Introduction to

Quantum Mechanics

Quantum Mechanics

Implications of

Quantum Mechanics

Quantum Mechanics

3. Overview of Understanding Quantum Mechanics.

Principles.

Summary

Sketches of particle, collapse, and many-worlds interpretations are given, along with the principles needed to evaluate these interpretations. The conclusion is that to make sense of quantum mechanics, we must each have a Mind outside quantum mechanics.

Almost all the mysteries of quantum mechanics arise because the theory gives many versions of reality; Schrödinger’s cat is both dead and alive at the same time. Interpretations of quantum mechanics are attempts to reconcile this many-version reality with our everyday perceptions and with the probability law. There are many interpretations, most of them corresponding to a particular view of ‘reality,’ and at first glance it is not obvious that one is better than another.

There is, however, an organized way to go about trying to understand what quantum mechanics implies about the nature of reality. One can derive a number of principles—listed at the end of this section—from experiments, our perceptions, and the mathematics of quantum mechanics. These principles put constraints on interpretations, and it is found that none of the current interpretations known to the author satisfy all these constraints. Thus we propose a new Mind-MIND interpretation.

The Three Major Interpretations

There are a number of interpretation, but we will consider only the three major ones—particles, collapse, and Everett’s many-worlds—in this overview. To the best of my knowledge, all the ‘minor’ interpretations violate one or more of the constraining principles.

The particle interpretation. In the particle interpretation, one supposes that, in addition to the many quantum versions of reality, there is an actual, objective reality made of particles, and it is the particles, rather than the wave functions, that we perceive. All the alleged evidence for particles can be reduced to five principles, summarized in No Evidence for Particles. The main ones are:

(1) The classical particle-likeproperties of mass, energy, momentum, spin and charge are presumed to be properties of particles.

(2) Particles produce localized effects, so experimentally observed localized effects are presumed to imply the existence of particles.

(3) A small part of a classical wave, say a light or sound wave, carries a correspondingly small part of the energy and momentum of the wave, so the same is presumed to hold for the wave function.

However, one can show, using group representation theory, that the particle-like properties are actually properties of the wave function (see Mass, Spin and Charge). Further, one can show that the wave function leads to the

*perception*of localized effects (see Localization and the Wave Function). And one can show that a small part of the wave function carries the full energy, momentum and so on (see Small Parts of the Wave Function). The result is that all the particle

*-like*attributes of matter can actually be explained by

*properties of the wave function alone.*Thus there is no evidence for the existence of particles!

A related interpretation assumes there are ‘hidden variables’—objective physical attributes not directly accessible to experimental validation—that determine which single version of reality we perceive. We show, however (see The Particle Interpretation), that in addition to the fact that there is no evidence for them, hidden variables do not really solve the problem of why we perceive a particular version. That is, there is no reason to suppose anything besides the wave function exists.

The collapse interpretation. A second potential way out of the multiple-versions-of-reality problem is to suppose the wave function ‘collapses’ down to just one version; the dead cat wave function might collapse to zero, for example, leaving just a live cat (wave function) to be perceived. However, we argue in No Evidence for Collapse, Mathematical Collapse Interpretations, and Observer-Induced Collapse that there is no evidence for collapse, and also that constructing theories based on collapse encounters severe problems. Thus collapse is also not a likely candidate for an interpretation.

The Everett many-worlds interpretation. The third major interpretation is to suppose all versions always exist, so there are many version of each of us!? This interpretation, bizarre as it sounds, actually does an excellent job for the most part. However, it has one fatal flaw; it cannot account for the probability law (see The Everett Many-Worlds Interpretation) and so it is not a viable interpretation of quantum mechanics.

Conclusion.

The implication of these results is that the theory of the physical universe, as it currently stands, is

*incomplete.*For if the probability law is to hold, there must be some ‘mechanism’ that singles out just one version as the one corresponding to our perceptions. But there is no evidence for, and substantial evidence against, the conventionally proposed mechanisms—particles, hidden variables and collapse. And the Everett many-worlds interpretation doesn’t work.

The failure of these three implies that the most likely candidate for the singling out mechanism at this time is a perceiving “Mind” which is not subject to the laws of quantum mechanics (in contrast to the physical brain, which is subject to those laws) and is thus ‘outside’ the physical universe. (See The Mind-MIND Interpretation for details.) Many scientists will say there is no evidence for such a ‘non-scientific’ interpretation. But the counter-argument is that all the proposed ‘scientific’ interpretations have very serious flaws. Thus if we accept the current state of physics—no evidence for particles, hidden variables, or collapse—we are pretty much forced to the Mind-MIND interpretation.

Principles which Constrain Interpretations

of Quantum Mechanics.

The principles fall into six categories:

[P1] - [P4] Basic background principles.

[P5] - [P8A] Quantum mechanics implies we perceive a ‘classical’ world.

[P9], [P10], [P17] - [P19] The probability law. The many-worlds interpretation is not valid.

[P11] - [P15] No evidence for particles.

[P20], [P21] No evidence for hidden variables.

[P16], [P22] No evidence for collapse.

[P1]sec 1 Our reasoning will be based primarily on four trustworthy facts:

(1) Our everyday perceptions of the world around us.

(2) The highly verified mathematical structure of quantum mechanics.

(3) The highly verified probability law of quantum mechanics.

(4) We must also rely on the results of experimental searches for particles, hidden variables, and collapse of the wave function.

[P2] sec 2 The wave function contains many versions of reality, with a different version of the observer in each one. Only versions of the observer perceive. No one version is singled out as being ‘special’, so quantum mechanics does not predict which version will correspond to our perceptions.

[P3] sec 2 In every case where both the calculations and observations can be carried out, our perceptions agree exactly—both qualitatively and quantitatively—with those of one version of the observer.

[P4] sec 7 Basic quantum mechanics, QMA, is defined as follows:

(1) No particles. There are to be no particles or hidden variables.

(2)

**No Collapse.**There is to be no collapse of the wave function, so that all versions of reality continue forever.

(3)

**No ‘sentient beings.’**There are to be no ‘sentient beings,’ outside the laws of quantum mechanics, which ‘look into’ physical reality and perceive just one version of reality.

(4)

**No probability law.**There is to be no

*a priori*assumption that the probability law holds.

(5)

**Linearity.**And finally, the theory is to be linear. (This is a technical point which basically implies that each version of reality is isolated from the others.)

[P5] sec 8 Different versions of reality in the wave function are in separate, isolated universes that cannot communicate with or affect each other in any way. Thus no version of the observer can perceive anything other than that which happens within its own, single universe.

[P6]sec 9 Basic quantum mechanics prohibits perception of more than one version of reality.

[P7] sec 9 Quantum mechanics implies that two observers can never disagree on what they perceive.

[P8] sec 9 If two observations are made successively, quantum mechanics implies the same consistency of results as one obtains in a classical universe. A technical version of this principle is that if one measures the same property twice in a row, quantum mechanics implies one will get the same result.

[P8A]sec 9B If a measurement is made on a physical quantity corresponding to some operator, the measurement will always yield one of the eigenvalues of the operator.

[P9] sec 10

**The |a(i)|**If an experiment is run many times, a physical reality with characteristics corresponding to version i will be perceived a fraction |a(i)|

^{2}probability law.^{2}of the time.

[P10] sec 10 The |a(i)|

^{2}probability law is the only functional form consistent with the rest of conventional quantum mechanics. This strongly suggests that the origin of the law must, to a large extent, somehow be

*within*conventional quantum mechanics, even though we haven’t yet figured out how. That is, it doesn’t make sense for there to be a probabilistic ‘mechanism’ that is entirely independent of the laws of quantum mechanics, but

*just happens*to be consistent with those laws.

[P11] sec 11 Linearity and the physical invariance properties—relativistic rotations, translations, internal symmetries—imply the particle

*-like*properties of mass, energy, momentum, spin and charge are properties of the wave function.

[P12] sec 11 Linearity and the invariance properties also imply that the usual conservation laws and laws of addition for energy, momentum, spin and charge hold in quantum mechanics.

[P13] sec 12 A spread-out wave function produces localized effects.

[P14] sec 13 In contrast to the classical case, small parts of the wave function carry the full mass, energy, momentum, spin and charge.

[P15] sec 14 There is no evidence for the existence of particles.

[P16] sec 15 Despite a number of ingenious and sensitive experiments, there is no evidence for collapse.

[P17] sec 16 The probability law cannot hold in the bare QMA scheme, where all versions of the observer are perceptually equivalent on each run.

[P18] sec 16 The probability law implies there must be some mechanism, not within QMA, which

*singles out*one version of the observer as the one corresponding to

*my*perceptions.

[P19] sec 16 One does not obtain a

*satisfactory*interpretive scheme by simply adding the probability law as a postulate to the first three principles of QMA because the singling out mechanism required by [P18] is not

*specified*.

[P20]* sec 20 It appears to be very difficult, and probably impossible, to explain in

*any*non-collapse hidden variable model why the quantum versions of the brain

*not*associated with the hidden variables cannot be consciously aware.

[P21] sec 21 There is no experimental evidence for hidden variables.

[P22] sec 22 There is currently no reason to be at all optimistic that there is either a mathematical theory of collapse which augments standard quantum mechanics or that collapse is caused by conscious observation.