Space_Exploration@Home

NASA's Stardust spacecraft is comming back to Earth bringing an important load from space: dust from the Comet Wild 2, that is believed to contain information about the conditions of our Solar System in the time of Earth's formation, and interstelar dust collect during the trip.

To analyse the dust, it is important to pinpoint the tiny particles in the aerogel in which they were collected using microscopy photos. It is important to know exactly where the dust is before trying to get it so as not to disturbing unnecessarily the rest of the sample. The odd thing is that NASA will recruit people all over the planet to do that by internet. All you have to do is to subscribe in the site with the name of the project Stardust@Home and as soon as the spacecraft arrive in Earth they will begin to apply a test to evaluate if you have the required ability to help the program.

Those who really find dust particles in the photos will even gain the right to name the dust particle as a reward for the discovery. A good oportunity to become a scientist if even you never thought in being one!

Some news about the project:

Internet users will hunt for Stardust@home

Public to look for dust grains in Stardust detectors

Stardust@home Project Brings Cosmic Dust to Your Desktop

Net Articles

Continuing my efforts to organize my stuff before leaving Brazil, I was organizing my bookmarks and found these links to interesting online articles:

Superstrings
Life in Extreme Environments
Why smart people defend bad ideas
Oklo (A natural nuclear reactor.)
Twistors --- What Are They?
Brief History of Artificial Intelligence
An Introduction to Lagrange Multipliers
A compendium of NP optimization problems
Notes on Functionals
On the Origins of Twistor Theory by Roger Penrose.

As with the links in the last post, finding more articles to post here is just a matter of time as my cleaning proceeds...

On my desk

• Quantum Information can be Negative, Horodecki et al. (quant-ph/0505062)


• Characterizing Entanglement, Bruss (quant-ph/0110078)

Picture taken from: perso.wanadoo.fr/overlord59/

Rusty Links

I took this last week of the year off to organize my things, cause I will probably move to UK next year to begin a work applying Statistical Physics to Cryptography. I was cleaning my wardrobe, which does not have only clothes but also books, old toys and a lot of papers. Then I found a folder and a notebook covered with some dust and with the title "Internet" (time goes by very fast...). I opened then and found a lot of links that I probably found interesting someday and I decided to put them in my del.icio.us page. I begun this task this morning and they are really interesting links. So, I decided to put them here for everyone who read this also have the chance to take a look at them. Let me list them in the exact order that I found them:

Sodaplay: classic. Everyone must know it by now, but I´m glad to have rediscovered it.

Jim Loy´s Homepage: the amount of information about science-related themes is huge. How this guy manage to write so much is a mistery to me.

2d Curves: a collection of mathematical bidimensional curves.

Igor Nikitin´s Homepage: has an interesting document on String Theory.

Kolmogorov: a very complete page about Kolmogorov.

Wilfrid Hodges´ Homepage

Douglas Arnold´s Homepage: with an interesting page about Some disasters attributable to bad numerical computing.

The Online Books Page

O Cerebro Nosso de Cada Dia: a site about the brain originally in Portuguese, but with an English translation as Our Daily Brain.

That´s it. Probably I will find more as my cleaning proceeds and I´ll put them here.

Happy New Year for everyone!

Picture: Rusty Chain by Hilly Wakeford

Phononic Crystals

I found an interesting article in Physics Web by Gorishnyy et al. named Sound ideas (the beautiful picture above was taken from this article). The article talks about a kind of crystal, named a phononic crystal, that can be constructed in such a way to create specific "band gaps" for waves travelling in this solid. This means that you can control which frequency cannot propagate in the crystal, creating, for example, materials that become isolators for particular sounds or mechanical waves.

The band gaps are created by carefull design of the crystals allowing a control of the dispersion relation, the relation between frequency and wave number, in phonons, which are quantized modes of vibration in a solid. This quantization of vibrational modes comes from a treatment using the machinery of quantum mechanics and is a very important mechanism that, among other things, influence the heat condictivity of materials. For a short introduction to the theory of elementary excitations in solids see Elementary Excitations in Solids : Lectures on Phonons, Electrons, and Plasmons by David Pines.

Phononic crystals may have a lot of interesting technological applications described in detail inside the article, in the words of the authors

"Phononic crystals will provide researchers in acoustics and ultrasonics with new components that offer the same level of control over sound that mirrors and lenses provide over light."

Over my desk:

• Quantum Theory from Quantum Gravity, Markopoulou & Smolin (gr-qc/0311059)


• Optical Quantum Cloning – A Review, Cerf & Fiurasek (quant-ph/0512172)


• Quantum Probabilities and Paradoxes of the Quantum Century, Belavkin (math.PR/0512415)


• Basics of M-Theory, Miemiec & Schnakenburg (hep-th/0509137)


• The quantum structure of black holes, Mathur (hep-th/0510180)

Cosmic Collision

A friend send me this link named Cosmic Collision this week. It is a subsite of the official Hubble site where it is described how it will look like the collision of our Milky Way with the Andromeda Galaxy. The site shows the story with a narrated video and have a lot of scientific explanations in a simple but precise way.

The Milky way is indeed colliding already with other minor galaxies of our local neighborhood in our trip in the direction of Virgo Cluster named the Local Group, like the Magellanic Clouds, but the collision with Andromeda will be much more espectacular due to the size of Andromeda. Our planetary system probably will not be affected due to its tiny size relative to interstelar distances, but in the site they show how the night sky will look like during the collision time. In the end, both galaxies will merge into a large elliptical galaxy.

The collision will occur in about 5 billion years from now, what remembered me of a story someone told me once (I don´t remember who...): A scientist was giving a lecture about the death of our sun. At some point, a person raised a shaking arm and asked in a trembling voice Excuse-me, professor, when did you say that will occur?. The professor answered In about 5 billion years.. The guy then took a deep breath and said in relief Oh... I thought you have said 5 MILLION...

As a last comment, the Hubble site has a lot of beautiful pictures and interesting explanations. Don´t be in a hurry when navigating there and you will enjoy every mouse click.

Over my desk:

1. Deriving Landauer’s erasure principle from statistical mechanics, Jacobs (quant-ph/0512105).

2. Spin Glasses: a Perspective, Sherrington (cond-mat/0512425).

3. Projective geometry and special relativity, Delphenich (gr-qc/0512125).

4. The Study of the Pioneer Anomaly: New Data and Objectives for New Investigation, Turyshev (gr-qc/0512121).

5. Quantum information and computation, Bub (quant-ph/0512125).

Picture: Colliding galaxies NGC 2207 and IC 2163, NASA.

Geometric Algebra

The algebra of complex numbers is related to geometry by the Argand plane. Using it, we see that the operation of multiplying by i is equivalent to a 90 degrees rotation in the counterclockwise direction. A little more advanced concept is that of quaternions, that as complex numbers, are a set of numbers that can represent rotations in 3D space. In both these cases, there is a beautiful connection between algebric structures and geometry that can be used to express physical laws in a concise way.

The notorious way to use geometry in physics is by means of Gibbs' vector calculus, which became widespread in physical sciences and engineering. In 1878 Clifford created a structure with the name geometric algebra uniting the dot and the cross products of two vectors into a single entity named the geometric product, which for two vectors a and b is written as
\[ab=a\cdot b +a \wedge b,\]
where the first term is the dot (scalar) product and the second the wedge or exterior product, which generalize the cross product that turns out to be a particular case in 3 dimensions.

Although it has a lot of applications in physics, it was eclipsed by Gibbs' vector calculus and was forgotten untill 1960 when David Hestenes, trying to recover the geometric meaning of the Clifford algebra related to spin discovered that geometric algebra is a "universal language for mathematics, physics and engineering."

There are a complete introductory course as Lecture Notes in the site of the Department of Physics of the University of Cambridge.

The interesting fact, that my former PhD advisor pointed me, is that there is a hope that this structure can lead to a geometric interpretation of the misterious use of complex numbers in Quantum Mechanics. However, I need to read more the lecture notes to talk about that.

Papers over my desk (or in my desktop):

• Vegetation's Red Edge: A Possible Spectroscopic Biosignature of Extraterrestrial Plants - Seager et al. (astro-ph/0503302)
• Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School) - Sorkin (gr-qc/0309009)
• The General Quantum Interference Principle and the Duality Computer - Long (quant-ph/0512120)
• Entropic Priors - Caticha and Preuss (physics/0312131)
• On Math, Matter and Mind - Hut et al. (physics/0510188)

Picture: Quantum Notions - Gerard von Harpe

A Matter of Doubt

In the most fundamental level of nature lies two concepts that are central to physics: energy and matter. Energy is a fundamental entity present everywhere. Even empty space contains energy (what renders the term "empty space" a little inaccurate).

Matter is a concept directly associated with mass. Matter particles are particles with mass. Mass started as two "different" quantities: a measure of inertia, what comes from Newton´s formulaand gravitational charge, again given by Newton aswhere the gravitational constant G is so small that renders gravity the weakest of all forces in nature. Although nothing in principle says that gravitational charge and coefficient of inertia should be the same thing, Newton already confirmed by making experiments that both concepts agree with great precision. This point was late clarified by General Relativity, where we learned that gravity is only a deformation in spacetime and what we see as an atractive force is just a geodesic path, but the detailed explanation can be found in, for example, Robert Wald's General Relativitybook and in Sean Carrol's Website under the title Lecture Notes on General Relativity, so I will postpone it for a future post.

Mass is known to be equivalent to energy since Einstein´s Special Relativity. His famous formulawhich is valid for a body AT REST, means that even objects with no movement and subject to no forces have some energy that can be extracted from its mass. Indeed, the atomic bomb relied on this formula to produce an amazing amount of energy from a relatively small piece of matter.

The making of the atomic bomb shows that to extract energy from matter is (relatively) easy, but the converse is not so. The main problem is that we still does not know what exactly is the mechanism that converts energy into matter. We have clues, both experimental and theoretical, but a complete explanation is still lacking.

In the first place, we expect that energy can be transformed into matter because we believe that in the beginning there was only energy in the universe and, somehow at some point in the far past, this energy gave birth matter particles. Second, we know that it can happen because there are experimental evidence for a phenomenon called pair creation, where a photon acquires sufficient energy and generates a positron and an electron. However, this is totally random and we cannot predict when and how this will happen.

There is a curious theoretical phenomenon called Unruh-Hawking Radiation, sometimes treated separetely as Unruh Effect and Hawking Radiation, which is related to matter creation too. It is theoretical because we can deduce it from quantum mechanics and relativity, but the effect was not observed experimentally at this moment. Hawking discovered that black holes can induce production of pairs of matter particles around its event horizon and the emnission spectrum of these particles is a black body spectrum with temperaturewhere g is the local gravity acceleration. The equivalence principle of general relativity requires that a gravitational field is equivalent to acceleration and this implies that an accelerated observer can see a background of matter particles where an observer at rest see only the vacuum, and this particles obbey the same spectrum distribution of the particles near the black hole with temperaturewhere a is the acceleration.

The only explanation till now about how particles acquire mass comes from the Higgs mechanism, a kind of symmetry breaking involving a particle called the Higgs boson. But the Higgs boson has not been found experimentally at the moment and there is another problem: we must assume that the Higgs has a mass itself, what only puts the problem in another level: from where comes the mass of the Higgs? A self-interaction, you would say, but it´s just a circular argument, does not help too much.

The matter-energy problem has not been in the first plane of research in the last decades, but there are something very fundamental in this problem that must be understood if we want to go on with our aim of understanding how the universe works and how it appeared.

Quantum Limitations

As I already said in another post, quantum mechanics is a wide confirmed and one of the most successful theories about nature we (humans) ever created. The agreement of predictions with experiments is amazing and there are no known experiments that contradict the theory.

However, this is not the end of the story. QM is successful for its mathematics describes nature with tantalizing precision, but the math was tailored from experiments to fit them. This means that QM, unlike Relativity, is not derived from some fundamental principle. The lack of this principle is what is behind the great numbers of alternative interpretations apart from the ortodox one, which leads to strange situations like the Schroedinger Cat.

The lack of a first principles derivation still is responsible for the existence of alternative theories that try to explain qunatum phenomena, like Bohmian Mechanics, where David Bohm tries to explain quantum behavior by a misterious quantum field that permeates spacetime, and Stochastic Electrodynamics, pioneered by Timothy Boyer, which uses classical mechanics plus a random background field of electric particles and is able to find a lot of good results. But no theory yet has been proven to be exactly equal or superior to QM.

When I talk about the success of QM, I´m not talking yet about quantum field theory (QFT). QFT arises from the merging of QM with special relativity. It has a lot of success, but the way these results are extracted from the body of the theory is very trick and most of scientists have the feeling that this should not be the final answer. Although when supplied with some experimental measurements QFT can give results that agree with experiments by one part in a billion (in QED, for example), the calculations come from infinite series expansions that do not converge. The expansions are truncated and a lot of work on renormalizing (take the infinites away) the theory must be made.

The point is that even giving the correct values for several quantities, QFT begins with a very questionable (in my view) procedure: you simply transform equations from classical physics in equations for fields, solve by expanding in Fourier series and then impose quantum commutation relations between the fields and the canonical conjugate momenta. It is a recipe. We don´t know exactly what we are doing, but we borrow the procedure of imposing these relations from plain QM and go on. Another thing: the conjugate momenta comes from a lagrangean density that is constructed in such a way that it gives the correct equations of motion, again without any fuindamental principle. This procedure works with some tricks for Electrodynamics and for Weak and Strong Forces (giving rise to electroweak theory and to QCD), but fails miserably with gravity.

In my view (and my only view, what means that it is not the current view of scientific community), without a clear understanding of what we are really doing, we can´t even be sure if we should quantize gravity. Critics of string theory say that after so much time without success, maybe string theory is a wrong way, but the endeavour of quantizing gravity is much older and we could not do it till this day. I´m not saying that quantum gravity is not worth pursuing, I´m just saying that maybe there is a tiny possibility that nature did not choose this path. However, today the probability that QG exists probably is higher than that it do not. We have to wait more theoretical results or experiments.

Just to cite a tentative for deriving QM from first principles, it is worth looking at the papers of Ariel Caticha, he is trying to show that QM can be obtained by applying principles of information theory and bayesian inference to physics. The main theory is in Insufficient reason and entropy in quantum theory (quant-ph/9810074). He is also trying to show that general relativity can be obtained from the same principles: The Information Geometry of Space and Time (gr-qc/0508108).

Picture: Quantum Foam - taken from http://www.journal-kempten.de/

Avalanches

Avalanches are physical phenomena of great interest, mainly because they represent a big risk for those who live or visit areas where this kind of natural disaster can occur. But avalanches are very complex. They arise from an instability in a pile of granular material like sand or snow. Granular materials can be piled but just until the slope of the sides of this pile is below a critical angle. When the slope is above this angle, any extra grain added to the pile can cause a chain reaction and start an avalanche. The point is that you never know exactly when the avalanche will start.

Avalanches are an example of what is called an emergent behavior. Complex systems, which are composed by a great number of interacting unities, can show exceptional characteristics that are not expected: strange organization phenomena and surprising effects.

Although the problem of modelling granular materials seems to be something easy at first sight, it is a difficult matter and to this date we haven´t a unified theory yet. There are different approaches to attack this problem. One is to try to model granular materials a kind of fluid with special properties. It is a hydrodynamical approach. The other is to build discrete toy models and analyze them mathematically.

The second approach is related to the famous Bak-Tang-Wisenfeld model of a sandpile, where they use a bidimensional cellular automaton to model a pile where at each time step a grain is added at random in some site. When a site has a slope above a critical slope relative to its neighbours, one or more grains is transferred to this neighbour. This model turn out to have a very special behavior called Self-Organized Criticality (SOC). This behavior is rrelated to the distribution of the sizes of the avalanches in the pile and to the fact that the pile has a set of quiescent states, named metastable states, where the pile is momentarily stable.

These models can be complicated or simplified as much as we want and their study is not an easy matter once they are models that should be studied out of equilibrium, and out-of-equilibrium phenomena and, once more, we don´t have a unified theory for them too. An interesting example of a simplified model where you can see "avalanches" was sent to me last week by a friend named Marlo who found it in the internet. It is a game where you have a bidimensional cellular automaton where each site can be in one of four different states. You can change the state of one site and the interaction between states can trigger an avalanche effect. The aim is to trigger the biggest possible avalanche, although it is funny just to look at the dynamics and the metastable states to see how they look like.

My friend becomes excited with the game and said to me that this could have a lot of consequences even in sociology... well, physicists already though of this and he is right. I´ll edit this post another day and will try to put some links to show this.

Picture taken from: Milford Road.

Kung Fu Science

I´m a kung fu fighter. After eigth years and two knee surgeries, last year I finally got my black belt. My style is Ton Long, or Praying Mantis, one of the several kung fu styles that exist. Most of the styles are inspired in the movements of animals, like Tiger (Hung Garr), Crane, Eagle´s Claws and Monkey, but there are others that do not follow the pattern, like Tai Chi Chuan, Drunk Style, Wing Chun (the style of Bruce Lee) or Suai Shiao. In fact, most of the styles are completely different martial arts and kung fu is a common name for all chinese martial arts. Kung fu is not even the correct name, its meaning is "hard work" and in China is used to every kind of art that needs a great effort to learn and master. The chinese name for their martial arts is wushu or kuoshu.

My passion for kung fu is well known among my friends and yesterday one of them send me a link about the physics of kung fu, a site entitled Kung Fu Science. The link is indeed about a study of the physics involved in breaking blocks with bare hands led by a young PhD student of atmosferic physics. The site has beautiful presentation and design and the text is very accessible for those who are not scientists too. There are links to related studies about the physics of other martial arts in the end of the webpage. It is worth to visit.

Picture taken from: International Chinese Kung Fu Association Website.

Write an instantaneous paper!

This is a program written by three guys from MIT: Jeremy Stribling, Max Krohn and Dan Aguayo. It generates random papers that seem real enough to fool someone who´s not a scientist. The incredible part, although, is that these guys submitted some of these papers to real conferences and were accepted!

I generated a paper with three other friends of mine. It even has some references to other papers with our names (although we never wrote them...).

You can generate your papers and read details and the whole story in their site:
SCIgen - An Automatic CS Paper Generator.

Physics & Artificial Intelligence

Last Thursday I finally earned my Ph.D. in Physics. The title of my work, together with my advisor Nestor Caticha, is "Learning on Hidden Markov Models", where we studied the performance of learning algorithms for HMMs, a kind of machine learning model that is a special case of a wider class named graphical models. Machine learning is an alternate name, although you can consider it as a particular area, of artificial intelligence. The diference between both terms is as diffuse as you want, but technically the former is preferred.

It may seems strange that a physics thesis is about machine learning, but statistical physics is an area with a lot of insterdisciplinar applications. It is an area that studies the interactions between systems composed of a large number of individual interacting units. It has already given a lot of important results when applied to the study of perceptrons, simplified models of artificial neural networks, and our hope in our work was that it could give interesting results for HMMs too. When I had prepared a suitable english version of my thesis and when our papers were submitted I will put links to them here.

But coming back to the main point, what exactly does physics have to do with machine learning? Well, one of the first insights of machine learning appeared when two guys, McCulloch and Pitts, introduced a simplified mathematical model of a neuron. The simplified model was inspired in the real neuron in the brain, it was composed of "synapses" from where the neuron received inputs in the form of numerical values, a "body", mathematically a function that processed the input turning it in an output numerical value that were transmitted to other unit by an output synapse. This model is in the paper "McCulloch, W. and Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 7:115 - 133".

Linking a great number of these units together by the synapses, one could construct a network as complicated as we want. It can be shown that these networks can be used to store memories and to infer answers to questions. These artificial neural networks (ANNs) can have complex or simplified architectures, the simplest one being the so-called (Rosenblatt) perceptron. Well, our brain is a natural neural network with about 10¹¹ neurons. It´s a huge number! So huge that for practical purposes we can treat this number as infinite. This is where physics enter, to be more specific, statistical physics.

Statistical physics studies systems with a great number of interacting individual units trying to make predictions of the typical behavior of the system as a whole. It makes the connection between Newtonian mechanics and Thermodynamics. In Newtonian mechanics the systems are described by position and velocity of each particle, but in thermodynamics a system is described by "bulk" macroscopic properties as temperature, pressure and volume. Thermodynamics is recovered from mechanics when we analyse the equations for a large number of particles and take averages, mathematically this limit, widely known as the Thermodynamical Limit, is attained only when the size of the system (the number of individual components) goes to infinity. This approach helped to understand interesting properties of matter, as the famous Phase Transitions (like water boiling or ice melting in water).

I turns out that there is a way to map neural networks into already studied physical systems such that when you apply the methods of statistical physics to then and take the thermodynamic limit, you can calculate properties! It was made for perceptrons and worked pretty well! Later, other methods of statistical physics were used with the same success, one of the most celebrated, and most controversial for most mathematicians, is a mathematical trick named the Replica Trick. But I´ve already written too much and will let those matters for another post.

Picture taken from:http://www.nada.kth.se/~asa/Game/BigIdeas/ai.html

Quantum Gravity: CDT

Causal Dynamical Triangulations (CDT) is a very recent approach to quantum gravity. Like LQG it didn't use any new principles or symmetries, but tries to quantize gravity using the Feynman path-integral approach to quantum mechanics.

The Feynman path-integral in quantum mechanics is a formalism that allows us to calculate the probability of scattering processes in quantum field theory (QFT) in a simple way that can be associated with graphs to easier visualization and calculation. The idea is that there is a quantity named the propagator that can be calculated as the weighted sum of the possible ways that a particle has to going from a point to the other of spacetime. In classical physics, there are some paths that are forbidden, the ones where the particle needs to travel faster than light, but the idea of Feynman was that in quantum mechanics all paths are allowed, but the resulting path is calculated by interference of all the paths. All the scattering probabilities can be calculated using the propagator and this approach allowed the quantization of electromagnetic theory (QED). But gravity is a very trick force and resisted to first attempts to be quantized in this way.

In gravity, the analogous quantity to a path in spacetime is a path in the space of all possible geometries of the universe. But this summation is divergent, i.e., the result is infinite and a lot of work has been done to try to find a way to make this sum convergent. The CDT approach consists of approximating spacetime by a mesh of triangles (in this case, 4-dimensional triangles), make the summation and then calculate it in the limit where the size of the triangles goes to zero. In this continuous limit, it's expected that the resulting theory is well behaved. The first results show that it could be.

CDT was developed by Renate Loll and Jan Ambjorn and has the advantage that a lot of simulations can be done and some interesting results appeared. One of the most interesting results is the possibility of spacetime to have different dimensionalities in different scales. This appears to be a little strange, but technically what happens is that if you put a particle moving at random (technically, executing a random walk) in space, its behavior is similar to a particle walking in a 2-dimensional space for short times (what is interpreted as for short scales) and similar to a particle walking in a 4-dimensional space for longer times. Mathematically what happens is that the particle is performing a diffusion in a fractal space and we have a formula for this that gives the so-called spectral dimension for the diffusion. The spectral dimension can be calculated by fitting a curve to the graphic of how much the particle walked versus the time spent and inserting the result in the formula. That is what they did and found these results.

As I said, CDT is new and there are not so many people working on it in the world, but if you are interested, search for it and for papers published by Loll and Ambjorn in the arXiv. They always put a preprint of their work there. And take a look at the discussions in the "Strings, Branes and LGQ" section of Physics Forums. You can always learn a lot of things there.

Redshift: the Quantum Explanation

Last year I attended a course about cosmology given by Prof. Raul Abramo at the Physics Institute of the University of São Paulo. At some point, he was explaining the Hubble´s law and how we could calculate the Hubble constant by measuring the (cosmological) redshift of far objects. The explanation for the redshift is that, as the universe expands, it stretches the electromagnetic waves so that their wavelength is increased. A larger wavelength means a lower frequency and then the light is redshifted, or equivalently, the frequency of a light wave emitted from an object goes in the direction of the red light and beyond (to the infrared and more…) as its frequency is lower than the frequency of blue light.

After the class, I was thinking about the effect and realized that I was told a classical (not quantum) explanation. The nature of light seems to be quantum and then a full quantum explanation should exist. I first asked for a former professor of mine, Prof. Henrique Fleming, and he told me that there was no official explanation, because we haven´t a Quantum Gravity theory yet, and the redshift was a relativistic, therefore a gravitational effect.

I thought about the question and arrived at the conclusion that the explanation probably would be given by an interaction between the photon and the graviton. Somehow, the photon should interact with the graviton and give it some part of its energy. As energy is proportional to the frequency, less energy means less frequency and a redshift. Then, last week, I saw in Physics Forums a comment about a preprint by Michael Ivanov entitled “Low-energy quantum gravity” that presented the idea in detail. I did not read the paper yet, but it seems that it is an interesting one. Although nobody is sure that the graviton really exists (and if you go to Physics Forums you will see a lot of people that will say that it didn´t), maybe as a low-energy approximation the concept could explain the redshift effect in a quantum mechanical way, something that was not done till now.

Picture: Barred Spiral Galaxy NGC 1300 - NASA

Charge and Time

There are two big problems in physics that all clues given by nature seem to indicate that they are related, but till now, no one is capable of explain exactly what is the relationship such that both could be solved. They are the arrow of time and the baryon asymmetry.

To be brief (and very unprecise), the arrow of time problem is the problem of why time goes on only in one direction since all equations of physics are symmetric with respect to the time variable. There are a lot of conjectures, but no one is really certain about that. The baryon asymmetry comes from the fact that we observe much more matter in our universe than antimatter, what is a problem for (electric) charge is conserved and if we suppose that in the beginning there was nothing and that everytime a matter particle is created its antiparticle is created together, we should have as much matter as antimatter in our universe.

Both problems are related by a symmetry of nature named CPT, that says that if we change the signs of the time, the charges and the parity in a physical system, all the equations of motion stay the same. Then, charge and time are related somehow. Generally, as Feynman pointed out, we can consider FORMALLY that an antiparticle is a particle going backwards in time.

Now, to the crazy idea I´ve been thinking about. I stress this point: IT´S JUST AN IDEA, I have to work over this to see if it has some chance to live or if it´s just nonsense. Maybe the reason why we see more matter is the same why time only goes in one direction. Somehow, particles and antiparticles may have an internally defined direction of time and as time goes on forwards, we see much more matter. Seems to me like a symmetry breaking induced by a field or a fluctuation. Anyway, I need to work more...

Edition (04-Nov-2005): I was reading around and found that there are ideas related, so that´s not so asurd at all.

Picture: A burst of light is emitted as the electron and its antiparticle, the positron, collide. (Image credit) NASA - Goddard Space Flight Center Scientific Visualization Studio