## Hidden Variables

The dual universe is a “hidden variables” theory, because it relies on entities that are unobservable, such as the quantized structure of spacetime and dimensionless interstitial energy. Theories of this type can be useful. For example, with unobserved atoms as hidden variables, Einstein predicted the nature of Brownian motion and brought the concept of atoms closer to acceptance. By assuming the presence of unobserved minimal elements of spacetime that are spherical and formed into a closely packed lattice, the dual universe theory suggests how a particle arrives at a specific point and why its behavior appears random.

It is the characteristics of contacts between spacetime quanta that produce apparent randomness in the motion of particles. And although much of this is removed by a guided wave that maintains the principle of least action, every particle is likely to be off track to some degree when a measurement is made on it. The behavior remains deterministic, to the extent that it obeys the law of conservation of energy and the principle of least action. But with many trillions of trillions of transitions between spacetime quanta along its path, the destination of any one particle cannot be predicted because the computation is too complex. The behavior therefore is treated as random although it is deterministic. This contrasts with the accepted quantum mechanical view, which regards nature at the individual particle level as inherently random, and consequently non-deterministic.

The dual universe also presents a “guided wave theory” in that the wave associated with a particle is considered a real wave that guides the particle. Such theories treat a wave and a particle as two separate entities. The viewpoint is clearly distinct from that of quantum mechanics, which is based on a single entity that can switch between being a wave and being a particle, two contradictory properties. However, the two theories are related in the sense that quantum mechanics has an unidentified wave hidden in its mathematics, when formulated as the Schrödinger equation.

In non-relativistic form, the equation is concerned with the total energy of a system of particles resulting from the interaction of kinetic and potential energy. It was developed by inserting a wave component of no clear origin into familiar Newtonian dynamics. The motivation came from early observations that newly found fundamental particles formed into patterns of waves. With the wave function added, Schrödinger’s equation accurately predicts for ensembles of particles the probable distribution of particle positions and velocities. Max Born identified this wave function as the amplitude of a traveling probability wave, immersing us in an ocean of fluctuating probabilities. This remarkable concept and wave-particle duality have become part of the accepted Copenhagen interpretation of quantum mechanics, attributable largely to the efforts of Neils Bohr [23] and considered by Einstein to be incomplete.

For Bohr, the laws of quantum mechanics are not deterministic: the destination of any one particle is not known until it is detected at a specific location. It will then clearly be there and not anywhere else. Prior to its arrival, the probability of the particle being where it arrived was calculated by the wave function to be a specific value between 1 and 0, such as 0.3 or 0.7. Suddenly, the probability changes to 1.0 for that location. The wave function predicting the probability is said to have collapsed at that point. This is an interesting way of saying its prediction was wrong. An alternative offered is that the prediction was correct but in another universe that formed spontaneously at that point. If this is the case, creation of universes is a simple matter that can proceed at great dispatch as one considers interactions among larger and larger numbers of particles. Unfortunately, with no access to alternative universes, we have no way of confirming this fascinating explanation.

The results from the the mathematics of quantum mechanics are excellent when they are used to predict the behavior of ensembles of particles. And since all practical applications of quantum theory involve large ensembles of particles, quantum mechanics has been enormously successful in practical applications in physics and chemistry. However, there are alternative techniques. Heisenberg produced matrix algebra, involving arrays of numbers; it is equally accurate but more cumbersome to apply. Feynman developed the path over histories approach, that also produces accurate predictions, demonstrating the optical properties of light [24]. Feynman also showed that an approach based on the principle of least action could produce the predictions of quantum mechanics [25] These and alternative techniques indicate we have a good idea of how fundamental particles behave, but we do not know why they behave that way.

Mathematics has got ahead of physical theory and is telling us we are dealing with a physical situation we do not understand. The guiding wave approach is an attempt to provide a physical picture we can understand. It offers a means to predict the trajectory of single particles and remove indeterminacy from quantum mechanics. The concept was put forward in 1927 by Duc Maurice de Broglie [26], but he abandoned it in the light of widespread acceptance of the Copenhagen interpretation of quantum mechanics. In 1952, David Bohm put forward an improved version of de Broglie’s concept that reproduced the predictions of quantum mechanics and predicted non-local interactions [27]. Again, it was rejected by the Copenhagen orthodoxy. And although Einstein had encouraged Bohm’s efforts, he apparently thought the approach not radical enough. In a letter to Born in 1952 [28] he suggested it was a low-cost modification to quantum mechanics. Einstein seems to have been hoping for some striking new principle that would change our view of the universe and particle behavior entirely.

Bohm was also criticized for producing a hidden variable theory, because John von Neumann proved mathematically in 1932 that such theories could not provide for non-locality [29]. After examining Bohm’s theory and recognizing its importance, John Bell analyzed von Neumanns’ proof and showed that it was invalid [30]. Bell also found some discrepancies in Bohm’s theory, but thought that these could be overcome.

The dual-universe theory and Bohm’s theory were developed from two different motivations. Bohm was seeking to modify quantum mechanics to remove indeterminacy from it and thought that elementary particles might in fact contain some internal structure that accounted for their behavior [31]. The dual-universe theory, which meets Einstein’s wish for a more radical approach, assumes elementary particles remain as particles and seeks to move beyond continuous spacetime to a theory of quantized spacetime and the atemporal, aspatial eternity of the clerics, while laying the basis for an alternative theory of gravitation.

Bohm’s guided wave theory and the dual-universe theory are both hidden variable theories. This may appear to bring them into conflict with a widely accepted theory by John Bell that hidden variable theories cannot account for quantum behavior if the Bell inequality is exceeded [32]. And experiments have confirmed that this inequality is indeed exceeded in particle behavior. However, Bell’s theory provides for the inequality to be exceeded if the hidden variable theory is non-local. Both Bohm’s pilot-wave theory and the dual universe are non-local.

## References

23 Bohr N 1987 The Philosophical Writings of Niels Bohr: Vol. 1, Ox Bow Press, Woodbridge, CT,

24 Feynman, Richard P.,QED the Strange Theory of Light and Matter by. Princeton University Press: Princeton, New Jersey, 1985, p56, 89

25 Feynman, Richard, P. “Principles of least action in quantum mechanics”, A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy, 1942.

26 Broglie, Louis de, ‘The wave nature of the electron’, Nobel lecture 1929. Reprinted in Nobel Lectures, Physics 1922-1941 Elsevier Publishing Company, Amsterdam, 1965.

27 Bohm, D., 1952 A suggested interpretation of the quantum theory in terms of ‘hidden variables’ 1 and 11. in Quantum Theory and Measurement Wheeler J A & Zurek W H eds, Princeton NJ; Princeton University Press 1983 pp 369-396.

28 Born M The Born-Einstein Letters 1916-1955: Friendship, Politics, and Physics in Uncertain Times (New York: Macmillan) p 189.

29 Neumann von J Mathematische Grundlagen der Quanten Mechanik (Berlin: 1932). Translated in Mathematical Foundations of Quantum Mechanics (Princeton, NJ: Princeton University Press)

30 Bell J S 1966 On the problem of hidden variables in quantum mechanics. Rev Mod Phys 38 3 447-451 Reprinted in John S. Bell on the Foundations of Quantum Mechanics. (Singapore: World Scientific 2001) p 1-6.

31 Bohm 1952 A suggested interpretation of the quantum theory in terms of ‘hidden variables’ 1 and 11. in Quantum Theory and Measurement Wheeler J A & Zurek W H eds, Princeton NJ; Princeton University Press 1983 pp 369-396.

32 Bell J S 1964 On the Einstein Podolsku Rosen Paradox Physics 1 3 195-200. Reprinted in John S. Bell on the Foundations of Quantum Mechanics. (Singapore: World Scientific 2001) p 7-126.