wavicle: an old topic

Mar 2019
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@ dragon:
Actually I learned the word " wavicle" from You two years ago...I think it's just a habitual name. We still called train " fire vehicle because the original power of it was coal...In the rabbit hole, it's uncertain and certain. I talked about this point in woody's wave particle thread too. Guys can see it can achieve the same effect of probability in a previous post of This thread...
 
Jun 2016
1,370
696
England
I can't remember where I first came across wavicle,
I think it was originally a half joke term to express the fact that neither particle or wave was a particularly good term
In fact there were no "good" terms to describe what was being seen
so this new term was invented.

Some people like it, others don't.
I feel that it helps us to avoid the habit of thinking about conventional particles and waves
but perhaps a totally new term (which ignores particle and wave altogether) might be better.

Perhaps a rabole (rabbit and hole pushed together).
 
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Mar 2019
938
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cosmos
In the rabole, the certain state is in 3D space and can be seen and so it can be described with trajectory. The uncertain states are not in 3D space and can not be seen and so they can not be described with trajectories. What the uncertain states represent are contrast of ability, I think. A vivid analogy is myself: this tramp in cosmos is a shabby guy without any social ability and even redundant in the local Jiangmen city. This is the aspect which the local people can see. But actually I can appear abroad and speak English. The local people can't see this aspect.
The probability is about the presentation of different ability rather than the presentation in different position in 3D space. So it concerns no such issue as "from point to point (in 3D space)".
Of course, the above comment is just about the property of the rabole itself without any interaction with others.
If talking about interaction, it's the wave characteristic of electric interaction. Rabbit posted his unit charge model long ago in the philosophy column. Of course, now I have renew the material and make it more explicit.
 
Jun 2016
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This is the "hidden variables" idea.
As you suggest this idea says that all the odd things in QM can be explained by properties of the raboles that we cannot see.
 
Mar 2019
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@ woody:
I agree with the term " hidden variables" very much. Regrettable, rabbit is sleeping in the Faraday cage while I am just a tramp in cosmos who will die hard as the local dark lord of Jiangmen city said.
他江门黑恶势力钟永康集团及新会一中九一四班全世界打靶啦。
 
Mar 2019
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In order to prevent losing the meaning of contrary or reference, in 4D space wave function, we engage that space and momentum, one is 4D space physical quantity, then the other is 3D space physical quantity. This is called the 1/2 Rule or the Special Engagement.

Blow is not something new. It's just a previous post. I move it here and make minor amendment to make the concept of the "hidden variables" a bit more explicit.
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The position space wave function for a free particle in 4D space is:

Ψ(X, t) = A exp( i(P ·X – Et )) Amplitude A is a constant. (omit “ℏ” and vector marks for convenience of observation)

X = X4x

Then, the probability density|A|² is a constant. It means the probability of appearance of the particle in any point of 4D position 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 with any momentum P in the 3D space or not (It has nothing to do with wavelength λ = h / P ).

The momentum space wave function for a free particle in 4D space is:

Ψ(P, t) = A exp( i(P·x – Et )) Amplitude A is a constant. (omit “ℏ” and vector marks for convenience of observation)

P = X4 P

Then, the probability density|A|² is a constant. It means the probability of appearance of the particle in any point of 4D momentum 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 with any momentum P in the 3D space or not (It has nothing to do with wavelength λ = h / P ).



Look at the 3D space wave function for free particle in QM again.
Ψ = A exp( i(p•x– Et )) omit “ℏ” and vector marks for convenience of observation.
When position x and momentum p are both determined at the same time, it will no longer be a wave function, instead, an oscillation function. It seems that the “wave character” should disappear either.
What interesting is it could be considered as a special situation and the calculation of probability is still applicable. “A” is a constant. |A|² is a constant. It means the probability of appearance of the particle in any space point is the same. In turn, it means the position of the free particle can not be determined.
Contradiction…

Next, resort to 4D space wave function. In the item P ·X or P·x, among space and momentum, if one physical quantity is 3D space quantity, then the other is 4D space quantity. It reflects that they two can not be determined simultaneously and avoid the dispute.

Classical physics describes the certainty in 3D space while QM describes the uncertainty in 4D space.
 

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Jun 2016
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Are suggesting a "hidden" 4th dimension within which the hidden variable will operate?
So if we were to include time, (for example in an effort to include relativity)
then your hidden 4th dimension would become a hidden 5th dimension?
 
Mar 2019
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Ahhhhhhh......I found something strange during cyber transition. It confused the upper case and lower case of the letter " p", e.g. the first "p" in the above post should be a lower case. The rabole 2020 version demonstrates them very explicitly.
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@ woody:
Given rabbit did not calculate that time has real number relationship with *4, I would not against the concept of hidden 5D either.
 
Mar 2019
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Actually, the factor *4 itself (hidden variables) represents the equal probability effect, no need resorting to wave function.
 
Mar 2019
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"...I would laugh at how lame it all sounds but it works"
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This tramp in cosmos wants to laugh at how lame it all sounds too ( in both rooms). But now I don't think " it" works. Perhaps it's something else works ( in the double slits experiment).

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