The vacuum in QFT. What is it. Why have it. Does everyone believe in it?

1. Sep 3, 2006

CarlB

Any good references on the meaning of the vacuum in QM? What were you taught in school? What made sense? What did not? What did you discuss with the other graduate students? Any paradoxes regarding the vacuum? Any thoughts on why string theory is inundated with them?

Bring em on. I want to hear.

Carl

2. Sep 3, 2006

David Burke

Do you mean Maxwells EM wave length being of any size and therefore allowing for infinite energy zero point gravitational curvature which doesn't actually appear to happen in experiments, so we use Fermion/ Bosson equivalence to cancell the infinity values? I've known this to be called vacume energy.

3. Sep 3, 2006

Maaneli

This is actually a controversial issue in QM and QFT. I'll try to respond with detail later.

4. Sep 3, 2006

CarlB

I think that's on topic, but what I was really getting at is that odd thing that you hit with a creation operator in QFT.

Carl

5. Sep 4, 2006

Epicurus

In a quantum field theory, the vacuum state is the state with the most symmetry. The number of vacua is related to the symmetry group of the underlying lagrangian

6. Sep 5, 2006

Mike2

If we can only measure changes in the vacuum state and not the absolute value of the vacuum energy, then we cannot distinguish the false vacuum of inflation, responsible for mass, from the true vacuum of today. The vacuum may have just fallen to a lower vacuum energy, and it may fall to an even lower energy state in the future.

If the vacuum does have a physical consequential energy density, then wouldn't this have an equivalent mass density that would be attracted to gravitational fields (if it is not itself the gravitational field). Wouldn't this not tend to accummulate extra energy density around large gravitating bodies and act like dark matter?

If the vacuum does have an energy density, then wouldn't this behave in waves and have a momentum? I have to wonder, if the expansion of space is carried by momentum beyond that forced by the vacuum energy, then at some point wouldn't that expansion put a force on the vacuum energy to fall to a new level? And isn't this what happened during inflation? If so, then could this new round of acceleration cause the vacuum energy to fall to a new low?

Are there any more complete papers on all the various means of measuring the differences in the vacuum state?

Last edited: Sep 5, 2006
7. Sep 6, 2006

Mike2

Or again, why can it not be true that the calculated value of the cosmological constant and the globally measured value both be correct? Maybe I'm missing something here. Could it not be that there is an actual difference between the measured vacuum energy here on earth inside the deep gravity well of our large galaxy and the overall measured value which is weighted by the vast majority of empty intergalatic space? If the vacuum energy is indeed influenced by gravity, then shouldn't we expect a difference between empty space and the heart of galaxies? Or is it that if the vacuum energy were to change then other observation would also change which we could theoretically observer. But isn't it by definition that we cannot measure anything in vast regions of intergalatic space because there is nothing there to measure? Or would very small galaxies have observable contradiction if their vacuum energy were different than ours? Thanks.

8. Sep 7, 2006

Haelfix

Vacuum energy most definitely 'gravitates', indeed for any other QFT other than gravity, a simple field redefinition would suffice to make it vanish as there is usually no canonical choice of zero. Not so in gravity, which is why it is indeed important and why it has such profound implications for spacetime evolution.

9. Sep 7, 2006

Mike2

Obviously QFT is background dependent since it assume a metric of a spacetime to begin with. And particles take on new meaning in curved spacetimes. Doesn't this all mean that the vacuum energy also changes with the curvature of spacetime? I wonder how many orders of magnitude difference there is between the vacuum energy of intergalatic space and here on earth?

10. Sep 8, 2006

Chronos

Reminds me of the ultraviolet catastrophe in classical physics. Obviously the QFT prediction of ZPE conflicts with the GR model. I'm fairly confident QFT is the tortfeasor in this case.

11. Sep 8, 2006

CarlB

Okay, now I know what a "tortfeasor" is.

Almost all physicists seem to be divided into three groups. The first group thinks that QFT is wrong. The second group thinks that GR is wrong. The third group thinks that neither GR nor QFT is wrong. The set of measure zero thinks that both GR and QFT are wrong.

Lee Smolin's latest book lists various physicists, both amateur and professional, that believe either GR/SR or QM is wrong. But he didn't list any who think that both are defective. Get's lonesome out here on the fringe. I think that SR needs to be modified in order to make QM more natural, and that the secret to doing this is to make time more complicated. Eventually that gets around to the vacuum, but it's sort of off topic.

What I had in mind when starting this thread was Julian Schwinger's "fictitious vacuum" that he brings into an elegant foundation for QM in his book "Quantum Kinematics and Dynamics".

Carl

12. Sep 9, 2006

Careful

Perhaps one could redefine the fourth class as those people who think both GR and QFT could be approximations (of some kind) to a deeper theory in the low energy regime. QFT is incomplete (unless you believe in MWI), contains divergences (which indicate a lack of understanding), and basically we don't have a Hilbert space formulation of them. So, I guess it is better to ask first why QFT should be right. GR has other problems ... it occurs to me that those who desperately stick to one or the other (although GR is the better choice in that respect) merely do this for reasons which have little to do with scientific consistency and logic.

Careful

13. Sep 9, 2006

Staff Emeritus

There are those who want to preserve the "essential points" of QM and GR, the quantum principle and background independence respectfully, and combine themsome way. This is more than just the "effective theory" philosophy; it asssumes that each of QM and GR has seen some deep truth.

14. Sep 9, 2006

ZapperZ

Staff Emeritus
At what point do we bring in experimental verifications/consistency? For some odd reason, other than what Chronos has mentioned, this aspect seems to have been complete ignored. Does the fact that QFT methodology agrees with experimental measurement is completely meaningless?

Or what about its use in condensed matter physics where the QFT vacuum state is the ground state of a fermionic system at 0 K? A ton of phenomena, ranging from your popular conductors to magnetism, start off from such a scenario.

I can understand people having "philosophical" issues with QFT. However, to dismiss it as being "incorrect" dispite the wealth of agreement it has produced to various reproducible phenomena in condensed matter physics is simply astounding. I'd suggest those people derive the Kondo effect first, for example, using other alternative methodology. If they can do that, then they're welcome to give me a call.

Zz.

15. Sep 9, 2006

turbo

If you will audit any of Penrose's recent talks (streaming video - just google his name), you will see that he belongs in your "measure zero" set. I happen to agree with him, but I think that GR is going to take a much bigger "hit" than QFT.

Last edited: Sep 9, 2006
16. Sep 9, 2006

Staff Emeritus
The latest buzz is over Connes' spectral geometry with neutrino physics. It does not, as Urs Schreiber emphasises, do the detailed numbers of the standard model, but it is pretty good at doing its general features. And someone noted that many of the features that it is customary for quantum physicists to attribute to quantization are in this model explained by geometry.

This might be seen as the latest event in the long range program of Einstein and Schroedinger, to geometrize all of physics, not just gravity.

17. Sep 9, 2006

CarlB

Of course it's not at all meaningless. It gives a very broad hint as to what the approximate (i.e. < 20 digits accuracy), extremely low energy (i.e. much smaller than Planck mass) small particle number (i.e. far smaller than number of particles in universe) limited spatial extent (i.e. very small compared to observable universe), short time scale (i.e. very short compared to age of universe) behavior of the underlying theory should be. That's not nothing.

Funny thing. In condensed matter, QFT is only an "effective theory". The underlying theory is plain old QM. The implication is that the QFT of the standard model might very well be an effective theory of some deeper theory.

I don't think that they're saying that QFT is "incorrect" when used in condensed matter. You might try Smolin's recent book, "The Trouble With Physics", which discusses the matter better than I could:

Carl

18. Sep 9, 2006

ZapperZ

Staff Emeritus
As compared to what? The way you're describing it is as IF it was Newton's Laws and that we have already a better way to describe it. Again, I ask for the alternative. There is none that have come close.

All you have to counter QFT is speculation. In my book, THAT is what's nothing. We may (or may not) be able to accurately describe experimental observation in a very "limited" sense of our universe, but this is certainly better than making guesswork of a theoretical formulation that doesn't even exist yet. Or do you usually use such a thing everyday?

Please define "effective theory". In my book, if "it works", that is a very damn good thing, more than what most philosophical ideology can claim. Again, talk is cheap. Come up with something that can match QFT's astounding successes in condensed matter, then I'll pay attention. I gave one concrete example already of the Kondo effect.

And I truly don't understand the statement that the "underlying theory is plain old QM".

If QFT is not "incorrect" when used in CM, then why is it being accused of being wrong in your message #11? Or do you think something can be correct in condensed matter but not in others? Need I remind you how many theories came out of condensed matter that have permeated all over the rest of physics?

In addition, it seems that people somehow cannot separate an objection based on TASTES, versus a valid objection based on empiricial evidence. Last time I checked, we are still doing physics, aren't we?

Zz.

Last edited: Sep 9, 2006
19. Sep 9, 2006

CarlB

If a better alternative were available we wouldn't be having this discussion. Instead, you'd be defending THAT theory as having no alternative.

I don't mean to "counter" QFT. I think that QFT is THE path to the next theory, far more important than GR. But there are some features of QFT that I think need to be changed, which is why I started this thread.

If you haven't come across this term in your QFT textbooks, then look in the index. If you don't have any textbooks, look it up in wikipedia.

The foundation of the quantum theory of crystals begins with a multiparticle Schroedinger equation [edit: with spin of course]. It is multiparticle because crystals have lots of particles. The Schroedinger equation is sufficient because the particles are not relativistic. The resulting equations are difficult to solve.

The physics principles underlying the QFT theory of solids is identical to the physics principles for the QM theory of solids. They're the same theory, the only advantage of QFT is the ease of calculation. But if you go to high enough energies, the QFT model of solids breaks down and you are left with, yes you guessed it, the QM model (maybe relativistic).

These are subjects that should be covered in any elementary introduction to solid state theory. I guess it's possible to learn the practice without understanding the physical principles behind it, but that doesn't seem to me to be much of an education in physics. More like an engineering class.

The context is in looking at the foundations of physics, not "squalid mechanics" in particular. For example, Newton's equations are sufficient in their context.

I'm not stupid. Of course I think something can be correct in condensed matter theory and not in general. So does Smolin and a bunch of other physicists. Heck, condensed matter theory generally doesn't include gravitation. And the last time I looked, condensed matter didn't have much use for neutrinos.

You don't need to remind me. My whole point was that QFT came from solid state. Solid state physics suffers from the interesting assumption of a solid media [edit: or more generally, some sort of matter that is "condensed"]. That defines a preferred reference frame [edit: i.e. the center of mass of the "condensed" matter]. It's not at all obvious that this should be a good sandbox to test real unified theories out in, especially when they are based on an assumption of special relativity.

I agree with this, at least in a reciprocal manner. One of the points that Smolin makes over and over is that the way the standard model is put together is largely due to the taste of physicists. Here, let me quote him:

Carl

Last edited: Sep 10, 2006
20. Sep 10, 2006

Chronos

I agree with Zapper on this issue. QFT works fantastically well at the quantum level. And GR is equally impressive macroscopically. They were made for each other, but, refuse to date. I suspect there is a hidden realm that completes the trinity. I'm even willing to allow for the existence of one lousy extra dimension - so long as it is not spatial.

21. Sep 10, 2006

Careful

There is no more effective theory philosophy'' present in what I said than the stuff you are alluding to. First of all, I don't know what the quantum principle is : is it the one of Bohm, de Broglie, Bohr, Barut, 't Hooft, Everett, Dirac, Adler, Penrose, Feynman .. ??? Second, as far as I remember, background independance also is a fishy concept. Both theories will take a blow: (a) quantum mechanics needs to be undressed from it's operational formulation, meaning that you need a decent *local* theory of single events (b) GR will have to be build up from the vacuum.

Careful

Last edited: Sep 10, 2006
22. Sep 10, 2006

ZapperZ

Staff Emeritus
Then I don't get the point of your thread. You are hoping that we do a bunch of speculative arguments on what COULD, MIGHT, be the next better mouse trap? Do you not see, after all the years you've been on here, how futile such a thing is? Besides, how do you know which one is more 'valid' than another, or even if you're on the right path considering that experimental evidence, at least in this thread, is considered as almost non-existent.

Sorry, but when I see the words "wrong" and "incorrect", those do not indicate to me that one believes that it is still the right "path" on the way to a more complete theory. Again, I don't see how you can accomplish your mission in "changing" QFT when (i) you are basing it on speculation and (ii) you sweep away experimental evidence.

I have, but NOT in the degoratory form that you have implied. That is why I asked YOU for what you meant as an "effective theory".

"Theory of crystals"? Hum... what a strange concept to use for "condensed matter physics", considering that it includes (i) BE and Fermionic condensation of gasses (ii) glassy phases (what is the "crystal" there?), and (iii) granular/soft condensed matter.

And what you have described above regarding "multiparticle" is a rather strange explanation. You DO NOT go from the many-body Schrodinger Equation and then arrive at the QFT description of the system. You START, as the First Principle, the QFT ground state. However, to say that just because you can also write the system as a Schrodinger equation that you can't solve, does NOT mean that it is the "underlying" theory. That's like saying that Newton's Laws are the "underlying" theory of Lagrangian mechanics just because I can also write down all the force equations of a system but I can't solve it because it's too difficult. There is nothing in your argument here that proves that one is more "fundamental" than the other. I claim that they're equivalent.

"The physics principles underlying the QFT theory of solids is identical to the physics principles for the QM theory of solids. They're the same theory, the only advantage of QFT is the ease of calculation. But if you go to high enough energies, the QFT model of solids breaks down and you are left with, yes you guessed it, the QM model (maybe relativistic)."

Please show me an example where the QFT model in CM breaks down at "high enough energies".

OK, now you're trying very hard to be insulting. I suggest you drop that Gell-Mann's ignorant word unless you want this to deteorate into gutter discussion, or before I point out to you all the "squalid" stuff that you have taken for granted, and I don't mean just squalid electronics. Furthermore, just because I ASKED you to state something clearly and disagree with how you "interpret" my field of study to be doesn't mean I didn't get "much of an education in physics". Again, if you wish to play dirty, that is what you'll get.

But you don't mind assuming that I am.

That's like saying Newton's law didn't have "neutrinos" and so it sufers from a huge shortcoming. Well HELLO? What does "application" of the most general equations have anything to do with what it can and cannot include? And since you are not stupid, I will point out something VERY simple here. Look at the single-particle propagator in its most elementary form. In the self-energy term, I could include ANY (and I repeat, ANY) bosonic interaction to that particle to broaden its self energy. In condensed matter, we just happen to use the popular interactions that are present in the system, such as phonons, magnons, polarons, etc.. etc. However, there's NOTHING there to prevent ANY kind of bosonic interaction. You want a graviton of spin 2? Hey, knock yourself out!

And I have only described the most simplest formulation. I haven't yet included fermionic exchange in more complicted systems. This is what Peter Higgs got, from of all places, the formulation of a magnetic system. The point here isn't WHAT is included in the formulation. The point here is that the formulation is system independent. If you have issues with the origin of such a formulation, I'm surprised that you don't think that QM is "wrong" because it didn't include "neutrinos" or was solved mainly for "atoms".

Aren't you putting the cart WAY before the horses first? It is obvious to me that you're trying to find a falsification of SR. Yet, you are approaching it from trying to find a "unified theory" first, rather than working on your own fundamental assumption in which SR isn't completely valid. Shouldn't you be hunting for that first? And unless I've been asleep these part few years, all the more refined tests on SR so far would indicate to me that it is you who have more "incorrect" and shaky assumptions than QFT.

Except some tastes have more valid experimental support than others.

I don't think the Standard Model will survive intact. But how this somehow gets dragged into QFT, I have no clue. Maybe it's my lack of a deep physics education.

Zz.

23. Sep 10, 2006

CarlB

No, I was looking for arguments for and against the existence of the vacuum that are deeper then "shut up and calculate". That much I already knew. Obviously you can't provide further.

If you don't want a derogatory response, don't write one yourself. Let's begin over from now, okay? You won't ask rhetorical questions about the definitions of things that everyone understands and I won't give sarcastic responses.

Yes, you are correct. I've edited my response appropriately.

I don't think I've explained my point very well here. While I have said "condensed matter" physics, what I am thinking of is "solid state" physics. It is in the context of solid state physics that the spontaneous symmetry breaking of QFT was developed. But if you add enough energy to a solid, it eventually becomes something else, and solid state no longer applies to it.

One can say that the analogy in condensed matter is where a solid changes phase, and in fact that is how the problem is approached in elementary particles. But my point is that in solid state, the symmetry breaking of the vacuum was caused by a very obvious physical source. In elementary particles, there is no such obvious source. The elementary particle analogy of the vacuum of solid state is just an analogy.

What's more, obvious calculations for the vacuum energy gives results that are "the worst calculation in physics" in that the actual energy of the vacuum is very small while the natural calculations give extremely large numbers. This is a sign that the analogy is just that, an analogy.

I believe that as far as the particles and forces of the standard model go, SR is indistinguishable from perfect. I also think that under the same limitation, QFT is indistinguishable from perfect. Of course I could be wrong about this so I'm not saying that people looking for minor deviations from SR in stuff that is well explained by the standard model are wasting their time. For that matter, I think that in its own experimental regime, GR has at least not yet been distinguished from perfect.

You seem to be saying that a theorist should never work on a new theory until evidence against the old theory has arisen and is well known. That seems to me to be a little extreme. For example, was Einstein wasting his time working on relativity when there was no evidence for a lack of conservation of mass, and no evidence for the doubled bending of starlight near the sun? Was Dirac wasting his time when he predicted the positron in the absence of experimental evidence? Were the physicists who figured out SU(3) remiss in pointing out the missing element of the decuplet? Was Maxwell too early when he predicted radio waves? Is it your position that there are no worthwhile physics papers written except in the presence of confirming evidence?

I think that the history of physics shows that if you wait until the evidence is out there, well known and agreed upon by all, you will find that you have started too late and that there are 100 papers already written on it before your own.

Carl

Last edited: Sep 10, 2006
24. Sep 10, 2006

cesiumfrog

Surely the best way to understand the problems with QFT is to learn it (ie. carefully "shut up and calculate" its most important results again for yourself).

Nobody liked the crackpot who, rather than take the time for a single semester GR unit, shows up at conferences brandishing Schwarzschild's original paper (untranslated no less) and claiming that all of GR's results can be obtained using highschool math except for the conspiracy of closed-minded physicists..

Last edited: Sep 10, 2006
25. Sep 10, 2006

CarlB

At dinner I realized that this is the crux of the issue. Fermions get masses in the standard model as vacuum expectation values coming from the Higgs. If QFT and QM are equivalent, then what does the vev correspond to in QM.

The only reference I've got that talks about a vacuum state in QM is Julian Schwinger's "Quantum Kinematics and Dynamics". Of course I've had his book for ages and was thinking about these passages before starting this thread, but I hoped to see some other connections brought up by other people. Instead the thread seems to be getting off topic with insults and comments about special relativity. So let me quote from Schwinger's book in my next post.

Carl