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There are two contradictory groups of statements from two different famous books on quantum physics.

Which one is correct?

Group (1) : Following statements are from Berkeley Physics Course Vol. 3, "Quantum Physics" by Wichmann, 1967

Page 204:

"The de-Broglie wave and the particle are the same thing; there is nothing else. The real particle found in nature, has wave properties and that is a fact."

Group (2): Following statements are from "An Introduction to Quantum Physics" by French & Taylor, 1978.

Page 234:

"When we come to particles other than photons, the wavelength again is a well-defined property, but only in terms of a large statistical sample. And for these other particles, we do not even have a seemingly concrete macroscopic property to associate with the wave, equivalent to electric and magnetic field of a beam of light. We arrive at the conclusion that the wave property is an expression of the probabilistic or statistical behavior of large number of identically prepared particles -- and nothing else!"

EDIT: According to 1st group, there is wave-particle duality. According to 2nd group, there are only particles (there are no waves) but the distribution of these particles (when they are detected) is wavy.

So which one is correct?

atom
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    Both are pretty old school and pretty poorly phrased statements. I wouldn't trust either, if I were you. To be honest, both are really completely wrong. – CuriousOne May 26 '16 at 11:17
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    @CuriousOne--What is correct then ? – atom May 26 '16 at 11:45
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    @CuriousOne: By the way, French & Taylor book was published in 1978. Ballentine's statistical interpretation was published in 1970 and is considered important interpretation alongwith Copenhagen interpretation. Both the books are at least 35 years old but are not old-school thoughts. Messiah's still older book is yet one of the best quantum physics books ever written and is still in use very widely. Yes, it is true that we should not believe blindly the contents of these books. – atom May 26 '16 at 12:17
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    Underneath it all is the mathematics that supports Physics. In the standard mathematics we can chose our 'base' and get absolutely equivalent mathematics. One choice is point features (particles) and the other is nice sine/cosine waves. And there is a full family of others choices between. So we have a wave - particle plurality. Some folk like waves, some like particles, it depends on how you see the local world. – Philip Oakley May 26 '16 at 14:47
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    @PhilipOakley: In 1929 Mott showed that "particles" emerge from wave mechanics trough a weak measurement process. At that point all fundamental interpretations of quantum mechanics in terms of particles were dead on arrival. Particles are a secondary phenomenon that, strictly speaking, is not necessary. One can do QM very happily in the wave picture without ever having to think about any sort of duality. Any author who didn't know that 40 years later around 1970 was, to be honest, simply not informed. – CuriousOne May 26 '16 at 16:24
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    To me there is no contradiction. The problem is in trying to express something in English that can't easily be expressed in English ... perhaps it's impossible because we have no words or metaphors in our conventional language to express the concepts. They are statements about interpretation. – garyp May 26 '16 at 18:05
  • @CuriousOne: I fully agree and thus I don't see why you dismiss Group 1 "The de-Broglie wave and the particle are the same thing". Except the little reservation I mention in my answer about "de Broglie wave", it looks like it fits your point of view. They don't even mention "duality". – L. Levrel May 26 '16 at 19:08
  • @L.Levrel: Because "the particle" is not the same thing. The particle phenomenology is caused by a high momentum state of the quantum field interacting weakly with matter (i.e. with a low momentum, high mass density state of itself). The quantum field always exists, even when the matter density is low, but particles don't show up until we or nature plant a detector in the middle of the room. – CuriousOne May 26 '16 at 19:47
  • @CuriousOne: Then, to me it's really only a terminology problem: I call particle any "small part of matter". With my students I carefully distinguish "particle" from "corpuscle" (but not in English, so the words may have slightly different meanings). Also, what you explain is not in contradiction with the second statement of group 1: "The real particle found in nature, has wave properties", is it? – L. Levrel May 26 '16 at 19:59
  • @L.Levrel: The "particles" found in detectors do not have wave properties. They are showing a random walk kind of behavior, instead. The term particle is well defined, by the way: in CM it's the approximation of the dynamics of an extended body by its center of mass. It doesn't even include rotation, if we want to be anal. I don't even know what I would need the term "corpuscle" for. QM, specifically QFT is a very well defined theory in terms of ontology. It has all we need and nothing we don't. In particular, it has quanta, but no particles. – CuriousOne May 26 '16 at 20:07
  • @CuriousOne: I hope you'll agree to say that CM was not made "completely wrong" by the advent of QM. QM gives a fundamental interpretation of CM laws, but a textbook on CM needn't start by a QM course. If you agree on this, then I would say there is a comparable situation with QM: QFT gives a fundamental interpretation of, say, Schrödinger's equation, but you can effectively model many phenomena (say, Compton diffusion or Čerenkov radiation) by considering "wavy" particles. Also, when you say "particles" found in detectors do not have wave properties, what about single-electron diffraction? – L. Levrel May 27 '16 at 11:59
  • @L.Levrel: The hierarchy of theories has nothing to do with the ontology of quantum mechanics or the sad state of teaching about the physical, rather than fictional, transition from QM to CM, which most textbooks still seem to screw up in spectacular ways. Schroedinger's equation doesn't say anything about "wavy particles". It has a rather simple interpretation that also doesn't contain particles but only quanta. Single electron diffraction doesn't happen in the detector, it happens on a crystal sample. By the time the electron "hits" the detector we don't need QM any longer. – CuriousOne May 27 '16 at 12:09
  • @CuriousOne: forget your detector for a second: speaking about ontology, how do you call the "being" that diffracts on the crystal? Also, do you have a word that covers fermions and bosons together? (Finally, if you have references of good textbooks I'll happily take note of them.) – L. Levrel May 27 '16 at 14:48
  • @L.Levrel: I call that a quantum field. It doesn't just diffract on the crystal, it is the crystal. That's one of the major ontological differences between single particle quantum mechanics, which introduces synthetic and arbitrary categories of "things" and effective potentials and QFT, which deals with one (well, still a few) self-interacting fields and which can take only one of a few forms, if we want the theory to be self-consistent to some degree. All I am saying is that an analysis based on the ontology of the Schroedinger equations is stuck with 80 year old physics. – CuriousOne May 27 '16 at 19:10

4 Answers4

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There is no contradiction.

This:

"The de-Broglie wave and the particle are the same thing; there is nothing else. The real particle found in nature, has wave properties and that is a fact."

is a more general statement. Note that it does not define what is "waving". It just states that the particle is characterized by a wave.

This goes into the details of the set:

"When we come to particles other than photons,

i.e. photons are identified with an electromagnetic wave but not other particles

the wavelength again is a well-defined property, but only in terms of a large statistical sample. And for these other particles, we do not even have a seemingly concrete macroscopic property to associate with the wave, equivalent to electric and magnetic field of a beam of light. We arrive at the conclusion that the wave property is an expression of the probabilistic or statistical behavior of large number of identically prepared particles -- and nothing else!

italics mine.

The paragraph identifies what is in general "waving" for quantum mechanical particles. It is the probability of finding them at $(x,y,z,t)$ with energy momentum $(E,p_x,p_y,p_z)$ that obeys a quantum mechanical wave equation ( Schrodinger etc.). The probability has a sinusoidal behavior.

The photon itself, as a quantum mechanical particle has a waving "probability" distribution. Single photon double slit experiments show this as clearly as single electron. The hits on the screen (or ccd for photons) are points for individual particles. It is the distribution that shows the probability of finding the particle at an (x,y) on the screen that shows wave properties.

L. Levrel
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anna v
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    I don't think so. According to 1st group, there is wave-particle duality. According to 2nd group, there are only particles (there are no waves) but the distribution of these particles (when they are detected) is wavy. – atom May 26 '16 at 11:15
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    The word "particle" has no meaning in physics by itself. The first identifies particles as waves, with no further attributes, i.e "what is waving".The second describes what experimental attributes the "wave" has. – anna v May 26 '16 at 11:36
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    But authors French & Taylor do not seem to discard "particle" concept at all. And particle has meaning in classical physics. – atom May 26 '16 at 11:44
  • In quantum mechanical dimensions, particle is a term to be defined. Classically a particle is characterized by fixed mass, volume and a center of mass (x,y,z). The study of the microcosm has shown that sometimes quantum mechanical entities behave as classical particles, i.e. have an (x,y,z) and an energy four vector describing them, but their trajectories are not classical particle trajectories, not orbits for electrons, but orbitals : proabbility loci. So one has to redefine and the two quotes are on the redefinition road. – anna v May 26 '16 at 11:49
  • @atom : Of course the two books are saying exactly the same thing, if you are prepared to understand QM. The de-Broglie wave *is* the probability wave of a particle, which is all we can say about it, so it is the particle itself, and, yes, it is assayed/mapped out by a large assembly of particles/dots on a detector tracing out the waviness. You can always imagine contradictions by misreading the respective statements, but appreciating QM amounts to realizing there aren't any. People were confused about this 90 years ago, but they have not been since. – Cosmas Zachos May 26 '16 at 13:32
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    So, is there a good reason for the second quote (French & Taylor) to explicitly except photons? Is there anything special about photons here? Or is there anything special about massless particles in this regard? – Jeppe Stig Nielsen May 26 '16 at 14:05
  • @JeppeStigNielsen It is a bit misleading as it is stated. The truth is that for photons, the frequency given in E=h*nu is the frequency of the classical electromagnetic wave that these photons will build up, where it is the E and B fields that are "waving". Massive particles do not build up to equivalent macroscopic fields . In this link the QFT build up of classical fields is discussed http://motls.blogspot.com/2011/11/how-classical-fields-particles-emerge.html – anna v May 26 '16 at 14:26
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    I have my problems with the “large number of identically prepared particles” phrase. As far as I understood, the wave function describes the behavior of even a single particle. – Holger May 26 '16 at 16:36
  • @Holger Squared it describes the probable behavior of even a single particle. That is why statistics are needed – anna v May 26 '16 at 16:37
  • anna v, cannot a Bose-Einstein condensate be considered as a macroscopic massive-particle field? Not macroscopic enough, maybe? (and not as common as EM fields of course) – L. Levrel May 26 '16 at 19:25
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    @L.Levrel yes, an effective QM field theory works , but I have not read of macroscopic fields with wavelengths coming from E=h*c/lamda . – anna v May 27 '16 at 04:10
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Group 2 has some non-objectable contents (“for these other particles, we do not even have a seemingly concrete macroscopic property to associate with the wave”), but is otherwise inconsistent (“We arrive at the conclusion...”: how does the “conclusion” relate to the previous statement in any way?) and wrong in the main aspect with which you're concerned (italics mine):

the wavelength again is a well-defined property, but only in terms of a large statistical sample (...) the wave property is an expression of the probabilistic or statistical behavior of large number of identically prepared particles -- and nothing else!

is contradicted by single-particle interference experiments, which were made not only with photons but also with particles with mass, e.g. electrons.

Group 2 leads to think that particles are just very small corpuscles (marbles), that the quantum indeterminacy is a consequence of their smallness. In short, that quantum mechanics are a variant of statistical mechanics.

Group 1 is true, though a little approximate: de Broglie waves are plane waves, thus a correct model for a monokinetic beam of particles. In general, particles are described by wavefunctions.

By the way, I am somewhat averse to this statement of @annav:

what is in general "waving" for quantum mechanical particles (...) is the probability of finding them at $(x,y,z,t)$ with energy momentum $(E,p_x,p_y,p_z)$

The wavefunction is not a probability. It is a so-called “amplitude of probability”: the squared modulus of the wavefunction is a probability density. This said, the wording “probability of finding them at” may again lead to think the particle is in some definite state unknown to us, which it is not. Additionally, there is no experimental mean to do a point measure, because measuring requires an interaction, and there is no point “thing” with which to do such interaction (hence the probability density that one has to integrate over a volume to obtain a probability proper).

Now, as you know, there are many interpretations of quantum mechanics.

L. Levrel
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  • @downvoter: your criticism is welcome in the comments if you think my answer is wrong, misleading, or malformed. Downvoting per se is pretty much useless. We all should aim at improving the site quality. – L. Levrel May 26 '16 at 19:28
  • Feynman, David Bohm (in his 1951 book) etc. say quantum entities e.g. electrons, photons are neither classical particles nor classical waves. In your answer, you said group 2 is correct. So do you mean particle and wave of group 2 are in this non-classical sense? Or in some another sense ? – atom May 27 '16 at 04:25
  • @atom: (you mean group 1 I guess) It's not fully clear to me what they mean by classical wave. The wavefunction in itself is like any other wave: it obeys a wave equation (thus some dispersion relation), which also leaves constant some quantities (e.g., energy for an EM wave, total probability for a particle wavefunction). Of course, a particle wavefunction is not associated with a usual macroscopic field, as anna v pointed out. There is a difference, namely quantification (of energy for photons, of number for matter particles), that shows up when these waves interact with something else. – L. Levrel May 27 '16 at 11:42
  • ... So yes, at the nanoscale, particles are waves (or the emergence of an underlying wave if you consider the QFT level, as CuriousOne points out), waves of their own nature, with a quantification property. – L. Levrel May 27 '16 at 11:44
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I agree with CuriousOne that you would be better off ditching both of these viewpoints and looking for something more modern. However, this is instructive because it does illustrate a common problem in QM education: many authors are invested in a particular interpretation, and present that interpretation (disingenuously, to my thinking) as the only correct way to think about the theory.

In reality there are at least two classes of interpretations of quantum theories, both of which are completely consistent with the measurable results. The first class, which is roughly matching the perspective of Wichmann*, is that the quantum superposition over possible results of an observation should be regarded as the actual physical reality of an object prior to measurement. The second class, roughly corresponding to the statement of French & Taylor, is that the quantum state should be regarded as a statement about what we know about the possible observable outcomes, or what is possible to be known about the outcomes, but that the system itself should be regarded as having well-defined properties prior to measurement. As a concrete example, this means the choice is between thinking that an electron cannot have a well-defined position and momentum simultaneously, or that it is not possible to know an electron's position and momentum simultaneously.

Both texts, at least in the excerpts given, appear to make a sin of omission by implying that one or the other of these interpretations is "correct." There are other problems too- I agree with L. Levrel that French and Taylor's singling out of the photon seems dubious, and seems to neglect the idea of a BEC. There are lots of better resources out there- keep reading and thinking!

*Okay, it is a little difficult from such brief quotes to know exactly what the authors are thinking, but this is what it seems likely to me that they intend- interpretations of interpretations... ;)

Community
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Rococo
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  • "thinking (...) that it is not possible to know an electron's position and momentum simultaneously." I thought this possible interpretation had been ruled out by experiment? (something to do with hidden variables) – L. Levrel May 28 '16 at 18:58
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    @L.Levrel despite how it sounds, this is not a local hidden variable theory. In particular, this idea doesn't in any way suggest that there is a deeper theory underneath quantum mechanics. All it says is that states should be thought of as properties of the observer's knowledge, not of the system itself. – Rococo May 28 '16 at 20:45
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    A popular form of this idea is the so-called "Quantum Baynesianism", see, e.g., https://en.wikipedia.org/wiki/Quantum_Bayesianism or https://www.quantamagazine.org/20150604-quantum-bayesianism-qbism/ . – Rococo May 28 '16 at 20:46
  • Thanks for the details! I now understand how "group 2" can be seen as correct (although QBism is posterior by 25 years!). From the WP page, it looks to me like QBism "rewrites" the evolution equation as something alike a Markov chain... – L. Levrel May 29 '16 at 09:04
  • ... But then, the fact that "states should be thought of as properties of the observer's knowledge, not of the system itself" does not necessarily imply that "the system itself should be regarded as having well-defined properties prior to measurement" (and in particular, simultaneously well-defined but not knowable position & momentum, which seems irreconcilable with single-particle interference). Does it? – L. Levrel May 29 '16 at 09:04
  • @L.Levrel Yes, my presentation is condensed and very ahistorical. Nonetheless, these two categories (sometimes called psi-epistemic and psi-ontic interpretations) are useful for classifying the older versions of the interpretations, like the Ballentine-style statistical interpretation, as well. – Rococo May 29 '16 at 15:48
  • @L.Levrel Re: 'But then... ' : You are correct that it does not require you to take this position, but it does permit it. There is no difference in result between ascribing a particle properties that can never be observed even in principle and saying that those properties do not exist- it is a purely philosophical distinction. – Rococo May 29 '16 at 15:51
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    Okay, this is getting too long, but here's one last helpful link: http://www.nature.com/news/experts-still-split-about-what-quantum-theory-means-1.12198 Note that 'votes were roughly evenly split between those who believe that, in some cases, “physical objects have their properties well defined prior to and independent of measurement” and those who believe that they never do' – Rococo May 29 '16 at 16:02
  • @Rococo: You said "All it says is that states should be thought of as properties of the observer's knowledge, not of the system itself". Then superposition state is not actual physical reality; it is property of observer's knowledge, isn't it? – atom May 30 '16 at 10:36
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It's neither a classical wave nor a classical particle. I think any attempts to describe it as either of those need to be qualified like this. It might look like one or the other, but both are only approximations.

The best theories we have describe quantum fields, and a particle is a field quantum. I don't really know how to describe a field quantum in classical terms other than "sometimes it can look like a classical particle, sometimes like a classical wave, and sometimes it's not really like either of those".

Roman Starkov
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