Tema 2
Desarrollo histórico del formalismo cuántico

2.3. Las relaciones de indeterminación

2.3.1. Origen y expresión

Nota: la mayor parte del contenido de este apartado es un resumen extraído de:

M. Jammer, The Philosophy of Quantum Mechanics, Wiley, 1974, cap. 3.

 

1927: Heisenberg publica las relaciones de indeterminación:

Ref. 2-39: Heisenberg, W.; “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik”, Zeitschrift für Physik 43 (1927) 172-198; “The physical content of Quantum Kinematics and Mechanics”, en [WHE-83], pp. 62-84, archivo heisenbergrelac.pdf.


Antes de continuar, hay que leer atentamente la ref. 2-44, una exposición por Heisenberg de sus recuerdos sobre estos años. Vamos a referir en lo siguiente a ella varias veces, de forma que conviene tenerla delante para irla consultando:

Ref. 2-44: Heisenberg, W.; “Reminiscences from 1926 and 1927", en [FRE-85], pp. 163-171; archivo heisenbergreminisc.pdf. Copiamos aquí un extracto del artículo, con unos párrafos mjuy ilustrativos:

"I now concentrated all my efforts on the mathematical representation of the electron path in the cloud chamber, and when I realized fairly soon that the obstacles before me were quite insurmountable, I began to wonder whether we might not have been asking the wrong sort of question all along. But where had we gone wrong? The path of the electron through the cloud chamber obviously existed; one could easily observe it. The mathematical framework of quantum mechanics existed as well, and was much too convincing to allow for any changes. Hence, it ought to be possible to establish a connection between the two, hard though it appeared to be.
It must have been one evening after midnight when I suddenly remembered my conversation with Einstein, and particularly his statement 'It is the theory which decides what we can observe'. I was immediately convinced that the key to the gate that had been closed for so long must be sought right here. I decided to go on a nocturnal walk through Faelled Park and to think further about the matter. We had always said so glibly that the path of the electron in the cloud chamber could be observed. But perhaps what we really observed was something much less. Perhaps we merely saw a series of discrete and ill-defined spots through which the electron had passed. In fact, all we do see in the cloud chamber are individual water droplets which must certainly be much larger than the electron. The right question should therefore be: Can quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity, and can we make these approximations so close that they do not cause experimental difficulties?
A brief calculation after my return to the institute showed that one could indeed represent such situations mathematically, and that the approximations are governed by what would later be called the uncertainty principle of quantum mechanics: the product of the uncertainties in the measured values of the position and momentum cannot be smaller than Planck's constant. This formulation, I felt, established the much-needed bridge between the cloud chamber observations and the mathematics of quantum mechanics. True, it had still to be proved that any experiment whatsoever was bound to set up situations satisfying the uncertainty principle, but this struck me as plausible a priori, since the processes involved in the experiment or the observation had necessarily to satisfy the laws of quantum mechanics. On this presupposition, experiments are unlikely to produce situations that do not accord with quantum mechanics. 'It is the theory which decides what we can observe'. I resolved to prove this by calculations based on simple experiments during the next few days.
Here, too, I was helped by the memory of a conversation I had once had with Burkhard Drude, a fellow student at Göttingen. When discussing the difficulties involved in the concept of electron orbits, he had said that it ought to be possible, in principle, to construct a microscope of extraordinarily high resolving power in which one could see or photograph the electron paths inside the atom. Such a microscope would not, of course, work with ordinary light rays, but perhaps with gamma rays. Now this ran counter to my hypothesis, according to which not even the best microscope could cross the limits set by the uncertainty principle. Hence I had to demonstrate that the principle was obeyed even in this case. This I managed to do, and the proof strengthened my confidence in the consistency of the new interpretation(...)".

Asimismo, conviene leer el artículo original en que Heisenberg publicó originalmente las relaciones de indeterminación. Es un artículo de gran valor histórico, que permite penetrar en las posiciones filosóficas de su autor, a contrastar con las de Bohr.

Ref. 2-39: Heisenberg, W.; “The physical content of Quantum Kinematics and Mechanics”, en [WHE-83], pp. 62-84; archivo heisenbergrelac.pdf; véase artículo original (en alemán).

Esencialmente, el contenido del artículo puede resumirse como la respuesta a dos preguntas:

1. El formalismo, ¿da cuenta del hecho de que la posición y la velocidad de una partícula son determinables, en un momento dado, sólo con un grado limitado de precisión?

-Heisenberg responde: ΔqΔp = h/4π .

2. Si se admite esta imprecisión, ¿es compatible con la precisión óptima obtenible en las medidas experimentales?

-La respuesta va a venir dada en este caso mediante el gedanken del microscopio de rayos γ, en cuya descripción Heisenberg adopta un punto de vista estrictamente operacional: un concepto científico es un código condensado de operaciones; su significado, una relación definida entre las impresiones de los sentidos del observador:

Ref. 2-66 (Heisenberg en ref. 2-39):

“When one wants to be clear about what is to be understood by the word 'position of the object', for example of the electron (relative to a given frame of reference), then one must specify definite experiments with whose help one plans to measure the 'position of the electron'; otherwise this word has no meaning”.

2.3.2. Interpretaciones. La controversia Bohr vs. Heisenberg

Hemos comentado varias controversias que acompañaron el desarrollo de la nueva teoría cuántica. Intente hacer un esquema-resumen en que figuren: a) entre quiénes se establece la controversia, y b) sobre qué versa. Exponerlo en el foro.

Lecturas:

-http://plato.stanford.edu/entries/determinism-causal/index.html
-http://www.aip.org/history/heisenberg/p07c.htm
-http://www.aip.org/history/heisenberg/p08.htm
-http://www.aip.org/history/heisenberg/p08a.htm
-http://www.aip.org/history/heisenberg/p08b.htm
-http://www.aip.org/history/heisenberg/p08c.htm

Sobre la vida de Heisenberg:

-http://www.aip.org/history/heisenberg/p01.htm


La voz de Heisenberg:

-http://www.aip.org/history/heisenberg/voice1.htm

 


2.3.3. Implicaciones filosóficas: el indeterminismo

El determinismo es fundamental en toda concepción filosófica que intente describir el mundo como uno en que todo lo que sucede esté determinado por algún acontecimiento pasado y por las conexiones legales entre los estados del mundo en un instante dado y sus estados en instantes distintos.

 


2.3.4. Actividades, vínculos, descargas y bibliografía

"Todo suceso tiene una causa": éste es un postulado (metafísico) fundamental para filósofos como Leibniz, Kant... ¿Recuerda algún autor que no compartiera este presupuesto? Repasar su ataque a la causalidad.

¿Considera que tras la oposición a la renuncia al determinismo puede haber también motivos religiosos? ¿Por qué? ¿Qué considera más compatible con el postulado del libre albedrío, el determinismo o su negación? Exponer las respuestas en el foro.

Lecturas:

-http://omega.ilce.edu.mx:3000/sites/ciencia/volumen3/ciencia3/150/htm/sec_9.htm
-http://omega.ilce.edu.mx:3000/sites/ciencia/volumen3/ciencia3/150/htm/sec_12.htm
-http://www.filosofia.org/enc/ros/det.htm (curiosidad para nostálgicos)
-http://www.hawking.org.uk/lectures/dice.html (conferencia de S. Hawking)

 


referencias.pdf
bibliografia.pdf
programa.pdf
heisenbergreminisc.pdf
heisenbergrelac.pdf

 


[ABR-51] Abro,d', The rise of the new Physics, Dover, 1951.

[GAL-89] Galindo, A. y Pascual, P.; Mecánica Cuántica, Eudema, Madrid, 1989.

[ICA-91] Icaza, J.J.; La construcción de la Mecánica Cuántica, Univ. del País Vasco, Bilbao, 1991.

[JAM-66] Jammer,M.; The Conceptual Development of Quantum Mechanics, McGraw-Hill, Nueva York, 1966.

[MEH-82] Mehra, J., Rechenberg, H.; The Historical Development of Quantum Mechanics, 6 vol., Springer-Verlag, Nueva York, 1982.

[MOO-96] Moore, W.; Erwin Schrödinger: una vida, Cambridge Univ. Press, Cambridge, 1996.

[WAE-67] Waerden, B.L. van der; Sources of Quantum Mechanics, Dover, Nueva York, 1967.

[WHE-83] Wheeler, J.A. y Zurek, W.H., ed.; Quantum Theory and measurement, Princenton Univ., Princenton, 1983.