# Example of experimental or observational proof of quantum indeterminacy before measurement

How do we know that certain properties are indeterminate or undefined until they are measured?

Take the example of quantum entanglement, saying that if you have two entangled particles, such as the spins of 2 electrons, and you know that their spins have to be opposite, and we measure one, so we know that the other spin collapsed into the other answer immediately, even if it's a million light years away, leading to the strange and immediate "spooky action at a distance."

If we applied Occam's razor to this situation, we could conclude that the 2 particles already had a definite spin before we measured them, we just didn't know what it was. Then when we measured it, we simply learned the spin (that was already definite) so then we knew the spin of the other particle. No spooky action, no faster than light action... Certainly the SIMPLEST explanation... But quantum mechanics tells us that apparently this isn't the correct explaination. (Too bad, Occam)

So, my question is, how do we KNOW this to be how the world works? What evidence have we seen that shows that properties such as spin are truly unknown, not just to us, but to the universe itself, until they are measured (or forced to 'make a decision' by the universe)

I have never had anyone give an answer to this... I don't want a theoretical, mathematical answer about how it makes sense if you think about it this way, or that way, I want experimental or observational evidence that certain properties truly aren't decided until measured or forced into being decided. Anyone have any examples of how we know this, instead of us guessing about it?

• Experiments on Bell's inequality constrain the possible content of theories purporting to describe reality, but you can't have a measurement of the state of the system before measurement, now can you? – dmckee Mar 2 '17 at 19:38
• – knzhou Dec 14 '18 at 13:19

For single spin measurements:

Take a Stern-Gerlach spin measurement on a large ensemble A of qubits.

Step 1: Measure your qubits' spin along the x-axis. Keep only those that have spin in the positive x direction, and label the state $|\rightarrow\rangle$. This is ensemble B. You know with $100\%$ certainty that all qubits in ensemble B are in state $|\rightarrow\rangle$ because if you redo the exact same measurement on ensemble B as many times as you want, you still find all its qubits in state $|\rightarrow\rangle$.

Step 2: On ensemble B, measure each qubit along the z-axis. You will find that about 1/2 of them have spin $\uparrow$ and 1/2 have spin $\downarrow$. Take this as an experimental finding.

Step 3: Redo step 1 on a new large ensemble A', and select a new ensemble B' as before. Now do step 2 on the new ensemble B', one qubit at a time, but before you measure each qubit try to predict what result you will get. When you are done do the statistics: how many times you predicted the correct result and how many times you didn't. Rinse and repeat this as many times as you want, on as many ensembles as you want. The result will always be the same: on average you will only predict the right result about half the time. Which is no better than flipping a coin. Which basically says you cannot predict much at all, so you really don't know a qubit's spin along z until after the z-measurement, although you do know its spin along x with $100\%$ certainty. But that one is again after an x-measurement.

For entangled pairs:

Step 1 is a measurement of the total pair spin. This will give a $100\%$ certain result, all pairs will show the same total spin.

Step 2 is pairwise separate measurements of individual qubits, say along z-axis. You will find again that you can't predict the spin direction for any single qubit, but amazingly entangled pairs are always correlated the right way.

Step 3 is to replace step 2 along the z-axis by a measurement along a different arbitrary axis and look at the correlations you get in this case. Calculate what you expect by QM rules, and what should happen if some hidden classical correlations would be responsible for entanglement. Bell's theorem tells you quantum rules give a result that is very different from the classical one, even with hidden correlations.

And this is what all the hype is about entanglement and the latest entanglement correlation measurements: they just confirm that nature is quantum to the core.

No, we do not have that experimental proof because that proof would also require observing the particle. As soon as you observe, it is no more undefined/unmeasured.

The measurement at this level is actually alignment. Either the electron aligns, or it does not. That is why there are only two possible outcomes. True measurement can have many possible outcomes, but we always have just one of the two outcomes.

Universe has to know it all the time, because universe is all that is there, and that includes information about the spin. If the information does not exist prior to measuring, then, we are creating the information as a result of measurement and so universe does not need to know the non-existent information. If the information exists, then it exists within the universe (nature), and that means universe knows it.

The spin can be changing (superposing) all the time, but when you intercept it in a particular angle, it either aligns, or it anti aligns. There is no third way to show. So, it is alignment, not true measurement.

For example, you throw a rotating stick. Do you know its direction? May be yes because we can picture the stick without setting its rotation direction. We can not do that with entangled electrons, i.e. can not measure their spin without aligning/anti-aligning them in some direction. At least, we can not do that with currently available tools.