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Electron: wave or particle?

  1. Mar 3, 2014 #1
  2. jcsd
  3. Mar 3, 2014 #2


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  4. Mar 3, 2014 #3
    Interesting, thank you!
  5. Mar 4, 2014 #4


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    Describing an electron as either a particle or a wave misses the point. An electron is a quantum object that obeys both wavelike and particle-like rules. Since waves and particles are different concepts, at least in classical physics on our scale, an electron is neither a particle nor a wave nor both. It is something else entirely. That's the best answer to this question that I've seen so far on PF. Of course, in Quantum Field Theory it is an excitation of a field, which complicates the question further.
  6. Mar 4, 2014 #5


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    I don't think that's a good way off expressing it.

    Really this wave particle duality stuff is a crock of the proverbial. Its neither - its quantum stuff.

    Its a leftover from De-Broglie waves and the Schroedinger wave equation when Schroedinger actually thought it was waves. It was seen to be incorrect when Dirac developed his transformation theory which is basically what goes by the name of QM today.

    The REAL essence of QM is not this wave and particle stuff - its basically a generalisation of probability theory:

  7. Mar 5, 2014 #6
    It's both. It's neither. Nobody knows exactly.

    I only watched the first minute of the youtube.....did not like it one 'bit' [pun intended] when the speaker pronounced "an electron IS a wave..."....

    No! That is merely how we represent one mathematically. Nobody has ever detected, not observed, such a wave/field. Not all mathematical entities can be experimentally observed.
    We have field theories which are really, really good at describing what we do observe: point particles in detectors. The Standard Model of particle physics is one of quantum field theories which exquisitely describe what we observe: point particle interactions.

    I think Drakkith's post is just fine for getting started. In QM one ends up being faced with experimental observations that require some mathematical changes from classical ideas....moving to mixed states and complex numbers for example. How you make that journey best seems personal preference.

    I like scott aransons ideas as well. Yet he kinda implies one could have [maybe obviously'] intuitively generalized probabilities....yet real world QM was forced upon 'experts' trying to describe previously unexplained phenomena, like entanglement....inteference. He seems to like the math more than the physics, which is fine as one but only one perspective.

    My favorite explanations of a particle: [never been able to hone it down to just one]

    [These are my own summaries mostly my own interpretations from lengthy forum discussions.]

    [1] There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields.

    [2]In general, in quantum mechanics, a thing that is time-independent like a particle is described by a time-independent wave function, and does not in any sense "move". An electron does not orbit the nucleus. A particle in the ground state of a harmonic oscillator does not slosh back and forth. And elementary particles with spin do not rotate.

    [3]A particle can be described mathematically as a wave [function] until it is detected as a local quanta; as far as we can tell a detected particle is point size...without measurable dimension. That's the Standard model of particle physics: wave descriptions of particles, point like [zero size] interactions. The wave function description of a particle is of the particle itself, not a trajectory. However if you know the double slit experiment you know that the wave like nature of a particle and superposition accounts for the paths and the point like displays.

    [4]In quantum field theory, modes with positive frequencies correspond to particles, and those with negative frequencies correspond to antiparticles. Complex numbers correspond to virtual particles.

    [5]And perhaps the craziest idea of all: It seems that expansion of geometry itself, especially inflation, can produce matter [particles]. Gravitational perturbations [inhomogeneaties in waves] in an expanding space produces observable [point] particles. Mathematical transformations between inertial and accelerated frames also seems to produce particles: such different observers see different vacuum energies...and such energy differences result in particle production. See the "Unruh effect."
  8. Mar 5, 2014 #7


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    The "wave-particle duality" behavior of electrons can be observed during any electron diffraction experiment:

    The electrons show wave interference effects while passing through the material.
    Yet they appear as particles, striking a single small spot, when they reach the detector.

    I have done these experiments ad nauseum during my doctoral research on ultrafast photo-electron diffraction. You get the same diffraction pattern if you send just a few electrons through the thin film at a time, and let them accumulate, or if you send the entire bunch all at once.

    The mathematics then seeks to describe this observed behavior. We seem to have gotten it mostly correct as long ago as Planck (Energy = h x frequency; 1900) and de Broglie (wave length = momentum/h; 1923), plus Heisenberg (there are no classical trajectories to be observed) - which all put together gives the physics behind Quantum Mechanics.

    The Heisenberg and Shroedinger methods still work - but if you want to work at smaller scales, and obtain more accurate results you need to switch to the quantum field theories. But the tools of specialists are not required to build physical intuition at a useful level.
  9. Mar 5, 2014 #8
    good point in post #7....see


    Richard Feynman says something like "Everything you need to know about QM can be gleaned from the double slit experiment.."

    Of course, he was a genius..... and also had other conflicting comments about QM:

  10. Mar 5, 2014 #9


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    That way of analysing it is a leftover from pre QM days - here is the correct QM analysis:

    Note it has nothing to do with either waves or particles.

    The problem here is this wave-particle stuff is often used to motivate fully blown QM. But what is not often done is to go back, and from the new formalism, show how the double slit experiment is explained once the fully blown theory is available.

    That's just one reason why IMHO textbooks should not be based on rehashing the historical development, but rather develop it from its conceptual core. Ballentine - QM - A Modern Development does it this way and books like this should be the goal of everyone interested in QM to dispel leftover myths from other approaches.

    BTW I am pretty sure Ultrafast is basically saying the same as me - just a bit differently and is simply meant to compliment what he said.

    Last edited: Mar 5, 2014
  11. Mar 5, 2014 #10


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    Yes he was.

    But Naty - this is at the beginning level. Once the full machinery of QM is available that is the correct way to analyse the double slit experiment - not via what was used to motivate it such as the wave particle duality or particles going through both slits simultaneously (which enthrones the sum over history approach - absolutely valid - but its only one aspect of the full quantum formalism).

    Why people want to hark back to explanations before the full quantum machinery was available or developed is beyond me, and IMHO leads to confusion.

    In QM a quantum particle is neither particle or wave - its described by a state which simply encodes the expected values of observables exactly as probabilities do. Its not particle or wave - its something entirely different and much more abstract.

  12. Mar 6, 2014 #11
    bhobba posts:

    yes....agreed....that much even I can understand!...
    and is what I posted for Sharnrock.

    ....I have always thought the Schrodinger wave, for example, convenient in visualizing certain measurement results....not an actual electron....not a pilot wave...not necessarily a physical wave. [And 'Collapse of the wavefuntion' even as a description seems even further astray as has been discussed in these forums.]

    Do you think Feynman's comment was before 'the full machinery' of QM was available?

    I'd be interested in your views on some points in Marcella's paper:
    Bottom page two....
    So is Marcella dismissing the prior scientists view that he mentions....Ballentine, Merzbacher...etc..if so what is ψ in HIS world view...

    [and by the way I have Merzbacher's book, and if anyone is familiar with what Marcella means in his paper I'd be interested...I bought the book old and used, 1970, after recommendation in these forums....the first hundred pages or so seem taditional 'old school' QM wavepackets and free particle motion, The Wave Equation, Stationary solutions, etc....Maybe I missed something 'new' later on???? or a newer version is updated??]

    What do you think about this:
    In CONCLUSIONS Marcella starts out...

    Born postulate??? I thought that postulate was 'old hat'....Seems like waves are there in relatively plain sight whether he wants to acknolwedge them or not....


    Or does Marcella mean something different do you think.....??

    So far I'm not understanding why you like this paper in preference to the older Schrodinger view...in other words, to a non mathmetician like me seems like a 'ho hum 'distinction....

    In equation 5 Marcella concludes 'no' interference, in 14, 'yes' inteference....I'll take him as correct as that math is more than I can handle. So do these particular formalisms lead to some additional insights in the the 'full quantum formalism' you mean? Or is this the same conclusion but maybe a slightly different start

    If that's what you had in mind, can you give an example or two.....Thanks...

    I've also quoted Roger Penrose and number of times in these forums where he says,

  13. Mar 6, 2014 #12


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    Obviously Feynman knew the full machinery. The quoted comments were from his lectures, books etc for beginning students and it is well known that he uses the double slit experiment as the basis to explain QM to beginning students. From that he derives his path integral formalism and then the usual formulation. What he should then do is go back and use that completed formalism to explain the double slit experiment - but doesn't. However his approach does not necessitate changes in anything once QM is fully developed.

    The usual approach based on the history of the subject however does. When the transformation theory of Dirac was developed the wave particle-duality became outdated at best and downright wrong when looked at carefully. They do not go back and analyse the double slit experiment either - but in this case it causes conceptual errors because people get the impression the concepts that pre-dated the full theory still hold - they don't. Quantum objects are not particles, they are not waves, they are described by a quantum state which is much more abstract.

    To really discuss it I need a link

    This view is quite simple. See Chapter 9 Ballentine. But it goes like this. Most of the time observation destroys what is being measured - it is only in measurements where its not destroyed the so called collapse postulate applies - it can be derived from other postulates from continuity so its not really a postulate in its own right - but that is by the by. Anyway these are called filtering type observations because a system is in some state then by the observation changed to another. Logically this is the same as a state preparation procedure, so guess what - one can associate states with a preparation procedure. This is the most modern view and is what Ballentine gives in his book.

    Where you get the idea the Born postulate is old hat is beyond me. Its absolutely fundamental, and is the second axiom in Ballentine's 2 axiom approach.

    Why you believe waves are in plain sight has me totally beat. The pilot wave theory is an INTERPRETAION that assumes the existence of a pilot wave the formalism is silent about.

    For that I need the paper.

    What paper?

    The full quantum formalism is the transformation theory of Dirac which is generally what goes by the name of QM these days. For definiteness lets take it as what Ballentine says in his text.

    Well there is a problem right there. The collapse of a wavefunction never was part of QM - it only exists in some interpretations eg the statistical interpretation doesn't have it. See Chapter 9 Ballentine.

    What you may be talking about is the measurement problem. It has a number of parts, but basically it's making sense out of the Born rule. The most difficult problem is - why do we get any outcomes at all. Some interpretations its a doodle eg MW and DBB but for most they stand powerless before it.

    However we are now getting way off discussing is the electron wave or particle, and if you want to discuss that I think another thread would be in order.

    Last edited: Mar 6, 2014
  14. Mar 7, 2014 #13
    Bill, thanks for your reply.....It was words/language, not concepts that seemed to separate us.....Your last post clarified my misunderstandings about what you were saying....

    Seems I am up to date after all....probabilities and states, not waves, not particles, describes quantum phenomena....as we both have already posted.

    You posted:
    good. I agree and was simply trying to clarify what you meant. [For the OP, there have been at least several discussions in these forums regarding additional details.]

    One clarification:
    The 'Marcella paper' I referred to in my post was via YOUR link, post #9.

    I could not glean anything really 'new' or more 'correct' from that paper because apparently I was already pretty much 'up to date' from discussions in these forums.

    And when I mentioned the Born postulate was 'old hat' what I meant was 'original and still valid' ....

    that it postulates the Schrodinger wave function not as a physical wave but the probability density of finding a particle....

    For the OP, that interpretation of the Schrodinger wave is the 'modern' one and supersedes any earlier ideas of pilot waves, wave function collapse, etc....
    Last edited: Mar 7, 2014
  15. Mar 7, 2014 #14


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    I'm rather partial to the "historical" view - though what we do in physics is hardly history, it is rather a synopsis of the parts that turned out to be useful, with the rest quietly jettisoned - so for example a great book to learn quantum physics, prior to studying quantum mechanics, is "Quantum Physics" (Berkeley Physics Course, Volume 4) by Eyvind H. Wichmann.

    Of course, once the student understands WHAT is happening, and WHY the classical ideas are insufficient, and even give wrong answers ... then the new theoretical framework can be developed. In addition it helps if the students have studied linear algebra, differential equations, and analytical mechanics prior to a first course in quantum mechanics.

    Certainly for a graduate course one can focus on the mathematical structure: linear vector spaces, operators, etc. Just so long as they don't forget to connect things to experiments!
  16. Mar 7, 2014 #15


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    It contains nothing new - just a different way of motivating QM based on a key idea rather than a historical development. That key idea is one must generalise probabilities to complex numbers so you can have continuous transformations between pure states in order to model physical systems that change continuously. It can also be shown its basically the same as requiring entanglement.

  17. Mar 7, 2014 #16


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    Of course this is science, and the ultimate justification for any scientific theory is experiment. If it disagrees with experiment its wrong - end of story:

    That said there is the issue of UNDERSTANDING a theory.

    IMHO the usual historical method of teaching QM obscures that understanding. We now know its conceptual core - ie its the most reasonable generalised probability model that allows continuous transformations between pure states.

    Teaching it that way right from the start IMHO avoids all these questions I often see in posts on this forum. Is an electron a particle or wave - once you understand the full machinery of QM you realize its a silly question eg you sometimes get solutions that are like waves, but they are waves in an abstract Hilbert space - not waves in any usual sense. Then we have that very common one - an observation requires an observer - it crops up all over the place. It doesn't require an observer any more than flipping a coin requires an observer to land heads or tales - and if you think of QM as a generalisation of probability theory its obvious.

    I personally believe we need a change in the way we teach QM at the beginning level so when you come across a 'proper' book like Ballentine you don't have to 'unlearn' anything. I know I did. I grappled with all sorts of stuff like particle wave duality, observers causing collapse etc until I saw a proper treatment in Ballentine. After that everything was much clearer. I just wish I had avoided that confusion from the start - as well as other issues of a mathematical nature such as what's this damnable Dirac Delta function.

    Last edited by a moderator: Sep 25, 2014
  18. Mar 8, 2014 #17
    I think this thread illustrates an apparent problem with the way that many threads progress on this forum.The problem is that I suspect that many of the responses here are at a level which does not take into account the present educational level of sharnock.

    None of us know the present level of sharnock and nobody has tried to find out. If he/she is a student from the UK I would assume from his or her post that that he or she is currently on an AS or A level course which is normally studied by students between the ages of 16 to 18. If my guess is right some of the responses here would most likely be too complex for sharnock to follow and some might even be damaging to his or her education.

    Here are just some of the syllabus requirements from one of the major UK examination boards: (AQA-A turning points in physics topic--a short course)

    Students would need to be familiar with certain topics, concepts and observations such as, photoelectricity, spectra, De Broglie wavelength and electron diffraction. This includes a basic knowledge of the workings of the transmission electron microscope. Of course things have continued to move on and students would be aware of this. But the emphasis on this part of the course is that:

    Students should "appreciate from a historical viewpoint the significance of major conceptual shifts" etc.

    Most sudents at A level go on to study other subjects such as medicine, engineering etc and in my opinion the quantum theory covered in the A level course is at a good level.Those who go on to do physics can look at the subject in more detail.

    Another problem here is that sharnock and other students who might be reading, are told things such as "the electron is not a particle" etc. Yet those same students (from approximately age 11-14 onwards) would know that the electron is a subatomic particle with a negative elementary charge. Many AS students would would have done an introductory course on the standard model and would know the electron as a lepton.
    Last edited: Mar 8, 2014
  19. Mar 8, 2014 #18


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    I agree ... it would sure be nice if people would record their educational level in their individual profile!

    IMHO this should be required!

    PS: I also agree with the rest of your post! I have worked with students at all levels: children, teens, undergrads, graduate students, and professionals. Questions need to be addressed at the level of current understanding if the answers are to be understandable.
  20. Mar 8, 2014 #19
    Hello Naty 1. I applaud what you are doing to get a better understanding of QM and I enjoy reading threads of this type. Unfortunately I think that sometimes threads go beyond the understanding of the thread opener and sometimes can be counter productive.
    Amongst other things a student of the type I referred to earlier would probably not have the time to use the approach you are using. The topic I referred to earlier carries approximately 4% only of the total A level marks and students have the whole of the rest of the course to consider.
    If answers became too complicated most would not give up but would look elsewhere.
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