> If the robot's protocol is to measure the particle twice, it will measure the same outcome twice.
But you cannot measure the same particle twice. If you think you can, describe the experimental setup for me.
> I didn't say that it was up, I said that it is up. Very important distinction.
Indeed. But by the time you see the outcome of the experiment, the particle you measured doesn't exist any more. So what does "is up" actually mean at that point?
> Seems like a distinction without a difference to me.
It's a crucial difference. Our mental models of our classical universe depend heavily on the continuity of identity, i.e. that there are things in the world with properties that persist across time. This what allows us to say things like, "The vase on the table is green." This presumes that the phrase "the vase" has an actual referent, that referent is a vase, and it is on the table, and it is green. We think this makes sense because we can see the vase on the table, and we can see that it is green.
But in order to see the vase, your eyes have to accumulate a lot of photons, and that takes time. So the vase on the table has to persist at least long enough for your eyes to accumulate enough reflected photons to see it. If you stop looking at the vase, the vase is still there. If you look at it again, the vase will still be on the table and it will still be green.
Particle measurements are fundamentally different. It really doesn't make sense to say "the photon in the left arm of the interferometer" or "the electron in the upper branch of the Stern-Garlach apparatus. If you doubt this, read the following:
That's playing word games. Let's remove the word "measure" and insert the word "bloop". If you bloop something twice, you get the same result twice. Even in QM. And bubble chambers bloop a trajectory.
> If you think you can, describe the experimental setup for me.
It's called the Stern-Gerlach experiment. See the section "Sequential experiments" on wikipedia:
> But in order to see the vase, your eyes have to accumulate a lot of photons, and that takes time. So the vase on the table has to persist at least long enough for your eyes to accumulate enough reflected photons to see it. If you stop looking at the vase, the vase is still there. If you look at it again, the vase will still be on the table and it will still be green.
I could similarly say that you cannot look at the same vase twice. By the time you measured the vase, the vase doesn't exist any more. Each photon in fact comes from a different vase. So what does "green" actually mean at that point?
This is an irrefutable philosophical position. It all depends on what you define as the same vase, and what measurement means. There are accepted meanings of these words in QM and those meanings coincide with the conventional meanings in the appropriate limit. I'm happy to use different words though, since you're right that those meanings are not exactly the same as the everyday meanings of those words.
> If you doubt this, read the following:
Have you considered the double slit experiment, where the whole point is the difference in length of trajectory?
Note the following facts, consequence of QM:
(1) the fact that if you bloop spin twice that you get the same result twice
(2) the fact that if you bloop a particle with a more or less spherically symmetric wave function (such as arising from a collision) in a bubble chamber, that you get linear tracks
(3) the fact that a single photon can interfere along paths of different lengths
You've painted yourself into a linguistic corner that makes all these phenomena incredibly difficult to understand, and causes you to make statements that contradict experimental evidence under a non-word-play interpretation of the words.
As for point (3), consider that Maxwell's equations are the quantum theory of a single photon. The reason they also work for macroscopic amounts of light, is that the equations are linear and photons only weakly interact with each other. One shouldn't think of a photon as a particle moving in straight lines at the speed of light. A photon is a wave distributed in both space and time. The wavefront tends to move at the speed of light, but you can't think about it as a point particle moving along trajectories. In some cases you can: there are solutions of Maxwells equations in which a wave packet more or less moves in a straight line at the speed of light, and the probability amplitude is more or less zero everywhere else. But the situation being set up in your experiment, or indeed in the double slit experiment, is not of that form.
Therefore, the outcome of your proposed experiment depends on the shape of the wave packet of the photon and the distance difference. If the wave packet is sufficiently localised in space and time, and the distance difference is sufficiently large, then there will be no interference. The wave packet will travel to the half-mirror and split into two, then those two packets will continue traveling such that they never meet again at the same point in space-time (you can see this by visualising the movie of what happens), and there will be no interference. There will be some probability distribution of observing the photon at a given point on the detector at a given point in time, with two peaks in space-time corresponding to the two wave packets.
If however, you decrease the distance difference so that the two wave packets will overlap in space-time again after the bounce, there will be interference.
No, it isn't. There's a reason that Schroedinger's cat and Wigner's friend and "the measurement problem" are a thing. (And see my last comment below.)
> Stern-Gerlach experiment.
The basic SG experiment setup has two components: the magnets, and a pair of detectors. When you compose multiple SG experiments you compose only one of these, the magnets. The detectors are all moved to the END, AFTER the electrons have transitioned all the magnetic fields. So you are not actually measuring the positions of the electrons at the intermediate stages, only at the end, and only once.
So no, the SG experiment is NOT an example of making two successive measurements on the same particle. Go back a re-read what I originally wrote:
> The best you can do is run a particle through a series of filters and look at where it ended up. You can then retrodict that the particle went one way or went another way, but you cannot actually measure its trajectory. In fact, you cannot even know that there even is a particle in your apparatus until the end when you actually measure it.
In the SG experiment, the magnets are the filters. You will find that ALL quantum experiments have the same constraint.
(BTW, the actual term used by physicist is "preparation". You can use multiple SG magnets in series to PREPARE your quantum system, but you can only actually MEASURE it once. Once you measure it, the wave function collapses, and you no longer have the same system.)
> Have you considered the double slit experiment, where the whole point is the difference in length of trajectory?
Yes, of course. You appear to have completely missed the point. The path-length difference in the experiment I pointed you to is orders of magnitude larger than the standard two-slit experiment. That matters.
> if you bloop spin twice
What does it mean to bloop something? You will find that you will have no more success in defining "bloop" than physicists have had in defining "measurement". Here's a hint: are bloops/measurements reversible?
> Once you measure it, the wave function collapses, and you no longer have the same system.
Comes down to definitions of words: same "system" (by which you mean wave function) vs same particle. See bubble chamber: particle interacts with several atoms along a trajectory. Sure, you can claim "the wave function has collapsed after the first interaction", so it's "not the same system"...but then you're just saying that measurement affects the wave function...well, yeah, it does. Or you can say that the bubble chamber "is just a series of filters"...ok sure, everything that happens is just a series of filters, with sufficiently broad interpretation of that phrase.
> You appear to have completely missed the point. The path-length difference in the experiment I pointed you to is orders of magnitude larger than the standard two-slit experiment. That matters.
Seriously? I explained in detail what will happen in your proposed experiment as a function of path length and why the explanation comes down to the same thing as with the double slit. You completely ignored this, and then say that I completely missed the point...I honestly find your behaviour quite rude.
If the robot's protocol is to measure the particle twice, it will measure the same outcome twice.
> that the particle "actually" was spin up
I didn't say that it was up, I said that it is up. Very important distinction.
> But it emphatically does NOT say that this outcome is actually real.
Seems like a distinction without a difference to me.
> but you cannot actually measure its trajectory
Bubble chambers do measure particle trajectories. https://cds.cern.ch/record/39474