One of the goals is to minimise them. Most of those left are blindingly obvious, but unprovable. They are technically there, but just part of the base assumptions of the models.
E.g. we couldn’t do science if an all powerful being was deliberately messing with our results. We also can’t prove the universe isn’t a computer program, only rendering what a “conscious” entity is looking at, while back calculating the required history on the fly.
How do you distinguish axioms from just another parameter of your model? If an all-powerful being is messing with our results, then you just get a stochastic model. In fact, we already have stochastic models in quantum physics. And whether or not the universe is a simulation doesn’t affect the model’s ability to make predictions at all, so why would it matter from a physics perspective? The model would be unchanged either way.
I think you might be confusing statistical with stochastic. Quantum mechanics makes incredibly precise predictions about the statistics of particle interactions. A stochastic model implies an experimental result could change depending on what day it is, when in fact quantum mechanical principles are relied upon every day for modern technology, and the screen you are reading this on is likely lit up because of the small but predictable chance an electron in an LED has to overcome an energy barrier it classically could not.
Maybe we use these terms differently in different domains. In my field, stochastic means that repeating the same experiment under the same conditions doesn’t guarantee the same results (e.g. rolling a die). The opposite of stochastic is deterministic. Something that changes depending on the day would be “a function of the date” or something that is “conditional on the date”. This can either be a deterministic function (e.g. calling date.today().day in Python, or a mapping from the date to a uniform distribution ranging from 0 to date.today().day) or a stochastic function (e.g. sample a uniform random integer between 0 and date.today().day).
Edit: I think what you’re talking about is the deterministic mapping from some variable into a distribution. We (as in my field specifically) do sometimes call that “stochastic” too, even though that mapping is deterministic. There may be a bit of terminology overloading here because what we care about in the end is the sample drawn from that distribution, which is actually stochastic.
No, that’s exactly what I mean and exactly what I think you are missing: quantum mechanical experiments have been reproduced thousands of times, and even as measuring instruments became sensitive, the predictions have held true. The statistical nature of it doesn’t make it any less predictable, and an experiment proving a different statistical value of an event than QM predicts would be world news.
Does the concept of an axiom actually exist and make sense in physics? I thought we just had models.
One of the goals is to minimise them. Most of those left are blindingly obvious, but unprovable. They are technically there, but just part of the base assumptions of the models.
E.g. we couldn’t do science if an all powerful being was deliberately messing with our results. We also can’t prove the universe isn’t a computer program, only rendering what a “conscious” entity is looking at, while back calculating the required history on the fly.
How do you distinguish axioms from just another parameter of your model? If an all-powerful being is messing with our results, then you just get a stochastic model. In fact, we already have stochastic models in quantum physics. And whether or not the universe is a simulation doesn’t affect the model’s ability to make predictions at all, so why would it matter from a physics perspective? The model would be unchanged either way.
I think you might be confusing statistical with stochastic. Quantum mechanics makes incredibly precise predictions about the statistics of particle interactions. A stochastic model implies an experimental result could change depending on what day it is, when in fact quantum mechanical principles are relied upon every day for modern technology, and the screen you are reading this on is likely lit up because of the small but predictable chance an electron in an LED has to overcome an energy barrier it classically could not.
Maybe we use these terms differently in different domains. In my field, stochastic means that repeating the same experiment under the same conditions doesn’t guarantee the same results (e.g. rolling a die). The opposite of stochastic is deterministic. Something that changes depending on the day would be “a function of the date” or something that is “conditional on the date”. This can either be a deterministic function (e.g. calling
date.today().dayin Python, or a mapping from the date to a uniform distribution ranging from0todate.today().day) or a stochastic function (e.g. sample a uniform random integer between0anddate.today().day).Edit: I think what you’re talking about is the deterministic mapping from some variable into a distribution. We (as in my field specifically) do sometimes call that “stochastic” too, even though that mapping is deterministic. There may be a bit of terminology overloading here because what we care about in the end is the sample drawn from that distribution, which is actually stochastic.
No, that’s exactly what I mean and exactly what I think you are missing: quantum mechanical experiments have been reproduced thousands of times, and even as measuring instruments became sensitive, the predictions have held true. The statistical nature of it doesn’t make it any less predictable, and an experiment proving a different statistical value of an event than QM predicts would be world news.