Testing translation
- las interpretaciones basadas en el colapso objetivo;
These phenomena included black-body radiation, the photoelectric effect, atomic spectra, and the stability of atoms. The work of scientists such as Max Planck, Albert Einstein, Niels Bohr, Louis de Broglie, Werner Heisenberg, Erwin Schrödinger, Max Born, and Paul Dirac gradually led to a new conception of nature.
One of the most important features of quantum mechanics is that it abandons the classical idea that all the properties of a physical system have perfectly defined values at all times. Instead, the theory uses a mathematical formalism that makes it possible to calculate the probabilities of obtaining certain results when a measurement is carried out.
Quantization of energy
The historical origin of quantum theory is usually placed in the year 1900, when Max Planck studied the radiation emitted by hot bodies. To correctly reproduce the experimental results, Planck proposed that energy was not exchanged in a completely continuous manner, but rather in discrete amounts later called quanta.
The energy of one of these quanta is given by:
<math>E = h\nu</math>
where:
- <math>E</math> is the energy;
- <math>h</math> is Planck's constant;
- <math>\nu</math> is the frequency of the radiation.
This hypothesis marked a break with the ideas of classical physics. In certain situations, some physical quantities can only take on certain permitted values.
A particularly important example appears in atoms. Electrons bound to an atom cannot possess just any value of energy, but only certain energy levels. When an atom moves from one energy level to another, it may absorb or emit a photon whose energy corresponds to the difference between the two levels.
Wave-particle duality
Another fundamental concept of quantum mechanics is the so-called wave-particle duality. In classical physics, particles and waves are clearly different objects. A particle has a relatively localized position, whereas a wave is distributed over a region of space.
In the quantum world, this distinction is less clear-cut.
Light, which had traditionally been described as an electromagnetic wave, can behave in certain experiments as a set of particles called photons. The photoelectric effect is one of the best-known examples of this corpuscular behavior.
Conversely, Louis de Broglie proposed that material particles could also exhibit wave properties. A wavelength can be associated with a particle of linear momentum <math>p</math>:
<math>\lambda = \frac{h}{p}</math>
This relationship was confirmed experimentally through electron diffraction experiments.
Wave-particle duality does not simply mean that a quantum object is sometimes a particle and sometimes a wave in the classical sense. Rather, it indicates that classical categories are insufficient to fully describe its behavior.
The wave function
In the formulation developed by Erwin Schrödinger, the state of a quantum system is represented by a wave function, usually denoted by the Greek letter <math>\psi</math>.
The time evolution of this function is determined by the Schrödinger equation. In its time-dependent form it can be written schematically as:
<math>i\hbar\frac{\partial}{\partial t}\psi = \hat{H}\psi</math>
where <math>i</math> is the imaginary unit, <math>\hbar</math> is the reduced Planck constant, and <math>\hat{H}</math> represents the operator associated with the total energy of the system, known as the Hamiltonian.
The wave function does not directly represent an observable property. According to the interpretation proposed by Max Born, the square of its modulus,
<math>|\psi|^2</math>,
is related to the probability density of finding a particle in a given region of space.
For example, in the case of an electron located around an atomic nucleus, one does not necessarily speak of a definite trajectory, like the orbit of a planet around the Sun. Instead, a probability distribution is used, indicating the regions where there is a greater or lesser probability of detecting the electron.
Quantum superposition
The superposition principle states that, if a system can be in several possible states, it can also be in a combination of those states.
If <math>\psi_1</math> and <math>\psi_2</math> represent two possible states, a combination such as
<math>\psi = a\psi_1 + b\psi_2</math>
can also represent a valid physical state, provided that the corresponding normalization conditions are met.
This principle gives rise to some of the most characteristic effects of quantum physics. In the famous double-slit experiment, for example, a particle can produce an interference pattern that requires considering simultaneously the different alternatives available during its propagation.
Superposition is also one of the foundations of quantum computing. Whereas a classical bit takes the value 0 or 1, a qubit can be in a superposition of the states associated with 0 and 1.
Measurement and probabilities
Measurement plays a particularly important role in quantum theory. Before a measurement is carried out, a system may be in a superposition of different possible outcomes. Quantum mechanics makes it possible to calculate the probability of obtaining each one of them.
For example, if a particular property of a particle is measured, such as its energy, the result obtained will be one of the values allowed by the system. If the experiment is repeated many times with identically prepared systems, a statistical distribution of results will emerge that is consistent with the probabilities predicted by the theory.
This probabilistic character gave rise to numerous philosophical debates among the founders of quantum mechanics. Albert Einstein, for example, repeatedly expressed his discomfort with the idea that probabilities were a fundamental element of nature. Nevertheless, the theory's probabilistic predictions have been verified experimentally with extraordinary precision.
Uncertainty principle
Werner Heisenberg discovered that there are certain pairs of physical quantities that cannot simultaneously possess arbitrarily precise values. The best-known example is the position and the linear momentum of a particle.
The uncertainty relation can be expressed as:
<math>\Delta x,\Delta p \geq \frac{\hbar}{2}</math>
where <math>\Delta x</math> represents the uncertainty in position and <math>\Delta p</math> the uncertainty in momentum.
Heisenberg's uncertainty principle should not be interpreted simply as a limitation caused by imperfect measuring instruments. It is a feature inherent to the quantum formalism. A state in which the position is very well defined necessarily presents a broader distribution of possible momentum values, and vice versa.
Entrelazamiento cuántico
Dos o más sistemas cuánticos pueden encontrarse en un estado conjunto denominado entrelazado. En ese caso, ciertas propiedades de los sistemas individuales no pueden describirse de forma independiente, incluso cuando las partículas están separadas espacialmente.
Las correlaciones asociadas al entrelazamiento fueron objeto de un famoso debate iniciado por Einstein, Podolsky y Rosen en 1935. Posteriormente, el físico John Stewart Bell desarrolló desigualdades matemáticas que permitieron comparar experimentalmente las predicciones de determinadas teorías de variables ocultas locales con las de la mecánica cuántica.
Numerosos experimentos han confirmado las correlaciones predichas por la teoría cuántica.
El entrelazamiento tiene actualmente aplicaciones potenciales y reales en áreas como:
- la criptografía cuántica;
- la computación cuántica;
- la teleportación de estados cuánticos;
- las redes de comunicación cuántica;
- determinados métodos de metrología de alta precisión.
Interpretaciones de la mecánica cuántica
Aunque las ecuaciones fundamentales de la mecánica cuántica están extraordinariamente bien verificadas, existe un debate sobre su interpretación conceptual.
La denominada interpretación de Copenhague, asociada principalmente a Niels Bohr y Werner Heisenberg, concede un papel fundamental al proceso de medición y considera que la teoría describe las probabilidades de los diferentes resultados observables.
Existen, sin embargo, otras interpretaciones. Entre ellas se encuentran:
- la interpretación de los muchos mundos;
- las teorías de variables ocultas;
- las interpretaciones basadas en el colapso objetivo;
- diferentes interpretaciones informacionales y relacionales.
Estas propuestas pueden ofrecer imágenes conceptuales muy diferentes de la realidad, aunque en muchos casos realizan las mismas predicciones para los experimentos habituales.
Importancia de la mecánica cuántica
La mecánica cuántica no es únicamente una teoría aplicable a experimentos muy especializados. Gran parte de la tecnología moderna depende directa o indirectamente de fenómenos cuánticos.
Entre sus aplicaciones pueden mencionarse los transistores, los circuitos integrados, los láseres, los diodos emisores de luz, las células fotovoltaicas, numerosos sensores y diversas técnicas de diagnóstico y análisis de materiales.
Además, la combinación de la mecánica cuántica con la relatividad especial dio lugar a la teoría cuántica de campos, que constituye la base matemática del Modelo Estándar de la física de partículas.
Conclusión
La mecánica cuántica modificó profundamente nuestra comprensión de la naturaleza. Conceptos como la cuantización, la dualidad onda-partícula, la función de onda, la superposición, la incertidumbre y el entrelazamiento muestran que la realidad microscópica no sigue siempre las intuiciones desarrolladas a partir de nuestra experiencia cotidiana.
A pesar de su carácter poco intuitivo, la mecánica cuántica constituye una de las teorías científicas que han sido comprobadas con mayor precisión. Sus principios son fundamentales para comprender la estructura de los átomos, las propiedades de la materia, la interacción entre la luz y las partículas elementales y una gran parte de la tecnología contemporánea.