Explanation why dosen't the electron fall into the nucleus?

[zincshow]

Again, there are many experiments and phenomena in which such superposition has been confirmed and verified. The measurement of the coherence gap in the Delft/Stony Brook experiments that I've mentioned repeatedly is a clear example.

Do you have any suggestions for good internet links for this experiment? A google search produces a lot of pages and I am not sure I am seeing a good one.

 

[zenith8]

Unfortunently I can't understand any of the math and equations behind all that, but if its true then that's pretty remarkable. Great read, thanks for linking it.

The math looked pretty straightforward to me.. can I help?

 

[ZapperZ]

Do you have any suggestions for good internet links for this experiment? A google search produces a lot of pages and I am not sure I am seeing a good one.

Do a search on here for the Delft/Stony Brook SQUID experiment.

Zz.

 

[lightarrow]

You might think that, but surely if you read PF with any regularity you must know by now that the whole thing can be 'explained' by thinking of the electron as a solid little particle with an accompanying wave which pushes it around (i.e. wave-particle duality => two things rather than one). This is the viewpoint of the de Broglie-Bohm theory, where QM is just a dynamical theory - the statistical mechanics of particles moving along non-classical trajectories - rather than a probability calculus for the results of measurements.

Within that model, it is simply obvious why the electron doesn't fall into the nucleus: the electron is held in a web of opposing forces (electromagnetic and quantum). Under the right circumstances (a stationary state with zero angular momentum such as the ground state of the hydrogen atom) the electron can even be stationary.

I have always had difficulties in understanding which are the real advantages of this interpretation: yes, a "corpuscle" paradigma is simpler, generally speaking, but in this case you still have to use the "field" paradigma as well, that is the "quantum potential". So dBB avoids the "field" paradigma reintroducing a non-local quantum potential along with the particle? What for?
This is not simpler, is more complicated...

 

[zenith8]

I have always had difficulties in understanding which are the real advantages of this interpretation: yes, a "corpuscle" paradigma is simpler, generally speaking, but in this case you still have to use the "field" paradigma as well, that is the "quantum potential". So dBB avoids the "field" paradigma reintroducing a non-local quantum potential along with the particle? What for?

Here you go:

State that 'probability' refers to the probability of an electron being at a certain position, rather than being found there in a suitable measurement.

The trajectories are then the streamlines of the probability current, which if you work it out, is v=\nabla S / m, where S is the phase of the complex wave function \Psi.

That's it. Do you see the quantum potential? The only thing here is the many-body wave function, which acts as a new kind of causal agent acting on the particles.

(PS: if you want to present the trajectories in second order form you can take the first time-derivative of the above trajectory equation, in which case you get essentially F = ma = -\nabla (V + Q) where Q is known as the quantum potential but this is (a) not necessary, and (b) just adds complication - as you rightly say. Hence in the deBB approach nothing is added to the standard approach, as you imply, it's all just a matter of looking at the Schroedinger equation in a slightly different way).

This is not simpler, is more complicated...

And yet I can explain why the electron doesn't fall into the nucleus - which is the point of this thread - and you can't.

Like anybody gives a toss..

 

[lightarrow]

Here you go:

State that 'probability' refers to the probability of an electron being at a certain position, rather than being found there in a suitable measurement.The trajectories are then the streamlines of the probability current, which if you work it out, is v=\nabla S / m, where S is the phase of the complex wave function \Psi.That's it. Do you see the quantum potential? The only thing here is the many-body wave function, which acts as a new kind of causal agent acting on the particles.

Ok. This allows you to predict where the photon will hit the detector screen?

And yet I can explain why the electron doesn't fall into the nucleus - which is the point of this thread - and you can't.

The electron could "fall" or not into the nucleus only if it were a localized corpuscle, so you first have to assume it is.

 

[zenith8]

Ok. This allows you to predict where the [electron] will hit the detector screen?

If you know precisely where it starts, yes, but you don't.

The electron could "fall" or not into the nucleus only if it were a localized corpuscle, so you first have to assume it is.

Yes, and your point is?

You're saying, effectively, "I refuse to speculate on what exists, therefore the OP's question is meaningless". And Ernst Mach used to say that because we will never be able to prove that atoms exist, there is no need to say understand 'pressure' and 'temperature' in terms of real microscopic entities, and this obviates the need for understanding, say, convergence to thermodynamic equilibrium.

As you say, I'm just taking the OP's question literally, but I'm telling him the answer in terms of quantum mechanics itself (remember QM does allow you to assume that particles exist, but only in the deBB context - and deBB is just looking at the Schroedinger equation in a different way).

Radical anti-realism can pretend to resolve interpretative paradoxes in virtually any context, but essentially it's just a kind of solipsism where one claims to 'solve' every problem in the history of science by denying that anything but one's own mental experiences exist. Hence all the fuss about 'observation' and 'measurement'. Looked at in the deBB way, QM is simply a dynamical theory of motion which happens independently of observation.

 

[lightarrow]

If you know precisely where it starts, yes, but you don't.

Is it because of technical difficulties or because you cannot even in theory? Because, if it's the second case, then what does the particle position need for? You say the particle is "there" but you will never be able to prove it.

Yes, and your point is?

You wrote that you can explain why the electron doesn't fall into the nucleus while I can't. I don't agree. I can explain it easily: the electron is not a localized corpuscle so it can't "fall" onto anything. Actually, the electron is already into the nucleus, since its wavefunction is not zero there.

You're saying, effectively, "I refuse to speculate on what exists, therefore the OP's question is meaningless". And Ernst Mach used to say that because we will never be able to prove that atoms exist, there is no need to say understand 'pressure' and 'temperature' in terms of real microscopic entities, and this obviates the need for understanding, say, convergence to thermodynamic equilibrium.

But there is a big difference: the atoms hypotesis allowed Boltzmann to elaborate a theory experimentally testable. If de DeBB theory will allow to predict experimentally testable results different from standard QM, then we will wait to see which teory is better.

 

[zenith8]

Is it because of technical difficulties or because you cannot even in theory? Because, if it's the second case, then what does the particle position need for? You say the particle is "there" but you will never be able to prove it.

Effectively - technical difficulties.

You wrote that you can explain why the electron doesn't fall into the nucleus while I can't. I don't agree. I can explain it easily: the electron is not a localized corpuscle so it can't "fall" onto anything. Actually, the electron is already into the nucleus, since its wavefunction is not zero there.

No you don't get away with it that easily. In order to answer the question, you need to have a theory of what an electron 'is', i.e. you have to have an ontology. You are implying that an electron 'is' equivalent to its wave function (contrary to standard QM which is purely about the results of observations and which does not imply that). And if that's what you're claiming then you run into little things like the 'measurement problem' (why do experiments have unique outcomes rather than all possibilities allowed by the Schroedinger equation?). You can't overcome these things if you believe that objects are 'made' purely of real waves mathematically represented by the Schroedinger wave function.

Which answers you earlier question: what is the particle position needed for? Because it solves the measurement problem (or more accurately the theory simply doesn't have a measurement problem) and it gives easily visualizable answers to all conceptual problems that arise in forums like this. Plus see my answer to the next bit.

But there is a big difference: the atoms hypotesis allowed Boltzmann to elaborate a theory experimentally testable. If de DeBB theory will allow to predict experimentally testable results different from standard QM, then we will wait to see which teory is better.

Which is precisely my point. Mach was wrong, both Boltzmann and Bohm were right. In fact there are experimentally testable consequences of the deBB theory (all involving the concept of 'quantum non-equilibrium' where the particle distribution is not the equal to the square of the wave field i.e. Born's rule is not obeyed.).

 

[Drakkith]

The math looked pretty straightforward to me.. can I help?

Only if you can teach someone who's taken College Math 100 to do whatever those equations are.

 

[ZapperZ]

The discussion on deBroglie-Bohm theory should end here in this thread, and restart if necessary in another thread (or one of the numerous EXISTING threads already made).

Zz.

 

[zenith8]

The discussion on deBroglie-Bohm theory should end here in this thread, and restart if necessary in another thread (or one of the numerous EXISTING threads already made).

Zz.

Why? Given that it's the only known way to sensibly answer the OP's question.

 

[ZapperZ]

"Sensible" is relative, and so is YOUR judgment that it is the "only known way".

Please do such discussion elsewhere, or this thread will be locked for going off-topic.

Zz.

 

[zenith8]

"Sensible" is relative, and so is YOUR judgment that it is the "only known way".

Please do such discussion elsewhere, or this thread will be locked for going off-topic.

Zz.

Look, I don't want to argue with you Zapper, but we were having a discussion about what it means to answer the OP's question. In no way is this 'off-topic'. What you mean is that the discussion was couched in terms of a theory of QM that you personally happen not to like. And that's fine - but you shouldn't try to ban such a discussion because of your personal preferences.

 

[ZapperZ]

This thread is done.

Zz.