Quantum mechanics or classical physics?

John Stewart Bell

The debate about which theory explains better the behavior of elementary particles, either quantum mechanics (with strange consequences such as state superposition and quantum collapse) or a still unknown classical physics-type theory that eliminates the need for such phenomena, has been going on since Bohr and Einstein started this debate almost one century ago.

The issue seemed to have been decided when John Steward Bell formulated in 1964 the famous Bell inequality, which I described in another post. However, as some physicists still raise the question, other means of distinguishing between the two types of theories are still being sought. One of them is the Leggett-Garg inequality (LGI), to which I will dedicate this post, based on a recent article in Physics World, dated August 12, 2024.

Determinism or indeterminism?

Modern science has revolutionized our vision of the world. In the eighteenth century, Newton's theory of gravitation could be considered established, and gave rise to a materialistic-deterministic vision of the universe which can be personified in one of the most significant scientists of the time, Pierre-Simon, Marquis de Laplace (1749-1827), whose fields of study covered mathematics, astronomy, chemistry and biology. The success of his studies on the dynamics of the solar system moved him to state that, if we knew the exact initial conditions of the universe, it would be possible to predict all its past and future development. This gave rise to materialistic determinism, so successful in the nineteenth century and still a part of the popular vision of the world, in spite of the three devastating attacks it has suffered during the twentieth century.

Hyperluminal speed in real life

Cherenkov radiation

We know that the special theory of relativity states that the speed of a body with rest mass greater than zero must be less than the speed of light in a vacuum, i.e., about 300,000 km/second. However, sometimes examples are given that seem to indicate, at first glance, that this limit can be transgressed. Let's look at them:

Do black holes have hair?

Black holes are strange objects. They are accumulations of extremely compact matter, which exerts such huge gravity that at less than a certain distance (the event horizon) nothing can escape their attraction, not even light. Hence their name.

The existence of black holes had been predicted in the 18th century by the English geologist John Michell and the French astronomer Laplace. At that time nobody paid attention, but from 1915, when Einstein formulated the theory of General Relativity, the interest in these mysterious objects grew. It was soon concluded that when a massive star exhausted its ability to produce nuclear fusion reactions, no force of nature would be able to overcome the gravitational pull of the remaining matter, resulting in a black hole. But for a long time there were doubts about their real existence, for the theory seemed to predict that the matter located inside a black hole would occupy a zero volume and therefore would have an infinite density. As physicists usually suspect that infinity is a mathematical concept that cannot happen in real life, there were two possibilities: either black holes do not exist, or Einstein's theory would have to be modified so that they wouldn’t have an infinite density.

Compatible, incompatible, possible, impossible

I wish to clarify the four concepts of the title, which are sometimes confused when talking about physical theories and their application:

• An event (real or imagined) can be compatible with a theory. In this case, if the event were real, it would not pose any problem for the theory, which admits in principle the possibility of that event taking place.

A Singular Universe

Javier Sánchez Cañizares is one of the contributors to the book Preguntas sobre Ciencia y Fe, published in 2014 and republished this year. In 2020, Javier has published a book in Spanish with the same title as this post, which can be considered as a book on philosophy of science at a high level of popularization. The goal of the book is to show that materialistic reductionism has no chance of providing a correct complete explanation, as our universe is singular because of several different reasons:

The debacle of determinism

Isaac Newton

By the end of the eighteenth century, Isaac Newton’s theory of universal gravitation was well established. As this theory makes it possible to predict very accurately the orbits of the bodies in the solar system, the French astronomer Pierre Simon de Laplace believed he had sufficient reasons to say the following:

An intelligence that knew all the forces that animate nature, as well as the respective situation of the beings that make it... could cover in a single formula the movements of the largest bodies of the universe and those of the lighter atom. Nothing would be uncertain and both the future and the past would be present before his eyes.

This assertion became the dogma of deterministic materialism, a philosophical (not scientific) doctrine asserting that only matter exists (taking the term broadly) and that the whole history of the universe is determined. Therefore there is no human freedom, nor intentionality, nor final causes in nature. There are just efficient causes.

Laplace’s statement can be expressed in more modern terms:

If we knew the position and the momentum of all the particles of the universe at a given instant, we could predict all their past and future development.

Bell’s inequality and causality

Niels Bohr

Quantum Mechanics took shape about ninety years ago. During the twenties, Niels Bohr and Werner Heisenberg formulated the Copenhagen interpretation, which added to the mathematical formulation some additional considerations such as the following:

• Physical systems with properties that can take concrete and opposing values ​​(such as direction of polarization or spin) in certain circumstances can be in a state where those properties do not take a defined value, but keep all the possibilities simultaneously open. For example, the direction of polarization of a photon can be simultaneously north-south and east-west. The spin of a particle can be both up and down.
• The act of measuring one of these properties causes the collapse of the wave function, which means that the result of the measurement can only be one of the possible values. The wave function gives us the probability of obtaining each value.
• It is possible to build a physical system formed by two or more interlaced particles with respect to some property, which means that if one of the particles collapses with a certain value, the other particle has no choice but to collapse with the other.

The theory of everything

In Joe Dacy’s science fiction novel Esquelle and the lost enclave (2015), which belongs to the hard science fiction genre, skillfully combined with espionage, adventure and political fiction, and covers 1500 years of future history, including the invention of time travel and the manipulation of the past, one can find the following quotation:

At this point, the Theory of Everything is actually the Theory of Not Very Much

Is Joe Dacy II right? Do we think we know a lot, but we know very little? What is this Theory of Everything, with such a grandiose name?

This name has been invented by a few physicists and cheered by the press, on the same line as the name of the God particle applied to the Higgs boson, possibly discovered in 2012. Yes, I say possibly, as it is not certain. Although the particle discovered had the predicted mass and decomposed in some of the predicted particles (not all of them), it has not yet been proved that the Higgs field exists.

What is meant by the name of Theory of Everything is that we know everything about the physical fundamentals of matter, that we do not need God.

The mystery of too many variables

Standard theory of particle physics

We have now two great physical theories:

·         On one side, quantum mechanics, which applies primarily to very small objects (those scarcely affected by gravity), and is the basic tool for the standard theory of particle physics.

·         On the other, general relativity, which applies to very large objects (from the planets to the whole universe, those for which almost nothing matters except gravity), and is the main tool for the standard cosmological (Big Bang) theory.

Unfortunately, the two theories are not mutually compatible, so that physics is far from having resolved its outstanding issues. Moreover, these two theories depend on about forty independent variables. Many physicists think that they are too many. If it were true, it would mean that the configuration space of nature has about forty dimensions. If it is difficult to imagine a four-dimensional space, what about forty!