After some contemplation, I've decided to ask a related question in this thread. I hope it's not viewed as hijacking the thread. Here's the question:
What is superposition (of, let's say, the polarization of a photon)?
In a certain sense, this is exactly the same question that Superposed_Cat asked. But let's think few a couple of relevant points.
* We often "measure" a photon (with measurement defined as sending it through a polarizer and then seeing if it got through). And, after measurement, we often say that it has "collapsed" into a certain state. However, any state, from an alternative perspective can be viewed as continued superposition. For instance, if we send a photon through a vertical polarizer (and it gets through), then, if we send it through a polarizer at 45°, it will appear superposed (with half getting through and half not getting through). Therefore, we can't say that
all the photons (that got through) "collapsed" into the exact same state.
* To reiterate the above, any "known" state (basis state) of a photon can be viewed differently and then appear superposed.
* We can also bring elliptical and circular polarization into this. For instance, let's say our polarization filter has the ability to not only filter linearly, but it has the ability to polarize elliptically and circularly as well. We often "imagine" linear polarizers as a "slit" in a screen. And we rotate this slit to measure linear polarizations at different angles. However, we might imagine that this "slit" can be "stretched open" making an ellipse. When it's "fully stretched open", it makes a circle. If we stretch it open even more, it just closes on the orthogonal axis (Y vs X, or X vs Y, with Z being the direction of photon progression). So, with an ellipse, we still have a major axis.
When we talk of elliptical or circular polarization, we can also talk about whether the photon wave is rotating clockwise or counter-clockwise (depending on how the phase is offset in the Z direction). This brings up an interesting point. It can be argued that, when a photon is sent through a vertical linear polarizer (and it gets through), that it is in a state of circular superposition. We don't know if it's undulating down first and then up, or if it's undulating up first and then down. We would have to send it through a circular polarizer to determine that, which would "collapse" (destroy, superpose) it's linear polarization. Therefore, without even changing our angle, we can view linear polarization as a continuing superposition. In a similar vein, we can argue that circular polarization is a superposition of vertical and horizontal linear polarizations.
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The concept of a Bloch sphere attempts to visually represent all possible polarization states, with the X,Z plane representing all linear polarizations (including their superpositions), whereas any non-zero value on the Y axis (regardless of X or Z values) represents elliptical and/or circular polarizations. (Values of Y=1 or Y=-1 would be circular, with values of Y closer to zero indicating elliptical polarization.)
Even with this visual concept of the Bloch sphere, we still have the unit Bloch vector pointing in some specific direction (defined by the polar coordinates theta and phi, where theta is 2 times the linear polarization and phi is the phase offset representing elliptical and circular polarization). To say again, we still have the unit Bloch vector. Therefore, from some specific perspective, the photon is
NOT in superposition, whereas, from all other perspectives it
IS in superposition. Sure, we move the Bloch vector every time we take a measurement, but this argument still holds.
Should we abandon the use of the word "collapsed" and, instead, use the words "reoriented as per measurement"? When we "peek into" the Bloch sphere at some point on the surface, if the Bloch vector isn't pointing straight at us, we then know that it's pointing directly away from us.
Does superposition truly make sense in terms of a single photon? Might we do better to say "random polarization among a group of photons"? And then, this goes back to Superposed_Cat's question. If we can argue that a single photon is NOT superposed from "some" perspective (even if that perspective is unknown), then why can't we say that that unknown perspective was determined at the emission of the photon from our EPR pair creator (and not at the time of measurement), thereby reclaiming Einstein's local causality?
Just some things I'm thinking about.
Again, I look forward to comments, even if they show flaws in my thinking.