I am a first-year undergrad studying maths and physics and whenever my professor introduces these concepts and the derivations of their associated laws i.e. conservation of momentum, work-energy theorem, I am unsure if these actual real physical things that actually exist out there in the real world or if they are just fictitious/abstract concepts that we invented to help us understand phenomena a bit better. And if they are just abstract concepts, what is the motivation for conceiving them? Thanks!
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In science, they are both abstract and physical. Science requires both theory and experiment. The theory is the abstract mental model, and experiments are used to ensure that our mental models map to things in the physical world.
Theory without experiment is just math or philosophy. Experiment without theory is just data. The scientific method is incomplete without both.
A scientist may say something like “time is the integral of the metric along a timelike worldline”, which is an abstract part of a mental model. The same scientist may also say something like “time is what a clock measures”, which is a concrete fact of the physical world. Both statements are correct and valid, and when a scientist says one they are not denying the other.
Dale
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You are on the border of an interesting question.
Things such as electric charge - no one really knows what that is. But when it is identified and named then its properties can be established and we can work with the notion we now have of an electric charge.
Properties such as momentum have been established over time. Aristotle, for example did not believe in momentum. For him, things only moved if a force acted on them, and when the force was removed, movement stopped. It was Galileo who first established modern theories of motion rigorously.
So, in one sense all those categories you mention are concepts, but all those concepts have been extensively studied and provide for us a map of reality as we now understand it.
You could, from the perspective of your question, ask, is friendship a real thing, or is it just something you made up yourself?
Rich
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This is a philosophical question. There are two major camps regarding the realness of science. Scientific realism claims that the principles we are uncovering are real in an ontological sense. Momentum is a thing. Scientific instrumentalism claims that the principles we are uncovering are mental abstractions to make sense of reality. Neither is provably right or wrong using the scientific method.
In my experience, science is universally taught in the realist language. Instructors state that things are. They then gave to backtrack when covering things like relativity and QM by saying that what had been taught was simply a special case of what is "real," and that they would teach the real thing now. Always drove me crazy, but it's useful for getting people to believe in principles that are expensive to test empirically.
Cort Ammon
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