How are electrons considered waves?

[mahela007]

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?

 

[ytuab]

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?

What I know now is as follows,

In page 96 (the Story of Spin)
--------------------------------------
He (Shrodinger) tended to think that his wavefunction(phi) was a wave in three-dimentional space.
For example, he considered e phi x phi as the charge density which actually exists in space and tried to treat the bulk of the density as an electron. The idea, however, did not work because phi x phi will spread with time and the density decomes diffuse.
-------------------------------

So, In the Shrodinger equation, the electron is not a wave, the wavefunction means the probability density of the electron.


But In page 110
-------------------------------
The Dirac equation is also the relativistic field equation for the electron and it cannot be considered to be an equation of probability amplitude in x,y,z space. They insisted that a concept like "the probability of a particle to be at x in space" is meaningless for relativistic particles- be they electrons, photons ...
------------------------------------

So they seemed to treat relativitic particles as the matterwave existing in space. (In this case, the wave doesn't mean the probability density...)
It's difficult to imagine, so I don't really understand this meaning.

 

[mgb_phys]

Considering an electron as a wave simply means you can't nail down a position for the electron to less than a certain distance.
It's not just electrons, everything is a wave, it's just that the wavelength gets smaller as the object gets bigger - so you only notice the effect for very small things

 

[zenith8]

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?

The obvious way to 'understand' it is to say that both waves and particles exist. The wave goes through both slits and produces an interference pattern. Particles goes through one slit or the other, and because they are pushed around/guided by the wave they generally end up heaped into clumps around the position of the interference maxima. This is the de Broglie-Bohm interpretation of QM.

This is a perfectly consistent point of view to take, and makes complete sense. Unfortunately for historical reasons (essentially, it was the direct opposite of what the power-mad Heisenberg had repeatedly insisted, and he didn't like being contradicted and made to look a fool) standard textbooks seem to be effectively banned from mentioning it, and and like a flock of sheep go into great detail about how 'weird' everything is. ('No-one understands quantum mechanics!').

As far as 'understanding' is concerned, the officially-sanctioned viewpoint gives you two options:

(1) 'QM is an algorithm for computing probabilities and the wave function doesn't correspond to anything physical' (which gives up on understanding on principle)

(2) 'The QM wave function represents a physical wave field and this is all that exists' (a viewpoint which leads to everything being 'weird' and does not lead to understanding, suggesting it is wrong).

Many people over the last decade (though not enough to penetrate the mainstream) have begun to realize that the banned third option of saying that particles exist as well as the wave field is the only view that actually allows you to make sense of the quantum world. What else would 'wave-particle duality' mean. Why not adopt it? I don't know.

In this view, QM is just classical statistical mechanics with a different dynamical law. Fun, huh?

 

[alxm]

Look, the answer is that they're neither particles or waves in the classical sense of those things. Neither. Quantum mechanical objects display some of the properties of waves in some ways, and some of the properties of particles in other ways.

That's all.

 

[zenith8]

Look, the answer is that they're neither particles or waves in the classical sense of those things. Neither. Quantum mechanical objects display some of the properties of waves in some ways, and some of the properties of particles in other ways.

Which quite clearly could be because sometimes you see the particle and sometimes you see the wave, depending on what experiment you do. As you're not going to admit.

 

[HallsofIvy]

The obvious way to 'understand' it is to say that both waves and particles exist.

Look, the answer is that they're neither particles or waves in the classical sense of those things. Neither. Quantum mechanical objects display some of the properties of waves in some ways, and some of the properties of particles in other ways.

That's all.

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

 

[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?

 

[Bob_for_short]

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?

It is easy. An electron is not unique. We deal with beams of electrons (similarly to photon beams), don't we? For example, to observe something tiny. It happens that the result of observing shows wavy behaviour despite it may contain many separate points. What is important to us - one point or the whole, say, interference picture? Of course the latter. The latter is desctibed with the wave function.

It happens that the electron position cannot be certain in certain cases but one can calculate the average, the dispersion, etc. QM does this just like Maxwell theory for EMF.

Any separate point is useless - it says nothing about a particular situation - no average, no other things. It is highly insufficient to describe a beam. We are interested in beams, not in one event. So QM is a science to describe beams or results of many separate measurements.

 

[zenith8]

It is easy. An electron is not unique. We deal with beams of electrons (similarly to photon beams), don't we? For example, to observe something tiny. It happens that the result of observing shows wavy behaviour despite it may contain many separate points. What is important to us - one point or the whole, say, interference picture? Of course the latter. The latter is desctibed with the wave function.

It happens that the electron position cannot be certain in certain cases but one can calculate the average, the dispersion, etc. QM does this just like Maxwell theory for EMF.

Any separate point is useless - it says nothing about a particular situation - no average, no other things. It is highly insufficient to describe a beam. We are interested in beams, not in one event. So QM is a science to describe beams or results of many separate measurements.

Which is exactly what the 'waves and particles' viewpoint explains, no?

One, or a few, particle detections appear to be randomly distributed. It is only after a great many detections that the distribution of spots on the screen begins to look like an interference pattern, because the particles are being guided by the accompanying wave. See the many videos of this process on the internet.

 

[dx]

zenith8,

I have a little question about Bohmian mechanics. Is there any experiment you can perform to determine the trajectories of the particles, either directly or indirectly? I.e., is there any situation in nature where the 'wave' alone is not enough to describe it, and one must also consider in detail the 'particles' and their classical trajectories?

 

[f95toli]

It is easy. An electron is not unique. We deal with beams of electrons (similarly to photon beams), don't we? For example, to observe something tiny. It happens that the result of observing shows wavy behaviour despite it may contain many separate points. What is important to us - one point or the whole, say, interference picture? Of course the latter. The latter is desctibed with the wave function.

That is simply not correct. There are plenty of examples of individual systems undergoing individual event that are still described by wave functions. One obvious example would be a quantum jump processes a \Lambda systems (e.g. a single ion in a trap).


You are basically using the same argument as Schroedinger, but that has turned out to be view that is in conflict with results of experiments: i.e. it is not a valid "interpretation" of QM.

 

[Bob_for_short]

zenith8,
I have a little question about Bohmian mechanics. Is there any experiment you can perform to determine the trajectories of the particles, either directly or indirectly? I.e., is there any situation in nature where the 'wave' alone is not enough to describe it, and one must also consider in detail the 'particles' and their classical trajectories?

It is mostly our desire to have a deterministic picture. It is not supported or imposed experimentally. For example, when one analyses the particle traces (trajectories) in a detector, one uses them to calculate (measure) energy-momenta of particles in reaction. Nobody compares a specific trajectories with "predictions" of a deterministic theory.

 

[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?

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.

Then, as de Broglie said in 1927, 'it seems a little paradoxical to construct a configuration space with the coordinates of points that do not exist'. So assume that the configuration on which the wave function is defined represents a configuration of particles, then lo.. all the usual predictions of quantum mechanics are reproduced, and we have a complete understanding of what appears to be happening.

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. The 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...

 

[Bob_for_short]

That is simply not correct. There are plenty of examples of individual systems undergoing individual event that are still described by wave functions. One obvious example would be a quantum jump processes a \Lambda systems (e.g. a single ion in a trap).

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

 

[zenith8]

zenith8,

I have a little question about Bohmian mechanics. Is there any experiment you can perform to determine the trajectories of the particles, either directly or indirectly? I.e., is there any situation in nature where the 'wave' alone is not enough to describe it, and one must also consider in detail the 'particles' and their classical trajectories?

Well, that's the difference between classical measurement and quantum measurement. The only difference is that in the quantum case the probe is as significant as the probed. Essentially any means of measuring the trajectory (I mean, what do you want to do? Bounce something off the electron every trillionth of a second?) will change the trajectory from what it would have been in the absence of the measurement. That's not metaphysical or weird - it's just an obvious truth.

This is a point as old as QM itself - see Leon Brillouin in a discussion taken from the 1927 Solvay conference proceedings:

"Mr. Born can doubt the real existence of the trajectories calculated by Mr. de Broglie, and assert that one will never be able to observe them, but he cannot prove to us that these trajectories do not exist. There is no contradiction between the point of view of Mr. de Broglie and that of the other authors."

If you want, you can retrodict trajectories e.g. observing where the particle hits the screen in the double-slit experiment tells you which slit it went through, but I don't think that's what you mean.

 

[alxm]

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

Well, that's essentially what I was saying - that saying a quantum-mechanical thing acted like a particle or wave, is making an analogy to a classical object.

 

[Bob_for_short]

If you want, you can retrodict trajectories e.g. observing where the particle hits the screen in the double-slit experiment tells you which slit it went through...

Wrong assertion. Both slots are important for the interference picture which is different from two-separate-slot superimposing pictures.

 

[zenith8]

Wrong assertion. Both slots are important for the interference picture which is different from two-separate-slot superimposing pictures.

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?

 

[dx]

Well, that's the difference between classical measurement and quantum measurement. The only difference is that in the quantum case the probe is as significant as the probed. Essentially any means of measuring the trajectory (I mean, what do you want to do? Bounce something off the electron every trillionth of a second?) will change the trajectory from what it would have been in the absence of the measurement. That's not metaphysical or weird - it's just an obvious truth.

This is a point as old as QM itself - see Leon Brillouin in a discussion taken from the 1927 Solvay conference proceedings:

"Mr. Born can doubt the real existence of the trajectories calculated by Mr. de Broglie, and assert that one will never be able to observe them, but he cannot prove to us that these trajectories do not exist. There is no contradiction between the point of view of Mr. de Broglie and that of the other authors."

If you want, you can retrodict trajectories e.g. observing where the particle hits the screen in the double-slit experiment tells you which slit it went through, but I don't think that's what you mean.

I'm not interested in what you may or may not imagine to 'exist'. You're free to imagine that the particles have classical trajectories if it helps you 'understand' it.

My question is unambigiuous: does the 'classical particle' part of bohmian mechanics have any observable consequences at all? I'm not asking about directly measuring the trajectories of the particles. I understand that bouncing things off small particles affects their state significantly, and there is a consequent uncertainty involved. But does it have any consequences that differ from quantum mechanics? For what reason do its supporters consider it superior to quantum mechanics? Is it purely a matter of taste?

I ask because ordinary quantum mechanics seems to be far superior in both the uniformity of its application and the comprehensiveness of its description of experiments, so I'm trying to undertand the point of view of Bohm supporters.

 

[Bob_for_short]

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

Larger spaces between your words will worsen readability we all got used to. On the other hand, longer thinking around would work for sure.

 

[zenith8]

I'm not interested in what you may or may not imagine to 'exist'. You're free to imagine that the particles have classical trajectories if it helps you 'understand' it.

They're not classical trajectories. They're quantum trajectories.

And it does help me understand it, a lot.

My question is unambigiuous: does the 'classical particle' part of bohmian mechanics have any observable consequences at all? I'm not asking about directly measuring the trajectories of the particles. I understand that bouncing things off small particles affects their state significantly, and there is a consequent uncertainty involved. But does it have any consequences that differ from quantum mechanics? For what reason do its supporters consider it superior to quantum mechanics? Is it purely a matter of taste?

Simple. Look at the original post. Like nearly every question about quantum mechanics posted here by a student, it is "Oh wah, I don't understand what [insert result of some quantum experiment] means.". Then if I or another Bohmian doesn't post, they are told to go away and often that they are 'not allowed to ask' for explanations. Once they've been told this 50 times (and 300 other people have weighed in with confusing meta-explanations based on their own misunderstandings) then the original poster will finally get that they must not ask these things, and then they spend the rest of their lives (a) confused and (b) impressing their girlfriends with how profound they are to be studying something so 'weird'. This is despite the fact that a simple explanation in terms of obvious concepts exist. You tell me, why are we 'not allowed to ask' about what actually happens during a quantum process? So even if BM made no predictions different from ordinary QM it is still useful because it allows you to visualize stuff, and things are no longer confusing. And that would save everyone's time - both on this board, and for teachers everywhere.

There are also some observable consequences, yeah. Mainly to do with the fact that particles and waves are now logically distinct entities. For example, the particles do not in principle have to be distributed according to the square of the wave function (but one can show that they do tend to become so distributed under ordinary Schroedinger evolution, and quite quickly too, even if they don't start that way). The experiments that might show up 'non-equilibrium' distributions of particles are tricky but some people have begun to think they can do them. Watch this space.

I ask because ordinary quantum mechanics seems to be far superior in both the uniformity of its application and the comprehensiveness of its description of experiments.

Bohmian mechanics just is ordinary quantum mechanics. The standard viewpoint has no monopolistic right to think the equations of QM belong to it alone.

 

[sokrates]

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?

How on Earth did you make such an incredible observation?
What you write here is most probably wrong, based on your (and only your) way of understanding quantum mechanics.

And you are attacking people because they don't follow this??

 

[zenith8]

Larger spaces between your words will worsen readability we all got used to.

Bob, if you're going to take the p*** out of me you need to read your sentences back to yourself before you post.

On the other hand, longer thinking around would work for sure.

Look. In Bohmian mechanics the possible electron trajectories cannot cross and there is an axis of symmetry in the middle of the apparatus. Therefore ... if ... the ... particle ... hits ... the ... left ... part ... of ... the ... screen, ... it ... went ... through ... the ... left-hand ... slit. Trust me. Brain the size of a planet.

 

[zenith8]

How on Earth did you make such an incredible observation?
What you write here is most probably wrong, based on your (and only your) way of understanding quantum mechanics.

And you are attacking people because they don't follow this??

It's not a real life observation, sokrates. I'm just quoting the results of Bohmian mechanics, as you know. And Bohmian mechanics is just ordinary quantum mechanics, since all consequences result from simply redefining the meaning of a couple of words.

It's not just me either. I mean, there's at least one other person on this forum who's bothered to read about it. Out of 20 million or so.

 

[dx]

They're not classical trajectories. They're quantum trajectories.

What? The particles that are 'guided' by the 'wave' are classical particles with classical trajectories, no?

There are also some observable consequences, yeah.

Great. That's all I wanted to know.

 

[dx]

Bohmian mechanics just is ordinary quantum mechanics. The standard viewpoint has no monopolistic right to think the equations of QM belong to it alone.

What I meant was that the way quantum mechanics describes experiments is more uniform than the way Bohmian mechanics does (especially in its teatment of observables), and Bohmian mechanics has not yet incorporated into its formalism many of the things that have long been understood in the ordinary framework.

 

[zenith8]

What? The particles that are 'guided' by the 'wave' are classical particles with classical trajectories, no?

OK, we have a different definition of the word classical.

For me a classical trajectory is one you get by solving Newton's equation of motion. Because in Bohmian QM there is an 'extra force' the trajectories are different to that, hence not classical.

For you, a classical trajectory just means that something which exists moves.

Clear?

 

[dx]

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.

 

[zenith8]

What I meant was that the way quantum mechanics describes experiments is more uniform than the way Bohmian mechanics does (especially in its teatment of observables).

Not so - if you're talking about average properties then Bohmian mechanics uses the same equations - so it gives the same results, so I fail to see the difference.

If you then look at individual quantum events, well - I find Bohmian mechanics enlightening because it teaches us many things about what, for example, we are 'measuring' in a quantum measurement. Which in most cases is nothing at all. This is because it is actually clear about what exactly an observable is, and because the ordinary framework refuses to explain this by design (I mean how can it, when it has no ontology?)

And it's Heisenberg's fault. His theory of quantum measurement is actually based on classical ideas of what momentum is and so on.. (as Einstein warned him in 1926: 'Your theory will one day get you into hot water', because 'when it comes to observation, you behave as if everything can be left as it was, that is, as if you could use the old descriptive language').

Bohmian mechanics has not yet incorporated into its formalism many of the things that have long been understood in the ordinary framework.

Name one.

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.

 

[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.