What Are Some Common Misconceptions About Quantum Mechanics?

[unseensoul]

By the way, if the wave-behaviour of a particle is related to where the particle might be found (wavefunction) why do particles diffract as well (in this situation it seems to behave like a REAL wave)? I can't relate both concepts...

 

[malawi_glenn]

Yeah that's just about it...
I was stressing that if you want to understand anything about QM, you have to do the math, because as Tac-Tics says, we don't know what happens in that "black-box."
Then the second part was the observation that something does.

A collision would be an example of something physical, yes. Sorry, I hate imprecise language as well, but I'm having trouble on precise formulation. Physical as in not just the mathematical formulation: that which causes the system to behave in the way described by the operator.
Something which "has material existence" (dictionary definition).

And since we don't know what happens, we should not perhaps extrapolate what happens in the "classical" macroscopic world at all.

 

[malawi_glenn]

By the way, if the wave-behaviour of a particle is related to where the particle might be found (wavefunction) why do particles diffract as well (in this situation it seems to behave like a REAL wave)? I can't relate both concepts...

why not? The math of wavefunctions is (almost) the same as for light waves. Just that the intepretation on what it is differs. In light, it is the density in electric field (and so on) and in QM it is the density of probability.

The probability DENSITY can be negative, and even complex valued! But the probability, which is the probability density modulus squared - is always positive.

 

[newbee]

unseensoul

By the way, if the wave-behaviour of a particle is related to where the particle might be found (wavefunction) why do particles diffract as well (in this situation it seems to behave like a REAL wave)? I can't relate both concepts...

Let me modify a phrase above to be more in line with the way physicists speak and see if it helps:

"if the wave-behaviour of a particle is related to where the particle might be found (wavefunction) why"

becomes

" ... if the theory of quantum mechanics predicts the probability of measuring a particle to be at a give position why ..."

Think about it for a while. Also:

(in this situation it seems to behave like a REAL wave)

According to QM it ALWAYS behaves as a probability density wave.

 

[Fredrik]

According to QM it ALWAYS behaves as a probability density wave.

Only when it's isolated from the environment.

 

[Phrak]

Simultaneous measurements of two non-commuting observables don't make sense in QM. Hurkyl knows that. He may have taken it a little too far by claiming that we can imagine a device that performs both measurements at once, but he was definitely right to point out that the uncertainty principle isn't about limitations of measuring devices. It's about a property of state vectors / wave functions.

A few thoughts about the possibility of a device that performs "a simultaneous measurement of two non-commuting observables" on a system... Let's take a spin-1/2 system as an example, and first consider an apparatus that "measures" the z component of the spin. Such a device only needs to produce an inhomogeneous magnetic field and detect the position of the spin-1/2 particle after it's deflected in one direction or the other by the inhomogeneous magnetic field. (Stern-Gerlach experiment).

A device that performs "a simultaneous measurement of the x component and the y component of the spin" would just be a device that produces two inhomogeneous magnetic fields in a location that's surrounded by detectors. It's easy to see what would happen in this case: A magnetic field is a vector quantity, so the "two fields" produced by the device would be equivalent to one that's stronger and pointing in the direction defined by the vector sum of the two field vectors.

I expect something similar to hold in all cases, not just in the case of the spin components of spin-1/2 particles. A "simultaneous measurement of two non-commuting observables" would always turn out to be just one measurement of one observable that isn't one of the two intended.

It strikes me that you can have such a device, Fredrik. One SG beam splitter. This feeds two SGs. One measures up; one measures down.

It seems that we have to specify, in the least, that the two non-commuting observables are measured in the same space-time region.

Interesting it itself, I suppose. But obvious in retrospect. When there is imposed temporal constraint one should beware of a lurking spatial constraint.

In addition, the regional constraint seems a necessary, but not completely sufficient condition.

 

[nfelddav]

And since we don't know what happens, we should not perhaps extrapolate what happens in the "classical" macroscopic world at all.

I agree completely. Trying to extrapolate what we cannot measure is beyond physics. I merely argued that we should acknowledge that something does.

 

[triplemaya]

Hi. Much the best explantion I have found is given in Nick Herbert's book Quantum Reality, I will do my best to precis in brief.

Wave information can be packaged in different ways, and analog or digitgal are very different. If you want to describe a sine wave by far the simplest way to do so is with an analog formula, a simple wave equation defines it completely, while to describe this digitally takes a large number of samples. Coversely, if you want to describe spike data, very few digital samples are required, while to define it using only sine wave formulae would require a very large number of waves designed to cancel each other out by addition leaving only the spike. The two methods are complementary, or better conjugate, in that the easier it is to describe wave information in one way the harder it is in the other way. However, obviously, the two ways are describing the same information. The conjugate properties of a quantum, such as position and momentum, are like digital and analog, two different ways of defining the same data. Of course, to us position and momentum seem like wildly different things, so this does not make sense, but that is how the quantum works. The two things are mutually exclusive conjugate properties, which basically means that they are not so much different properties of the quantum, as they appear to us to be, but conjugate attributes of a single property, positionmomentum.
Making a measurement of position is the same thing as finding out the digital spike version of the information and making a measurement of momentum is the same thing as finding out the analog sine wave version of the information. You can do one or the other not both ( well, you can do both, but only partly, so that you have a partial measurement of position and a partial measurement of momentum. )

As Herbert states "the conjugate attributes correspond exactly to conjugate wave form families (eg sine wave and digital)" thus if you measure a quantum for position, digital measurement, you can have no information about momentum because you have no sine wave information, and vice versa. What Heisenberg is saying is that it is not a question of what we can measure, the quantum itself is of that nature, it's a thing which has conjugate properties, or more accurately properties which have conjugate forms, and if one is precisely defined the other is inherently undefined, thus embracing all possible values.

This can be seen as simple and direct evidence that physical reality *is* the wave function, and there is no underlying 'real physical stuff', it doesn't work like that! The real physical stuff is how the wave function appears to us at our macroscopic level.
HTH

 

[Naty1]

If you are looking for introductory explanations try the following

Wikipedia, online

Warped Passages, Lisa Randall

The Fabric of the Cosmos, or The Elegant Universe, Brian Greene

The Trouble With Physics,or Three Roads to Quantum Gravity*, Lee Smolin

* The most detailed non mathematical discussion, about 200 pages

For a more mathematical approach: The Road to Reality, Roger Penrose