Abstract Decisions made by two (or more) independent players in a dynamical system can result in an indeterminable, yet non-stochastic, outcome. The mechanism can be presented as a thought experiment in which two pilots attempt to steer a spacecraft but, in stabilizing its pitch and yaw, lose all knowledge of its forward motion. It is useful to think of this pilots’ dilemma as a classical analogue of Schrödinger’s ‘cat in a box’ thought experiment. In both, the outcome of a life or death scenario is indeterminate until it is directly observed, but in place of the probabilistic radioactive source in Schrödinger’s problem, the discontinuous action of the pilots’ decisions create the classical indeterminacy. We discuss the wider implications of the phenomenon, such as predicting indeterminate scenarios in optimal transport or other network problems. The behaviour only becomes apparent when a system’s dynamics is sufficiently taken into account.
Abstract Decisions made by two (or more) independent players in a dynamical system can result in an indeterminable, yet non-stochastic, outcome. The mechanism can be presented as a thought experiment in which two pilots attempt to steer a spacecraft but, in stabilizing its pitch and yaw, lose all knowledge of its forward motion. It is useful to think of this pilots’ dilemma as a classical analogue of Schrödinger’s ‘cat in a box’ thought experiment. In both, the outcome of a life or death scenario is indeterminate until it is directly observed, but in place of the probabilistic radioactive source in Schrödinger’s problem, the discontinuous action of the pilots’ decisions create the classical indeterminacy. We discuss the wider implications of the phenomenon, such as predicting indeterminate scenarios in optimal transport or other network problems. The behaviour only becomes apparent when a system’s dynamics is sufficiently taken into account.
A quantum entity is intrinsically indeterminate and is not in a determinate (classical) state when it is not being observed. The quantum entity is found to be in a determinate state only if an experiment is carried out to observe it, as discussed in Baaquie (2013e). The indeterminate behavior of the quantum entity is described by the formalism of quantum mathematics discussed in Chapter 2. The measure of quantum indeterminacy and uncertainty is Planck's constant ħ. Randomness also exists in classical systems; however, a classical system's randomness is in principle different from quantum indeterminacy, since a priori, a classical random system is intrinsically in a determinate state. Classical randomness arises entirely due to our lack of complete knowledge of the determinate state. The theory of classical probability describes a classical system about which one has incomplete knowledge. There are many ways of introducing randomness in a classical system, depending on its nature. A classical random system in thermal equilibrium is described by statistical mechanics. A classical system undergoing random time evolution can be described by taking the classical equations of motion and adding a random force to it. The evolution of the classical particle is then described by a stochastic process. The random force is usually represented by Gaussian white noise. Classical random processes driven by white noise, such as those that arise in finance and other areas, form a wide class of problems that can be described by classical probability theory. It is shown in this chapter that the mathematical framework of quantum mechanics, and in particular, the Hamiltonian operator and path integrals, provide an appropriate mathematical formalism for describing processes that are driven by Gaussian white noise.
Schrödinger's cat states A prerequisite to getting quantitative information on the microscopic world is the existence of measuring apparatuses that indicate definite measuring results.The idea that a pointer of a measuring device is itself in an indeterminate state waiting for someone to make the wavefunction for the combined system (object + measuring apparatus) collapse by simply having a look on the apparatus, thus reading it out, appears absurd. I think, there is no doubt that measuring devices will behave like other objects in the macroscopic world in which there is no place for ‘intrinsic’ uncertainty. Actually, this fact becomes questionable, at least it needs further theoretical investigation, when it is claimed that the quantum mechanical description applies also to macroscopic bodies, in particular measuring devices. (There are physicists who do not shrink back from attributing a single wavefunction even to the whole universe!) The dilemma originates from the quantum mechanical rule following from the linearity of the Schrödinger equation, that a pure quantum state remains a pure quantum state during its evolution. So, assuming that both the microscopic system to be observed and the measuring apparatus are initially in a pure state each, the combined system (object + measuring apparatus) will still be in a pure state after the interaction has taken place. Hence one will need ‘someone’ to bring about the collapse of the wavefunction. (In a realistic approach to this problem, the agent is recognized to be the environment with its virtually infinite number of degrees of freedom.) Schrödinger, being fully aware of this dilemma, illustrated it ingeniously through a fictitious ‘diabolic device’.
In 1935 Erwin Schrödinger proposed a thought experiment to show the absurd consequences of applying quantum mechanics to everyday objects. Schrödinger imagined placing a cat in a box, along with a vial of deadly poison that is connected to a radioactive atom. If the atom decays, it releases the poison and kills the cat. When the box is closed we do not know if the atom has decayed or not, which means that it can be in a "superposition" of two states (decayed and non-decayed) at the same time. Therefore, protested Schrödinger, the cat can be both dead and alive at the same time – which is clearly absurd. There was obviously, he thought, some boundary between the microscopic world of atoms and quantum mechanics, and the macroscopic world of cats and classical mechanics.
The physicist Erwin Schrödinger described, back in 1935, one aspect of this strange phenomenon. He placed his cat in a sealed box with a piece of radioactive material which might or might not send out a sub-atomic particle. If it did, the Geiger counter was designed to trigger a release of poisonous gas in the box, and thereby kill his cat. The counter was set up to be triggered just enough to give a 50-50 chance of a particle being detected, and therefore the cat an even chance of being poisoned or not. (In those days, this sort of experiment was acceptable, particularly as it was only a thought experiment.) Radioactive behaviour is unpredictable (except in a general, statistical probability kind of way). There is no rule for working out whether or not the Geiger counter will be triggered. If the sub-atomic event does not occur, the cat lives. Otherwise, it dies. Just as a photon (in that famous experiment from ‘real-life’ physics) will quite happily go through both of two parallel slits in a screen – until someone tries to measure or detect it, at which point what the physicists call ‘the collapse of the wave function’ takes place – the particle can both trigger the poison gas and not trigger the poison gas. That is, until someone looks, Schrödinger’s idea is that his cat, for a while, is both alive and dead!
We reopen Erwin Schrodinger's thought experiment involving a cat in an informationally impenetrable box. A common view is that the cat enters a superposition of alive/dead because of a lack of observation, leading to uncertainty about the state of the cat. We, on the other hand, argue that the cat only enters a superposition if everything about the cat is known prior to the box being closed. The superposition results from a lack of uncertainty inside the box. Rather than interpreting this state of affairs as a live and dead cat interacting with each other, we suggest that the more natural interpretation is that of an inability to precisely position events within spacetime due to the lack of uncertainty. We clarify how stable measurement depends on a diversified portfolio of statistical uncertainty, and how the lack of such uncertainty in Schrodinger's box precludes stabilization.
The physicist Erwin Schrödinger described, back in 1935, one aspect of this strange phenomenon. He placed his cat in a sealed box with a piece of radioactive material which might or might not send out a sub-atomic particle. If it did, the Geiger counter was designed to trigger a release of poisonous gas in the box, and thereby kill his cat. The Geiger counter was set up to be triggered just enough to give a 50-50 chance of a particle being detected, and therefore the cat an even chance of being poisoned or not. (In those days, this sort of experiment was acceptable, particularly as it was only a thought experiment.) Radioactive behaviour is unpredictable (except in a general, statistical probability way). There is no way of working out whether or not the Geiger counter will be triggered off. If the sub-atomic event does not occur-the cat lives. Otherwise, it dies. Just as the photon (in Problem 93) will quite happily go through both slits until someone tries to measure or detect it, at which point what the physicists call ‘the collapse of the wave function’ takes place, the particle can both trigger the poison gas and not trigger the poison gas. Until someone looks, Schrödinger’s idea is that his cat, for a while, is both alive and dead!