Quantum mechanics grabs the attention of so many people for some good reasons.

Quantum mechanics deals in the atomic and subatomic realms. In the reductive scientific program it is about as small and basic as you can go based on actual experiments.

The results of these studies have led to highly reproducible observations and measurements.

These findings have led to technologic breakthroughs.

 And because quantum mechanics is counterintuitive, bizarre and no matter how hard you try to picture it, model it in your head, think it through, intellectualize, fit in into your daily four-dimensional experience of reality, you will fail, like thousand upon thousands of great minds have failed for a hundred years.

Let me start with an example. I will give others in future posts.

Lets say we are going to measure whether someone is standing upright, and call standing with her head up U for up and standing on her head (head down) D for down.

She could also be lying down, with her head to the left L would be measured and with her head to the right R would be measured.

We will assume for now those are the only four choices. Yes, she can be off angle, and we could deal with that with simple trigonometry, but it adds nothing to our understanding for now. Off angle measurements will come up later though, it is better not get sidetracked with that at this point. Lets savor the incredible weirdness first.

Now, say we can’t see her, but we have a device that if we align it upright to measure whether or not she is standing it will report U or D, reflecting whether she is standing upright head up (U) or if she is upside down standing on her head (D).

If we align the device horizontally it will also report R or L reflecting whether she is lying with her head to the right or left respectively.

We can only measure U and D or L and R at one measurement depending how our device is oriented.

Also assume once measured, she stays in that position until a measurement in a different orientation of the device is made.

So say we both have our devices aligned upright and you measure U so I know she is standing upright, and indeed that is what I get when I measure her position with my device after you made your measurement. It is as we expected. We both get U. She is standing upright, head up, feet on the ground.

 Now, you would expect that if you measured with your device aligned for standing and you get U indicating that she is upright I would measure neither R nor L if I aligned my device horizontally for lying down. I mean, after all, the person is upright, which is the opposite of lying down. It is 90 degrees away! Nothing overlapping here, standing up versus lying down, we have a clear dichotomy.

Indeed that is what should happen for people-size devices and measured objects. Say the way I knew whether the person was lying down was to look for her head or her  a couple of feet to either side of her belly button. If I find the head to the left, feet to the right, it tells me that she is lying down and in the L direction (head left). But if she is standing (whether on her feet or head) I wouldn’t find the head or her feet off-center, they would only be off to the left or right if she is lying down! No feet or head off to either side when the person is standing, whether upright or upside down. I should get nothing (zero), no R or L going on, when measuring the lying down aspect of her position.

And that is true for measuring the position of the person. Get a measurement with the first device that she is standing, whether on her feet or head, and then you won’t get a measurement indicating that she is lying down when you measure with the second Device. These are mutually exclusive measurements.

But in the quantum world it is different.

If you measure a subatomic particle as standing (meaning, say, measuring the particle’s polarization or spin, characteristics of particles that do have direction that can be U or D, L or R) and you get a U or D indicating the particle is say spin up or down, when I measure it’s lying down/horizontal position (again, whether spin or polarization, for example) with the second device I DO get a R or L!!!!

It is standing AND lying down? It is spin up and spin to the horizontal?

And even weirder, if we repeat this a bunch of times, when you send me a series of U particles I get a series of  R’s and L’s in the horizontal direction:

Y0u send me a series of U’s and I may get:

R, R, L, R, L, L, L, R, L, R, L, R, R, R, L, L, L, R, L, R, R, etc.

And if you do it enough times, like heads and tails in a fair coin toss, the total number of R’s and L’s will be the same for the series of U particles, they in effect cancel each other out, meaning the AVERAGE horizontal position is zero in the upright particle!

So, how do upright particles give a horizontal answer in the quantum world? And how does the “system” that includes repeated measurements know to average out the results over time? Where in the universe does the “memory” of previous measurements reside so it “knows” to average out to 0, to no “net” horizontal spin in the spin up electron system (or no net horizontal polarization in the vertical polarized photon)?

If you say it is in the property of the electron or photon, then where is this property residing in these fundamental particles? How does a new particle know the property of the last particle? Or of the particle measured a second or hour ago, a billion years or a trillion particles ago?

If you say it is a property of the system of measurement, it may be that could true, but again, where and how so? Where are these properties “written” how are they stored?

There are mathematical and experimental reasons to think that indeed it is not  a matter of such “hidden variables,” and later that may be worth exploring, but even just conceptually, where could they be hidden and how would the next particle know where to find them?

Kind of screws a bit with any mental picture you may have of time and space and what a fundamental thing is, doesn’t it?