This article reconsiders the double-slit experiment from the nonrealist or, in terms of this article, "reality-without-realism" (RWR) perspective, grounded in the combination of three forms of quantum discontinuity: (1) "Heisenberg discontinuity", defined by the impossibility of a representation or even conception of how quantum phenomena come about, even though quantum theory (such as quantum mechanics or quantum field theory) predicts the data in question strictly in accord with what is observed in quantum experiments); (2) "Bohr discontinuity", defined, under the assumption of Heisenberg discontinuity, by the view that quantum phenomena and the data observed therein are described by classical and not quantum theory, even though classical physics cannot predict them; and (3) "Dirac discontinuity" (not considered by Dirac himself, but suggested by his equation), according to which the concept of a quantum object, such as a photon or electron, is an idealization only applicable at the time of observation and not to something that exists independently in nature. Dirac discontinuity is of particular importance for the article's foundational argument and its analysis of the double-slit experiment.
This article reconsiders the double-slit experiment from the nonrealist or, in terms of this article, "reality-without-realism" (RWR) perspective, grounded in the combination of three forms of quantum discontinuity: (1) "Heisenberg discontinuity", defined by the impossibility of a representation or even conception of how quantum phenomena come about, even though quantum theory (such as quantum mechanics or quantum field theory) predicts the data in question strictly in accord with what is observed in quantum experiments); (2) "Bohr discontinuity", defined, under the assumption of Heisenberg discontinuity, by the view that quantum phenomena and the data observed therein are described by classical and not quantum theory, even though classical physics cannot predict them; and (3) "Dirac discontinuity" (not considered by Dirac himself, but suggested by his equation), according to which the concept of a quantum object, such as a photon or electron, is an idealization only applicable at the time of observation and not to something that exists independently in nature. Dirac discontinuity is of particular importance for the article's foundational argument and its analysis of the double-slit experiment.
This article reconsiders the double-slit experiment by establishing a new type of relationship between it and the concept of entanglement. While the role of entanglement in the double-slit experiment has been considered, this particular relationship appears to have been missed in preceding discussions of the experiment, even by Bohr, who extensively used it to support his argument concerning quantum physics. The main reason for this relationship is the different roles of the diaphragm with slits in two setups, S1 and S2, defining the double-slit experiment as a quantum experiment. In S1, in each individual run of the experiment one can in principle (even if not actually) know throughout which slit the quantum object considered has passed; in S2 this knowledge is in principle impossible, which impossibility is coextensive with the appearance of the interference pattern, once a sufficient number of individual runs of the experiment have taken place. The article offers the following argument based on two new concepts, an "experimentally quantum object" and an "ontologically quantum object." In S1 the diaphragm can be treated as part of an observational arrangement and thus considered as a classical object, while the object passing through one or the other slit is considered as an "ontologically quantum object," defined as an object necessary to establish a quantum phenomenon. By contrast, in S2, the diaphragm can, via the concept of Heisenberg-von-Neumann cut, be treated as an "experimentally quantum object," defined as an object treatable by quantum theory, even while possibly being an ontologically classical object. This interaction is not an observation but a quantum entanglement between these two quantum objects, one ontologically and one experimentally quantum. This argument is grounded in a particular interpretation of quantum phenomena and quantum theory, which belongs to the class of interpretations designated here as "reality without realism" (RWR) interpretations. The article also argues that wave-particle complementarity, with which the concept of complementarity is often associated, plays little, if any, role in quantum physics, or in Bohr's thinking, and may be misleading in considering the double-slit experiment, often explained by using this complementarity.
The article argues that-at least in certain interpretations, such as the one assumed in this article under the heading of "reality without realism"-the quantum-theoretical situation appears as follows: While-in terms of probabilistic predictions-connected to and connecting the information obtained in quantum phenomena, the mathematics of quantum theory (QM or QFT), which is continuous, does not represent and is discontinuous with both the emergence of quantum phenomena and the physics of these phenomena, phenomena that are physically discontinuous with each other as well. These phenomena, and thus this information, are described by classical physics. All actually available information (in the mathematical sense of information theory) is classical: it is composed of units, such as bits, that are-or are contained in-entities described by classical physics. On the other hand, classical physics cannot predict this information when it is created, as manifested in measuring instruments, in quantum experiments, while quantum theory can. In this epistemological sense, this information is quantum. The article designates the discontinuity between quantum theory and the emergence of quantum phenomena the "Heisenberg discontinuity", because it was introduced by W. Heisenberg along with QM, and the discontinuity between QM or QFT and the classical physics of quantum phenomena, the "Bohr discontinuity", because it was introduced as part of Bohr's interpretation of quantum phenomena and QM, under the assumption of Heisenberg discontinuity. Combining both discontinuities precludes QM or QFT from being connected to either physical reality, that ultimately responsible for quantum phenomena or that of these phenomena themselves, other than by means of probabilistic predictions concerning the information, classical in character, contained in quantum phenomena. The nature of quantum information is, in this view, defined by this situation. A major implication, discussed in the Conclusion, is the existence and arguably the necessity of two-classical and quantum-or with relativity, three and possibly more essentially different theories in fundamental physics.
This article reconsiders the concept of physical reality in quantum theory and the concept of quantum measurement, following Bohr, whose analysis of quantum measurement led him to his concept of a (quantum) "phenomenon," referring to "the observations obtained under the specified circumstances," in the interaction between quantum objects and measuring instruments. This situation makes the terms "observation" and "measurement," as conventionally understood, inapplicable. These terms are remnants of classical physics or still earlier history, from which classical physics inherited it. As defined here, a quantum measurement does not measure any preexisting property of the ultimate constitution of the reality responsible for quantum phenomena. An act of measurement establishes a quantum phenomenon by an interaction between the instrument and the quantum object or in the present view the ultimate constitution of the reality responsible for quantum phenomena and, at the time of measurement, also quantum objects. In the view advanced in this article, in contrast to that of Bohr, quantum objects, such as electrons or photons, are assumed to exist only at the time of measurement and not independently, a view that redefines the concept of quantum object as well. This redefinition becomes especially important in high-energy quantum regimes and quantum field theory and allows this article to define a new concept of quantum field. The article also considers, now following Bohr, the quantum measurement as the entanglement between quantum objects and measurement instruments. The argument of the article is grounded in the concept "reality without realism" (RWR), as underlying quantum measurement thus understood, and the view, the RWR view, of quantum theory defined by this concept. The RWR view places a stratum of physical reality thus designated, here the reality ultimately responsible for quantum phenomena, beyond representation or knowledge, or even conception, and defines the corresponding set of interpretations quantum mechanics or quantum field theory, such as the one assumed in this article, in which, again, not only quantum phenomena but also quantum objects are (idealizations) defined by measurement. As such, the article also offers a broadly conceived response to J. Bell's argument "against 'measurement'".
Following the view of several leading quantum-information theorists, this paper argues that quantum phenomena, including those exhibiting quantum correlations (one of their most enigmatic features), and quantum mechanics may be best understood in quantum-informational terms. It also argues that this understanding is implicit already in the work of some among the founding figures of quantum mechanics, in particular W. Heisenberg and N. Bohr, half a century before quantum information theory emerged and confirmed, and gave a deeper meaning to, to their insights. These insights, I further argue, still help this understanding, which is the main reason for considering them here. My argument is grounded in a particular interpretation of quantum phenomena and quantum mechanics, in part arising from these insights as well. This interpretation is based on the concept of reality without realism, RWR (which places the reality considered beyond representation or even conception), introduced by this author previously, in turn, following Heisenberg and Bohr, and in response to quantum information theory.
This article reconsiders E. Schrödinger's cat paradox experiment from a new perspective, grounded in the interpretation of quantum mechanics that belongs to the class of interpretations designated as "reality without realism" (RWR) interpretations. These interpretations assume that the reality ultimately responsible for quantum phenomena is beyond conception, an assumption designated as the Heisenberg postulate. Accordingly, in these interpretations, quantum physics is understood in terms of the relationships between what is thinkable and what is unthinkable, with, physical, classical, and quantum, corresponding to thinkable and unthinkable, respectively. The role of classical physics becomes unavoidable in quantum physics, the circumstance designated as the Bohr postulate, which restores to classical physics its position as part of fundamental physics, a position commonly reserved for quantum physics and relativity. This view of quantum physics and relativity is maintained by this article as well but is argued to be sufficient for understanding fundamental physics. Establishing this role of classical physics is a distinctive contribution of the article, which allows it to reconsider Schrödinger's cat experiment, but has a broader significance for understanding fundamental physics. RWR interpretations have not been previously applied to the cat experiment, including by N. Bohr, whose interpretation, in its ultimate form (he changed it a few times), was an RWR interpretation. The interpretation adopted in this article follows Bohr's interpretation, based on the Heisenberg and Bohr postulates, but it adds the Dirac postulate, stating that the concept of a quantum object only applies at the time of observation and not independently.
We argue that the double-slit experiment can be understood much better by considering it as an experiment whereby
one uses electrons to study the set-up rather than an experiment whereby we use a set-up to study the behaviour of electrons.
We also show that the concept of undecidability (like e.g. occurs in G\odel's theorem) can be used in an intuitive way to make sense of the double-slit experiment
and the quantum rules for calculating coherent and incoherent probabilities. We meet here a situation where the electrons always behave in a fully
deterministic way, while the detailed design of the set-up may render the question about the way they move through the set-up experimentally undecidable.
It is very important to make a distinction in quantum mechanics
between the determinism of nature (Einstein)
and the decidability of a question within an experimental set-up (Bohr).
The former is about the absolute truth of an answer to a yes or no question, and follows binary logic
(true or false),
the latter about what an experimental set-up
can decide and tell about the truth of that answer, and follows ternary logic (true, false or undecidable).
Binary and ternary logic are incompatible.
The viewpoints of Bohr and Einstein are thus operating on different levels and it is only by confusing these two levels
that these two viewpoints seem to be irreconcilable.
We show that the expression ψ1+ψ2 for the wave function of the double-slit experiment is numerically correct, but logically flawed. It has to be replaced in the interference region
by the logically correct expression ψ1′+ψ2′, which has the same numerical value as
ψ1+ψ2, such that ψ1′+ψ2′=ψ1+ψ2,
but with ψ1′=2ψ1+ψ2e4π=ψ1 and
ψ2′=2ψ1+ψ2e−4π=ψ2.
Here ψ1′ and ψ2′ are the correct
contributions from the slits to the total wave function ψ1′+ψ2′.
We have then $p = |\psi'_{1} + \psi'_{2}|^{2} = |\psi'_{1}|^{2} + |\psi'_{2}|^{2} = p_{1}+p_{2} $ such that the paradox
that quantum mechanics (QM) would not follow the traditional rules of probability calculus disappears.
The paradox is rooted in the wrong intuition that ψ1 and ψ2 would be the true physical contributions to
ψ1′+ψ2′=ψ1+ψ2 like in the case of waves in a water tank.
The solution proposed here is not {\em ad hoc} but based on an extensive analysis of the geometrical meaning of spinors within group representation theory
and its application to QM. Working further on the argument one can even show that an interference pattern is the only way to satisfy simultaneously
two conditions: The condition obeying binary logic (in the spirit of Einstein) that the electron has only two mutually exclusive options to get to the detector (viz. going through slit S1 or going through slit S2) and the condition obeying ternary logic (in the spirit of Bohr)
that the question which one of these two options the electron has taken is experimentally undecidable.
A very important element in the analysis is the problem of the non-existence of {\em common} probability distributions for different experimental set-ups.
And this is a recurrent theme in other situations that are felt as paradoxical.
The CHSH inequality used in the experiments of Aspect {\em et al.}
clashes with quantum mechanics because it
is based on the assumption that there would exist a {\em common} probability distribution for the
hidden variables in the different experiments that have to be made to determine the various quantities that intervene in the inequality.
That common probability distribution for measured quantities does not exist is well known from quantum mechanics itself (because the operators that come into play do not commute and therefore do not have common eigenstates, i.e.
common probability amplitudes). But this non-existence of common probability distributions applies also to certain variables in the set-ups of the different experiments and the latter fact
can also be explained by purely classical reasoning.