Imaginary numbers are no more imaginary than real numbers. The name trips a lot of people up. If you want to call imaginary numbers “dark unicorns” then you really should say the same thing of the numbers 1, 2, and all other numbers as well.
Imaginary numbers are no more imaginary than real numbers. The name trips a lot of people up. If you want to call imaginary numbers “dark unicorns” then you really should say the same thing of the numbers 1, 2, and all other numbers as well.
You’re thinking of topological closure. We’re talking about algebraic closure; however, complex numbers are often described as the algebraic closure of the reals, not the irrationals. Also, the imaginary numbers (complex numbers with a real part of zero) are in no meaningful way isomorphic to the real numbers. Perhaps you could say their addition groups are isomorphic or that they are isomorphic as topological spaces, but that’s about it. There isn’t an isomorphism that preserves the whole structure of the reals - the imaginary numbers aren’t even closed under multiplication, for example.
Yeah, you’re close. You seem to be suggesting that any measurement causes the interference pattern to disappear implying that we can’t actually observe the interference pattern. I’m not sure if that’s what you truly meant, but that isn’t the case. Disclaimer: I’m not an expert - I could be mistaken.
The particle is actually being measured in both experiments, but it’s measured twice in the second experiment. That’s because both experiments measure the particle’s position at the screen while the second one also measures if the particle passes through one of the slits. It’s the measurement at the slit that disrupts the interference pattern; however, both patterns are physically observable. Placing a detector at the slit destroys the interference pattern, and removing the detector from the slit reintroduces the interference pattern.
2 may be the only even prime - that is it’s the only prime divisible by 2 - but 3 is the only prime divisible by 3 and 5 is the only prime divisible by 5, so I fail to see how this is unique.
Why stop there? They’re just as real as any number.