My Alternate View columns have been appearing in Analog every other month since the July-84 issue. Many of my columns have been devoted to quantum mechanics, its peculiarities, and its interpretations. I've written about quantum time travel [Analog-April-91], about Bell's theorem and the problem of nonlocality [Analog-January-90], and about the Calcutta scheme for faster than light communication with K0 mesons [Analog-September-88]. I've also compared the orthodox Copenhagen interpretation with two unorthodox interpretations, with the Everett-Wheeler or "Many-Worlds" interpretation [Analog-November-84] which splits the universe into alternate worlds with each quantum event and with my own "Transactional" interpretation [Analog-November-86] which accounts for quantum behavior through wave-exchange handshakes across space-time.
In this column I want to turn once again to the weirdness of quantum mechanics (QM), but with a new twist added by recent work in "non-linear" quantum mechanics. It appears, as we shall see, that the Copenhagen interpretation has suffered a serious, possibly fatal wound. Moreover, if the quantum world is very slightly nonlinear we can test the validity of the transactional interpretation against the many-worlds interpretation using backward-in-time and inter-universe communication.
We'll start with a short review of quantum mechanics and its interpretations. Quantum mechanics is the physics theory which deals at the smallest distance scale with objects (atoms, nuclei, photons, quarks) so small that the lumpiness or quantization of physical variables becomes important. QM was formulated in the mid-1920s to explain the growing body of new experimental facts that didn't fit the then-standard theories of physics. Two brilliant young physicists, Werner Heisenberg and Erwin Schrödinger, invented mathematical tricks that gave valid predictions of experimental results. They worked independently, each using some combination of deep mathematical insight, intuition, and plain good luck to formulate his theory. The two theories are very different in appearance, but are, as it turns out, equivalent. Today this mathematics is used and trusted by all physicists. The use of the QM procedures is clear and unambiguous, but even now, six decades after their work, the meaning of the QM formalism remains controversial. One often hears that "mathematics is the language of science". Quantum mechanics demonstrates that the language may lack a proper translation.
Consider this example: a radioactive atom decays by ejecting a fast-moving electron. In the QM picture of this event a wave corresponding to the electron spreads out from the parent atom in all directions, an ever-widening spherical wave front like the ring of ripples from a stone thrown into a pond. The electron is represented by the wave and is equally present over the whole wave front. The moving electron-wave then arrives at a second atom which it hits, resulting in a measurement of the electron's position. Immediately the expanding spherical electron-wave "collapses" like a soap bubble pricked by a pin. The wave completely disappears from all of space except the immediate vicinity of the struck atom, where the electron suddenly pops into existence. The electron as an expanding wave has vanished, to be replaced by the electron as a particle. This process is called "wave function collapse". It is considered "nonlocal" because the wave function abruptly disappears from locations quite distant from the point of detection. More subtle nonlocal correlation effects are exhibited in the so called Einstein-Podolsky-Rosen (EPR) experiments that have been used to test Bell's Theorem.
The orthodox Copenhagen interpretation of the mathematics of quantum mechanics is accepted by most physicists. It was invented by Niels Bohr and Werner Heisenberg in the 1920s and 30s. In the Copenhagen view the QM mathematics is a description not of a physical event but of the knowledge of an observer who is watching the event. The observer makes a measurement and the wave function, the QM description of his state of knowledge of the system, "collapses" to a simpler form which reflects the new information gained from the measurement. In the Copenhagen view the Schrödinger equation, a wave equation relating the mass, energy and momentum of the electron in its travels, has solutions which describe knowledge in the mind of the observer rather than real waves travelling in the real universe. The wave solutions change as the observer makes measurements and gains knowledge.
This "explains" many of the peculiarities of the QM formalism, but it also leads to new problems including a long list of QM interpretational paradoxes: the Schrödinger's Cat paradox, Wigner's Friend paradox, Wheeler's Delayed Choice paradox, etc., all of which are rooted in the way the Copenhagen interpretation conjures with the observer and his state of knowledge.
Most practicing physicists are not concerned with these interpretational problems, since the predictions of quantum mechanics have been compared with experiment many times and have always been found to be valid. Quantum mechanics works, so they use it without concern for the bizarre behavior that the equations suggest.
A minority of physicists has continued, without much attention from the mainstream physics community, to confront the interpretational paradoxes of quantum mechanics and seek their resolution. The Many-Worlds interpretation of quantum mechanics is such an effort. Its originator, Hugh Everett III, was a graduate student working with Prof. John A. Wheeler at Princeton University in the mid-1950s. Everett considered it "unreal that there should be a `magic' process in which something quite drastic occurred (the collapse of the wave function), while at other times systems were assumed to obey perfectly natural continuous laws."
Everett's PhD dissertation presented his new QM interpretation, a radical approach which uses neither collapsing wave functions nor observer knowledge. Instead it proposes a deceptively simple alternative: the wave function never collapses. Instead, at every occasion where a quantum event has more than one outcome (e.g., when an electron may strike one atom or another), the universe splits. We have one universe where the electron hits atom A, another where it hits atom B, and so on for all of the possible outcomes. Similarly, if a light photon might be transmitted or reflected, if a radioactive atom might decay or not, the universe splits into alternative worlds, with one new universe for each and every potential outcome. This is the Many Worlds (MW) interpretation.
From the MW viewpoint, the universe is like a tree that branches and re-branches into myriads of new sub-branches with every passing picosecond. And each of these new branch universes has a slightly different sub-atomic "history". Because an observer happens to have followed one particular path through the diverging branches of this Universe-Tree, he never perceives the splitting. Instead he interprets the resolution of the myriad of possibilities into one particular outcome as a Copenhagen-style collapse. But the observer plays no active role in the splitting.
Events at the quantum level, of course, must lead to consequences in the every-day world. There should be a MW universe in which every physically possible event has happened. There should be MW universes where the dinosaurs dominate the planet, where the Persians defeated the Athenians at Marathon, where Caesar and Jesus and Napoleon and Einstein and Ronald Reagan were never born, where World War IV has just reduced your present location to a smoking radioactive ruin. Even as you read this sentence your universe may be fragmenting into a number of branches too large to count.
And then again, it may not. The Many Worlds interpretation is not the only way of dealing with the interpretational problems of quantum mechanics. My favorite approach (perhaps because I invented it) is the transactional interpretation. The transactional interpretation is suggested by the formalism of quantum mechanics itself. The predicted "expectation value" of some property p of a physical system, in the QM formalism, is: <p> = ōdv(y* P y), where P is a mathematical operator describing the measurement of p, ōdv is a volume integration over 3-dimensional space, and yis a wave function, the solution of the Schrödinger wave equation which describes the system being measured. We call y a retarded wave because it has a built-in time delay so that it arrives at some distant location later than it started. The wave function y* is the time-reverse (or complex conjugate) of y. It is an advanced wave which arrives earlier than it started. In other words, y* is a wave that travels backwards in time.
The transactional interpretation takes the QM pairing of an advanced and a retarded wave quite literally. It describes any quantum process as a transaction, a handshake across space-time performed by the two-way exchange of advanced and retarded waves between the initial system and the final system, a two-way contract between the future and the past for the purpose of transferring energy, momentum, etc.
The transactional interpretation is explicitly nonlocal because, through such handshaking, the future in a limited way is affecting the past on the same basis that the past affects the future. A delicate balance in the formalism (in QM lingo, the commutation of separated-measurement operators) suppresses "advanced effects" and prevents faster-than-light and backward-in-time signalling (EPR communication). The transactional interpretation resolves all of the many paradoxes listed above. It eliminates the need for half-dead-half-alive cats, universes with split ends, observer-dependent reality, and "knowledge" waves. In the transactional interpretation the Schrödinger waves act in the external world as precursors of a quantum transaction. It demotes the observer from his major Copenhagen role as the anointed collapsor of wave functions to the minor role of superfluous bystander, watching a few of the transactions and recording their outcomes.
Which of these QM interpretations is the best? Up to now it has not been possible to test QM interpretations because it is the QM formalism which makes testable predictions. The choice between interpretations has been decided by taste, aesthetics, and what you were taught in graduate school.
Non-linear quantum mechanics may change that. Steven Weinberg, Nobel laureate for his work in unifying the electromagnetic and weak interactions, has recently been investigating "non-linear" corrections to standard quantum mechanics. The onset of non-linear behavior is seen in other areas of physics and may, he suggests, also be present but unnoticed in quantum mechanics. Weinberg's non-linear QM subtly alters certain properties of the standard theory, producing new physical effects that can be detected through precise measurements.
As mentioned above, the mathematics of quantum mechanics is delicately balanced to block EPR communication. However, a recent paper in Physical Review Letters by Joseph Polchinski has demonstrated that Weinberg's non-linear corrections upset this balance, unblocking observer-to-observer EPR communication. Separated measurements on the same quantum system begin to "talk" to each other and faster-than-light or backward-in-time signalling becomes possible. Polchinski describes such an arrangement as an "EPR telephone".
He goes on to describe an "Everett-Wheeler telephone". In standard QM in the Many Worlds scenario in which the wave function does not collapse, a measurement performed in one MW universe can have no effect on a measurement made in another. Polchinski demonstrates that in non-linear QM such measurements "talk" and can be used for transmission of information from one MW branch universe to another. With Polchinski's non-linear quantum telephones you could talk to yourself at an earlier time or to your alter ego in an alternate universe.
The Weinberg/Polchinski work had implications that are devastating for the Copenhagen repersentation of the wave function as "observer knowledge". Polchinski has shown that a tiny non-linear modification transforms the "hidden" nonlocality of the standard QM formalism into a manifest property that can be used for nonlocal observer-to-observer communication which is inconsistent with the "knowledge" interpretation.
Thus, the Copenhagen interpretation is not "robust" because it is inconsistent with a tiny modification of the standard formalism. The transactional interpretation and the many-worlds interpretation, on the other hand, are so robust that they can be tested and verified (or falsified) by the same effect. If quantum mechanics has any detectable nonlinearity, we get a backwards-in-time telephone or a telephone to alternate universes, depending on which interpretation is valid.
But is quantum mechanics non-linear? Atomic physics experiments have been used by several experimental groups to test Weinberg's non-linear theory. So far these tests have been negative, indicating that any non-linearities in the quantum formalism are very small, if they exist at all. In my view the negative results are not surprising because the atomic transitions involve only a few electron-volts of energy. If quantum mechanics does have non-linear properties, I would expect them to depend on energy and to appear only at a much higher energy scale. Weinberg-Polchinski tests should be made, if possible, with the highest energy particle accelerators. Perhaps then we can find out what connections can be made with Polchinski's quantum telephones.
Hugh Everett, III, Reviews of Modern Physics 29, 454 (1957);
Bryce S. DeWitt and N. Graham, eds., The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press, Princeton (1973).
and Copenhagen Interpretations:
John G. Cramer, Reviews of Modern Physics 58, 647 (1986);
John G. Cramer, International Journal of Theoretical Physics 27, 227 (1988).
Steven Weinberg, Physical Review Letters 62, 485 (1989);
Joseph Polchinski, Physical Review Letters 66, 397 (1991).
This page was created by John G. Cramer on 09/14/2015.