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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?

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    $\begingroup$ 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. $\endgroup$ – CuriousOne May 26 '16 at 11:17
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    $\begingroup$ @CuriousOne--What is correct then ? $\endgroup$ – atom May 26 '16 at 11:45
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    $\begingroup$ @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. $\endgroup$ – atom May 26 '16 at 12:17
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    $\begingroup$ 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. $\endgroup$ – Philip Oakley May 26 '16 at 14:47
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    $\begingroup$ @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. $\endgroup$ – CuriousOne May 26 '16 at 16:24
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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... ;)

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  • $\begingroup$ "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) $\endgroup$ – L. Levrel May 28 '16 at 18:58
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    $\begingroup$ @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. $\endgroup$ – Rococo May 28 '16 at 20:45
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    $\begingroup$ A popular form of this idea is the so-called "Quantum Baynesianism", see, e.g., en.wikipedia.org/wiki/Quantum_Bayesianism or quantamagazine.org/20150604-quantum-bayesianism-qbism . $\endgroup$ – Rococo May 28 '16 at 20:46
  • $\begingroup$ 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... $\endgroup$ – L. Levrel May 29 '16 at 9:04
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    $\begingroup$ Okay, this is getting too long, but here's one last helpful link: nature.com/news/… 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' $\endgroup$ – Rococo May 29 '16 at 16:02
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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.

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    $\begingroup$ 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. $\endgroup$ – atom May 26 '16 at 11:15
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    $\begingroup$ 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. $\endgroup$ – anna v May 26 '16 at 11:36
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    $\begingroup$ But authors French & Taylor do not seem to discard "particle" concept at all. And particle has meaning in classical physics. $\endgroup$ – atom May 26 '16 at 11:44
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    $\begingroup$ 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? $\endgroup$ – Jeppe Stig Nielsen May 26 '16 at 14:05
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    $\begingroup$ 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. $\endgroup$ – Holger May 26 '16 at 16:36
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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.

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  • $\begingroup$ @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. $\endgroup$ – L. Levrel May 26 '16 at 19:28
  • $\begingroup$ 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 ? $\endgroup$ – atom May 27 '16 at 4:25
  • $\begingroup$ @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. $\endgroup$ – L. Levrel May 27 '16 at 11:42
  • $\begingroup$ ... 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. $\endgroup$ – L. Levrel May 27 '16 at 11:44
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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".

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    $\begingroup$ I'm happy to see that some QFT-savvy people do use the word "particle" to name field quanta. :) $\endgroup$ – L. Levrel May 28 '16 at 19:19

protected by Qmechanic May 28 '16 at 6:00

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