Wave function collapse

The third problem is like the confusion caused in MT by maintaining the concept of the Ether. Most practitioners of QM think about microscopic systems in terms of the principles of QM probability distributions, superposition principle, uncertainty relations, complementarity principle, correspondence principle, wave function collapse. These principles are an approximate summary of what QM really is, and following them without checking whether the Schrddinger equation actually confirms them does lead to error. 

All of the many supposed ghost-like properties associated with quantum theory are of the same ilk. The most bizarre is perhaps the many-worlds theory, which states that whenever an observer opens an eye on the world a wave function collapses and the universe splits into two. The observer persists in only one of these and keeps on creating an endless number of irrelevant universes. Any serious student of quantum theory should be advised to ignore this sensational stuff at the outset. There are enough poorly understood real issues to keep the keenest minds occupied. 

The advanced wave is emitted backward in time as the retarded wave arrives at A and it arrives back at E at the instant that the retarded wave is being emitted. The two sites E and A may be astronomical distances apart and in the same way that simultaneity is not defined relativistically, the concept of instantaneous response also looses its meaning. The interaction between E and A is therefore non-local, irrespective of time differences. On absorption of the photon energy the wave function collapses everywhere. The photon represents the handshake between emitter and absorber, and therefore has no velocity. The constant c refers to the transmission of radiant energy between E and A, and the photon exists for the duration of the transmission. 

The crisis of the GME method is closely related to the crisis in the density matrix approach to wave-function collapse. We shall see that in the Poisson case the processes making the statistical density matrix become diagonal in the basis set of the measured variable and can be safely interpreted as generators of wave function collapse, thereby justifying the widely accepted conviction that quantum mechanics does not need either correction or generalization. In the non-Poisson case, this equivalence is lost, and, while the CTRW perspective yields correct results, no theoretical tool, based on density, exists yet to make the time evolution of a contracted Liouville equation, classical or quantum, reproduce them. 

At this stage, we are confident that a clear connection between Levy statistics and critical random events is established. We have also seen that non-Poisson renewal yields a class of GME with infinite memory, from within a perspective resting on trajectories with jumps that act as memory erasers. The non-Poisson and renewal character of these processes has two major effects. The former will be discussed in detail in Section XV, and the latter will be discussed in Section XVI. The first problem has to do with decoherence theory. As we shall see, decoherence theory denotes an approach avoiding the use of wave function collapses, with the supposedly equivalent adoption of quantum densities becoming diagonal in the pointer basis set. In Section XV we shall see that the decoherence theory is inadequate to derive non-Poisson renewal processes from quantum mechanics. In Section XVI we shall show that the non-Poisson renewal properties, revealed by the BQD experiments, rule out modulation as a possible approach to complexity. 

Both the case where the Laplace transform of K(t) of Eq. (24) diverge (superdiffusion) or vanish (subdiffusion) must be treated with caution. These conditions will be the main subject under study in this review. The existence of environment fluctuations makes it possible for us to interpret the electron transport as resulting from random jumps, without involving the notion of wave-function collapse, but this is limited to the case of Poisson statistics. Anderson... 

We are now in the right position to reach a preliminary conclusion. Although the decoherence theory is an attractive and efficient way of defeating the emergence of quantum effects at a macroscopic level, the authors of Ref. 112 did not feel comfortable with it. The reason is that when the observer has the impression that a wave-function collapse occurs, actually the quantum mechanical coherence is becoming even more extended and macroscopic, since it spreads from the system to the environment, Eq. (256). 

After more than one 100 years of unquestionable successes [128], there is a general agreement that quantum mechanics affords a reliable description of the physical world. The phenomenon of quantum jumps, which can be experimentally detected, should force the physicists to extend this theory so as to turn the wave-function collapse assumption, made by the founding fathers of quantum mechanics, into a dynamical process, probably corresponding to an extremely weak random fluctuation. This dynamical process can be neglected in the absence of the enhancement effects, triggered either by the deliberate measurement act or by the fluctuation-dissipation phenomena such as Brownian motion. This enhancement process must remain within the limits of ordinary statistical physics. In this limiting case, the new theory must become identical to quantum mechanics. 

We have seen that decoherence theory, according to its advocates [128], makes the wave-function collapse assumption obsolete The environmental fluctuations are enough to destroy quantum mechanical coherence and generate statistical properties indistinguishable from those produced by genuine wave-function collapses. All this is unquestionable, and if a disagreement exists, it rests more on philosophy than on physical facts. Thus, there is apparently no need for a new theory. However, we have seen that all this implies the assumption that the environment produces white noise and that the system of interest, in the classical limit, produces ordinary diffusion. As we move from... 

In this context, it is worthwhile to recall the quantum jump approach developed in the quantum optics community. In this approach, an emission of a photon corresponds to a quantum jump from the excited to the ground state. For a molecule with two levels, this means that right after each emission event, = 0 (i.e., the system is in the ground state). Within the classical approach this type of wave function collapse never occurs. Instead, the emission event is described with the probability of emission per unit time being Fp (t), where Pee(0 is described by the stochastic Bloch equation. At least in principle, the quantum jump approach, also known as the Monte Carlo wave function approach [98-103], can be adapted to calculate the photon statistics of a SM in the presence of spectral diffusion. 

In such a case, Alice s measurement would falsify the state due to wave function collapse (it would give either 0) or 1) cf. p. 24). 

Bob knows therefore, that if Alice sends him 100), this means that the teleportation is over he already has his photon in state < If Alice sends him one of the remaining possibilities, he would know exactly what to do with his photon to prepare it in state 0. and he does this with his equipment. The teleportation is over Bob has the teleported state 0, Alice has lost her photon state 0 when performing her measurement (wave function collapse). 

Assume that photon A (number 1) from the entangled state belongs to Alice, and photon B (number 2) to Bob. Alice and Bob introduce a common fixed coordinate system. Both photons have identical polarizations in this coordinate system, but neither Alice nor Bob know which. Alice may measure the polarization of her photon and send this information to Bob, who may prepare his photon in that state. This, however, does not amount to teleportation, because the original state could be a linear combination of the 0> (parallel) and 1) (perpendicular) states, and in such a case Alice s measurement would falsify the state due to wave function collapse (it would give either 0> or 1>), cf. p. 23. 

According to Bohr, the energies of photons and electrons are always transferred and observed as complete quanta, When an observation is made, the wave function collapses instantaneously everywhere. One of Einstein s most famous sayings is God does not play dice, which is a reference to Bohr s interpretation of quantum mechanics, with which he disagreed. 

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