How are electrons considered waves?

[zenith8]

Hey enotstrebor - did you know your name spells Robert Stone backwards?Leibniz, Boole and Goedel worked with logic.

You work with logic.

Therefore you are Leibniz, Boole and Goedel.

The first law of logic says A is either A or not A then the particle P can not be a duality (sometimes A wave, sometimes B particle), P can only be a wave particle unity.

The experimental evidence say that there exists both particles and waves.

Your chain of impeccable logic doesn't appear to allow for this possibility.

Therefore you are not thinking hard enough.

If P then Q is true, does not mean that if Q then P is true.

This sentence doesn't appear to make sense.

There is a word missing from this sentence.

Therefore I get confused.

If you understand that QM is not a model of the electron that produces the behavior, but a model of just the behavior, then one understands that QM, being a "Q" model, is not required to give us the correct picture of the particle "P".

QM is an algorithm for predicting experimental results, yes. But what we are doing here is indulging in interpretation, which involves assigning meaning to the terms that appear in the equations (by mapping them onto real objects), and to some extent trying to understand why it works. If you don't think that's a valid thing to do, because you're not interested in it, or because quite clearly we can never definitely know the ultimate reality of anything, or whatever - then that's fine.

But the the fact remains that if you give the terms in the equation their obvious meaning (the {\bf x}_i that appear in Schroedinger's equation are the positions of particles, and the wave that is a solution of a wave equation is er.. a wave) then everything comes out perfectly in agreement with experimental results. Only now unlike orthodox QM we have a definite picture of what's going on, which gives us a clear framework for understanding, speaking, communicating, teaching, and God knows what else.

People are allowed to do this in every other branch of physics except quantum mechanics. Why not us?

But then most theoretical physicists have rejected logic, declairing "Nature is absurd" rather than recognizing that taking a Q model's absurd implications as true, is what is absurd, not to mention, unscientific.

But to do so would deminish [sic] the glory of mans [sic] accomplishment, not to mention, having to admit that they haven't got a clue as to how to make a P model.

So, they use the Q model to prove a P model is not possible and declare victory.

Er.., hang on, you're agreeing with me aren't you? No-one ever does that..
Women are illogical.

Women like to go to parties.

Therefore logicians are no fun at parties.

Beware.

 

[strongstring]

The way electrons are waves are as follows:
Electrons have no definate position, they can be found anywhere, it is when they are observed that we know there whereabouts within a region, when multiplied by delta p is larger than h-bar. The elctrons has a probability wave that is expressed on a 3-d graph, however the ellectron cannot be found anywhere because waves can cancel each other out, therefore the electron can be found in places where the wae has not been cncelled out (you can also picture waves amplitudes adding together, a greater chance of finding thie electron there). There is also another feature, energy * time, the higher this is, the less chance there is of finding the electron there. The answer is measured in Action, like h-bar. Whenever two features of an Electron are measured that affect one another when measuring it, the product of the two variables must be greater than h-bar (6.63*10 to the power -34)/2pi. This effect of not knowing the exact whereabouts of a particles has its place in alpha radiation aswell, because we never know where a particle is, a piece lof alpha radiation can either be within the confines of the strong force, or just outside, it is the random PROBABILITY that states whther it is emitted or not.

Hope this helps :)
Will Evans

 

[sokrates]

Women are illogical.

Women like to go to parties.

Therefore logicians are no fun at parties.

Beware.

What's your point? This is not your talk show either. And you are not being funny.
enotstrebor raises a decent point. How can electrons be waves or particles depending on the circumstances?

The only answer you gave him in your irrelevant reply was to say "experimental evidence says so"..

Just because you cannot narrow the facts effectively down to a level where you can make precise, consistent predictions about nature doesn't mean nature is intrinsically "illogical"

Logical reason has served us very well over the course of history, and there's no reason to simply drop it out just because we have some confounding phenomena. And if you think hard about it, you'll remember that everything in science is in fact about logic...

Beware that a sound and concrete interpretation of quantum mechanics is still an active area of research. So instead of acting like a smug physicist who knows the answer, being a little polite and cautious about the issue will help, considering you don't even know the answer.

 

[ZapperZ]

What's your point? This is not your talk show either. And you are not being funny.
enotstrebor raises a decent point. How can electrons be waves or particles depending on the circumstances?

The only answer you gave him in your irrelevant reply was to say "experimental evidence says so"..

Just because you cannot narrow the facts effectively down to a level where you can make precise, consistent predictions about nature doesn't mean nature is intrinsically "illogical"

Logical reason has served us very well, and there's no reason to simply drop it out just because we have some confounding phenomena.

Beware that a sound and concrete interpretation of quantum mechanics is still an active area of research.

There is nothing illogical about any of this. This is because the concept of "wave" and "particle" came OUT of experimental observations themselves. These concepts are not derived out of "logic". Therefore, they are susceptible to experimental observations themselves.

There is another issue that has been ignored here, and that is PHYSICS. Logic is the tools that one use to go from one part to the other in physics, but logic cannot derive the starting basic principles. Try using logic to derive the symmetry principles that produce all our conservation laws. Can you derive conservation of momentum?

We also know (if you've read the FAQ in the General Physics forum) that there really isn't any "duality" in QM. The "wavelike" and "particlelike" behavior that we see are all described using one, consistent formulation. We do not have to switch gears at all to describe all of the phenomena that we observe. Using the photon picture, for example, we get the photoelectric effect, the anti-bunching phenomena, along with all the diffraction/interference phenomena (read the Marcella paper that I've referred to so many times). So there is NO duality in the formalism. We continue to talk about such "duality" because for those who do not understand QM, the wave and particle behavior are considered different in classical understanding, so we tend to use those as conceptual foundation.

We need to keep this discussion based on PHYSICS and not purely philosophy, or else this thread will be moved to the Philosophy forum.

Zz.

 

[strongstring]

This issue was resolved in 1987, by schroedinger and others (dont know how to do the accents). Your knowledge is limited, you only know certain principles in which physics is guided. Thorough experimental evidence shows us this, and shows us that the reason they are also waves is what i have written above. Schroedinger said that those who are not baffled by quantum mechanics have not understood it, and Feynman himself said "You are not thinking, you are being logical". Logicality is an aspect of physics thgat has been abandoned many years ago, there is this answer,, there is no need for all hese pages.
You do not know much about physics, that is clear to tell, either that or your understanding is poor.
:)

 

[WaveJumper]

We also know (if you've read the FAQ in the General Physics forum) that there really isn't any "duality" in QM. The "wavelike" and "particlelike" behavior that we see are all described using one, consistent formulation. We do not have to switch gears at all to describe all of the phenomena that we observe. Using the photon picture, for example, we get the photoelectric effect, the anti-bunching phenomena, along with all the diffraction/interference phenomena (read the Marcella paper that I've referred to so many times). So there is NO duality in the formalism. We continue to talk about such "duality" because for those who do not understand QM, the wave and particle behavior are considered different in classical understanding, so we tend to use those as conceptual foundation.

I think the "duality" has to do with the ontology and the meaning of QM's formalism.

Are you saying the Measurement Problem has been solved many years ago? Or that it never even existed?

 

[ZapperZ]

I think the "duality" has to do with the ontology and the meaning of QM's formalism.

Are you saying the Measurement Problem has been solved many years ago? Or that it never even existed?

I never said that, and why is this relevant to what I posted? That's the problem with this type of "discussion" - it goes off on a wild goose chase somewhere else while the main, narrow topic doesn't get solved.

Again, I asked you, where is the "duality" in the formalism of quantum mechanics. People are arguing back and forth about the "logic" or problem with it. Shouldn't one go back to the EXACT source and see if this is really the case? Is duality really in the formalism, or is it simply a means to convey an idea that is meant more for the consumption of the masses? Have you taken a course in QM and encounter an example where QM had to switch gears and adopt a completely different formalism to produce a "particle" and then a "wave"? Open Griffith's text, for example and satisfy yourself one way or the other.

There are many other issues that are important in the fundamental aspect of QM. You've mentioned some. This "duality" isn't one of them, and in fact, may be a consequence of more fundamental aspect of QM. So you're chasing the shadow of the object, rather than the object itself. Knowing the object (i.e. the formalism of QM intimately) is what should separate this discussion, in the physics section of PF, than the one in the Philosophy forum.

Zz.

 

[eaglelake]

Almost every textbook and website just says "This is wave particle duality" but none of them actually explain how or why an electron can be considered to be both a wave and a particle. The double slit experiment proves that wave particle duality is in fact true .. but <again> WHAT does it mean to consider an electron as a wave?

Let us try to simplify things, if that is possible. First, a quantum event is different from a classical one. We had to invent quantum mechanics because the classical laws of Newton and Einstein fail on the atomic level. Unfortunately, we are not willing to give up the mechanical universe given to us by classical physics. Further, our 'common sense' is really 'classical sense', since our entire existence is spent observing classical things behaving in a classical way. When we say that we want to understand something, we really mean to describe it in a classical way, using the language of classical physics. This is a terrible stumbling block when we seek to 'explain' quantum phenomena.

Consider a quantum experiment. Quantum mechanics (QM) allows us to calculate only two things about the experiment: 1. the possible results of the experiment and
2. the probability distribution of those results.
QM does not explain 'how the experiment works' and there is no classical explanation either! Only those things that can be experimentally verified have any meaning. If we take QM at face value, then there is nothing else. In particular, QM does not describe the behavior of particles moving through the experimental apparatus.

As a simple example, consider an electron passing through a very small single slit. It is detected on a distant screen. There are no forces acting on the electron at any time. Classically, we expect the electron to move in a straight line trajectory, and, if we repeat the experiment, the electron always hits the screen in the same spot. But that is not what happens! Rather, the electron is deflected without benefit of a deflecting force, and when we repeat the experiment, chances are it will be deflected elsewhere and hit the screen in a different location. Repeating the experiment many times gives us the probability distribution of all possible locations. This looks like the diffraction pattern we would get when we pass light waves through a slit.

But the electrons are not waves. Individual electrons are always detected as particles; we see a dot on the screen. Only when we observe many electrons hitting the screen in different locations at different times do we begin to see wave-like properties emerge [1]. It is the probability distribution that we identify as wave diffraction. This is what we mean when we say electrons have wave properties. But, we have no idea how different electrons can arrange themselves in such a manner.

To make matters worse (in a classical sense), we shouldn't talk about the electron as an individual entity independent of the apparatus with which it interacts. Rather, QM describes the entire experimental apparatus, including the detector and the experimental result as a single entity [2]. The individual parts are not separable, as in classical physics. There is no electron. There is only the entire apparatus. An electron with inherent properties that have values prior to measurement is a classical construct. In QM we only know the property value at the instant the measurement is made. The quantum electron doesn't exist until it is detected! If we assume the electron exists before detection, as in the EPR [3] experiment, we get erroneous results.

Therefore, a quantum particle has no trajectory. Although all this is difficult to accept (Einstein never did!), we must remember that this is not classical physics and the images of particles moving through space-time from place to place no longer apply.

[1] A. Tonomura, et al, Amer. J. Phys., 57, 117-120 (1989)
[2] This is the non-separability principle first enunciated by Bohr. See Wheeler, J. A. and Wojciech, W. H (eds): "Quantum Theory and Measurement". Princeton University Press, Princeton, New Jersey, 182-213 (1983), 3-7
Also Google in, Non-Separability Principle of quantum mechanics
[3] Einstein, Podolsky, and Rosen, Phys. Rev. 47, 777-780 (1935)
This is not an easy read. You will need some background in physics. But there is much about this on the net, just Google in EPR experiment

 

[WaveJumper]

So you're chasing the shadow of the object, rather than the object itself. Knowing the object (i.e. the formalism of QM intimately) is what should separate this discussion, in the physics section of PF, than the one in the Philosophy forum.

Zz.

I think if the "object" made sense, we wouldn't have 50+ interpretations and we'd probably have a theory of QG. One approach would be to take the equations as fundamental postulates and leave it at that. But surely, I myself, cannot be satisfied with this approach; much more satisfying would it be to derive these equations from more fundamental principles, that would bring some ontological sense and make clear if QM is essentially probabalistic or purely deterministic, clouded by our ignorance of the workings of a pilot-wave or another similar entity( i and many others believe it should in principle be possible).
Maybe the forum needs a new subforum - "Ontology of QM", so that instrumentalists wouldn't feel that physics isn't being done justice.

 

[ZapperZ]

I think if the "object" made sense, we wouldn't have 50+ interpretations and we'd probably have a theory of QG. One approach would be to take the equations as fundamental postulates and leave it at that. But surely, I myself, cannot be satisfied with this approach; much more satisfying would it be to derive these equations from more fundamental principles, that would bring some ontological sense and make clear if QM is essentially probabalistic or purely deterministic, clouded by our ignorance of the workings of a pilot-wave or another similar entity.
Maybe the forum needs a new subforum - "Ontology of QM", so that instrumentalists wouldn't feel that physics isn't being done justice.

Sorry, but using "sense" as an argument is very weak. What doesn't makes 'sense' to you could makes sense to me! Common sense is nothing more than an accumulated knowledge. I can show you many things that do NOT make any sense to you now, but after you learn more about it, will make more sense.

Deriving things don't make sense either. For example, "c" isn't derived, and neither are the postulates of SR. So why pick on QM?

And I SENSE that many part of this discussion is based on ignorance of the formalism of QM. Again, my question remains unanswered, as has happened each time I prod people to be more SPECIFIC, rather than simply argue things based on some personal preference. Where, exactly, in the formalism of QM (or if you don't want to cover the higher level QM, start with the standard intro QM that every single physics student has to go through, i.e. Griffiths level) is there a "duality"?

Failure to show that means that you're chasing an imaginary object that doesn't exist, rendering this whole discussion rather moot. After all, why are we wasting time on something that isn't there? I am looking for the PHYSICS. I'm not looking for someone's personal preference.

Zz.

 

[HallsofIvy]

Go on, why not?

Before I could answer that, I would have to know what you mean by "particle" and "wave"!

 

[WaveJumper]

Sorry, but using "sense" as an argument is very weak. What doesn't makes 'sense' to you could makes sense to me! Common sense is nothing more than an accumulated knowledge. I can show you many things that do NOT make any sense to you now, but after you learn more about it, will make more sense.

So, as you claim that you can make ontological sense of the formalism of QM, does the mathematical formalism tell you if QM is purely a statistical field of physics or causal and deterministic?

Deriving things don't make sense either. For example, "c" isn't derived, and neither are the postulates of SR. So why pick on QM?

The ontology of Spacetime in SR isn't clear either. Have you made sense of that too?

And I SENSE that many part of this discussion is based on ignorance of the formalism of QM. Again, my question remains unanswered, as has happened each time I prod people to be more SPECIFIC, rather than simply argue things based on some personal preference. Where, exactly, in the formalism of QM (or if you don't want to cover the higher level QM, start with the standard intro QM that every single physics student has to go through, i.e. Griffiths level) is there a "duality"?

'Duality' simply conveys the inadequacy of classical concepts. The fact that you believe that the mathematical formalism is all there is to 'understand' about QM is your preference. Mine is that it is NOT. And my position is supported by the multitude of brilliant physicists around the globe spending their lifetimes on building a successful ontological model of the universe that would unite the quantum and the classical scale.

Failure to show that means that you're chasing an imaginary object that doesn't exist, rendering this whole discussion rather moot. After all, why are we wasting time on something that isn't there? I am looking for the PHYSICS. I'm not looking for someone's personal preference.

Zz.

You have not shown that the evolution of a quantum system according to SE is fundamental. Where is the evidence for that? It's your personal preference that appears to imply that we have reached the end of physics.

 

[ZapperZ]

So, as you claim that you can make ontological sense of the formalism of QM, does the mathematical formalism tell you if QM is purely a statistical field of physics or causal and deterministic? The ontology of Spacetime in SR isn't clear either. Have you made sense of that too?'Duality' simply conveys the inadequacy of classical concepts. The fact that you believe that the mathematical formalism is all there is to 'understand' about QM is your preference. Mine is that it is NOT. And my position is supported by the multitude of brilliant physicists around the globe spending their lifetimes on building a successful ontological model of the universe that would unite the quantum and the classical scale.
You have not shown that the evolution of a quantum system according to SE is fundamental. Where is the evidence for that? It's your personal preference that appears to imply that we have reached the end of physics.

You are now rambling here, and somehow, my request for you to show where the formalism of QM results in "duality" has somehow morphed into my claim that we've reached the end of physics. And you talk about things that should make sense?

My conclusion from this is that you are unable to show where in QM formalism, there is this "duality". Am I correct? I certainly am so far since I've asked this several times already. Do you not even own a copy of a standard undergrad QM text? Or have you never formally done QM? And not knowing the thing you are trying to discuss makes any sense to you? It doesn't to me.

Then this discussion is done, because I'd rather discuss something that actually exists and legitimate, not something made up in someone's imagination.

Zz.

 

[ZapperZ]

It is appropriate for me, I think, to mention here that I'm not the only one who is fed up with this kind of misrepresentation of QM.

Are there plenty of conceptual problems with QM? Sure there are! Is the "duality" a problem in QM? NOPE! It is a problem only when we try to look at the QM-classical boundary. But the formalism of QM itself does NOT have such dualism. I've mentioned this many times.

In fact, for many experts in this field, it has gotten to the point of annoyance. Refer to the rather pointed letter in AJP by N. G. van Kampen titled "The scandal of quantum mechanics," (Am. J. Phys. 76, 989-990 (2008)). Here, he expressed his frustration that people seem to forget the the formalism is very much clear on what it can do, while others seems to be tripping over themselves at trying to make "interpretation" using purely classical concepts!

Art Hobson even responded to that article with his comments that was also published in AJP, and that can be found here:

http://physics.uark.edu/hobson/pubs/08.11.AJP.html

Note his first few sentences:

It is indeed a scandal that there are still so many "interpretations" of quantum physics when the theory actually provides a complete and adequate description of phenomena. Van Kampen correctly attributes these unnecessary interpretations to the difficulties experienced by "someone who still thinks of electrons as individual particles rather than as manifestations of a wave function." Indeed, electrons are not individual particles.

Edit: One might want to consider looking at his article in Physics Teachers on "Teaching Quantum Mechanics without Paradoxes".

http://physics.uark.edu/hobson/pubs/07.02.TPT.pdf

Done!

Zz.

 

[zonde]

One might want to consider looking at his article in Physics Teachers on "Teaching Quantum Mechanics without Paradoxes".

http://physics.uark.edu/hobson/pubs/07.02.TPT.pdf

Sure. From this link:

Briefly, the resolution is that material particles and photons are the quanta of extended spatially continuous but energetically quantized fields.

and

This quantum comes from the entire continuous, space-filling field—a “nonlocal” effect—and it interacts instantaneously and randomly with the screen in accordance with the probability amplitude specified by the EM field. We see immediately that nonlocality and uncertainty are inherent in quantum physics.

And this is called "Teaching Quantum Mechanics without Paradoxes"?
This is not even funny.

 

[Born2bwire]

What's the paradox?

 

[ZapperZ]

What's the paradox?

I'd like to know as well. Sometime people confuse "conceptually difficult" with "paradox".

Zz.

 

[zenith8]

What is true is that the very concepts of "particle" and "wave" are not valid in the very micro, quantum, domain.

Go on, why not?

Before I could answer that, I would have to know what you mean by "particle" and "wave"!

See my post #15 in the https://www.physicsforums.com/showthread.php?t=340864".

I repeat my original question.

 

[zonde]

Sometime people confuse "conceptually difficult" with "paradox".

Indeed it is difficult to explain how can entity dissolve into the field and form back without admitting that it can actually vanish into and emerge from the field.

 

[Peter Morgan]

It's so much fun talking past each other. I'll play, staying fairly close to Copenhagen.

There are only "particles" (in fact, "events") when we put what we call "measurement apparatuses" near other objects that we call "preparation apparatuses", the whole being the "experimental apparatus". If we have only preparation apparatuses, then we see no "measurement events". Taking the (rather fiercely empiricist) Copenhagen line, if there are no measurement events, then we cannot speak of there being something there. Even if we observe thermodynamic events in a detector, we have to take the dubious step of insisting that there must be a cause of the events (this is a dubious step even if the events are correlated in the sense that they are in an almost straight line, but of course everyone -- except empiricist purists -- takes this step because it is so often useful to assume that there are causes).

The "measurement events" are just as decidedly classical as the experimental apparatus they are observed in, in that they are thermodynamic transitions from a "ready" state to an "excited" state of a "measurement" device that is deliberately engineered to have those states (and in the modern case to cycle from the excited state back to the ready state, in contrast to a photographic plate). Everything observed is at the classical scale.

The introduction of something nonclassical, QM, depends on an assumption that different preparation apparatuses can be described by the same density operator regardless of what measurement apparatus we use with the preparation apparatus (and, vice versa, that we can describe a measurement apparatus by the same POVM regardless of what preparation apparatus we use with the measurement apparatus). This assumption is essentially a (very useful) convention in QM, whereas it is not plausible in a classical model of an experiment. This assumption results in major differences between classical and quantum models.

The idea that "particles" somehow cause "events" is not necessarily the best way to understand Physics. An alternative is to think of there being a field that causes the events in the measurement apparatuses. I would argue that we can think of the field being either a quantum field or a random field (not a classical continuous field), but it takes a moderate degree of sophistication to do so, and I may be wrong, because I have only worked out some of the details so far. If we say that the "quantum field" causes the events, and describes the statistics and correlations between the events very effectively, the gatekeepers will be less likely to torture us until we cry uncle. The measurement apparatus is tuned to make transitions from the ready state to the excited state, which will happen with different statistics depending on what preparation apparatus is placed close to it. It takes time and care for an experimentalist to produce a given statistics and correlations of events, but this is what experimentalists do. Of course this also introduces an essentially speculative "cause", the "field", but that could be said to be what Physics is about.

 

[zonde]

The idea that "particles" somehow cause "events" is not necessarily the best way to understand Physics. An alternative is to think of there being a field that causes the events in the measurement apparatuses.

Seems reasonable. But what is the role of quanta in this? Is it for all distinguishable things the same as "particle" or is it something different?

 

[Peter Morgan]

Seems reasonable. But what is the role of quanta in this? Is it for all distinguishable things the same as "particle" or is it something different?

Good question. Quanta come to two things: (1) some operators have discrete spectra. We observe discrete spectra that can be modeled rather well as the eigenvalue spectrum of an operator, such as the energy spectrum of the Hamiltonian of an electron in a bound state.

I personally think that bound states are problematic in the Standard Model of quantum field theory, insofar as perturbation theory largely deals with scattering, whereas the mathematics of bound states is much less developed. Nonetheless, we can introduce various central potentials and produce quite nice results, including fine details like the Lamb shift. The introduction of a particular central potential, however, is problematic from a QFT perspective, in which such forces ought to be derived as a result of gauge fields. As far as I know, it is mostly a matter of faith that we will eventually be able to derive from the QCD Lagrangian what the effective central forces are for specific nuclei. [Given the nontrivial magnetic moments of nuclei and electrons, however, it's clear that the effective forces are not central forces. There are a lot of details to keep track of!]​

(2) Just as delicately, superselection sectors give a discrete structure in quantum field theory. However creation and annihilation operators of modes of the electromagnetic field do not map between superselection sectors, so that there is no natural discrete structure associated with the electromagnetic field. The same is true for simple Boson fields such as the Klein-Gordon field. This has been a debated issue in the quantum field theory literature for at least 20 years, with a large section of the literature coming down against there being discrete structure (and certainly against there being particle structure) for the electromagnetic field --- Feynman diagrams and the ways that Physicists talk about photons notwithstanding. [Maybe it's helpful to point out that just because a continuous curve can be decomposed as the sum of Fourier components doesn't necessarily mean that there is a natural discrete structure to the continuous curve.]

Fermion fields and non-abelian gauge fields are associated with specific discrete charges, electric charge in the case of electrons, so there is this discrete structure to be found for almost all fields except the electromagnetic field. The closest analogy to the superselection sectors of QFT that I know of are the topological sectors of continuous fields. Determining which superselection sector a given state is in requires global measurement, just as when we try to determine which topological sector a given state is in (think of a mobius strip -- locally, we can't tell whether there's a twist or not; only by checking the whole loop can we determine whether there's a twist or not). Unfortunately, continuous functions are not adequate to model Physics, because it is not possible to introduce thermal and quantum fluctuations in a mathematically acceptable way (probability distributions over continuous fields result in problems). There is a classical object called a random field that allows us to model thermal and quantum fluctuations as well as a quantum field can, but, again, this is an idea that is so far only to be found in a few published papers, all by me (which means that there are a few referees who thought the papers were not so ridiculous that they wouldn't let them be published, not that the referees thought the papers were brilliant -- they definitely had reservations). The papers are available through my web-page (links to both arXiv and published versions). I explain random fields multiple times in those papers; they could be thought of as what you need to do to deal with proper mathematical care with probability densities over a generalized function space (certainly a more generalized function space than just the space of continuous functions, so that everything is measure theoretical instead of differentiation). After years of working with random fields, they seem very simple and pretty mathematics to me, but there is a sophistication to them that is pretty much equal to that of quantum fields (as you should expect would be needed), and indeed my latest papers show that there are random fields that are empirically equivalent to the complex Klein-Gordon quantum field (published) and to the quantized electromagnetic field (so far unpublished).

The final discrete structure (3!) is the engineered thermodynamics of the detection apparatuses, which I would say has nothing to do with quanta. When we construct an apparatus that has two thermodynamic states, a ready state and an excited state, which are macroscopically discernible in the sense that we can see that it is on one or the other thermodynamic state, then, inevitably, we observe discrete events. When we tune the two states so that the apparatus may be as delicately balanced as a pencil on its tip (with a feedback mechanism for getting it back to vertical as soon as something knocks it out of its unstable thermodynamic ready state), we observe different statistics for transitions depending on what other apparatus we put near it. Modern Physics is about determining the response of different kinds of such delicately balanced thermodynamically nontrivial apparatus to different kinds of preparation apparatus (which is generally about as nontrivial in its own way). [I've been looking for an alternative to the words "measurement apparatus" that doesn't imply so strongly that there is something that is measured, perhaps "response apparatus" is OK.] It is fundamental that all this happens in the presence of quantum fluctuations, which are distinct from thermal fluctuations.

It's amazing to me that this kind of detailed analysis of what happens in a measurement is not common parlance amongst Physicists, but to my knowledge it's not. A study of the changes of the response of an apparatus to different inputs is a commonplace for control systems.

 

[ZapperZ]

Indeed it is difficult to explain how can entity dissolve into the field and form back without admitting that it can actually vanish into and emerge from the field.

But you're just illustrating the fact that there isn't a "paradox", but rather a conceptual difficulties by some people (you). You should not confuse those two - they are not identical.

Zz.

 

[zonde]

Peter,
Your answer was very interesting to read but I didn't found direct answer. I took out some sentences that as I understand hint about possible answers:

some operators have discrete spectra
...
superselection sectors give a discrete structure in quantum field theory. However creation and annihilation operators of modes of the electromagnetic field do not map between superselection sectors, so that there is no natural discrete structure associated with the electromagnetic field.
...
Fermion fields and non-abelian gauge fields are associated with specific discrete charges, electric charge in the case of electrons, so there is this discrete structure to be found for almost all fields except the electromagnetic field.

From these sentences I guess that the aim is to make field so discrete that it will allow to speak about something like particles.
But I will try to answer myself:
Particles has certain energy (mass) and spatial borders so that we can unambiguously identify what energy belongs to particle and what does not belong.
For quanta we have certain energy so there is match for particle. Unclear thing for me is whether quanta can spatially overlap with other quantas.
You mentioned superselection sectors but this is mathematical concept and does not give me any hint about this overlapping question. My guess is that quanta can overlap with other quanta.

The final discrete structure (3!) is the engineered thermodynamics of the detection apparatuses, which I would say has nothing to do with quanta.

I understand that empirical approach is safer meaning that there we are free from uncertain assumptions but in case of quanta that would mean that we should talk about black body radiation. However there are a lot of indirect empirical data for meaningful speculations about quanta as it seems to me.

There is a classical object called a random field that allows us to model thermal and quantum fluctuations as well as a quantum field can

I understand that this is a topic that you would really want to discuss. But I just don't really understand at what your approach is aimed. I guess it's related to some QFT questions.

 

[Peter Morgan]

Peter,
Your answer was very interesting to read but I didn't found direct answer. I took out some sentences that as I understand hint about possible answers:

To be honest, my post was long enough that I expected that I was writing for myself, trying to clarify issues in my head that I expect to write about in papers that I will hope to be published. I took your post as a starting point, but at least in part I got carried away. I'm glad that you read all that!

From these sentences I guess that the aim is to make field so discrete that it will allow to speak about something like particles.
But I will try to answer myself:
Particles has certain energy (mass) and spatial borders so that we can unambiguously identify what energy belongs to particle and what does not belong.

I would say that it's difficult to say that energy (or mass, stuff, or whatever) identifiably belongs to one particle or another. To revert to (the problematic analogy of) the topology of a strip paper that has two twists in it, there is no natural way to say which part of the paper is one of the twists and which part of the paper is in the other twist. If we introduce a coordinate system in the 3-space that the paper loop is embedded in, we may be able to identify different parts of the paper to assign to each of the twists relative to that coordinate system, but I would say that introducing a strong structure such as a coordinate system (or some other structure that allows an assignment of parts of the whole to individuals) is not to be done lightly.

Separability is well-known to be extremely delicate in quantum mechanics, so that it seems better to think in terms of particle number as a global topological property (insofar as one thinks in terms of analogies instead of taking the safer road of just using whatever mathematics turns out to be empirically effective). I take it to be one of the most important properties of the empirical data that the discrete particle number is conserved over time. Properties of a whole system are not necessarily expressible in terms of properties of parts of the whole system taken separately.

All that said, I take it that the de Borglie-Bohm interpretation would do much of what you are asking for, but there are too many reasons not to like it (the way that it uses configuration space instead of real space, the way in which nonlocality is introduced, and whether a relativistic version exists at all). I'm more impressed by Nelson stochastic mechanics and by Stochastic electrodynamics, but I prefer not to introduce point-like particles embedded in a field, which effectively rules out these classes of models.

For quanta we have certain energy so there is match for particle. Unclear thing for me is whether quanta can spatially overlap with other quantas.
You mentioned superselection sectors but this is mathematical concept and does not give me any hint about this overlapping question. My guess is that quanta can overlap with other quanta.

Because I don't take particular parts of energy or space-time to be allocated to quanta, this is a non question for me. If you can find a specific natural way to allocate parts of energy and space-time to particular quanta, I'm sure that would answer your question. I suspect that you won't be able to, but of course I've been prejudiced in favor of random field models for too long to be any help to you.

I understand that empirical approach is safer meaning that there we are free from uncertain assumptions but in case of quanta that would mean that we should talk about black body radiation. However there are a lot of indirect empirical data for meaningful speculations about quanta as it seems to me.

What we take to be the empirical data is a very important question! What answer we give goes a long way to determine what our theory will look like. I am not an empiricist in the 1920s positivist style. The post-positivist critique that was mostly constructed through the 1950s to the 1970s includes a strong claim that our descriptions of experiments are theory-laden, which I personally think is undeniable. [There are other aspects to the post-positivist critique that I also think have weight, incommensurability, underdetermination, and the pessimistic meta-induction, but those are not directly relevant to this particular point.]

If we say that one empirical idea is an empirical principle, as Einstein did with the speed of light in vacuum, we set it above other empirical ideas. If other people espouse different empirical principles, the mathematics they do will look very different. If one goes to Foundations of Physics conferences, or looks at the table of contents of the journal Foundations of Physics, it is very striking that very different parts of the empirical data are taken to be most important, less important, rather indirect, etc.

I effectively take random fields on Minkowski space as a starting point, because I take it that there must be some mathematical structure that can be taken to be the substrate for the thermodynamics of response apparatus events, but I'm not willing to use particles because I see the mathematics of classical particles leading to trouble. Part of the reason for taking random fields as a starting point is that they are the closest classical mathematics to quantum fields, which I take to be empirically strongly enough supported that they have to be taken seriously -- at least.

I understand that this is a topic that you would really want to discuss. But I just don't really understand at what your approach is aimed. I guess it's related to some QFT questions.

Oh yes, QFT is a major target, because there are some senses in which I think it looks easier to understand/interpret QFT than it is to understand/interpret non-relativistic quantum mechanics.

I see that you were the person who took ZapperZ to task for suggesting that Art Hobson's "Teaching Quantum Mechanics without Paradoxes" is a good way to go. I agree with you that Art doesn't get there, certainly not enough for Zz to cite him as a definitive source, but I personally find Art's attempt to use quantum field theory as the way to go very refreshing. I read some of Art's ideas as somewhat counter-culture. I think I read them generously, however, in the sense of bringing in other field-related ideas, and particularly random fields, which I find enough to make sense of him.

 

[zonde]

I take it to be one of the most important properties of the empirical data that the discrete particle number is conserved over time.

Can you expand this?
Do you mean particle number is conserved statistically? And what empirical data do you have on mind?

Because I don't take particular parts of energy or space-time to be allocated to quanta, this is a non question for me. If you can find a specific natural way to allocate parts of energy and space-time to particular quanta, I'm sure that would answer your question. I suspect that you won't be able to, but of course I've been prejudiced in favor of random field models for too long to be any help to you.

I am not sure I understand your position. Where do you see physical significance of quanta then?
Surely you must take that there is some physical significance of quanta at least in interactions (photon absorption by electron for example).

I have to say that I have some rude ideas how energy can be physically allocated to quanta but these are for my own comfort so to say.

And do you have some link with introduction in random fields? I looked into wikipedia but it is very short about this topic. Maybe there is any of your own papers that are not very specific?

 

[zonde]

But you're just illustrating the fact that there isn't a "paradox", but rather a conceptual difficulties by some people (you). You should not confuse those two - they are not identical.

From wikipedia:
A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition.

I would say it's subjective what is considered "paradox".

 

[Peter Morgan]

Can you expand this?
Do you mean particle number is conserved statistically? And what empirical data do you have in mind?

By particle number, I mean the number of particles minus the number of anti-particles in a state. Strictly, I would say that charges are conserved, which imply the conservation of particle number. I would take the conservation of electrical charge —absolutely, not statistically— to be an empirical principle that is essentially unquestioned. Electric charge is of course intimately related to the U(1) gauge group in the standard formalisms. Physical states apparently can be mixtures of states that have different charges, but they cannot be superpositions of states that have different charges, which is just to say that there is a superselection principle for electric charge.

As far as the conservation of other charges is concerned, of electroweak and color charges, or perhaps of hadron number conservation, I would regard these as more open to question, but, in the absence of any definite reason, it suits me for now to give the Standard Model of Particle Physics the benefit of the doubt. My understanding of the detailed phenomenology of Particle Physics needs a lot of brushing up.

I take it to be a significant key to how we should construct theories that electric charge is an integer multiple of the charge on the electron in almost all circumstances.

I am not sure I understand your position. Where do you see physical significance of quanta then?
Surely you must take that there is some physical significance of quanta at least in interactions (photon absorption by electron for example).

I have to say that I have some rude ideas how energy can be physically allocated to quanta but these are for my own comfort so to say.

And do you have some link with introduction in random fields? I looked into wikipedia but it is very short about this topic. Maybe there is any of your own papers that are not very specific?

Where did you last see a photon absorbed by an electron? It's a standard way of talking, of course, justified by a naive interpretation of a tree level Feynman diagram, but if we introduce loop level Feynman diagrams, and get past renormalization, a similarly naive interpretation would have to say that there are infinite numbers of electrons and photons of infinitely varied energies, both on and off shell, interacting together, which is just messy.

At the empirical level, I would be (somewhat) more happy to say that a photon was absorbed by a macroscopic object, causing a thermodynamic transition from a ready state to an excited state that I can see with a microscope, or that is amplified electrically to the point that a computer memory bit is modified. There's always a question whether any given event was caused by a cosmic ray, was a result of an internal fluctuation of the macroscopic object, was caused by a stray electron, neutron, neutrino, or whatever, from an unshielded piece of apparatus in the room, etc.. If we see the rate of events change just after we turn on a light, we can only say that a particular discrete thermodynamic transition was quite likely caused by the light being turned on, not that it was definitely caused by a photon. I'm happy saying that the change of the statistics was caused by turning on the light, but we should be careful what we say about individual events.

As I said a few messages back, I take there to be three fairly incontrovertible discrete structures, charges, discrete spectra (something like the spectrum of Hydrogen, say, which are modeled as the eigenvalues of observables), and thermodynamic transitions of macroscopic objects. The idea that there are "quanta" is too vague to be thrown around without any indication of what mathematics we're using. Insofar as Planck's constant is what we're talking about when we talk about "quanta", I take it to be a measure of irreducible quantum fluctuations, which have effects on most small-scale Physics, which can be observed in large-scale Physics when we take appropriate steps to engineer amplification. My papers talk about this in an evolving way that is not entirely coherent over time.

As far as references on random fields are concerned, please get back to me immediately if you find something accessible on the web or in the literature! My own attempts at explaining random fields only scratch at the surface of the mathematics. There are a number of books in the Yale libraries,
Preston, Christopher J., Random fields, Springer-Verlag, 1976.
Vanmarcke, Erik., Random fields, analysis and synthesis, MIT Press, c1983.
Rozanov, Yu. A, Random fields and stochastic partial differential equations, Kluwer Academic, c1998.
Spitzer, Frank Ludwig, Random fields and interacting particle systems, Mathematical Association of America, 1971.

Another book is Stanley P. Gudder, Stochastic Methods in Quantum Mechanics, North-Holland, 1979, which I have taken to citing in papers, referring particularly to chapter 6, because the discussion of random fields is quite nicely done and geared to quantum field theory ways of thinking.

As you see, most of these references are from 20-30 years ago.

The algebraic methods I'm using to construct random fields and states over them, of creation and annihilation operators, are not in the literature in any direct way to my knowledge, although they are not particularly difficult mathematics. People haven't much thought it would be interesting to work with random fields, so finding effective ways of using them has not been investigated. The mathematics I'm using is partly just that of commutative *-algebras, for the field observables, whereas the algebra of creation and annihilation operators are very similar to what is used in quantum field theory. The literature of C*-algebras to a limited extent applies also to *-algebras, although the lack of a norm for the local observables has plenty of consequences.

Andrei Khrennikov has been using a mathematics that can be thought of as random fields, although I have not liked his formalism much. His papers can be found on arXiv.

Random fields are used in Physics at the Cosmological scale (indeed it was someone who works on Cosmology who was the second person to point out this mathematics to me, about six years ago), but I don't know whether there is a standard reference for random fields in that literature. So I've written to that person to find out whether there's a standard reference to cite or for sending graduate students to it.

 

[ZapperZ]

From wikipedia:
A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition.

I would say it's subjective what is considered "paradox".

Intuition? I can show you plenty of situations that defy your "intuition", but will later makes sense after you UNDERSTAND the physics. So relying on your intuition to challenge a theory, much less, a VALID theory, is not a valid challenge, nor is it a valid argument against something.

Even using that definition, where is the "contradiction" here? The existence of a paradox is claimed, but that was simply a statement without justification. It takes zero effort and knowledge to make such statement. I can say you're wrong and left it at that without bothering to explain why. Do we expect physics to be as flimsy as political discussion you get on TV?

Zz.

 

[encrypted]

Howdy everyone, too much to read for a business major with ADD. I don't know what most of the physics majors in this thread have posted and I couldn't manage to read past page 1 cause it got too detailed for me (thanks ADD) and I didn't read past it anyways. But I have such an undying love for the world differentiating the quantum world vs. Einstein's general relativity word, which is how I ended up on this forum.

In layman's terms as I understand it, electrons (whether you consider them particles of matter or a quantum wave at the sub-atomic level are pretty much the same thing and) are possibilities of an outcome with endless possibilities resulting from a certain action, in the absence of an observer i.e. when someone is not watching (or not). A particle (whether a piece of matter or otherwise) can be in several places at the same time (i.e. a million outcomes of a single action and be it at several positions/locations at the same time). As a result, we find the "quantum wave" tends to answer so many more mathematical un-naturalities and potentials in the sub-atomic world.

But what makes it so intriguing is that when you as an individual or a measuring device is placed at a critical phase during the experiment, the particle "realizes" that it's being observed and changes itself to behave like an ordinary particle atom i.e. going into a "yes or no" outcome of an experiment.

The simple act of "observing" a particle basically made if behave differently, as though the particle was aware if was being observed, thanks to us being the "observer".

Which begs the ultimate question, does the particle behave differently in the eyes of the ultimate observer (i.e. God) vs. us (as humans) and yet, furtherly different in the absence of no state of observence.

 

[zenith8]

Which begs the ultimate question, does the particle behave differently in the eyes of the ultimate observer (i.e. God) vs. us (as humans) and yet, furtherly different in the absence of no state of observence.

Hi encrypted. The most obvious interpretation of what the equations mean - it was so obvious that it was the first one postulated in 1927 by de Broglie - is that the electrons are just perfectly ordinary particles 'guided' or pushed around by a wave (the usual quantum mechanical 'wave function'). Quantum mechanics is then just the same as classical (statistical) mechanics but with an extra force. All the whizzo 'isn't this weird' God observer cat stuff was tacked on by Bohr and his mates in the late 1920s - essentially because they were influenced by a temporarily fashionable philosophical prejudice called positivism (which was later violently disproved by the philosophers themselves in a process almost entirely unnoticed by the physics community.).

You probably think I sound like a crackpot. But that's how Bohr and the others won - by kindly accusing the behaviour of people like me as being due to our having had a full-frontal lobotomy or something like that.

Seriously - you think electrons don't have trajectories and only manifest themselves when an observer looks at them? Try following the streamlines of the probability current. Might be a revelation. Look up de Broglie-Bohm 'pilot wave' theory.

 

[Phrak]

You probably think I sound like a crackpot. But that's how Bohr and the others won - by kindly accusing the behaviour of people like me as being due to our having had a full-frontal lobotomy or something like that.

Do you think there are only two alternative camps?

Seriously - you think electrons don't have trajectories and only manifest themselves when an observer looks at them? Try following the streamlines of the probability current. Might be a revelation. Look up de Broglie-Bohm 'pilot wave' theory.

And then comes relativity. Where are the Lorentz invariant pilot waves?

 

[zenith8]

Lazy, knee-jerk criticism of something you plainly know nothing about.

And then comes relativity. Where are the Lorentz invariant pilot waves?

In the Lorentz invariant pilot-wave theory. Read the literature.. (or just allow it to be Lorentz invariant on average).

 

[zonde]

So relying on your intuition to challenge a theory, much less, a VALID theory, is not a valid challenge, nor is it a valid argument against something.

Prove that.

For that purpose I propose to consider photon EPR experiment with two sites with PBSes and 4 detectors at each output of two PBSes. In one of four channels between detector and PBS we insert wave plate that rotate polarization angle by 90 deg. Does this additional wave plate change outcome of experiment (compared to outcome without this plate)?
What says your understanding of physics and what says your intuition?
My intuition says that wave plate for this modified channel will invert correlations with other site's two channels.

 

[Peter Morgan]

Lazy, knee-jerk criticism of something you plainly know nothing about.

In the Lorentz invariant pilot-wave theory. Read the literature.. (or just allow it to be Lorentz invariant on average).

I'm curious what you take to be the Lorentz invariant pilot-wave theory literature. Do you mean Shelly Goldstein et al? In any case, I'd be interested in, say, 3 citations, that you think best make the case. arXiv or published would be OK.

I'm also curious whether anyone has been careful enough with the mathematics to get a paper published on allowing "it to be Lorentz invariant on average". Again, I'd be interested in arXiv or published.

It is of course possible not to know all the literature despite an honest attempt to do so. In response to someone who apparently doesn't know about a given literature, it's better to give citations than to tell them to "read the literature" if you want to be taken seriously. It also could be said to be less lazy, perhaps, and surely to be more polite? And, I suppose, there is more chance of persuading anyone of your point of view.

Physicists' perception of the inadequacies of de Broglie-Bohm models is, as I presume you know, not just a question of whether there is a Lorentz-invariant version of the theory, which as you suggest is routinely trotted out as a get-rid-of-this-fool reason for rejecting de Broglie-Bohm models. It's irritating, and don't diss the minority laws ought to be applied against such ex Cathedra statements, but don't let it get to you. Personally, I simply feel more comfortable with Hilbert space mathematics than working with the trajectory equations of de Broglie-Bohm, and I feel somewhat uncomfortable with the use that is made of configuration space, both because it's 3N dimensional and because it's not phase space. I follow the literature more-or-less, though not actively, but I always come away dissatisfied.

It may be that I'm not seeing what you see in the de Broglie-Bohm approach, but, given that I've done my best to see whether there's something interesting there, I think that means that you have more to do to make it clearer what you see. That means that you have to make a serious attempt to clarify, in papers on arXiv at least, but preferably with the care required to get something published (yes, with enough care papers on de Broglie-Bohm approaches have been published), why the various reasons people have for not thinking de Broglie-Bohm approach as seriously as, say, Nelson trajectories or the trajectories of Stochastic Electrodynamics, or as seriously as other interpretations of quantum theory, for all their failings. Two line rejoinders don't make much impression.

 

[Naty1]

A comment on
"WHAT does it mean to consider an electron as a wave?"

also posts 64 (Zapper) and perhaps reply in part to post #80 at the same time.

The following quote is from Roger Penrose celebrating Stephen Hawking 60th birthday in 1993 at Cambridge England...this description offered me a new insight into quantum/classical relationships:

Either we do physics on a large scale, in which case we use classical level physics;the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrodinger equation: deterministic, time symmetric and and local. These are exactly the same words I used to describe classical physics.

However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction isnon deterministic,time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w,z, complex numbers...an essential ingredient of the Schrodinger euqation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to..keeping them sitting there is quantum linearity...
QUOTE]
and he goes on to relate this linearity and superposition to the double slit experiment.

So I finally "get" what Zapper was stating in another thread about quantum consistency...
the "ambiguity" is in the classical to quantum interface and conversion...YET

Penrose goes on to say

My own view is that quantum theory is an approximate theory and we have to seek some new theory which supplants all three procedues.. classical, reduction and quantum...

(He subsequently notes lots of people would not agree)

(The above comes from The Penrose lecture, The problem of spacetime singularities:implications for quantum gravity, pages 63-67, THE FUTURE OF THEORETICAL PHYSICS AND COSMOLOGY, 1993..)

 

[zenith8]

That means that you have to make a serious attempt to clarify, in papers on arXiv at least, but preferably with the care required to get something published (yes, with enough care papers on de Broglie-Bohm approaches have been published)..

Stop treating me like a child, Morgan. Look - no offence, but I can't be bothered to take you on. These things have all been discussed ad nauseam in recent threads, and one just loses the will to live (particularly since this thread is specifically not about this issue).

Detailed references for many of the er.. several thousand papers that the naughty Bohmians have been lucky enough to have published are included on the website for the http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" . Click the 'Further Reading' tab. For relativistic stuff you should look under the section "Relativistic stuff and non-locality" - a good summary/review is included in the opening part of the recent paper "A Dirac sea pilot-wave model for quantum field theory" S. Colin, W. Struyve (2007). Some of the modern general review articles also have good discussions.

I'm also curious whether anyone has been careful enough with the mathematics to get a paper published on allowing "it to be Lorentz invariant on average". Again, I'd be interested in arXiv or published.

How about er.. D. Bohm, Prog. Theo. Phys. 9, 273 (1953). Quite a recent development then.