What path do electrons actually take in an orbital

[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.