It has been debated whether quantum mechanics and special relativity are compatible and whether there is a preferred Lorentz frame if they are incompatible. Bell’s theorem is an important cornerstone, but it does not give us a definite answer due to the existence of supplementary assumptions or theoretical loopholes; there are unitary quantum theories which evade Bell’s theorem.
In recent years, there has been stimulating discussion about superobservers, which might help settle the important issue of whether unitary quantum theories are compatible with special relativity. This online workshop aims to highlight the existing debates and address the controversies.
Workshop Date: Thursday, August 1, 2019 to Sunday, September 1, 2019
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Quantum theory is incompatible with relativity: A proof beyond Bell's theorem
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July 28, 2019 at 10:56 am #5512
It has been debated whether quantum mechanics and special relativity are incompatible and whether there is a preferred Lorentz frame if they are incompatible. Bell’s theorem is an important cornerstone, but it does not give us a definite positive answer due to the existence of supplementary assumptions or theoretical loopholes; there are unitary quantum theories which evade Bell’s theorem and claim that they are compatible with special relativity.
In this paper, I address the important issue of whether unitary quantum theories are compatible with special relativity. I propose a new Gedankenexperiment, a variant of the EPR-Bohm experiment with a superobserver who can undo a measurement. In this experiment, there is a stronger correlation (between the results of two spacelike separated measurements) than the correlation investigated in Bell’s theorem. Based on an analysis of the correlations in different Lorentz frames, I prove that unitary single-world theories are incompatible with special relativity, and in order to avoid the incompatibility, there must exist a preferred Lorentz frame in these theories. Moreover, I argue that the incompatibility proof also applies to a proper version of the many-worlds interpretation of quantum mechanics. This closes the major theoretical loopholes of Bell’s theorem, including relationalism, retrocausality, and superdeterminism.
Finally, I argue that the stronger correlation found in the Gedankenexperiment cannot be explained by retrocausal processes or even the common causes in the past, but only be explained by nonlocal processes or actions at a distance. This provides a test of unitary quantum theories, as well as a further support for the new incompatibility proof beyond Bell’s theorem.
Comments are welcome!August 3, 2019 at 5:09 pm #5555
I’ve started looking at this interesting paper, but I do have to note that there is an exception to the general observation that ‘Collapse theories single out a preferred frame’. The Transactional Interpretation is a collapse theory, but it does not single out a preferred frame. This is made explicit in its relativistic development, RTI, where the collapse occurs with respect to an invariant spacetime interval between emitter and absorber. RTI is fully consistent with relativity.
(There may be other relativistically compatible collapse theories, such as ‘rGRWf’, but as far as I know, they involve ad hoc changes to the Schrodinger dynamics, which is not the case for RTI.)August 4, 2019 at 2:17 am #5558
Thanks for your interesting comments! In my paper, I said:
“In collapse theories, the collapse of the wave function is simultaneous in different regions of space in a preferred Lorentz frame.”
I think this is correct. Otherwise, if the collapses of the wave function in different regions of space are not space-like seperated in any frame, then the theory cannot explain the violation of Bell’s inequalities.
Can RTI explain the violation of Bell’s inequalities without space-like seperated collapses?
ShanAugust 5, 2019 at 12:27 am #5563
Again, collapse in TI for any detected quantum is associated with both emission and absorption of that quantum–two events for each detected quantum, not one. This is an important difference bewteen TI and other collapse theories, which view collapse as singling out a particular time index. That is not the case in TI. In TI, collapse establishes an invariant spacetime interval. Of course, absorption events for two entangled quanta can certainly be spacelike separated in RTI, and their entanglement will enforce the correlations, thus violating Bell’s inequality. It’s just that the collapse itself, for any individual quantum, occurs along the invariant spacetime interval between the emitter and absorber of that quantum. So the crucial new idea here is that in TI, ‘collapse’ is not equal to ‘event’. RTI is fully relativistic and Lorentz-covariant and also consistent with observed violations of Bell’s inequality, since it is empirically equivalent to standard QM.August 5, 2019 at 2:20 am #5571
I think the issue is not really related to the detials. Consider a particle is in a superposition of two well-separated boxes. When one measures the particle in one box, then the whole superposition collapses to the state in one of the two boxes. Now if the collapses of the superposition in the two boxes are not space-like seperated in any frame, then the theory cannot explain the violation of Bell’s inequalities in this case; the results of two spacelike measurements on the particle in the two boxes will not be correlated.August 5, 2019 at 3:50 am #5573
Yes, I think the definition of ‘collapse’–what collapse means physically–does matter for the issue of concern to you. In this latest post you seem to be talking about a single quantum, not an entangled state, right? Bell’s inequality concerns correlations between entangled particles.
In any case, for this single-particle measurement, the detection and non-detection in the two boxes available to the particle can of course be spacelike separated, but that does not mean that collapse itself occurs along that spacelike interval. It doesn’t, because collapse involves not just the usual retarded state from the emitter, but also the advanced absorber responses. This is what allows TI to avoid the usual ‘instantaneous collapse of the wave function.’
The collapse for a single particle establishes the invariant spacetime interval between the emitter and the absorber/detector of the box found to contain the particle. The other box without the particle is a ‘null event’ or null measurement. Again, the two boxes–constituting the two events, the detection and the non-detection, may be spacelike separated, but the collapse–which is the actualization of the transaction–still occurs along the invariant interval between the emitter and the box/absorber that detects the particle. So in TI there is an important distinction, not present in the usual collapse theories, between the two box outcome events (although for a single quantum, one is a non-event) and the collapse itself, which involves more than just those two events–i.e., it involves the emitter, the retarded state, and the advanced state(s) from the absorber(s). It involves the choice of projection operators |k><k| where each k labels a particle going from the emitter to a particular ‘box’. Nothing about this selects a preferred frame. That is, the collapse in TI does not define a time order for the two events, which of course have no invariant time order, nor do they need to be considered ‘simultaneous.’
Concerning an EPR-type experiment with entangled particles: Remember that TI is a time-symmetric theory and
Cramer discussed, in his original 1986 paper, how EPR-type correlations can be accounted for through light-like or time-like’zig-zags’ between spacelike separated events, back and forth, by way of the emitter. Though I interpret the transactional process differently (not a literal ‘zig-zag,’but rather the emergence of new spacetime inteverals),the same basic idea holds: collapse is along timelike or lightlike intervals, not the spacelike intervals between the detection events, even though spacelike-separated events can be established through the transactions available to quanta in an entangled state. This is very clear from the original 1986 paper. Again, the key difference in collapse between the usual collapse theories (which involve only the usual retarded quantum state modified by some ad hoc time-indexed collapse) and TI is the time-symmetry of the basic transactional process, which involves not just the usual quantum state |k> (an ‘offer wave’ in TI), but also the advanced response or confirmation <k| . RTI is definitely relativistically covariant, since it is based on the Davies relativistic direct-action theory. As Davies shows, this theory is empirically equivalent to standard relativistic quantum field theory regarding any probabilistic predictions, so it also predicts the usual violations of Bell’s inequality.
However, if your main concern is basic quantum nonlocality–e.g., a momentum eigenstate is a nonlocal entity–then of course there is the usual tension between QM and relativity. But the key point is that collapse in RTI is not tied to any single time index, since it is a binary process between emitters and absorbers. So no frame is singled out as a preferred frame. (And of course if one gives up the idea that quantum states are spacetime objects, which mathematically they can’t be anyway for entangled states, then relativity can be understood as applying at the level of spacetime events emergent from ‘collapse’, and then there is no conflict between QM and relativity.)August 5, 2019 at 8:13 am #5574
Thanks, Ruth! I will need to undertand your idea more deeply.
Here is what I thought. Suppose ALice measures the particle in box 1, and then Bob meqasures the particle in box 2. These two measurements are spacelike and almost simutaneous. Then, when Alice have dectected the particle in box 1, the superpostion should collapse also in the remote box 2, otherwiese the Born rule will be violated; it will predict that Bob has a nonzero probability to detect the particle in box 2.
I still cannot see how a collapse theory can explain this process without assuming the collapse happens faster than light in a frame.August 5, 2019 at 6:20 pm #5576
Thanks Shan for this question. If the measurement events are spacelike separated, then according to relativity, there is no invariant time order for the two events. That is, it’s not possible to consider them simultaneous in any invariant sense–that would pick out a preferred frame, and relativity doesn’t allow that. For an observer heading toward Alice, Alice’s measurement will occur first; for an observer heading toward Bob, Bob’s measurement will occur first. So there is no temporal matter of fact about ‘when’ Alice detects her particle with respect to Bob’s measurement. For these spacelike separated detections, there is no observation that could violate the Born Rule. All that Alice and Bob will see is that, for an ensemble of particles prepared in a superposition of boxes, they will each detect the particle half the time. There is no way for Alice and Bob to check with their spacelike-separated counterpart on any individual particle–ie., no way for Alice to check that when she detected, say particle #25, that Bob did not get that particle, because in order to do that, the two would have to exchange classical information faster than light. So the Born Rule will never be violated for any individual instance. The Born Rule is essentially hidden from ‘checking’ for spacelike-separated detections.
I think the subtle point here is that collapse is not a spacetime process. It is not something that occurs ‘in spacetime.’ Perhaps that is what is bothering you–it is indeed a nonlocal process, but that’s because wavefunctions themselves are nonlocal: clearly a single particle cannot ‘really’ be heading in spacetime both to Alice and to Bob, since there is only one particle! These imagined trajectories are only possibilities, they are not real spacetime trajectories of any actual particle. Since the wavefunction components corresponding to ‘heading to Alice’ and ‘heading to Bob’ are not real spacetime trajectories, we can’t think of collapse as something ‘happening in spacetime’ either. So collapse cannot really be associated with any actual spacetime frame or any actual spacetime process. Of course, if one is only working with a nonrelativistic limit, which is the usual retarded quantum wavefunction, then one has already lost Lorentz covariance since that wavefunction itself picks out a preferred frame! This is why one needs RTI, which does not pick out any particular time index as preferred (since it treats measurement in the Heisenberg picture and observables can be covariantly defined wrt a proper time). This is discussed in my latest book “Adventures in Quantumland,” Chapter 3.
Another thing to note about RTI is that it has a growing ‘causal set’ structure, with new spacetime intervals added through actualized transactions. Sorkin et al have shown that such causal sets preserve Lorentz covariance if the new events are added in a Poissonian manner. This is precisely the case for RTI, since ‘measurement’ (collapse) rates corresponds to emission/decay rates, which are Poissonian.
Besides, RTI, I think there is a version of GRW, called rGRWf, that preserves covariance. But again I’m not a fan of that, since it has the ad hoc changes to the Schrodinger evolution, and it also involves some degree of time-symmetry (which is inevitable if one is going to accommodate relativity), so if one is going to embrace time-symmetry, one might as well just go with RTI that doesn’t have to make those ad hoc changes.August 6, 2019 at 3:43 am #5578
You said “no way for Alice to check that when she detected, say particle #25, that Bob did not get that particle, because in order to do that, the two would have to exchange classical information faster than light.”
Yes, you are correct. But this is not necessary to verify the anti-correlation. They just need to record the results, and then compare them later. But a collapse theory must be able to explain the anti-correlation between the results of the two spacelike separated measurements.
As I argued in my last post, this explanation requires that the collapse should happen faster than light at least in one frame.August 6, 2019 at 8:27 pm #5583
But the existence of the observed correlation does not compel the idea that there is some sort of collapse signal that ‘travels faster than light.’ You might be supposing that such a ‘collapse signal’ is needed to enforce the correlation, but that is not the case in TI, where the correlation is enforced through the combination of the quantum state (retarded offer wave) and the advanced confirmations from the detectors. The interaction of the OW and CWs sets up projection operators 1/2 |kA><kA| and 1/2 |kB><kB| for the photon momentum components corresponding to Alice and Bob, respectively. At this point there is of course still a form of nonlocality, as I mentioned previously, since one photon cannot really go to both boxes, and it is not in fact proceeding in spacetime to both the boxes. There are no real spacetime trajectories from the photon’s source and both boxes; these are just possibilities. The ‘collapse’ is not any signal in spacetime but is simply the actualization of only one of these, since only one can occur in spacetime. One can think of the choice as taking place at the emitter, which has the choice of which absorber to emit the real photon to. That’s all that happens–a choice of photon momentum for actualization–so there is no need for any additional enforcement through any ‘collapse signal’ sent between Alice and Bob’s detectors. The correlation is enforced through the two incipient transactions that are set up, as dictated by the prepared state and the advanced responses, neither of which choose any particular frame. Since the incipient transactions (for each momentum component) can’t both happen, only one can be actualized (with the appropriate probability as given by the Born Rule). The emitter, in choosing where to send the photon–or the photon itself (however one wants to view the locus of the ‘choice’), does not care about the time order of the Alice and Bob’s measurements. And this is as it should be.
I think you have a certain concept of ‘collapse’ in mind, arising from standard one-vector approaches (which as noted above are noncovariant anyway) that you want to impose on the TI picture, but it is not part of the model. If it were, one would be able to point to ‘the preferred frame’ allegedly singled out by a measurement like this, but in TI there simply isn’t one. In TI the Born probabilities are enforced through the combination of the prepared state and the advanced responses from detectors. This sets up two incipient transactions, represented by projection operators as above, only one of which can be actualized. Nothing about the process requires that a ‘collapse signal’ or similar influence be sent from Alice’s detector to Bob’s detector or vice versa, or at infinite speed if they were ‘simultaneous’ (which would define a time order that is not permitted in relativity). It’s simply not necessary, and it doesn’t happen. RTI has no need of any time order or simultaneity to enforce the correlations. It is completely covariant and does not impose any preferred Lorentz frame. I should also note that Tumulka has devised a relativistic version of the GRW ‘spontaneous collapse’ model with no preferred frame (https://arxiv.org/pdf/quant-ph/0602208.pdf), although his model is approximate to a high degree of accuracy (in contrast to RTI which is exact). So one really cannot generalize that all collapse models require preferred frames. (Tumulka then draws a conclusion based on ‘currently available models’ that doesn’t take into account TI, which is a counterexample to his conclusion–but that’s a separate issue 😉August 7, 2019 at 5:15 am #5586
Ok, Ruth. I see. Then RTI is not really the usual collapse theory such as the GRW model for one-vector. So, in RTI, there is no real dynamical collapse of the wave function. Then my analysis of collapse theories does not apply to RTI.
Now I think my analysis of unitary quantum theories will apply to RTI. See my paper section about the retro-causal theories. I guess Ken worried about this.August 7, 2019 at 12:50 pm #5587
I’m afraid this is not the correct conclusion. While RTI is certainly not the usual ad hoc collapse theory, it certainly is a non-unitary objective reduction theory (see below). So it cannot be subject to your argument concerning unitary-only theories. There is real dynamical reduction in TI–it just does not take the form that you’ve assumed regarding ‘wave function collapse’. It is not the picture you have in mind of ‘collapse of a non-invariant wavefunction’ somehow traveling in spacetime, because reduction does not occur with respect to such an object. TI has a form of objective reduction — actualization of one outcome out of many — that does not involve collapse of a non-invariant wave function. This is due to the advanced responses from absorbers, which give the emitter all the information it needs to ‘choose’ one out of several responding absorbers for receipt of the transferred quantum. Since it does choose (in accordance with the Born probabilities), there is reduction, but it is not through ‘collapse of a single non-invariant wavefunction’ as you seem to be assuming in your analysis.
One thing to note is that in your argument above for superluminal collapse communication, it appears that you tacitly assumed that Alice or Bob’s measurement ‘really’ comes first and that such a signal has to be sent to make sure that the second measurement correctly reflects a posterior probability of zero for detection, ‘after’ it has been detected elsewhere. But that formulation doesn’t work, because the argument itself assumes a preferred frame, so the argument itself violates Lorentz covariance. Or, if it doesn’t assume that one or the other ‘really’ comes first, it is just the usual observation that collapse has to be simultaneous in a frame, but that applies only to single-wavefunction formulations, not TI. As I mentioned before, the Born rule could not really be empirically violated at the level of individual pairs, because neither Alice nor Bob could check the ‘posterior Born probability’ for any individual particle. precisely because they are spacelike separated. The availability after-the-fact of a list of detections is of no use for testing the Born Rule in any individual case (i.e. making sure that when Alice received particle #25, Bob had a ‘posterior Born probability’ of zero for detecting it). Such an after-the-fact list tests nothing except the statistical correspondence between the Born rule and the prepared superposition of the ensemble of particles. So I don’t think this argument establishes the claim you want to make. Of course, in theories with ‘instantaneous collapse,’ a preferred frame is picked out by the definition of simultaneity. But that’s a different matter, and RTI does not do that.
I would respectfully suggest re-evaluating the either/or categories you seem to have set up concerning what the available sorts of analyses and conclusions are possible. You’ve set up a dilemma here that purports to condemn ALL quantum interpretations as allegedly violating Lorentz invariance:
(1) Either a theory is an ‘objective collapse’ theory that you assume must have a faster-than-light collapse in some frame, therefore violating Lorentz invariance; or
(2) A theory is unitary-only and subject to your analysis of unitary-only theories as also violating Lorentz invariance.
I have to note that it’s rather serious to charge that a theory violates Lorentz invariance when it manifestly does not. RTI is fully relativistic and fully Lorentz covariant. This is quite clear from the fact that it is based on a quantum relativistic treatment by Davies:
Davies, P. (1971).”Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain I. Scattering Processes,” J. Phys. A: Gen. Phys. 6, 836.
Davies, P. (1972).”Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain II. Emission Processes,” J. Phys. A: Gen. Phys. 5, 1025-
(Davies notes that the theory has intrinsic non-unitarity, although at the time of writing these papers he found that perplexing since the transactional picture had not been proposed yet.)
It would be completely inaccurate to characterize the transactional picture as unitary-only, since it is quite clear that under TI (RTI) only one outcome is actualized (https://www.ijqf.org/archives/4871), and as noted above, Davies shows that the quantum relativistic direect-action theory has non-unitarity. So RTI is simply not a unitary-only theory by any stretch of the imagination. There are no ‘super-observers’ or ‘superobservables’ under TI. The paper I’ve posted in another topic regarding the FR paradox notes that under TI such ‘absurd’ macroscopic superpositions never arise.
So what I”m pointing out is that (1) does not apply to RTI, even though TI certainly does have objective reduction (nor may (1) apply to rGRWf or Penrose & Hameroff’s gravitational OR) and that it is needed to consider more carefully what sorts of assumptions go into your assumption (1). It is simply not as universal as you claim.August 7, 2019 at 4:19 pm #5589
Dear Ruth, I would like to add a comment concerning the role of preferred frames in a quantum ontology and in connection with retrocausality. It is indeed possible to develope Bohmian like model without preferred frames. There is one recent approach by Sutherland but I also recently proposed a different one [https://arxiv.org/abs/1904.08134] where backward in time motion plays a role and where preferred frames are not anymore problematic. May be a topic on that will be interesting.August 7, 2019 at 7:01 pm #5592
Thanks Aurelien, I am indeed aware of the Sutherland model and you are correct that it is covariant, except perhaps for the final boundary condition which has to be defined in a particular frame (but it’s a matter of debate as to whether that ‘really’ fixes a preferred frame). Other than the final B.C., the model preserves full Lorentz covariance.
So, as I’ve attempted to make clear here, it’s a problematic overgeneralization to claim that all QM interpretations or models (both non-unitary and unitary) must violate Lorentz invariance. Sutherland’s approach is a counterexample (modulo the final BC perhaps), although it’s not my personally preferred option since it invokes hidden variables that I don’t think we need. RTI is also a clear counterexample, since it comes right out of a relativistic quantum theory and does not require any preferred frame. Of course, there are certain tensions between QM and relativity since QM forces a larger space than 3+1 spacetime (i.e. we have to deal with a complex Hilbert space rather than a 3+1 real space). That’s a legitimate concern, but it does not lead to a necessary conclusion that any QM model or interpretation must violate Lorentz covariance (since that’s simply not the case, as shown by the counterexamples). So an argument purporting to imply such a conclusion involves premises that need critical re-examination.
I approach the puzzle of the tension between QM & relativity by allowing that QM describes pre-spatiotemporal possibilities, but under RTI, any ‘collapse’ is the promotion of one of those possibilities to an actuality, where the actuality corresponds not just to a single event but to an invariant spacetime interval. So no frame is singled out by the actualization resulting in the invariant interval. Other counterexamples are ‘rGRWf’ (although it is not exact but a close approximation to standard QM) and the Penrose gravitational collapse theory, as far as I know. So it’s just not tenable to claim that all QM interpretations or models violate Lorentz covariance. Thanks again for your important comment.August 8, 2019 at 1:56 am #5593
Thanks, Ruth! I will need more time to understand your RTI. As far as I see, your RTI does not assume a real collapse of the real wave fucntions. Maybe in RTI the wave function is not ontic?August 8, 2019 at 7:28 am #5596
Dear Ruth, thank you for answering. I agree that an approach like the one of Sutherland requires two boundaries (one in the past and the other in the future) and that the foliation needed is arbitrary. However, the choice could have a cosmological meaning breaking the symmetry. Anyway, I think that this is the same for all retrocausal intepretations including TI. In the TI or in Costa de Beauregard interpretation wave functions also require foliations so that the problem is here aswell. This very clear in the interpretation of Aharonov and Gruss which is a form of TI where two states and thus two boundaries are needed. By the way you say that you dont want hidden variables but you include a sub-empirical level whihc is hidden so what is the difference?August 9, 2019 at 3:48 pm #5614
Thanks Shan. In RTI the quantum state |Psi> is fully ontic. But the advanced state <Psi| is also fully ontic, so RTI is a different animal from the usual ‘quantum interpretation.’ This is why it is not subject to the dilemma you pose. It has real ontic collapse, but the collapse is not with respect to just a forward-propagating quantum state. In RTI, the collapse occurs with respect to a set of projection operators, not with respect to some preferred time index, and this is what makes the collapse Lorentz covariant. As I noted, of course this set of projection operators, as objectively real possibilities for outcomes, cannot all be entities ‘in spacetime’–that’s why I interpret quantum theory as requiring a new ontological category of possibility. So the collapse is the process of emergence of a new spacetime interval. But because it is a new interval, it is a Lorentz-invariant object.
I’m well aware (wrote about this in my 2012 book) that the usual concept of collapse, which conventionally applies only to the forward-propagating state, is ‘instantaneous’ and therefore not Lorentz-covariant. But that has nothing to do with RTI, in which collapse is a choice among invariant spacetime intervals, and does not require or impose any notion of simultaneity. Again, this is because collapse in RTI is a binary process–involving both the emitter and potential absorber(s), and the collapse is a competition among Lorentz-invariant projection operators. It’s Lorentz-invariant because it can be defined in terms of a proper time in the Heisenberg picture of the operator being measured, so that the time index attaches to the operator as a proper time, not to the quantum state as a time coordinate of some preferred inertial frame.
It may be still be a matter of debate as to whether hidden-variable theories such as the deB-Bohm model and time-symmetric HV survive both your argument and the Frauchiger-Renner paradox. But RTI certainly is immune to these. And it is fully ontic.
I think what you have shown is that most (if not all, if the HV models run afoul of FR) the conventional approaches fail to reconcile QM with relativity. But RTI breaks out of that mold because it is based on the direct-action (absorber) theory. That’s why it works, although many don’t want to consider it because there tends to be a stigma attached to absorber theory based on its alleged abandonment by Wheeler and Feynman, even though there is nothing wrong with it and Wheeler went back to championing it in 2003 (see reference in my 2018 paper with Cramer, in this journal). WF originally left absorber theory because they were trying to eliminate all self-action, but that turned out to be needed for such things as the Lamb shift. So it didn’t satisfy a particular motivation they had for developing it, but that has nothing to do with its efficacy wrt interpretive challenges in quantum theory.
Thanks again for the discussion.August 9, 2019 at 4:00 pm #5615
Dear Aurelien, RTI does not require any preferred foliation; it does not require any future boundary condition. It is not a hidden variable approach nor does it rely on a notion that measurement outcomes are ‘already there’ in the future–i.e. it is not a block world ontology. I understand that the original TI may have seemed to imply that, but the relativistic development does not impose any future B.C. nor does it depend on a de Beauregard ‘zig-zag’ invisioned as occurring ‘within spacetime’. See my most recent reply to Shan for some discussion of the possibilist ontology. “Collapse” in RTI is actualization of a single invariant spacetime interval from a set of non-spatiotemporal set of possibilities, represented by weighted projection operators (the weights being Born Rule probabilities). The conceptual issues are discussed in my recent books “Understanding Our Unseen Reality” and “Adventures in Quantumland.”
RuthAugust 10, 2019 at 2:10 am #5616
Thanks, Ruth. So, the collapse is not the superposition psi1 + psi2 randomly becomes psi1 or psi2 for the forward-propagating state or the the backward-propagating state?August 10, 2019 at 12:00 pm #5619
Dear Ruth, thanks a lot . Still I don’t think that you are completely right : your view is like the one of Heisenberg for the passage from the potential to the actual and when you wrote ” “Collapse” in RTI is actualization of a single invariant spacetime interval from a set of non-spatiotemporal set of possibilities, represented by weighted projection operators (the weights being Born Rule probabilities).” that is also the way of thinking of Costa de Beauregard. All the machinery you use is only a way do deal with quantum causality even if following Bohr this is a more illusion.
For me your sub empirical level is like a hidden variable in disguise. In your neo-copenhagen ontology only detections events have a physical objective meaning so why do you want to introduce a mathematical formalism with offer and confirmation waves if you dont believe in some way in the possibility to describe this sub-empirical level?
A last point : a offer wave require a boundary into the past and a confirmation a boundary into the future or at least in the present. Every thing in between is hidden but you need any way two boundaries.August 13, 2019 at 7:53 pm #5625
To Shan: That is correct. The collapse occurs with respect to projection operators (outer products), not with respect to kets. That is, from absorber response to each component we get two weighted projection operators:|Psi1><Psi1| and |Psi2><Psi2|, where each is weighted by the Born Rule based on the prepared state. So if the prepared state was |Y>, then the two incipient transactions are |<Psi1|Y>|^2 |Psi1><Psi1| + |<Psi2|Y>|^2 |Psi2><Psi2|.August 13, 2019 at 8:03 pm #5626
Reply to Aurelien: No, RTI has emphatically nothing to do with Bohr or the Copenhagen interpretation, which I criticize and reject here:https://arxiv.org/abs/1601.07545
If you read my publications, you will find that I assign objective physical reality to quantum states and the advanced states. You seem to be implicitly assuming that for something to have objective reality, it must be a spacetime object, but that is exactly what I am questioning. For specifics on this point, see: https://www.sciencenews.org/blog/context/quantum-mysteries-dissolve-if-possibilities-are-realities
The sub-empirical level is implicitly part of standard quantum theory since, e.g., a quantum state for 2 or more entangled particles is a Hilbert space object, not a spacetime object. In my approach we just take seriously the fact that Hilbert space objects have the wrong mathematical structure to fit into 3+1 spacetime and we allow that they describe sub-empirical possibilities that are physically real. There are no hidden variables in RTI; nothing at all is added to the theory. The only change is that the fields propagate as in the direct-action theory.
Costa de Beauregard had a particular metaphysical view involving a ‘zig-zag in spacetime’ which is not part of RTI, even though Cramer used that concept at times; it has been completely superceded in RTI. Measurement outcomes really are uncertain in RTI and it has a growing universe ontology that is completely compatible with relativity, as I show in my publications wrt Sorkin’s covariant causal set theory.August 14, 2019 at 1:35 am #5627
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