Tracking states of randomness with three states

[Zachary Nichols]

I know that matter can only exist in one state at a time; however at the quantum level knowing what state it is in at a set time is impossible to know for sure until you look at the system. Like with how Schrödinger cat is in a state of randomness between the two states of dead and alive until you open the box.That leads me to the question, how does it work when it comes to three states over two, because I've only been able to find how it works with two. A system to think about would be the color charge of quarks.

 

[Nugatory]

Let's put Schrödinger's cat aside, because neither Schrödinger nor anyone else has seriously suggested that the cat is both alive and dead at the same time; the cat is either dead or alive just as a coin sitting on the floor is either heads-up or heads-down even if you're not close enough to see which it is. Schrödinger proposed this paradox to point out a flaw in the then-current (75 years ago) understanding of quantum mechanics: although there was no doubt that the cat would always be either dead or alive, quantum mechanics did not satisfactorily explain why. Much progress has been made in this area since then (google for "quantum decoherence", but be warned that some of the math is heavy going).

So with that said: there are plenty of states in which there are more than two possible measurement outcomes. Put a system into one of those states and make a measurement, and you might get any of those outcomes. An example would be an electron in free space: there is an infinite number of positions (mostly fairly close to one another) where you might find it if you make a sufficiently precise measurement of its position.

 

[Zachary Nichols]

Thank You this has really helped me understand a few things, but is there anyway you could explain it in math terms. I'm trying to do a science fair project and I need to explain the math portion. If you can't can you direct me to a starting point.

 

[Nugatory]

Thank You this has really helped me understand a few things, but is there anyway you could explain it in math terms. I'm trying to do a science fair project and I need to explain the math portion. If you can't can you direct me to a starting point.

What is your math background?

 

[Zachary Nichols]

ap calc with a little calc 2 and 3 (self study)