# Does hidden variable quantum mechanics imply the collapse of atoms(electrons falling into the nucleus)?

why do atoms not collapse on themselves. Doesnt this problem rule hidden variables as invalid as the heisenburg uncertainty is the solution to the problem because it says electrons exist in a probability cloud and is in many places at once, not at a single location. If hidden variables are right the electron has a well defined position orbiting the nucleus and where does the energy come from? Doesnt this mean if HV are right it would collapse in again. whats the answer?

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Comment to the question(v1): The title question is currently a possible duplicate of physics.stackexchange.com/q/9415/2451 and links therein. The main text contains another question about hidden variables. It would be good if OP (or somebody else?) could make the title reflect the main purpose of the question. – Qmechanic Jan 23 '13 at 11:34
Depends what you mean by hidden variable theory. The paradigmatic example of a hidden varialbe theory that works (in that it exactly reproduces the predictions of ordinary QM) is Bohmian mechanics, which explains all of nonclassical behaviour through a non-local "quantum potential" that enters into the equation of motion for particles (a slight generalisation of $F=ma$). If you mean a local hidden variable theory then these are already ruled out by entanglement experiments. – Michael Brown Jan 23 '13 at 11:43
Michael, others would disagree with you on that. If we assume they are valid option, are they ruled out by the fact atoms would collapse in on themselves because having a well defined postion at all times would mean they collapse in? – lee hudson Jan 23 '13 at 11:50
and what does this mean for observed atoms in other interpretations?. observed atoms have there wavefunction collapse so that they have a single definite location and the observed electron would have a single definite orbit. in this case why wouldnt the atom collapse in on itself? – lee hudson Jan 23 '13 at 12:06
@leehudson "having a well defined postion at all times would mean they collapse in" - No. It depends on the dynamics. Bohmian mechanics is a counter-example - a hidden variable theory where electrons have definite positions but atoms are stable. It achieves this by modifying the laws of motion in a non-local way. Only non-local hidden variable theories have a chance of working. Local ones are ruled out by other experiments. There really isn't any debate about this, except for semantic loopholes. – Michael Brown Jan 23 '13 at 12:31

The fact that atoms exist does not rule out a hidden variable formulation (though for the record such formulations are ruled out by other experiments).

For example the electron wavefunction of a hydrogen atom gives us the probability of finding the electron at any particular point. However the electron could still have a definite hidden position, which would of course be a function of time. As an analogy consider a rubber ball bouncing around at very high velocity in a closed box. We can define a function that gives us the probability of finding the tennis ball at any particular point in the box, but the tennis ball still has a well defined position.

The point is that in the macroscopic case of the tennis ball there is a well defined position, but for the electron in the hydrogen atom the position is simply not defined until we interact with the atom in some way that localises the electron. The position we get is the position at which the electron interacts, not some hypothetical position where it was located immediately prior to the interaction.

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john and others, so electrons can have a definite single location at all times, orbit a nucleus like this and not collapse in on the nucleus according to HV theories? – lee hudson Jan 23 '13 at 13:48

One possible hidden variable theory is that the hidden variable is just the positions of all the particles. In that case for the ground state the probability distribution for position doesn't change. So it is easy to make a hidden variable theory where in the ground state the electron isn't moving. Not moving, no change in hidden variable, no change in probability distribution.

Your reasoning basically goes: classically charges orbit other charges and radiate and spiral in rather quickly, in hidden variables particles have positions and I'll just assume that the hidden variables act just like classical mechanics and isn't this a problem between hidden variables and quantum mechanics? It would be a problem in thousands of ways if the hidden variable theory was just not doing quantum mechanics. When you do hidden variables, then in order to get quantum mechanics with it, you have to do things differently than you do in regular classical physics. Doing otherwise would be like trying to do special relativity but refusing to do time dilation because you have time from Newtonian physics and don't want to allow a new theory to do anything differently.

One intuitive way to think about a hidden variable is to imagine that there is a state (and hidden variable) based force that pushes the particles around differently than they would if there was just classical mechanics.

Since at every moment you could do a position measurement, there needs to be a probability density $\rho$ for position. And these can sometimes change (but for a ground state they don't have to) so we should have a probability current $\vec J$ that satisfies $\frac{\partial \rho}{\partial t}=-\vec\nabla \cdot \vec J$ to get conservation of probability (just like current allows conservation of charge). So based on where the particle would be according to the hidden variable, we need additional forces to move it around so that the probability flux matches what quantum mechanics says it does. These additional forces could sometimes be totally opposite the classical forces (for instance in a ground state) and in general can do whatever they need to do to make the probability move around how it has to move. And since quantum is different than classical, it will have to move differently at least when quantum and classical disagree.

It turns out it will have to move differently for different states. It turns out it will have to move in a nonlocal way. But since all measurements eventually become a measurement of position (position of the ink on the paper you write up your results if nothing else) having the state and the position as the hidden variable suffices. It'll just have to be weird how the position changes, weird from a classical bias.

Which is the other truck sized loophole. Since quantum is different than classical, your hidden variables were allowed to introduce new forces (state dependent forces, forces that can be large even when things are far apart, etc.) to make the results agree with quantum mechanics. So you can freely change how electromagnetism works and radiation and such too, for the same reason, change whatever you have to to make your predictions agree with quantum mechanics. It's not wrong to do what you need to do to agree with experiment.

We are free to make any theory that agrees with experiment. If you make your hidden variable theory agree with quantum mechanics you are free to do anything you need to do to make it do that. Is it worth the effort? Depends, it could be easier to remember, or do a classical limit or correspondence, or could be easier to teach or inspiration for modifications. Could be better or easier to implement computationally could be an alternative implementation just to confirm you did it right, two implementations and calculations can be better than one. But there is no obvious answer if it is worth it for a particular person. There is an obvious danger not to take too seriously a story about what happens before you look. But if you can tell the difference between what you compute that can be observed and what you compute is about the internal dynamics between times you look, then you can avoid taking the story too literally. And I'm not sure it is better to pretend that things that have been done can't be done.

If you want a theory where your ground states have no particle motion and don't radiate, it's been done.

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why do atoms not collapse on themselves.

The reason is explained in answer to this question . In a nutshell, our observations/measurements lead to the quantum mechanical framework for atoms molecules and elementary particles and a probabilistic theory, quantum mechanics. The positions and energies of the particles are not determined but given by a probability amplitude.

Doesnt this problem rule hidden variables as invalid as the heisenburg uncertainty is the solution to the problem because it says electrons exist in a probability cloud and is in many places at once, not at a single location.

It is a postulate of quantum mechanics that there are no hidden variables, and QM is validated by the data.

If hidden variables are right the electron has a well defined position orbiting the nucleus and where does the energy come from? Doesnt this mean if HV are right it would collapse in again. whats the answer?

Probability distributions are not unique and were not applied first to Quantum Mechanics. Statistical mechanics gives probability distributions too. In statistical mechanics the trajectories of the particles making up the ensemble are classical, but they are an underlying level on which the equations of statistical mechanics are a meta level.

People working on hidden variable theories are working at a lower level than the observed and validated quantum mechanical. The hidden variables are supposed to reproduce the probability distributions observed and explained by quantum mechanics, by making quantum mechanics a meta level to the hidden variables level.

An example of a hidden variable theory is the de Broglie-Bohm theory, or pilot wave theory. This reproduces the Schrodinger equation quantum mechanics in a much more complicated way, and is often called an interpretation of QM.

The theory results in a measurement formalism, analogous to thermodynamics for classical mechanics, that yields the standard quantum formalism generally associated with the Copenhagen interpretation. The theory's explicit non-locality resolves the "measurement problem" which is conventionally delegated to the topic of interpretations of quantum mechanics in the Copenhagen interpretation The Born rule in Broglie–Bohm theory is not a basic law. Rather, in this theory the link between the probability density and the wave function has the status of a hypothesis, called the quantum equilibrium hypothesis, which is additional to the basic principles governing the wave function.

There are various problems in predictions that do not agree with the data.

Bohmian mechanics also known as de Broglie-Bohm theory is the most popular alternative approach to quantum mechanics. Whereas the standard interpretation of quantum mechanics is based on the complementarity principle Bohmian mechanics assumes that both particle and wave are concrete physical objects. In 1993 Peter Holland has written an ardent account on the plausibility of the de Broglie-Bohm theory. He proved that it fully reproduces quantum mechanics if the initial particle distribution is consistent with a solution of the Schrödinger equation. Which may be the reasons that Bohmian mechanics has not yet found global acceptance? In this article it will be shown that predicted properties of atoms and molecules are in conflict with experimental findings. Moreover it will be demonstrated that repeatedly published ensembles of trajectories illustrating double slit diffraction processes do not agree with quantum mechanics. The credibility of a theory is undermined when recognizably wrong data presented frequently over years are finally not declared obsolete.

There are people working on hidden variable theories, some of them quite prominent, as Gerald 't Hooft, who has also discussed his views here on this site some time ago.

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Sometimes some atoms collapse. Take a positronium as an example. It collapses for sure. Other atoms can collapse if a neutrino hits them. There is a capture of electron and conversion of an electron, proton, and neutrino into a neutron. It happens rarely, so we see atoms as stable ones.

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thanks. when we observe and measure the electron also the wavefunction collapses and we get a single electron in a definite state going around the nucleus? - is that right? – lee hudson Jan 23 '13 at 13:58
@leehudson: Right. But I do not like the term "wave function collapse" because it does not collapse. Instead, in one measurement we retrieve one bit of information about the wave function. The latter needs many bits to be fully described, just like a photo needs many pixels to be meaningful. – Vladimir Kalitvianski Jan 23 '13 at 14:01