Does the concept of infinity have any relevancy or application in Physics and applied Physics? I must admit that I am not particularly knowledgeable in the area of Physics, but I have never seen the concept of infinity being of actual use in Physics. It seems like it's a construct that's there to future-proof Physics in general. Am I wrong? Could you explain and give some examples?
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Usually, physicists consider infinities unphysical and try to make them disappear when they arise. It is for example most famously the case in quantum field theory, where the correction to measurable quantities (such as mass, charge, etc) due to quantum effects happens to be infinite. This problem led to the concept of renormalization, a prominent feature of our theory today.
Another example of an infinity arising in physics is the charge density at the exact position of a charged point particle. It turns out to be infinite, and it makes sense since you are "distributing" all the charge in a single point. In that case, you could say that the infinity means you have met a particle, but you could also imagine that the infinity is there only because you have defined your particle to be point-like. If particles turned out not to be point-like, then this infinity can also be regarded as an "error" like in the first example.
Let me also add that infinities are usually regarded as "ill-defined". They have lots of weird properties that are difficult to reconcile with our idea of reality. An amusing example is Hilbert's hotel paradox. In short, the paradox states that a fully booked hotel with infinitely many rooms can still accommodate people.
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