Publication: Verificación experimental de la analogía de la emisión estimulada de Hawking con ondas gravitatorias en un canal
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2012
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2012-07-26
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Abstract
Una de las más fascinante aportaciones de la teoría de la relatividad es la predicción de los agujeros negros. Un agujero negro es una región del espacio-tiempo que debido a la existencia de una gran concentración de masa en su interior impide que nada pueda escapar del mismo, ni siquiera los fotones de la luz. De igual forma se predicen sus opuestos, los agujeros blancos, regiones del espacio-tiempo en las que nada puede penetrar. Tan fascinantes como su predicción matemática son algunas de las propiedades postuladas teóricamente sobre ambos (las propiedades demostradas par agujeros negros son fácilmente demostrables para agujeros blancos y viceversa). Posiblemente una de las más conocidas, y a su vez objeto de mayor polémica, sea la radiación de Hawking. La radiación de Hawking consiste en la emisión de partículas, posibilitada por las fluctuaciones cuánticas en el vacío y con una distribución idéntica a la de un cuerpo negro, por parte del horizonte de sucesos de un agujero negro. Hecho que permite asociar una temperatura propia al agujero negro, relacionando los conceptos cuánticos con la relatividad general en el estudio de los agujeros negros y estableciendo una relación entre gravedad y termodinámica. El problema de estas y otras propiedades reside en la dificultad de ser corroboradas experimentalmente, pues desafortunadamente parece improbable que podemos tratar con agujeros negros en el laboratorio. Por este motivo surgen las analogías de agujeros negros (y blancos). En ellas se usan fenómenos que obedecen a ecuaciones de movimiento similares a las de los campos en las proximidades del mismo para así estudiar algunas de las propiedades más singulares de éstos. Existen diferentes propuestas de analogías, aunque en nuestro caso trabajaremos con la analogía de ondas gravitatorias, para ser precisos con la analogía de ondas gravitatorias para un agujero blanco. En concreto nuestro proyecto consistirá en el diseño y puesto a punto de una instalación experimental para el estudio de ondas de gravedad, a la vez que se detallan las técnicas empleadas para su generación y caracterización. En esta instalación se reproducirán los experimentos publicados en el artículo de Weintfurtner y otros, Measurement of stimulated Hawking emission in an analogue system [Ref.2]. El objetivo de la publicación es demostrar la naturaleza térmica del proceso así como mostrar la estrecha relación entre las emisiones estimuladas y espontáneas demostrando la generalidad del proceso de Hawking. Para ello se recurre a un canal abierto provisto de un obstáculo fuselado que crea sobre él una región de alta velocidad (flujo supercrítico) donde las ondas largas, que se propagan aguas arriba, serán bloqueadas reflejándose como ondas cortas. El proceso experimental consiste en forzar las fluctuaciones cuánticas a modo de ola incidente (ondas largas) en dicho canal. La ola se propagará hasta llegar a una región donde, como ya hemos dicho, se le impida el paso de forma intencionada, lo que la hará reflejarse transformándose en dos nuevas olas, a las que denominaremos reflejadas. Estas olas son análogas al par partícula-antipartícula creado en las inmediaciones del horizonte de sucesos, causantes de la radiación de Hawking. La reproducción de dichos resultados no solo nos permite contrastar los mismos, si no que además sirve de ejemplo para enumerar el procedimiento a seguir, tanto en el campo del análisis de imagen como en el de señal, para la correcta caracterización de ondas de gravedad en un canal. Este procedimiento consiste en la metodología para el filmado de las imágenes, en las que se empleará iluminación a contraluz y fluorescencia inducida por láser. También se detallará los algoritmos de umbralización y detección de bordes necesarios para la detección del borde de la superficie libre y finalmente se aplicarán las técnicas de autocorrelación y periodograma de Welch para el análisis de la señal. Nuestros resultados mostrarán, a partir del análisis de señal mencionado, las longitudes de onda identificadas para las tres ondas implicadas comentando su adecuación a la relación de dispersión propia de las ondas de gravedad en las citadas condiciones. Desafortunadamente, aunque el propósito inicial del trabajo era reproducir totalmente los resultados de Weintfurtner y otros consiguiendo validar el carácter universal de la radiación de Hawking, debido a las limitaciones del canal, que también se explicarán de forma detallada, esto no ha sido posible. Weintfurtner y otros validan experimentalmente la estrecha relación entre el carácter estimulado y espontáneo de la emisión a partir de normas basadas en la amplitud de las dos ondas reflejadas, en nuestro caso ante la dificultad de caracterizar simultáneamente estas dos ondas no hemos podido proceder al cálculo de las mismas. No obstante se mostrarán las longitudes de onda que sí se han conseguido identificar y se enumerarán las mejoras con el propósito de medir las longitudes de onda restantes de cara a próximos trabajos. ____________________________________________________________________________________________________________________
One of the most fascinating predictions of the theory of general relativity is the potential existence of black holes –i.e. space-time regions from which nothing is able to escape due to the large concentration of mass inside, not even light photons. Similarly, the theory also postulates white holes, space-time region where nothing can penetrate. As fascinating as their mathematical prediction are some of the properties theoretically postulated (black holes properties are easily translated to white holes and vice versa). Possibly the best known, and most controversial, is Hawking radiation. Hawking radiation is black body radiation predicted to be emitted by black holes, due to quantum effects near the event horizon. This fact allows to define a black hole temperature, that relates quantum concepts to general relativity applied to the study of black holes and to establish a relationship between gravity and thermodynamics. The problem with these and other properties lie in the difficulty of their experimental verification, because unfortunately it seems unlikely that one can observe black holes in the laboratory. Analogs, which obey similar dynamic field equations of around the black holes, raise the possibility of demonstrating some of the most unusual properties of black holes in the laboratory. There are different proposals for analogies, but in our case we will work with the analogy of gravity waves that, to be precise, is related to white holes. Specifically, we will design and develop an experimental facility for the study of gravity waves, carefully detailing the techniques used for their generation and characterization. In this facility we will aim to reproduce the experiments reported by Weintfurtner and others in Measurement of Stimulated emission in an analogue Hawking system [Ref.2]. The aim of the publication is to demonstrate the thermal nature of the conversion process for this system. Given the close relationship between the stimulated and spontaneous emission, demonstrating this finding supports the generality of Hawking’s process. This is done in an open water channel, in which a streamlined obstacle has been placed whose role is to generate a section of high velocity (supercritical flow) where the long waves, propagating upstream towards this region, are blocked and converted into short waves. The experimental process consists of forcing the quantum fluctuations as an incident wave (long wave) in the channel. The wave travels upstream until it reaches a region where, as we have said, it is prevented from passing. At this section it will reflect transformed into two new waves, which we will call reflected waves. These waves are analogous to the particle-antiparticle pair created near the event horizon, causing the Hawking radiation. The reproduction of these results not only allows us to validate the findings of Ref. 2, but also serves as an application to develop techniques to characterize gravity waves, both in the field of image processing and signal analysis. This procedure involves methodology for the filming of images to be used in backlight and laser induced fluorescence. Also we develop threshold and edge detection algorithms needed to detect the free surface. Finally, we apply the autocorrelation and Welch periodogram methods for signal analysis. We report the results of our attempts to characterize the three waves interplaying in the theory, and the goodness of the theoretical dispersion relation to accommodate our measurements. Unfortunately, although the initial purpose of the work was to reproduce Weintfurtner & others’ results and validate the generality of Hawking process, due to the limitations of the channel, which are explained in detail, this has not been possible. Weintfurtner and others validated experimentally the close relationship between the stimulated and spontaneous emission from standards based on the amplitude of the two reflected waves. In our case, due to the difficulty of characterizing these two reflected waves simultaneously we could not proceed to the calculation just mentioned. However, we have succeeded in identifying some of the waves predicted by the theory. Furthermore, improvements are listed with the purpose of measuring the remaining wavelengths in future works.
One of the most fascinating predictions of the theory of general relativity is the potential existence of black holes –i.e. space-time regions from which nothing is able to escape due to the large concentration of mass inside, not even light photons. Similarly, the theory also postulates white holes, space-time region where nothing can penetrate. As fascinating as their mathematical prediction are some of the properties theoretically postulated (black holes properties are easily translated to white holes and vice versa). Possibly the best known, and most controversial, is Hawking radiation. Hawking radiation is black body radiation predicted to be emitted by black holes, due to quantum effects near the event horizon. This fact allows to define a black hole temperature, that relates quantum concepts to general relativity applied to the study of black holes and to establish a relationship between gravity and thermodynamics. The problem with these and other properties lie in the difficulty of their experimental verification, because unfortunately it seems unlikely that one can observe black holes in the laboratory. Analogs, which obey similar dynamic field equations of around the black holes, raise the possibility of demonstrating some of the most unusual properties of black holes in the laboratory. There are different proposals for analogies, but in our case we will work with the analogy of gravity waves that, to be precise, is related to white holes. Specifically, we will design and develop an experimental facility for the study of gravity waves, carefully detailing the techniques used for their generation and characterization. In this facility we will aim to reproduce the experiments reported by Weintfurtner and others in Measurement of Stimulated emission in an analogue Hawking system [Ref.2]. The aim of the publication is to demonstrate the thermal nature of the conversion process for this system. Given the close relationship between the stimulated and spontaneous emission, demonstrating this finding supports the generality of Hawking’s process. This is done in an open water channel, in which a streamlined obstacle has been placed whose role is to generate a section of high velocity (supercritical flow) where the long waves, propagating upstream towards this region, are blocked and converted into short waves. The experimental process consists of forcing the quantum fluctuations as an incident wave (long wave) in the channel. The wave travels upstream until it reaches a region where, as we have said, it is prevented from passing. At this section it will reflect transformed into two new waves, which we will call reflected waves. These waves are analogous to the particle-antiparticle pair created near the event horizon, causing the Hawking radiation. The reproduction of these results not only allows us to validate the findings of Ref. 2, but also serves as an application to develop techniques to characterize gravity waves, both in the field of image processing and signal analysis. This procedure involves methodology for the filming of images to be used in backlight and laser induced fluorescence. Also we develop threshold and edge detection algorithms needed to detect the free surface. Finally, we apply the autocorrelation and Welch periodogram methods for signal analysis. We report the results of our attempts to characterize the three waves interplaying in the theory, and the goodness of the theoretical dispersion relation to accommodate our measurements. Unfortunately, although the initial purpose of the work was to reproduce Weintfurtner & others’ results and validate the generality of Hawking process, due to the limitations of the channel, which are explained in detail, this has not been possible. Weintfurtner and others validated experimentally the close relationship between the stimulated and spontaneous emission from standards based on the amplitude of the two reflected waves. In our case, due to the difficulty of characterizing these two reflected waves simultaneously we could not proceed to the calculation just mentioned. However, we have succeeded in identifying some of the waves predicted by the theory. Furthermore, improvements are listed with the purpose of measuring the remaining wavelengths in future works.
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Keywords
Ondas gravitatorias, Relatividad (Física), Radiación de Hawking, Astrofísica