You can do so by simply not "observing" your measuring device. Let's say you have an electron in the sate $\frac{1}{\sqrt{2}}\left(|\uparrow\rangle+|\downarrow\rangle\right)$ (which means you have a 50% chance of measuring it being spin up, and a 50% change of measuring it down. It's in a superposition of up and down), and that you have a measuring device which can measure zero [$|0\rangle$ for "hasn't made a measurement yet"], up ($|\uparrow\rangle$), or down ($|\downarrow\rangle$). The system starts in the state:
$$\frac{1}{\sqrt{2}}\left(|\uparrow\rangle+|\downarrow\rangle\right)\otimes |0\rangle$$
(the symbol "$\otimes$" called the tensor product is the way of concatenating states in quantum mechanics. $|\uparrow\rangle\otimes |0\rangle$ means 'the electron is in the quantum "up" state, and the measuring device is in the quantum "unmeasured" state.')
When you flip your measuring device on, the state evolves to:
$$\frac{1}{\sqrt{2}}\left(|\uparrow\rangle \otimes |\uparrow\rangle+|\downarrow\rangle\otimes |\downarrow\rangle\right)$$
where $|\uparrow\rangle\otimes |\uparrow\rangle$ means 'the electron is in the quantum "up" state, and the measuring device measured up"'.
This final state has the solution to all your problems! Imagine you are the measuring device inside a very well sealed box inside some mad scientist's laboratory. You can be up, down, or zero. To the person in the laboratory who has not interacted with you in any way, you are in state up or state down, each with 50% probability, and nothing more can be said.
The part of this formula that reads $|\uparrow\rangle\otimes|\uparrow\rangle$ should be seen as the version of you in the up state. To the version of "you" in the up state, the electron is in state $|\uparrow\rangle$ with 100% certainty, and you've destroyed its original superposition of $\frac{1}{\sqrt{2}}\left(|\uparrow\rangle+|\downarrow\rangle\right)$.
Likewise, to the version of you in the $|\downarrow\rangle\otimes|\downarrow\rangle$ world, the electron is in state $|\downarrow\rangle$ with 100% probability, and you've destroyed its original superposition.
The point is this:
- The "collapse" of the wavefunction is nothing more than its interaction with the measuring device.
- The interaction -- meaning the way the measuring device works -- chooses what to measure, and in doing so chooses what the state "collapses" into. In this case the interaction "chose" $\uparrow$ and $\downarrow$, but if it interacted with the system in a different way, it could have chosen to measure $\frac{1}{\sqrt{2}}(|\uparrow\rangle+|\downarrow\rangle)$ and $\frac{1}{\sqrt{2}}(|\uparrow\rangle-|\downarrow\rangle)$ (which in the electron experiment is equivalent to measuring "left" and "right" instead of "up" and "down").
- The tricky thing is to conceptualize living inside/BEING a quantum state. The wavefunction of the person in the laboratory tells them that you have a 50% chance of being in either state, and in fact that is the most fundamental picture of the universe that the lab person can see, even though the person inside the experiment gets the result of the experiment and knows 100% the state of the electron, breaking its superposition.
