Max Born and probability waves

[RegalPlatypus]

This isn't homework - just some questions that have come up from reading The Fabric of the Cosmos:

1) Say you measure the position of an electron for a hydrogen atom on Earth and, beating all odds, find that it's actually on the moon (forget any details as to how you'd actually find it if it's on the moon). Once its been located in that new position does it retain its previous probability wave centered about the proton on Earth, or does a new wave have to be calculated for it? In the latter case, does that mean an atom can simply lose electrons without any external forces applied to it? Or would it never actually be 'lost' until you measured its position?

2) In the above situation, if it retains its probability wave and you re-run the experiment and find the new position of the electron to be within the 1S orbital, how do you avoid problems with special relativity if it made that trip from the moon the last time you measured it to the Earth the second time you measured it faster than light? Maybe because it's a random event and no actual information is capable of being transmitted between the two positions?

3) What's the threshold for quantum effects? Do entire atoms, entire molecules have probability waves, or only elementary particles?

 

[jtbell]

Once its been located in that new position does it retain its previous probability wave centered about the proton on Earth, or does a new wave have to be calculated for it?

After you've made the measurement, the electron is in a new state. I would expect that it is almost certainly no longer bound to the proton on Earth.

In the latter case, does that mean an atom can simply lose electrons without any external forces applied to it? Or would it never actually be 'lost' until you measured its position?

The latter. In order to make the measurement you have to interact with the system. Without any interaction, the state remains a bound state.

 

[CompuChip]

Note that this means that your classical picture of electrons circling and statements such as "this molecule has 8 electrons" have to be replaced with concepts like an "electron cloud" and proper averages.

 

[RegalPlatypus]

Would it be wrong to say that elementary particles exist at all possible points within their probability wave until they are measured at which point they take on a definite position? Or do they actually have definite positions the entire time?

 

[peter0302]

Most QM interpretations say that the particles have no position until measured. Before that there's only a state vector describing the likelihood of finding the particle at particular positiions.

 

[JesseM]

Most QM interpretations say that the particles have no position until measured. Before that there's only a state vector describing the likelihood of finding the particle at particular positiions.

I don't know if "most" interpretations say that--the Copenhagen interpretation does, the Bohm interpretation definitely doesn't, the MWI is sort of "none of the above" (the state vector is the only thing that exists, even after measurement), and I'm not too sure about the transactional interpretation.

 

[peter0302]

I'm not too sure about the transactional interpretation.

I don't think anyone is too sure about that one... ;)

 

[vanesch]

1) Say you measure the position of an electron for a hydrogen atom on Earth and, beating all odds, find that it's actually on the moon (forget any details as to how you'd actually find it if it's on the moon). Once its been located in that new position does it retain its previous probability wave centered about the proton on Earth, or does a new wave have to be calculated for it? In the latter case, does that mean an atom can simply lose electrons without any external forces applied to it? Or would it never actually be 'lost' until you measured its position?

As others pointed out, if - again all odds - you found it on the moon, then it has now a new wavefunction which has relatively important amplitudes centered on the moon.

The entire discussion (the interpretational issues) is "about what happened", and even "whether it makes sense to ask what happened".

2) In the above situation, if it retains its probability wave and you re-run the experiment and find the new position of the electron to be within the 1S orbital, how do you avoid problems with special relativity if it made that trip from the moon the last time you measured it to the Earth the second time you measured it faster than light? Maybe because it's a random event and no actual information is capable of being transmitted between the two positions?

But as it doesn't keep its original wavefunction, this question is now moot.

3) What's the threshold for quantum effects? Do entire atoms, entire molecules have probability waves, or only elementary particles?

We know for sure that quantum theory applies to elementary particles, atoms, small molecules, but also to other systems such as the entire cloud of valence electrons in a piece of semiconductor, the lattice of atoms in a crystal, ...

We have no indications that it doesn't apply to other, bigger stuff, but we have also no indications that it does. This is because as objects get "bigger", that they "decohere" more easily by spurious interactions, and that the *expected* quantum effects become less and less obvious, until they completely disappear and are compatible with classical behaviour. The reason is that the key proof to quantum effects is quantum-mechanical interference, which is a distinct signature from "classical statistical uncertainty", and when spurious interactions make states "decohere" then they start behaving more and more as classical statistical ensembles.

So it might very well be that big objects are ruled by classical physics, and not by quantum mechanics. That means that there is somehow a "transition" (which was postulated by Bohr) from the quantum to the classical. But it might also be that big objects are ruled also by quantum mechanics - as all statistical results are the same, there's no telling.

One tries hard to try to test quantum interference in a lot of different situations, but the "bigger" the objects, the harder the experiment.

 

[jtbell]

We know for sure that quantum theory applies to elementary particles, atoms, small molecules, but also to other systems such as the entire cloud of valence electrons in a piece of semiconductor, the lattice of atoms in a crystal, ...

And Bose-Einstein condensates. I wonder what's the largest BEC that's been created so far, say in terms of number of atoms?

 

[colorSpace]

3) What's the threshold for quantum effects? Do entire atoms, entire molecules have probability waves, or only elementary particles?

Quantum interference has been demonstrated for C60 moecules for example in 1999, and for C60F48 molecules for example in 2003.

That's quite big already.

http://www.quantum.at/research/molecule-interferometry/wave-particle-duality-of-c60.html

http://www.quantum.at/research/mole...-biomolecules-and-fluorinated-fullerenes.html