# What does “measurement” mean? Can a quantum particle measure another quantum particle? If not, what is a classical particle?

Say there are two particles in the x axis. Initially, with high probability one staying at $$x=-1$$ and going to the right, and the other $$x=1$$ going to the left. Will they collapse when both arriving at $$x=0$$?

If one does not use the Born rule, one has only a combined $$\psi(x_1,x_2,p_1,p_2,t):\mathbb{R}^4\times\mathbb{R} \rightarrow \mathbb{C}$$ wave function, where $$|\psi(x_1,x_2,p_1,p_2,t)|^2$$ is the probability of particles being respectively at position $$x_1$$ and $$x_2$$ at time $$t$$ with momentum $$p_1, p_2$$. In this case, will the particles eventually collapse? If not, what does it mean to "measure"? Is "measuring" a primitive concept like "particle", not defined in terms of other concepts? So that it is implicitly understood what does it mean when physicists say "measuring".

Born rule says if a measurement is performed on the $$x$$ axis, then $$\psi$$ will become $$\phi$$, with $$|\phi(x_1,x_2,p_1,p_2)|^2=1$$ for some $$x_1,x_2,p_1,p_2$$. And this happens with probability $$|\psi(x_1,x_2,p_1,p_2)|^2$$.

Is it right to say that "if I am not there" no collapse occur?

So, if one considers the whole universe, who is making the universe collapse?

Is this question solved by defining another concept: a particle is either classical either quantum? And saying that "a collapse occurs when a classical system interacts with a quantum system". In this case, how "interaction" is defined? In the example, above, say the particle on the right is classical: its probability of being is some $$x(t)$$ with momentum $$p(t)$$ is 1 at all times. Will the two particles interact as soon the probability of the two of being near each other is non zero? $$\exists \epsilon,x: \; |\psi(x-\epsilon,x+\epsilon)|^2 > 0$$. And in this case the Born rule will roll the dice and take a definite position for the left particle?

Incidentally, when you say that $$ψ$$ is a function of $$x_1,x_2,p_1,p_2$$, that's incorrect. It can be written as a function of $$x_1$$ and $$x_2$$ or as a function of $$p_1$$ and $$p_2$$ but not of all four.