Does the wave–particle duality apply only to electrons and photons?

[Femme_physics]

Does the wave–particle duality apply only to electrons and photons?

 

[Curl]

no...

 

[Femme_physics]

I wonder, is there an exact certain size where classical ends and quantum begins?

 

[Oudeis Eimi]

I wonder, is there an exact certain size where classical ends and quantum begins?

No, there's no well defined 'border' (and, as a matter of fact, even the
'classical' world is actually quantum!).

Every physical system is always interacting to some degree with the
environment it's immersed into (even if the system is in space, as
the 'vacuum' is actually filled with radiation). This interaction tends to
diminish the purely quantum effects (like interference or 'spreading')
associated with the 'wavy' nature of quantum objects. For simple systems
like small molecules, single atoms or free electrons, the effect is generally
rather weak, but for more complex systems like large molecules and up,
it is much more noticeable, so these tend to behave much more classically.
For macroscopic systems, the effect is exceedingly strong and fast.

But even very simple systems can behave almost classically if the
interaction with the environment is strong enough. An example would be
a small ion in liquid water at room temperature.

 

[Femme_physics]

Hmm, I'm not sure how much I understand you, Qudeis, so let's see... I'll start from the beginning-- You say that the classical world is behaving quantum! How? If Newton's equations are applied correctly to classical systems, why do we need Einstein in the picture?

Every physical system is always interacting to some degree with the
environment it's immersed into (even if the system is in space, as
the 'vacuum' is actually filled with radiation). This interaction tends to
diminish the purely quantum effects (like interference or 'spreading')
associated with the 'wavy' nature of quantum objects.

So a particle left to itself in a vacuum will act quantum, and with other particles and electromagnetic radiation, will act more "classical"?

For simple systems
like small molecules, single atoms or free electrons, the effect is generally
rather weak, but for more complex systems like large molecules and up,
it is much more noticeable, so these tend to behave much more classically.
For macroscopic systems, the effect is exceedingly strong and fast.

So since there is so much interaction with the environment to bigger objects, the effect is felt less? Is that what you're saying?

 

[alxm]

'Wave' and 'particle' here are classical concepts. The quantum-mechanical viewpoint is more that they're neither, but depending on the context they can act more 'particle-like' or 'wave-like'. This applies to everything. To make this all a bit less mysterious, you can define 'particle-like' behavior as something which has a definite location in space, and 'wave-like' behavior as something which does not. A quantum-mechanical particle does not have a specific location in space. It only has a certain probability of being at a given location. But: Once you measure it, that probability distribution disappears. It's now at that location, and isn't exhibiting 'wave-like' behavior, for the time being at least.

What happens after that, if you leave the particle alone, is that the probabilities of where you may find the particle spread out over space. It 'smears out' again.

Now there are two factors involved here. Oudeis Eimi explained one, which is that if the particle in interacting with the environment a lot (which is equivalent to being 'measured', in the quantum-mechanical sense), it can't spread as far before its location gets 'measured', and put into a definite location again. So if the location of the particle is constantly being 'measured' through interactions with the environment-at-large, then it can't 'smear out' very far and exhibit wave-like behavior. This is called the "Quantum Zeno Effect". The other factor here, which is just as important is the speed at which the particle 'spreads out'. As implied above, this occurs at a quite finite speed, and that speed is dependent on the mass of the particle. The heavier the particle is, the more slowly it 'smears out' (or in QM-jargon, 'evolves into a superposition').

If you remember some chemistry from school, one of the most basic ideas in chemistry is chemical structure. That's the fact that the properties of a molecule don't depend just on the number of atoms and their elements, but also how those atoms are arranged in space. Ethanol (CH₃CH₂OH) and dimethyl ether (CH₃OCH₃) have the exact same atoms, same number of electrons, protons, neutrons etc, but they're not the same chemicals at all. But if quantum mechanics says that particles (any particles) don't have a definite location in space, the question arises: How does that work? Shouldn't ethanol be able to rearrange its atoms and become dimethyl ether (or vice-versa)? So after quantum mechanics was 'invented', one of the first things they needed to do was explain this thing that all the chemists already knew about.

The answer to this is that the nuclei of atoms are so very heavy in relation to their distances in molecules, that it would require that they be left undisturbed for an astronomical amount of time before they'd have any significant probability of rearranging themselves. As far as chemistry is concerned, atomic nuclei behave almost entirely classically. Only the very lightest elements (e.g. hydrogen) exhibit a measurable amount of 'quantum mechanical motion'. (A paper in JACS last year claimed to have measured such an effect with carbon in a particular reaction. I'm skeptical of that result, however) The electrons in an atom or molecule, on the other hand, only weigh 1/1800 of the lightest nuclei. They behave entirely quantum-mechanically (and that was the problem which was the start of quantum mechanics). So in practice, chemistry straddles the domains of quantum and classical. When doing quantum chemistry, one describes the electrons entirely quantum-mechanically, but the nuclei are usually treated classically or semi-classically.

There are some situations where quantum effects become larger. You can deduce them from the conditions above: When particles aren't interacting a lot with their environment, such as when you have low temperatures, low pressures, or rigid materials (all amounting to fewer interactions/random bumping and jostling around). It's also in those kinds of situations you see quantum behavior on the larger scale, such as superfluids, superconductivity, Bose-Einstein condensates, etc. That said, we have been able to measure 'wave-like' behavior in objects as large as a buckyball (C₆₀ molecule). But I think it should be stressed that that's more of an experimental feat (in part due to the particular properties of C₆₀) rather than due to the fact that they behave particularly quantum-mechanically.

Classical physics is a limiting case of quantum mechanics, as you move towards heavier objects and more interactions. There are still some unanswered questions on how you get from one state of affairs to the other, particularly regarding exactly how 'measurement' occurs (a process known as decoherence). But we don't need to describe classical systems quantum mechanically, since by definition, classical systems don't behave quantum mechanically to a significant extent. As I said, the area where this occurs in practice is on the level of chemistry. The motion of an electron in a molecule is quantum, but the motion of a molecule in a fluid is almost always well-described classically (assuming you know the intermolecular forces, which are quantum-mechanical in origin, but which can be described quite accurately without explicit quantum mechanics)

 

[sci-guy]

I'm interested in this too -- thanks alxm for that great explanation. A few questions:

'Wave' and 'particle' here are classical concepts. The quantum-mechanical viewpoint is more that they're neither, but depending on the context they can act more 'particle-like' or 'wave-like'. This applies to everything. To make this all a bit less mysterious, you can define 'particle-like' behavior as something which has a definite location in space, and 'wave-like' behavior as something which does not. A quantum-mechanical particle does not have a specific location in space. It only has a certain probability of being at a given location. But: Once you measure it, that probability distribution disappears. It's now at that location, and isn't exhibiting 'wave-like' behavior, for the time being at least.

Isn't that somewhat true at a classical level too? If you have a water wave, it obviously has wave-like properties, but if you measure it at any point in time, it's at a specific place (like taking a photo of it). Then the question becomes:

What happens after that, if you leave the particle alone, is that the probabilities of where you may find the particle spread out over space. It 'smears out' again.

My question here applies mainly to QM. My understanding is that the act of measuring changes the wave-particle. Is that only in the sense of reducing the wave state down to a point, or does it mean that, once measured, the wave changes in some way AFTER the measurement. If it's the former, that's identical to what happens classically (measuring the water wave at any point doesn't change the wave form). Only in the latter case is there a real distinction between QM & classical behavior (at least on this point). I must be missing something here, because I know there IS a difference between the two -- can you clarify exactly what it is?

There are some situations where quantum effects become larger. You can deduce them from the conditions above: When particles aren't interacting a lot with their environment, such as when you have low temperatures, low pressures, or rigid materials (all amounting to fewer interactions/random bumping and jostling around). It's also in those kinds of situations you see quantum behavior on the larger scale, such as superfluids, superconductivity, Bose-Einstein condensates, etc.

What about laser light, which (as far as I know) doesn't involve low temperature. What allows the macroscopic quantum behavior?

 

[sci-guy]

Re effects of measurement on the system, I found the answer: measurement of the quantum state DOES affect the future evolution of the system, so that IS a difference between QM and classical (discounting the more common "observer effect" that may occur).

 

[alxm]

Isn't that somewhat true at a classical level too? If you have a water wave, it obviously has wave-like properties, but if you measure it at any point in time, it's at a specific place (like taking a photo of it).

The water in the wave isn't in a specific place. That's about as far as the analogy extends. The wave function is not the same thing as a classical wave.

My question here applies mainly to QM. My understanding is that the act of measuring changes the wave-particle. Is that only in the sense of reducing the wave state down to a point, or does it mean that, once measured, the wave changes in some way AFTER the measurement.

A quantum system can be in a superposition of many states, but only measured to be in one of those states. A measurement changes the wave function, and it therefore also changes its evolution after that point.

What about laser light, which (as far as I know) doesn't involve low temperature. What allows the macroscopic quantum behavior?

Photons aren't macroscopic, and their behavior isn't really more quantum mechanical in laser light than otherwise.
The unique properties of laser light is that it's monochromatic and in-phase; both of which are also classical properties of light.

 

[sci-guy]

Then why is laser light held as an example of macroscopic quantum coherence?

 

[alxm]

A coherent state in quantum mechanics isn't the same thing as coherence in classical optics and wave mechanics.

Laser light is highly coherent, in the classical, in-phase sense. It also corresponds to a coherent state of the light field. The EM field isn't a macroscopic object, or even an object at all, really. The electrons emitting the light aren't in a coherent state, and aren't macroscopic either.

 

[ArjenDijksman]

Re effects of measurement on the system, I found the answer: measurement of the quantum state DOES affect the future evolution of the system, so that IS a difference between QM and classical (discounting the more common "observer effect" that may occur).

Well said. In quantum measurements, the probes (photons, electrons,...) with which we observe the system are in the same size range. In classical physics, the effect of the probe is generally ignored: the light shining on a marble has no noticeable effect on its observed trajectory. Not true for the light shining on electrons, which will "cohere".

Interestingly, one can "upsize" quantum effects like wave-particle duality, double slit interference, tunneling, quantized orbitals, etc, if we upsize the "quantum" particles as is done in the bouncing droplet experiments done by the groups of Couder in Paris and John Bush at MIT (see his paper http://www.pnas.org/content/107/41/17455.extract").

 

[sci-guy]

A coherent state in quantum mechanics isn't the same thing as coherence in classical optics and wave mechanics.

Laser light is highly coherent, in the classical, in-phase sense. It also corresponds to a coherent state of the light field. The EM field isn't a macroscopic object, or even an object at all, really. The electrons emitting the light aren't in a coherent state, and aren't macroscopic either.

Are you saying then, that this statement from Wikipedia (link) is false?:

"Large-scale (macroscopic) quantum coherence leads to novel phenomena. For instance, the laser, superconductivity, and superfluidity are examples of highly coherent quantum systems, whose effects are evident at the macroscopic scale."

That site gives the impression (if I understand correctly) that the defining feature of quantum coherence is that the entire quantum system can be defined by a single wavefunction. At any rate, thanks for that clarification.

In quantum measurements, the probes (photons, electrons,...) with which we observe the system are in the same size range.

Thanks for pointing out WHY quantum measurement alters the outcome. So it's NOT some result of the physicist's mind being inserted into the equation as some suggest; rather, it's due to the measurement probes (as you call them) being of the same size and energy of that which they measure, so their interaction alters the outcome.

 

[sci-guy]

I just looked into wavefunction collapse and the so-called "measurement problem," which IS (if this debated topic is proven true) an example of the act of measuring (i.e. "the physicist's mind") altering the outcome of the quantum state.

So that's distinct from what I pointed out in the previous post? Am I understanding correctly?

 

[ArjenDijksman]

I just looked into wavefunction collapse and the so-called "measurement problem," which IS (if this debated topic is proven true) an example of the act of measuring (i.e. "the physicist's mind") altering the outcome of the quantum state.

So that's distinct from what I pointed out in the previous post? Am I understanding correctly?

There are different features in the measurement problem.

Initially, we have a quantum system of which we know don't exactly know the state. So mathematically, the best way we can describe it is as a linear combination of the allowed states. These states are represented by rotating vectors (just arrows). A rotating arrow has a position and a momentum (particle nature of the quantum system) and a periodically evolving phase (wavy nature). Its projection on an axis is a wave-function. Now, there are roughly two possible interpretations:
1. because we describe the state as a linear combination of states, the system is effectively in a superposition of states,
or, 2. the system is in only one of the allowed states, but because we don't exactly know the state, we can't do better than to describe its state by a superposition of states.

There's no consensus among physicists about one or the other interpretation and maybe there never will be, because the state is intrinsically unknown before a measurement.

Then, if we want to know something more about that system, we need to interact with it. Interacting with a quantum system means disturbing it, which means altering the state. So whether we consciously measure something about the state (the physicist's mind) or whether we interact with the system without noticing the result (no information processed by the mind), there's a "wave-function collapse" into an altered state.

Finally, if the observer's mind has processed the measurement result, it can update the mathematical representation of the quantum state by discarding those terms of the linear combination that don't fit with the result. It has consciously "collapsed" the wave-function that was physically altered before.

So we should distinguish between:
- the physical wave-function collapse where the quantum state is physically altered,
- and the conscious mathematical updating of the quantum state by the physicist's mind.

 

[sci-guy]

So you're saying it IS possible to measure something about the state (and thereby collapse the wave function) WITHOUT physically interacting with it (i.e. via a measurement 'probe' particle as you mentioned before)? If that's true, then the observer's mind DOES alter the outcome.

And thanks for this:

...mathematically, the best way we can describe it is as a linear combination of the allowed states. These states are represented by rotating vectors (just arrows). A rotating arrow has a position and a momentum (particle nature of the quantum system) and a periodically evolving phase (wavy nature). Its projection on an axis is a wave-function.

Now I have some kind of a picture of what a wavefunction represents. One question though:

I had thought the wave part of the equation was that we don't know the exact position of the particle, but you seem to suggest that it pertains to the particle's evolving phase in time -- or were you just over-simplifying?

 

[ArjenDijksman]

Now I have some kind of a picture of what a wavefunction represents. One question though:

I had thought the wave part of the equation was that we don't know the exact position of the particle, but you seem to suggest that it pertains to the particle's evolving phase in time -- or were you just over-simplifying?

Both interpretations are relevant. The evolving phase of the wavefunction can be seen as the phase of a wave and as the evolving orientation of the vector representing the particle. This is a de Broglie-Bohm viewpoint, where there's phase matching between the particle's phase and its pilot wave.