The classical aether vs. the modern vacuum

[Maxwell's Beard]

I have been reading a few old texts from around the turn of the 20th C. and have noticed that in at least two there is mention of the aether in connection with electromagnetic phenomena. In these texts a statement to the effect of "the space around the coil is altered in some way by the passage of current in the wire". Or one even says "the medium surrounding the magnet is clearly stressed by the flow of charge..."

These are intriguing statements that have an undertone of some deep intuition on the part of the writers.

We know now that the "medium" of the aether is nonexistent . But is it really? Maybe it isn't a gaseous fluid such as early thinkers thought, but is it any less real?

The modern quantum vacuum, while far stranger than anything 19th C minds were grasping, is for every aspect as far as classical EM is concerned, the aether is it not?

Space being filled with this quantum fluid, as it sometimes behaves, makes a lot of things intuitively satisfying. The spatial "stresses" of electric and magnetic fields, the propagation of light through "empty" space, maybe even inertia seem to "feel better" in this view.

Am I just totally off base with this? I know there are some semantics between old and new descriptions of phenomena, and even new ideas that didn't exist in the aether heyday. But were the Grand Old Men of electrodynamics, who clearly possessed some sort of deep physical intuition on the nature of matter, all that wrong?

 

[Hurkyl]

Why would one give the name "aether" to the vacuum (of QM) when it already has a perfectly good name?

 

[jtbell]

A rhinoceros shares some features with the mythical unicorn. Should we therefore think of a rhinoceros as a sort of unicorn?

 

[Maxwell's Beard]

A rhinoceros shares some features with the mythical unicorn. Should we therefore think of a rhinoceros as a sort of unicorn?

No, perhaps a unicorn as a rhinoceros. I think what I mean is aren't they the same? Just because they called it "aether" and ascribed the properties of a massless gas to it makes it less real? I think these 19th C scientists were aware of the vacuum of modern theory. Just lacking the proper tools to really study and define it. They imagined it had properties that "made sense", but that doesn't work all the time for a quantum field, so turns out that what properties they were looking for and at what energies and levels they were looking at, are nonexistent.

That isn't, however, proof of it being absolutely unreal. The relativists came along and suddenly you are a crackpot if you believe in any slight way in the existence of a universe-pervading "fluid" that under different stresses manifests itself as various kinds of fields. But Relativity doesn't require us to cast the "aether" out. What what we are told, by SR, is that an absolute frame of reference is unnecessary and nonexistent. Therefore, if you are an early 20th C physicist and you believe that the "aether" is Newton's absolute frame, then yes, you are wrong.

Then along comes the quantum theorists, and things get a little weird, and older guys, like our "aetherians", already cowed by a berating from the relativists, fade into history, without ever speaking up again. Dirac and his ilk come about and talk of the vacuum as a real thing that can be teased to produce a variety of fields and particles, given the right conditions. They call it a quantum vacuum and space is seething with energy and properties all it own, and not the same emptiness of the relativists.

Basically, aether supporting scientists were ahead of their time. They were trying to describing the spacetime of Dirac with the thermodynamics of Clausius. They were, then, wrong about many aspects of it. But the general field was correct. Had they kept researching, they may have eventually derived some of the concepts of quantum mechanics. But that is now moot.

Perhaps, in an attic somewhere, in an old desk drawer of some shunned and long-dead aether theorist, we may find a breakthrough paper, written 100 years ago but outcast and ridiculed by the research and publication community for being crackpot.

 

[meopemuk]

Am I just totally off base with this?

I think you are. And you are not alone. Just look at today's arXiv

http://www.arxiv.org/PS_cache/arxiv/pdf/0709/0709.4101v1.pdf

Eugene.

 

[Maxwell's Beard]

I think you are. And you are not alone. Just look at today's arXiv

http://www.arxiv.org/PS_cache/arxiv/pdf/0709/0709.4101v1.pdf

Eugene.

Thanks, Eugene. But referring to my last post, you will see that I am not arguing the aether as an absolute frame of reference. That, I believe, is incorrect.

Why do most people automatically associate "aether" with only that specific usage? Just because SR doesn't require it and refutes its use as an absolute reference, doesn't mean that it is unreal. All that simply means is that special relativity doesn't use the vacuum for anything more than as space for events to occur in. Because SR doesn't require it as a frame of reference, we can drop that aspect of it, but we don't drop the whole thing, because, while wrong about absolute relative motion, the GRAND OLD MEN OF ELECTRODYNAMICS GLEANED A HINT OF OUR MODERN QUANTUM VACUUM AND CALLED IT THE AETHER, NEVER UNDERSTANDING, AS WE DO NOW, WHAT THEY WERE FOLLOWING. THESE IDEAS WERE SHUNNED AND PUSHED ASIDE AND NO LONGER PURSUED UNTIL, YEARS LATER, SOMEONE CAST IT IN A NEW LIGHT AS THE QUANTUM VACUUM.

 

[masudr]

Caps lock much?

 

[meopemuk]

Hi Maxwell's Beard,

I have a (not very popular) point of view that there is no such a thing as "quantum vacuum". My understanding of quantum field theory (based on the "dressed particle" approach) tells me that vacuum is just an empty space (no particles) without any observable properties. In order to observe something there should be at least one physical particle, and I don't believe in any particle-vacuum interactions, such as those leading to particle "self-energies" or "vacuum polarization". For these reasons I cannot accept your vacuum/aether analogies.

Eugene.

 

[cesiumfrog]

Beard, since you have entered this forum, you must want to communicate to us. To do this, you need to use the same names for concepts as we use, otherwise we won't understand your message.

We use the name ether for the thing with the properties that your grand old men were thinking of, and we use the name quantum vacuum for the modern concept that you think is closely related (but we disagree).

In addition to using the same language, it would be polite (which is good for you because we will respect you in return and thereby be more attentive to what you wish to say) if you also pay respect to the other customs we have accepted here. For example, seeing excessive capitalisation (in fact, any font style other than the default) to most of us is unpleasant like listening to shouting (since it is distracting, more difficult to read, and overrides the personal preferences we have configured for display of text on our individual computers). For another example, it is fine to ask for a discussion of the similarities and differences between the concepts of ether and quantum vacuum, but we don't want threads here to outright assert that those concepts should be identified with one another (nor any other assertion contrary to the mainstream physics viewpoint that we are aiming to learn).

 

[JesseM]

That isn't, however, proof of it being absolutely unreal. The relativists came along and suddenly you are a crackpot if you believe in any slight way in the existence of a universe-pervading "fluid" that under different stresses manifests itself as various kinds of fields.

How can any sort of physical "fluid" fail to have a rest frame? Just to be clear, when you say that you reject an absolute frame of reference, are you somehow proposing it makes sense to call something an "aether" even if it lacks any sort of rest frame (even locally), or are you saying you think there might be an aether with a rest frame, but you just aren't claiming that its rest frame is any sort of "absolute" frame? (much like how the cosmic microwave background radiation has a rest frame but this isn't taken as evidence for absolute space) If the latter, do you think the aether's rest frame would be measurable in some way, so that effects relating to the aether would not all be Lorentz-symmetric?

 

[Maxwell's Beard]

Beard, since you have entered this forum, you must want to communicate to us. To do this, you need to use the same names for concepts as we use, otherwise we won't understand your message.

We use the name ether for the thing with the properties that your grand old men were thinking of, and we use the name quantum vacuum for the modern concept that you think is closely related (but we disagree).

In addition to using the same language, it would be polite (which is good for you because we will respect you in return and thereby be more attentive to what you wish to say) if you also pay respect to the other customs we have accepted here. For example, seeing excessive capitalisation (in fact, any font style other than the default) to most of us is unpleasant like listening to shouting (since it is distracting, more difficult to read, and overrides the personal preferences we have configured for our individual computers). For another example, it is fine to ask for a discussion of the similarities and differences between the concepts of ether and quantum vacuum, but we don't want threads here to outright assert that those concepts should be identified with one another (nor any other assertion contrary to the mainstream physics viewpoint).

Thank you CesiumFrog. I used caps to try to emphasis that I am not speaking of the aether in the sense of an absolute frame of reference. That seems to be a point which keeps popping up, which I keep refuting, on the grounds of SR.

I am trying to convey my thoughts on the subject as clearly as I can in writing, which is very hard, and further complicated by the fact some aetherists were also subscribers to Newton's absolute reference frame, which seems to have caused everyone to rail against anyone using the term "aether" as an anti-relativist.

I suppose I can see how it looks as if I want someone to tell me I'm right. But it is actually the contrary. I want someone to tell me why I'm wrong. No one has yet to do it without invoking the "because there is no absolute frame" argument. That argument is correct, and I agree whole-heartedly.

Ok, I may be able to pose it this way, as you say that you disagree that the old aether is the new vacuum.

Other than a lack of a better understanding and the acceptance of an absolute frame, what is all that different about a 19/20th C scientist saying a "stressed" aether gives rise to electric and magnetic fields, compared to a modern scientist believing that an "excited" vacuum gives rise to electromagnetic fields?

 

[meopemuk]

I want someone to tell me why I'm wrong.

So far you are neither right nor wrong. Stating that "aether = quantum vacuum" you haven't made any statement about physics. Physics is science about experimental observations. So, if you want to talk about physics you should tell what are the properties of your "aether", how it interacts with other objects (particles), in which experiments these properties and interactions can be measured, how your predictions are different from existing theories?...

Eugene.

 

[Maxwell's Beard]

How can any sort of physical "fluid" fail to have a rest frame? Just to be clear, when you say that you reject an absolute frame of reference, are you somehow proposing it makes sense to call something an "aether" even if it lacks any sort of rest frame (even locally), or are you saying you think there might be an aether with a rest frame, but you just aren't claiming that its rest frame is any sort of "absolute" frame? (much like how the cosmic microwave background radiation has a rest frame but this isn't taken as evidence for absolute space) If the latter, do you think the aether's rest frame would be measurable in some way, so that effects relating to the aether would not all be Lorentz-symmetric?

I'm saying that the difference between the the aether and the quantum vacuum is precisely the name. Sure the word "aether" makes one think of a classical (that is, non-quantum) fluid. But it was classical (that is, non-quantum) men who named such things. I do not wish to discuss what frame the aether represents, because it is not what my original post was about anywho. That, in my mind, is that same question as what frame does the vacuum represent.

I have an old text that says something like, and I'm paraphrasing, forgive me, "the motion of the electric charges in the coil cause a change in the properties of the medium immediately surrounding it. It is this stress in the aether that is manifested to us as a magnetic field B surrounding the coil".

This rings with modern quantum vacuum, even if it uses different wording. What is different about a "stressed aether" giving rise to electric and magnetic fields, compared to an "excited vacuum" giving rise to an electromagnetic field?

 

[Maxwell's Beard]

So far you are neither right nor wrong. Stating that "aether = quantum vacuum" you haven't made any statement about physics. Physics is science about experimental observations. So, if you want to talk about physics you should tell what are the properties of your "aether", how it interacts with other objects (particles), in which experiments these properties and interactions can be measured, how your predictions are different from existing theories?...

Eugene.

I am not trying to make any statements about physics, I'm making a statement about physicists. I am not now, nor have I previously, attempted to state any new postulates about modern quantum mechanics or classical electrodynamics. I simply believe that the men that called the thing "aether" were really describing (incompletely, and in many ways incorrectly) what is now called the quantum vacuum. I suppose I am trying to credit these men, Faraday, Maxwell, Heaviside, et al, with being the first to recognize Dirac's vacuum, though through the lens of the 19th C.

Please forgive me all if I have seemed pigheaded. But there is no experiment that I can do to validate my claims, as my claims are purely non-physical and rely on the fact that while words can be different, meanings can and often are one in the same.

So I pose this question again: what is all that different about a "stressed aether" giving rise to electric and magnetic fields, compared to an "excited vacuum" giving rise to an electromagnetic field?

 

[JesseM]

I'm saying that the difference between the the aether and the quantum vacuum is precisely the name. Sure the word "aether" makes one think of a classical (that is, non-quantum) fluid.

I don't think it makes sense to call a quantum field a "fluid", either quantum or classical, if it has nothing like a rest frame. Even a quantum fluid like a superfluid, or weird non-fluid states like Bose-Einstein condensates, still have some kind of expectation value for a rest frame I think (i.e. the frame where their position is most likely to remain constant).

 

[meopemuk]

So I pose this question again: what is all that different about a "stressed aether" giving rise to electric and magnetic fields, compared to an "excited vacuum" giving rise to an electromagnetic field?

These two notions are, indeed, very similar, because they both are completely fictional and non-observable.

Eugene.

 

[yogi]

The void has properties - the difficulty is in modeling it in terms of convention wisdom. How can space stretch as Robertson proposes, or rotate about a black hole, or link with local matter to bring about Newtonian reaction as Einstein deliberated, or exhibit a characacteristic impedance or a capacity or permitivity or communicate rotation via Thirring ...there does not seem to be a something that can exhibit all these characteristics - it is a classic case of the failure of traditional theories based upon particles and fields.

There is an oft quoted phrase "absence of proof is not proof of absence" The existence of a medium has never been falsified, but to understand its nature seems at this point to require the abandonment of internal consistency

 

[yogi]

It is frequently stated that Einstein renamed the "aether" space. He seemed to treat his space as having all the qualities of the classical ether except motion, which would have contradicted SR. The issue of the modern vacuum and the classical aether is subjective - it is not an issue that should be settled by majority vote - or who shouts the loudest on this forum, or most depreciative.

 

[Hurkyl]

Just because they called it "aether" and ascribed the properties of a massless gas to it makes it less real? I think these 19th C scientists were aware of the vacuum of modern theory.

Upon what grounds do you make such an assertion?

The ancient Greek philosopher Democretus talked about how all matter was made out of indivisible atoms. Do we credit him with the discovery of the atomic theory of matter? Of course not! Democretus' philosophy doesn't resemble Dalton's theory at all, except for that one superficial similarity!

Why do you think this situation is any different?

 

[Maxwell's Beard]

I don't think it makes sense to call a quantum field a "fluid", either quantum or classical, if it has nothing like a rest frame. Even a quantum fluid like a superfluid, or weird non-fluid states like Bose-Einstein condensates, still have some kind of expectation value for a rest frame I think (i.e. the frame where their position is most likely to remain constant).

You are just picking at me now. You know full well that "fluid" doesn't mean any real fluid, classical or quantum. It is just a picture for the mind's eye. Even Dirac called the vacuum a "sea".

 

[Maxwell's Beard]

Upon what grounds do you make such an assertion?

The ancient Greek philosopher Democretus talked about how all matter was made out of indivisible atoms. Do we credit him with the discovery of the atomic theory of matter? Of course not! Democretus' philosophy doesn't resemble Dalton's theory at all, except for that one superficial similarity!

Why do you think this situation is any different?

That is a good point, and has caused me to think. I think that the difference between that ancient Greek and the aetherists is that the aetherists were actually making observations. They could detect and map a magnetic field or lines of force from an electrophorous or pick up Hertzian waves at a distance. These observations had them believing that there was some underlying field that if you tickled it in the right way you could cause it to show itself, sometimes as an electric field, other times a magnetic field, and sometimes it would produce a self-sustaining wave that moved at the speed of light.

I am not giving them credit for "discovering" Dirac's vacuum, I am simply saying that these men had enough genius to actually begin finding traces of it, even if they came to the wrong conclusion.

 

[Maxwell's Beard]

These two notions are, indeed, very similar, because they both are completely fictional and non-observable.

Eugene.

OK. I am glad you said it. That is a good point of view

 

[Maxwell's Beard]

It is frequently stated that Einstein renamed the "aether" space. He seemed to treat his space as having all the qualities of the classical ether except motion, which would have contradicted SR. The issue of the modern vacuum and the classical aether is subjective - it is not an issue that should be settled by majority vote - or who shouts the loudest on this forum, or most depreciative.

I think you have said what I have been trying to say. That is beautiful, for I cannot seem to boil my thoughts down to such a compact statement. Thanks, yogi.

 

[OOO]

I think you have said what I have been trying to say. That is beautiful, for I cannot seem to boil my thoughts down to such a compact statement. Thanks, yogi.

Maxwell's Beard,

The problem with physics is that we have to use names that appeal to intuition in order to be able to memorize things. But when you have studied physics in a bit more detail you gradually notice that your initial intuitive feelings about these names were quite inaccurate when compared to how different concepts are used in actual work (e.g. formulae and the results they generate, or application of formulae and names to real world experiments).

So, as cesiumfrog has emphasized, the word ether means nothing if you cannot find a consensus about its usage. As I can judge from my episodic knowledge of the history of science, a lot of the problems at the beginning of the 20th century originated from inaccurate language. Even today experts sometimes use different language and get into arguments about things they basically agree upon.

Today the meaning of the word ether refers only to the concept of allowing or not allowing you to distinguish between absolute movement and rest. Nothing more about fluids or something.

As to your conceiving electromagnetic fields as something that alters space, well that's how Maxwell's theory is actually used classically. But actually one has still different layers of alteration of space, i.e. gravitational fields, electromagnetic fields, gluon fields... So at least today there seems to be no meaningful way of thinking of the electromagnetic field (or even some other unified field) as the properties of space.

As to quantum field theory and the vacuum: the fundamental difference is that the vacuum of QFT has a non-zero probability amplitude for non-zero fields. I.e. even in the ground state (the state of lowest energy) of your system you will probably measure non-zero fields (you may equally well measure precisely vanishing fields with a certain probability). So this is quite different from the classical vacuum where fields exactly vanish by definition.

 

[JesseM]

You are just picking at me now. You know full well that "fluid" doesn't mean any real fluid, classical or quantum. It is just a picture for the mind's eye. Even Dirac called the vacuum a "sea".

No, I didn't know that. I earlier asked "How can any sort of physical 'fluid' fail to have a rest frame?" and you responded "Sure the word "aether" makes one think of a classical (that is, non-quantum) fluid. But it was classical (that is, non-quantum) men who named such things." So, I genuinely thought you were claiming that although it's not a classical fluid, it's some kind of "quantum" fluid.

It seems I misunderstood, and your earlier statement "The relativists came along and suddenly you are a crackpot if you believe in any slight way in the existence of a universe-pervading 'fluid' that under different stresses manifests itself as various kinds of fields" was not meant to suggest that the quantum vacuum be seen as any sort of actual fluid. If this is the case, it seems to me that the one thing all "aether theories" have in common, and which is at the heart of most people's concept of what "aether theory" means, is explaining electromagnetic phenomena in terms of density changes in an actual physical substance filling space--fluid, solid, or whatever. So calling something an "aether theory" if it doesn't share this basic feature is unnecessarily confusing IMO.

 

[meopemuk]

As to quantum field theory and the vacuum: the fundamental difference is that the vacuum of QFT has a non-zero probability amplitude for non-zero fields. I.e. even in the ground state (the state of lowest energy) of your system you will probably measure non-zero fields (you may equally well measure precisely vanishing fields with a certain probability). So this is quite different from the classical vacuum where fields exactly vanish by definition.

I don't think there was ever performed an experiment measuring a non-zero probability of *anything* in vacuum. Vacuum (by definition) is a state without particles, and if there are no particles, there is nothing to measure.

Eugene.

 

[Hurkyl]

That is a good point, and has caused me to think. I think that the difference between that ancient Greek and the aetherists is that the aetherists were actually making observations. They could detect and map a magnetic field or lines of force from an electrophorous or pick up Hertzian waves at a distance. These observations had them believing that there was some underlying field that if you tickled it in the right way you could cause it to show itself, sometimes as an electric field, other times a magnetic field, and sometimes it would produce a self-sustaining wave that moved at the speed of light.

It doesn't sound like you're talking about classical aetherists at all! They were rejecting the notion of an underlying field, and instead asserting that the electromagnetic field describes the bulk properties of an underlying material.

e.g. the stereotypical line "How can you have a wave if there isn't anything for it to wave through?"

 

[OOO]

I don't think there was ever performed an experiment measuring a non-zero probability of *anything* in vacuum. Vacuum (by definition) is a state without particles, and if there are no particles, there is nothing to measure.

Eugene.

This sounds reasonable but it's not what quantum field theory says. QFT says that a photon is a harmonic oscillator of its field amplitude and as you surely know there is a non-zero probability to detect the harmonic oscillator off the origin, even if it's in the ground state.

I think the Casimir effect is usually considered an experimental confirmation of this but I'm not sure.

 

[meopemuk]

This sounds reasonable but it's not what quantum field theory says. QFT says that a photon is a harmonic oscillator of its field amplitude and as you surely know there is a non-zero probability to detect the harmonic oscillator off the origin, even if it's in the ground state.

Yes, this is how it's written in QFT textbooks. However, these explanations never made sense to me. Traditional QFT is formulated in terms of "bare vacuum" and "bare particles". These states have very distant relationships to the "physical vacuum" and "physical particles" that we observe in nature. Bare states are not even eigenstates of the Hamiltonian. So, I am not sure how one can build physical interpretations based on these unphysical states.

In my posts I was trying to advertize a different viewpoint on QFT. This viewpoint is based on the "dressed particle" approach in which "physical" vacuum and "physical" 1-particle states play the central role. In this approach, there are no physical particles in the physical vacuum, and, certainly, there are no any "harmonic oscillators" there. I think that the "dressed particle" picture better corresponds to physical reality than the traditional "bare particle" picture.

I think the Casimir effect is usually considered an experimental confirmation of this but I'm not sure.

Yes, the Casimir effect is often cited as an evidence for non-trivial properties of vacuum. Frankly, I am not convinced. It seems more logical to explain forces between material bodies by interactions between constituent atoms rather than by properties of the vacuum between them. I don't have my own theory of the Casimir effect, but there are some people holding a similar point of view:

R. L. Jaffe, "The Casimir effect and the quantum vacuum" http://www.arxiv.org/abs/hep-th/0503158

Eugene.

 

[genneth]

In my posts I was trying to advertize a different viewpoint on QFT. This viewpoint is based on the "dressed particle" approach in which "physical" vacuum and "physical" 1-particle states play the central role. In this approach, there are no physical particles in the physical vacuum, and, certainly, there are no any "harmonic oscillators" there. I think that the "dressed particle" picture better corresponds to physical reality than the traditional "bare particle" picture.

Come on, Eugene: you don't have to push the dressed particle theory at *every* opportunity. We can discuss and criticize the interpretation of "standard" QFT without confusing the issue with possible extensions.

OOO: however, Eugene is correct in that what QFT calls particle states are not the physically measurable states -- this is in fact well accepted. They approximate the measured states when the particles are far from any interaction. In particular, they're *very* good approximations when you're measuring the particles going in and out of a collision in a particle accelerator. The interaction occurs in a tiny volume of space while the detectors are metres away. What I believe Eugene is criticising is the fact that QFT is founded on making accurate predictions about high energy particle collisions, and in doing so actually neglects other, just as important applications, like finding the time evolution of a system. Thus, the issue of interpretation is a very serious one in QFT once you move beyond a particle accelerator. To be even more frank, it's actually already an issue in its application to QCD, where the asymptotic states are not free -- thus leaving things like quarks in an ontologically difficult place.

 

[meopemuk]

Come on, Eugene: you don't have to push the dressed particle theory at *every* opportunity. We can discuss and criticize the interpretation of "standard" QFT without confusing the issue with possible extensions.

I am sorry, I am possibly too passionate about "dressed particles", so I want to tell everybody about them at every occasion.

On the other hand, I strongly believe that if we are going to discuss physical vacuum in terms of all these traditional non-observable concepts (bare particles, harmonic oscillators, zero-point vibrations, etc.) we will never leave the state of permanent confusion.

What I believe Eugene is criticising is the fact that QFT is founded on making accurate predictions about high energy particle collisions, and in doing so actually neglects other, just as important applications, like finding the time evolution of a system. Thus, the issue of interpretation is a very serious one in QFT once you move beyond a particle accelerator.

You are absolutely right.

Eugene.

 

[OOO]

Come on, Eugene: you don't have to push the dressed particle theory at *every* opportunity. We can discuss and criticize the interpretation of "standard" QFT without confusing the issue with possible extensions.

OOO: however, Eugene is correct in that what QFT calls particle states are not the physically measurable states -- this is in fact well accepted. They approximate the measured states when the particles are far from any interaction. In particular, they're *very* good approximations when you're measuring the particles going in and out of a collision in a particle accelerator. The interaction occurs in a tiny volume of space while the detectors are metres away. What I believe Eugene is criticising is the fact that QFT is founded on making accurate predictions about high energy particle collisions, and in doing so actually neglects other, just as important applications, like finding the time evolution of a system. Thus, the issue of interpretation is a very serious one in QFT once you move beyond a particle accelerator. To be even more frank, it's actually already an issue in its application to QCD, where the asymptotic states are not free -- thus leaving things like quarks in an ontologically difficult place.

I have to apologize if I have missed some point about bare particles. Since I'm doing (or at least try to do...) lattice calculations where everything is (or at least seems to be) so easy, I'm a bit reluctant against concepts stemming from perturbation theory. So I guess you mean renormalization has something to do with the question if we measure non-zero fields in vacuum, right ?

 

[OOO]

What I believe Eugene is criticising is the fact that QFT is founded on making accurate predictions about high energy particle collisions, and in doing so actually neglects other, just as important applications, like finding the time evolution of a system.

But isn't the time evolution defined by adding up all "path" amplitudes ? That's what I've learned so far. Moreover in lattice field theory this principle is driven to perfection by the transition to euclidean space and the subsequent interpretation of the "path" amplitude as a virtually classical Boltzmann probability. I cannot see how this could emerge if the time evolution was not determined.

 

[meopemuk]

I have to apologize if I have missed some point about bare particles. ... So I guess you mean renormalization has something to do with the question if we measure non-zero fields in vacuum, right ?

No, renormalization by itself does not provide you the physical vacuum and 1-particle states. The renormalization is simply addition of (infinite) mass and charge renormalization counterterms to the Hamiltonian. So, in the renormalized theory you have the same bare particles, but now with infinite masses and charges. It is very difficult to speak about any physical interpretation in such an unphysical basis.

The only way (known to me) to formulate the theory in terms of physical observable states is to perform an additional unitary dressing transformation of the Hamiltonian (with renormalization counterterms), i.e., to introduce the dressed particle picture.

Eugene.

 

[OOO]

No, renormalization by itself does not provide you the physical vacuum and 1-particle states. The renormalization is simply addition of (infinite) mass and charge renormalization counterterms to the Hamiltonian. So, in the renormalized theory you have the same bare particles, but now with infinite masses and charges. It is very difficult to speak about any physical interpretation in such an unphysical basis.

The only way (known to me) to formulate the theory in terms of physical observable states is to perform an additional unitary dressing transformation of the Hamiltonian (with renormalization counterterms), i.e., to introduce the dressed particle picture.

Eugene.

My problem is that I'd prefer to deepen my knowledge of standard QFT before I delve into non-standard works with about 400 pages...

So genneth told me that it is well accepted that the states we primarily describe in theory are not the ones we measure. What key words do I have to search for or, more specifically, which chapter do I have to read in one of the standard textbooks in order to understand this better ?

 

[genneth]

My problem is that I'd prefer to deepen my knowledge of standard QFT before I delve into non-standard works with about 400 pages...

So genneth told me that it is well accepted that the states we primarily describe in theory are not the ones we measure. What key words do I have to search for or, more specifically, which chapter do I have to read in one of the standard textbooks in order to understand this better ?

Useful keywords might be something along the lines of "locality of measurement in QFT". The basic problem is that operators which measure the Fock states need to have infinite spacetime extent. This paper explains it beautifully: http://arxiv.org/abs/gr-qc/0409054 Unfortunately it's not published, but it does reference papers that talk more about the problem (and less about the solution) which are published.

For more stuff on criticism of QFT and quantum mechanics in general: http://arxiv.org/abs/quant-ph/0609163

It's important to read these things critically however: authors often have a bias even when they don't want to. That one above has a heavy dose of Bohm.

 

[OOO]

Useful keywords might be something along the lines of "locality of measurement in QFT". The basic problem is that operators which measure the Fock states need to have infinite spacetime extent. This paper explains it beautifully: http://arxiv.org/abs/gr-qc/0409054 Unfortunately it's not published, but it does reference papers that talk more about the problem (and less about the solution) which are published.

For more stuff on criticism of QFT and quantum mechanics in general: http://arxiv.org/abs/quant-ph/0609163

It's important to read these things critically however: authors often have a bias even when they don't want to. That one above has a heavy dose of Bohm.

Thanks, I actually had textbooks in mind when I remembered you telling about things being "well accepted". But I'll take a look at those. Yes, I'm aware of that Bohm bias. I have also dedicated some time to studying Bohm and although interesting one has to take it or rather its advocates with a grain of salt.

 

[genneth]

Thanks, I actually had textbooks in mind when I remembered you telling about things being "well accepted". But I'll take a look at those. Yes, I'm aware of that Bohm bias. I have also dedicated some time to studying Bohm and although interesting one has to take it or rather its advocates with a grain of salt.

Yes, I would have preferred to give a textbook reference too. Unfortunately, textbooks tend to not deal with issues which are currently accepted as issues, but for which an accepted resolution is not available -- after all, it's more confusing for someone trying to learn from it. It's one of those things where almost everyone you talk to knows about the problem, but no one seems to know where is an authoritative source. I'm going to keep hunting for a while, to see if I can find something...

 

[meopemuk]

But isn't the time evolution defined by adding up all "path" amplitudes ?

The most fundamental way to define time evolution in quantum mechanics or QFT is through the Hamiltonian. It is not an accident that the Hamiltonian is also called "the generator of time translations". If | \Psi(0) \rangle is a state vector at time t=0, then at later time the state vector is (in the Schroedinger representation)

|\Psi(t) \rangle = \exp(\frac{i}{\hbar}Ht) |\Psi(0) \rangle...(1)

Perhaps you can describe the time evolution in an alternative way (with path integrals, etc.), but whatever you do it should be equivalent to eq. (1).

Now, the bare particle Hamiltonian of QFT will immediately lead to a trouble with eq. (1). For example, in the creation/annihilation operator representation the Hamiltonian of QED has the form

H = H_0 + a^{\dag}b^{\dag}c^{\dag} + \ldots...(2)

where H_0 is the free particle Hamiltonian, a^{\dag}b^{\dag}c^{\dag} describes simultaneous creation of 3 particles (electron + positron + photon), and the ellipsis denotes (a lot of) other terms, which are not relevant at this point. Substituting (2) into (1) we can obtain the following time evolution of the bare vacuum state

|0(t) \rangle = \exp(\frac{i}{\hbar}Ht) |0 \rangle \approx (1+ \frac{it}{\hbar}(H_0 + a^{\dag}b^{\dag}c^{\dag}) |0 \rangle = |0 \rangle + \frac{it}{\hbar} a^{\dag}b^{\dag}c^{\dag} |0 \rangle

So, at nonzero t we obtain a non-zero contribution from the 3-bare-particle state a^{\dag}b^{\dag}c^{\dag} |0 \rangle. Three new particles are created spontaneously from the vacuum. I consider this a sign of a serious trouble, because nobody has ever seen experimentally creation of extra particles from the vacuum and 1-particle states. I believe that vacuum and 1-particle states must be eigenvectors of the full Hamiltonian. Only "dressed" vacuum and 1-particle states satisfy this requirement.

My problem is that I'd prefer to deepen my knowledge of standard QFT before I delve into non-standard works with about 400 pages...

So genneth told me that it is well accepted that the states we primarily describe in theory are not the ones we measure. What key words do I have to search for or, more specifically, which chapter do I have to read in one of the standard textbooks in order to understand this better ?

Unfortunately, I haven't seen a clear explanation of the problems with bare particles in QFT in textbooks. In standard QFT, where you are interested only in the scattering (S-)matrix, the unphysical character of bare states is not a pressing issue, and one can perform sensible calculations without paying attention to such "subtleties". By the way, the 400+ pages that you mentioned were written for readers who don't have any previous knowledge of QFT, so they may be less intimidating than they look.

Eugene.

 

[OOO]

|0(t) \rangle = \exp(\frac{i}{\hbar}Ht) |0 \rangle \approx (1+ \frac{it}{\hbar}(H_0 + a^{\dag}b^{\dag}c^{\dag}) |0 \rangle = |0 \rangle + \frac{it}{\hbar} a^{\dag}b^{\dag}c^{\dag} |0 \rangle

So, at nonzero t we obtain a non-zero contribution from the 3-bare-particle state a^{\dag}b^{\dag}c^{\dag} |0 \rangle. Three new particles are created spontaneously from the vacuum. I consider this a sign of a serious trouble, because nobody has ever seen experimentally creation of extra particles from the vacuum and 1-particle states. I believe that vacuum and 1-particle states must be eigenvectors of the full Hamiltonian.

That confuses me since the vacuum is defined as the lowest eigenstate of the Hamiltonian. So your claim amounts to saying that either you are working with the false vacuum state or the Hamiltonian of QED does not possesses a lowest eigenstate.

By the way, the 400+ pages that you mentioned were written for readers who don't have any previous knowledge of QFT, so they may be less intimidating than they look.

I acknowledge that. Nevertheless you can't tell what you need and what you don't by looking at the front cover.

 

[meopemuk]

That confuses me since the vacuum is defined as the lowest eigenstate of the Hamiltonian. So your claim amounts to saying that either you are working with the false vacuum state or the Hamiltonian of QED does not possesses a lowest eigenstate.

The bare vacuum state (which I denoted |0 \rangle) is the lowest (zero) energy eigenstate of the free Hamiltonian H_0. However, as you correctly pointed out, it is not an eigenstate (lowest energy or otherwise) of the full interacting Hamiltonian H. Actually, traditional QFT doesn't bother to find the true vacuum state (the eigenstate of H). In order to calculate the S-matrix elements (which is the major goal of the traditional QFT)

S_{if} = \langle 0 | abc \ldots S \ldots c^{\dag} b^{\dag} a^{\dag} | 0 \rangle

it is sufficient to know the bare vacuum | 0 \rangle, bare particle creation and annihilation operators a, a^{\dag}, \ldots, and the expression of the scattering operator S through these bare particle operators.

Eugene.

 

[Maxwell's Beard]

It doesn't sound like you're talking about classical aetherists at all! They were rejecting the notion of an underlying field, and instead asserting that the electromagnetic field describes the bulk properties of an underlying material.

e.g. the stereotypical line "How can you have a wave if there isn't anything for it to wave through?"

I write like I talk I guess so a lot is lost if we aren't in the same room together. I have said numerous times that these guys were wrong, wrong, wrong in their conclusions and definitions. My assertion is that they may not have been in the right ballpark, but they were in the right league. The aetherists believed that even a vacuum wasn't empty, the quantum field theorists posit the same.

 

[meopemuk]

Maxwell's Beard,

I think that fundamentally you are right. Modern physicists tend to ascribe to the empty space (vacuum) properties of some material substance/medium/continuum/... However, they will swear that this has nothing to do with the long discredited aether. You should take these statements with healthy scepticism.

The vacuum with non-trivial properties appears in different sections of modern physics. We already discussed the "vacuum polarization" in basic QFT. Those studying "spontaneous symmetry breaking" in quantum gauge theories may tell you that physical vacuum is "like superconductor". In general relativity it is assumed that the space-time has certain properties, including curvature, momentum-energy, etc. Many people believe that at the Planck scale one would find some non-trivial space-time structures, like discreteness, non-commutativity, and who knows what...

All these models of vacuum are extremely complicated, and what is worse, they have no direct experimental manifestations. In these respects, the similarities with the 19th century aether are striking. You are certainly right about that. In my opinion, the weapon against "physical vacuum" should be the same as Einstein used in 1905 against the aether - focus on experimental measurements.

Eugene.

 

[Hurkyl]

I write like I talk I guess so a lot is lost if we aren't in the same room together. I have said numerous times that these guys were wrong, wrong, wrong in their conclusions and definitions. My assertion is that they may not have been in the right ballpark, but they were in the right league. The aetherists believed that even a vacuum wasn't empty, the quantum field theorists posit the same.

That's an incredible stretch. As far as comparisons go, it doesn't seem much better than saying that anyone who thinks that the universe contains stuff with properties has an intuitive grasp of {insert any scientific theory here}.

 

[OOO]

The bare vacuum state (which I denoted |0 \rangle) is the lowest (zero) energy eigenstate of the free Hamiltonian H_0. However, as you correctly pointed out, it is not an eigenstate (lowest energy or otherwise) of the full interacting Hamiltonian H. Actually, traditional QFT doesn't bother to find the true vacuum state (the eigenstate of H). In order to calculate the S-matrix elements (which is the major goal of the traditional QFT)

S_{if} = \langle 0 | abc \ldots S \ldots c^{\dag} b^{\dag} a^{\dag} | 0 \rangle

it is sufficient to know the bare vacuum | 0 \rangle, bare particle creation and annihilation operators a, a^{\dag}, \ldots, and the expression of the scattering operator S through these bare particle operators.

Eugene.

As I have indicated I haven't cared much about perturbation theory yet. But one thing I tentatively assume: If one uses the vacuum of the free Hamiltonian one is not to expect that it is also the vacuum of the coupled Hamiltonian.

Thus I cannot see any contradiction in what you have said:

|0(t) \rangle = \exp(\frac{i}{\hbar}Ht) |0 \rangle \approx (1+ \frac{it}{\hbar}(H_0 + a^{\dag}b^{\dag}c^{\dag}) |0 \rangle = |0 \rangle + \frac{it}{\hbar} a^{\dag}b^{\dag}c^{\dag} |0 \rangle

So, at nonzero t we obtain a non-zero contribution from the 3-bare-particle state a^{\dag}b^{\dag}c^{\dag} |0 \rangle. Three new particles are created spontaneously from the vacuum. I consider this a sign of a serious trouble, because nobody has ever seen experimentally creation of extra particles from the vacuum and 1-particle states. I believe that vacuum and 1-particle states must be eigenvectors of the full Hamiltonian.

 

[meopemuk]

If one uses the vacuum of the free Hamiltonian one is not to expect that it is also the vacuum of the coupled Hamiltonian.

Why not? What is the reason to think that interaction should change the definition of vacuum and 1-particle states? The word "inter-action" itself suggests that this is something present when there are two or more particles. Zero-particle and 1-particle states should not care whether there is interaction or not. This means that interaction Hamiltonians should yield zero when acting on such states, and this is the main postulate of the "dressed particle" approach.

If you assume that interaction is present also in the vacuum and 1-particle states, i.e., that "bare" and "physical" vacuum and particles are different, then you'll need to deal with ugly problems of "vacuum polarization", "self-energies", renormalization, etc. All these problems don't have any physical meaning, in my opinion, and they are absent in the "dressed particle" approach.

Eugene.

 

[OOO]

Why not?

Well, because you said so. In the equation

H = H_0 + a^{\dag}b^{\dag}c^{\dag} + \ldots

H and H0 can clearly only have the same vacuum state (with the same vacuum energy) if

(a^{\dag}b^{\dag}c^{\dag} \ldots)|0\rangle = 0

but then these terms do not create any particles from the vacuum.

 

[meopemuk]

Well, because you said so. In the equation

H = H_0 + a^{\dag}b^{\dag}c^{\dag} + \ldots

H and H0 can clearly only have the same vacuum state (with the same vacuum energy) if

(a^{\dag}b^{\dag}c^{\dag} \ldots)|0\rangle = 0

but then these terms do not create any particles.

Here is an example of the Hamiltonian, which, in my opinion, is entirely satisfactory

H = H_0 + V
V = a^{\dag}b^{\dag}ab + a^{\dag}b^{\dag}c^{\dag}ab + a^{\dag}b^{\dag}abc...(1)

Clearly

V | 0 \rangle = 0
V a^{\dag}| 0 \rangle = 0
V b^{\dag}| 0 \rangle = 0
V c^{\dag}| 0 \rangle = 0

so the interaction does not act in the vacuum and 1-particle states. The first term in (1) describes direct interaction between particles a and b. The second term describes emission of particle c in a+b collisions. The third term in (1) describes absorption of particle c in a+b collisions. More complicated particle-number-conserving and non-conserving terms can be added to (1), if needed.

It is however important that one should avoid terms of the type a^{\dag}b^{\dag}c^{\dag}, a^{\dag}c^{\dag}a, etc. which have non-trivial actions on 0-particle and 1-particle states. There is no experimental evidence that particles can be spontaneously created from vacuum and (stable) 1-particle states. So, the presence of such terms in the Hamiltonian is not welcome.

Eugene.

 

[gamburch]

Having one's aether and living in it too.

The following is an exerpt from a paper I have recently written on this very subject. It's a little long, but if you are really interested I can e-mail a copy of the whole thing and would like to get your feedback. I believe there is an aether, but not of the kind considered to date.

Albert Einstein described a treatment of physics consistent with the results of Michelson and Morley in the Special Theory of Relativity. In this theory all observers in motion with respect to each other, surprisingly, measure the same rules for all physical laws in their own frames of reference. This democracy among observers in motion is inconsistent with the concept of a three-dimensional aether. With a three-dimensional aether it is to be expected that different motions with respect to the aether will result in measurably different effects upon the propagation of light and other physical phenomena as seen by different observers, each in their own frames of reference. Einstein's Special Theory, however, represents there are no such measurable effects arising from motions by different observers with respect to any supposed aether thus contradicting the properties of the aethers envisioned at the time. The Special Theory has been shown to be in accord with experiment in all respects tested to date. As a result physics of the 20th Century was, for the most part, bereft of aethers.

In spite of the experimental success of the Special Theory, however, some of the epistemological beauty of physics has been lost by its validation. With Special Relativity all observers see surrounding space as stationary with respect to them. In other systems, for example, a sound source moving through air, a disturbance takes place with respect to the surrounding medium. Cause and effect are easily and readily imagined and measured. With Relativity, however, different observers, irrespective of their motions, see no movement relative to the medium in which they move. Such thoughts suggest that the aether is either carried with the body or arises from some other rather mysterious cause that is not subject to normal analogy. The first option was long ago discredited by means of experiment. The state of present knowledge is the latter.

In this paper we propose a different way to address these matters and seek to describe physical systems in such a way that disturbances from moving objects propagate with respect to the aether in which the disturbances arise, thus rectifying common sense with physical theory. Yet our model supports Relativity Theory with the fact that observers in motion with respect to each other each appear to be stationary with respect to happenings in the space they observe. We propose the existence of a four-dimensional aether in a space with four spatial coordinates and a time parameter so that properties of the aether at each point may vary both in space and time; which “time” is assumed uniform for all parts of the aether and increasing at a constant rate. Disturbances in the aether may propagate with reference to the aether. Thus if a signal is initiated in the aether by either a stationary (with respect to the aether) or moving object, the signal propagates in the same way in the stationary aether. The object moving with respect to the aether has any disturbance it initiated move with respect to the object after the initiation since the disturbance is propagating in the stationary aether. This situation is like acoustics or waves in a river. The appealing aspect of this situation is that, in initiating a signal, an object operates upon something, in this case the aether. Such an interaction is local. The results do not depend upon the rate of motion of the object in the aether since the emission, by its nature, is local. One thus maintains a simple and clean concept of causality in the case of four-space aether discussed herein.

In this four-space let us conceive of a particle (as opposed to the object of the previous paragraph) as a point moving on a path in the four-space. The particle’s size in the three-space perpendicular to its direction of travel is assumed to be small. The path can be in any direction in four-space and, for Special Relativity, need not be curved. The particle travels along this path at the speed of wave propagation in the aether with time determining its position along the path. Since particles traveling more or less in the same direction at nearly the same time can be put together to make observers (all observers are assumed to be collections of particles), we shall consider that all observers are moving at the same rate as a particle, and this rate is the same as signal propagation in the aether.

Since observers communicate with each other with signals traveling at the same rate as their speed with respect to the aether, we must examine the effects of motion of each observer with respect to the aether and each other. Observers following paths in different directions of limited angle with respect to the each other appear to be moving with respect to each other. Since the aether is isotropic and all observers are moving at the same speed with respect to the aether, we should expect each to see the same situation as any other. Furthermore, since each observer is moving at the same speed as his means of communication in the four-space, the coordinate in his direction of motion is annihilated so that he observes a three-space. This three-space, with its fourth coordinate obscured by being in the direction of travel of the observer, can rotate in four-space to change its direction of motion with respect to other observers. By these means observers see the space of Special Relativity. We attempt to make these matters somewhat more clearly in the body of the paper using some simple diagrams.

 

[cyberdyno]

If the aether is physical but non-material, with no landmarks, how could it represent a fixed frame?

Einstein was right, the Universe is background free.