I suppose the word 'real' is kinda hard here. From classical experimental point of view electron is a particle that can be observed and has an identity and exis

I suppose the word 'real' is kinda hard here. From classical experimental point of view electron is a particle that can be observed and has an identity and existence regardless of context, whereas quasiparticles such as phonons manifest only in mathematical models that 'can be instantiated' in specific experimental setup, or describe physics only in specific limited context, such as the experiment here. I'm of the school though that adheres to the notion that maths can be used to model the world, and while it strongly suggests 'the world is made of math' this is not conclusively the case. So, to me, mathematical equivalence does not mean 'physically equal' since physical systems can exhibit many more degrees of freedom than just those captured in a specific model. Sometimes the maths and physics match astoundingly well.