I The thermal interpretation of quantum physics

[A. Neumaier]

So in essence particles are fields of nothing but numbers sometimes localised and others extended greatly, correct.

No.

In general, fields are just themselves, not composed of other stuff. The temperature field in a room is not composed of anything but describes how warm it is in different places. Similar for other fields, e.g. the water level of the moving surface of a lake, or the salt concentration in the lake. They are not composed of water but describe properties of the lake.

Electron fields and other fundamental stuff are not much different in principle, only in their quantum properties.

Partcles are moving localized aspects of fields, described by bloblike or beamlike currents. The paths they travel are often more real than the particles themselves. Think of rain pouring down or of moving water wavelets, but don't take the imagery too seriously!

 

[ftr]

Particles are moving localized aspects of fields

And Fields are aspects of what?

 

[DarMM]

And Fields are aspects of what?

They're just fields as such, same as they are in classical field theory, just the structure of their properties is different.

 

[ftr]

They're just fields as such, same as they are in classical field theory, just the structure of their properties is different.

In classical field theory temperature field is an aspect of energy of the particles. The post said that particles are aspect of fields while everybody knows that fields must be aspect of particles.

 

[DarMM]

In classical field theory temperature field is an aspect of vibration energy of the particles. The post said that particles are aspect of fields while everybody knows that fields must be aspect of particles.

In QFT in general, not specifically the Thermal Interpretation, the fields aren't generally "aspects of particles". There are several states that don't really admit a particle interpretation, particles only emerge at asymptotic times, the particle content is observer dependent (i.e. Unruh effect). I don't see how the fields are aspects of particles.

 

[A. Neumaier]

And Fields are aspects of what?

They are aspects of what we can observe.

 

[A. Neumaier]

In classical field theory temperature field is an aspect of energy of the particles.

No. This holds only for ideal gases, but not for the temperature of liquid water, say, as it figures in the Navier-Stokes equations.

everybody knows that fields must be aspect of particles.

Everybody who looks deeper knows that the fundamental theory of Nature is quantum field theory, and not quantum particle theory. Particles are described in terms of fields.

 

[ftr]

I don't see how the fields are aspects of particles.

Ever since I was born in QM theory world I was taught that particles and fields are dual description, and since we say here is a particle and not here is a field I presume that fields are aspects of particles.

 

[DarMM]

Ever since I was born in QM theory world I was taught that particles and fields are dual description

I don't see how that could be possible in general interacting field theories which have states without a particle decomposition.

 

[A. Neumaier]

we say here is a particle and not here is a field I presume that fields are aspects of particles.

Informally, we say here is a particle (mainly because of tradition), but looking at the math involved in their relativistic description one finds that the particle picture is purely figurative, while everything is expressed in terms of fields.

 

[ftr]

I don't see how that could be possible in general interacting field theories which have states without a particle decomposition.

Informally, we say here is a particle (mainly because of tradition), but looking at the math involved in their relativistic description one finds that the particle picture is purely figurative, while everything is expressed in terms of fields.

First I hear that fields are fiction(i.e. mathematical), now I hear that particles are fiction.
then this post

They are aspects of what we can observe

The interpretation was suppose to make things clear, was it?
edit: ok I admit this has made me to think a lot harder.

 

[A. Neumaier]

First I hear that fields are fiction(i.e. mathematical), now I hear that particles are fiction.

In some sense, only Nature is real, and all talk about it is already fiction. In any case, particles are more superficial fiction than quantum fields. Nobody ever has seen a particle. We just imagine it as a tiny cannon ball or a tiny wavelet, or whatever...

The interpretation was suppose to make things clear, was it?

The thermal interpretation is supposed to resolve the issues with the traditional interpretations, primarily the measurement problem.

Clarity will rule only 5-10 years after a single interpretation is accepted by the majority, and textbooks are rewritten accordingly. Thus you need to be patient.

The only shortcut is to learn to understand things from the ground, starting with the math, rather than from what you hear people say.

 

[julcab12]

First I hear that fields are fiction(i.e. mathematical), now I hear that particles are fiction.
then this postThe interpretation was suppose to make things clear, was it?

Fields are real and particles blurry bundles of real in approximation. The usual convention is coined behavior, depending on how you view it. For loopy guys- are interactive, transformative via timelike slices-- Thermal Time (Still Blurry Though). In terms of field--mathematical abstraction are often so closely related to "real" stuff that they're confused with each other. A vector is not real, a force is. But we're so used to vector forces, we swap them carelessly. We can do so only because we know forces behave (with an extremely fine approximation) as vectors, but vectors are not real. Vector fields are not real, for the same reasons vectors are not real; the electrical field is real and you could feel it if you had the right organs. Hilbert spaces are not real, superposition is.

 

[ftr]

Fields are real

Although "real" is hard to define, but typically in physics we mean that something that has certain property that can be measured directly or indirectly. I don't know of any experiment that has measured electron field and typically the fields are expressed using imaginary numbers.

 

[A. Neumaier]

I don't know of any experiment that has measured electron field

Then you can learn something new!

Atomic force microscopy displays the surface of the electron cloud around a nucleus, not a number of tiny electron particles surrounding the nucleus. See ''Does an atom mostly consist of empty space?'' from my theoretical physics FAQ.

 

[ftr]

Then you can learn something new!

That is what attracts me to science, I get very bored when I sail an open sea. What is the unit of measurement.

P.S. I don't see a single sentence that says "electron field" in your first reference.

 

[DarMM]

I forgot to ask this. Is the Thermal Interpretation contextual?

If I have a set of nine devices for a four level system that represent one of the nine orthogonal bases in Cabello's proof of Kochen-Specker. And "let us say" that to keep determinism we end up with a contextual assignment whereby projector $P_5$ is assigned a value of $1$ (i.e. is the result that will occur) when measured as part of operator $A$, but assigned a value of $0$ when measured as part of operator $B$. This determination $\nu(P_5,A) = 1$ implicitly includes the full dynamics of the environment, since it is just a statement of the value that will obtain.

How does this contextuality arise in the thermal interpretation? I assume it is that given a fixed environmental state $\rho_E$ the metastable states on devices implementing $A$ and $B$ are different enough that under influence from the environment one will decay onto the $P_5$ component of the slow manifold and the other will not.

 

[A. Neumaier]

That is what attracts me to science, I get very bored when I sail an open sea. What is the unit of measurement.

P.S. I don't see a single sentence that says "electron field" in your first reference.

It talks about forces. Forces are vector fields (generalizing the gravitational forces familiar to anyone). The detailed force measured depends on the instrument, but they are all calculated from the interaction with the electron field (plus the Coulomb fields of the nuclei).

 

[A. Neumaier]

I forgot to ask this. Is the Thermal Interpretation contextual?

Of course, since quantum mechanics is. The stochastic influences depend on the environment, which is the context. No two environments are identical. (But conventional contextuality discussions are not applicable since they assume sharp outcomes, while the thermal interpretation is about explaining when sharp outcomes should be expected.)

Note that the thermal interpretation gives no details, only the conceptual intuition needed to turn each specific problem into a precise problem of statistical mechanics. To find out how the slow manifold looks like is for each case a separate statistical mechanics problem.

In Part III, I discussed two particular measurement situations treated by AB&N and B&P, respectively. The techniques generalize, but have not yet been applied to generic measurement situations which would allow to treat not only particular cases but fairly general settings.

Thus there is still a lot of research potential in the application of the thermal interpretation.

 

[DarMM]

Of course, since quantum mechanics is.

I think this is a difference of phrasing. Quantum Mechanics (in the typical view) retains nonconextuality by sacrificing determinism, i.e. there are sets of projectors to which one cannot assign elements of ${0,1}$ noncontextually. Either you give up determinism, i.e. assign real values elements of $[0,1]$, or you accept the contextuality.
Although some call any violation of either contextuality.

Regardless the explanation is as I expected. Have you read:
Heywood, P., & Redhead, M. L. G. (1983). Nonlocality and the Kochen-Specker paradox. Foundations of Physics, 13(5), 481–499

It contrasts the different forms of locality implied by different methods of having contextuality, i.e. ontological vs environmental contextuality.

 

[A. Neumaier]

Have you read:
Heywood, P., & Redhead, M. L. G. (1983). Nonlocality and the Kochen-Specker paradox. Foundations of Physics, 13(5), 481–499

I had studied the Kochen-Specker theorem in detail, but didn't read all of the surrounding literature.

I lost interest in quantum-logic related results (though I read the book Quantum logic by Karl Svozil and more) long ago, when I realized that quantum logic is a very poor logic in which not even implication is sensibly defined. Thus one can make only the most primitive logical arguments. The fact is that all predictive power in quantum physics comes from applying classical logic to get results about q-expectations, and nothing but confusion comes from considering quantum logic.

 

[A. Neumaier]

Three reviews (Part I, Part II, Part III) of my three papers are now on PhysicsOverflow, together with some comments by me.

 

[Mentz114]

[..]

I discussed two particular measurement situations treated by AB&N and B&P, respectively. The techniques generalize, but have not yet been applied to generic measurement situations which would allow to treat not only particular cases but fairly general settings.

Thus there is still a lot of research potential in the application of the thermal interpretation.

I have to say it looks incredibly hard. I doubt if a general theory is possible.
I looked at buying a copy of the B&P book but the earliest delivery date for a new one is June !
I'm not sure if Breuer et al (2015) is cited in the Thermal papers but it gives a foretaste and is available on arXiv.

Non-Markovian dynamics in open quantum systems
Heinz-Peter Breuer, Elsi-Mari Laine, Jyrki Piilo, Bassano Vacchini

arXiv:1505.01385v1 [quant-ph] 6 May 2015

I like very much the re-synthesis of QT in the Thermal interpretation. Dropping particles gets rid of a lot of Platonic nonsense. Nice move.

 

[A. Neumaier]

I looked at buying a copy of the B&P book but the earliest delivery date for a new one is June !
I'm not sure if Breuer et al (2015) is cited in the Thermal papers but it gives a foretaste and is available on arXiv.

H. P. Breuer & F. Petruccione,
Stochastic dynamics of open quantum systems: Derivation of the
differential Chapman-Kolmogorov equation,
Physical Review E51, 4041-4054 (1995).

is freely online and related to what I discuss. But it works with pure states rather than with the mixed states required for the thermal interpretation.

 

[A. Neumaier]

I looked at buying a copy of the B&P book

You may wish to look at bookfinder! (But your shipping country and hence the prices may be different.)
I wonder why used copies may be more expensive than new ones by a large factor...

 

[A. Neumaier]

I assume it is that given a fixed environmental state $\rho_E$ the metastable states on devices implementing $A$ and $B$ are different enough that under influence from the environment one will decay onto the $P_5$ component of the slow manifold and the other will not.

The state of the universe probably never factors even approximately into an environmental state and a system state. Exact factorization is just an assumption made (in addition to other highly idealized assumptions such as that this environmental state is a harmonic heat bath) in many discussions of the measurement problem, to be able to do something at all.

 

[vanhees71]

I don't think that's true. It's neither true that the weirdness is resolved by the minimal interpretation, nor is it true that it has anything to do with prejudice by "common sense". The minimalist interpretation is pretty much what Bell was criticizing in his essay. To quote from it:

Here are some words which, however legitimate and necessary in application, have no place in a formulation with any pretension to physical precision: system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, information, measurement.

Well, Bell's merit for me lies not so much in his philosophical ideas but to the contrary in bringing philosophical unsharp considerations, particularly from the EPR article and the even weirder reply by Bohr to it into a sharp scientifically intervestigable quantitative realm. By deriving his famous inequalities with their clear contratidction to the probabilistic prediction of QT he has set the "macroscopic prejudices" by EPR to the test. The better and better Bell tests with all kinds of quantum systems, particularly quantum optics (photons), decides forQT with an astonishing significance. Although Bell seems not to have liked this, that's an empirical fact about nature.

Now, a physical theory has to describe all phenomena, and among the very persistent phenomena is the classical behavior of macroscopic systems. It's not enough for QT to describe the microscopic constituents (nowadays quarks, leptons, some gauge fields, and the Higgs field) but also the emergent classical behavior of matter (from the hot and dense elementary-matter gas of the early universe to the rather cold matter surrounding us in everyday life), and that's why all the words, Bell doesn't like are of substantial importance for physics. If you want to understand macroscopic matter from first principles you have to use many-body methods, make use of the separation of the "micro vs. macro scales". The key to understand many-body statistical physics is indeed the notion of information a la Shanon, Jaynes, and von Neumann.

To make sense of what's observed, particularly when dealing with the microscopic constituents there's no other way to also think about the measurement devices, which are to explained by the same many-body physics as anything else. Even the very definition of the microscopic constituents in a physical, i.e., operational sense, hinges on this understanding of what's observed. E.g., a photon (or more generally any state of "electromagnetic fields") manifest themselves finally still by their interaction with macroscopic matter. Einstein's perception of the em. field as particle-like photons is self-contradictory, while modern quantum optics naturally explains it by the observable manifestations of the interaction between the electromagnetic field with the matter fields describing the detectors, i.e., the photoelectric effect.

 

[vanhees71]

Just to understand. Take a particle reaction like $\pi^{+} \rightarrow \mu^{+} + \nu_{\mu}$. In the thermal interpretation I assume what is happening here is that locally devices probe $\pi^{+}, \mu^{+}, \nu_{\mu}$ fields (of course these are not fundamental fields, but let's ignore that for now). Via interaction with the fields each of the devices' slow modes are placed into a bistable state and environmental noise triggers these to decay into the detection/non-detection states?

That's an excellent example for my case against Bell's unrealistic attempt to forbid fundamental notions of physics as an empirical science in #177 since the mentioned weak-decay process involves a "muon neutrino".

Now what is a neutrino within the fundamental models we have to describe them? That's a more complicated question than one might think, because it relates to the only really estabilshed fact about physics beyond the standard model, namely that there is what's called "neutrino mixing".

In the usual pragamatic interpretation of the meaning of the pion-decay we deal with particles. Now particles within relativistic quantum field theory are only well defined in the sense of asymptotitic free states, where a Fock-space description makes sense and one thus can define (generalized) mass-momentum-spin eigenstates of occupation number 1, i.e., a "single-particle Fock state".

Now the mass-eigenstates of the neutrino fields cannot be prepared since neutrinos are produced via the weak interaction (like the above considered pion decay), and the corresponding weak current couples to flavor not mass eigenstates. The flavor eigenstates however cannot be interpreted as one-particle Fock states, because they have indetermined mass.

What we detect as "neutrinos" are indeed not "neutrinos as particles" but the reaction of the neutrino with the detector material. Indeed, the long-baseline experiments prove neutrino-mixing, and it may well be that the "muon neutrino" from the pion decay is detected as an "electron neutrino" due to the "neutrino oscillations". Seen from this perspective, in the QFT formalism neutrinos make only sense as "internal lines in Feynman diagrams", i.e., one has to consider both the creation process (here the pion decay) as well as the detection process (not mentioned above) to have a consistent interpretation of "what's measured".

 

[stevendaryl]

Now, a physical theory has to describe all phenomena, and among the very persistent phenomena is the classical behavior of macroscopic systems. It's not enough for QT to describe the microscopic constituents (nowadays quarks, leptons, some gauge fields, and the Higgs field) but also the emergent classical behavior of matter (from the hot and dense elementary-matter gas of the early universe to the rather cold matter surrounding us in everyday life), and that's why all the words, Bell doesn't like are of substantial importance for physics.

I think you misunderstand Bell if you think that he doesn't like measurements and observations and so forth. What he's saying is that a fundamental theory should not be expressed in terms of those concepts, because they are very subjective and fuzzy. Fuzziness is often hiding contradictions.

So the minimal interpretation, with its distinction between measurements and other interactions is a subjective, fuzzy interpretation. Measurements are certainly important to our discovering facts about the world, but physics is supposed to describe the world in a way that doesn't require there to be anyone or anything performing measurements. For example, presumably enough hydrogen will collapse into a star and produce energy by nuclear fusion even if nobody is around to look at it (as was the case for the first few billion years after the Big Bang).

Because it is described in terms of "measurement", the minimal interpretation doesn't seem very minimal at all, to me. It's sweeping a huge amount of complexity under the rug using that term. For example, we could define a measurement of a property is an interaction that triggers an amplification process resulting in an irreversible change, where different initial values of the property result in macroscopically distinguishable end states. I think that covers the usual cases that we would consider "measurement". But it's enormously complicated and fuzzy. Irreversibility, like macrosopic, is a fuzzy large-numbers concept. There is no actual irreversibility, only for all practical purposes (FAPP) reversibility. (I don't know whether Bell coined that acronym, but he uses it.) There is no actual macroscopic/microscopic distinction, we only call something "macroscopic" when it becomes too complex to analyze all the parts in complete detail. So the minimal interpretation is, in my mind, built on sand. Measurement is a fuzzy concept that is ultimately subjective. If your physics depends on measurement as a fundamental concept, then your physics is fundamentally subjective.

 

[MathematicalPhysicist]

If your physics depends on measurement as a fundamental concept, then your physics is fundamentally subjective.

What's bad with subjective physics, if there's no objective reality?

 

[stevendaryl]

What's bad with subjective physics, if there's no objective reality?

Certainly, if there is no objective reality, then you're not going to have an objective physics. However, I think most physicists would agree that there is something objective about physics. The theories that I develop seem to work for you, too.

 

[vanhees71]

I think you misunderstand Bell if you think that he doesn't like measurements and observations and so forth. What he's saying is that a fundamental theory should not be expressed in terms of those concepts, because they are very subjective and fuzzy. Fuzziness is often hiding contradictions.

So the minimal interpretation, with its distinction between measurements and other interactions is a subjective, fuzzy interpretation. Measurements are certainly important to our discovering facts about the world, but physics is supposed to describe the world in a way that doesn't require there to be anyone or anything performing measurements. For example, presumably enough hydrogen will collapse into a star and produce energy by nuclear fusion even if nobody is around to look at it (as was the case for the first few billion years after the Big Bang).

Because it is described in terms of "measurement", the minimal interpretation doesn't seem very minimal at all, to me. It's sweeping a huge amount of complexity under the rug using that term. For example, we could define a measurement of a property is an interaction that triggers an amplification process resulting in an irreversible change, where different initial values of the property result in macroscopically distinguishable end states. I think that covers the usual cases that we would consider "measurement". But it's enormously complicated and fuzzy. Irreversibility, like macrosopic, is a fuzzy large-numbers concept. There is no actual irreversibility, only for all practical purposes (FAPP) reversibility. (I don't know whether Bell coined that acronym, but he uses it.) There is no actual macroscopic/microscopic distinction, we only call something "macroscopic" when it becomes too complex to analyze all the parts in complete detail. So the minimal interpretation is, in my mind, built on sand. Measurement is a fuzzy concept that is ultimately subjective. If your physics depends on measurement as a fundamental concept, then your physics is fundamentally subjective.

Hm, physics is about observations and measurements. So why shouldn't it be allowed to use these very concepts in formulating the theory discribing them? Also, I don't see, why you think that the minimal interpretation leads to a distinction between measurements and other interations. To the contrary within the minimal interpretation there is no such distinction. The measurement devices' functions are based on the fundamental laws of physics and thus are part of the general concepts provided by the corresponding theories, including quantum many-body theory, including stars formed by clouds of hydrogen due to gravitation and held stable by nuclear reactions and the underlying quantum-statistical thermal physics.

Also "sweeping a huge amount of complexity under the rug" is in the nature of the subject! There's no way to even describe the state of a macroscopic system at one instant of time, let alone to solve its dynamics in every detail. The "classicality" of macroscopic objects is just an emergent phenomenon of the necessity (and possibility!) to sweep this huge amount of complexity under the rug. Fortunately there's no need for all the microscopic details and there is usually a separation of scales, leading to effective descriptions of much coarse-grained macroscopic observables which still provide sufficient details to describe the relevant phenomena.

I think that you quite accurately hit the point about what "measurement" means, and I don't see, why consider this as "fuzzy". It's at least not too fuzzy to make more and more accurate observations over several orders of magnitude (from the tiny subatomic scale of elementary particles to descriptions of huge objects of cosmic dimensions like galaxies, galaxy clusters, and finally even the overall structure of the universe, each on their appropriate scales with effective theories for the corresponding adequately coarse-grained observabels, but still derivable from the fundamental theories, as incomplete these still might be).

I don't know, which science (or humanity?) you have in mind, but if it's not based on observation and measurement, then it's not physics. Also, there's no hint in contemporary physics that it is subjective. To the contrary, it's based on pretty robust and stable concepts leading to well-reproducible measurements, independent of the individual physicist and his or her believes. Particularly quantum physics is pretty robust against all the weird interpretations out there. No matter, how they interpret the notion of quantum states, observables, and measurements the phenomena are always described by the same objective results.

 

[stevendaryl]

Hm, physics is about observations and measurements.

I would say, no, it's not. That's confusing the subject of physics with the tools of physics. It's like saying that chemistry is about test tubes.

Observation and measurements are how we find out about the world, but they are not the subject of science. They are the tools of science.

 

[MathematicalPhysicist]

Certainly, if there is no objective reality, then you're not going to have an objective physics. However, I think most physicists would agree that there is something objective about physics. The theories that I develop seem to work for you, too.

Most physicists at the time didn't accept Einstein's theories.
Just because the majority thinks something doesn't mean they are right of course.

 

[stevendaryl]

Most physicists at the time didn't accept Einstein's theories.
Just because the majority thinks something doesn't mean they are right of course.

Well, if it's all subjective, then what does "right" mean?

 

[DarMM]

Well it is possible to have a theory with subjective outcomes, but still have other theories be wrong, e.g. QBism has subjective outcomes but would say those outcomes still have to obey Born statistics. Similarly Rovelli's relational view. Relativity has subjectivity of time and space. I guess it requires some sort of objective bedrock, none of the QM views have total subjectivity of a literal "anything goes" form.

Regardless the Thermal Interpretation is not like any such view.

 

[ftr]

It talks about forces. Forces are vector fields (generalizing the gravitational forces familiar to anyone). The detailed force measured depends on the instrument, but they are all calculated from the interaction with the electron field (plus the Coulomb fields of the nuclei).

I think this has been talked about endlessly before, the forces are real but the fields( which included the notorious VP concept) are calculational tools and cannot be measured. Also QFT is nothing but a generalization of the "wavefunction" which YOU described as nothing, so how is it that they become (all of sudden) the basis of your interpretation.

 

[MathematicalPhysicist]

Well, if it's all subjective, then what does "right" mean?

Well, if it's subjective then everyone are right and wrong... :-D

If you think that's nonsense, you haven't heard of paraconsistent logics.

 

[Auto-Didact]

I lost interest in quantum-logic related results (though I read the book Quantum logic by Karl Svozil and more) long ago, when I realized that quantum logic is a very poor logic in which not even implication is sensibly defined. Thus one can make only the most primitive logical arguments. The fact is that all predictive power in quantum physics comes from applying classical logic to get results about q-expectations, and nothing but confusion comes from considering quantum logic.

I fully second this point of view and this also seems to be the consensus point of view among most experts, so this cannot be stressed enough: quantum logic is a prematurely born logic!

 

[romsofia]

Observation and measurements are how we find out about the world, but they are not the subject of science. They are the tools of science.

What's the subject of science then if not to predict the universe?

Chapter 7 (Classical Theory of Measurement) of "The Global Approach to Quantum Field Theory" By Bryce DeWitt says it best:"The purpose of any physical theory is to make sense of observations, to codify them in some at least partial way. If the codification can be successfully based on a small number of principles, these principles are said to constitute a theory, and the theory is regarded as "explaining" the observations. A theory also suggests new observations. The experimental underpinnings of a physical theory depend on controlled observations, in which precise measurements are made with carefully designed equipment. It is important to understand generically what measurements are and how their accuracy can be estimated. "

 

[stevendaryl]

What's the subject of science then if not to predict the universe?

I would say the point of science is to understand how the universe works. Prediction and measurement are the way to test your understanding.

Chapter 7 (Classical Theory of Measurement) of "The Global Approach to Quantum Field Theory" By Bryce DeWitt says it best:"The purpose of any physical theory is to make sense of observations, to codify them in some at least partial way. If the codification can be successfully based on a small number of principles, these principles are said to constitute a theory, and the theory is regarded as "explaining" the observations. A theory also suggests new observations. The experimental underpinnings of a physical theory depend on controlled observations, in which precise measurements are made with carefully designed equipment. It is important to understand generically what measurements are and how their accuracy can be estimated. "

I agree with that.

 

[julcab12]

Also QFT is nothing but a generalization of the "wavefunction" which YOU described as nothing, so how is it that they become (all of sudden) the basis

QFT is the best general idealization of dynamic in Quantum landscape. Realization of wave picture can be an artifact(Relational View) which came from notion that time/things passes at different rate, so does the evolution of fields to particle and localized using a distinctive mathematical tool-- wavefunction in a single world while fields are geometric and waves are manifestation from that field. It is safe to say that --it is a generalization of wavefunction. Besides, fields doesn't concern position or location. Similarly, In field Theory, it just changing values of some field in some point in space-transformative, thing of the same kind.

Or the conventional--universality time of QM, that particles are always there and are everywhere-Vacuum in a sea of particles in some ground states.

 

[A. Neumaier]

physics is about observations and measurements.

But not primarily. if this were the true goal of physics, work in physics would not be funded, and would not be of interest to society. Physics is about understanding the properties of matter and radiation to an extent that it can be used for understanding and controlling the world at large. Observations and measurements are tools to ensure that the models we form to do this are indeed adequate.

Also "sweeping a huge amount of complexity under the rug" is in the nature of the subject! There's no way to even describe the state of a macroscopic system at one instant of time, let alone to solve its dynamics in every detail.

No. Only knowing the detailed state is impossible. But its existence - and an interpretation of what it means - must be assumed even to apply the methods of statistical mechanics:

The "classicality" of macroscopic objects is just an emergent phenomenon of the necessity (and possibility!) to sweep this huge amount of complexity under the rug. Fortunately there's no need for all the microscopic details and there is usually a separation of scales, leading to effective descriptions of much coarse-grained macroscopic observables which still provide sufficient details to describe the relevant phenomena.

Thus unless quantum mechanics has intrinsic limitations it must be possible - as in Laplace's classical clockwork universe - to phrase quantum mechanics such that it applies to (and models) everything in the universe, no matter how big or complex it is.

why shouldn't it be allowed to use these very concepts in formulating the theory describing them

Because it is needed nowhere in classical physics, although there the same limitations you mention apply. Having measurement in the foundations makes the foundations depend on human activities. But physical laws must also apply for physical systems never measured by humans, like distant galaxies of which we only measure very little light, or the early stages of the solar system, of which we can measure nothing but only infer information by assuming the validity of physical laws.

 

[A. Neumaier]

QFT is nothing but a generalization of the "wavefunction"

Your sweeping statements are dead wrong and only show your ignorance of the subject. Please learn the basics before contributing to threads beyond your level of knowledge.

Quantum fields generalize the notion of observables, not that of states!

 

[ftr]

Your sweeping statements are dead wrong and only show your ignorance of the subject. Please learn the basics before contributing to threads beyond your level of knowledge.

I was just asking questions. I know I strongly worded it, I apologize. Your FAQ and your three papers( which I am not qualified to judge only trying to understand) have been very helpful. I think with a bit of polishing they will be great reference( maybe you should write a book) to anybody who started learning QM/QFT and save the students a lot of grief.

 

[A. Neumaier]

I was just asking questions.

No, you asserted that:

QFT is nothing but a generalization of the "wavefunction" which YOU described as nothing

Only then you asked a question, and even that phrased without a question mark, making it sound like an assertion! But even asking questions above your level of grasping things is unproductive.

 

[stevendaryl]

Your sweeping statements are dead wrong and only show your ignorance of the subject. Please learn the basics before contributing to threads beyond your level of knowledge.

Quantum fields generalize the notion of observables, not that of states!

I would cut a little slack for the claim that QFT is a generalization of the wave function of quantum mechanics. Many-particle quantum mechanics can be formulated in a way that looks almost identical to QFT (which is what is done in solid state physics).

It is true that QFT typically focuses on the operators, rather than the state, but you can do nonrelativistic quantum mechanics with such a focus on operators, as well. That's the Heisenberg picture.

 

[A. Neumaier]

Unbounded space and unbounded energy are needed to make dissipation possible!

In the numerical analysis of scattering processes (and especially for calculating reaction rates in quantum chemistry), working with spatially bounded approximations leads to nonphysical reflection effects at the boundaries used. This is avoiding in practice by imposing absorbing boundary conditions through the addition of an imaginary https://core.ac.uk/download/pdf/16200801.pdf vanishing in the region of interest but gradually suppressing outgoing waves. The optical potential makes the Hamiltonian non-Hermitian and thus introduces dissipation. The same technique is also used to compute first hitting times (and from this classical transition rates) in the theory of stochastic processes.

 

[A. Neumaier]

I would cut a little slack for the claim that QFT is a generalization of the wave function of quantum mechanics. Many-particle quantum mechanics can be formulated in a way that looks almost identical to QFT (which is what is done in solid state physics).

This justifies to call QFT a generalization of QM, if you like, but has nothing to do with wave functions!

It is true that QFT typically focuses on the operators, rather than the state, but you can do nonrelativistic quantum mechanics with such a focus on operators, as well. That's the Heisenberg picture.

But this makes quantum fields via annihilation and creation operators a generalization of position and momentum, if you like, and not of the wave function!

 

[A. Neumaier]

Why do you say bullet 2 is different from bullet 1? I use the same trace formula of course. What else? It's the basic definition of an expectation value in QT, and it's the most general representation-free formulation of Born's rule.

Since the interpretation is different. To say that a q-expectation always approximates a single measured valued is a nonstatistical statement and applies to any system and any $A$, even nonhermitian ones. But to say that a q-expectation is necessarily a statistical average of many measured values is a severe restriction of applicability. It requires lots of measurements (and hence needs separate justification whenever one applies the formula without any obvious measurement context), and it applies only to self-adjoint $A$, and hence not to many actual uses, which don't care what kind of operators the trace formula is applied to. In particular, it does not apply in most of your work, where you derive and use the 2PI formalism in terms of q-expectations but without any reference to measurement. As an example, consider the terms in (3.1.34) of your lecture notes on Nonequilibrium Relativistic Quantum Many-Body Theory from August 16, 2017, where - against your minimal interpretation - you, like everyone in the field, refer to expectation values of operator products that are not Hermitian, let alone self-adjoint! The measurements you compare your results to are not the measurements the Born rule allegedly applies to, but have only an extremely indirect relation to it.

you say on the one hand the thermal interpretation uses the same mathematical formalism, but it's all differently interpreted. You even use specific probabilistic/statistical notions like "uncertainty" and define it in the usual statistical terms as the standard deviation/2nd cumulant. Why is it then not right to have the same heuristics about it in your thermal interpretation (TI) as in the minimal interpretation (MI)?

Because the interpretation is very different; only the formulas are the same. The same mathematical formulas can get very different interpretations - a vector in a real vector space is often not a little arrow as the terminology suggests but can be a 3-dimensional vector, a complex number, a polynomial, a continuous function, etc.! In each case the interpretation is different but the same formulas are being used. In the same way one can (as Gibbs first did; see Subsection 2.4 of Part II) use the formulas of statistics without intending any statistical meaning.