Particle States in Quantum Field Theory: Local vs. Global Approximations

[Naty1]

For instance an accelerated observer will see more particles (Unruh).

http://arxiv.org/abs/gr-qc/0409054
What is a particle?

(I don't have a specific question here, but observations/insights on the above paper or following excerpts are welcome...)

Marcus posted the above in another thread...And I do wish he would STOP that type of thing because everytime I read another paper I discover something else I had not thought about and therefore clearly do not understand! (just joking,partly, but it never seems to end...peeling a layer simply reveals yet another layer...)

On curved spacetime, in general there is no symmetry group, no preferred set of modes and no preferred decomposition into positive and negative frequency.
As a consequence, there is no preferred vacuum state, and the interpretation of the field states in term of particles appears to be difficult...The defining properties of the particles, mass and spin (or helicity), are indeed the invariants of the Poincar´e group. Now, strictly speaking we do not live in a Poincar´e invariant region of spacetime: does this means that, strictly speaking, the world around us has no particles?

OMG, not only is space and time frame dependent, seems like particles are too...and in more ways than simply the virtual particle pairs of Unruh...

Such arbitrariness and ambiguity of the particle concept have led some theoreticians like Davies to affirm that “particles do not exist” , a view shared by several relativists. ... other theoreticians ... who hold that QFT is fundamentally a formalism for describing processes involving particles, such as scattering or decays... A typical example of this position is Weinberg who cannot certainly be suspected of ignoring general relativity. These difficulties become serious in a background-independent quantum context. For instance, in loop quantum gravity quantum states of the gravitational field are described in terms of a spin network basis. Can we talk about gravitons, or other particle states, in loop quantum gravity. A common view among relativists is that we cannot, unless we consider the asymptotically flat context.

So there are some fundamental differences among theorists about what particles are...

...we observe that if the mathematical definition of a particle appears somewhat problematic, its operational definition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier.

So we are back to the old reliable, "I don't know exactly what it is, but at least I can measure whatever it is...thank heaven for "observables"..."

Therefore, strictly speaking there are two distinct notions of particles in QFT. Local particle states correspond to the real objects observed by finite size detectors. ... On the other hand, global particle states...can be defined only under certain conditions. Global particle states are simpler to define and they approximate well the local particle states detected by local measurements. Therefore the global particle states, when they are available, give a good approximate description of the physics of the “real” particles detected by the detectors...In the paper we illustrate the difference between these two classes of states, and discuss their relation. The precise sense in which global states approximate local particle states is subtle.

This sounds reminisescent not only of the Unruh effect but also things like "relativity of simultaneity" and the apparent affects of gravity (curved spacetime) on local versus distant time...is nothing constant in this universe except lightspeed?

 

[marcus]

Heh heh Thanks for the backhand compliment, Naty.

I think besides the first all your other quotes are from the Rovelli Colosi 2004 paper.
I'm not sure there is anything very new or controversial. But Rovelli gave a nice talk with the same title at Abhay Ashtekar's birthday party conference, the 2008 "Abhayfest". I can get a link, if you want.
It sort of updates and sharpens the message of the paper, and there are Q&A with the audience afterwards.

I guess we all know that for example gravitons have no fundamental existence and gravity can be analyzed using gravitons (as a mathematical tool) only in restricted situations. Admittedly the particle idea is very useful as an analytical tool in situations where it applies.

As a general rule the world is not made of particles, it is more correct and less confusing to say that it is made of fields. Unless I'm mistaken all or most of us at the Forum realize this?

 

[meopemuk]

As a general rule the world is not made of particles, it is more correct and less confusing to say that it is made of fields. Unless I'm mistaken all or most of us at the Forum realize this?

I don't count myself in this group. As Naty1's quote said "particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier." This means that particles (not some mysterious fields) are the objects studied by real experimental physics. If "curved spacetime" does not agree with the particle concept, so bad for the "curved spacetime".

Eugene.

 

[rewebster]

think of particles -> matter, is like dust -> dust bunnies

[that's just the Buddhist in me though]

 

[marcus]

...As Naty1's quote said "particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier."...

There we go! You are echoing what Carlo Rovelli, the LQG guy, says. This is what he says:
==quote==
...we observe that if the mathematical definition of a particle appears somewhat problematic, its operational definition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier...
==endquote==

You are agreeing with something taken out of context however. Maybe you should read the paper itself, that Naty was quoting.

http://arxiv.org/abs/gr-qc/0409054
What is a particle?
Daniele Colosi, Carlo Rovelli
(Submitted on 14 Sep 2004)
"Theoretical developments related to the gravitational interaction have questioned the notion of particle in quantum field theory (QFT). For instance, uniquely-defined particle states do not exist in general, in QFT on a curved spacetime. More in general, particle states are difficult to define in a background-independent quantum theory of gravity. These difficulties have lead some to suggest that in general QFT should not be interpreted in terms of particle states, but rather in terms of eigenstates of local operators. Still, it is not obvious how to reconcile this view with the empirically-observed ubiquitous particle-like behavior of quantum fields, apparent for instance in experimental high-energy physics, or "particle"-physics. Here we offer an element of clarification by observing that already in flat space there exist --strictly speaking-- two distinct notions of particles: globally defined n-particle Fock-states and *local particle states*. The last describe the physical objects detected by finite-size particle detectors and are eigenstates of local field operators. In the limit in which the particle detectors are appropriately large, global and local particle states converge in a weak topology (but not in norm). This observation has little relevance for flat-space theories --it amounts to a reminder that there are boundary effects in realistic detectors--; but is relevant for gravity. It reconciles the two points of view mentioned above. More importantly, it provides a definition of local particle state that remains well-defined even when the conventional global particle states are not defined. This definition plays an important role in quantum gravity."As in any mathematical science there must be both operational definitions AND consistent mathematical models. Operationally, the particle is equated with the detection event. But can a complete mathematical picture be made exclusively of detection events?

Because context is often helpful to have, let me quote the entire third paragraph on page 2 of the Rovelli Colosi paper:

==quote, page 2==
To address these questions, we observe that if the mathematical definition of a particle appears somewhat problematic, its operational definition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier. Now, strictly speaking a particle detector is a measurement apparatus that cannot detect a n-particle Fock state, precisely because it is localized. A particle detector measures a local observable field quantity (for instance the energy of the field, or of a field component, in some region). This observable quantity is represented by an operator that in general has discrete spectrum. The particles observed by the detector are the quanta of this local operator. Our key observation is that the eigenstates of this operator are states of the quantum field that are similar, but not identical, to the Fock particle states defined globally.
==endquote==

 

[meopemuk]

A particle detector measures a local observable field quantity (for instance the energy of the field, or of a field component, in some region). This observable quantity is represented by an operator that in general has discrete spectrum. The particles observed by the detector are the quanta of this local operator. Our key observation is that the eigenstates of this operator are states of the quantum field that are similar, but not identical, to the Fock particle states defined globally.
==endquote==

I like more the logic presented in Weinberg's "The quantum theory of fields" vol.1: The primary objects are particles described by irreducible unitary representations of the Poincare group. For realistic systems with varying numbers of particles we build the Fock space as a direct sum of products of irreducible representations spaces. Then the sole purpose of quantum fields (=certain linear combinations of particle creation and annihilation operators) is to provide "building blocks" for interacting generators of the Poincare group in the Fock space. In this logic quantum fields are no more than mathematical tools.

I think that gravity can fit into this logic pretty well if we reject the idea of "curved spacetime".

Eugene.

 

[tom.stoer]

The method to use unitary representations of the Poincare group is stil OK in curved spacetime. You build a Fock space usingfield operators (creation and annihilation operators) and classify the locally measured excitations according to these representations. So locally the particle concept is well-defined.

The problem arises when you want to make statements which are globally valid, or when you change the reference frame as you do in the Unruh effect. Then you find that you haver to change Hilbert spaces. A zero-particle state (vacuum) is not mapped to another zero-particle state, so the two vacua are not one-to-one. The problem is that constructing the states uses a certain Minkowski vacuum which is not globally valid (as you can see in the Hawking effect). In the very end the Unruh and the Hawking effect have a rather similar origin (according to GR acceleration and gravitation are identical, the Unruh effect has something to do with a horizon as well)

But you should keep in mind that similar affects are knwon already from QFT in flat spacetime, e.g. neutrino oscillations: again you classify particles according to some representations of symmetry groups, but unfortunately the states in one irr.-rep. are mixed when you go to the other irr.-rep. The number of particles is not changed, but the particles states are mixed causing the oscillations.

So in the later case you can say that the transformation mixes states within one N-particle subspace, whereas in the Unruh-case the transformation mixes the different N-particle subspaces.

 

[meopemuk]

The method to use unitary representations of the Poincare group is stil OK in curved spacetime.

I am against using words "Poincare group" and "spacetime" in the same sentence.

In the Weinberg's approach the Poincare group is NOT the group of isometries of the Minkowski spacetime. It is a group of transformations connecting different inertial observers. The fact that this group coincides with the group of isometries of the 4D pseudo-Euclidean spacetime is just a mathematical coincidence.

If we want to build a relativistic theory of an electromagnetic system, e.g., the hydrogen atom, we must build a unitary representation of the Poincare group in the Hilbert space of the two particles. This guarantees that system's descriptions by different inertial observers are correctly connected with each other.

Quite similarly, if we want to build a theory of gravitational interaction between the electron and the proton we need to build a (different) unitary representation of the Poincare group in the 2-particle Hilbert space. The fact that the electron and the proton interact gravitationally does not make the idea of inertial observer invalid. There is no need to introduce non-inertial observers and the curved spacetime.

The same is true in a less obvious example of a two-particle system - Sun+Earth. The ideas of inertial observers, the Poincare group, and its representations remains perfectly valid in this case as well. There is no fundamental difference between the Sun+Earth and proton+electron cases.

Eugene.

 

[Fra]

There is no need to introduce non-inertial observers

I don't follow this conclusion, but I'll try to see if I can guess.

Quite similarly, if we want to build a theory of gravitational interaction between the electron and the proton we need to build a (different) unitary representation of the Poincare group in the 2-particle Hilbert space. The fact that the electron and the proton interact gravitationally does not make the idea of inertial observer invalid.

It seems your view of gravity here is an "external view", where the observer itself is not subject to gravitational interactions but he is observing a system which has "internally" gravitational interplay?

It seems then you constrain the "set of possible observers", to those where your scheme makes sense: ie. an external observer, making regular QM-style measurements on a small subsystem?

How does cosmological pictures fit into your view? Ie. the situation where a complex controlled laboratory is not available, simply because the observer itself is a small subsystem immersed in an unkonwn environment. Do you reject that scenario as outside science?

Not to change the topic but as I see it, we have the same core issue here as in the other thread.

It seems you stick to an extrinsic view, rather and intrinsic view. If we keep inflating the imaginary context of the extrinsic view, I see that we can keep a form of "simplicity" but this method seems to me to be in violation to the measurement ideal that you also seem to hold dear?

Ie. shouldn't the INFORMATION of the STATE OF transformations and symmetries in the set of all possible states of inforamtion about the system of study also be subject to the same measurement principle, rather than realism?

/Fredrik

 

[Dmitry67]

Ha Ha. Unruh effect is cool.
It is a weapon against old school saying that "only real particles are real, virtual particles are just math"

 

[tom.stoer]

In the Weinberg's approach the Poincare group is NOT the group of isometries of the Minkowski spacetime. It is a group of transformations connecting different inertial observers.

It depends whether you talk about active or passive transformations.

All what I want to say is that you can construct the representations and this works locally, but not globally. Your problem with Minkowski spacetime and Poincare invariance fades away as soon as you introduce curvature, because the n Poincare invariance is no longer a global symmetry (nevertheless you can construct a gravitational gauge theory using Poincare invariance as local gauge group).

It is like asymptotic symmetries in particle physics (e.g. chiral symmetry is only an asymptotic symmetry in the naive quark model, nevertheless it is very usefull). You know that something breaks the symmetry, nevertheless you are using this symmetry to classify particles, put a structure on the Hilbert space etc. In a second step you calculate the effects of the symmetry breaking. In the case of curvature and acceleration its not only the "type" of the particle that changes, it's the "concept" of a particle.

But the particle concept based on asymptotic plane waves is a mathematical artefact. It is heavily used in perturbative calculations but is less usefull in non-perturbative regimes, e.g. in strong interactions. In strong interactions there is no known regime where it makes sense to talk about gluons as free (asymptotically observable) particles only. Because you have never seen a gluon, you are not bothered by that fact. In GR the surprise is due to the fact that there IS a regime where the particle concept makes sense, but that there are other regimes where it does NOT.

 

[Fra]

All what I want to say is that you can construct the representations and this works locally, but not globally.

To connect the different phrasings: local vs global is a different view of intrinsic vs extrinsic but where it's related as I see it.

The global connection of local observables is what I called "extrinsic".

The main distinction I make between local/global and instrinsic/extrinsic is that local/global somehow refers to position or distance on a spacetime or manifold. intrinsic/extrinsic as I think of of instead refers to what's decidable or at hand and what's not.

Extrinsic view then represents information that is not encoded by an observing system, it's just an imagined embedding. Similiarly there is an ambigousness in the global connections given only a local info.

(?) I think what Meopemuk suggested is that given a sufficiently complex embedding, the gravitatioanl interaciton inside the system can still be described relative to a massive reference. Because then a "constrained" semi-global descirption can still be encoded locally, if by local we mean beloning to the external context (the qualifying context). And this works fine for subsystems, but not for cosmological models or if you consider that the theory literally LIVES inside an horizon, embedded in large unkonwn environment.

/Fredrik

 

[Naty1]

I almost did not post the original excerpts thinking nobody would be much interested...but it seemed interesting to me and I'm gald I did...and it reminded me again about 'local' versus 'global' reality...

I guess we all know that for example gravitons have no fundamental existence and gravity can be analyzed using gravitons (as a mathematical tool) only in restricted situations.

I'm not sure I understand the first part entirely and did not know about the second... "restricted" in what sense??

As a general rule the world is not made of particles, it is more correct and less confusing to say that it is made of fields. Unless I'm mistaken all or most of us at the Forum realize this

I'd not readily agree that anybody knows so much about any of the fundamentals in physics...especially what "exists" or doesn't and what's "real" or not...If there is anything I've learned over the last six or eight years of catching up on physics (at least a little) it's that things at the most fundamental levels are NOT nearly so simple as they appear... hence many theories, many mathematuical constructs, many interpretations...which description "fits" usually seems to be associated with the theory you start with and the situation(s) you are describing...

 

[marcus]

"restricted" in what sense??
...

static typically flat geometry. The underlying geometry is restricted to some idealization.

...If there is anything I've learned over the last six or eight years of catching up on physics (at least a little) it's that things at the most fundamental levels are NOT nearly so simple as they appear...

I'll buy that! That's part of what I was trying to say. You can't just naively accept idealizations---they are all approximations with limited applicability. But I also think there are questions of degree. Maybe all concepts are incorrect and confusing but some conceptualizations are more incorrect and confusing than others.

 

[tom.stoer]

Particles appear in rare situations, namely when they are registered.

The concept of (virtual) particles is useful in rare cases, namely when one wants to describe measurements, when one talks about plane wave states (asymptotically), effects in low order perturbation theory etc.

Even in standard QFT there are effects like instantons, condensates or vacuum expectation values, confinement etc. which cannot be described by particles but by fields (or field operators).

In QG there is another difficulty, namely that the methods of standard QFT do no longer apply; the Unruh effect is one prominent example, because the concept of a "particle" is shown not to be invariant. Two observers will in general not agree on the number of particles they observe.

 

[marcus]

I am against using words "Poincare group" and "spacetime" in the same sentence.

In the Weinberg's approach the Poincare group is NOT the group of isometries of the Minkowski spacetime. It is a group of transformations connecting different inertial observers. The fact that this group coincides with the group of isometries of the 4D pseudo-Euclidean spacetime is just a mathematical coincidence. ...

Ha Ha. Unruh effect is cool.
It is a weapon against old school saying that "only real particles are real, virtual particles are just math"

Both these comments spice up the discussion for me, I hope other people are entertained by the ideas as well. Dmitry, do you say here that Unruh effect blurs the distinction between real and virtual because (?) by accelerating the observer we can turn virtual ones gradually into real ones?

 

[marcus]

Particles appear in rare situations, namely when they are registered.
...

I was going to say that sort of thing to Naty! The trouble with the particle concept is that one cannot attribute a permanent existence. It only exists at the moment it is detected.

The rest of the time there is a kind of spread out thing---a cloud---a wave---a field---something that is less "particular".

And as Rovelli Colosi show you cannot in general say how many particles are "there". This is semantically at the root of the particle idea---that one should be able to count them. If you can't even count them, forgetaboutit

 

[meopemuk]

It seems your view of gravity here is an "external view", where the observer itself is not subject to gravitational interactions but he is observing a system which has "internally" gravitational interplay?

It seems then you constrain the "set of possible observers", to those where your scheme makes sense: ie. an external observer, making regular QM-style measurements on a small subsystem?

Yes, this is true. Observer is not a part of physical system. This separation system/observer is recorded in the formalism of quantum mechanics: physical system is represented by a vector in the Hilbert space, while observer (or measuring apparatus) is represented by a Hermitian operator.

Such separation is possible in the case of gravity as well. For example, if we are interested in the gravitational system Sun+Earth, then we should choose our inertial observers to be far from the Solar system, so that Sun's gravity has no effect on them. Then we can apply the Poincare group and relativistic QM formalism just as freely as in the proton+electron case.

How does cosmological pictures fit into your view?

There is a problem in applying quantum mechanics to such objects as Solar system or Universe. Quantum mechanics calculates probabilities. This implies preparation of multiple copies (ensemble) of identical systems. The Solar system and Universe are unique, so formally QM does not apply to them. But quantum effects at cosmological scale are negligible, so we can do well with classical mechanics only.

Eugene.

 

[meopemuk]

Particles appear in rare situations, namely when they are registered.

But only these situations are relevant in physics! According to scientific method we are not allowed to speculate about things that cannot be registered/observed/verified. If we do use such unobservable things (e.g., wave functions, quantum fields, etc) in our formalism we should keep in mind that these are mathematical tools unrelated to the physical world.

Two observers will in general not agree on the number of particles they observe.

Why this is an argument against particles? What's wrong with the fact that different observers see different number of particles? For example, I see one neutron. Fifteen minutes later (this can be regarded as an observer translated in time with respect to the observer from the preceding sentence) I see three decay products (proton + electron+ antineutrino). This does not undermine my trust in the particle picture.

Eugene.

 

[meopemuk]

And as Rovelli Colosi show you cannot in general say how many particles are "there". This is semantically at the root of the particle idea---that one should be able to count them. If you can't even count them, forgetaboutit

The number of particles is a QM observable similar to other observables like position, momentum, energy. I guess, you are not troubled by the fact that these other observables may have different values (and uncertainties) for different observers. Then you should not be troubled by the fact that different observers count different number of particles or that the particle count has usual quantum-mechanical uncertainty.

Eugene.

 

[tom.stoer]

But only these situations are relevant in physics! According to scientific method we are not allowed to speculate about things that cannot be registered/observed/verified. If we do use such unobservable things (e.g., wave functions, quantum fields, etc) in our formalism we should keep in mind that these are mathematical tools unrelated to the physical world.

I am aware of this. But with the concept of particles alone you are not able to calculate anything beyond classical physics. No quantum mechanics, no atoms, no spectra, no nuclei, no nucleons, no quarks, ... they all rely on concepts like wave functions, field operators, Hilbert spaces, etc. You can't measure these mathematical entities, you can't register them, but have to life with them if you want to do physics. And in the very end the formalism (which you can't measure) produces results in nearly perfect agreement with measurements. So you can't avoid the conclusion that this unrealistic formalism describes nature.

Why this is an argument against particles? What's wrong with the fact that different observers see different number of particles? For example, I see one neutron. Fifteen minutes later (this can be regarded as an observer translated in time with respect to the observer from the preceding sentence) I see three decay products (proton + electron+ antineutrino).

This is not the problem I am talking about. I don't know if know what the Unruh effect means. Think about an unaccelerated observer sitting in completely empty space. There is nothing, no particle, no light - just void. So this is what he calls vacuum. No think about another observer moving with (constant) acceleration through the same region of space, quite close to the first observer. She sees not empty space but a kind of thermal heat bath filled with particles with temperature

$$T_\text{Unruh} = \frac{\hbar a}{2\pi k_Bc}$$

where a is the acceleration of the observer.

http://en.wikipedia.org/wiki/Unruh_effect

So the second observer sees something totally different than vacuum.

That means that both observers do not agree on the number of particles they observe.

The reason is that the definition of a "particle" relies on the definition of a vacuum state which has to be (at least asymptotically) flat; acceleration spoils this concept because acceleration is equivalent to gravity and therefore undermindes the basis of relativistic (which means special relativistic) quantum field theory. So both observers can construct quantum field theory, but both theories will be be inequivalent as they do not use the same notion of vacuum.

So switching on gravity means that (at least partially) the concept of particles becomes meaningless.

 

[meopemuk]

I am aware of this. But with the concept of particles alone you are not able to calculate anything beyond classical physics. No quantum mechanics, no atoms, no spectra, no nuclei, no nucleons, no quarks, ... they all rely on concepts like wave functions, field operators, Hilbert spaces, etc. You can't measure these mathematical entities, you can't register them, but have to life with them if you want to do physics. And in the very end the formalism (which you can't measure) produces results in nearly perfect agreement with measurements. So you can't avoid the conclusion that this unrealistic formalism describes nature.

I have nothing against the mathematical formalisms of quantum mechanics or QFT, which involve wave functions, field operators, and Hilbert spaces. My point is that this formalism is simply a tool for describing/predicting results of measurements performed on particles. So, the primary physical objects are particles. Quantum fields are simply mathematical constructs which make writing of particle Hamiltonians somewhat easier (see Weinberg).

I don't know if know what the Unruh effect means.

Yes, I know about the Unruh effect. I also know that this effect has not been observed yet. So, referring to this theoretical speculation does not prove anything.

Eugene.

 

[tom.stoer]

So, referring to this theoretical speculation does not prove anything.

I does! Maybe it does not prove anything regarding real particles (whatever this could be), but it proves that the theoretical concept of particles is cumbersome.

Of course you can talk about the registration of a particle in a measurement device, but can't calculate how that particle moved to the measurement device through a double-slit. As soon as you use the wave function the calculation works and it agrees with experiment. So perhaps the wave function is not real (whatever this should mean), but it is related to the physical world in the sense that it allows you to predict physical reality. Unfortunately what you call reality (the particle) does not allow you to make this prediction.

 

[meopemuk]

Of course you can talk about the registration of a particle in a measurement device, but can't calculate how that particle moved to the measurement device through a double-slit. As soon as you use the wave function the calculation works and it agrees with experiment. So perhaps the wave function is not real (whatever this should mean), but it is related to the physical world in the sense that it allows you to predict physical reality. Unfortunately what you call reality (the particle) does not allow you to make this prediction.

The fact that wave functions allow us to predict results of the double-slit experiment simply tells us that we should abandon the naive idea that particles are small balls moving along classical trajectories. Quantum mechanics tells us that it is wrong to ask how particles look when they are not observed (between the preparation and the measurement). This question simply does not have any satisfactory answer. The best we can do is to design a mathematical formalism (with wave functions, Hilbert spaces, quantum fields, etc.) which allows us to predict the results of measurements without giving us any clue about how the "unobserved particle" looks like.

I disagree that wave function tells us "how that particle moved to the measurement device through a double-slit". Wave function is just a (useful) mathematical abstraction. It should not be promoted to the rank of "physical reality".

It is OK to leave some questions (like "how things look like while they are not observed?") without answers as long as all questions related to actual observations are answered correctly.

Eugene.

 

[SimonA]

It is OK to leave some questions (like "how things look like while they are not observed?") without answers as long as all questions related to actual observations are answered correctly.

Eugene.

I agree. But why then is it okay to invent a "many worlds" multiverse when we only observe one. Using "dark flow" as evidence would be like sending someone to jail just for doing something strange in the vicinity of a murder. The same goes for explaining youngs slit experiment.

This question simply does not have any satisfactory answer. The best we can do is to design a mathematical formalism (with wave functions, Hilbert spaces, quantum fields, etc.) which allows us to predict the results of measurements without giving us any clue about how the "unobserved particle" looks like.

But that leaves me unsatisfied. Is there a particle at all ? Is it a packet of energy in any dimension, or is it a wave that is only absorbed at a single point ? If the latter, then what is waving ? Space ? Time ? Consider a photon moving through a vacuum. Why does it move at constant velocity ? What does that say about the nature of space ?

Is it fair to say that we have a mathematical formalism that is realiable, but is it fair to say that we don't have even a basic idea about the nature of space, time, matter and particles ?

 

[Haelfix]

A couple clarifications.

The Unruh effect by itself is not a demonstration of the lack of a good particle concept in curved space. Now it is true that accelerated detectors will register different particle counts than an inertial detector... However, this is *kind of* true even in special relativistic classic electromagnetism and the subject of certain paradoxes. Consider an electron on a table, and two observers (one at rest relative to the electron, the other accelerating by it). To the observer in the noninertial frame, it will look like the electron is accelerating. Accelerating electrons are supposed to radiate classically. So one person presumably registers radiation (eg it might heat up a glass of water), and the other does not. What gives? The resolution is technical (it depends on what you mean by 'radiation'), but the punchline is you have to be a little careful and make sure that both observers agree about the state of an experiment (at least with Lorentz invariant observables), see a bunch of SR/GR forum posts about this.

The biggest issue in quantum fields in curved space, is not the fact that there is no unique vacuum (this is not true, even in flat space as evidenced by the Unruh effect), but rather that there is not even such thing as a canonical agreed upon vacuum for all *inertial* observers (it is only true in Minkowski where they are all in the same Poincare equivalence class).

In curved space, even where you have nice asymptotically flat boundary conditions (in the far past and the far future) and hence a good observable quantity like an SMatrix, if you are interested in global quantities like the particle number operator you must always in addition to specifying the interaction and SMatrix in question, also specify the state of motion of the detector. The particle number operator is thus an observer dependant quantity and the usefullness of the concept comes into question.

In essence, passing from flat to curved space, global quantities (like total energy, particle number and so forth) cease to have the same usefullness and instead we must try to create good local observables. Unfortunately this is very hard to do. The aforementioned SMatrix is a good one, but then it fails to make sense for different boundary conditions.

 

[Fra]

Meopemuk, I think I roughly see your perspective my primary comment to your view is that I find a conceptual inconsistency in it

(1) embracing of observer/measurement perspective (on which I agree is sound)
(2) your non-measurement perspective of the symmetries in the set of possible observers

You presuppose a symmetry in the set of all physically possible observers, rather than consider it something that should be inferred from experiment?

What do your require that information about the state of the atom should be a result of measurements, when information about the symmetry of communicated measurements by other observers must not?

How do you distinguish between what information you demand to be subject to a measurement process, and what information you accept as something you can define or assign in a spirit similar to classical realism?

For example, if we are interested in the gravitational system Sun+Earth, then we should choose our inertial observers to be far from the Solar system, so that Sun's gravity has no effect on them. Then we can apply the Poincare group and relativistic QM formalism just as freely as in the proton+electron case.

What I react on here is your idea that we can freely CHOOSE the observer?

What I seek is how the laws of physics look to ANY observer. You constrain yourself to a reduced set of observer, where everything gets simplified?

So to me, it seems you are trying to avoid the difficulty rather than solve it face on?

In the inside view, a given observer has the task to infer the laws of physics from interacting with it's environment. This observer is not helped by wishing he was somewhere else.

In the idealised scenario of particle experiments in lab, then yes, we can CHOOSE where to place the detectors etc, the motion of detectors etc. However, in an intrinsic perspective, there is no such choice. The observer just is, and it's basically doing a random walk in an environment it can not fully control. Your idealisations deny the problems I personally think the future physics need to solve.

Quantum mechanics calculates probabilities. This implies preparation of multiple copies (ensemble) of identical systems. The Solar system and Universe are unique, so formally QM does not apply to them. But quantum effects at cosmological scale are negligible, so we can do well with classical mechanics only.

I guess my preferred solution to this problem is to find out what "probabilities" really mean in the cosmological perspective, ie. when repetitive experiments and ensembles simply aren't possible. Then another way is a subjective bayesian interpretation, then ensembles aren't needed, and "probability of something that happens only once" could instead be understood differently.

I guess your idea is that this is unnecessary, and that the old scheme works fine and you instead consider the cases where it obviously doesn't as situations where QM doesn't apply.

/Fredrik

 

[meopemuk]

What I seek is how the laws of physics look to ANY observer. You constrain yourself to a reduced set of observer, where everything gets simplified?

Strictly speaking there can be no inertial observers in nature. If we have a physical system (e.g., an atom) and an observer, then there is definitely some interaction (perhaps very weak) between the two. So, the observer is no longer inertial. I can agree with that. But I also think that adopting your "intrinsic perspective" (which I understand as considering the observer as a part of the physical system) will lead you nowhere. I could be wrong, but my feeling is that you can't build a viable theory on this assumption. The idea of separation between physical system and inertial observer is an approximation, but, in my opinion, it is a good approximation, which should be sufficient for all practical purposes.

Then another way is a subjective bayesian interpretation, then ensembles aren't needed, and "probability of something that happens only once" could instead be understood differently.

I guess it would be very hard for you to explain me how one can measure the probability of an event which happens only once. I just don't get it.

Eugene.

 

[Fra]

But I also think that adopting your "intrinsic perspective" (which I understand as considering the observer as a part of the physical system) will lead you nowhere. I could be wrong, but my feeling is that you can't build a viable theory on this assumption.

I fully respect your scepsis because this extreme inside-view does lead to an intrinsic loss of decidability, but then my point is that the decidability you how now, is deceptive and only effective anway. So the difference is smaller than one might think.

It sure is possible that this instrinsic program will fail, but I am quite confident and it's certainly the problem of the advocates to show that this view can lead to improved predictability and understanding.

Some key things to pull this of, is a new intrinsic formulation of information theory and indirectly "probability theory", and then put this in an evolving perspective where the set of observers and the set of encoded laws evolve together.

I guess it would be very hard for you to explain me how one can measure the probability of an event which happens only once. I just don't get it.

I'll try to line it out later, although it's probably going to be hard for you to accept it, given your position :) The idea does lead to new "problems", that you will see as circular and subjective, but this is why the only solution is then to consider an evolution, where objectivity is emergent just like the laws of society is emergent by negotiation, cycles of conflict and equilibrium. There simply is no intrinsic static theory. That's how I view it. I can try to line out the basic ideas and the good traits later. But I do not have the answers of course. I just figure it's a decent first step to distinguish the right questions and try to find the direction to work in.

/Fredrik

 

[tom.stoer]

Quantum mechanics calculates probabilities. This implies preparation of multiple copies (ensemble) of identical systems.

I can't agree with this view.

There are many qm calculations which do not calculate probabilities: spectra of atoms, in general eigenvalues of observables, symmetry structures, masses of particles.

 

[Naty1]

The wikipedia discussion on virtual particles is interesting, but I don't get a number of explanations,,especially the one I have boldfaced below:

There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. As such, virtual particles are also excitations of the underlying fields, but are detectable only as forces but not particles. They are "temporary" in the sense that they appear in calculations, but are not detected as single particles. Thus, in mathematical terms, they never appear as indices to the scattering matrix, which is to say, they never appear as the observable inputs and outputs of the physical process being modeled. In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment.

This appears closely related to some of our discssions above. Is the boldface correct, and what does it mean?? Is this a reference to dark energy... the cosmological constant? ise Seems likes forces (fields) and particles (quanta) are two sides of the same coin.

 

[meopemuk]

The wikipedia discussion on virtual particles is interesting, but I don't get a number of explanations,,especially the one I have boldfaced below:

I really dislike the wikipedia's "polit-correct" way of addressing virtual particles: They try to please everybody and say: on the one hand virtual particles exist, on the other hand they don't. This relativism is very confusing for people trying to learn this stuff.

In fact, what they call "virtual particles" are simply certain factors in Feynman-Dyson expressions (integrals) for scattering amplitudes. It is very confusing when people use the term "particle" to describe a mathematical factor/function.

Eugene.

 

[tom.stoer]

In fact, what they call "virtual particles" are simply certain factors in Feynman-Dyson expressions (integrals) for scattering amplitudes. It is very confusing when people use the term "particle" to describe a mathematical factor/function.

I agree.

In Feynman-diagram language an external line corresponds to a physically real particle, whereas an internal line corresponds to a virtual particle. So it is common belief that only real particles (asymptotoc states) can be detected. But as soon as a particle is detected it interacts with the measurement device; this interaction - in terms of Feynman diagrams -has to be described via a vertex at which the line of the detected particle ends - so in essence it is turned into a virtual particle.

Virtual particles / Feynman diagrams are book-keeping tools only.

 

[meopemuk]

Virtual particles / Feynman diagrams are book-keeping tools only.

Ironically, by introducing his highly useful diagrams, Feynman also made a great disservice for understanding of QFT. Many people started to believe that these diagrams are some snapshots of real physical processes. In fact, the diagrams are simply a peculiar notation for some integrals. No more than that. For example, 4-momenta of internal (loop) lines are just dummy integration variables. These variables are void of physical meaning.

Eugene.

 

[qsa]

The wikipedia discussion on virtual particles is interesting, but I don't get a number of explanations,,especially the one I have boldfaced below:



This appears closely related to some of our discssions above. Is the boldface correct, and what does it mean?? Is this a reference to dark energy... the cosmological constant? ise Seems likes forces (fields) and particles (quanta) are two sides of the same coin.

QM teaches us that full meaning of a particle concept is in the probability of detecting them, so that is done. The problem mostly comes when there is an interaction. QFT and solution to Schrödinger eq(SH. EQ.) ,not to mention the notorious Dirac eq., for even the simplest of problems becomes more an art than science. QFT looses it altogether in the interaction point, it cannot tell you about what is exactly happening to the particle (as probabilities in space-i.e. there goes your main definition of particles out of the window.).

Even in the simplest model in SH. EQ. the potentials are put in by hand and are classical quantities. When you go to QFT again all interaction potentials i.e. symmetry ansatz have been decided upon which the theory does not predict. Which means the theory not only does not know how to properly describe a particle in an interaction, the interaction terms themselves (the forces) are great guess work. This is how 99.9% of high end physics papers start "we -use,assume,take... the lagransian to be .. so an so. And all the competition is in my lagransian is better than yours! I am not in the mood (now)to go into the bare mass ,dress mass or smeared charge and all that fancy foot work.

Particles and forces are all probabilities in space points related to the energy contents at that point. Imagine two spherical balls made of putty, make them stick together and then separate them. The region in between (before they break) has probabilities that can be equated (approximated if you wish) with the concept of the force particle. Any QFT should take a hint from the hydrogen 1s, it shows the interaction in probability terms, but it has to also predict the A field that was caused by the interaction. Not the other way around, then there will be no mystery as to what is the fundamental entity which QM has clearly stated.