Zafa Pi said:
Myths paper? Is there something wrong with what I wrote?
I think I posted what Copenhagen was about the time of Bohr - but for completeness will do it again:
1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)
Now let's look specifically at principle 4 - wave-particle duality:
Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
To examine it more carefully let's see what that paper says:
In introductory textbooks on QM, as well as in popular texts on QM, a conceptually strange character of QM is often verbalized in terms of wave-particle duality. According to this duality, fundamental microscopic objects such as electrons and photons are neither pure particles nor pure waves, but both waves and particles. Or more precisely, in some conditions they behave as waves, while in other conditions they behave as particles. However, in more advanced and technical textbooks on QM, the wave-particle duality is rarely mentioned. Instead, such serious textbooks talk only about waves, i.e., wave functions ψ(x, t). The waves do not need to be plane waves of the form ψ(x, t) = e^i(kx−ωt) but, in general, may have an arbitrary dependence on x and t. At time t, the wave can be said to behave as a particle if, at that time, the wave is localized around a single value of x. In the ideal case (see the equation in the paper - it involves that dreaded Dirac Delta Function) then the position x of the particle has a definite value x The state is the eigenstate of the position operator, with the eigenvalue x. Typically, the wave attains such a localized-particle shape through a wave-function collapse associated with a measurement of a particle position. Moreover, the wave may appear as a point like particle for a long time if the particle position is measured many times in sequence with a small time interval between two measurements. This makes the wave to appear as a classical particle with a trajectory, which occurs, e.g., in cloud chambers. However, the position operator is just one of many (actually, infinitely many) hermitian operators in QM. Each hermitian operator corresponds to an observable, and it is widely accepted (which, as we shall see later, is also one of the myths) that the position operator does not enjoy any privileged role. From that, widely accepted, point of view, there is nothing dual about QM; electrons and photons always behave as waves, while a particle like behavior corresponds only to a special case. In this sense, the wave-particle duality is nothing but a myth. But why then the wave-particle duality is so often mentioned? One reason is philosophical; the word “duality” sounds very “deep” and “mysterious” from a philosophical point of view, and some physicists obviously like it, despite the fact that a dual picture is not supported by the usual technical formulation of QM. Another reason is historical; in early days of QM, it was an experimental fact that electrons and photons sometimes behave as particles and sometimes as waves, so a dual interpretation was perhaps natural at that time when quantum theory was not yet well understood. From above, one may conclude that the notion of “wave-particle duality” should be completely removed from a modern talk on QM. However, this is not necessarily so. Such a concept may still make sense if interpreted in a significantly different way. One way is purely linguistic; it is actually common to say that electrons and photons are “particles”, having in mind that the word “particle” has a very different meaning than the same word in classical physics. In this sense, electrons and photons are both “particles” (because we call them so) and “waves” (because that is what, according to the usual interpretation,they really are). Another meaningful way of retaining the notion of “wave-particle duality” is to understand it as a quantum-classical duality, because each classical theory has the corresponding quantum theory, and vice versa. However, the word “duality” is not the best word for this correspondence, because the corresponding quantum and classical theories do not enjoy the same rights. Instead, the classical theories are merely approximations of the quantum ones.
BTW in the above wave does not mean an actual wave - it is short for wave-function.
Now look again at the wording:
Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
You are correct in saying sometimes it
seems like a particle, and sometimes it
seems like a wave. To be even plainer - there is nothing wrong with it at all. But that isn't what the above says - especially the bit: in some experiments both of these complementary viewpoints must be invoked to explain the results. It never needs to be invoked - period. A wave-function is simply the representation of a state in terms of position eigenvectors. That's all that needs to be invoked - nothing at all to do with wave-particle duality - its simply how some results 'seem' that way, as you say but only in very special circumstances. In virtually all circumstances it acts neither like a particle or a wave. Its OK to talk about this stuff in popularization's and/or beginner texts (although I wouldn't) but once one becomes more advanced it confuses more than illuminates because you now deal with all sorts if things - like a particle in a well, the hydrogen atom., the harmonic oscillator - none of which it acts like a particle or a wave. Yet student have been told it does. If you go back and correct that to something like you say - OK - but why bother - simply don't use it in the first place. Its a concept that is simply not needed.
Its not a founding principle of QM (merely what QM says in some special circumstances), its simply a left over form the early days of QM before it was understood as well as it is now, I would argue ever since Dirac published his textbook it should have been banished - but has hung on, and on, and on.
Yes - I agree Bohr should have remained silent about the status of the measuring device - but IMHO Bohr should have remained silent about a lot of things since I think much of what he says confuses rather than illuminates. That's just my view - he obviously was one of the greatest physicists that ever lived and grappled with QM as well as anyone could at the time - except maybe Dirac. But then again for Dirac it was - the math ma'am, just the math. Many do not have that attitude.
Thanks
Bill