Undergrad What Are Fascinating Examples of Emergence for a School Project?

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The discussion focuses on examples of emergence for a school project, emphasizing the relationship between properties at different scales and the role of interaction. The user seeks specific instances that can be mathematically demonstrated and potentially experimented with, such as the emergence of classical mechanics from quantum mechanics. Suggestions include the glass transition, biological signaling networks, negative refractive index materials, and large-scale coherent structures in turbulent flow. The conversation highlights the complexity and subjective nature of what constitutes an "interesting" example of emergence. Overall, the thread aims to gather diverse and applicable cases of emergence for educational purposes.
MiKiDe
For a school project, I've got to choose a subject. I chose "Emergence", but I have to narrow it down a little bit.
So, that's why I'm creating this topic.

The definition of emergence that I use:
By emergence, I mean the fact that proprieties of one scale implies other proprieties by changing scale. This process is called emergence.

My question :
Do you have any example of emergence that may be interesting to study?

For this subject, I'd like:
- To show mathematically that one theory implies proprieties in another scale.
- that it has to deal with the term "interaction".
- And if possible, to make some experiment.

I hope my question is clear enough (and I'm sorry if I made some mistakes in English, I tried not to...).

Thanks in advance to all :smile:
 
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Thanks for your answer. I already read this, but I'm looking for more specific example.
For example, it is said that "The laws of classical mechanics can be said to emerge as a limiting case from the Rules of Quantum Mechanics applied to large enough masses": do you have any example of this?
 
MiKiDe said:
Thanks for your answer. I already read this, but I'm looking for more specific example.
For example, it is said that "The laws of classical mechanics can be said to emerge as a limiting case from the Rules of Quantum Mechanics applied to large enough masses": do you have any example of this?

I think the implication of emergence is that the whole is greater than the sum of its parts. Classical mechanics doesn't "emerge" from QM in the same sense .
 
MiKiDe said:
I'm looking for more specific example.
What about temperature and pressure?
 
MiKiDe said:
My question :
Do you have any example of emergence that may be interesting to study?

"Interesting" is subjective, but a few examples are:

glass transition
biological signalling networks
left-handed/negative refractive index materials
large-scale coherent structures in turbulent flow
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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