Are there unverifiable assertions about probabilities

[jk22]

Suppose we obtain a probability of $1/\sqrt{2}$ from QM for example.
This will be never verifiable since experiments can only give rational numbers even more : finite digits.

Does this mean that such a theory cannot be real in some sense since it would need an everlasting expetiment ?

Are there any attempts or approaches to get only rational numbers from the theory ?

 

[fresh_42]

Suppose we obtain a probability of $1/\sqrt{2}$ from QM for example.
This will be never verifiable since experiments can only give rational numbers even more : finite digits.

Does this mean that such a theory cannot be real in some sense since it would need an everlasting expetiment ?

Are there any attempts or approaches to get only rational numbers from the theory ?

Consider $\pi$ instead:


Now we have eliminated any "reality" of the "theory", because all we have used is a circle. From this point on you can eternally talk about realism, Plato and other philosophies. The mathematical resp. physical essence is, that we cannot actually create a circle, we can only come as close as we want to, depending on the effort we put in. Under the electron microscope, however, ...

Our models are all idealizations. The real world is discrete!

 

[A. Neumaier]

The real world is discrete!

No. It is fuzzy!

Suppose we obtain a probability of $1/\sqrt{2}$ from QM for example.
This will be never verifiable since experiments can only give rational numbers even more : finite digits.

Does this mean that such a theory cannot be real in some sense since it would need an everlasting experiment ?

No. One never expects predictions to be accurate to infinite precision - except in pure mathematics!

 

[Vanadium 50]

Does this mean that such a theory cannot be real in some sense since it would need an everlasting expetiment ?

What theory doesn't?

I have a theory that reindeer can't fly. I gather a hundred reindeer, and push them off my roof to their deaths. All I have shown is that these hundred reindeer can't (or at least didn't) fly. What about #101? Or #1001? Or #100000000000001?

 

[DarMM]

What theory doesn't?

I have a theory that reindeer can't fly. I gather a hundred reindeer, and push them off my roof to their deaths. All I have shown is that these hundred reindeer can't (or at least didn't) fly. What about #101? Or #1001? Or #100000000000001?

Was this conditioned on the presence of a red nose?