How are electrons considered waves?

[zenith8]

By classical trajectory, I mean a position at each instant of time, i.e. a world-line in spacetime. It's the standard usage of the word as far as I am aware.

Exactly. If that's the standard usage then so be it, but it is confusing because the word 'classical' to most people implies a particular dynamics (Newton).

 

[dx]

Name one.

High energy physics based on relativistic quantum mechanics.

And just to be contrary - you should know that very little is actually 'understood' in the ordinary framework. Copenhagen is a carefully designed means of avoiding understanding - and I don't mean that in a pejorative sense - that is genuinely how Bohr et al. designed it.

Obviously we have have different ideas of what 'understanding' means. If a theory describes a wide class of phenomena, then that theory is, in a sense, a kind of 'pattern' behind the phenomena. As far as I am concerned, understanding is simply the appreciation of such patterns in nature that we cannot directly percieve. In this sense, nothing beats quantum mechanics in the understanding it provides, because it practically underlies all phenomena that have ever been observed as far as we can tell.

 

[RonC]

I understand my bias because of a certain level of study from Stanford University that concerns this question raised.

If you have had the privilege to attend one of Dr. R.B. Laughlin lectures, a Noble Prize recipient I was persuaded that the election as quantum mechanical entity which consisted of waves of nothing.

First, this was disturbing to me so my question was how did you arrive at this conclusion? He explained, and I believe (?) he has also published and written a book explaining that the Newtonian idea of position and velocity by distinguishing an object is no longer correct and should be replaced by the wave function.

Spending time and doing the calculation in that time period of my life (work was in progress), I was confounded and then convinced he might be correct.

How do you feel about this?

 

[zenith8]

High energy physics based on relativistic quantum mechanics.

Not so. Relativistic Bohmian theories exist which reproduce all the predictions of the regular theories. The only problem as far as I am aware is that the theory disagrees with some ideas of relativistic metaphysics (i.e. Lorentz invariance being an average property, rather than one which is strictly true in every quantum event. And the existence or not of preferred frames and things like that). But there is no disagreement with physics.

Obviously we have have different ideas of what 'understanding' means. If a theory describes a wide class of phenomena, then that theory is, in a sense, a kind of 'pattern' behind the phenomena. As far as I am concerned, understanding is simply the appreciation of such patterns in nature that we cannot directly percieve.

OK, I appreciate your point. But to me 'reproducing the results of experiments' is not the same as 'understanding'. In the ordinary human sense of the word, understanding would imply that you had some idea of why your experiments gave the results they did. In other physical theories this is often done by mapping the mathematical objects in your equations onto some objectively existing things in the real world, but there are other methods.

So your two-slit experiment produces a distribution of individual electrons shaped like a cos^2 interference pattern on the screen. Your theory (QM) tells you the probability of electrons appearing on the screen has the same cos^2 shape. If I stop there, you have not understood anything, have you? You've just allowed yourself to make predictions, which might be useful for engineering purposes.

 

[zenith8]

I understand my bias because of a certain level of study from Stanford University that concerns this question raised.

If you have had the privilege to attend one of Dr. R.B. Laughlin lectures, a Noble Prize recipient I was persuaded that the election as quantum mechanical entity which consisted of waves of nothing.

First, this was disturbing to me so my question was how did you arrive at this conclusion? He explained, and I believe (?) he has also published and written a book explaining that the Newtonian idea of position and velocity by distinguishing an object is no longer correct and should be replaced by the wave function.

Spending time and doing the calculation in that time period of my life (work was in progress), I was confounded and then convinced he might be correct.

How do you feel about this?

If Laughlin states this as a fact then I'm afraid that cannot be substantiated. He may well be correct, but as far as I know the idea that electrons consist only of waves cannot be deduced from anything that we know - it is simply a point of view.. And I would say it is a much less obvious point of view than the one I have been advocating here. The idea that particles and waves exist in the de Broglie-Bohm sense is perfectly consistent with all known quantum-mechanical theories, and is suggested by many experiments. And believe me, if it wasn't, then we would know about it. Elderly people who were educated before the 1980s were trained that Bohrian Copenhagenism was the only logically consistent way to think ('We see that it cannot be otherwise'. ' The situation is an unavoidable one'. 'This is something that there is no way round.' etc..) so if you didn't think like that, then you were a fool. Ever since the 1950s people have been itching to have a go at the Bohmian quantum heretics - like the Inquisition guys wanted to burn people who said the Earth went round the sun - but no-one has ever succeeded in landing a fatal, or even slightly damaging, blow.

Laughlin's old, isn't he?

 

[zenith8]

If you have had the privilege to attend one of Dr. R.B. Laughlin lectures, a Noble Prize recipient I was persuaded that the election as quantum mechanical entity which consisted of waves of nothing.

By the way, take care never to win one of those prizes yourself. Not being able to spell it might be a tad embarrassing.. :!)

 

[dx]

OK, I appreciate your point. But to me 'reproducing the results of experiments' is not the same as 'understanding'. In the ordinary human sense of the word, understanding would imply that you had some idea of why your experiments gave the results they did. In other physical theories this is often done by mapping the mathematical objects in your equations onto some objectively existing things in the real world, but there are other methods.

I didn't say reproducing results of experiments is understanding. Familiarity with, and an appreciation for, the detailed and intricate structure of our successful theories of physics is what I call understanding, because they reflect the structure of nature. The idea of a 'classical trajectory' is just that, an idea. It is an idea that is present in some of our theories of motion of large scale objects, and an idea that naturally suggests itself because it is close to experience. But, the same theory can be formulated in a completely different way, which uses waves rather than particles (Hamilton-Jacobi theory). Now, does Hamilton-Jacobi theory provide in any sense lesser understanding than Newtonian mechanics? Obviosuly not, because it is the same structure, seen from a different point of view. If anything, it provides more understanding, because it is far easier to see the beautiful aspects of classical mechanics from the point of view of Hamilton-Jacobi theory than it is from the point of view of Newtonian mechanics. In the end, what is important is to see the structures. To see the patterns that are not directly accessible to the senses. And in this process, I see no place for insisting that we must always think in terms of familiar things like classical trajectories of particles, and insisting that only that can be considered 'real' understanding. Nature may choose to reveal more of its structure if looked at from another point of view. What matters to me is to see the patterns, and appreciate them, in whatever form I can.

 

[zenith8]

I didn't say reproducing results of experiments is understanding. Familiarity with, and an appreciation for, the detailed and intricate structure of our successful theories of physics is what I call understanding, because they reflect the structure of nature. The idea of a 'classical trajectory' is just that, an idea. It is an idea that is present in some of our theories of motion of large scale objects, and an idea that naturally suggests itself because it is close to experience. But, the same theory can be formulated in a completely different way, which uses waves rather than particles (Hamilton-Jacobi theory). Now, does Hamilton-Jacobi theory provide in any sense lesser understanding than Newtonian mechanics? Obviosuly not, because it is the same structure, seen from a different point of view. If anything, it provides more understanding, because it is far easier to see the beautiful aspects of classical mechanics from the point of view of Hamilton-Jacobi theory than it is from the point of view of Newtonian mechanics. In the end, what is important is to see the structures. To see the patterns that are not directly accessible by the senses. And in this process, I see no place for insisting that we must always think in terms of familiar things like classical trajectories of particles, and insisting that only that can be considered 'real' understanding. Nature may choose to reveal more of its structure if looked at from another point of view. What matters to me is to see the patterns, and appreciate them, in whatever form I can.

Well quite, but 'understanding the structure' of Newtonian mechanics and of Hamiltonian-Jacobi should tell you precisely why they work.

Hamilton-Jacobi theory shows you that the problem of dynamics as defined by Hamilton's equations can be formulated in terms of a partial differential equation determining the evolution of a field S. The role of the S function is to generate a momentum vector on the configuration space through the relation p = grad S. Integral curves along the field are possible trajectories of the N-particle system.

Now the point here is that this theory is quite clearly connected with an ENSEMBLE of identical systems rather than a single trajectory as in the other ways of formulating classical mechanics (this must be so, because two completely different S functions can lead to the same dynamics). This reflects the fact that the state of a material system is completely exhausted by specifying its position and momentum - the S function plays no role in either defining the state or in determining the dynamics.

So I would say that your particular example actually supports my point of view rather than yours. By considering the patterns, you see that Newtonian mechanics must refer to a single system, and Hamilton-Jacobi theory to an ensemble. Thus to base your ontology on the latter (and therefore state that particles don't have trajectories, and therefore waves exist) would be plain wrong. Surely a 'deep familiarity and appreciation' of the 'detailed and intricate structure' of Hamilton-Jacobi theory should be able to spot that?

 

[f95toli]

Tell us more about it and how it conradicts to what I have written, please.

I am not sure exactly what you are asking. The contradiction comes from the fact that e.g. quantum jumps (and many other systems) do not necessarily "happen" in ensembles, we can -at least in principle- measure a single experimental realization of the state of a single ion. It is perhaps worth pointing out that we can now trap single ions for several months; so "single ion" really means a single individual ion, it is not unheard of for researchers to name their ions...

My point is that it is not quite correct to say that QM is just a "statistical" theory as you implied; there are cases where we can observe single trajectories.

Martin Plenio published a nice review on quantum jumps a few years ago. As far as I remember (I haven't done anything related to jumps in quite a while) it is quite a good introduction to the topic.

It is available on the arXiv
http://arxiv.org/abs/quant-ph/9702007

 

[dx]

My example was not to show that trajectories don't exist, which they clearly do in the classical case. I was just arguing aginst your claim that "very little is actually 'understood' in the ordinary framework" and the wrong notion of 'understanding' implied by that statement.

 

[Peter Morgan]

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?

Hi mahela007, if you're still hanging in there,
My preferred approach is to note that "detectors" are thermodynamically sophisticated devices that are designed to make thermodynamic (and hence discrete) transitions from a ready state to a "registration" state. Detectors always have a "dark rate", which is the rate at which the detector will make thermodynamic transitions to its registration state even when it is shielded as well as we can achieve from any state preparation devices (lasers, stars, LHC, etc.). A photographic plate of course is unable to make a transition back to its ready state, but I will suppose that we're using a more modern detector.

Suppose now that we move a state preparation device close to the detector. The rate at which the detector will make thermodynamic transitions from the ready state to the registration state (and other more sophisticated time-series analysis statistics of the events) will change to be different from the dark rate. Precisely how the statistics change depend on what state preparation device we put close to the detector, where we put it, and what other apparatus there is in the room.

It's best to take the discrete transitions of the thermodynamic device that Physicists call detectors not to imply that a "particle" has passed between the state preparation device and the detector. The discrete event would not have occurred if the detector were not there, so it should be considered as much a property of the detector as of anything that might have caused the event (this effectively takes the event to be "contextual", which is well-known to be a way to evade the Kochen-Specker paradox; it's not so well-known, one could say, for the violation of the Bell inequalities). Thinking that there are particles gets into a degree of trouble when we consider experimental apparatus that is now routine in Physics labs (although if you want to adopt a de Broglie-Bohm or Nelson-type interpretation of QM, you can make it work, at the cost of introducing a type of nonlocality that is not classically very natural).

You can make a field understanding of QM work rather better, in my opinion. When we introduce a double slit between a point source and a detector, the effect on the statistics is as if there is a field between the point source and the detector, but of course the introduction of the double slit doesn't change the nature of the detector, which is to make thermodynamic transitions from the ready state to the registration state every now and then, with the rate depending, more-or-less, on the intensity of the field.

A classical field is not a general enough mathematical structure to reproduce all the Physics that can be described by a quantized field, however there is a more general mathematical structure that is known as a "random field" that is adequate, at least for non-interacting quantum fields. I refer you to my EPL 87 (2009) 31002, "Equivalence of the Klein-Gordon random field and the complex Klein-Gordon quantum field" (http://pantheon.yale.edu/~pwm22/Morgan-EPL-2009.pdf". For interacting quantum fields, renormalization is out of order enough as mathematics that it will take time to find comparable empirically equivalent random fields --- and it may not be possible, if I'm not smart enough. Also adding to the fun are fermion fields, like electrons.

 

[Peter Morgan]

Thought some more about why a classical field is not adequate, and how to explain it in an elementary way. A quantum field not only describes the statistics of where events happen, it also describes correlations between events, statistics of event pairs, event triples, etc.

Suppose that a preparation apparatus causes two events to happen in a correlated way -- that is, when an event happens in one detector, an event also happens in another detector that's part of the same experimental apparatus. A physical theory has to describe not only what changes there would be to the statistics of the events at each detector singly if either of them were moved, the theory also has to describe what changes there would be to the statistics of the event pairs if either or both of the detectors were moved. A classical field theory can describe the way in which single event statistics change, but describing the way in which event pairs and triples, etc. change requires a more sophisticated mathematical structure.

In quantum field theory, the appropriate mathematical structure is Fock space, or an equivalent. For a classical equivalent of comparable mathematical power, one needs random fields, or an equivalent.

Note that almost all quantum optics experiments are deeply concerned with correlations between the times at which events happen in the thermodynamically nontrivial devices that are usually called "detectors", not just with the statistics of individual events. For an exercise, however, consider in detail how the times at which events happen in different detectors are eliminated as part of the data analysis of http://arxiv.org/abs/quant-ph/9810080" . This experiment could reasonably be taken to be a paradigm for the way in which the times at which events in an experimental apparatus should be recorded and reported, and is certainly a paradigm for how the times at which events happen are manipulated out of the high-level model of the experiment's dataset. The classic twin-slit experiment is trivial compared with this level of data recording and analysis, since correlations between the times at which events happen are not recorded in the former (indeed, a photographic plate is almost the paradigm detector for the classic twin-slit experiment, which obviously makes no record of times at which transitions of the photographic emulsions occur).

 

[alxm]

Kind of off-topic, but..

If you have had the privilege to attend one of Dr. R.B. Laughlin lectures, a Noble Prize recipient

It's a noble prize indeed, but the spelling is Nobel. (NO-bell)

They picked this year's chemistry prize winner just yesterday, btw.

 

[mahela007]

Well.. Didn't understand much of what was said in the first few posts. I learned something from a website... (I can't find it now). It said that the wave nature of the electron meant that the position of the electron would be a probability wave depicting it's position.
Is it accurate?

 

[Peter Morgan]

Well.. Didn't understand much of what was said in the first few posts. I learned something from a website... (I can't find it now). It said that the wave nature of the electron meant that the position of the electron would be a probability wave depicting it's position.
Is it accurate?

You can probably live well enough with that idea, but I suggest you try to inject a slightly more empiricist attitude. On the technical side, the wave function can be a wave function of multiple electrons, not just a wave function of one electron, describing the evolving probability of where you would expect to see multiple events (which one can say is caused or modeled by the electrons, or, better, by the quantized electron field). Note that the results of real experiments are very often not modeled as position measurements, even when they model thermodynamic transition events of a "detector" at a fairly well-defined position.

Good luck.

 

[RonC]

Kind of off-topic, but..It's a noble prize indeed, but the spelling is Nobel. (NO-bell)

They picked this year's chemistry prize winner just yesterday, btw.

Thank you for pointing out my typo grammatical-typos will still always be my "Achilles' heal". IMHO, wanted to share the wave nature on a QM scale, I believe my attempt was poorly stated.

Olaf Nairz, Markus Arndt, and Anton Zeilinger conducted DSE with C60, and I will quote so that I do not make another typo.

Wave–particle duality is frequently the first topic students encounter in elementary quantum physics. Although this phenomenon has been demonstrated with photons, electrons, neutrons, and atoms, the dual quantum character of the famous double-slit experiment can be best explained with the largest and most classical objects, which are currently the fullerene molecules. The soccer-ball-shaped carbon cages C60 are large, massive, and appealing objects for which it is clear that they must behave like particles under ordinary circumstances. We present the results of a multislit diffraction experiment with such objects to demonstrate their wave nature. The experiment serves as the basis for a discussion of several quantum concepts such as coherence, randomness, complementarity, and wave–particle duality. In particular, the effect of longitudinal (spectral) coherence can be demonstrated by a direct comparison of interferograms obtained with a thermal beam and a velocity selected beam in close analogy to the usual two-slit experiments using light. ©2003 American Association of Physics Teachers.

This is the crux of my impute,
RonC

 

[zenith8]

This is the crux of my impute.

I just googled 'crux of my impute' and apparently you are the first person ever in the history of the internet to type those four words in that order. Cool..

Anyway, so a fullerene molecule goes through a slit. The accompanying wave field goes through both slits and pushes/guides the molecule into the general area of the interference maxima. I don't see the problem.

 

[WaveJumper]

Oh God, Bob. Keep up. The particle goes through one slit. The wave goes through both.

It's difficult for me to speak slowly when writing - perhaps I should put larger spaces between the words?

Do you know of a reference that explains unambiguosly quantum tunneling under deterministic and causal Bohmian mechanics? Something that i might in principle be able to roughly explain to my neighbour?

 

[zenith8]

Do you know of a reference that explains unambiguosly quantum tunneling under deterministic and causal Bohmian mechanics? Something that i might in principle be able to roughly explain to my neighbour?

Yep.

pp. 26-28 of http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html" lecture 3 for a succinct summary suitable for neighbors.

Large parts of Holland's http://www.amazon.com/dp/0521485436/?tag=pfamazon01-20 textbook (1993) for the full treatment.

 

[enotstrebor]

Seriously, there is a great deal of experimental evidence that both waves and particles exist.

Take that as a given, and say that the Schroedinger wave function represents a real wave. ...

It doesn't matter what actually exists in actual fact.

What matters is when people say 'waves and particles have no meaning in the quantum domain' or state categorically that 'neither waves and particles exist' they are simply wrong. They could perfectly well exist, and if they do, then that is perfectly consistent with all the results of QM.

See, mahela007, what did I tell you? Everybody really really doesn't want to accept this, including the 2008 PF Award Physics Guru, and Mr. "23960 posts!" PF Mentor...

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

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".

There is a difference between being fundamentally accurate (a good Q model) and being fundamentally correct (a P model).

Proof that the wave particle duality is a Q model?

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.

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 the glory of mans 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.

 

[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.