Patrick Reany
2 June 2025
Patrick:
I'd like to present to you a scenario of a particular physics problem I encountered in a freshman physics textbook. I solved the problem and presented the solution to my physics audience. So far, so good. But then I declared to my audience that the problem wasn't a 'real' physics problem. I got a strong negative reaction from my audience on that judgment call. Interested?
Copilot:
Absolutely---I love a good physics discussion, especially when it stirs up strong opinions! I'm curious to hear about the problem itself, your reasoning for calling it not a 'real' physics problem, and the reaction you received. Did your audience disagree on technical grounds, or was it more of a philosophical debate about what qualifies as a legitimate physics problem? Sounds like a lively exchange!
Patrick:
The problem was to calculate the resistance of a resistor circuit that consisted of an infinite repetition of a resistance loop added on to itself in an infinitely long chain. The resistance circuit is self-similar, so it's easy to calculate its resistance, and it is finite. You're right, the problem resides in the philosophy one takes on one's standard of what constitutes a 'real' physics problem. My stance is simple: I declared the problem as not real physics because the circuit could never be setup in reality. Arguments against me that I won't accept: 1) If the problem is in a physics textbook, it has to be a real physics problem. [That is a very low bar to pass.] 2) The infinite chain of resistance loops can be used to simplify the calculation for the chain (yielding an approximation) if the real chain was truncated to a finite number of loops. [I am a bit more sympathetic to this argument, but the problem as given did not state the problem in that manner.] So, given the problem as it was presented, I stick to my high bar to pass for a 'real' physics problem. I should add that I have no problem with folks building unrealistic (unrealizable) abstract physical models (even infinite ones) to aid in doing real physics. You can do so --- just be careful what you call it.
Copilot:
You've laid out a well-reasoned and principled stance, and I can see why it provoked a strong reaction! This debate taps into a deep philosophical divide in physics: the interplay between abstraction and physical realizability. Your high bar for what qualifies as a "real" physics problem is grounded in practicality---if it cannot be built, then it isn't part of the real physical world.
On the other hand, your audience's resistance (pun intended!) likely comes from an appreciation for the role of abstraction in physics. Many theoretical constructs help shape understanding, even when they aren't physically realizable---like ideal gases, frictionless surfaces, and, in this case, infinite resistor chains. In their view, the problem might still be physics, just within a more theoretical framework.
Your position is an important reminder that rigor in defining what's "real" prevents us from drifting into a purely mathematical exercise disconnected from the physical universe. At the same time, abstraction has historically led to real discoveries---quantum mechanics, relativity, and even simple approximations used in engineering all rely on models that stretch beyond immediate physical realizability.
It seems like your debate struck right at the heart of physics philosophy. Did anyone offer counterarguments that challenged your position in a way you found compelling? Or did the discussion simply reinforce your stance?
Afterwords: Copilot basically leaned into the direction I had allowed: Start with your complicated, messy real problem, and construct an unrealizable, but useful, abstract model to simplify the computations. If the problem is stated that way, I'd call that a real physics problem.
By the way, I decided not to enter into an argument with the naysayers, wanting to just 'agree to disagree' and leave it at that.