You can build arbitarily-phase-shifting optical components. There’s no reason one couldn’t make half-silvered mirrors with a coating that makes it act like Eliezer’s… and any physicist ought to know this. Plus, the real issue is the total difference in phase across the two paths, and you can tweak that however you like by adjusting the path lengths.
SO, either fix it numerically or include a note to that effect, because there’s no reason this needs to fall to a silly nitpick.
Both. The sequence is technically off on that detail, but someone who knows their stuff should know better than to complain about it. The simplest fix is to just say that this is a special custom half-silvered mirror that has these phase shifts.
I was going to say that the cleanest fix would be to make the math right, but looking at the math, it seems that the real math is so much messier and harder to explain (half-silvered mirrors invert or not based on which side you half-reflected from!) that getting it right would muddy the waters far more than using your power of arbitrary setups to make an idealized apparatus.
Motivated reasoning made its masterpiece there—the guy does know his stuff, but he basically found one tiny nit and went “THIS IS CLEARLY ALL BOGUS, AS AN EXPERT I IMPLORE YOU ALL TO IGNORE EVERY WORD”. That was why I posted to Physics Exchange about it, to demonstrate to a friend that when he says “trust me, I’m an expert” you can’t trust him.
Not directly related, but just wanted to mention that unqualified statements like
“A photon heading toward A”—and it’s out there in the territory.
are way too strong, and unnecessarily so.
A single photon is not a part of reality, it’s just a simplified convenient model of electromagnetic emission and absorption, which happens to work well in certain circumstances. Consider the question “When was the photon emitted?”. Unless you measure the recoil of the emitter (a classical measurement), you don’t know. You can reconstruct this time if you use a sensitive enough photomultiplier in the detector, which is again a classical measurement.
A somewhat more detailed QED-based model describes spontaneous emission as unitary evolution of an excited atom into a superposition of the multitude of the states of the form (a recoiled ground state of atom * a corresponding excited state of the EM field). This is not a well-defined single photon, but rather a superposition of all possible photons emitted at all possible times in all possible directions. What makes it into a single photon is the post-selection process (selecting a single possible world out of infinitely many ones, in the MWI picture).
So “A photon heading toward A” is not the territory, it’s a useful simplification of a more accurate model. Which only underscores the point that “distinct configurations are not distinct particles”.
That’s a different point you raised elsewhere, yes. I meant on the point you raised above.
Would you be satisfied on this other front if he restricted himself to saying that whatever it ends up being, it’s not going to be an objective collapse theory? A distressingly large number of people haven’t gotten that memo.
Oh, I don’t disagree that claiming that some form of objective collapse is the “reality” is not very smart. While QM can be simulated this way, and usually is, there is no reason to expect that this ad hoc rule is as deep as it gets. Unless we are in a poorly written simulation.
A concrete example of a paper using the add-i-to-reflected-part type of beam splitter is the “Quantum Cheshire Cats” paper:
A simple way to prepare such a state is to send a horizontally polarized photon towards a 50:50 beam splitter, as depicted in Fig. 1. The state after the beam splitter is |Psi>, with |L> now denoting the left arm and |R> the right arm; the reflected beam acquires a relative phase factor i.
The figure from the paper:
I also translated the optical system into a similar quantum logic circuit:
Note that I also included the left-path detector they talk about later in the paper, and some read-outs that show (among other things) that the conditional probability of the left-path detector having gone off, given that D1 went off, is indeed 100%. (The circuit editor I fiddle with is here.)
It’s notable that my recreation uses gates with different global phase factors (the beam splitter is 1/2-i/2 and 1/2+i/2 instead of 1/sqrt(2) and i/sqrt(2)). It also ignores the mirrors that appear once on both paths. The effect is the same because global phase factors don’t matter.
edit My ability to make sign errors upon sign errors is legendary and hopefully fixed.
Will the QM sequence be checked over for mathematical errors? These have been used in practice to quickly dismiss the sequence.
You can build arbitarily-phase-shifting optical components. There’s no reason one couldn’t make half-silvered mirrors with a coating that makes it act like Eliezer’s… and any physicist ought to know this. Plus, the real issue is the total difference in phase across the two paths, and you can tweak that however you like by adjusting the path lengths.
SO, either fix it numerically or include a note to that effect, because there’s no reason this needs to fall to a silly nitpick.
To be clear, is the criticism just wrong, or should the sequence be adjusted? What exactly needs to be done to fix it numerically?
Both. The sequence is technically off on that detail, but someone who knows their stuff should know better than to complain about it. The simplest fix is to just say that this is a special custom half-silvered mirror that has these phase shifts.
I was going to say that the cleanest fix would be to make the math right, but looking at the math, it seems that the real math is so much messier and harder to explain (half-silvered mirrors invert or not based on which side you half-reflected from!) that getting it right would muddy the waters far more than using your power of arbitrary setups to make an idealized apparatus.
Motivated reasoning made its masterpiece there—the guy does know his stuff, but he basically found one tiny nit and went “THIS IS CLEARLY ALL BOGUS, AS AN EXPERT I IMPLORE YOU ALL TO IGNORE EVERY WORD”. That was why I posted to Physics Exchange about it, to demonstrate to a friend that when he says “trust me, I’m an expert” you can’t trust him.
Not directly related, but just wanted to mention that unqualified statements like
are way too strong, and unnecessarily so.
A single photon is not a part of reality, it’s just a simplified convenient model of electromagnetic emission and absorption, which happens to work well in certain circumstances. Consider the question “When was the photon emitted?”. Unless you measure the recoil of the emitter (a classical measurement), you don’t know. You can reconstruct this time if you use a sensitive enough photomultiplier in the detector, which is again a classical measurement.
A somewhat more detailed QED-based model describes spontaneous emission as unitary evolution of an excited atom into a superposition of the multitude of the states of the form (a recoiled ground state of atom * a corresponding excited state of the EM field). This is not a well-defined single photon, but rather a superposition of all possible photons emitted at all possible times in all possible directions. What makes it into a single photon is the post-selection process (selecting a single possible world out of infinitely many ones, in the MWI picture).
So “A photon heading toward A” is not the territory, it’s a useful simplification of a more accurate model. Which only underscores the point that “distinct configurations are not distinct particles”.
Would you be satisfied if he pointed out that there’s no way to achieve such a well-specified initial condition in real life?
I would be happy if he did not claim that a specific model is the reality.
That’s a different point you raised elsewhere, yes. I meant on the point you raised above.
Would you be satisfied on this other front if he restricted himself to saying that whatever it ends up being, it’s not going to be an objective collapse theory? A distressingly large number of people haven’t gotten that memo.
Oh, I don’t disagree that claiming that some form of objective collapse is the “reality” is not very smart. While QM can be simulated this way, and usually is, there is no reason to expect that this ad hoc rule is as deep as it gets. Unless we are in a poorly written simulation.
A concrete example of a paper using the add-i-to-reflected-part type of beam splitter is the “Quantum Cheshire Cats” paper:
The figure from the paper:
I also translated the optical system into a similar quantum logic circuit:
Note that I also included the left-path detector they talk about later in the paper, and some read-outs that show (among other things) that the conditional probability of the left-path detector having gone off, given that D1 went off, is indeed 100%. (The circuit editor I fiddle with is here.)
It’s notable that my recreation uses gates with different global phase factors (the beam splitter is 1/2-i/2 and 1/2+i/2 instead of 1/sqrt(2) and i/sqrt(2)). It also ignores the mirrors that appear once on both paths. The effect is the same because global phase factors don’t matter.
edit My ability to make sign errors upon sign errors is legendary and hopefully fixed.