaborate what you mean by Albert's article - I cant recall referencing one by someone of that name - but then again my memory is far from perfect.

Thanks
Bill

10. Dec 24, 2016

### Staff: Mentor

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

Its unstable - quantum fluctuations are again simply a heuristic. But again you need someone more expert in this area than me.

Of late eternal inflation seems the 'in' theory:
https://en.wikipedia.org/wiki/Eternal_inflation

Again note the reference to quantum fluctuations - its insidious and I understand people getting confused when the experts here say its a crock. Its really probably something like spontaneous emission where instability is caused by a non stationery state - but like I say an expert is required.

Thanks
Bill

11. Dec 24, 2016

### asimov42

vanhees71, thanks, that extremely helpful! This certainly answers my question about free particles propagating in the vacuum. Just for my own understanding, the probability distribution for the quantized Klein–Gordon field in the vacuum state is non-zero (that is, you may 'see' a configuration containing particle(s), and I'm reaching beyond my knowledge here), but you're saying that any true observation (hence the quotes previously) would require having a 'real' test particle there to observe, thus destroying the vacuum?

Ultimately, then, the vacuum itself cannot have an effect on the motion of a test particle, which makes sense. It's quite frustrating that, as Bill mentions, there's a picture that's been built of the idea of particle pairs popping in and out of existence, etc., and that this is pervasive even in some technical literature.

Last edited: Dec 24, 2016
12. Dec 24, 2016

### asimov42

Sorry Bill, that's my fault - I meant Arnold Neumaier's article, which you cited (in my sleepy condition I somehow got 'Albert', apologies).

I'll have a closer look at the material on eternal inflation! Thanks!

13. Dec 24, 2016

### secur

That's "crutch" not "crux". PF'ers make such mistakes constantly, and it has nothing to do with physics ... But for a few of us, it's quite maddening actually.

14. Dec 25, 2016

### asimov42

Would anyone have a reference for the layperson, or at the undergraduate level, that explains (sets the record straight as it were) regarding the existence of vacuum fluctuations? I.e. that clearly refutes the idea that there are random fluctuations in the vacuum, etc.

A tall order, I know - I'd love to dive into QFT directly, but will need to do a lot of work before I'm able to fully grasp the implications of the math.

Thanks!

15. Dec 25, 2016

### Staff: Mentor

That's the exact issue.

At the beginner level these falsehoods that aid intuition are used freely. As you delve deeper you see they are falsehoods but even some experts still stick to them.

To see its false you must go to an advanced level. The minimum would be:

As a build up I like:

It treats QFT and standard QM in exactly the same way by focusing on the symmetry operators so you get a unified view.

Thanks
Bill

Last edited by a moderator: May 8, 2017
16. Dec 27, 2016

### asimov42

Thanks for the reference Bill!

17. Dec 27, 2016

### asimov42

Folks - out of curiosity, from a layman's perspective, can one debunk the ideal of virtual particles 'popping into and out of existence' in the following way:

A free electron is travelling in the vacuum - if a virtual electron-positron pair were to 'pop of of the vacuum', the virtual positron could annihilate with the real electron (a la a Feynman diagram), leaving the remaining virtual electron. To maintain conservation of momentum and energy, this virtual electron would then need to be observable (or real), just like the original free electron... but this means it would have needed to be observable in the first place.

So, is it not the case that, were the above scenario actually true, a test apparatus would have to register two 'real' electrons (at least statistically) ... which clearly can't happen.

I realize none of the above is necessary given a proper understanding of QFT - I'm just wondering if the above is a simple, non-technical (but logical) way to refute the whole virtual particle 'popping-in-and-out' idea.

18. Dec 27, 2016

### asimov42

One last thing (sorry to beat a dead horse) - I'm well on my way to debunking the vacuum fluctuation / virtual particle myth (in my head anyway). I'm curious about the above post being an easy way to see that there are clear problems with the 'layperson' picture of virtual particles.

The last item: I have heard time and again that every particle will eventually be annihilated in some process, and hence no particle is truly 'on shell' exactly. In turn, the popular literature will say that all particles are in some sense virtual (i.e., there's no crisp line in the sand, as it were). However, I can clearly measure, e.g., the electrons (some, anyway) in my body... so they are observable and hence real. How does on square these two notions?

19. Dec 28, 2016

### Staff: Mentor

That's a new one on me.

Strictly speaking many particles are like the electron in spontaneous emission and not in a stationary state so eventually decays in some way.

Our models are to some extent just approximate eg strictly speaking pure states do not exist because they are entangled with its quantum field that often interact with other quantum fields.

Thanks
Bill

20. Dec 28, 2016

### asimov42

Thanks Bill - I hate to quote Wikipedia, but here's what is has to say at the end of the page on virtual particles:

"However, all particles have a finite lifetime, as they are created and eventually destroyed by some processes. As such, there is no absolute distinction between "real" and "virtual" particles. In practice, the lifetime of "ordinary" particles is far longer than the lifetime of the virtual particles that contribute to processes in particle physics, and as such the distinction is useful to make."

The implication is that any particle that has a finite lifetime is not exactly 'on shell.' There's also a note that:

"In many cases, the particle number operator does not commute with the Hamiltonian for the system. This implies the number of particles in an area of space is not a well-defined quantity but, like other quantum observables, is represented by a probability distribution. Since these particles do not have a permanent existence, they are called virtual particles or vacuum fluctuations of vacuum energy."

I'm still somewhat confused by the above - since virtual particles aren't observable.

Last edited: Dec 28, 2016