One of the concepts that’s playing a big role in contemporary discussions of the laws of nature is the notion of “vacua”, the plural of the word “vacuum”. I’ve just completed an article about what vacua are, and what it means for a universe to have multiple vacua, or for a theory that purports to describe a universe to predict that it has multiple vacua. In case you don’t want to plunge right in to that article, here’s a brief summary of why this is interesting and important.

Outside of physics, most people think of a vacuum as being the absence of air. For physicists thinking about the laws of nature, “vacuum” means space that has been emptied of *everything* — at least, emptied of ** everything that can actually be removed**. That certainly means removing all particles from it. But even though vacuum implies emptiness, it turns out that empty space isn’t really that empty. There are always fields in that space, fields like the electric and magnetic fields, the electron field, the quark field, the Higgs field. And those fields are always up to something.

First, all of the fields are subject to “quantum fluctuations” — a sort of unstoppable jitter that nothing in our quantum world can avoid. *[Sometimes these fluctuations are referred to as “virtual particles”; but despite the name, those aren’t particles. Real particles are well-behaved, long-lived ripples in those fields; fluctuations are much more random.]* These fluctuations are always present, in any form of empty space.

Second, and more important for our current discussion, some of the fields **may have average values that aren’t zero**. [In our own familiar form of empty space, the Higgs field has a non-zero average value, one that causes many of the known elementary particles to acquire a mass (i.e. a rest mass).] And it’s because of this that the notion of vacuum can have a plural: forms of empty space can differ, even for a single universe, if the fields of that universe can take different possible average values in empty space. If a given universe can have more than one form of empty space, we say that “it has more than one vacuum”.

There are reasons to think our own universe might have more than one form of vacuum — more than just the one we’re familiar with. It is possible that the Standard Model (the equations used to describe all of the known elementary particles, and all the known forces except gravity) is a good description of our world, even up to much higher energies than our current particle physics experiments can probe. Physicists can predict, using those equations, how many forms of empty space our world would have. And their calculations show that our world would have (at least) two vacua: the one we know, along with a second, exotic one, with a much larger average value for the Higgs field. (Remember, this prediction is based on the assumption that the Standard Model’s equations apply in the first place.) An electron in empty space would have a much larger mass than the electrons we know and love (and need!)

The future of the universe, and our understanding of how the universe came to be, might crucially depend on this second, exotic vacuum. Today’s article sets the stage for future articles, which will provide an explanation of why the vacua of the universe play such a central role in our understanding of nature at its most elemental.

“There are reasons to think that our own universe might have more than one form of vacuum …” What might be the implications for theories of the vacuum if ‘t Hooft’s speculations on super determinism are correct?

http://arxiv.org/abs/1308.1007 “The Fate of the Quantum” by Gerard ‘t Hooft, 2013

Good morning, Matt. You say,

“An electron in empty space would have a much larger mass than the electrons we know and love (and need!)”

Isn’t the space no longer “empty” if there is an electron in it? If so what are the implications?

Space would not be empty then, obviously. Empty, except for the electron.

But the properties of empty space are what determine the properties of electrons. That’s why the Higgs field (which is present everywhere in space) determines the masses of elementary particles that move in otherwise-empty space.

How this is done is described (if you know some small amount of college math) here: https://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/ , https://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-the-higgs-field-works-with-math/

“Why is there something rather than nothing” Some ancient theologian

“Because nothing is unstable” Laurance Krauss

But WHY is it unstable?

Because, ‘there is no reason why an invariance of the Hamiltonian of a quantum-mechanical system should also be an invariance of the ground state of the system” – Coleman (1975), when introducing the notion of spontaneous symmetry breaking.

I’ve been waiting for the chance (when it wasn’t off-topic) to ask this elementary question: when a physicist says that a field has a non-zero value, what is that a value of? I’ve tried to find the answer in other posts but must have missed it.

Also, I saw a post on Sean Carroll’s site where he and some colleagues are strongly questioning the universal presence of quantum fluctuations. Would be interested in your comments!

Thanks very much.

I read that paper as specifically applying to the condition of slow-roll inflation, per Guth’s conjecture modified by Linde and others. I didn’t read it as applicable during the re-hearing process that resulted in our Hot Big Bang, or to any other condition, proposition or theory. Before reading the paper by Carroll et al, I had this notion that there could be some ‘build-up’ from quantum fluctuations thru each successive discrete inflation ‘event’ making up the dozens of them that came before the Hot Big Bang, but Carroll et all appear to be saying, No, the stuff that banged hotly all came in from the re-hearing in the last in that line.

Shiesh: those “re-hearing”s should be read as “re-heating”s.

@Avattoir

Thanks. I realize that discussing Sean Carroll’s paper is off-topic to Matt’s post. From the follow-up comments to Matt’s full article (and those to Carroll’s) I realize I’m out of my depth, but appreciate your effort to clarify the issue. To the extent I understand your point, it’s helped.

His blog posts and the comments Carroll responds to suggests it covers any vacuum in de sitter space. A couple of times he refers to the far future of the universe as well as its beginning.

I was also interested in what Professor Strassler thought of this, but its rather out of my league already so Im not sure Id be capable of understanding any response. (Im also not sure if theyve released the necessary information for any real review, Carroll suggests they will be covering mathematical details in the future.)

Bob B: “Im also not sure if theyve released the necessary information for any real review”

Ladies & gents, girls & boys of all ages, we all know none of us is getting out of this thing alive, but let’s all shed a special tear for the real sad sacks sobs of humanity, those who, while conceding they haven’t read something, still feel all pumped up full of vim & vinegar & beans with going ahead & posting on the Internet their ‘understanding’ of a ‘wild and cah-razy idea’ in a paper written by someone actually in the business, with the training, accreditation, papers, books & Feynman desks to prove expertise, who’s actually not just read but written the dang paper, when they haven’t even read it yet & we don’t even know if they’re got the math necessary to understanding it. Don’t be one of those sad sack sobs: go to Carroll’s site, and read his paper that is clearly, conveniently, prominently HYPERLINKED right in the middle of the frickin’ laser beams of his post.

Or, for those having trouble finding their way back out of the woods because the dang birds & ants carted off their breadcrumb trail: http://arxiv.org/pdf/1405.0298v1.pdf

Perhaps if you werent so busy being ridiculously condescending, youd have noticed that at no point in my post did I question or dispute Sean Carrolls vastly superior understanding of the subject area. Half the point of what I wrote was that it was beyond my understanding and I was here to ask for more information.

I read through the paper but that does not permit me the magical power of understanding it.

I have no idea who you are, what qualifications you have or if anything youve said is even remotely accurate, and instead of explaining why what I said (Which was essentially written by Sean Carroll on his blog…) was flawed you opted to mock me for not reading a paper Id already made clear I dont really understand.

I dont know what purpose you think behaving so arrogantly and rudely serves but if you cant bring yourself to be civil then dont worry, I wont bother to respond to anything you have to say ever again.

I’ll have to find some way to keep on living.

Look: it’s what you yourself said – I quoted YOU to you.

But I’m not replying just to cement we part forever on bad terms, so indulge me this hint: Start by considering what Carroll et al mean when they use the term “quantum fluctuations”. In particular, consider whether what their calculations are telling them goes not to their existence as to their nature, that is, that the environmental conditions under which such might ‘exist’ are not completely wide-open, but are constrained in certain circumstances, such as during inflation.

You yourself noted they seem to YOU to be saying their calculations tell them that quantum fluctuations do not exist AT ALL. But look at the paper’s opening sentence:

“We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no quantum fluctuations”

See those? “under certain plausible assumptions” & “settles into”.

Then later in the same opening paragraph:

“We argue that an analogous conclusion holds whenever

a patch of de Sitter is embedded in a larger theory with an

infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum.”

Are WE now in an “infinite dimensional Hilbert space”? Start by asking, What IS a Hilbert space? It’s a tool for calculating. It’s an abstraction for the purposes of exploring possibilities. Now look, in the same opening paragraph, at to where Carroll et al themselves say that using this tool led them:

“It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed.”

It does NOT say that perturbations do not happen: it says they “do not cohere” in a specific situation: “while slow-roll inflation occurs”. Ask yourself: Are we now in slow-roll inflation? Of course not; if otherwise, we wouldn’t be having this enjoyable chat.

It does NOT say what pananca2 took it to say on quantum fluctuations. It DOES say that, based on “certain plausible assumptions”, quantum fluctuations don’t occur DURING “slow-roll inflation”, and that, assuming this universe derived from multiple slow-roll inflation ‘events’, the assumed fact of their not occurring during those ‘events’ has particular implications, namely, eradication of the Boltzmann brain concern and at least constraint on the eternal inflation concern.

Finally, one nice thing about Carroll is he doesn’t tend to paper and run: rather, he papers, discusses, books, discusses some more. That pattern suggests he’ll discuss this a lot more in future. He, & also Frank Wilczek (& to some extent Steve Weinberg, assuming you’ve read his The First Three Minutes & his periodic articles in The New York Review of Books), are obviously intending to run with at least some implications of the BICEP2 findings (& the several experiments in the same area, findings pending).

I take it vacuum is unstable and the Higgs surfaced on the light side of predictions? Couple this with the fact the universe is expanding at an accelerate pace, could space stretch itself apart leave behind a) “island universes” and/or b) leave regions of literally dead zones (opposite to a black holes or c) burn out in a chaotic fire ball?

Does the equation: Energy ~ Function (space) … where the intensity of energy is proportional to the degree of stretching (from a normal curvature to more linear path). i.e. the more space curves the higher the potential energy becomes?

What exactly _is_ a quantum field?

Classical fields, whether scalar (eg, temperature) or vector (eg, electric or fluid velocity) usually associate a physical measureable with every point & time (x,y,z,t).

But unclear to me what “exists” at (x,y,z,t) in a quantum field.

Another article referred to “Feynman diagram is actually a calculational tool, not a picture of the physical phenomenon”

Is a quantum field also just a calculational tool?

That is a tricky question!

First a general remark: When we ask what X

is, we usually want to know how X is made up of other things. When we reach a fundamental level, such answers are (by definition) no longer possible. The only statements we can make about fundamental entities are about how they are related to each other and how we can model their behavior. If we could say more about them, they would not be fundamental. (We don’t know whether quantum fields are ultimately fundamental, but in today’s standard theories they are.)You correctly state the meaning of classical fields. But note that classical physics also does not tell you what a field

isin the usual sense. It rather says something like: “You can measure field X this way, and it can be modeled by a mathematical function obeying those equations.”For the most simple fields, the definition as you stated it can be taken over for quantum fields: A field is a quantity which can be observed (an “observable”) at any point in space and time. In the framework of quantum mechanics this means that a field is represented by a family of hermitian operators, one operator for each point in space and time. For technical reasons, this is not true for all quantum fields. There are quantum fields which are not directly observable, but in those cases you can build observables from simple combinations of the fields, so the basic idea remains valid.

In quantum mechanics the relation of physical states (“what is there”) to observables is subtle, and that is the big difference between classical and quantum physics. One cannot separately answer the question what “exists at a point (x,y,z,t)”. You can think of an observable like “the field X at the point (x,y,z,t)” as a specific angle of view on the overall physical state, which itself is not localized. It is a very abstract relation, but it has a precise mathematical description. Unfortunately, natural languages are not well suited to state it.

I would not say that quantum fields are “just” calculational tools. Quantum fields appear as fundamental elements in mathematical models of the physical world. These models are so spectacularly predictive and successful – they match the physical world so well – that we can say quantum fields are as good an explanation of “what is really there” as we can possibly have at the moment.

I’d say that last paragraph of yours also qualifies as “tricky” – not that you’re trying to delude: the whole construct is tricky!

A quantum field is a structure of POTENTIAL, right? Not what “is”, either in our level of reality or ‘just’ at the quantum level, but what’s possible. Tom H correctly described Feynman diagrams as tools for calculation; QFT could be best appreciated as a tool for gaining understanding on what MIGHT happen, together with the probabilities of those things actually happening.

Were talking distribution of energy & the effects of a given distribution, yes? And we start by assuming the characteristics of any universal – I mean the big, overall, everything universal, applying also to any subuniverse or Linde “world” – include that energy WILL seek out the lowest potential state. We use QFT to imply STRUCTURE to, not just that potential state but, all potential states for all energy-mass combinations. Thus, the QF for the top quark operates at ‘higher’ plane than the QF for the graviton (the lowest potential state or QF of all?). But it doesn’t exist in the same way the energy itself that’s seeking that lowest potential state exists; it doesn’t even operate AT ALL if the little bit of energy there is simply can’t flow to the lowest state on offer.

It seems like a way to address my theory of the universe being made of discrete components. Not really vacua! http://www.vixra.org/abs/1403.0502

Professor Matt<

I'm having trouble reading the very first sentence in your above linked article .

“Getting a rough understanding the basics of particle physics — our current understanding of the most elementary aspects of the universe — isn’t that hard.”

I’m tired of the consequences of jumping to conclusions; mis-interpretations, wrong or inaccurate understandings, ambiguities, and wasted time.

Sorry for nitpicking~

Thanks for a wonderful blog.

“Above linked article”?

https://profmattstrassler.com/articles-and-posts/particle-physics-basics/fields-and-their-particles-with-math/

Thank you Professor for an excellent post,

can you explain Spontaneous symmetry breaking of strong gauge invariance (marble) into “exotic vacuum”, during “Asymptotic freedom” at higher energies ?

Einstein saw reality as fields upon fields including spacetime.So how can we talk about vacua if removing everything means removing reality?

Firstly, it doesn’t matter how Einstein ‘saw reality’ any more than it matters how I see it.

Secondly, vacua here *do* contain fields, and possibly more things. They are, very roughly, volumes of space where everything that can be removed is.

Finally, relativity and quantum theories are not compatible. One or both of them is incomplete. We should not take ‘Einstein’ as meaning ‘God’ when it comes to physics.

Kudzu

There is a self consistent quantum theory of gravity http://www.worldscientific.com/doi/abs/10.1142/S0219887814500595

Also this paper will be discussed at the following workshop by experts on Quantum gravity where I have been invited http://www.sissa.it/app/esqg2014/participants.php

“some of the fields may have average values that aren’t zero. [In our own familiar form of empty space, the Higgs field has a non-zero average value,”

“Some?” of the fields. What are the examples of the fields with non-zero average value besides the Higgs field? and what are they doing in the observable universe?

This depends on what theories you’re working with; as noted in the article many theories exist only a very few which can be said to describe our actual universe to the best of our knowledge.

Dear Prof.Strassler

–In your post you mention fields(electric,magnetic,etc.)as potentially existing in a vacuum,including their unavoidable quantum fluctuations.

–However,as far as I know the only field that is all-pervasive and unavoidable is the gravitational field that you do not mention.

–The fields that you did mention could, all of them ,be annulled in finite regions of space by a variety of means.

–Therefore the “minimum” possible vacuum is a “sea” of gravitational field whose quantization (quantum gravity) is still arguable.

I would appreciate your comment

Abraham

If say the electromagnetic field did not fill all of space, waves within that field would be ‘banished’ from places where it did not exist. Those waves are light (photons). Therefore if there are areas in the universe where photons cannot exist, even as virtual particles, they will be areas that are perfectly reflective, excluding incoming light from entering them. Atoms could not exist in such volumes.

If the Higgs field did not do similar there would be volumes of the universe where matter itself broke down. The absences of other fields have likewise detectable effects. That the universe seems to function like it does here all over is powerful evidence that such absences cannot be large or common and probably do not exist.

The confusion may be in that gravity is the only force we see acting on large scales because it isn’t ‘cancelled out’ like electromagnetism or utilize short range interactions like the weak force. But this does not mean it is the only universal force.

Dear Kudzu

–I appreciate your comments

–Still I do hope that Prof. Strassler will kindly share with us his expert opinion

Abraham–

This is just the result of the poor predictability of low-dimensional models, when the high-dimensional physics get involved. The physicists are in situation of floater which interacts with it neighborhood via surface waves. These waves do form a regular circles at proximity, but when their scope increases, their deterministic character will disappear [RES ignored duplicate image][1] due to scattering.

And all these thoroughly developed and tested deterministic models aren’t working anymore. It still doesn’t mean, there are multiple vacua or water surfaces. It’s all consequence of the same emergent geometry.

Of course, the first instinctive reaction of theorists isn’t: “voila, our models get broken!” but “I see, there are multiple overlapping water surface, each of which indeed still fits our existing theories well”.

It’s not difficult to guess, that this stance has psychosocial and political roots. As Feynman once said, “String theorists do not make predictions, they make excuses”. Well, and the multiverse model is such an excuse too: it just helps to keep the existing research business running.

The multiverse concept has its roots in community of string theory from good reason: the string theory is based on mutually inconsistent postulate set, so it can never lead to single unique solution by its whole definition. And it’s quite easy to understand it just with water surface analogy of space-time.

The string theory is based on Lorentz symmetry, which maintains the background independence of this theory with respect to Lorentz transform in the same way, like the surface ripples, which don’t interact with underwater in any physical way. But this theory considers another postulates too, like the assumption of additional extradimensions. In another words, the string theory considers the (additional dimension of) underwater, but the Lorentz invariance prohibits its existence instead.

Which leads into logical paradox: one postulate is violated with another ones in a way, which isn’t obvious, until you have no such geometry before eyes. Such a model can be still solvable in limited extent, but it cannot never lead to single ultimate solution. It leads to the whole system of solutions, which is impossible to falsify in context of string theory itself.

Case is closed.

Why not call them “Vacuums”?

Vacuum is a Latin word and traditionally the Latin plural is used. (Medium, media, optimum, optima and so on.) However genuine debate exists with the words ‘penis’ and ‘octopus’ as to plurals.

But “vacuous” is the prefect descriptor for modern theoretical physics.

Are you talking about the same theoretical physics that successfully predicted the Higgs particle and that produces cosmological models matching the observed data like this: http://trenchesofdiscovery.blogspot.de/2013/03/planck-all-we-need-is-six-numbers-to.html ?

Such a general dismissal of theoretical physics is just completely unfounded.

Sorry, But I think these brilliant successes are mostly mere model-building.

The putative Higgs mass was predicted to be somewhere between 100 GEV and the Planck mass, which is quite a range! Some “prediction”!

The substandard model has 7 serious shortcomings that clearly indicate that it is provisional model-building.

The LHC results gave the Bronx cheer to decades of “beyond the substandard model” theories.

The cosmological simulations are model-building tweaked over decades to reproduce observations.

Shall I go on, or do you get the point?

Robert, no, I don’t get your point. As for the Higgs mass: Picking out the Higgs mass as a bad “prediction” makes no sense, because the mass is exactly the one property of the Higgs particle that the Standard Model does

notpredict, at least not in any direct way. Before its discovery at the LHC, there were only rough indications for the scale of the mass. All its other properties like its spin and the interactions with other particles are directly predicted by the Standard Model and can now be tested at the LHC, and so far it seems to fit.It’s not COMPLETELY open: consider the octopenile.

Octopus isn’t Latin, so Latin plurals would be wrong. Personally I prefer to treat it as English, as “octopodes” (apparently the correct Greek version) just doesn’t seem right to me.

You know, I was being slightly facetious when I posted this question, but the replies have been fascinating! Not only have I learned about the etymology of the words vacuum, octopus, and penis; but reading physicists taking shots at each other is highly entertaining!

Dark matter is now understood to fill what would otherwise be considered to be empty space.

Dark matter is displaced by the particles of matter which exist in it and move through it.

What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the dark matter.

The Milky Way’s halo is curved spacetime.

The Milky Way’s halo is the state of displacement of the dark matter.

The state of displacement of the dark matter is gravity.

Vacua, vacuums, closely linked, but my spelling check doesn’t care for vacua, it prefers vacuums.

Virtual particles come and go and a particle is a long lasting ripple in a wave. Why is it long lasting? What keeps it from disappearing along with virtual particles?

Real particles have a specific (range of) energy\wavelength that repeats periodically in an orderly fashion. As such there are certain things they cannot do, their energy cannot become zero (or many other values) nor can they dissipate into other fields. (Though they will make their mark in all fields they are connected to.)

Virtual particles by contrast do not have a fixed energy or regular wavelength. They lack the order needed to not fall apart. In some sense they may be considered not separate particles at all but just part of the background wiggle of fields. They mix with other ripples, split apart or are absorbed into the ripples of connected fields.

One of the easiest modes of decay to imagine is splitting apart. A real electron moving at speed x is stable. It moves at a constant speed determined by its energy.

A virtual electron however has no specific energy. The bits of it with low energy move slower and the bits of it with high energy faster. As it moves then it will quickly ‘spread out’ as the faster bits leave the slower bits behind.

Why would the electrons we know not have a much larger mass in the empty space we know?

This is actually a very deep question. Initially we had to ask ‘Why do particles have the masses they do?’ because we had no reason. To explain this we invoked the Higgs mechanism which tells us that the mass of a particle depends on how strongly it couples with the Higgs field. So the answer to your question would be ‘Because in the space we know the Higgs field has a certain value and the electron couples to it.’

But that just moves the question back a step; now we must ask ‘Why do particles have the specific values of coupling constants that they do? We know electrons have had their current mass as far back as we can see and we know how it comes about, but we don’t know why they have the specific mass they do.

If you are right, it apparantly does not matter whether the empty space is exotic or not. So, if in both empty spaces an electron’s mass would be much larger than the ones we know, then what is the issue?

Oh no, you asked about ‘the empty space we know’; if the vacuum were exotic because the value of the Higgs field in it was different then the electron’s mass would be different because the Higgs field affects that mass.

But it would be predictably different. If the Higgs vev were twice as large then the electron’s mass would be twice as large. (On the other hand if the vacuum was exotic for a non Higgs reason the electron’s mass should be the same.)

At present we can say the electron’s mass is 2077eV per GeV of Higgs vev. But WHY is it 2077? That we don’t yet know. We haven’t discovered any reason that it should be that, but we know *something* has kept it at pretty much exactly that value from the start of the universe.

Thank you.