Quantum Measurement Cannot Be a Local Physical Process

According to quantum mechanics, the outcome of an experiment exists rela-tive to an Experimenter who performs a measurement on the system under study. Witnessing the outcome of an experience requires the measurement on a physical system whose size must match the complexity of the Experimenter’s observation. We argue that such a physical system must have a certain space-time extension so that it can encode the rich and complex data embedded in the witnessed experience. The complementarity principle in quantum mechanics leads us to conjecture that the observable events constituting an experience have space-like separation with each other. This seems to be in contradiction with our perceived locality of physical laws, and encourages us to think that the act of measurement is not a physical process, in the sense that a measurement outcome witnessed by an Experimenter is not necessarily related to the physical description of the Experimenter observed from the outside.

for the whole universe [4] [5]. In other words, the result observed by an actor becomes a universal truth for any other observer. With such an assumption, all observers are equivalent and there is indeed no need to precise who is performing a given measurement on which system.
In most practical cases this approximation does not cause an issue. However any observer, regardless of its size, remains a finite physical system and its evolution, seen from the outside by another observer, should be continuous and linear. This is in contradiction with the discontinuous evolution experienced by the inner observer, and this paradox has been captured in particular in the Wigner's friend paradox [6] and more recently in an extended version of it [7].
This paradox tells us that in quantum theory it is fundamentally important to specify precisely who is the observer and which physical system is being observed [6]. Surprisingly, at least in the author's knowledge, there is little discussion in the literature about what constitutes exactly the physical system being observed by a given observer. This could be explained by the above implied assumption that all observers are equivalent in the mainstream acceptation of quantum mechanics.
The goal of the present paper is to examine what constitutes the physical system being observed by the Experimenter and to discuss its characteristics. We assert that the outcome witnessed by an Experimenter is in general sufficiently complex so that it requires a set of observable events with a certain extension in space-time. In order to access these information, the observer therefore needs to perform a measurement on observables that are separated in space-time with each other. Quantum measurement theory does not specify how such a joint measurement is done, which observables are measured, or whether there is a constraint on the space-time extension of the system being measured. In particular, can we say something about the choice of the observables that are part of the measured system, and the nature of the space-time separation between these observables?
We find that quantum mechanics complementarity principle [8] strongly suggests that these observables must have space-like separation. However, quantum mechanics does not tell whether there is a limitation on the distance between these observables, as long as they are space-like separated. This result is at odds with our intuition. How can a unified experience result from measurement of systems which are space-like separated?
It is also in contradiction with the locality principle, which states that one cannot convey information at a speed faster than light. Indeed, if I could observe the present state of a physical system located very far away, I could act on that information and violate the locality principle.
We propose few alternatives that could solve this contradiction, but we also argue that there might not be such a contradiction to start with. Even if an Experimenter has a subjective experience of what is happening at light-years distance now, as long as his actions seen from the outside does not betray this experience, we argue that physical locality is not violated. And seen from the Journal of Quantum Information Science outside, the behaviour of the Experimenter can be fully explained by physical laws without involving the subjective experience witnessed by the Experimenter.
These arguments lead us to accept that the observation made by an Experimenter is a subjective concept, enjoying a certain independence from the physical support containing the information, and the physical reaction of the Experimenter following the observation.

An Observation Cannot Be Limited to a Measurement at a Single Point in Space Time
Whenever we observe the outcome of an experiment, our experience is never limited to the single experimental quantities we were proposing to measure. Instead, our experience encodes all the contexts accompanying the experiment, such as the experimental setup, the preparation of the initial state, the state of the environment, etc. All these information constitute a unified experience which cannot be decomposed into smaller independent experiences. Because of its complexity, the information embedded in this experience cannot be encoded into a single point in space-time but requires a physical system with a certain extension in space-time to encode it. Let's take an example. Suppose that an Experimenter wants to determine whether a photon impinges a given photo-detection unit. The outcome of such experiment would usually have a simple structure as a "true" or "false" statement. However, this description is an oversimplification corresponding to a restricted view of what the Experimenter actually witnesses as we are completely ignoring the output of any other measurement devices that could be present, or the eventuality that the photo-detector explodes for instance (in which case does this count as "true" or "false"?).
Finally the information "true" or "false" by itself is meaningless without context.
It is only given the context of the experimental setup, for instance the placement of the different experimental instruments and the preparation of the initial state, that the outcome "true" or "false" has a meaning. As such, the context of the experiment should be part of the experiment outcome [9]. The context is usually omitted from the experimental result as it is considered to be an unmovable assumption, but this is a questionable assumption: in theory, the context of the experiment is encoded in a physical medium, and it can itself evolve as the experiment unfolds [10].
The purpose of this paper is not to discuss how the output of an experiment should be encoded and why. What we want to stress on here is that the information returned by observing the outcome of an experiment has a complex structure, which cannot be encoded in a single elementary physical system: Conjecture 1. Describing the outcome of an experiment requires a data structure which encodes everything witnessed by the Experimenter. This entails a data structure which cannot be encoded in an elementary physical system such as an elementary particle.
It seems therefore very unlikely that the full outcome of an experiment can Journal of Quantum Information Science be encoded into a physical system that is located at a single point in space-time. Albeit not proven, it is far more intuitive to assume that the encoding of the outcome of an experiment requires a physical system that has a non-zero extension in space-time: Definition 1. We call an observable event a physical observable quantity at a given space time coordinate ( ) , t x in a given reference frame. Conjecture 2. Observing the outcome of an experiment requires the measurement of a physical system that has a non-zero extension in space-time, such as a set of elementary observable events which have a non-zero space-time separation between themselves.
For instance, we could imagine that the information obtained by the Experimenter could be encoded in the spin of a series of electrons 1, 2, although such representation is unlikely to be the actual one.

An Observation Is Equivalent to a Measurement of Observable Events that Have Space-Like Separation
Observation of the outcome of a real experiment implies a measurement of observable events that are separated from each other. Can we say more about the nature of this separation?
At first we are tempted to think that these observable events are "linked" with each other by physical mean, for instance by the exchange of elementary particles, so that the set of observable events presents somehow a "coherent and unified" view of the experiment's outcome. This would imply in particular that these observable events are time-like separated with each other (we recall that events However, the properties of quantum measurement, and in particular, the complementary principle, imply on the contrary that these observable events should be separated so that no physical interaction is possible between them. To see this, suppose that we have an experimental outcome whose observation requires the measurement of two observable systems A and B. Suppose that we want to observe the state of these systems at space-time events ( ) To see this, suppose that the systems A and B are two qubits, and that A is prepared in the state ψ which is chosen randomly between the states of an orthonormal basis { } 0 , 1 or the states of the conjugate basis ( ) ( ) The complementarity principle tells that no measurement is possible that allows H. Inamori Journal of Quantum Information Science In such a description, we would introduce two ancillary quantum systems A' and B' which come into interaction with the systems A and B at space-time location   being separated space-like, as this would ensure that no physical medium can link the observed events. We therefore propose that: Conjecture 3. The observation of an experiment outcome is equivalent to a measurement of space-like separated observable events.

Is Measurement a Local Physical Process?
The observation witnessed by an Experimenter is the outcome of measurement made on observable events that are space-like separated. If there is no limitation on the extent of this separation, there is no theoretical reason why an Experimenter could not witness very remote observable events such as an event on Earth and an event on a distant star light-years away, as long as these events have space-like separation. This is of course at odds with our daily experience, and our intuition tells us that such observation would be in contradiction with the locality principle.
To circumvent this apparent contradiction, we could add an ad-hoc limitation on the extent of the separation that is allowed between events that can be observed conjointly. If we are told that an Experimenter can witness observable events that have a space-like separation, but only within an extension of 20 cm, then the contradiction-albeit still existing in theory-would seem much more acceptable.
Another similar alternative would be to postulate that the act of measurement takes some finite time duration to complete. The observation does still reflect observable events that have space-like separation, but we suppose that there is an incompressible time duration required to integrate these data into the observation witnessed by the Experimenter. If we assume that this time duration is larger than the time required to establish physical interaction between the observed Journal of Quantum Information Science as long as this knowledge does not transpire to another experimenter, we could defend that physical locality is preserved. In a way, the subjective experience of one Experimenter is of no importance to another Experimenter [11].
We can summarize our discussion as follows: Proposition 1.  An Experimenter witnesses observable events that are space-like separated.
 There is no theoretical limitation known on this space-like separation.
 However, seen from the outside, the action of the Experimenter based on his observations does not violate the locality principles.
The Experimenter has a unified experience of what he can observe from an experiment. Our discussion above leads us to think that this unified experience does not necessarily correspond to anything unified if we observe the Experimenter as a physical system from the outside. Rather, the different pieces of information Journal of Quantum Information Science are encoded in observable events that are space-like separated. Seen from the outside, the behaviour of the Experimenter can be explained using physical laws, via local interactions on separate physical systems that convey different pieces of information. The outsider does not need to assume the existence of a unified view witnessing space-like separated observable events. As such, we could argue that the outcome of a measurement is purely subjective: the subjective experience may reflect observable events that are space-like separated, but it does not lead to non-locality. The externally visible behaviour of the Experimenter is not the consequence of the subjective experience made by the Experimenter. Seen from the outside, the Experimenter is just another physical mechanism interacting locally with its immediate physical environment.
Quantum measurement, the process leading to this subjective experience, is not a local process as it involves space-like separated events. This non-locality is however not an issue as the description of the observer as a physical system does not depend on this subjective experience. In this sense, we conjecture that quantum measurement-a key feature of quantum physics-is not a local physical process.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.