In the EPRB experiments, in the standard one-state vector quantum formalism, a polarization measurement on Alice's side changes the quantum state on both sides. So, from a formal point of view, Alice’s measurements cause instantaneous “collapses-at-a-distance” of Bob’s photon state, in apparent violation of relativistic causality (despite the impossibility to use this alleged relativistic causality violation to send information between space-like separated events).
Let’s go a little bit further. Actually, a polarization measurement on Alice’s side causes an irreversible record of information, hence a creation of entropy on her side (e.g. a loss of so-called irrelevant information). On the contrary, as far as Bob doesn’t perform any polarization measurement, Bob’s alleged photon’s state “collapse-at-a-distance” doesn’t give rise to any observable effect. Indeed, Bob’s photon “collapse-at-a-distance” doesn’t cause any entropy creation on his side...
...But an entropy creation would be necessary to get an observable record of this supposed phenomenon. From a positivist point of view, according to Occam’s razor, the absence of any observable effect of Bob’s photon collapse is enough to assert that this alleged objective Bob’s photon collapse doesn’t actually happen on Bob’s side when only Alice performs a polarization measurement on his side.
Nevertheless, such an answer may be considered doubtful. Indeed, the here above positivist answer needs adhering to a positivist interpretation of quantum state and quantum collapse (the ireversible quantum measurement process breaking the unitary quantum evolution of the quantum state. A process modeled by the projection of the quantum state on an eigenspace of the observable). Bohmian mechanics and its explicit non local effects, a more realist view of quantum physics than the standard quantum formalism, has proven to be a consistent mathematical model, compatible with observable quantum effects. So, the here above positivist assertion doesn’t and can’t discard the possibility of an objective, explicitly non local interpretation of the EPR effect, violating the relativistic causality at an interpretive level.
Let us dig a little bit more. Actually, in the one-state vector standard quantum formulation, there is a lack of information, a subtle hidden variable. This is the second state vector accounted for in the 2-state vector T-symmetric formulation. Actually, as Einstein had guessed, the one-state vector quantum formalism provides an incomplete description of the quantum state, hence an incomplete description of quantum phenomena. That lacking information is hidden in the future, cf. Can a future choice affect a past measurement’s outcome, §6 Summary, b).
The apparent instantaneous “collapse-at-a-distance” of Bob’s photon doesn’t show up in the more complete two-state vector formulation. Indeed, according to Each moment of time a new universe Aharonov, Cohen and Elitzur article, §5 EPR measurement, fig7, a measurement on Alice’s side causes a change of the two-state vector of her photon but no change of the two-state vector of Bob’s photon. There is even more to say about this absence of any real Bob’s photon collapse. Let us see why.
The article Each instant of time a new universe of Aharonov, Popescu and Tollaksen, presents:
- a T-symmetric formulation of the temporal “evolution” of a quantum system which does not evolve (H=0)
- a very important consequence predicted thanks to this formulation concerning the interpretation of the EPRB experiment.
This very interesting 8 pages article is quickly read and a video is presented by Popescu. Thanks to their 2-state vector T-symmetric formalism, Aharonov, Popescu and Tollaksen notably highlight the following facts:
as long as no quantum measurement is carried out on a given quantum system (undergoing a H=0 Hamiltonian evolution) the 2-time measurement O(t2) - O(t1) between instants t1 and t2 vanishes whatever the observable O. This proves the existence of a time correlation between successive states of a quantum system as long as it does not undergo any quantum measurement.
On the other hand, the correlation O(t2) - O(t1) = 0 is broken between instants t1 and t2 respectively preceding and following a quantum measurement of the considered system (except in the specific cases when the measurement result is an eigenstate of O).
Hence, concerning EPRB type experiments, this document indicates (§5 Measurements on EPR state):
- The break, on Alice's side, of the 2-time correlations between instants t1 and t2 preceding and following a quantum measurement by Alice. Indeed, except in a particular case when the measurement result is an eigenvalue of O, the 2-time correlation O(t2) - O(t1) = 0 is lost.
- The conservation, on Bob's side, of the 2-time correlations O(t2) - O(t1) = 0. This means that nothing changes on Bob’s side as long as he doesn’t make any measurements on his side.
Now, let us recall 2 hereunder EPR non-locality interpretations at stake:
- In a realist interpretation: the quantum state is assumed to be the model of an objective physical state (cf. On the reality of the quantum state) and the collapse of the wave packet is assumed to cause an instantaneous collapse-at distance, hence an instantaneous, non-local AND objective collapse also on Bob’s sides (cf. Bohm, Bell, Goldstein, Bricmont, Scarani, Valentini, Selleri, Percival, Towler, Hemmick, Aspect, Special Relativity and possible Lorentz violations consistently coexist in Aristotle space-time...)
- In a positivist interpretation: on the contrary, the instantaneous and "non-local collapse of the wave packet" is interpreted as an irreversible and local record, hence up to be read by an observer carrying out the measurement (cf. Peres, Fuchs, Rovelli, Jaynes §The Bell inequalities (1)...) without any objective change of Bob's photons state when only Alice performs polarization measurements on her photons.
When only Alice carries out measurements on her side, the prediction of the conservation of the 2-time correlation on Bob's side decides in favor of the positivist interpretation of the EPR effect. This interpretation thus becomes a falsifiable physical assertion instead of a pure philosophical question.
So, such an experimental verification seems solving a 40 years debate between positivist and realist interpretations of Bell's inequalities violation. Hence, this experimental validation seems deserving to be carried out if it has not already been done. I don’t know if this verification has been performed. That’s why I have asked that question on physics stack exchange today.
An additional remark
Now, there is an additional remark I think useful adding to the here above answer. It concerns the EPR non-locality interpretation by Aharonov, Cohen and Elitzur. Despite my using of their 2-time correlation conservation to prove the validity of the positivist interpretation of EPR non locality (when no measurements are performed on Bob’s side) it’s important to note that these authors are, on the contrary, committed to a realist (e.g. observer independent) interpretation of physics.
In particular, they are committed to an observer independent interpretation of causal relations. They interpret the correlation between strong and weak measurements, for instance, as causal from strong measurements to weak ones independently of their time ordering. Hence, the correlation between weak and strong measurements is considered by these authors as causal when weak measurements are performed after strong measurements and retrocausal when weak measurements are performed before strong measurements.
There is no inconsistency there. Indeed, if the statistical thermodynamic grid of reading of the macroscopic observer is considered as irrelevant contrary to a positivist interpretation (cf. Incomplete descriptions and relevant entropies, Balian, 1999) then the irreversible flow of time is interpreted as an illusion as proposed by Einstein (2) or by Thibault Damour (3) for instance (due to their realist interpretation of physics aim).
Consequently, for Aharonov, Cohen, Elitzur, Vaidman and physicists committed to their school of thought, there is no reason to ascribe a causal character to time-symmetric correlations only in a direction consistent with the causality principle. Indeed, due to their observer independent interpretation of physics, this time-asymmetric principle and the irreversible flow of time disappear. They are considered as pure illusions as any other time-asymmetric effects (noteworthy tracks of the past and classification of events as past or future events, cf. The arrow of time issue, an overview, Chaverondier, April 2024)…
…as well, nevertheless, in my positivist opinion, as any physics properties. Indeed, physics properties are encoded as information recorded in tracks of the past, and these tracks exist thanks to the macroscopic observer's grid of reading. That’s why the retrocausal interpretation of the correlation between strong measurements and previous weak measurements for instance is, in my opinion, an unnecessary additional assumption to their outstanding studies and experimental verifications.
(1) Note, however, that E.T. Jaynes supports a realist interpretation of physics and its role despite, paradoxically, his insistence on the importance of Bayesian inference and the broad development he gave to this approach (cf. Maxent)
(2) Time’s arrow: Albert Einstein’s letters to Michele Besso
For people like us who believe in physics, the separation between past, present and future has only the importance of an admittedly tenacious illusion.
(3) Proust and Einstein: In Search of Time
Thibault Damour, Permanent Professor at the Institut des Hautes Études Scientifiques, delves on the experience of Time through the work of Marcel Proust “À la recherche du temps perdu” and Albert Einstein… Both the novelist and the physicist held the view that the flow of time is an illusion.
