Yesterday I talked about using skepticism to analyze personal beliefs. Today I’m going to talk about the validity of mythology within those beliefs. Right now I am rather shaky on the subject. But as with all my skeptical analysis, I’m just going to talk it out and see what makes sense.

Douglas Adams once said “Isn’t it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?”

People believe what has been culturally ingrained. The Celts believed in the Fae and they were, as far as Bronze Age people go, a little bit advanced. Druidism came from the Celts and to this day many people practice a mdernized version. With that practice comes the mythos.

When I was Wiccan I knew people who would leave a little shot glass of beer or a saucer of milk to appease the fairy folk. They were always surprised when, the next day it was gone. Or, if it wasn’t, they chalked it up to the local Fae not being hungry that day. I was actually one of those people for a while. When my abusive first husband lost his keys or the computer messed up for no real reason that I could see, I chalked it up to the local fairies liking me and trying to protect me.

As a skeptic who wants to believe in fairies, this is something that I keep looking for a scientific explanation for. For a time I even thought I found the explanation in quantum physics theory. There is a theory stemming from experiments that there are multiple dimensions beyond the one we exist in.

I keep hoping that one of these dimensions is the one that the Fae live in. Others have said that fairies Do exist and their dimension is so close that it tends to overlap in certain places. That’s how people can see fairies from time to time.

I have to wonder though if by dimensions, scientists aren’t talking about dimensions such as Time. People talk about string theory and eleven dimensions. But other physicists have said that string theory holds no water. There doesn’t seem to be a consensus. Right now it’s all just mathematical theory with no way to test it as far as I know. I’ve got to do more reading on the subject. That much is certain.

Even if they do exist, what ARE these other dimensions? Are they like ours? Are they some odd, mathematical construct? Would the same laws of physics theory apply to them? The more I read, the more questions I have.

Fortunately a friend on Twitter gave me a starting point and I am passing it along to you.

http://en.wikipedia.org/wiki/Multiverse

I have NO idea how valid this information is. I’m hoping someone knowledgeable in the field will stumble across this and help. In the mean time, Tinkerbell and her kind are much like Schroedinger’s Cat. Alive and dead.  Existing and non-existent. And right now, I’m alright with that.

Since my last post, I have been working through a lab on nuclear spectroscopy to develop an understanding of the kind of equipment and techniques I will use later to measure the lifetimes of positrons.  This involved setting up two of the detectors described in my last post and taking data on the photons emitted from the decay of  the radioactive isotope 22Na.

Radioactive isotopes like 22Na are constantly emitting radiation as they decay in the form of gamma rays, positrons, electrons (Beta – particles), and helium nuclei (alpha particles).  Using the detectors and software described previously I was able to measure the number of photons emitted at a various energies as 22Na decayed.  An initial spectra revealed two distinct peaks, indicating that the sample was emitting radiation at two different energies.  Consulting a reference on the known decay scheme of 22Na, I found that these peaks represented a 0.511 Mev gamma ray emitted from the annihilation of a positron, and a 1.28 MeV gamma ray emitted as part of the normal radioactive decay of the isotope.  This spectra is shown below, and though the x axis is not yet calibrated for energy, the 1st peak corresponds to the 0.511 Mev gamma ray, and the 2nd to the 1.28 MeV ray.

To further investigate the decay, I turned to a more in depth measurement – coincidence spectra.  Coincidence spectra determine whether two events occur at the same time.  In this case, I wanted to know what was found in detector #2 at the same instant one of the 0.511 MeV gamma rays from positron annihilation was detected in detector #1.  To accomplish this I used an SCA timing device and a gate to signal detector #2 to let measurements through only when a photon within a certain energy range (about 0.511 Mev) entered detector #1.  This way I could see what else was emitted when the positron annihilation occurred.

When the detectors were aligned at 180° to each other (facing one another), with the 22Na sample in the center, spectra from detector #2 showed a peak at 0.511 MeV.  This tells me the 0.511 Mev gamma ray has at least one partner gamma ray emitted during positron annihilation, which is what theory predicts.  Before annihilation, the electron and positron (basically) have zero total momentum, and conservation of momentum requires that the system maintains this zero momentum after annihilation.  To accomplish this, two gamma rays must be emitted with equal energies, in opposite directions – so that the sum of their momenta is zero.  We should therefore expect to find the partner gamma ray at 180° relative to the detection of the first detected ray, and none in other directions.

However, turning the detectors so that they are at 90° relative to each other, with the sample in the center, we actually find a very small peak at 0.511 MeV (shown above). This is not an indication of the breakdown of conservation laws, but that there is actually a very small probability that during the brief time the gate lets signal pass in response to detection of the 1st 0.511 MeV gamma ray, a second positron annihilation occurs that happens to land in detector #2.  We also find a small peak at 1.28 MeV, since there is also a chance of non-positron related emission during the time the gate is open.

I’m still working up to taking measurements for the core research, but after some more training oscilloscopes and other lab equipment coincidence spectra to measure the time between the birth and death of positronium.

What is the hardest part of embarking on any new project? Usually it’s fear of the unknown. However, when this fear has been overcome, the next hardest thing is actually starting the project. Some people stay in the planning stage forever. Strangely enough, the key is to just begin the project and slowly gain momentum. But, what is momentum?

Momentum – A property of a moving body that determines the length of time required to bring it to rest when under the action of a constant force (Merriam-Webster’s Online Dictionary)

Momentum is a wonderful term in physics theory used to describe the relationship between the mass of a body and its speed. If a body is large, it will have a large momentum. If a body is moving quickly, it will also have a large momentum. Using the definition from the dictionary, momentum is related to the amount of time it takes to stop a body that is moving. Once momentum starts to increase, it becomes more and more difficult to stop.  In other words:

Large Body – - – > Large Momentum – - – > Long time to stop motion

Like most scientific principles, this law of momentum is connected to everyday life and human behavior:

Major Project – - – > Major Momentum – - -> Long time to Stop Working

Think about this: Ever been in a situation where you’re just setting up your books to study some material and then someone calls you? Is it more difficult to quit when you haven’t started or to ignore the phone? You might find yourself saying, “Let me finish this paragraph” or “Let me solve these problems and then I’ll call back.”  How about when you decided to start saving up for emergencies? How much easier was it to spend on a whim when the emergency fund was empty as opposed to when you’re a quarter of the way to the goal?

I have been dreading writing my proposal (mentioned in my Goal Report) since I realized I had to do one. This dread led me to continually postpone while I kept thinking about the perfect structure in the back of my mind. Well, I never got the perfect structure I wanted until I began typing. Once I started, my ideas started to take shape and I was able to rearrange and integrate my thoughts better within the structure of the proposal.  The same thing happened when it came to investing. I had been talking about investing since I started graduate school 5 years ago but I didn’t start until this year. I always just told myself I didn’t know enough. Last March, I decided to just plunge in and this forced me to begin to learn more. I initially sought advice from 2 uncles who had been involved in financial markets before and they provided tips on what to look for (one uncle actually thought I had started because I had talked about it so much). It wasn’t until I began investing that I learned the different kinds of mutual funds that were out there and then started looking for funds with low expense ratios.

What have I learned?  The way to overcome the lethargy of beginning a new project is to just start (Nike slogan comes to mind here), no matter how small the actions are. You want to save $1000, start by saving 2%-5% of your income today and slowly increase that. You want to improve your cardio rate: start by jogging for 5-10 minutes a day. You want to start investing:  there are mutual fund companies that begin at $25 and others at $50 per month for mutual fund accounts. It takes time to get the ball rolling, but as time passes with you chipping away, it becomes a lot harder to stop. Take a step today, it may be in the wrong direction but you won’t know unless you step.

“¿Mecánica cuántica fractal?” nos lleva a “La bella teoría” donde el autor afirma: “Curiosamente, si buscamos en Google “mecánica cuántica fractal” o bien en inglés “Fractal quantum mechanics”, prácticamente no encontramos nada. En español he encontrado este estupendo enlace a Ciencia Kanija. En mi entrada sobre “Diez dimensiones, supercuerdas y fractales“, podéis leer algo más sobre todo esto. Un saludo amigos.“

Curioso, ya que si se busca “fractal quantum mechanics” en Google Scholar se encuentran decenas de miles de entradas muchas de las cuales satisfarían al autor de “La bella teoría.” Permitidme una entrada al respecto.

¿Por qué la mecánica cuántica es como es? Muchos han pensado que existe un espacio subyacente, precuántico, con una estructura estadística similar a un proceso estocástico de Wiener que observado de forma efectiva nos muestra las propiedades de la física cuántica. Este espacio precuántico podría ser un espaciotiempo con propiedades fractales. Entre las muchas propuestas publicadas en los últimos 30 años y de las que he tenido constancia, la que a mí más me gusta es la de G. N. Ord, “Fractal space-time: a geometric analogue of relativistic quantum mechanics,” Journal of physics theory A: Mathematical and General 16: 1869-1884 (1983) [artículo citado 125 veces en el ISI WOS]. La figura de arriba está extraída de dicho artículo y muestra la trayectoria precuántica de una partícula entre dos puntos del espaciotiempo, sean A y B.

Ord aplica el principio de relatividad de Einstein y el principio de correspondencia de Bohr a un espaciotiempo fractal. En el espacio fractal, las trayectorias espaciales de todas las partículas están descritas por un espacio de Hausdorff con dimensión D=2. Estas prepartículas son llamadas “fractalones” por Ord. Aunque su derivación matemática no es completamente rigurosa, el resultado es sorprendente, aparece “mágicamente” el principio de incertidumbre de Heisenberg. Ord va más allá y considera que el tiempo en lugar de ser unidimensional y continuo (sus dimensiones topológica y de Hausdorff coinciden) es bidimensional y fractal, o sea, con dimensión de Hausdorff D=2. Espacio y tiempo, ambos fractales y en pie de igualdad. El resultado es una teoría covariante (invariante ante transformaciones de Lorentz) en la que la existencia del tiempo fractal permite derivar en la escala macroscópica una ecuación de Klein-Gordon (el equivalente relativista a la ecuación de Schrödinger no relativista para una partícula escalar).

La idea de sacrificar el tiempo unidimensional y sustituirlo por un tiempo bidimensional y fractal parece muy exótica. Quizás por ello la teoría de Ord tuvo poco éxito entre la corriente estándar en física teórica.

Entre los seguidores de Ord destaca sin lugar a dudas Laurent Nottale. Publicó una serie de artículos en revistas la editorial Word Scientific de Singapur que culminaron en un famoso libro de dicha editorial “Fractal space-time and microphysics theory: towards a theory of scale relativity‎,” 1993. Su artículo más famoso de esta época es “Fractals and the quantum theory of spacetime,” International Journal of Modern physics theory A 4: 5047-5117 (1989) [citado 75 veces en ISI WOS]. Su artículo más citado es posterior, “Scale relativity and fractal space-time: Applications to quantum physics theory, cosmology and chaotic systems,” Chaos, Solitons & Fractals 7: 877-938 (1996) [citado 106 veces en ISI WOS]. La producción científica de Nottale está gratis en PDF en su propia web para los interesados.

Nottale denomina a su teoría como “relavitidad de escala” (scale relativity) y gracias a ella logra derivar la ecuación de Schrödinger para la mecánica cuántica no relativista y todos los postulados de la mecánica cuántica, por ejemplo, en “Derivation of the postulates of quantum mechanics from the first principles of scale relativity,” J. Phys. A: Math. Theor. 40: 14471-14498 (2007) [ArXiv]. Nottale como muchos “tocados por la mano divina” aplica su teoría a todo lo habido y por haber, desde la cosmología a los seres vivos, pasando por la teoría cuántica de campos. La mayoría de estos superresultados no son derivaciones formales ni rigurosas, sino más bien numerológicas. Sus predicciones son muy pocas, la mayoría son retrodicciones (deducir lo ya conocido pero desde un enfoque nuevo). Quizás por eso, la mainstream de la física teórica obvia gran número de sus resultados científicos. Aún así, ha logrado ser director del CNRS (el equivalente al CSIC francés)

Más información sobre Laurent Nottale en la wiki.

La física precuántica a la escala de Planck no falsable tiene un gran problema: no es ciencia, sino pseudociencia. Aún así, tanto Nottale como Ord publican sus artículos en las mejores revistas de investigación, y tienen un gran número de seguidores, sobre todo porque El Naschie (ex-editor) de Chaos, Solitons & Fractals ha favorecido que publiquen fácilmente muchos artículos en su revista (una de las de mayor índice de impacto en Matemática Aplicada).

I THINK THE TITLE SAYS ENOUGH. HAHA.

one week break now, and much of the load has been … unloaded.

yay for project runway (: though the contestants this season have less outstanding designs. but it’s a start!

many movies to watch once prelims’ over, like phobia2 :O :O and there’s 5 of them this time round!

i wish i could draw well ):

Si quieres que te toque la lotería tienes que apostar. En ciencia, los grandes avances requieren hipótesis arriesgadas. ¿Qué es la energía oscura? Nadie lo sabe, aunque hay multitud de hipótesis. Sólo los experimentos decidirán cuál es la correcta. ¿Puede explicarse la energía oscura utilizando el Modelo Estándar? Urban y Zhitnitsky han observado que el lagrangiano quiral de la cromodinámica cuántica (QCD), la teoría de los quarks, embebido en un espaciotiempo curvo, genera una densidad de energía del vacío que se puede interpretar como un término cosmológico pequeñísimo, pero suficiente para forzar la aceleración de la expansión del universo que se ha observado con supernovas tipo Ia. La unión de gravedad y QCD conduce de forma natural a la energía oscura. El mayor problema de esta propuesta, por lo demás, técnicamente muy ingeniosa pero sencilla, es que conduce a una ecuación de estado para la energía oscura con w=-0.75, cuando los experimentos favorecen un valor más próximo a w=-1. Sorprendentemente, la evolución del parámetro de Hubble no es muy sensible a este valor y se reproduce muy bien su evolución observada experimentalmente. El artículo técnico es Federico R. Urban, Ariel R. Zhitnitsky, “The QCD nature of Dark Energy,” ArXiv, Submitted on 14 Sep 2009, secuela de los dos anteriores “The cosmological constant from the Veneziano ghost which solves the U(1) problem in QCD,” ArXiv, Submitted on 11 Jun 2009, y “The cosmological constant from the ghost. A toy model,” ArXiv, Submitted on 11 Jun 2009 [publicado en Phys.Rev.D 80: 063001, 2009].

El secreto de la energía oscura se encuentra en el campo fantasma de Veneziano. ¿Qué es eso? Muchas teorías cuánticas de campos presentan partículas y campos que no son físicos, que se denominan “fantasmas” (ghosts). Cuando se une la gravedad a una teoría cuántica de campos, como es el caso en el artículo que estamos comentando, es habitual que aparezcan partículas fantasmas en la versión clásica de la teoría, previa a su versión cuántica. Como estos fantasmas son considerados no físicos (unphysical) normalmente se busca un procedimiento de cuantización que los elimine en la versión cuántica de la teoría. Sin embargo, Urban y Zhitnitsky han considerado sus efectos físicos si no fuesen eliminados. ¿Fantasma de Veneziano? Bueno, los autores no han considerado la QCD completa sino una versión aproximada a baja energía de dicha teoría desarrollada por Veneziano (uno de los creadores de las primeras teorías de cuerdas a finales de los 1960, época en que se usaban para explicar la fuerza nuclear fuerte, cuando todavía no se había desarrollado la QCD). El análisis de dicha teoría efectiva en un universo curvo conduce a la aparición del campo fantasma de Veneziano.

Por supuesto, el trabajo de Urban y Zhitnitsky es un modelo muy sencillo, casi de juguete (toy model). La teoría correcta debería considerar la QCD completa (en 3+1 dimensiones o 4D) inmersa en un espaciotiempo curvo, es decir, acoplada con la gravedad. Analizar esta teoría completa no parece fácil. Según los autores del estudio, la contribución del fantasma de Veneziano tiene características únicas que hacen pensar que seguirá actuando de la misma forma cuando se extienda el análisis al caso más realista de la QCD en 4D. Ellos afirman que este campo sin masa está protegido y sobrevivirá en dicho caso. Además, afirman que es el único campo lineal sensible a la topología global del espaciotiempo que se espera observar en el acomplamiento de la QCD 4D con un campo gravitatorio (espaciotiempo curvo).

Por supuesto, todo esto no es más que una hipótesis. Demasiado buena para ser verdad. Lo más razonable para los próximos meses (años) es la confirmación del resultado obtenido en el modelo de juguete utilizando métodos numéricos (QCD en redes o lattice QCD). Si se obtuviera, sería un fuerte acicate para que los teóricos dediquen sus esfuerzos al fantasma de Veneziano en la QCD 4D. Si no se obtuviera, todo quedaría en una hipótesis más en el pajar de las hipótesis para explicar la energía oscura. ¿Quién encontrará la aguja en dicho pajar?

http://discovermagazine.com/2009/mar/20-things-you-didn.t-know-about-time

The beginning, the end, and the funny habits of our favorite ticking force.                      by LeeAundra Temescu

From the March 2009 issue, published online March 12, 2009

1 “Time is an illusion. Lunchtime doubly so,” joked Douglas Adams in The Hitchhiker’s Guide to the Galaxy. Scientists aren’t laughing, though. Some speculative new physics theory theories suggest that time emerges from a more fundamental—and timeless—reality.

2 Try explaining that when you get to work late. The average U.S. city commuter loses 38 hours a year to traffic delays.

3 Wonder why you have to set your clock ahead in March? Daylight Saving Time began as a joke by Benjamin Franklin, who proposed waking people earlier on bright summer mornings so they might work more during the day and thus save candles. It was introduced in the U.K. in 1917 and then spread around the world.

4 Green days. The Department of Energy estimates that electricity demand drops by 0.5 percent during Daylight Saving Time, saving the equivalent of nearly 3 million barrels of oil.

5 By observing how quickly bank tellers made change, pedestrians walked, and postal clerks spoke, psychologists determined that the three fastest-paced U.S. cities are Boston, Buffalo, and New York.

6 The three slowest? Shreveport, Sacramento, and L.A.

7 One second used to be defined as 1/86,400 the length of a day. However, Earth’s rotation isn’t perfectly reliable. Tidal friction from the sun and moon slows our planet and increases the length of a day by 3 milli­seconds per century.

8 This means that in the time of the dinosaurs, the day was just 23 hours long.

9 Weather also changes the day. During El Niño events, strong winds can slow Earth’s rotation by a fraction of a milli­second every 24 hours.

10 Modern technology can do better. In 1972 a network of atomic clocks in more than 50 countries was made the final authority on time, so accurate that it takes 31.7 million years to lose about one second.

11 To keep this time in sync with Earth’s slowing rotation, a “leap second” must be added every few years, most recently this past New Year’s Eve.

12 The world’s most accurate clock, at the National Institute of Standards and Technology in Colorado, measures vibrations of a single atom of mercury. In a billion years it will not lose one second.

13 Until the 1800s, every village lived in its own little time zone, with clocks synchronized to the local solar noon.

14 This caused havoc with the advent of trains and timetables. For a while watches were made that could tell both local time and “railway time.”

15 On November 18, 1883, American railway companies forced the national adoption of standardized time zones.

16 Thinking about how railway time required clocks in different places to be synchronized may have inspired Einstein to develop his theory of relativity, which unifies space and time.

17 Einstein showed that gravity makes time run more slowly. Thus airplane passengers, flying where Earth’s pull is weaker, age a few extra nano­seconds each flight.

18 According to quantum theory, the shortest moment of time that can exist is known as Planck time, or 0.0000000000000000000000000000000000000000001 second.

19 Time has not been around forever. Most scientists believe it was created along with the rest of the universe in the Big Bang, 13.7 billion years ago.

20 There may be an end of time. Three Spanish scientists posit that the observed acceleration of the expanding cosmos is an illusion caused by the slowing of time. According to their math, time may eventually stop, at which point everything will come to a standstill.