# wavicle: an old topic

#### Woody

@Neila
Where does your initial equation for the speed of the probability wave come from?

#### neila9876

@Woody:
It's from Duck de Brogile, the ancestor of probability (matter) wave...

1 person

#### topsquark

Forum Staff
Just a stray thought that might have some bearing on what you are asking. Waves have two speeds: group and phase speed. The group speed is $$\displaystyle v_g = \dfrac{d \omega }{dk}$$ and is what you would say is the speed of the wave. The phase speed is $$\displaystyle v_p = \dfrac{ \omega }{k}$$ and can be faster or slower than the group speed.

A light wave has $$\displaystyle v_g = c$$, whereas the phase speed can actually be faster than this.

-Dan

#### neila9876

simple vs complicated

@dragon:
Why must you talk about group speed? Can you use simplified method to explore physical principle and highlight the emphasis?

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#### HallsofIvy

@Woody:
It's from Duck de Brogile, the ancestor of probability (matter) wave...
By the way, it is "Duc" (French for "Duke) de Broglie

2 people

#### topsquark

Forum Staff
@dragon:
Why must you talk about group speed? Can you use simplified method to explore physical principle and highlight the emphasis?
I mentioned it because, honestly, I still don't know what you are asking in that last post! I was taking a guess that what I said might be relevent.

-Dan

#### neila9876

relevant

@no one:
I would rather talk about the ancient Chinese fiction Travelling to the West again...
Monk Pig (猪八戒) always considered that the beautys were relevant to himself...
The master as well as the captain Monk Tang (唐僧) simplified the world and considered that only the Buddism was relevant to himself...and he got the "trueth".

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#### neila9876

SG experiment

I’ m in bad health and bad mental situation due to absolute conspiracy of the local dark force (江门地方黑恶势力钟永康集团) to confine me, sometimes I even can't read physics, but I tried to take a glimpse of the Stern-Gerlach experiment.
In my humble opinion, perhaps some guys misrefered to the concepts of “electron spin”, “spin angular momentum” and misassume “spin magnetic moment” in the explanation of the experimental phenomenon. Trouble came from two aspects.
1.Misconsider that the orbital angular momentum is zero when the electron is in ground state. Actually, the electron will not stop turning around the nucleus even when it is in ground state. And the “ground state” means only the electron is in “lowest” energy state. It demonstrates that the traditional method of description about orbital angular momentum in QM is insufficient.
Below is a brief analysis in which I try to explain why atoms separated into two symmetric parts with the bilateral current concept (charge moves relative to charge). And I understand it better in my only way.
1.If view from the point of the nucleus, assume the electron turns around the nucleus counterclockwise on the paper, we got a single current clockwise. (Figure 1)
2.If view from the point of the electron, we got a single current counterclockwise. (Figure 2)
That will lead to two different magnetic moment in counter directions.
What will nature do? To be FAIR.
That’s why those atoms separated into two symmetric parts.
This is an intuitive method of description. If resorting to the 4D space mathematical method of representation/4D space current concept, it will demonstrate that the Stern-Gerlach experiment is the direct proof of the existence of 4D space (put aside time for simplicity).
note: again I failed to attach the doc file.

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#### topsquark

Forum Staff
Thank you for sharing.

-Dan

#### neila9876

If we use 4D space in the wave function for free particle,
Ψ = A exp( i(p•X– Et )) omit “h-” and vector marks for convenience of observation.
Then,｜A｜² is a constant. It means the probability of appearance of the particle in any point of 4D space is the same. In turn, it means the probability of the X4 state the free particle be in is the same. The situation is the same in any position x in the 3D space.
Because it’s a free particle, no interaction is concerned, the above analysis reflects the property of the particle itself regardless it is moving or not.
When X4 = 1, X = x, the 4D space is equivalent to the 3D space.
The macroscopic “glass” in the topic of this thread is made up of microscopic particles. So the same principle is applicable.
In traditional QM, value area for 3D space x is (-∞, +∞). In X4 Theory, it’s a bit different, positive values of X4 represent “not anti” while negative values of X4 represent “anti”. So, 4D space has something to do with matter state. The value area can be either positive or negative. Put it aside temporarily.
The purpose of this step is to use a special (space) dimension to accommodate the uncertainty.
(4D space definition see htam9876's thread "tramp and electron" in philosophy.)

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