What Does It Mean Particles Only Have Location if Measured?

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I'm not a physics person (just an interested layperson) and have read that quantum particles don't have any location until they are measured. First, is this true? And, if so, what does that mean? For example, if you don't know where a particle exists, then how can you even measure it? And what does it mean they don't normally have location? If not, how do you know they even exist at all?
 
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What Does It Mean Particles Only Have Location if Measured?
... the concept of "position" only makes sense if the position has been detected.

if you don't know where a particle exists, then how can you even measure it?
... you put a detector in a random location. If it goes off, then you have just measured stuff about the particle. If it doesn't - then you have some other knowledge about the particle (i.e. it wasn't there) ... you never been on a treasure hunt? How do you locate an easter egg that is hidden?

Think how you normally measure the position of something. You start out with some idea about where it is ... say you saw it with your eyes. The act of seeing it with your eyes makes a measurement of the position. Then you break out a ruler of some kind and make a more precise measurement.
It is the same with particles - before conducting an experiment we prefer to have a good reason to believe there is something to measure... like we just shone a laser thataway ... this gives us a rough idea where to look for photons so we can make more precise measurements.

And what does it mean they don't normally have location? If not, how do you know they even exist at all?
If you don't know where the particle is, you are still presupposing it's existence. It's existence is an axiom of the problem. No point doing the math for particles that don't exist.
Not having a position is not the same as nonexistence.