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This is really not an answer to your question - just an elaborate comment, and opinion based rather than factual. I hope I will be forgiven... The idea of breaking "science" into disciplines at an early age goes counter to the way exploration by young minds ought to work, in my mind. When I, as a four year old, was playing with a magnifying glass to burn ...

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Attempt to answer questions posted here on the Physics SE. Start by choosing a simple question that looks interesting, and if you can't answer it then start Googling for articles and books on the subject and try reading those. If you still can't answer it then wait for someone else to answer then attempt to understand that answer. If you can almost ...

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You might also try this site for a "physics problem of the week" kind of thing: www.fearofphysics.com, although the problems seem like they've been running for just a couple of months.

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Historically, one motivating experiment for kinetic energy was dropping balls into clay and noting the relation between impact speed $v$ and the impact depth $d$: $$v^2 \propto d$$ I suspect this experiment could be modified to show the role that mass plays and obtain $d\propto mv^2$. A different experiment would be to launch a cart using some type of ...

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Simply because it is usually taught from historical, heuristic and pragmatic point of view, rarely from axiomatic point of view (e.g. Wightman axioms, as mentioned in a comment by ACuriousMind). This is because it is taught to be useful, as most QFT calculations boil down to scattering and decay amplitudes, and as Sean Carroll said: Heuristic QFT, on ...

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From a decoherence point of view, fields are more fundamental as they give rise to particle-like behavior from the wave behavior if interactions with the environment are strong. In the end though, quantum mechanics only describes correlations between macroscopic changes in detectors (or other materials), so whatever kind of ontology you want to take in the ...

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A good thing to do is to talk to professors in your department and see what ideas they have for projects since most undergraduate projects I've heard of involve professor mentorship. Other than that, your question as it stands now is way too broad to produce any good answers. There is a humongous breadth and depth of potential research projects to get ...

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