What path do electrons actually take in an orbital

[mn4j]

Ok, so 'particles' do not have a 'position' in a classical sense

I can explain why I don't like the answer 'we don't know'. Because it is confusing: it sounds like 'there is some path but we just don't know it/can not measure'. I sounds exactly like a theory with the hidden variables which is proven to be wrong (Bell's theorem)

1. 'We don't know' is a claim of ignorance. It does not exclude any of the three logical possibilities. (a) That particles do not move at all, (b) that particles move but are stationary in this case, (c) that particles move and are in motion in this case.

2. If particles do not have a position, then they do not have a velocity either which means particle accelerators are fiction, etc. Which is more confusing, just admitting that you do not know the position or going down this slippery slope. Remember that the wavefunction only makes sense in the space-time coordinate system. If particles do not have a position, then quantum mechanics breaks down. Or maybe you can define 'position' in the quantum sense.

3. Bell's theorem does not disprove hidden variable theorems. Tons of articles have been written about it. In fact computer simulations have been done which reproduce the quantum result and violate bells inequalities without making use of quantum mechanics. But that is a whole 'nother topic.

 

[Dmitry67]

1. Again, the classical definition of 'movement' is not applicable here. Option (b) is a closest to the reality.

2. Not correct. Read about the uncertenity principle

3. Please provide at least one article.

 

[mn4j]

1. Again, the classical definition of 'movement' is not applicable here. Option (b) is a closest to the reality.

2. Not correct. Read about the uncertenity principle

3. Please provide at least one article.

1- What definition of movement/position apply. Or do you claim there is no concept of movement or position at all.
2- Please read about the meaning of the word "uncertainty".
3- Event-by-Event Simulation of Einstein-Podolsky-Rosen-Bohm Experiments:

http://www.springerlink.com/content/p28v88867w7213mu/ Open Access
http://arxiv.org/pdf/0712.3693

Abstract We construct an event-based computer simulation model of the Einstein-Podolsky-Rosen-Bohm experiments with photons. The algorithm is a one-to-one copy of the data gathering and analysis procedures used in real laboratory experiments. We consider two types of experiments, those with a source emitting photons with opposite but otherwise unpredictable polarization and those with a source emitting photons with fixed polarization. In the simulation, the choice of the direction of polarization measurement for each detection event is arbitrary. We use three different procedures to identify pairs of photons and compute the frequency of coincidences by analyzing experimental data and simulation data. The model strictly satisfies Einstein’s criteria of local causality, does not rely on any concept of quantum theory and reproduces the results of quantum theory for both types of experiments. We give a rigorous proof that the probabilistic description of the simulation model yields the quantum theoretical expressions for the single- and two-particle expectation values.​

 

[Dmitry67]

1. I don't suggest anything new except what already exists in QM. And you are trying to take back from the grave the theory of the hidden parameters. In fact, even in QM people use words 'position of a particle', 'moving', etc.
2. See 1.
3. Ha ha ha!
People who believe in hidden variables write *computer program* to make their own version of reality, and then use it to 'prove' something :)

 

[tim_lou]

I am surprised that nobody bought up the idea that the funny orbitals you get from chemistry books are only stationary solutions. In general, you can visualize an electron as a wave packet traveling in space. You can even think about the electron as like a cloud (a probability cloud), whose shape changes and it moves around according to Schrodinger's eq. The mean of the position will actually move like in classical mechanics (elliptical orbits).The "orbit" that you speak of depends on the initial shape of wave. I haven't seen any program around that shows you this... However, you can search around google for quantum harmonic oscillator applet to get a feeling of what I am talking about.

In my personal opinion, I feel that many people really make quantum mechanics a lot more abstract than it really is. To me, quantum mechanics is nothing but adding an additional structure to the concept of particle. In CM, you get a point moving around, whereas in QM, you get a cloud moving around while the shape of the cloud changes from time to time.edit: of course, the picture of electron moving around is neglecting things like photoemissions, but this phenomenon comes from QFT and not ordinary QM. A electron will radiate in addition to moving around and will likely end up in the (stationary) ground state after ~10^-9 seconds. Hey, this should be expected classically, since accelerated charges are suppose to radiate (and collapse to nothing) so their orbits aren't really elliptical.

 

[Vanadium 50]

A few comments:

First, Mills' theories are crackpottery.

Second, the question of whether or not electrons have a velocity is something QM can answer. For the ground state of hydrogen, the expectation value of an electron's velocity is < \psi_{100} | \hat{v} | \psi_{100} > = \frac{\hbar}{a_0 m_e} = \alpha c. It's a well defined question with a well defined answer.

Finally, the question of whether or not electrons have a trajectory is also something QM can answer. They do not. A trajectory means that one has simultaneous knowledge of position and momentum at each point. This is not allowed. The closest we can get is a series of position measurements of the electron, but we have no knowledge of how it got from one point to the next.

 

[mn4j]

It must be a new type of physics where electrons have position, velocity but no trajectory. The concepts of 'velocity', 'position' and 'trajectory' are interrelated. You can not have one without the other. By definition, a particle with velocity has a trajectory. In other words, it is what we mean when we say velocity.

You are confusing epistemology with ontology. If you get a series of position measurements of the electron in time, THAT is the trajectory! The question of HOW is irrelevant in this case. The important thing is that it did go from one position to another. A moving car has a trajectory irrespective of whether it was driven from point A to B, or carried from point A to B.

There are millions of cars in the world with position velocity and trajectory which you know nothing about. Not knowing about them does not mean they don't exist and are not moving? Ignorance is a property of the human mind not nature.

 

[mn4j]

1. I don't suggest anything new except what already exists in QM. And you are trying to take back from the grave the theory of the hidden parameters. In fact, even in QM people use words 'position of a particle', 'moving', etc.
2. See 1.
3. Ha ha ha!
People who believe in hidden variables write *computer program* to make their own version of reality, and then use it to 'prove' something :)

I doubt that you know what you are talking about. You still have not defined 'movement' in a quantum sense. Either do that or admit that there is no 'movement' in QM and face the consequences of that.

Again, once you define 'movement' in the QM sense, you will realize that the definition of 'trajectory' will follow from it, unless there is no 'movement' in QM in which case you will be admitting that QM is not a physical theory.

"Uncertainty", it is an epistomogical concept not an ontological one. By definition, "uncertainty" assumes that there is a true value about which we are not sure. It describes our knowledge of the true value, not the true value itself. It makes absolutely no sense to say you are uncertain about the position of an electron and at the same time say that the electron does not have a position. It begs the questions, what are you uncertain about? what are you trying to measure? Only a fool will attempt to measure something that does not exist.

HUP is about the fact that momentum by definition being uncertain at a fixed position, not because we know or don't know the position. Momentum by definition involves of the rate of change of position, ie a certain value for momentum must involve a multitude of positions.

Finally, it was a popular claim by QM people that it was impossible to write a hidden variable based computer simulation which will violate bells inequalities and give the quantum result. That was supposedly proof that hidden variables were dead. They were wrong. You can laugh at it all you want, it doesn't change the facts.

 

[Vanadium 50]

It must be a new type of physics where electrons have position, velocity but no trajectory.

Yes, it's called Quantum Mechanics. Lots of strange things happen there.

Finally, it was a popular claim by QM people that it was impossible to write a hidden variable based computer simulation which will violate bells inequalities and give the quantum result. That was supposedly proof that hidden variables were dead. They were wrong. You can laugh at it all you want, it doesn't change the facts.

I predict this will not end well.

 

[mn4j]

Yes, it's called Quantum Mechanics. Lots of strange things happen there.
I predict this will not end well.

You are right. When so called physicists are happy and willing to claim that a system can have velocity but no trajectory, it is an bad ending. In case you don't see the irony, what you are claiming is the same as saying a wave has wavelength but no frequency. Trajectory is a logical necessity in a system with velocity and vice versa. You can not define 'velocity' or 'trajectory' in ANY theory such that it does not imply the other. Otherwise Dmitry would have done it. It's not up to you or QM.

If QM actually claims that, which it does not, then it should be junked.

 

[Dmitry67]

Just to give you an example from a classic mechanics,

Astronomers were able to measure the star's velocity without measuring the distance.

I think the problem is that in CM velocity is defined as how quickly the position changes: v=dx/dt
So the position is more 'fundamental' then the velocity, and to measure the velocity you need to measure the position in different times.

But in QM it is more logical to talk about the momentum then to talk about how fast the position changes. In QM position and momentum do not commute, hence v=dx/dt does not make any sense, and the quoted below is wrong

Trajectory is a logical necessity in a system with velocity and vice versa. You can not define 'velocity' or 'trajectory' in ANY theory such that it does not imply the other.

 

[feynmann]

If electrons are found somewhere within an orbital, what kind of path do they travel within it? ie- is it similar to the orbits of the planets or more random like?

Thanks.

I think this is more of interpretation problem.
In the Copenhagen interpretation, the position of electron is not even defined until it's measured. In Bohm hidden-variable theory, the pilot wave is everywhere and it will guide the particle, the electron how to move in space.

 

[mn4j]

Just to give you an example from a classic mechanics,

Astronomers were able to measure the star's velocity without measuring the distance.

I think the problem is that in CM velocity is defined as how quickly the position changes: v=dx/dt
So the position is more 'fundamental' then the velocity, and to measure the velocity you need to measure the position in different times.

But in QM it is more logical to talk about the momentum then to talk about how fast the position changes. In QM position and momentum do not commute, hence v=dx/dt does not make any sense, and the quoted below is wrong

I wonder why you have still been unable to define either "momentum" or "velocity" according to QM. What are you talking about and what exactly do you mean whey you talk about those terms in QM? You will never make any sense unless you define those terms in QM.

Also, in case you did not know, position and momentum do not commute in Classical Mechanics. The uncertainty principle is not limited to Quantum Systems.