The quantum language

The quantum language deals with mathematical probabilities, while the language of classical physics deals with empirical facts. Our knowledge of the world consists of an inseparable mixture of probabilities and facts. Our description of the world must be made up of a blend of quantum and classical states.

As a classical definition, we assume that the Sciences should provide an accounting for the behavior of physical objects, forces, and masses that obey the laws of causality and continuity: there is a deterministic story to describe, employing the observable quantifications, in order to calculate some predictions about the future. In classical physics, objects always have a determined location at a specific time and place.

But quantum mechanics is a theory designed to measure a much different set of objects, where determinism is left out... (the fundamental indeterminacy in the theory will never affect larger objects because quantum activity takes place on a very small scale).

Quantum mechanics is a theory for measuring the mechanical phenomena of subatomic size, and the results of its mathematical formalism are calibrated to fit scientific experiments observations: they are a epistemological channel for the objectivity of a measurement at the quantum level. These measurements are obtained from the amplification of the interactions of the quantum objects (subatomic particles) with the detector instrument.

In classical physics, mathematical probabilities express the unknown, some lack of information. But the conceptual nature of the probabilities in quantum theory is different, assuming that definitive and precise knowledge is void at the atomic level, according to the principle of quantum uncertainty. Quantum objects are measured within a fog of probabilities, and objects have some chance of being at point A, and another chance to be at the point B, and so on.

Scientific knowledge arises from the interpretation of the experimental data and the empirical tests of the theory: a hypothesis based on the description that we make about the inner nature of the object measured.

The study of the wave-particle phenomenology, where one particle can exist in more than one place at the same time, moving from one location to another without passing through intermediate positions - has led the scientists to draw some quite arbitrary quantum properties to explain the mathematical results and the formalism of the theory, in an effort to interpret these strange properties of matter in the subatomic universe. Their quantum formulation consists of a set of abstract rules with principles and postulates where the counterintuitive properties of subatomic matter are presented as possible-reasonable in theory.

How can one particle be at the same time also a wave? How to point out the identity of a particle that is indistinguishable from an equivalent one? The identity of an object is one only, and from this derives the logic (Aristotelian) of to be or not be true identity and contradiction. 

But quantum logic changes everything when classical logic stops working. No matter how much the physics and the logic seem exact; if anything observed demonstrates its incorrectness, then the physicists have to invent some physics to explain it better, and in this new explanation the distributive property of Boolean logic cannot be reconciled with the quantum mechanics considerations.

The empirical results of quantum experiments can provide the basis for the revision of the classical logic as correlated and equivalent to reality. Yes, the principles of logic are susceptible to a review based on empirical microscopic facts.

The formal laws of a physical theory are justified by a process of repeated controlled observations. In Science, this is the argument for the empirical nature of these laws.

Classical logic restricts us to the realm of macroscopic reality and becomes a more limited case of this new quantum logic. As we watch classical logic being rejected by the results of quantum experiments, the argument that the rules of logic are empirical triumphs over.

The difficulty in quantum physics is that it can be demonstrated and proved experimentally, in its principles, but the reasoning we need to understand these principles requires an understanding of the relative time theory, a non-existent notion in the thinking representations that we have developed throughout the evolution of the human reasoning.

It is not true that logic does not apply to quantum mechanics; it is our intuition about what are the fundamental physical laws that do not work in the way we thought it did. Quantum physics is a theory where a new set of physical laws is presented, allowing certain peculiarities to make sense. Following an inductive logic that studies the logical relations between theorems and evidence, one can reach a mathematical method for evaluating the truth of a hypothesis.

All thoughts follow logics based on some axioms. In fact, quantum theory has not shown that classical logic is wrong, but that it is simply insufficient.

Fundamental Ontology

When a few sets of subatomic objects are prepared for an experiment where their quantum attributes and attitudes are observed through a detector device, when the particle system and the detector instrument get entangled in the quantum sense. There is an impossibility of a sharp separation between the behavior of atomic objects and their interaction with the measuring instruments, defining the conditions under which the phenomena appear in the experiment. 
An unambiguous interpretation of measurements should be compatible with the finite and uncontrollable interaction between the objects and the measuring instruments, and it is the ultimate goal in the field of quantum theory.

The quantum uncertainty relations between the complementary quantities to be measured determine a limit to how to prepare the experiment, and without this preparation, the measurement is impossible, and the experiment will fail.

Macroscopic reality is different from microscopic reality. In the objective reality that is visible to the naked eye, all classical objects are defined by a set of real numbers that characterize their physical properties (position, velocity, etc.); and they can be confirmed by numerous independent observations. The properties of classical objects exist independently whether they are measured or not, known or not. The macroscopic objects that we know well have their physical properties easily extended to us.

But this is not so for the strange quantum properties of matter particles, seen nowhere but at the microscopic size level.

There is a limit blocking what we know about the subatomic world, and it could be a theoretical problem, or our inaccurate instruments, or yet a fundamental truth about how Nature behaves at the atomic scale, unlike the macroscopic world.

The definition of complementary physical quantities (momentum x position, for example), allows the new laws in physics to set the notion of complementarity that is very difficult to reconcile with the basic principles of the sciences. At this entirely new situation as regards to the description of the microscopic physical phenomena that the notion of complementarity aims at characterizing.

The reality at the quantum level is the same reality of this room? What is, and how is the subatomic reality?

The quantum objects (subatomic particles) move as rippling waves when we are not measuring positions. When we measure one particle, it will be found in one of the (statistically predictable) positions on the ripple. The matter wave is scattered "over" these positions, also as superpositions of many momenta. Still and all, whenever it is measured, we always find only one value for position or for momentum.

The interpretation of the meaning of measurement, the reduction (or collapse) of the quantum wave function is a source for philosophical debates about the ontology of the quantum states, scientific realism, and the epistemology of quantum experiments.

The properties of all quantum systems are permanently undefined, except when in relation to experimental ensembles. We cannot ask what a particle is doing between measurements, the measurements in quantum experiments reveal no pre-existing values but rather "create" their results. The only and sufficient condition for the existence of a measured quantity in a quantum object is to measure this object.

The properties of a quantum object reveal any values only if there is a measurement, only at the time that a measurement is performed, and apply exclusively to be measured, not having an existence or any physical location until they are measured and begin "to exist".

Probabilities require the gathering of multiple data, and an experiment with a separate particle is actually part of an ensemble. After a number of measurements, a statistical ensemble is formed by the set of states that are associated with certain probabilistic weights. A statistical ensemble is often represented by a density matrix, a complete and comprehensive mathematical tool that can incorporate quantum uncertainty (due to overlap) and classical uncertainties (due to lack of information) in a consistent way. A physical observable X in quantum mechanics can be noted as an operator, X̂. An operator is a mathematical function device: given one observable function input, comes with a derivative function value as output. A quantum state is a mapping, starting from the observables to their expected values.

These are some philosophical issues raised by quantum mechanics: what is the relationship between physical objects and their representations? Why can’t we discuss separately the reality we choose to measure? Would we ever understand the true objective reality (if it exists independently from the human mind), or do we have access to nothing beyond appearances? Are we condemned to a life in a world of deceptive appearances?

Quantum physics cannot give us an accurate ontological account of the fundamental reality because of the effects of quantum inseparability, something that does not allow us to associate physical quantum objects with simple images, such as a picture of an atom that is both true and reliable. Within the image that we can perceive, a particle is but one facet of a much more complex and perhaps inaccessible entity.

plasma tokamak

Does the quantum uncertainty principle demonstrate that there are limits to what can be effectively measured and maybe reality is created by the observer, or is there a subatomic reality that is independent of observation? Is the quantum wave function just a mathematical tool, whose phase cannot be observed directly (but has many measurable effects), or is the quantum wave function a physical part of the objective reality?

The idealistic interpretation of subatomic realism says that objective reality exists independently of the observer's consciousness. But can we understand and describe or even apply some theory to this reality?

By employing a purely mathematical description of the atomic electron configuration, the quantum formalism is able to explain the subatomic reality in its own way with a great deal of success (though no one has actually seen a many-electron configuration). The math matches the empirical data and explains, for example, how two electrons can coexist in the same orbital or position.

Why the electron? The study of the electron is precious because the electron is responsible for the chemical bonds and the reactivity for molecules formation, both fully quantum entities (if we can understand what an electron is, where it is and how it behaves).

In the problem of how the electrons move around the nucleus of the atom, called the electrons cloud, an electron appears to be in different places without being possible to say precisely where it has been or where it will be at any given time, without a predictable path from point A to B to C; so the fundamental principle of causality cannot be applied to the path of an electron. The wave-particle duality undoes the schematic image of the atomic nucleus surrounded by electrons; there is no way to depict the atom, unless perhaps by inventing arbitrary mathematical rules to fit the observed mathematical data.

This impossibility leads the physicists to a new and unexpected problem: the electrons surrounding the atomic nucleus appear to have no objective movements; the past and the future of these events are indeterminate and scientifically elusive, not only for the mathematical language but also for a definition in words.

Quantum theory describes the problem above as being the quantum leaps of electrons to other levels of orbitals around the atomic nucleus, postulating that it is necessary to admit a lack of path causality when passing from a level A to level B or from A to C, because an electron moves from one orbit state to the next while we cannot predict, except perhaps statistically, which would be its next quantum leap or exactly how an electron travels from the state A to C or to B.

The classical laws of physics presuppose the existence of ongoing natural processes to be represented in their equations. Deterministically, if given the initial position, the momentum and other pieces of information about the present, the future can be predicted. So it is clear that quantum leaps cannot be predicted by the classical laws of physics. Now, the problem is to find the new laws that govern the quantum transfers.

Atoms are deliberately obscure; we may never know exactly what will happen to them in the future, all we can do at present is to calculate the odds of actually being at certain places.

If everything we see is made up of atoms, and we only can figure them out by using mathematical concepts, then must we give up the possibility to imagine how the atom looks like and continue to describe it only mathematically?

The electron itself is inherently unknowable; the detection of its position or speed is only possible by means of a mathematical set of probabilities in a density matrix (and organizing symmetries in relation to consistent possible patterns).

This is the depiction of the atom that we can go for obtaining predictions of the atomic behavior: the quantum numbers density matrix, an innovative way of thinking, since we cannot describe the atoms with imageries of a realistic picture of the quantum states, but we can make do with pure abstract statistics. 

Is Nature fundamentally probabilistic?

Is quantum mechanics a complete theory of subatomic measurement because it can explain the observed data? If so, we can presume that the nature of the subatomic realm is probabilistic and randomly changes every time it is measured in experiments.

Before measuring the position of a quantum object we have moving ripples of a wave, provided there is no interference. At the time of measurement, the particle is located at a single position along the ripple. A wave packet moves in many places at the same time, not just at the point where the experiment was measured. By repeating the experiment, other results for a position will be obtained. When we say that the particle's position is indeterminate, this means that there is no single position associated with the particle; its wave is spread over many locations. This does not mean that the particle has a real defined position and we do not know what it is. It is more as if at each repetition of the same measurement experiment the result is a different quantity, which makes no sense in classical physics. Eventually, a statistical calculation points to a probability distribution, but not to the exact locations.

Many physicists apparently doubt the existence of a deeper objective reality in the quantum scale and, instead, rely solely on the mathematical formalism of quantum mechanics to obtain their answers. But the probabilistic nature of quantum theory only provides the probabilities for the results to be obtained with each repetition of the quantum experiment. At best, quantum reality has causal connections, but it is non-deterministic /probabilistic.

Measurement introduces indeterminism in the quantum theory. The evolution of a lone wave function follows a deterministic way if it is not disturbed by any interference, or by an observational measurement that "gives" a probability value for that occurrence.

A full specification of the state of the matter wave (that propagates undulating) and of everything that interacts with it is not enough to determine what will be its altogether future state. We can only make the prediction that each of the position measurements is a possible one, and will appear with so much probability.

Thus,  determinism fails when we consider measurement because when we measure the position of a particle in a wave packet, we're not sure which of the positions will be revealed. The best we can do is to list the candidate positions and, by using the standard rule, to compute each probability.