Quantum Measurement: On This Side of Paradox

Gelengül Koçaslan

As it has served as a basement for all sciences Newtonian Physics has served for Economics as well. Consequently Newtonian causality appeared as economic determinism in economic theory. Recently quantum physics called into question the philosophy of determinism and focused on possibility rather than certainty. Decision making under risk and uncertainty has been reviewed by scientists from different disciplines. Since it is revealed that individual behavior contradicts with the basic tenets of the theory; economists, psychologists, neurologists and physicists have devoted much to better understand the basic motives underlying irrational behavior. This study adapts quantum approach to decision making under risk considering Allais Paradox and reinterpret it not from the side of the subject but from the side of the observer. In this way it is aimed to reconsider Allais Paradox referring to quantum measurement problem and the observer effect.

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A. J. Leggett

Francesco R. Ruggeri

Gibb’s paradox seems to arise when one considers an ideal gas of N particles, energy E, temperature T in a box of volume V and compares its entropy to two subsystems created by inserting a partition into the middle of the container without doing work. Each subsystem has N/2 particles, occupies V/2 and has E/2 and T. The issue is that one wishes to have 2 S subsystem = S full system, i.e. to have entropy be extensive. To do so, a function of N is inserted into the entropy formula and it is argued that this has to do with identical particles and ultimately with quantum mechanics. We argue that there seems to be a problem with this picture, namely the assignment of N/2 particles to each subsystem as this involves a measurement and hence changes entropy. To simplify matters, we consider a full system of 2 particles. Boltzmann’s notion of entropy is - k ln( number of states). Here the issue primarily seems to be with volume states, i.e. a particle can be in any tiny volume cell with equal probability. In the full V case, each of the two particles can be in any volume cell in V, but the same is true if one inserts a partition separating V into two V/2 cells. One cannot possibly know if one particle is in each cell unless one makes a measurement before inserting the partition and making a measurement changes entropy. When writing the number of states, these are probabilistic scenarios. It is possible that 2 particles are on one side of the partition and 0 on the other or 1 on each. The number of possible states for the partitioned system is the same as for the full volume. As a result, there is no paradox. There is only a paradox if one assumes that there is 1 particle on each side which is an assumption which cannot be made without making a measurement.

Joel Weijia Lai, Jean Ren Adriel Tan, Huiyi Lu +2 more

Two losing games can be played in a certain manner to produce a winning outcome-a phenomenon known as Parrondo's paradox. Of particular interest is the emergence of quantum game theory and the attempt to model known Parrondo's games through quantum computation notation. In this article, we investigate whether flipping four-sided quantum coins will result in the emergence of Parrondo's paradox. We discover that by playing two losing games A and B in a sequential order, a winning scenario can be derived. Furthermore, four-sided quantum coin is the first instance where the ratcheting effect from the classical Parrondo's game is necessary. Crucially, our study is designed with quantum protocols as its basis and does not have a direct classical counterpart.

R. W. Rendell, Michael Steiner