My fundamental misunderstandings of quantum mechanics

[alsey42147]

so now I'm finally getting to grips with the maths of quantum mechanics, I'm getting really confused about what it means physically. sorry this is quite long but it seems like the more i think about quantum mechanics, the more my understanding of it disintegrates.

first, does quantum mechanics actually say what a particle is, or what its doing? as i understand it, a particle is described by a wavefunction which doesn't actually 'exist' but probability information can be derived from it. is that right? it seems strange to me that you have a theory which doesn't actually tell you what's going on, it just predicts results.

what about de broglie waves? are they the same things as wavefunctions? I'm guessing not, because de broglie waves have real wavelengths and stuff but wavefunctions are complex - is that right? if so, then what are de broglie waves?

then there's the double slit experiment. first I'm a bit confused about which double slit experiments have actually been done, and which are thought experiments. i know its been done with light, electrons, and single electrons, but what about the one where an electron is detected going through one of the slits - has that actually been done? if someone could give me a paper reference or something that would be great.

in the case of the one electron at a time experiment, where a single electron interferes with itself, i don't actually know what is meant by waves in this context. are we talking about actual physical waves, or wavefunctions which just give probability information? i used to interpret it like this:

a wave (a physical thing that exists) goes through the slits and an interference pattern is observed, so the electron must have gone through both slits simultaneously.

now I'm starting to think that's wrong and I'm getting horribly confused. do you instead have a wavefunction (that doesn't physically exist) going through a slit, which then interferes with another wavefunction which went through the other slit, resulting in a probability distribution which gives the interference pattern? i.e. two wavefunctions in different places but only one electron. or, do you have one wavefunction that goes through both slits together and then evolves so that the interference pattern is obtained? i.e. one wavefunction, one electron. or is it something different?

i'm hoping if i can make sense of this, i might be able to make some sense out of what happens when you observe an electron going through one of the slits.

one final thing; if you shoot single electrons through a single slit, do you get a peak that decays (like light), or do you just get a line?

 

[masudr]

While for a single particle, the wavefunction can be described in 3 spatial dimensions, this picture is no longer useful for any other system which is more complicated. In this sense, the wavefunction is rarely a good physical picture.

Most of your problems appear to have arisen from trying to see what the wavefunction is doing in physical space. Instead, understand that the wavefunction exists in configuration space, which is completely detached from our spacetime; the only link between the two appears to arise from the process of measurement (or interference with a system with many orders of magnitude larger degrees of freedom, if you like...)

 

[vanesch]

so now I'm finally getting to grips with the maths of quantum mechanics, I'm getting really confused about what it means physically.

Everybody who has given it some thought is confused about what it means physically, and that's now 80 years that it lasts: it is called the "measurement problem" of quantum mechanics.

That doesn't mean that there are no "views" or "interpretations" of quantum mechanics, but they all have something rather odd to them. If you're in need of "a physical picture", you can take whatever suits you best. I have mine (it's MWI), others have theirs.

But then, some people think one shouldn't waste time with that.
That's why many people take on the "shut up and calculate" attitude.

 

[madness]

Surely things as important as whether wavefunctions and de Broglie waves are the same thing or whether or whether there are two or only one wavefunctions in the double slit experiment will affect the things that you "shut up and calculate"? I'm having similar problems now that I have started quantum mechanics and don't seem to be getting any answers anywhere.

 

[alsey42147]

Most of your problems appear to have arisen from trying to see what the wavefunction is doing in physical space. Instead, understand that the wavefunction exists in configuration space, which is completely detached from our spacetime; the only link between the two appears to arise from the process of measurement (or interference with a system with many orders of magnitude larger degrees of freedom, if you like...)

so quantum mechanics doesn't actually tell you what particles are or what they do? you just have a wavefunction from which you can get probabilities that have some relation to real measurement?

Everybody who has given it some thought is confused about what it means physically, and that's now 80 years that it lasts: it is called the "measurement problem" of quantum mechanics.

lol, everyone i ask about this tells me the same thing. is this because no one actually knows? i don't find it very reassuring that everyone else is as confused as i am.

my basic questions are:
-are de broglie waves the same things as wavefunctions? if they're not, then what are they?
-in the double slit experiment, is there any theory that describes the physical movement of real things through the slits, or do you just have evolving non-existant wavefunctions?
-how many wavefunctions are involved in the double slit experiment? is it just one wavefunction that interferes with itself, or are there two separate wavefunctions which interfere with each other?
-what do you observe if you shoot electrons through a single slit?

i hope this doesn't sound offensive in any way, but it would be nice if someone could answer these questions instead of telling me that everyone else is confused too.

 

[jtbell]

what about de broglie waves? are they the same things as wavefunctions? I'm guessing not, because de broglie waves have real wavelengths and stuff but wavefunctions are complex - is that right? if so, then what are de broglie waves?

From a simplistic introductory-textbook point of view, the two are the same thing. From a historical point of view, I suspect that de Broglie's original mental picture of his waves was rather different from how the $\psi$ function actually turned out. So it would probably be more accurate to say that de Broglie's waves were the inspiration for what we now know as the QM wavefunction $\psi$. (Disclaimer: I have not actually studied the history of QM in detail, so don't take me as an expert.)

You should view "de Broglie wave" as a historical term. Whether or not it is really the same thing as $\psi$, the important thing is that in present-day QM, $\psi$ is what matters.

And even though $\psi$ is complex, it has a real wavelength $\lambda$ and a real frequency $f$, as in the monochromatic plane wave

$$\Psi(x,t) = A e^{i(kx-\omega t)}$$

where $k = 2 \pi / \lambda$ and $\omega = 2 \pi f$.

 

[alsey42147]

right, so de broglie waves are kind of an obsolete concept? is the de broglie wavelength then just the wavelength of a wave which the particle behaves like, but that wave doesn't actually exist as something physical?

 

[RobtO]

so quantum mechanics doesn't actually tell you what particles are or what they do? you just have a wavefunction from which you can get probabilities that have some relation to real measurement?

Right. The wavefunction tells all. But it doesn't exist physically. (My interpretation, YMMV.)

my basic questions are:
-are de broglie waves the same things as wavefunctions? if they're not, then what are they?

See jtbell's answer above.

-in the double slit experiment, is there any theory that describes the physical movement of real things through the slits, or do you just have evolving non-existant wavefunctions?

Evolving wavefunctions is all. Unless you subscribe to Bohm's version.

-how many wavefunctions are involved in the double slit experiment? is it just one wavefunction that interferes with itself, or are there two separate wavefunctions which interfere with each other?

One wavefunction.

-what do you observe if you shoot electrons through a single slit?

In principle, you'd see a diffraction pattern, just like with light. But I don't think this experiment has ever been done with any particle.

i hope this doesn't sound offensive in any way, but it would be nice if someone could answer these questions instead of telling me that everyone else is confused too.

Hope I helped.

 

[alsey42147]

you did, thanks!

 

[ZapperZ]

In principle, you'd see a diffraction pattern, just like with light. But I don't think this experiment has ever been done with any particle.

Yes it has. Here's an example:

http://prola.aps.org/abstract/RMP/v60/i4/p1067_1

Zz.

 

[Thrice]

Yeah I think the record right now is interference with buckyballs. That's a molecule of around 100 atoms.

 

[Thrice]

Surely things as important as whether wavefunctions and de Broglie waves are the same thing or whether or whether there are two or only one wavefunctions in the double slit experiment will affect the things that you "shut up and calculate"? I'm having similar problems now that I have started quantum mechanics and don't seem to be getting any answers anywhere.

Well, no. In fact that's the whole point to interpretations. They're (ironically) designed to not output any empirical results.

 

[madness]

Of course it would make a difference, if wavefunctions were not the same as the de Broglie waves for electrons then you wouldn't use the schrodinger equation to explain the double slit experiment and the whole idea of probabilities would be removed.

 

[Anonym]

so now I'm finally getting to grips with the maths of quantum mechanics

I doubt; it is not follow from your questions above.

i'm getting really confused about what it means physically.

The answer is the superposition of two pure states:

1.QT is the extension of the field theory.
2.Adequate formulation of QT is not achieved yet.

In contrast with the classical field theory, QT is the field theory of massive waves. In Classical World we consider the matter as the material point (and ensemble of the material points in many particle systems). In Quantum World the single material particle behaves also as a field. The maths of quantum mechanics is the adequate mathematical framework that allows to describe that. There is nothing mysterious in QM; however, to understand QM one should understand classical field theory first.

as i understand it, a particle is described by a wavefunction which doesn't actually 'exist' but probability information can be derived from it. is that right?

Wrong completely. The wave function describes a physical system state, but is an unobservable quantity. In the classical field theory the situation is exactly the same. You can obtain indirectly the necessary information about EM field but you can’t catch it as a ball using your hand and you can’t see it in the Classical World since it is spread (field). In addition, the true description of EM field is given in terms of EM potentials which are unobservable quantities exactly as wave functions in QM. The gravitation field has exactly the same properties. Therefore, when you are forced by the experimental evidence to describe the material point as a field it is not reasonable to expect that it will behave differently.

No information can be obtained from wave function. I repeat: the system state in QM is unobservable quantity. The information about QM system is obtained through measurements of eigenvalues of different dynamical variables associated with the given QM system. No information can be obtained from dynamical variables without knowledge of the system state. If the system state is not defined (real in the sense of the reality), then one will talk about dynamical variables of what? Everything that I said above seems to me obvious and even trivial. This is clearly written in the “Mathematical Foundations of QM” by J. von Neumann. If you “finally getting to grips with the maths of quantum mechanics”, then it should be obvious for you. The only problem is that I have no idea what are the textbooks you used during your studies. In addition, it seems that the noticeable portion of the present generation of the teachers of QM has no idea what they are talking about neither physically nor mathematically.

I consider the single electron/photon experiments available only recently the outstanding experimental achievements. For me personally to see A. Tonomura et al build up pictures contribute much more than all N.Bohr vs A. Einstein discussion. Now I see How it is in the real life. Notice that your “probability information” is only your interpretation and no physical theory exist that require any interpretation. When we talking about single particle physical system it means that the particle are doing statistics with itself. This is not what I know from the statistical mechanics. For the explanation of selfinterference read P.A.M. Dirac. If you will not understand him, leave quantum physics. It explains also why you meet Quantum Physics immediately when you start study the statistical systems.

Adequate formulation of QT is not achieved yet. Instead of wasting your time in analysis of stupid interpretations, consider for example, that SE apparently is the static analog of the classical mechanics and perhaps the dynamical generalization is required. And the relativistic version still not formulated.