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Butch

Position of of an electron?

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Can an electron have the property of position via center of charge and/or center of mass?

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Center of mass or charge doesn't tell you the position.

The center of mass and charge of an electron in a hydrogen atom is at the center of the nucleus (neutral charge, so the probability distribution is spherically symmetric). But the odds of you finding the electron there are small.

 

Even for a classical system, or a Bohr orbit (which we know is wrong) where the electron is never in the nucleus, we still have a symmetric system, so the center of mass/charge is the center. It's like saying the earth is inside the sun, because our average position is (roughly) the center of our orbit. It doesn't work.

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16 minutes ago, swansont said:

Center of mass or charge doesn't tell you the position.

The center of mass and charge of an electron in a hydrogen atom is at the center of the nucleus (neutral charge, so the probability distribution is spherically symmetric). But the odds of you finding the electron there are small.

 

Even for a classical system, or a Bohr orbit (which we know is wrong) where the electron is never in the nucleus, we still have a symmetric system, so the center of mass/charge is the center. It's like saying the earth is inside the sun, because our average position is (roughly) the center of our orbit. It doesn't work.

Would that not involve a span of time? Aren't you saying that the average center of charge is at the nucleus?

Perhaps I should have said instantaneous position?

Edited by Butch

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15 minutes ago, Butch said:

Would that not involve a span of time? Aren't you saying that the average center of charge is at the nucleus?

Perhaps I should have said instantaneous position?

Yes, perhaps. That removes classical examples.

But the average position of hydrogen's electron is in the center, and the most probable position is only defined in terms of r, not any of the angles. Nothing is localized any better than that. 

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25 minutes ago, swansont said:

Yes, perhaps. That removes classical examples.

But the average position of hydrogen's electron is in the center, and the most probable position is only defined in terms of r, not any of the angles. Nothing is localized any better than that. 

We do not think in terms of velocity of an electron, but realistically even if an electron magically never occupies any space between two points but occupies one point after another point isn't that apparently velocity?

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6 minutes ago, Butch said:

an electron ... occupies one point after another point

It doesn't.

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Concepts like position, velocity, mass and size are macro concepts. To put it simply, they do not exist at the subatomic scale. They are so-called emergent properties from something that nobody fully understands yet.

In any case, we know that it is not possible to understand or describe what happens at the subatomic scale in these kinds of concepts because if it was then we would have figured this out a long time ago. I think we should give past and current generations of scientists some credit.

Edited by Leon1961

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Let's try an analogy that might make it easier for the OP. Look at a waveform on a scope. You now have a 2d image, this can be described by a Hermitean space using 2 by 2 matrixes. (Just to include how extensive this analogy applies)

What is the position of that waveform? 

What is its momentum ?

What is its size ?

Now consider all observable particle states are described by Operators and are wavefunctions.

Edited by Mordred

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15 minutes ago, Leon1961 said:

Concepts like position, velocity, mass and size are macro concepts. To put it simply, they do not exist at the subatomic scale. They are so-called emergent properties from something that nobody fully understand yet.

I think the first part is spot on. Not so sure about the last sentence. Yes, the macroscopic concepts we are familiar with in everyday life emerge from the underlying quantum reality, in ways we don't fully understand.

But I think it would be going a bit too far to say we do not understand the quantum realm "at all". Arguably, we understand it as well as any other area that we have accurate models for. Perhaps it feels like we don't understand it as well because it is less intuitive than some of the other models we have.

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17 minutes ago, Strange said:

 

But I think it would be going a bit too far to say we do not understand the quantum realm "at all". Arguably, we understand it as well as any other area that we have accurate models for. Perhaps it feels like we don't understand it as well because it is less intuitive than some of the other models we have.

 A large part from my experience with others I've helped in the past tends to revolve around discarding the billiard ball image of a particle. By focusing on wave mechanics and the subsequent vector and spinor relations one can learn to understand the bulk of QM and QFT. This applies to its tensor groups as well.

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4 hours ago, Leon1961 said:

Concepts like position, velocity, mass and size are macro concepts. To put it simply, they do not exist at the subatomic scale. They are so-called emergent properties from something that nobody fully understands yet.

As momentum grows, the deBroglie wavelength shrinks. At some point the object is physically larger than its wavelength. The uncertainty in position starts to lose meaning. 
 

I wouldn’t put mass on that on the list. 

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5 hours ago, Strange said:

I think the first part is spot on. Not so sure about the last sentence. Yes, the macroscopic concepts we are familiar with in everyday life emerge from the underlying quantum reality, in ways we don't fully understand.

But I think it would be going a bit too far to say we do not understand the quantum realm "at all". Arguably, we understand it as well as any other area that we have accurate models for. Perhaps it feels like we don't understand it as well because it is less intuitive than some of the other models we have.

You have a wonderfully abstract mind! Many do not have that attribute to work with, many can only see such things as math or physical laws... If your mind can draw pictures of these abstract ideas, do not take it for granted, you are certainly blessed.

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9 hours ago, Butch said:

You have a wonderfully abstract mind! Many do not have that attribute to work with, many can only see such things as math or physical laws... If your mind can draw pictures of these abstract ideas, do not take it for granted, you are certainly blessed.

It's not an either/or situation. Drawing mental pictures based on the math and physical laws is kinda what scientists do.

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On 2/12/2020 at 6:15 AM, swansont said:

It's not an either/or situation. Drawing mental pictures based on the math and physical laws is kinda what scientists do.

By abstract I mean apart from the math or physical laws... Not in disagreement with them certainly. Abstract thought leads to math and physical laws that have not been revealed. As an example, Einstein had first to consider how light would appear (with existing theory) if he were traveling at c and thus he produced new physical laws and the math for them. Abstract thought is often the pathway to discovery.

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5 hours ago, Butch said:

By abstract I mean apart from the math or physical laws... Not in disagreement with them certainly. Abstract thought leads to math and physical laws that have not been revealed. As an example, Einstein had first to consider how light would appear (with existing theory) if he were traveling at c and thus he produced new physical laws and the math for them.

What Einstein did was apply a known behavior to a different aspect of physics. The math he used for special relativity was algebra. The result was novel, but arguably not a new physical law. The title of the paper was "On the electrodynamics of moving bodies" —  he was applying a concept of electrodynamics to mechanics. 
His imaginations included trying to be constrained by physical law. If you lack that, what you're imagining is magic.

 

In any event, how people conceive of new ideas is not limited by your notions of their processes.

5 hours ago, Butch said:

Abstract thought is often the pathway to discovery.

 

"Abstract" does not mean "ignoring constraints of math"

 

 

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6 hours ago, Butch said:

By abstract I mean apart from the math or physical laws... Not in disagreement with them certainly. Abstract thought leads to math and physical laws that have not been revealed. As an example, Einstein had first to consider how light would appear (with existing theory) if he were traveling at c and thus he produced new physical laws and the math for them. Abstract thought is often the pathway to discovery.

The word 'Abstract'  means 'apart' in the sense of 'removed from' not 'different from' .

Man has been abstracting qualities from things around him for thousands of years (as well as metals form ore and alcohol from fermentation products).

So the ancinet Greeks abstracted the ideas of a square, circle triangle and so on from the natural shapes they found.

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Quote

 

abstract

adjective |abˈstrakt ˈabˌstrakt| 

existing in thought or as an idea but not having a physical or concrete existence: abstract concepts such as love or beauty.

dealing with ideas rather than events: the novel was too abstract and esoteric to sustain much attention.

 

 

 

Math itself is an abstraction

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