#### Science Forum

1. 27 Mar '18 14:44
I have always been curious as to why electrons do not crash into protons given such a powerful attraction.Durac's wave function was the best explanation I had found until reading the Feynman lecture today.

Here is an excerpt from the link below:

"You know, of course, that atoms are made with positive protons in the nucleus and with electrons outside. You may ask: “If this electrical force is so terrific, why don’t the protons and electrons just get on top of each other? If they want to be in an intimate mixture, why isn’t it still more intimate?” The answer has to do with the quantum effects. If we try to confine our electrons in a region that is very close to the protons, then according to the uncertainty principle they must have some mean square momentum which is larger the more we try to confine them. It is this motion, required by the laws of quantum mechanics, that keeps the electrical attraction from bringing the charges any closer together."

http://www.feynmanlectures.caltech.edu/II_01.html

Can anybody explain "mean square momentum" to me in the context of Feyman's lecture? I am familiar with the uncertainty principal, but not enough that I have heard that term. I did an internet search but had a difficult time finding info about it in the right context.
2. 28 Mar '18 16:36
Feynman is using the phrase "mean square momentum" here because the expectation value of the momentum of an electron bound to an atom will be zero since it can take positive and negative values with equal probability. The mean square is always positive.

https://en.wikipedia.org/wiki/Root_mean_square
3.  sonhouse
Fast and Curious
28 Mar '18 20:38
Originally posted by @kazetnagorra
Feynman is using the phrase "mean square momentum" here because the expectation value of the momentum of an electron bound to an atom will be zero since it can take positive and negative values with equal probability. The mean square is always positive.

https://en.wikipedia.org/wiki/Root_mean_square
What is negative momentum?
4. 29 Mar '18 07:41
Originally posted by @kazetnagorra
Feynman is using the phrase "mean square momentum" here because the expectation value of the momentum of an electron bound to an atom will be zero since it can take positive and negative values with equal probability. The mean square is always positive.

https://en.wikipedia.org/wiki/Root_mean_square
I don't understand. Can you explain it to me as if I were a child?
5.  joe shmo
Strange Egg
29 Mar '18 14:27 / 6 edits
Originally posted by @metal-brain
I don't understand. Can you explain it to me as if I were a child?
Its not easy to explain to a child, otherwise small children everywhere would be doing quantum physics. I don't know my a## from a hole in the ground when it comes to QM, but I thin that Kazet is saying something to the effect of:

The electrons momentum is described as a wave, so lets look at a common wave ( the electrical current ) that runs all through our homes to get a better understanding.

The electricity in our homes provided by AC generators takes the form of a sine wave.
What is the average value of the voltage over one cycle?

If you guessed zero you would be correct.

What is the average value of the current over one cycle?

again, If you guessed zero you would be correct.

(Real - purely resistive loads) Electrical power is given by P = V*I. So, from this relationship what is the average power delivered to a device in your home over one cycle?

again, If you guessed zero you would be correct.

Obviously the average value is not the value we want to use when describing wave like voltage, current, and power. Its always zero in this case. and because of this its not a useful measurement to describe electrical systems. So instead we use RMS ( root mean square) voltage, current and power to describe what happens when you flick on the light switch.

Root Mean Square ( voltage, current, power) is a computation performed on the wave that yields the effective DC ( direct current) circuit values of these wave properties. It is constant and always positive. In your home ( in America) the RMS voltage is about 120 Volt. using these quantities it tells me when I flick the light switch, when the light comes on its RMS power consumption is nonzero.

So back to the mean square momentum of the electron. If I understand Kazet, the average value of the electrons momentum is zero ( because it is described by a wave type function). I think what Feynman is saying is that because conservation of momentum holds, an electron orbiting a proton has some positive momentum that is described by the RMS value of its wave function. It is orbiting at some distance R. It has a certain angular momentum given by

L = R x ( m*v) = constant ( or angular momentum is conserved)

Lets say you try to force the electron closer to distance "r", and we solve the relationship for v' ( the electrons velocity in the closer orbit)

R x ( m*v ) = r x ( m*v' )

v' = R x ( v ) / r

In the equation above hold big R and ( mv ) - "electrons linear momentum" constant and decrease the distance "r". v' asymptotically approaches infinity as "r" approaches zero. This means its RMS momentum must also approach infinity as the orbit is forever decreasing. It becomes larger without bound.

I think that is what he was saying.
6. 29 Mar '18 15:27
Originally posted by @joe-shmo
Its not easy to explain to a child, otherwise small children everywhere would be doing quantum physics. I don't know my a## from a hole in the ground when it comes to QM, but I thin that Kazet is saying something to the effect of:

The electrons momentum is described as a wave, so lets look at a common wave ( the electrical current ) that runs all thro ...[text shortened]... s forever decreasing. It becomes larger without bound.

I think that is what he was saying.
Sounds like he just picked the most complicated way of saying "see Durac's wave function".
7.  joe shmo
Strange Egg
29 Mar '18 16:05 / 1 edit
Originally posted by @metal-brain
Sounds like he just picked the most complicated way of saying "see Durac's wave function".
I think you have it backwards. "Dirac's Wave Function" is not the "simple" explanation in any sense of the word. If I'm wrong please tell me specifically what portion of the following relation explains that?

https://en.wikipedia.org/wiki/Dirac_equation#Mathematical_formulation

What I think is happening... is the miniscule formal training I have in physics enables me ( when I gaze upon that wiki page) to admit I am woefully out of my depth. I don't think you are having that problem...Your statement seems to imply that you get it.
8. 29 Mar '18 20:52 / 2 edits
Originally posted by @joe-shmo

What I think is happening... is the miniscule formal training I have in physics enables me ( when I gaze upon that wiki page) to admit I am woefully out of my depth. I don't think you are having that problem...Your statement seems to imply that you get it.
Don't know if you are right about that first part because I get the impression that you know more about it than me but, you got it wrong about that second part because, trust me, he has NOT got it but has his usual delusions that he has and he has frequently shown this. You modestly say you are out of your depth here but, regardless of whether that is true, he certainly is out of his depth and always will be but doesn't understand this.
9. 29 Mar '18 21:13
Originally posted by @sonhouse
What is negative momentum?
It is easier to understand classically. If you consider a point mass with respect to some origin, then the components of momentum p = (px, py, pz) can all be negative. Something analogous happens in the quantum case.
10. 30 Mar '18 00:14
Originally posted by @humy
Don't know if you are right about that first part because I get the impression that you know more about it than me but, you got it wrong about that second part because, trust me, he has NOT got it but has his usual delusions that he has and he has frequently shown this. You modestly say you are out of your depth here but, regardless of whether that is true, he certainly is out of his depth and always will be but doesn't understand this.
Let me get this straight. You admit he knows more about it than you, yet you know he is wrong when he says I get it.

You obviously have let your personal resentment against me cloud your judgment. You make no sense at all.
11. 30 Mar '18 07:09 / 1 edit
Originally posted by @metal-brain
Let me get this straight. You admit he knows more about it than you, yet you know he is wrong when he says I get it.
.
correct.
And you confirmed you usually don't get it in the other thread with the
"I have NO IDEA what he is talking about." (my emphasis)
You have repeatedly shown you have no idea what you are talking about.
12.  joe shmo
Strange Egg
30 Mar '18 13:12 / 1 edit
Originally posted by @humy
Don't know if you are right about that first part because I get the impression that you know more about it than me but, you got it wrong about that second part because, trust me, he has NOT got it but has his usual delusions that he has and he has frequently shown this. You modestly say you are out of your depth here but, regardless of whether that is true, he certainly is out of his depth and always will be but doesn't understand this.
As I said, I don't know my butt from a hole in the ground, and that still stands. After doing a bit of reading on the matter, I would liken my explanation to something Newton would have pictured. Unfortunately for my explanation, modern physics has advanced quite a bit since him, and I'm now certain that what I said about the electron (effectively treating it classically) was said in vain.

https://van.physics.illinois.edu/qa/listing.php?id=1226

https://io9.gizmodo.com/why-dont-electrons-just-fall-into-the-nucleus-of-an-ato-1597851164
13.  sonhouse
Fast and Curious
30 Mar '18 16:17
Originally posted by @kazetnagorra
It is easier to understand classically. If you consider a point mass with respect to some origin, then the components of momentum p = (px, py, pz) can all be negative. Something analogous happens in the quantum case.
You mean one of the three could be negative but the other 2 are positive? What does it mean in the physical world if all three components are negative?
14. 30 Mar '18 20:46
Originally posted by @sonhouse
You mean one of the three could be negative but the other 2 are positive? What does it mean in the physical world if all three components are negative?
It doesn't mean anything special, it is just related to your choice of frame.
15. 31 Mar '18 00:26
Originally posted by @humy
correct.
And you confirmed you usually don't get it in the other thread with the