Explore The Vacuum Fluctuation Myth in Quantum Theory
This Insight Article is a sequel of the Insight Articles ”The Physics of Virtual Particles” and “Misconceptions about Virtual Particles“ which make precise what a virtual particle is and what being real means, document some of the liberties taken in physics textbooks in the use of this concept, and mention the most prominent misuses. A further Insight Article, ”Vacuum Fluctuations in Experimental Practice”, shows the example of a recent article in the scientific literature how some authors claim the observation of vacuum fluctuations, justified only by superficial, invalid reasoning.
In short, the concept of virtual particles is well-defined and useful when restricted to its use in Feynman diagrams and associated technical discussions. But it is highly misleading when used to argue about vacuum fluctuations as if these were processes happening in space and time. The latter is a frequent misunderstanding, a myth that has not the slightest basis in particle physics. (The proper meaning of some terms related to the vacuum is explained at the end of ”The Physics of Virtual Particles”.)
The two articles mentioned do not, however, explain how it is possible that this misunderstanding is so widespread, and even serious experts resort to misleading imagery when explaining the subject to the general public. This is answered here at the example of Steve Carlip’s page on Hawkings radiation, where Steve Carlip, a well-known theoretical physicist working on quantum gravity, gave a lucid but completely mythical narrative about how vacuum fluctuations create Hawking radiation. This vacuum fluctuation myth comes from taking pieces of intuition and connecting them with a plausible narrative. The following is a reconstruction of the sort of thoughts that combine to justify the myth in the eyes of those who use this language. (For those interested, a non-mythical description of Hawking radiation is given by Sabine Hossenfelder here.)
The starting point is the sound knowledge that there are technical notions of vacuum fluctuations (= nonzero vacuum expectation values), virtual particles (=internal lines in a Feynman diagram), and that in bare quantum field theory with a cutoff, the vacuum is a complicated multiparticle state depending on the cutoff – though in a way that it diverges when the cutoff is removed, so that nothing physical remains. Then the question arises: Is is possible to convey a bit of this to ordinary people? It is highly unsatisfactory not to be able to talk about what one is doing in one’s research…
So one goes for analogies and images. Already calling internal lines ”virtual particles” is a step in this direction. Allow yourself a little more liberty and combine it with Feynman’s classical absorber theory of radiation; after all, Feynman also invented the diagrams bearing his name, possibly even inspired by this analogy. The lines defining the virtual particles look like world lines in a classical process, so why not interpret them (in one’s imagination) as the quantum remnants of the classical world lines of Feynman’s earlier (later abandoned) theory? This happy accident makes the story possible. It is not completely accurate but plausible (in the absence of the correction of the intuition by mathematical formulas) because both classical particles and virtual particles are represented pictorially by lines, and it is something that ordinary people can imagine. This is the beginning of the myth. An extra reassurance that you are on a good path is that the arrows that physicists draw on their diagrams (to indicate the sign of conserved quantum numbers) happen to match Feynman’s classical (later abandoned) idea that antiparticles are just particles moving backward in time.
To bring in more physics one has to be able to interpret complete Feynman diagrams. Tree diagrams are easy but bring in a new aspect. They talk about real and virtual particles. On an electron line containing two external vertices, the electron changes its status from being real (external) to being virtual (internal) and back (external) again. We learn from it a new fact – a virtual particle can become real, and conversely. The interpretation as world lines teaches us other things: A single Feynman diagram should in fact be considered just as a tiny snapshot of an extended web containing all particles in the universe; after all, world lines do not begin and end nowhere. Thus ”in reality” (meaning in the simplified virtual reality painted for the general public) all particles should be viewed as virtual until they are observed (where they obviously are real). This matches a version of the highly respected Copenhagen interpretation: Unobserved particles have a sort of ghost existence since properties emerge only when they are subjected to quantum measurement. You are pleased by this coincidence – it seems to say that there is a coherent story to be told. Also, since most of the lines in the Feynman diagram end, you have a layman’s picture for decaying particles: What you see in a bubble chamber is just a Feynman diagram made visible! This is the first serious manifestation of the myth. In spite of lacking any grounding in real physics (being grounded instead in the visual analogy), you feel entitled to make this identification – it serves your final goal to make some of the intricacies of microphysics accessible to the general public. No one there will ever ask how it can be that two virtual particles can bend as in a Feynman diagram with a loop – so that they find each other exactly at the right place and with exactly the right momentum to annihilate. Therefore such impossibilities – that would spoil the goal of giving a simplified picture of what happens – are silently swept under the carpet.
The next thing is to interpret the bare multiparticle state. It is obviously a complex superposition of bare particles. Make the next move to identify bare particles with virtual particles; after all, both are unobservable but appear in some version of the formalism. Now you have the picture of the vacuum as teeming with particles. From the form of Feynman diagrams with one or more loops, you can read off that in order to make sense of the narrative these particles have to pop in and out of existence. This is the birth of the next item in the myth. That in a superposition nothing dynamical happens is a small nuisance that you happily sacrifice in order to be understandable to your intended audience. After all, you can now give an illusion of having conveyed something of the complexities of the naive perturbative approach without having to talk about perturbation theory. In addition, without asking for it, you have found an unexpected visual interpretation of the notion of a vacuum fluctuation: A teeming vacuum where particles constantly pop in and out of existence clearly fluctuates, and every single act of popping may rightfully be regarded as a fluctuation of the vacuum. Another piece of the myth has found its place. Never mind that there is not the slightest way of justifying this analogy on the level of mathematical formulas. What counts is how the picture appeals to the general public, and it is obvious that drastic simplifications are needed to achieve this goal.
Now one needs to worry about the basic principles of physics in all this. After all, one doesn’t want to talk about particles alone but conveys some general physics as well. Let us bring in conservation laws. Everyone knows that energy is conserved in Nature. But wait, doesn’t the creation of particles require some energy? Never mind, quantum mechanics comes to the rescue. People will have heard of the Heisenberg uncertainty relation, and if they haven’t this is an opportunity to make your audience acquainted with it. It states the intrinsic uncertainty of position and momentum in nonrelativistic mechanics. What does it tell about energy conservation? Nothing at all, but analogy comes to the rescue. In relativistic physics, time is the 4th coordinate of position, and energy the 4th coordinate of momentum. Thus we don’t make a big blunder if we consider a time-energy uncertainty relation. (Though in mainstream quantum physics, time is not an observable – it has a completely different status.) Uncertain energy can be liberally interpreted as a slightly inaccurate conservation law. After all, one can derive from quantum mechanics only that the expectation of the energy operator is conserved. Expectation brings to mind that whatever you measure inaccurately must be measured many times for getting an improved accuracy. Thus only the average energy needs to be conserved. Reinterpret the physical ensemble average (in the service of simplifying the physics to give your audience a coherent story) as an average in time.
Thus you found the solution: Energy can be borrowed for a short period of time if it is returned on average. The next item of the myth arrived. Now you are quite confident that you’ll be able to get a full and rich story (for laymen only, so all the small and big blunders made can be excused) and continue to turn it into something you’ll tell in public (or write in a book). You hope that the attentive audience will not ask where the energy is borrowed from, but unfortunately, you told the story first to a colleague with an unbiased mind and he insisted on that this should be clarified first. You need to look at some more pieces of information to get the next input. Fortunately, you soon find it: The zero-point energy of a harmonic oscillator had in the past always been ignored by saying that only energy differences are observable. Maybe it is the bank from which the virtual particles lining up for popping into existence can borrow their energy. And yes – it turns out that the bare quantum field has a huge amount of zero-point energy – an infinite amount if you take the physical limit. Clearly, this must be the source – and no ordinary person will be interested to question it. Thus the final piece of the myth arrived. You are happy – it will be a really good story conveying a lot of physics while still being understandable to ordinary people.
That there is no physical mechanism for how the borrowing works is a small nuisance that (for the layman) can be ignored – after all, they want a simple story that they can believe, not a technical discussion of all the problems involved – they know that quantum mechanics is full of unresolved problems. At this point, your story is already so convincing that you don’t mind that all observable quantities also become infinite in the limit considered and that when you instead do a proper renormalization (needed to get the high accuracy predictions quantum field theory is famous for) the whole capital of the vacuum energy bank shrinks to zero!
Now the particle philosophy for the laymen is essentially complete. Only a few – to laymen imperceptible – jumps of the imagination were needed in the service of understandability. Like in a cinema, where the pictures jump in discrete steps but provide a sufficient illusion for the audience to see a continuous story. To make sure that the audience, captured by the imaginative illusion, will not take it for physical reality, and to ensure that your status as a respected scientist is preserved, you begin with a caveat (like Steve Carlip did on his page on Hawkings radiation, in the inconspicuous first line after the heading ”An Incomplete Glossary” – long forgotten at the time the reader enters the mythical narrative linked to above): ”Be warned – the explanations here are, for the most part, drastic oversimplifications, and shouldn’t be taken too literally.” But in spite of this, you can instead be sure that most of your audience will ignore this sentence said in the first few seconds in favor of the nice mental pictures that you took a whole hour to explain and make intelligible.
When Hawking discovered what was later called Hawking radiation this picture for the general public was already well entrenched. So he only had to figure out how his discovery would fit in – and it fitted well. Instead of talking about gravitational energy (not visible, hence a sort of vacuum) creating a particle-antiparticle pair one partner of which escapes there is only a small step to saying what the educated general public expects. Since the particles are not (yet) observable by the faraway observer seeing only the radiation, they must be sold according to the philosophy developed above as virtual particles created (hence vacuum fluctuations in action). Years later, when one of the particles is finally observed by the faraway observer, it becomes real as a piece of the observable Hawking radiation.
Thus if you want to summarize to lay people the Hawking effect in a single phrase, what is more, natural than to say that ”vacuum fluctuations cause the Hawking radiation” without repeating the warning that this ”shouldn’t be taken too literally”?
Full Professor (Chair for Computational Mathematics) at the University of Vienna, Austria
[QUOTE="mfb, post: 5663324, member: 405866"]It is challenging to answer "how does a neutron decay" or "how does the study of rare decays helps with new physics searches" without the concept of virtual particles.And the experts you mention later are using the concept of virtual particles exactly in those cases.”The concept of virtual particles is well-defined and useful when restricted to its use in Feynman diagrams and associated technical discussions. But it is highly misleading when used to argue about vacuum fluctuations, as if these were processes happening in space and time.
[QUOTE="PeterDonis, post: 5662850, member: 197831"]If you want a good brief summary of the lesson to be learned from the article and this discussion, I would say it is that you should not even try to use the concept of virtual particles; it causes more problems than it solves.”It is challenging to answer "how does a neutron decay" or "how does the study of rare decays helps with new physics searches" without the concept of virtual particles.And the experts you mention later are using the concept of virtual particles exactly in those cases.
[QUOTE="Mordred, post: 5662594, member: 351508"]virtual particles has real measurable influences”But not a causal influence. It is an influence like the influence of the spectral theorem on results of measurements since the latter measure eigenvalues predicted by the spectral theorem.
Your right my last post is an oversimplification but I would have thought you would recognize the relations of the creation/annihilator operators in terms of the zero-point energy.http://www.google.ca/url?sa=t&source=web&cd=2&ved=0ahUKEwii3KySg7nRAhWEilQKHdikDqUQFggcMAE&url=http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf&usg=AFQjCNGAHbSIOpMVp8w6m9gF4DjnD70Kbg&sig2=TEYpS-0cDfRPwaE4EOumEw
[QUOTE="PeterDonis, post: 5662850, member: 197831"]…It's unfortunate that we can't put level labels on Insights thread discussions. If we could, this thread would be firmly labeled "A". It's hard to even understand the reasons why the Insights article was written without a graduate level background in quantum field theory, or the equivalent.If you want a good brief summary of the lesson to be learned from the article and this discussion, I would say it is that you should not even try to use the concept of virtual particles; it causes more problems than it solves. QFT says the fundamental concept is quantum fields, not particles; even "real" particles are not fundamental entities in QFT. There are ways in which experts can use the concept of "virtual particles" that can be useful, but those experts already know who they are; if you have to ask whether you are one of those experts, the answer is no. :wink:”THANK YOU!!!!! :bow:I was getting the feeling that I was the only person in the world that couldn't comprehend what the article was about.[QUOTE="OmCheeto, post: 5654967, member: 103343"]I still don't know what "the myth" is, and I read the article 3 times.Perhaps, some of us were not meant to know.”So would you like to hear my theory on what virtual particles are? I offered to explain this to D. J. Griffiths, as he is a neighbor of mine, but he has mysteriously remained silent. :rolleyes:
[QUOTE="Mordred, post: 5662908, member: 351508"]on the first quote why didn't you completely quote the entire sentence?”Because my responses to the first part and the second part of the sentence were different, so I quoted each part separately.
Umm on the first quote why didn't you completely quote the entire sentence? I didn't complete the sentence to indicate any meaning beyond that which is contained in the full sentence.
[QUOTE="PeterDonis, post: 5662850, member: 197831"]if you have to ask whether you are one of those experts, the answer is no. :wink:”Will never have the nerve to claim that, even if I was. I have many books(ZEE for example) that do talk about VP, so if only in the know know, then what is the purpose of PF if not to clarify thing satisfactorily.
[QUOTE="Mordred, post: 5662872, member: 351508"]in QFT treatments every point in space is a field”More precisely, there is a field at every point in spacetime.[QUOTE="Mordred, post: 5662872, member: 351508"]of creation/annihilation operators”This is one way of describing the field, but not the only one.[QUOTE="Mordred, post: 5662872, member: 351508"]In essence a sea of Virtual particles”And this is just picturesque language that doesn't help (and often hinders) understanding the physics. So is most of the rest of your post.[QUOTE="Mordred, post: 5662872, member: 351508"]One commonly known example being zero-point energy. Which essentially prevents absololute zero from being possible.”Um, what? Zero point energy is the energy a system has at absolute zero.
Well in QFT treatments every point in space is a field of creation/annihilation operators. In essence a sea of Virtual particles. In some texts this is an overlapping field sometimes referred to as virtual space. Normal particles being in observational space. There is some debate that as this is a mathematical treatment that isn't reflective under other treatments its not considered real with the counter argument that a field or energy/density vacuum of value zero is simply a global average. Locally at the quantum levels their is always inherent quantum fluctuations. One commonly known example being zero-point energy. Which essentially prevents absololute zero from being possible.
[QUOTE="ftr, post: 5662770, member: 465682"]It seems the discussion is becoming an entanglement of many situations.”No, it is demonstrating that what looks to you like "an entanglement of many situations" is really a mixture of approximations, heuristics, and misstatements from pop science sources, and only very rarely actually describes our best current model of the fundamental physics.[QUOTE="ftr, post: 5662770, member: 465682"]the discussion here is about "Vacuum fluctuation".”The Insights article is about how the term "vacuum fluctuation" is a myth–it's not a very useful concept even as a heuristic or approximation, and it certainly is not part of our best current model of the fundamental physics.[QUOTE="ftr, post: 5662770, member: 465682"]these fluctuation are considered under interaction and non interaction”I'm not sure quite what this is referring to, but as far as our best current model of the fundamental physics is concerned, there is no such thing as a "non-interacting" quantum field (quantum fields are the fundamental concept here). Sometimes we can consider particular quantum systems to be "non-interacting" as a reasonable heuristic or approximation, but that's all. Fundamentally all quantum fields are interacting fields.[QUOTE="ftr, post: 5662770, member: 465682"]with interaction I don't know if we can look at it as if vacuum had already "virtual particles" in it or started appearing once interaction started?”Neither of these ideas have anything to do with our best current model of the fundamental physics. Your comment illustrates that "virtual particles" is not even a very good heuristic, since it is hindering your understanding rather than helping it.[QUOTE="ftr, post: 5662770, member: 465682"]The discussion here seem to be veering towards "particles" in the vacuum.”I'm not sure what you are basing that on, but I seriously doubt that the article's author would agree with it. Of course he can correct me if I'm wrong.[QUOTE="ftr, post: 5662770, member: 465682"]I think we need to be clear what we are talking about and not assume the reader can figure it out”It's unfortunate that we can't put level labels on Insights thread discussions. If we could, this thread would be firmly labeled "A". It's hard to even understand the reasons why the Insights article was written without a graduate level background in quantum field theory, or the equivalent.If you want a good brief summary of the lesson to be learned from the article and this discussion, I would say it is that you should not even try to use the concept of virtual particles; it causes more problems than it solves. QFT says the fundamental concept is quantum fields, not particles; even "real" particles are not fundamental entities in QFT. There are ways in which experts can use the concept of "virtual particles" that can be useful, but those experts already know who they are; if you have to ask whether you are one of those experts, the answer is no. :wink:
It seems the discussion is becoming an entanglement of many situations. First, the discussion here is about "Vacuum fluctuation". Second, these fluctuation are considered under interaction and non interaction. Then with interaction I don't know if we can look at it as if vacuum had already "virtual particles" in it or started appearing once interaction started? The discussion here seem to be veering towards "particles" in the vacuum. It is becoming like the old joke "who is on the first base", I think we need to be clear what we are talking about and not assume the reader can figure it out, I certainly can't.
no problem it is after all your insight article. Just making my take on the subject. I recognize the need to keep it as simple as possible for the average layperson.
[QUOTE="Mordred, post: 5662424, member: 351508"]I guess my point is whether or not a particle is observable or not isn't the same thing as whether its real or not.”In my first insight article about virtual particles, I defined real as having a state. This is objective, very natural and consistent with the use in most of physics. In this sense, virtual particles are not real. That's why they are called virtual. While you have only a vague and informal view of what should be real, with which one cannot argue because it is up to everyone to fill it with meaning. The arxiv article (which I knew already for a long time) doesn't improve the situation. Strassler's page (which I also knew before) is for the lay person, not for those who want to gain a deeper understanding. It also dabbles in words without giving them a precise meaning. At the end Strassler admits: ''particles are just not simple objects, and although I often naively describe them as simple ripples in a single field, that’s not exactly true.''
I guess my point is whether or not a particle is observable or not isn't the same thing as whether its real or not.
[QUOTE="Mordred, post: 5662181, member: 351508"]maybe you should read Strasslers site itselfhttps://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/as you obviously didn't read the arxiv article I posted. I'm more than familiar with your violin string”I'm fairly sure your familiar with the cluster decomposition theorem.
maybe you should read Strasslers site itselfhttps://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/as you obviously didn't read the arxiv article I posted. I'm more than familiar with your violin string. Personally I'd rather listen to a professor in particle physics over a professor in cumputational mathematics. Particularly one that can't be bothered reading a reference provided that is written by expert's within the specific field.For example a quasi particle ie phonon is a collective excitation by its very definition. So how can you state this excitation isn't every bit as real as the excitation of an electron?
did you even bother to read the arxiv article?
[QUOTE="Mordred, post: 5662151, member: 351508"]In some aspects I like prof Strasslers description "virtual particles are wavefunctions that aren't quite nice"”This is meaningless gibberish. Virtual particles have no associated wave functions at all. Wave functions are obtained by creation operators from the vacuum state, and this is possible only for on-shell particles. You should read the other Insight Article ”The Physics of Virtual Particles”, which contains an exposition of definitions that are physically justified, and in particular makes precise what a virtual particle is and what being real means.[QUOTE="Mordred, post: 5662151, member: 351508"]how can an excitation not fluctuate to a certain degree? Is that not what an excitation is in the first place?”Take a violin string. The fundamental excitation is harmonic and oscillates very regularly. Unlike noise, a harmonic excitation does not fluctuate in any meaningful sense. The same holds for excitations of other physical systems, including the quantum field vacuum.
Good article but I do have issues with this whole which excitation is more real. Particles themselves are excitations, so is virtual excitations. Which is more real comes down to simply conventional rational. That's the real myth. Physics doesn't define real. We simply describe aspects of what we can describe as reality. In some aspects I like prof Strasslers description "virtual particles are wavefunctions that aren't quite nice" Not very detailed but certainly more accurate than "on shell"/ "off shell". Quite frankly there is no way one can define real. At least not with 100% accuracy. We can measure relations/interactions but these are all under specific treatments. Fields themselves are mathematical treatments. By definition a field is simply a collection of objects. Those objects can be mathematical constructs such as a vector/scalar field or a collection of events. Wave/particle duality itself is simply aspects of these field excitations neither defines the excitation as they are both aspects/properties of that excitation. When you think about it different particle species are simply excitations that display certain characteristics that can be classified under various particle names with specific wavefunction characteristics. This is what I feel should be stressed. Not real particles vs virtual particles. Just my take on the subjectNow the question I have is how can an excitation not fluctuate to a certain degree? Is that not what an excitation is in the first place?
[QUOTE="mfb, post: 5655825, member: 405866"]See the previous pages, we discussed this (mainly with the Z as example) in detail. It depends on your point of view.”actually it was discussed in the pages commenting on the Misconceptions about Virtual Particles.
[QUOTE="tzimie, post: 5653889, member: 517789"]I have a question.How that usual claim (virtual particles are not real, they are just math) can be interpreted in a framework of MUH (Mathematical Universe Hypotesis) – as obviously in MUH there is no distinction between "actually happening" and "being just math".”I think MUH does not claim to have the exact mathematical structure, it just conjectures from all the present physics that reality is a mathematical structure. So, since there is no acceptable quantum gravity theory yet , none of the math that is being done in physics today can be taken as the actual math, only that they are approximate models. Hence no ontology is involved.
Thanks. An interesting read.
Oh right, wrong thread. See the virtual particle thread.
I think it's in the thread about virtual particles.
[QUOTE="mfb, post: 5655825, member: 405866"]See the previous pages, we discussed this (mainly with the Z as example) in detail. It depends on your point of view.”I looked through (fairly quickly through the whole thread) but couldn't find what you were referring to. Do you have a post number?
See the previous pages, we discussed this (mainly with the Z as example) in detail. It depends on your point of view.
I am curious as to how those who say that virtual particles are a myth would describe "resonances" such as the ##Delta(1232)## that appears in pion-nucleon scattering. This is usually called a particle as its sits in the baryon decouplet of SU(3). Yet it seems to have all the characteristics of a "virtual particle" in that it is extremely shortlived and because it is seen as a peak in the scattering cross-section and can be viewed as having uncertain mass — suggesting temporary violation of energy conservation over an interval inversely proportional to the width of the bump. (In order to allocate a precise mass, one has to allow the mass to be complex, the imaginary part given by the width of the bump and representing the uncertainty in real energy.)
[QUOTE="clarkvangilder, post: 5653536, member: 612213"]Perhaps a quick comparison of these virtual particles to the point-particle model in classical mechanics? It seems that virtual particles are much much more than just a model? (Not that you or anyone else said otherwise). The title of this article below sort of captures the spirit of misconception relative to this topic. Scientific American is not a great journal of physics; but the person who wrote it ought to be an expert.https://www.scientificamerican.com/article/are-virtual-particles-rea/“I am more than puzzled, I am seriously dissapointed.
[QUOTE="vanhees71, post: 5653878, member: 260864"]Hm, I'm a bit puzzled how an expert in particle physics can write such an article :-(. As an practicioner of QFT, I'm sure he knows very well that a particle interpretation of relativistic QFT is possible in clear terms only for asymptotic free states, and for vacuum QFT (i.e., the theory describing scattering events) the only observable outcomes are S-matrix elements, i.e., transition rates for going from an asymptotic free in state (usually two particles) to an asymptotic free out state (which can be any many-particle state, that is only restricted by the conservation laws like energy-momentum, angular momentum conservation and the conservation of various charges like electric charge etc.) or, equivalently, cross sections. All this is discussed already at length in this thread!”I''m also puzzeled. I can't make anything of that article.
I still don't know what "the myth" is, and I read the article 3 times.Perhaps, some of us were not meant to know.
Well, it should be Copenhagen without collapse, i.e., the minimal statistical interpretation. Some people think that's alreayd MWI, but I don't need unobservable branches of the universe where something else happens than what's observed in the branch I'm living in ;-)). Happy New Year!
[QUOTE="vanhees71, post: 5654043, member: 260864"]Hm, if you call the minimal interpretation Copenhagen, then of course the Insights are biased towards these, since this is a science and not a philosophy forum!” It is perfectly fine to say that you don't want to talk about interpretation wars because it is philosophy, not physics.If there is a big period after that claim.But after the point you added that Copenhagen is the best/minimal/etc – then your position is inconsistent. I don't want to start Interpretation Wars. It is science forum and not a philosophy one. Ah, and BTW, Copenhagen doesn't make any sense and MWI is the best )))Happy New Year! )))
Hm, if you call the minimal interpretation Copenhagen, then of course the Insights are biased towards these, since this is a science and not a philosophy forum!
[QUOTE="Demystifier, post: 5653922, member: 61953"]According to MUH, any self-consistent mathematical theory, even a theory which directly contradicts observations, is true.”1. It is not "true", it "exists" in some methaphysical way.2. And only some of these universes are "observed"Anyway, I think the "insights" are not interpretation-neutral (actually they are Copenhagen-biased) hence not universally valid. (Am I wrong?)
[QUOTE="tzimie, post: 5653889, member: 517789"]I have a question.How that usual claim (virtual particles are not real, they are just math) can be interpreted in a framework of MUH (Mathematical Universe Hypotesis) – as obviously in MUH there is no distinction between "actually happening" and "being just math".”According to MUH, any self-consistent mathematical theory, even a theory which directly contradicts observations, is true.
How does Bohmian mechanics solve "the measurement problem" (I assume you mean the question, why you find sharp values when measuring an observable on a system at a state which is not an eigenstate of the observable)? It assumes unobservable, i.e., ficticious, trajectories, but it doesn't claim that all observables are determined before the measurment, right?
I have a question.How that usual claim (virtual particles are not real, they are just math) can be interpreted in a framework of MUH (Mathematical Universe Hypotesis) – as obviously in MUH there is no distinction between "actually happening" and "being just math".
[QUOTE="clarkvangilder, post: 5653536, member: 612213"]Perhaps a quick comparison of these virtual particles to the point-particle model in classical mechanics? It seems that virtual particles are much much more than just a model? (Not that you or anyone else said otherwise). The title of this article below sort of captures the spirit of misconception relative to this topic. Scientific American is not a great journal of physics; but the person who wrote it ought to be an expert.https://www.scientificamerican.com/article/are-virtual-particles-rea/“Hm, I'm a bit puzzled how an expert in particle physics can write such an article :-(. As an practicioner of QFT, I'm sure he knows very well that a particle interpretation of relativistic QFT is possible in clear terms only for asymptotic free states, and for vacuum QFT (i.e., the theory describing scattering events) the only observable outcomes are S-matrix elements, i.e., transition rates for going from an asymptotic free in state (usually two particles) to an asymptotic free out state (which can be any many-particle state, that is only restricted by the conservation laws like energy-momentum, angular momentum conservation and the conservation of various charges like electric charge etc.) or, equivalently, cross sections. All this is discussed already at length in this thread!
[QUOTE="ftr, post: 5653585, member: 465682"]I don't have a scientific survey but I would say(10 years of watching) the majority here and elsewhere do not agree with that point of view.”Thanks for that insight … I was hoping/thinking that must be true.
[QUOTE="clarkvangilder, post: 5653536, member: 612213"]Perhaps a quick comparison of these virtual particles to the point-particle model in classical mechanics? It seems that virtual particles are much much more than just a model? (Not that you or anyone else said otherwise). The title of this article below sort of captures the spirit of misconception relative to this topic. Scientific American is not a great journal of physics; but the person who wrote it ought to be an expert.https://www.scientificamerican.com/article/are-virtual-particles-rea/“I don't have a scientific survey but I would say(10 years of watching) the majority here and elsewhere do not agree with that point of view.
[QUOTE="ftr, post: 5653468, member: 465682"]The best reference I could find for you with reasonable explanation in English is thishttp://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html“Perhaps a quick comparison of these virtual particles to the point-particle model in classical mechanics? It seems that virtual particles are much much more than just a model? (Not that you or anyone else said otherwise). The title of this article below sort of captures the spirit of misconception relative to this topic. Scientific American is not a great journal of physics; but the person who wrote it ought to be an expert.https://www.scientificamerican.com/article/are-virtual-particles-rea/
[QUOTE="clarkvangilder, post: 5653411, member: 612213"]NOTE: I freely admit that I may have missed what some are saying in this thread. Just trying to glean as much as I can with some direct questions. Feel free, however, to recommend further reading. I am not opposed to doing homework. ;-)”The best reference I could find for you with reasonable explanation in English is thishttp://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html
[QUOTE="clarkvangilder, post: 5653411, member: 612213"].is it safe to say that the summary of all of this wrangling is that quantum fluctuations are a useful fiction? Useful in the sense that its metaphorical import is useful in describing some process or set of processes? Could the same be said of the probability waves that come with the overall game in QM?”I would say that it is important to keep in mind that terms like "quantum fluctuations", "probability waves", etc. are not the actual theory. They are attempts to describe some aspect of the actual theory in ordinary language. But ordinary language is vague and imprecise, and often there is no way to describe the theory in ordinary language without distortion. So you have to be very, very, very careful in trying to reason about the theory using ordinary language descriptions. That is why physicists themselves don't use these descriptions in their work; they use math. The mathematical description of the theory, and the concrete predictions derived from the math, are the actual theory, and to be sure you are reasoning correctly about what the theory says, the math is what you need to use.
[QUOTE="ftr, post: 5653429, member: 465682"]You can start with Googling for Vacuum Fluctuation Quantum Fluctuation, vacuum polarization…etc. And read the references within.You Know, even if you want to understand the simple ten commandments you have to read the bible and what was written about the bible and what was written about what was written…so on. Even then there is no grantee that confusion will not set in.:biggrin:“Seriously? Google? Who could have guessed that one?I was hoping for something more substantive than that. I have enough skill to read a textbook on QM and even do some of the math, and I am in fact doing that currently. However, I am not sure that an undergraduate level textbook is going to get me all the way there; but it will surely lay a foundation.
[QUOTE="clarkvangilder, post: 5653411, member: 612213"]NOTE: I freely admit that I may have missed what some are saying in this thread. Just trying to glean as much as I can with some direct questions. Feel free, however, to recommend further reading. I am not opposed to doing homework. ;-)”You can start with Googling for Vacuum Fluctuation Quantum Fluctuation, vacuum polarization…etc. And read the references within.You Know, even if you want to understand the simple ten commandments you have to read the bible and what was written about the bible and what was written about what was written…so on. Even then there is no grantee that confusion will not set in.:biggrin:
So…for the novice here…is it safe to say that the summary of all of this wrangling is that quantum fluctuations are a useful fiction? Useful in the sense that its metaphorical import is useful in describing some process or set of processes? Could the same be said of the probability waves that come with the overall game in QM?NOTE: I freely admit that I may have missed what some are saying in this thread. Just trying to glean as much as I can with some direct questions. Feel free, however, to recommend further reading. I am not opposed to doing homework. ;-)
[QUOTE="PeterDonis, post: 5644742, member: 197831"]No, any physics theory has to establish correspondence with the experimental evidence we use to test it. What, if any, correspondence it has with "physical reality" is a question of philosophy or metaphysics, not physics.”I don't know about metaphysics but experimental(observational in general) evidence IS "physical reality" in physics by definition.
[QUOTE="zonde, post: 5644377, member: 129046"]Mathematical statements however do not depend on the correspondence we attach to mathematical objects.”Um, what? A mathematical symbol refers to a mathematical object. That's why we use it.[QUOTE="zonde, post: 5644377, member: 129046"]my statement assumes that there is "wrong" way to describe physics in English.”My response still applies with this interpretation.[QUOTE="zonde, post: 5644377, member: 129046"]don't forget that there is experimental side to physics. This side of physics needs ordinary language along with mathematical language.”Experimental apparatus can be described mathematically; in fact it has to be in order to compare experimental results with theoretical predictions. One does need a correspondence between mathematical symbols and actual objects in the laboratory (e.g., this 4-vector corresponds with this measuring device sitting in the lab).[QUOTE="zonde, post: 5644377, member: 129046"]any physics theory has to establish correspondence with physical reality.”No, any physics theory has to establish correspondence with the experimental evidence we use to test it. What, if any, correspondence it has with "physical reality" is a question of philosophy or metaphysics, not physics.
[QUOTE="zonde, post: 5644377, member: 129046"]There are symbols in physics theories that correspond to physically measurable things. Mathematical statements however do not depend on the correspondence we attach to mathematical objects. In that sense symbols that are used as placeholders for mathematical objects are not names for anything.”Most definitions in amthematics define language naming things. The concept of group, of multiplication, of a field, a vector sspace, a vector, a set …, the symbol + * / etc. All are creating descriptive language.
[QUOTE="vanhees71, post: 5644374, member: 260864"]You have the same notion also in classical statistical mechanics: A phase-space distribution function implies an uncertainty in energy or momentum and thus implies ("thermal") fluctuations of these quantities.”Except that therrmal fluctuations in classical statistical mechanics are usually regarded (by invoking the ergodic hypothesis) as happening in time, Thus they are regarded as true fluctuations. While in quantum mechanics such a view is not really well-defined.
[QUOTE="atyy, post: 5644428, member: 123698"]The other way to see the post is that it justifies the myth – one just has to accept the path integral picture, and an interpretation of the path integral picture. So the myth is not a myth, provided we accept that it describes the path integral picture and not the canonical picture. In other words, it is not a myth, provided we add the words "shouldn’t be taken too literally". Already, in Copenhagen, the wave function is not taken literally. So quantum mechanics is intrinsically mythical. There is nothing wrong with adding the path integral as metamyth.”I guess there are quantum fundamentalists, who take it literally, and quantum Unitarians, who take it all metaphorically.[QUOTE="atyy, post: 5644428, member: 123698"]The other way to see the post is that it justifies the myth – one just has to accept the path integral picture, and an interpretation of the path integral picture. So the myth is not a myth, provided we accept that it describes the path integral picture and not the canonical picture. In other words, it is not a myth, provided we add the words "shouldn’t be taken too literally". Already, in Copenhagen, the wave function is not taken literally. So quantum mechanics is intrinsically mythical. There is nothing wrong with adding the path integral as metamyth.”
[QUOTE="zonde, post: 5644377, member: 129046"]This side of physics needs ordinary language along with mathematical language.”:thumbup:…[QUOTE=Arthur Eddington]We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'.”An interesting thread, please… carry on.
The other way to see the post is that it justifies the myth – one just has to accept the path integral picture, and an interpretation of the path integral picture. So the myth is not a myth, provided we accept that it describes the path integral picture and not the canonical picture. In other words, it is not a myth, provided we do not
[QUOTE="stevendaryl, post: 5644422, member: 372855"]It's a little more subtle than that. If you have an ensemble of a million human beings, there will be a nonzero standard deviation for the height, but that doesn't imply that anybody's height is fluctuating. On the other hand, if the quantity [itex]frac{d (height)}{dt}[/itex] has a nonzero standard deviation, as well, then that would support the claim that heights are fluctuating.”In the quantum case, though, it seems interpretation-dependent. According to some interpretations, no physical variable has a value until it is measured, so the fact that [itex]frac{dQ}{dt}[/itex] has a nonzero standard deviation doesn't imply that [itex]Q[/itex] is fluctuating, only that if you ever happen to measure [itex]frac{dQ}{dt}[/itex], you will likely get something nonzero.
[QUOTE="vanhees71, post: 5644374, member: 260864"]Well, although I'm not a native English speaker I'd formulate it more precisely as: Any quantum state implies uncertainties of position and momentum. This in turn implies fluctuations in the sense of an ensemble interpretation of probabilities. How else would you define fluctuations?You have the same notion also in classical statistical mechanics: A phase-space distribution function implies an uncertainty in energy or momentum and thus implies ("thermal") flucutations of these quantities.”It's a little more subtle than that. If you have an ensemble of a million human beings, there will be a nonzero standard deviation for the height, but that doesn't imply that anybody's height is fluctuating. On the other hand, if the quantity [itex]frac{d (height)}{dt}[/itex] has a nonzero standard deviation, as well, then that would support the claim that heights are fluctuating.
[QUOTE="vanhees71, post: 5644378, member: 260864"]It's the other way around: Plane everyday languages (it's not restricted to English of course) are no replacement for math ;-).”Certainly. However math depends on ordinary language while ordinary language does not depend on math. ;)[QUOTE="vanhees71, post: 5644378, member: 260864"]I don't care about history when it comes to the scientific content of physics. The state never was understood as the state vector but as an equivalence class of state vectors, called rays.”Well, it seems you are right. Historically state was associated with energy states of electrons in atoms. At least it seems that way after glancing at Schrodinger's paper (1926).
[QUOTE="zonde, post: 5644288, member: 129046"]Math is no replacement for English. These are two totally different things that have different functions.One of the functions of ordinary language is to name things. Math has no such function.Besides it's physicists themselves that have messed up English in physics. The usage of word "state" as statistical distribution is totally confusing not only for lay people but for physicists themselves. The word "state" has very important but different meaning as current physical configuration for some potentially changing situation. Historically it was state vector that was understood with the word "state" and there the correspondence is rather intuitive and clear.”It's the other way around: Plane everyday languages (it's not restricted to English of course) are no replacement for math ;-).The usage of the word "state" in the context of QT is not confusing but the essence of its content. A state is defined operationally as an equivalence class of prepartation procedures and the knowledge about the state implies the knowledge of probababilities (and only probabilities!) for outcomes of measurements, given the preparation of the measured system in this particular (pure or mixed) state.I don't care about history when it comes to the scientific content of physics. The state never was understood as the state vector but as an equivalence class of state vectors, called rays. There are some textbooks that are imprecise with this, and that leads to a lot of confusion. The most general definition of a quantum state in the formalism is of course the Statistical Operator which includes both pure states (i.e., the Stat. Op. is a projector) and mixed states (describing the situation that one has only incomplete knowledge about the quantum state as is usually the case for macroscopic systems).
[QUOTE="PeterDonis, post: 5644293, member: 197831"]Really? What are mathematical symbols? They are names for things.”There are symbols in physics theories that correspond to physically measurable things. Mathematical statements however do not depend on the correspondence we attach to mathematical objects. In that sense symbols that are used as placeholders for mathematical objects are not names for anything.[QUOTE="PeterDonis, post: 5644293, member: 197831"]This assumes that there is some one "right" way to describe physics in English (or any other ordinary language). There isn't. Ordinary language is based on ordinary experience, but physics is based on experiences that are not ordinary–if they were, we wouldn't need elaborate physical theories. The best we can do is to agree on some consistent terminology, at least in a particular field. But the terminology only helps if you understand the concepts it is referring to. And once you understand them, you understand that no ordinary language description is really the "right" one, because the concepts are not the ones that our ordinary language was built to express.”No, my statement assumes that there is "wrong" way to describe physics in English. And don't forget that there is experimental side to physics. This side of physics needs ordinary language along with mathematical language.[QUOTE="PeterDonis, post: 5644293, member: 197831"]Historically "state" has had a bunch of different meanings, depending on the theory. Picking one particular meaning from one particular formulation of one particular theory and saying that is the "right" one does not strike me as a fruitful way to proceed.”I am speaking about Quantum theory. And any physics theory has to establish correspondence with physical reality. So obviously physical reality needs description that is independent from particular physics theory. Statement that state vector (or density matrix) describes the state is such a correspondence rule IMO as "state" is primarily concept of physical reality and only secondarily concept of theory as much as theory corresponds to physical reality.
[QUOTE="mfb, post: 5644004, member: 405866"]But that's what we were talking about all the time? "The state has an intrinsic position uncertainty", or more general "The state has an intrinsic position/momentum uncertainty". The position/momentum uncertainty is a property of the state.”Well, although I'm not a native English speaker I'd formulate it more precisely as: Any quantum state implies uncertainties of position and momentum. This in turn implies fluctuations in the sense of an ensemble interpretation of probabilities. How else would you define fluctuations?You have the same notion also in classical statistical mechanics: A phase-space distribution function implies an uncertainty in energy or momentum and thus implies ("thermal") flucutations of these quantities.
[QUOTE="zonde, post: 5644288, member: 129046"]One of the functions of ordinary language is to name things. Math has no such function.”Really? What are mathematical symbols? They are names for things.[QUOTE="zonde, post: 5644288, member: 129046"]it's physicists themselves that have messed up English in physics.”This assumes that there is some one "right" way to describe physics in English (or any other ordinary language). There isn't. Ordinary language is based on ordinary experience, but physics is based on experiences that are not ordinary–if they were, we wouldn't need elaborate physical theories. The best we can do is to agree on some consistent terminology, at least in a particular field. But the terminology only helps if you understand the concepts it is referring to. And once you understand them, you understand that no ordinary language description is really the "right" one, because the concepts are not the ones that our ordinary language was built to express.[QUOTE="zonde, post: 5644288, member: 129046"]Historically it was state vector that was understood with the word "state"”Historically "state" has had a bunch of different meanings, depending on the theory. Picking one particular meaning from one particular formulation of one particular theory and saying that is the "right" one does not strike me as a fruitful way to proceed.
[QUOTE="PeterDonis, post: 5643846, member: 197831"]I would state this a bit differently: I would say that because English is vague, unlike math, there is no one "correct" use of English words to describe the physics. That's why, when we really have to be precise, we use math.”Math is no replacement for English. These are two totally different things that have different functions.One of the functions of ordinary language is to name things. Math has no such function.Besides it's physicists themselves that have messed up English in physics. The usage of word "state" as statistical distribution is totally confusing not only for lay people but for physicists themselves. The word "state" has very important but different meaning as current physical configuration for some potentially changing situation. Historically it was state vector that was understood with the word "state" and there the correspondence is rather intuitive and clear.
I get the impression that it is not only a semantic problem behind this, it is a conceptual divide. It hinges critically on whether one understands the meaning of the outcomes of EPR experiments and accepts what they imply or not. Briefly, the outcomes of those experiments require anyone who understands them to abandon local realism. Traditionally this requirement used to be separated on a choice between giving up locality or giving up classic realism, but let's say everybody here accepts QFT and relativity(wich everybody should) so that leaves as only choice giving up classic realism. In the context of this thread giving up classic realism is equivalent to disregard states as entities separated from their measurments. If one does this the alleged distiction between uncertainty in the state versus uncertainty in the measurement, and the rejection of the word fluctuation to refer to Heisenberg's uncertainty are not possible.Fortunately most people in this thread seem to understand and assume the Bell theorem as per the emprical results of EPR experiments. I can understand that those who don't will have a hard time accepting or understanding what serious physicists mean when they refer to quantum fluctuations(basically refer to obeying the Heisenberg uncertainty in different contexts), because for them the statistical fluctuation from noncommuting relations refers only to measurements separated from states, they give wavefunctions an ontological existence that is classically separated from measurements. I can see how a pure mathematician could disregerd experimental evidence though, I would not expect it from physicists.
[QUOTE="A. Neumaier, post: 5643971, member: 293806"]Wouldn't those you address in the first of the quoted sentence be lost when you do the second?”It's true that people who don't understand the professional jargon might not understand the math either, but that just means they are going to have to do more work themselves, to acquire the necessary background. Telling them to be sure to use a certain English word a certain way won't help, because they don't have access to the technical concept that it refers to. The only reason professionals can use English words to name certain technical concepts is that they already understand the technical concepts using math, so they can all agree on what a particular English word or expression means.What I am saying is that if your goal is to make lay people, who don't understand the math, correctly understand physics when expressed in ordinary language instead of math, I'm not sure that goal is achievable. But if your goal is to make lay people, who don't understand the math, understand that they don't understand the physics, and shouldn't try to reason based on ordinary language descriptions that might not correctly express the physics, I think that's a more modest goal that might be achievable.
[QUOTE="A. Neumaier, post: 5643588, member: 293806"]An uncertainty in the position means that the position is not known exactly.”But that's what we were talking about all the time? "The state has an intrinsic position uncertainty", or more general "The state has an intrinsic position/momentum uncertainty". The position/momentum uncertainty is a property of the state.
Thanks for the detailed answer, I was just wondering now that you mentioned quantum gravity, in string theory the landscape problem is interpreted as different universes. So can different universes have different vacua. Moreover, in LQG space itself is seen as fluctuating which I presume is the quantum analog of GR, or is that a myth also.Edit: I guess you are not against the vacuum having intrinsically a constant scalar(or vector) field of sort.
[QUOTE="PeterDonis, post: 5643946, member: 197831"]in many cases you will have people who don't know any of the precise professional technical terms in any field. In such a case I would argue that it is often better to just admit up front that ordinary language is inadequate and to make sure to be clear about what precise concepts you are referring to, expressed in mathematical terms.”Wouldn't those you address in the first of the quoted sentence be lost when you do the second? One needs some mediation between the two, to make the shift from being used only to ordinary language to getting used to the math easier. Just because PF caters for different groups of people one also needs different ways of trying to say the same.
[QUOTE="A. Neumaier, post: 5643852, member: 293806"]With some proper care, one can use the English language in an astonishingly precise way”I agree that this can be done, and inside a particular professional community, it is reasonable to expect it to be done. But PF is not such a community; there are people here from various professional communities, but there are also people here who are not math or science professionals at all. So at the very least, you are going to have people who are used to different usages of ordinary language to refer to precise concepts, and in many cases you will have people who don't know any of the precise professional technical terms in any field. In such a case I would argue that it is often better to just admit up front that ordinary language is inadequate and to make sure to be clear about what precise concepts you are referring to, expressed in mathematical terms.
[QUOTE="PeterDonis, post: 5643846, member: 197831"]I would say that because English is vague, unlike math, there is no one "correct" use of English words to describe the physics. That's why, when we really have to be precise, we use math.”With some proper care, one can use the English language in an astonishingly precise way, and doing this is usually of much help. Mathematicians (like me) like to be very precise, not only in their formulas (where it is a must) but also in the informal language and imagery that goes with it. This is why mathematicians never generate the same amount of public interest (precision is an antidote against sensations) as physicists even when they try to be popular. It is also the ultimate reason why mathematics is far more precise than theoretical physics. However, there are parts of theoretical physics (such as classical Lagrangian and Hamiltonian mechanics or quantum optics proper) where the English language is used in a far less misleading way as it is done in the popular quantum myths.
[QUOTE="mfb, post: 5643548, member: 405866"]it is not about physics, but the use of English words.” Wouldn't the best way to deal with that be to taboo those English words and restate everything in terms of math? This thread seems to me to have way too many posts arguing about terminology instead of physics; as far as I can tell everyone agrees on the physics. [QUOTE="A. Neumaier, post: 5643588, member: 293806"]in both cases it is a matter of the correct use of English words.” I would state this a bit differently: I would say that because English is vague, unlike math, there is no one "correct" use of English words to describe the physics. That's why, when we really have to be precise, we use math.
[QUOTE="ftr, post: 5643652, member: 465682"]Arnold, You are talking about the mathematical "vacuum" right and not the real world vacuum where the existence of particles and radiating fields complicate things and make it actually seething.”No. I am talking about what the quantum field theoretic textbooks call the vacuum. Mostly (not to complicate things) the vacuum according to the standard model, i.e., in a flat space-time, with a nonaccelerated observer. The real world vacuum must also account for gravitation, and for the lack of consensus about quantum gravity it is difficult to say much definite about that. But some things seem to be firmly established in (semiclassical) quantum gravity (in curved space-time, but without dynamical quantization of the gravitational field), and are consistent with what I am saying:In quantum gravity, the notion of vacuum (and hence of particles) is an observer-dependent notion. In a generally covariant description it is impossible to formulate the particle concept; only fields make sense. Particles appear only when modeled in the rest frame of a particle detector. Thus it seems that it is the particle detector (commonly called the observer) that turns fields into particles (by creating spots on a screen, peaks of a current, clicks in a counter, tracks in a fluid or a wire chamber). Characteristic for this is the Unruh effect: What appears to an observer A at rest (in its frame) as a vacuum [the observer excepted – which is acceptable in a cosmological setting] appears to a uniformly accelerated observer B as a thermal bath of particles. The basic reason is that in a system that appears as a vacuum to the observer at rest, the accelerated observer B is surrounded in its own rest frame not by a vacuum but by a strong gravitational field (created by the inertial forces) that excite the detector. Thus general covariance implies the observer dependence of the notion of vacuum. (Something similar happens in the Hawking effect for black holes.)If one tries to interpret the Unruh effect in terms of a seething vacuum it is paradoxical that the first observer sees and observed nothing of this seething, while the accelerated observer observes it. It is far more natural to explain everything in terms of the inertial forces, where it is clear that not the vacuum seen by A but the uniform acceleration (which requires energy input) creates the conditions leading to the detector response. In more technical terms: It is well-known that in curved space-time there is no generally covariant vacuum state, and that its place is taken by the class of Hadamard states, which transform into each other under arbitrary diffeomorphisms (coordinate transformations). These Hadamard states are seen by each observer (defined by a world line) at a particular time (selecting a point ##x## in space-time) as an external (classical) gravitational field in the Minkowski space tangent to the space-time manifold at ##x##. The observer interprets everything in terms of a traditional quantum field theory on this tangent space, where the typical scattering calculations for finding cross sections are performed. In most Hadamard states, the resulting gravitational field is nonzero, hence the system is not in a vacuum state, no matter which observer interprets it. In some special Hadamard states there are a minority of very special observers (on a set of measure zero) who would see a true vacuum (like observer A in the above, standard description of the Unruh effect). These observers are related to each other by a Lorentz transformation, so that they agree on what happens within the effects known from special relativity. All other observers – the overwhelming majority – don't see these special Hadamard states as anything special but are immersed in a nonzero gravitational field.
[QUOTE="stevendaryl, post: 5643521, member: 372855"]The disagreement is about whether the heuristic itself has any value. There are two sides of this question: (1) On the plus side, does the heuristic help in suggesting new phenomena that can then be investigated more rigorously? (2) On the minus side, does the heuristic lead us astray, in the sense of suggesting that things ought to be possible, when they really aren't? The fact that the detailed calculations don't involve fluctuations at all to me isn't an example of the heuristic being misleading, as long as everyone is clear that it is only a heuristic.”Some of the frustration with this topic comes, I think, from that balance being different with lay audiences who will never do the calculations and with serious students. For the former, the heuristic means that the vacuum is full of particle-antiparticle pairs appearing and annihilating themselves, real objects that just happen to have a very short lifetime. It's fair to dismiss that as a "myth" and (as a volunteer mythbuster at PF) I'm comfortable assigning it a fairly high negative value.
[QUOTE="A. Neumaier, post: 5643653, member: 293806"]I just noticed that the German version of wikipedia is far better than the English version on vacuum fluctuations, virtual particles, and the like!”Indeed, that's rare! :smile:
[QUOTE="A. Neumaier, post: 5643621, member: 293806"]Thus the fluctuation is only present in the measured ensemble, where they have the same statistical nature as in classical stochastic ensembles – that each realization differs a bit from each other one.”Sure, that's how observables are defined, at least for me as a proponent of the minimal interpretation.
[QUOTE="A. Neumaier, post: 5642564, member: 293806"]Even wikipedia describes it as a change, though in a completely unscientific manner (not surprisingly, since it also promotes lots of other nonsense about virtual particles):”I just noticed that the German version of wikipedia is far better than the English version on vacuum fluctuations, virtual particles, and the like!