4 ms·

Newtonian mechanics are not completely accurate at any time. However as you point out, the error in the model is often dwarfed by the error in the measurement.

• Dylan16807 12y ago
  If it gives the exact correct answer, who are you to say it's not accurate?
  • gress 12y ago
    It's not the exact correct answer. It's an approximate answer.
    • Dylan16807 12y ago
      In certain kinds of abstract thought experiments, it might not match. If you're doing orbital calculations, it's often wrong. In the vast majority of real world calculations, it's not approximate. It gives the same answer as relativistic calculations. Oh, I have an analogy. It's like using 64 bit integers instead of bigints. Any time you input real world numbers, they never go above ten million. Both models give you the correct answer, no error. No model ever captures the entire nuance of reality. Even a notion of speed is misleading when your objects contain heat. So don't peek inside the model and judge it based on how the pieces interact inside. Judge it based on the results. And Newtonian physics typically give you ideal perfect results. --- Or maybe I should put it a different way: Newtonian physics are an approximation for the question "In a counterfactual thought experiment where my measurement had infinite precision in trailing zeroes, what would the answer be?" Newtonian physics are exact for the question "What is the answer based on my measurement?"
      • gress 12y ago
        The drawback in this reasoning is that with Newtonian mechanics alone you cannot know whether your measurements are in the domain for which it is accurate or not. For that you need relativity and quantum mechanics. Newtonian mechanics alone is seriously wrong, but if you know (because you understand relartivity and quantum mechanics) that you are in a domain for which it is sufficiently accurate, then you can use it to produce accurate results.