This brief paper is a spin-off from my previous QM model. All mature feedback is welcome!
https://goo.gl/Lkv4s5
https://goo.gl/Lkv4s5
Discerning Between QM Interpretations
- Thread starter RJBeery
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That's... pretty interesting, actually. I'm skeptical, because I know there are some results implying that at least some of the interpretations you listed predict identical results for all experiments in principle. But even if that is the case, the measurement-like effect of conservation laws isn't something I'd thought of before. I'll definitely think some more on this!
In order we have:
1) Skeptical introduction of QED into a QM paper
2) Conflation of local conservation of momentum in QFT with Newton's Third Law
3) Misunderstanding of momentum conservation in QFT
4) Assuming the reality of something that is interpretation dependent when you ultimately seek to distinguish between interpretations.
5) Conflation of local conservation of momentum in QFT with Newton's Third Law
6) Misunderstanding of momentum conservation in QFT
7) Ignoring the role of the slit in the the double-slit experiment
This renders the foundational paragraph of the paper as baseless pseudoscience.
8) Skeptical introduction of QED into a QM paper
9) Using a paper about the confrontation of theory and experiment as a citation for "theory"
10) Confusing introduction of angle of polarizer with topic of circularly polarized light and individual photons makes one think you have conflated circular and linearly polarized light and haven't mastered the topic of superposition of states.
11) Timeout to calculate. If a photon of known linear polarization hits an ideal linear polarizer inclined at relative angle ΔΘ which absorbs that which it doesn't transmit, is there necessarily a torque? Neglecting overall phase, we have:
In photon state: ⎢0°⟩ = ⎢↕︎⟩ = √½ ⎢⟲⟩ + √½ ⎢⟳⟩
Out photon state: (cos ΔΘ) ⎢ΔΘ⟩ + (sin ΔΘ) ⎢absorbed⟩ = (cos² ΔΘ) ⎢0°⟩ + (cos ΔΘ)(sin ΔΘ) ⎢90°⟩ + (sin ΔΘ) ⎢absorbed⟩
= (cos² ΔΘ) ⎢↕︎⟩ + (cos ΔΘ)(sin ΔΘ) ⎢↔︎⟩ + (sin ΔΘ) ⎢absorbed⟩
= (cos ΔΘ)(cos ΔΘ − i sin ΔΘ) √½ ⎢⟲⟩ + (cos ΔΘ)(cos ΔΘ + i sin ΔΘ) √½ ⎢⟳⟩ + (sin ΔΘ) ⎢absorbed⟩
= (cos ΔΘ) ( exp −iΔΘ )√½ ⎢⟲⟩ + (cos ΔΘ)( exp iΔΘ ) √½ ⎢⟳⟩ + (sin ΔΘ) ⎢absorbed⟩
So at no point is there a change in the angular momentum of the linearly polarized photon, as the amplitude of the ⎢⟲⟩ is equal to that of ⎢⟳⟩, only the relative phases have been tweaked. Thus conservation of angular momentum suggests that there can be no torque on the linear polarizer from a beam of linearly polarized light.
12) People familiar with measurement of polarization of single photons would know that each test is a destructive test, so this "measure the polarization" bit is not well thought out. This is why instead of a polaroid filter, a beam splitter with two photodetectors is usually used in the EPR experiment.
13) Since the EPR experiment doesn't predict any particular polarization, the first paragraph is a more mathless digression than introduction. There is no indication that the methods of EPR experiments or reference [2] were understood. Nor is there basis to suppose that there is a torque on the polarization elements as the state of the photon and the nature of the polarizer and measurement were never explored.
Since the experimental methods and documented behavior of photons, various polarizers, detectors were so poorly understood, there is no support for the next section which dives into the fantasy of your earlier paper now consigned to Pseudoscience.
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1, 8) You're presuming my skepticism of QED when it does not exist. When I say "accepted" or "theory suggests" I'm laying out what is commonly understood. Disqualifying certain interpretations does not threaten quantum mechanics in any way, although it may perhaps disqualify your personally preferred one.
2, 3, 5, 6) They are necessarily conflated. Either a photon imparts momentum to its emitting particle and its absorbing particle, or it does not...this paper looks to answer the question either way.
7) I appreciate that the slit may alter the path of the photon but the fact remains that the path of the photon, and the angle from which it is emitted, is different depending on which slit is ultimately traveled through.
10, 11) Please reread this paragraph
My proposed test is but a single suggestion, and if the particulars were to fail then there are many other potentials. If we are considering the light in terms of photons then when the photon passes the polarizer we simply don't know if torque has been imparted to it...but we cannot deny that "something" has changed in the same way that we presume that momentum is imparted to the polarizer when the photons do not pass through it. Your question "is there necessarily a torque?" and later statement of "the state of the photon and the nature of the polarizer and measurement were never explored" is unusually baffling, by the way...because that is literally what the paper is exploring. How you think making a proposal and laying out the foundations for testing that proposal should be immediately relegated to Pseudoscience while keeping the threads on perpetual motion machines in the Physics forums...is perplexing to say the least. ¯\_(ツ)_/¯
So I took a longer look at your paper, and I came away with two criticisms.
1. rpenner is right that it's not at all obvious momentum conservation will do what you claim it will in the situation described. I think you're right that there is some configuration in which the 3rd law action on the emitter will be different depending on what output state is detected, but it's important to be precise when determining exactly how that works.
2. More importantly, I think what your analysis is missing is the possibility that the photon could be entangled with the emitter. In the usual picture of double-slit-like experiments, we implicitly assume that the state of the emitter before and after emitting a photon is the same regardless of what kind of photon is emitted. Formally, if $$|E_0\rangle$$ and $$|E_1\rangle$$ are the states of the emitter before and after emission, respectively, and $$|+\rangle$$ and $$|-\rangle$$ are the polarization states of the photon, then the emission process can be described as
$$|E_0\rangle\rightarrow \frac{1}{\sqrt{2}}(|+\rangle + |-\rangle)|E_1\rangle$$.
The $$|E_1\rangle$$ at the end factors out, and we can look at just the photons when predicting interference behavior. More realistically, there will probably be some difference between the detector states depending on what kind of photon was emitted (perhaps due to the torque effect you considered), but as long as it is small (i.e. $$|\langle E_2|E_1\rangle|\approx 1$$), degradation of coherence will be minimal and we can still treat the photons by themselves to good approximation. But what if we look at the opposite limit, where $$|\langle E_2|E_1\rangle|\approx 0$$? Now, the emission process is a highly entangling one:
$$|E_0\rangle\rightarrow \frac{1}{\sqrt{2}}(|+,E_1\rangle + |-,E_2\rangle)$$.
Because the polarization states are associated with nearly-orthogonal detector states, they won't interfere, and you basically just have a highly correlated, 50/50 probability distribution of photon states and emitter states.
1. rpenner is right that it's not at all obvious momentum conservation will do what you claim it will in the situation described. I think you're right that there is some configuration in which the 3rd law action on the emitter will be different depending on what output state is detected, but it's important to be precise when determining exactly how that works.
2. More importantly, I think what your analysis is missing is the possibility that the photon could be entangled with the emitter. In the usual picture of double-slit-like experiments, we implicitly assume that the state of the emitter before and after emitting a photon is the same regardless of what kind of photon is emitted. Formally, if $$|E_0\rangle$$ and $$|E_1\rangle$$ are the states of the emitter before and after emission, respectively, and $$|+\rangle$$ and $$|-\rangle$$ are the polarization states of the photon, then the emission process can be described as
$$|E_0\rangle\rightarrow \frac{1}{\sqrt{2}}(|+\rangle + |-\rangle)|E_1\rangle$$.
The $$|E_1\rangle$$ at the end factors out, and we can look at just the photons when predicting interference behavior. More realistically, there will probably be some difference between the detector states depending on what kind of photon was emitted (perhaps due to the torque effect you considered), but as long as it is small (i.e. $$|\langle E_2|E_1\rangle|\approx 1$$), degradation of coherence will be minimal and we can still treat the photons by themselves to good approximation. But what if we look at the opposite limit, where $$|\langle E_2|E_1\rangle|\approx 0$$? Now, the emission process is a highly entangling one:
$$|E_0\rangle\rightarrow \frac{1}{\sqrt{2}}(|+,E_1\rangle + |-,E_2\rangle)$$.
Because the polarization states are associated with nearly-orthogonal detector states, they won't interfere, and you basically just have a highly correlated, 50/50 probability distribution of photon states and emitter states.
I agree with both of you that this is speculative. The reason it is speculative is precisely because it hasn't been tried before, of course...but there is an intuitive reason to believe that an instrument cannot change the configuration of a system without also experiencing change itself; additionally, as mentioned in the paper, if this proposal does not work there are others which may work (e.g. magnetism on charged fermions).
This is certainly possible but not really relevant. From the experimenter's perspective, it would necessitate the condition of "retrocausality" and the persistent pure quantum state would indeed be detected, regardless. To say that such a pure state between emission and absorption "might have been different had the outcome been different" is nonsensical, if you think about it.Fednis48 said:
I think it's a bigger issue than you're giving it credit for. What do you mean that "the persitent pure quantum state would indeed be detected?" In general, the only way to distinguish a pure quantum state from a mixed or collapsed one is to check for interference. And if your photons are entangled with the emitter, they will not exhibit interference. To put it another way, your experiment wants to examine the behavior of the emitter after it creates a photon but before the photon's wavefunction is collapsed. If the photon's state is entangled with the emitter's, then its wavefunction will collapse at the moment of emission, making such an experiment impossible.
I'm making no prediction one way or the other, I'm providing a way to potentially disqualify certain interpretations. In your example, if the wavefunction collapses "at the moment of emission" then it never existed in the first place. What I'm calling a persistent pure quantum state means that the entangled nature of the wavefunction has no physicality because all particles (and photons) have a definite configuration at all times. I know this seems somehow "anti-QM" but retrocausality allows for the hidden variables to reside in the future.
Again...I'm not advocating for retrocausal interpretations (even though they are my preference), I'm just pointing out that, in my estimation, any physical manifestation of the wavefunction would violate conservation laws. Maybe they're violated? I'm not the one to dictate to Nature.
I'm trying to think of the most straightforward way to explain this. Consider the Schrodinger equation. No interpretations, no measurements, just unitary evolution under the Schrodinger equation. Based on the reasoning in my last two posts, you'll find that if the final state of the emitter depends on the state of the photon, then interference will not occur. Turning that around, we arrive at a pretty important prediction that all QM interpretations must make in order to follow the Schrodinger equation: measuring the state of the emitter in a working double-slit experiment will never tell you anything about what kind of photon was emitted. That in itself is kind of surprising from a conservation-of-momentum perspective, but it does put a big hole in your proposal.
Ah! I now understand your point and I agree.
What you're saying is that a positive result in measuring a persistent "classical" state of a particle (which QM would normally consider to be in a mixed state) would mean that we are still left with explaining the mixed state results over a series of tests. In other words, retrocausality itself may not be sufficient and many time-symmetric interpretations may be incomplete. On the other hand, we are both in agreement that the absence of a persistent pure quantum state (meaning that the wavefunction does have a physical significance) would apparently require conservation principles to be violated.
De Broglie-Bohm theory would cover both bases. It's a completely deterministic theory with both a persistent pure quantum state of the particle and the physical "guiding" wavefunction presence required to produce the results expected. Transactional Interpretation would as well, I believe. Not that I want to sidetrack this discussion but I'd also mention that my pet theory has the potential to explain this. Fednis, have you ever thought about strictly defining locality?
I feel the need to suggest (for discussion) that most (if not all) photons are 'produced' omnidirectionally. Except lasers of course. Any directional qualities of a 'beam' arise from later reflections and absorptions. If (say) an atom gains momentum it is caused by some internal mechanism of reflection or absorption after the photon hatched. True or false?
Half true. You're right that most photons are emitted in a broad pattern. Not necessarily omnidirectional - the exact pattern depends on the geometry of whatever is doing the emitting - but not usually a tight beam, either. Until the photon is absorbed, its wavefunction will be a superposition of different position/momentum states, spreading out in space. If at some point a detector absorbs the photon, it will collapse into a particular momentum state, sampled from the probability distribution described by said wavefunction.
Conservation of momentum implies that the emitter has to get a momentum kick that is equal and opposite to the momentum of the emitted photon. What does this mean when the photon's momentum is itself in a broad superposition? The emitter's momentum must also be in a superposition. Specifically, the emitter's momentum is entangled with the photon's, and measuring one will (at least partially) collapse the other.
Note that the "at least partially" caveat is actually essential to the double slit experiment. If the emitter is a macroscopic laser, its natural momentum spread is huge compared with the momentum of one photon, and the recoil from emission will barely entangle its state with the photon's at all. To excellent approximation, we can treat the photon as an isolated system, and it exhibits strong interference. On the other hand, if the emitter is a single atom, the recoil can actually matter. Even typical atomic momenta are pretty big compared with photons, but from personal experience I know that if one's atoms are cold enough, the recoil momentum can be enough to cause significant noise in an experiment. That's what I was trying to get at above: if your emitter's momentum is precisely defined enough that you can measure the recoil momentum on top of it, then the resulting entanglement will cause double-slit interference to fail.
Fednis, I have a few questions for you:
1) What do you think about the feasibility of the experiment outlined (EPR with photons, not the double-slit) with today's technology?
2) Assuming it's viable, what would you expect the results to be? Do you consider testing for a pure quantum state at the moment of measurement to be an act that would make the entangled nature of the system disappear?
3) What kind of investment would be needed for such an experiment? Are the required instruments something that a University physics lab would have?
I have almost zero connection with real-world physics labs. What I might do is literally walk down to Uni and trap a Professor in his office.
1) What do you think about the feasibility of the experiment outlined (EPR with photons, not the double-slit) with today's technology?
2) Assuming it's viable, what would you expect the results to be? Do you consider testing for a pure quantum state at the moment of measurement to be an act that would make the entangled nature of the system disappear?
3) What kind of investment would be needed for such an experiment? Are the required instruments something that a University physics lab would have?
I have almost zero connection with real-world physics labs. What I might do is literally walk down to Uni and trap a Professor in his office.
I had not considered this, and I need to think about it. Do you have more information on this? The reason I ask is because I've always considered our attempts to glean information about the photon's path to be futile, not because "we can't fool nature", but because information is only available at these scales through disturbing the system.Fednis48 said:
". . . . . information is only available at these scales through disturbing the system." An excellent observation/reminder to all - the basis for all scientific discovery!
If we're talking about using a standard, room-temperature emitter, than the experiment should be easy to do. If we want a cold, single-atom emitter, than the experiment should still be feasible - one would basically have to take well-established atom trapping technology and wrap it in an assembly to redirect the emitted light into a double slit - but it would be a significant endeavor. As a very rough guess, I bet a university group with atoms traps already established could do it in a year. But I don't think the experiment would actually tell us anything interesting, because...
If you're using a room-temperature emitter, your photons will exhibit canonical EPR entanglement, while the emitter's momentum will look like white noise (uncorrelated with the photon states). If the emitter is a single atom with root-mean-squared momentum comparable to the emission recoil momentum, then the photon states will be correlated with the emitter's momentum, but the entanglement we ultimately measure will be degraded. Crucially, there will never be a situation where the momentum of the emitter depends on whether the photons have been measured yet. The reason for this is essentially laid out in post 7, although if you want I can explain it in more detail once I have some time to do detailed TeX formatting.
Hi Fednis, seems we got our wires crossed. In the paper I brought up the dual-slit experiment only to point out that a physically manifested wavefunction would not conserve momentum. The experiment I later propose was intended to determine whether or not the wavefunction is physically manifested through the search for torque on the polarizers of entangled photons in an EPR arrangement. The idea is that, given that torque would be expected from a photon with a known polarization angle as we measure it along another angle (and this is of course speculation), then we should be able to declare a pure state of the entangled photons prior to measurement if torque exists while measuring them. Alternatively, if the measurement act itself somehow causes a collapse of the wavefunction to bring the photons into pure states then we would not expect to see such torque. This is the specific experiment I'm asking about in regards to technical feasibility.
The issue you brought up about the laser emitter and the dual-slit experiment is a fascinating one, though, so please feel free to expand on it as well (if and when you get the time).
I guess now I'm confused again. Are you saying that you want to send EPR entangled photons through polarizers, and then look at the torque on the polarizers? Sending the photon through a polarizer is itself a measurement, so you wouldn't be looking at a "pure" state afterwards under any interpretation.