# Two contradictory groups of statements from two different books on quantum physics

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 thatthe 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.

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.

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... ;)